experimental condition range T=20-40C, pH=1-4
1 rem unit should be mol,kgw-1 and second-1
2 rem parm(1) is surface area in the unit of m2/kgw
3 rem calculation of surface area can be found in the note
4 rem M is current moles of minerals. M0 is the initial moles of minerals
5 rem parm(2) is a correction factor
10 rem acid solution parameters
11 a1=2.82E+02
12 E1=56900
13 n1=-0.25
14 n3=0.55
```
30 rem neutral solution parameters

```
31 a3=2.64E+05
32 E3=56900
33 n2=0.500
36 rem rate=0 if no minerals and undersaturated
40 SR_mineral=SR("pyrite")
41 if (M<0) then goto 200
42 if (M=0 and SR_mineral<1) then goto 200
43 if (M0<=0) then SA=PARM(1) else SA=PARM(1)*(M/M0)ˆ0.67
50 if (SA<=0) then SA=1
60 R=8.31451
75 Rate1=a1*EXP(-E1/R/TK)*ACT("H+")ˆn1*ACT("Fe+3")ˆn3 #acid rate expression
80 Rate2=a2*EXP(-E2/R/TK)*ACT("O2") #neutral rate expression
90 Rate=(Rate1)*(1-Sr_mineral)*SA*parm(2)
100 moles= rate*Time
200 save moles
Stibnite
1 rem unit should be mol,kgw-1 and second-1
2 rem parm(1) is surface area in the unit of m2/kgw
3 rem calculation of surface area can be found in the note
4 rem M is current moles of minerals
5 rem M0 is the initial moles of minerals
6 rem parm(2) is a correction factor
40 SR_mineral= SR("Stibnite")
41 if (M<0) then goto 200
42 if (M=0 and SR_mineral<1) then goto 200
43 if (M0<=0) then SA=PARM(1) else SA=PARM(1)*(M/M0)ˆ0.67
50 if (SA<=0) then SA=1
60 k=1.25E-10*EXP(298.2/TK)
70 J=k*ACT("H+")ˆ0.475
90 Rate=J*(1-SR_mineral)*SA*parm(2)
100 moles=Rate*Time
200 save moles
KINETICS
  Arsenopyrite
    -M 0.0
    -M0 0.0
    -parms 1.0 1.0
    -tol 1e-8
  -steps 1 min
  -step_divide 10
  -runge_kutta 3
```
Chalcopyrite(alpha) -M 0.0 -M0 0.0 -parms 1.0 1.0 -tol 1e-8


Berthierite 1.33 0.0 Bornite(alpha) 17.03 0.0 Chalcocite(alpha) 2.75 0.0 Chalcopyrite(alpha) 6.21 0.0 Covellite 1.42 0.0 Djurleite 2.76 0.0 Galena 2.57 0.0 Marcassite 4.15 0.0 Orpiment 0.92 0.0 Pyrite 4.84 0.0 Stibnite 3.25 0.0

### **References**


## *Article* **Soultz-sous-Forêts Geothermal Reservoir: Structural Model Update and Thermo-Hydraulic Numerical Simulations Based on Three Years of Operation Data**

**Clément Baujard 1,\*, Pauline Rolin <sup>2</sup> , Éléonore Dalmais <sup>1</sup> , Régis Hehn <sup>3</sup> and Albert Genter <sup>1</sup>**


**Abstract:** The geothermal powerplant of Soultz-sous-Forêts (France) is investigating the possibility of producing more energy with the same infrastructure by reinjecting the geothermal fluid at lower temperatures. Indeed, during the operation of the powerplant, the geothermal fluid is currently reinjected at 60–70 ◦C in a deep fractured granite reservoir, and the MEET project aims to test its reinjection at 40 ◦C. A 3D hydrothermal study was performed in order to evaluate the spreading of the thermal front during colder reinjection and its impact on the production temperature. In the first step, a 3D structural model at fault scale was created, integrating pre-existing models from 2D vintage seismic profiles, vertical seismic profiles, seismic cloud structure and borehole image logs calibrated with well data. This geometrical model was then adapted to be able to run hydrothermal simulation. In the third step, a 3D hydrothermal model was built based on the structural model. After calibration, the effect of colder reinjection on the production temperature was calculated. The results show that a decrease of 10 ◦C in the injection temperature leads to a drop in the production temperature of 2 ◦C after 2 years, reaching 3 ◦C after 25 years of operation. Lastly, the accuracy of the structural model on which the simulations are based is discussed and an update of the structural model is proposed in order to better reproduce the observations.

**Keywords:** Soultz-sous-Forêts; deep geothermal reservoir; structural model; thermo-hydraulic simulations; MEET H2020 project

#### **1. Introduction**

The Upper Rhine Graben is known for its great potential for the exploitation of geothermal energy at high temperatures. Indeed, it is characterized by strong local geothermal anomalies. Usually, the geothermal gradient in continental crust is approximately 30 ◦C/km. However, it can reach 100 ◦C/km in the Upper Rhine Graben (URG) thanks to large convection loops in the granitic basement and the Triassic sandstone [1], up to the Muschelkalk in some parts of the graben.

Soultz-sous-Forêts is located at around 50 km north of Strasbourg in the URG. The geothermal project began in 1984 and the first drilling began in 1987 [2]. The initial goal was to use the heat in the deep crystalline rocks to produce electricity by fracturing the granite to create an artificial heat exchanger as part of a hot dry rock (HDR) project. For this, an initial phase of drilling, stimulation, circulation tests and observation was carried out until 2007 to study the crystalline rock and the feasibility of future operations. This showed that hydrothermal fluid circulation was occurring in the natural fracture system. The geothermal fluid is a 100 g/L NaCl type brine. Hydraulic, thermal and chemical stimulations were performed to increase the permeability and the connections between

**Citation:** Baujard, C.; Rolin, P.; Dalmais, É.; Hehn, R.; Genter, A. Soultz-sous-Forêts Geothermal Reservoir: Structural Model Update and Thermo-Hydraulic Numerical Simulations Based on Three Years of Operation Data. *Geosciences* **2021**, *11*, 502. https://doi.org/10.3390/ geosciences11120502

Academic Editors: Gianluca Groppelli and Jesus Martinez-Frias

Received: 28 September 2021 Accepted: 6 December 2021 Published: 9 December 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

the reservoir and the wells [3]. The term Enhanced Geothermal System (EGS) was defined from the research work on Soultz-sous-Forêts. The site gradually shifted from a research to industrial facility. Commercial electricity production began in June 2016 [4].

Three wells are currently operated, GPK-2, GPK-3 and GPK-4, reaching a depth of more than 5000 m. Their trajectories are distributed in the north–south direction, following the maximum horizontal stress direction. GPK-2 is the production well and GPK-3 and GPK-4 are used as injection wells. The powerplant uses an organic Rankine cycle (ORC) to convert the heat into electricity to produce a gross power of 1.7 MWe. Currently, the powerplant produces, in a sustainable manner, fluid at more than 150 ◦C and the injection temperature is approximately 60–70 ◦C [5].

The MEET H2020 project (Multidisciplinary and multi-context demonstration of EGS exploration and Exploitation Techniques and potentials) aims at improving deep geothermal energy development in Europe in different ways [6]. In existing EGS plants, it plans to demonstrate the feasibility of reinjecting at lower temperatures, down to 40 ◦C, thus increasing the potential heat valorization of 30%. For this purpose, various investigations have been carried out in the framework of the MEET project, regarding the on-site feasibility of colder reinjection [7] and its chemical effects [8]. The objective of the works presented here was to evaluate the potential consequences of a decrease in the injection temperature on the production temperature on a long-term basis.

#### **2. Materials and Methods**

#### *2.1. Pre-Existing Soultz Structural Models*

The European Cenozoic Rift System groups several rifts formed in response to Alpine and Pyrenean orogens at the beginning of the Cenozoic era. The URG is one of these Tertiary rifts. The rifting began during the Lower Eocene due the Pyrenean compressive tectonic phase, which created or reactivated N–S and NE–SW Variscan faults. It was followed by an E–W extension tectonic phase during the Oligocene, which was characterized by strong subsidence [9]. This crustal thinning induced the rise of the Moho, which formed regional thermal anomalies at URG scale.

The basement has been reached at 1400 m at Soultz-sous-Forêts. It is composed of two different granites: a porphyritic monzogranite and a fined-grained two-mica granite. The latter is found at the bottom of wells, at around 4500 mTVD [10]. The first one can be very hydrothermally altered, especially around nearly vertical fault zones, which are very abundant within the first km at the top basement. The small-scale fractures associated with fault zones are mostly sealed with secondary quartz, calcite and illite.

The monzogranite is covered by sedimentary layers from Permo-Trias to Quaternary. The Permian is poorly represented. The Trias sequence is the most important in this sedimentary cover, from 1350 m to 750 m, characterized by sandstones, alternation of limestone, marls and dolomites (from marine to fluvial environment). Then, Jurassic layers with alternation of limestones and marls appear from 750 m to 600 m. The Tertiary era marked the opening of the rift with the presence of evaporites and deposits of thin lacustrine sediments.

Three pre-existing structural models of the nearby Soultz reservoir have been used in order to build the complete structural model presented in Section 4.1:


#### *2.2. Operation Data and Calibration Dataset 2.2. Operation Data and Calibration Dataset*

*Geosciences* **2021**, *11*, x FOR PEER REVIEW 3 of 16

The powerplant is operated with GPK-2 as a producer and GPK-3 and GPK-4 as injectors. GPK-2, GPK-3 and GPK-4 are cemented to 1431, 1447 and 1446 mMDGL (Measured Depth from Ground Level), respectively. At these depths, GPK-2 has been drilled in 8"1/2 until 5057 mMDGL and cased in 7" until 4440 mMDGL. GPK-3 and GPK-4 have been drilled in 9"5/8 until 4592 and 4767 mMDGL and in 8"1/2 until 5111 and 5270 mMDGL. In these wells, a zone between 4000 m and 4500 m TVD is cemented. GPK-2 is cemented between 4200 m and 4500 m. The powerplant is operated with GPK-2 as a producer and GPK-3 and GPK-4 as injectors. GPK-2, GPK-3 and GPK-4 are cemented to 1431, 1447 and 1446 mMDGL (Measured Depth from Ground Level), respectively. At these depths, GPK-2 has been drilled in 8″1/2 until 5057 mMDGL and cased in 7″ until 4440 mMDGL. GPK-3 and GPK-4 have been drilled in 9″5/8 until 4592 and 4767 mMDGL and in 8″1/2 until 5111 and 5270 mMDGL. In these wells, a zone between 4000 m and 4500 m TVD is cemented. GPK-2 is cemented between 4200 m and 4500 m.

• In another model [13], the two-mica granite interface was considered as a layer.

Feeding zones behind the casing have been reported [14] (in the upper granite reservoir section) for GPK-2 and GPK-3, connecting the well to its annulus from, respectively, 1431 and 1447 mMDGL to 4170 and 3988 mMDGL. As GPK-4 does not present any significant leaks in its casing between 1400 m and 4500 m, only its open hole below 4767 mMDGL is considered. The trajectory of GPK-2 and GPK-3 was taken from the top of Buntsandstein the bottom to take into account the known feed zones. Indeed, the cased section is cemented at the top and bottom only, and nearly the entire granite section can be considered an open hole. The Buntsandstein is then cemented but has been taken into account for its hydrothermal connection with upper granite via nearly vertical fault zones. Feeding zones behind the casing have been reported [14] (in the upper granite reservoir section) for GPK-2 and GPK-3, connecting the well to its annulus from, respectively, 1431 and 1447 mMDGL to 4170 and 3988 mMDGL. As GPK-4 does not present any significant leaks in its casing between 1400 m and 4500 m, only its open hole below 4767 mMDGL is considered. The trajectory of GPK-2 and GPK-3 was taken from the top of Buntsandstein the bottom to take into account the known feed zones. Indeed, the cased section is cemented at the top and bottom only, and nearly the entire granite section can be considered an open hole. The Buntsandstein is then cemented but has been taken into account for its hydrothermal connection with upper granite via nearly vertical fault zones.

Operation data used for model calibration range from 25 June 2016 to 24 June 2019 (3 years). The average production rate is 25–30 L/s. Injection is 100% in GPK-3 until the beginning of March 2017 (almost 7 months) and is then split into GPK-3 and GPK-4 (see Figure 1). Operation data used for model calibration range from 25 June 2016 to 24 June 2019 (3 years). The average production rate is 25–30 L/s. Injection is 100% in GPK-3 until the beginning of March 2017 (almost 7 months) and is then split into GPK-3 and GPK-4 (see Figure 1).

**Figure 1.** Soultz-sous-Forêts operation data used for calibration. Temperature absolute values are hidden for confidentiality reasons. Source: GEIE EMC. **Figure 1.** Soultz-sous-Forêts operation data used for calibration. Temperature absolute values are hidden for confidentiality reasons. Source: GEIE EMC.

#### *2.3. Software and Codes Used 2.3. Software and Codes Used*

The works presented in this paper could be carried out using two commercial software licenses: The works presented in this paper could be carried out using two commercial software licenses:


The meshing of the simplified structural model was performed with MeshIt, a software program for the three-dimensional volumetric meshing of faulted reservoirs, developed by GFZ [15].

#### **3. Results**

#### *3.1. Structural Model*

#### 3.1.1. Complete Structural Model

For this study, the model of Renard and Courrioux 1994 [10] was used as the basis. The horizons and regional faults provided in this model are based on vintage 2D seismic line interpretations. The horizons and regional faults of this model were loaded and reconstructed in Petrel. The well trajectories of GPK-1, GPK-2, GPK-3, GPK-4, EPS-1 and 4550 were also imported into the model. The two-mica granite layer [11] was also imported as a layer according to the depth in GPK-3 and GPK-4 where it was observed.

The major faults from this model, identified in the sedimentary units (Kutzenhausen, Soultz and Hermerswiller faults), were extended into the basement.

For the lower part of the structural model, information about local faults was collected thanks to different data [13,16]:


As a result, the constructed model contains six geological layers. A total of 50 structures representing local faults could be integrated into the Petrel model (Figure 2). Each fault was added by informing its orientation and its dip in the table of the well that is intersected. Then, in the 3D model, each fault identified in several wells was linked to create surfaces.

#### 3.1.2. Simplified Structural Model for Meshing

The sedimentary faults are considered far enough from the wells to not have any influence on the simulations, so it was decided to not keep them in the 3D hydrothermal model. Indeed, these faults are located at a distance greater than the downhole distance between the wells, which is generally considered the well radius of influence in the reservoir for geothermal systems.

To study the hydrothermal circulation in the granite and between wells, faults were selected based on the following criteria:


**Table 1.** Estimated flow contributions of the faults, derived from flow log data.


**Figure 2.** Complete 3D structural model of Soultz-sous-Forêts (in gray: regional fault zones from 2D seismic data interpretation; in color: local fault zones). The arrow on the bottom right of the figure indicates north. **Figure 2.** Complete 3D structural model of Soultz-sous-Forêts (in gray: regional fault zones from 2D seismic data interpretation; in color: local fault zones). The arrow on the bottom right of the figure indicates north. GPK-3 65% (FZ1800 + FZ2120) 35% - - GPK-4 - - - - 100%

the hydraulic test and it matches with the microseismic structure MS-GPK-3-2003a. It also intersects the leakage of GPK-2 at 3900 mMDGL. **Figure 3.** Simplified 3D structural model of Soultz-sous-Forêts. The arrow on the bottom right of the figure indicates north. **Figure 3.** Simplified 3D structural model of Soultz-sous-Forêts. The arrow on the bottom right of the figure indicates north.

Finally, five faults were chosen (Figure 3):


## *3.2. Mesh*

The horizons and faults were extracted from Petrel as surfaces and imported in MeshIt, intermediate software that allows the building of units. Once the model was structured, it was imported into FEFLOW. The entire model was refined by the Tetgen algorithm, especially near the surfaces of faults where the distance between two points was 20 m and the well trajectory where the refinement varied between 5 and 1 m near the intersection between faults and wells (Table 2). This created an unstructured 3D tetrahedral mesh (Figure 4). Faults were assigned to their corresponding surface as 2D discrete feature elements.

#### **Table 2.** Meshing parameters.


*3.2. Mesh* 

**Table 2.** Meshing parameters.

**Figure 4.** (**a**) Meshing of the 3D structural model and (**b**) magnification of the refinement meshing near GPK-4 and the fault FZ4925 (right). **Figure 4.** (**a**) Meshing of the 3D structural model and (**b**) magnification of the refinement meshing near GPK-4 and the fault FZ4925 (**b**).

*3.3. Boundary Conditions and Initial State*

*3.3. Boundary Conditions and Initial State*  The boundary conditions are defined as follows:

The boundary conditions are defined as follows: • Constant head of 10 m (=hydrostatic pressure gradient) boundary conditions on the lateral sides and on top of the model.

The horizons and faults were extracted from Petrel as surfaces and imported in MeshIt, intermediate software that allows the building of units. Once the model was structured, it was imported into FEFLOW. The entire model was refined by the Tetgen algorithm, especially near the surfaces of faults where the distance between two points was 20 m and the well trajectory where the refinement varied between 5 and 1 m near the intersection between faults and wells (Table 2). This created an unstructured 3D tetrahedral mesh (Figure 4). Faults were

> **Parameter Value**  Mesh type Tetrahedron

Volume total 411.6 km3 North–south extent 7 km East–west extent 7 km

Depth −8 km above sea level Top surface 400 m above sea level

Number of units 3 Number of tetrahedrons 257,491 Number of nodes 43,013

Number of discrete features 5 Number of elements in discrete features 19,491

assigned to their corresponding surface as 2D discrete feature elements.

	- of the reservoir (see green line in Figure 5), where a conductive-only heat transport • The temperature is 10 ◦C at the surface (0 m).

regime is assumed. The initial state is defined by:


during the 30 years of simulations discussed in this study.

• A hydrostatic pressure gradient in the model.

• A non-linear temperature distribution, varying with depth (Figure 5). As the model does not simulate convection and does not aim at reproducing long-term fluid flow, which would explain the observed temperature profile in Soultz (suggesting upwelling of hot fluid), the measured temperature profile at the wells was imported as a temperature distribution for the initial state. A simple transient hydrothermal simulation assuming no well use showed that this temperature profile remained almost unchanged over 50 years (see red points in Figure 5). Thus, within the timeframe of the simulation, the temperature distribution is representative of the real temperature profile of GPK-3

**Figure 5.** Comparison between GPK-3 temperature profile measured at equilibrium (in blue) and initial condition of the model (in yellow). The red points show the temperature extracted from the model after 50 years without pumping. The green line shows the result of a 0.072 W/m2 conductiveonly thermal regime. **Figure 5.** Comparison between GPK-3 temperature profile measured at equilibrium (in blue) and initial condition of the model (in yellow). The red points show the temperature extracted from the model after 50 years without pumping. The green line shows the result of a 0.072 W/m2 conductive-only thermal regime.

#### *3.4. Calibration Results*

*3.4. Calibration Results*  The calibration must respect:


ferent fault zones. The calculations were run in a steady-state hydraulic regime and transient thermal regime. Fluid parameters were derived from the analysis realized at the nearby Rittershoffen geothermal site (thermal conductivity of 0.681 W/m/K and thermal capacity of 3.86 MJ/m3/K). The calibration was done manually by varying the hydraulic parameters of faults and matrix as the hydraulic conductivity and the thickness of faults. Initial geological layers and faults' hydraulic parameters were derived from the literature [13,14,18,19]. Fault thickness was derived from geological data (cutting analysis), also reported in these publications.

A sensitivity analysis was manually performed in order to calibrate the model. It highlighted the high impact of the fault hydraulic properties (hydraulic conductivity and thickness). The calibration was carried out in two steps. At first, the flow contributions of the faults and well pressures were fitted at best (see Table 3) using realistic parameters, in order to calibrate the fault transmissivity. Then, the hydraulic conductivity and thickness of each fault were adjusted, keeping the transmissivity of each fault constant. As a result, GPK-

2 0 s production temperature could also be acceptably fitted (see Figure 6). It is important to mention that the output GPK-2 production temperature from FEFLOW is a mean temperature from the different contributions. Therefore, it was necessary to correct the FEFLOW output to take into account temperature losses in the well when the fluid circulates upwards over a few kilometers in the well in order to be able to compare the model results with observed temperature data (wellhead measurements). The temperature losses were calculated using a polynomial function of the flowrate and reservoir temperature, calculated using wellbore simulator HEX-B for the GPK-2 well [20]. The same work was realized on the input injection temperature for GPK-3 and GPK-4 (i.e., the input temperature given to FEFLOW is higher than operation values as it takes into account the heating of the fluid when going down in the well). It must be pointed out that numerical instabilities (oscillations) were observed in the calculated temperature after the shutdown/restart of the plant, inducing rapid fluid velocity changes in the model.

**Table 3.** Fault contributions obtained at the end of the calibration (in bold). Estimated real contributions from Table 1 are recalled in italic.


**Figure 6.** Comparison between simulated and operation data. The corrected value (orange line) takes into account temperature losses in the well in order to be comparable to wellhead values. **Figure 6.** Comparison between simulated and operation data. The corrected value (orange line) takes into account temperature losses in the well in order to be comparable to wellhead values.

At the end of the calibration, the faults had transmissivities between 6.30 × 10−5 and 3 × 10−4 m2/s, except the FZ4760 one, which showed significantly higher transmissivity. Indeed, this fault is known as a main contributor to GPK-2 from logging data. However, many structures contribute to the production of the GPK-2 open-hole with an important connection to the far-field [17]. In order to reproduce the high contribution of this zone to the system, the best solution was to artificially extend this fault to the boundary of the model. As a result, this fault represents the entire contribution of the far field to the pro-At the end of the calibration, the faults had transmissivities between 6.30 <sup>×</sup> <sup>10</sup>−<sup>5</sup> and 3 <sup>×</sup> <sup>10</sup>−<sup>4</sup> <sup>m</sup>2/s, except the FZ4760 one, which showed significantly higher transmissivity. Indeed, this fault is known as a main contributor to GPK-2 from logging data. However, many structures contribute to the production of the GPK-2 open-hole with an important connection to the far-field [17]. In order to reproduce the high contribution of this zone to the system, the best solution was to artificially extend this fault to the boundary of the model. As a result, this fault represents the entire contribution of the far

duction well. The final geological layers and fault parameters are shown in Tables 4 and

Hydraulic Conductivity [m/s] 5e-08 1e-08 7e-09 Specific Storage [1/m] 8e-07 5e-07 1.75e-08 Porosity [-] 0.1 0.03 0.03 Thermal Conductivity [W/m/K] 2.8 2.5 2.5 Thermal Capacity [J/m3/K] 2e06 3.2e06 2.9e06 Heat Production [W/m3] 5e-07 5e-07 3e-06

**Parameter Units FZ1800 FZ2120 FZ4760 FZ4770 FZ4925**  Hydraulic Conductivity [m/s] 6.08e-06 1.7e-05 0.05 2e-05 6.3e-05 Specific Storage [1/m] 2e-06 2e-06 2e-06 2e-06 2e-06 Porosity [-] 0.1 0.1 0.1 0.1 0.1 Thermal Conductivity [W/m/K] 2.5 2.5 2.5 2.5 2.5 Thermal Capacity [J/m3/K] 2.9e06 2.9e06 2.9e06 2.9e06 2.9e06 Thickness [m] 12 15 8 15 1 Heat Production [W/m3] 3e-06 3e-06 3e-06 3e-06 3e-06 Transmissivity [m2/s] 7.3e-05 2.55e-04 0.4 3e-04 6.3e-05

**Sediments Buntsandstein Granite** 

**Table 5.** Fault parameters after calibration.

**Parameter Units Upper** 

5.


**Table 4.** Geological layer parameters after calibration.

field to the production well. The final geological layers and fault parameters are shown in

**Table 5.** Fault parameters after calibration.


#### *3.5. Long-Term Simulation Results 3.5. Long-Term Simulation Results*

Figure 7).

Tables 4 and 5.

In order to calculate the reinjection temperature effect over a long period, the simulation was run over 30 years, including the first 3 years of calibration. Four runs were carried out, simulating reinjection temperatures of, respectively, 70, 60, 50 and 40 ◦C (see Figure 7). In order to calculate the reinjection temperature effect over a long period, the simulation was run over 30 years, including the first 3 years of calibration. Four runs were carried out, simulating reinjection temperatures of, respectively, 70, 60, 50 and 40 °C (see

**Figure 7.** Variation in calculated production temperature in GPK-2 with injection temperatures, calculated over 30 years. The figure shows corrected values (comparable to wellhead values). **Figure 7.** Variation in calculated production temperature in GPK-2 with injection temperatures, calculated over 30 years. The figure shows corrected values (comparable to wellhead values).

The results show that a decrease of 10 °C in the injection temperature in GPK-3 and

Additional simulations were run using this numerical model, assuming a lower reinjection temperature in the reservoir for 4 months only, and then returning to the actual

perature, which would drop from one to two degrees one year after the injection temperature changes. This effect disappears approximately 2 years after returning to the initial

GPK-4 is expected to produce a drop of approximately 2.8 °C in the production temperature at GPK-2 over 30 years. It is interesting to note that this drop does not increase significantly with time, as the drop is already significant (2 °C) after 2 years of operation (i.e., after 5 years of simulation). *3.6. Short-Term Simulation Results*  The results show that a decrease of 10 ◦C in the injection temperature in GPK-3 and GPK-4 is expected to produce a drop of approximately 2.8 ◦C in the production temperature at GPK-2 over 30 years. It is interesting to note that this drop does not increase significantly with time, as the drop is already significant (2 ◦C) after 2 years of operation (i.e., after 5 years of simulation).

injection temperature of 70 °C.

#### *3.6. Short-Term Simulation Results*

Additional simulations were run using this numerical model, assuming a lower reinjection temperature in the reservoir for 4 months only, and then returning to the actual (70 ◦C) reinjection temperature (Figure 8). This showed that the effect of a lower injection temperature over a few months would have a short-term impact on the production temperature, which would drop from one to two degrees one year after the injection temperature changes. This effect disappears approximately 2 years after returning to the initial injection temperature of 70 ◦C. *Geosciences* **2021**, *11*, x FOR PEER REVIEW 12 of 16

**Figure 8.** Variation in calculated production temperature in GPK-2 using colder reinjections over 4 months only, shown over 10 years. The figure shows corrected values (comparable to wellhead values). **Figure 8.** Variation in calculated production temperature in GPK-2 using colder reinjections over 4 months only, shown over 10 years. The figure shows corrected values (comparable to wellhead values).

#### **4. Discussion 4. Discussion**

#### *4.1. Outcomes of the Simulations 4.1. Outcomes of the Simulations*

The works presented here are part of a wider simulation effort aiming at understanding the Soultz-sous-Forêts geothermal site's behavior. Thus, the results presented here are a work in progress, but the calculations to come aim at understanding how the far-field contribution integrates in the Soultz system (by which fault connections). Therefore, the remaining work will not change or update the results/conclusions of the works presented here. The simulation results show that: • A temporary decrease (over a few months) in the injection temperature does not af-The works presented here are part of a wider simulation effort aiming at understanding the Soultz-sous-Forêts geothermal site's behavior. Thus, the results presented here are a work in progress, but the calculations to come aim at understanding how the far-field contribution integrates in the Soultz system (by which fault connections). Therefore, the remaining work will not change or update the results/conclusions of the works presented here. The simulation results show that:


rity issues. Thus, from a reservoir point of view, this work confirms that using colder injections to increase the total produced energy is perfectly feasible. To summarize, a significant decrease in the injection temperature (from 70 ◦C down to 40 ◦C) in order to produce more energy appears to have a clear but limited impact on the reservoir and on the production temperature. This impact is mainly due to fast connections, likely to occur in the upper part of the reservoir, due to production casing integrity issues. Thus, from a reservoir point of view, this work confirms that using colder injections to increase the total produced energy is perfectly feasible.

#### *4.2. Simulation Results vs. Observations*

In the framework of the MEET project, a low-temperature ORC unit was tested in Soultz-sous-Forêts. It was installed after the existing high-temperature ORC unit, thus taking fluid at 70 ◦C as an input (output temperature of the existing ORC unit). This small additional ORC unit has been running for 3 months, from mid-March to mid-June 2021 [6]. The objective of this test was (1) to quantify the efficiency of such a low-temperature ORC unit and (2) to reinject fluid at a lower temperature in Soultz during a few months and observe the effect on the reservoir. This would have allowed comparison of the model results with observation data. Unfortunately, the thermal power of the ORC unit was too low to create a significant change in the reinjection temperature.

A recent observation of the production temperature suggests that the injection temperature has a slightly stronger effect than that inferred by the model (which shows that a decrease of 10 ◦C in the injection temperature is expected to produce a drop of approximately 2–3 ◦C in the production temperature after a few years). Indeed, it is suspected that the permeability of the main fault zones (which are the largest flow contributors to the wells) has been increasing since the system begun operation. This leads to a faster connection between wells. This seems to be confirmed by the pressure decrease observed at the injection wells.

The process behind the possible permeability increase in the most permeable faults is unclear. Indeed, mineral crystallization during brine circulation could lead to a permeability decrease in the circulation zones, as mineralization could progressively close the fractures [21]. Nevertheless, this effect might be compensated by other processes, either purely thermal (fracture aperture increasing as the surrounding rock is being cooled down) or mechanical (fracture aperture increasing due to failure processes). The cooling of the reservoir and subsequent stress change around the injection well could also positively impact the fracture's mechanical behavior, allowing fracture opening by jacking at lower pressures. Interestingly, this possible permeability increase in the most permeable faults leads to the conclusion that the most permeable fault network located in the first kilometer of the Soultz granitic basement is a promising geothermal target. The successful geothermal Rittershoffen project targeting such local faults located in the first kilometer of the top basement confirmed this observation [22].

#### *4.3. Structural Model Update*

The calibration effort led the model to reproduce realistic values of the wellhead pressures, to fit accurately the contribution of the faults at the wells and leading to a good fit of the production temperature over the 3 year calibration period. This certainly shows that the structural model is representative of the reservoir.

Nevertheless, the calibration also showed the limitations of the structural model behind the simulations. Indeed, it appeared necessary to extend one of the faults (FZ4760) to the boundary of the model and to attribute to this structure higher transmissivity values than inferred during the hydraulic tests of the well, in order to obtain the far-field contribution from the reservoir to the system. It is possible that the hydraulic properties of this fault increase with time since testing, as mentioned previously, but this possibly shows that some of the faults included in the model could be connected to great extension structures such as the Soultz horst border faults, which have at least 500 m of vertical offset that connects the system to the regional geothermal reservoir.

In 2018, Electricité de Strasbourg conducted a 3D seismic acquisition survey [23]. This seismic acquisition covered the Soultz-sous-Forêts wells and reservoir. Processing was on-going when the structural model presented here was built and the interpretation was finalized recently; thus, detailed structural results of the 3D seismic acquisition were not available for this work.

Thus, it was decided to update the local Soultz structural model by considering the 3D seismic interpretation results. In light of the seismic results, some faults in the granite included in the model, derived from imaging well data, are connected to regional-scale

structures derived from the 3D seismic survey (see Figure 9), especially in the upper part of the reservoir (1500–2500 m—for example, FZ2120). This could possibly validate the contribution of the far field to the Soultz hydraulic system through the upper part of the reservoir. However, this update could also prove to be insufficient to reproduce the far-field contribution in the deep reservoir and show that connections to the far field exist in the deep reservoir but could not be seen in the 3D seismic data. of the reservoir (1500–2500 m—for example, FZ2120). This could possibly validate the contribution of the far field to the Soultz hydraulic system through the upper part of the reservoir. However, this update could also prove to be insufficient to reproduce the farfield contribution in the deep reservoir and show that connections to the far field exist in the deep reservoir but could not be seen in the 3D seismic data.

included in the model, derived from imaging well data, are connected to regional-scale structures derived from the 3D seismic survey (see Figure 9), especially in the upper part

*Geosciences* **2021**, *11*, x FOR PEER REVIEW 14 of 16

**Figure 9.** (**a**) the image shows the new regional faults on the upper part of the reservoir (yellow, orange, blue, green and violet structures) and faults in the deep reservoir used in the model presented in this paper. (**b**) the image shows the same new regional faults, the new horizons top Muschelkalk (brown), top Buntsandstein (pink) and top Granite (red) and the new structural fault model in the granite. **Figure 9.** (**a**) the image shows the new regional faults on the upper part of the reservoir (yellow, orange, blue, green and violet structures) and faults in the deep reservoir used in the model presented in this paper. (**b**) the image shows the same new regional faults, the new horizons top Muschelkalk (brown), top Buntsandstein (pink) and top Granite (red) and the new structural fault model in the granite.

#### *4.4. Future Work*

New numerical simulations will be carried out for the testing of various fault contribution calibrated with operation data. In order to allow more flexibility during the gridding/meshing process (from the structural model to the calculator), it was decided to run these numerical simulations with ECLIPSE, which uses a regular grid, as it is a finite difference code, in contrast to FEFLOW, which needs a mesh as it is based on finite elements. The gridding process used by ECLIPSE should allow more flexibility at the interface between the structural model and the numerical simulation results. These new simulations should help to validate the hypothesis of a far-field reservoir connection through regional faults in the upper part of the reservoir.

**Author Contributions:** Materials and methods, C.B.; structural model, P.R., É.D. and A.G.; meshing, P.R. and R.H.; calibration, P.R. and R.H.; long-term simulation, P.R. and R.H.; discussion, C.B. Authorship is limited to those who have contributed substantially to the work reported. All authors have read and agreed to the published version of the manuscript.

**Funding:** This project has received funding from the European Union's Horizon 2020 research and innovation program under grant agreement no. 792037 (MEET project).

**Data Availability Statement:** Relies on mostly confidential data owned by us.

**Acknowledgments:** The authors would like to warmly thank the Soultz-sous-Forêts site owner, EEIG Exploitation Minière de la Chaleur, for data access and GFZ Potsdam, especially Mauro Cacace and Guido Blöcher, for their support and the use of MeshIt.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


**Saeed Mahmoodpour 1,\*, Mrityunjay Singh 1,\* , Aysegul Turan <sup>1</sup> , Kristian Bär <sup>1</sup> and Ingo Sass 1,2**


**Abstract:** The deep geothermal energy project at Soultz-sous-Forêts is located in the Upper Rhine Graben, France. As part of the Multidisciplinary and multi-contact demonstration of EGS exploration and Exploitation Techniques and potentials (MEET) project, this study aimed to evaluate the possibility of extracting higher amounts of energy from the existing industrial infrastructure. To achieve this objective, the effect of reinjecting fluid at lower temperature than the current fluid injection temperature of 70 ◦C was modeled and the drop in the production wellhead temperature for 100 years of operation was quantified. Two injection-production rate scenarios were considered and compared for their effect on overall production wellhead temperature. For each scenario, reinjection temperatures of 40, 50, and 60 ◦C were chosen and compared with the 70 ◦C injection case. For the lower production rate scenario, the results show that the production wellhead temperature is approximately 1–1.5 ◦C higher than for the higher production rate scenario after 100 years of operation. In conclusion, no significant thermal breakthrough was observed with the applied flow rates and lowered injection temperatures even after 100 years of operation.

**Keywords:** Soultz-sous-Forêts; EGS; hydro-thermal modeling

#### **1. Introduction**

Geothermal energy is a clean, renewable and low-cost solution for heating and power generation. One of the most challenging problems that humanity is facing is how to mitigate climate change and the anthropogenic emission of carbon dioxide, in order to achieve the target of the Paris agreement, which limits the atmospheric temperature rise to 2 ◦C or less [1]. Carbon geosequestration is the most desirable solution to this problem [2–5]. However associated cost and underdeveloped technology limits the industry from its implementation. Therefore, use of geothermal energy to replace the carbon-based energy sources is gaining momentum [6]. A milestone of the installation of 2 million heat pumps by the European geothermal heat pump market was achieved in 2019 [7]. The geothermal heat usage and electricity production in Europe is expected to grow up to 880–1050 TWh/year and 100–210 TWh/year in 2050 respectively. This contribution is equivalent to 4–7% of European power generation in the year 2050 [8]. As part of the Multidisciplinary and multicontact demonstration of EGS exploration and Exploitation Techniques and potentials [9] project, a numerical hydrothermal model was developed to critically validate the flow behavior of the Soultz-sous-Forêts geothermal power plant from existing operational data. Furthermore, our model was enhanced by including discrete fault structures and validated with operational data to allow for a realistic prediction of the future operational behavior.

Soultz-sous-Forêts is located in the central Upper Rhine Graben, France and has a great potential for geothermal energy exploitation. Soultz-sous-Forêts is the most investigated site in terms of geoscientific studies. The top 1.5 km of the geological succession is made of

**Citation:** Mahmoodpour, S.; Singh, M.; Turan, A.; Bär, K.; Sass, I. Hydro-Thermal Modeling for Geothermal Energy Extraction from Soultz-sous-Forêts, France. *Geosciences* **2021**, *11*, 464. https:// doi.org/10.3390/geosciences11110464

Academic Editors: Béatrice A. Ledésert, Ronan L. Hébert, Ghislain Trullenque, Albert Genter, Eléonore Dalmais, Jean Hérisson and Jesus Martinez-Frias

Received: 23 September 2021 Accepted: 7 November 2021 Published: 9 November 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

thick Quaternary and Tertiary sediments, Mesozoic to Paleozoic sedimentary rocks above the crystalline basement, which is represented by naturally fractured granite. The Mesozoic to Paleozoic sedimentary rocks can be subdivided into two layers: Buntsandstein and Permian. The Buntsandstein is approximately 350 m thick and comprised of fluvial deposits whereas the Permian represents more alluvial continental deposit filling the paleo-basin of the variscan orogeny [10]. The basement is composed of monzogranite with K-feldspar mega crystals with localized concentration of biotite (depth between 1420 and 4700 m) and a two-mica granite containing muscovite (depth between 4700 and 5000 m) [11,12]. In Table 1, the rock properties for the two sandstone layers and granite are listed [13,14]. It must be noted that the data presented in Tables 1 and 2 are based on the calibration through the field data and discussed in the unpublished works of the MEET project. The sedimentary section has a maximum geothermal gradient of up to >100 K km−<sup>1</sup> making the Soultz-sous-Forêts site ideal for geothermal energy extraction [15]. Figure 1 shows that the temperature around the wellbores of Soultz-sous-Forêts is higher than that of the surrounding region. Free convection along the major faults [16–18] is the primary reason causing the increased thermal gradients. For depths greater than 3700 m, the geothermal gradient becomes 10 K/km. The Mesozoic to Paleozoic sedimentary rocks can be subdivided into two layers: Buntsandstein and Permian. The Buntsandstein is approximately 350 m thick and comprised of fluvial deposits whereas the Permian represents more alluvial continental deposit filling the paleo-basin of the variscan orogeny [10]. The basement is composed of monzogranite with K-feldspar mega crystals with localized concentration of biotite (depth between 1420 and 4700 m) and a two-mica granite containing muscovite (depth between 4700 and 5000 m) [11,12]. In Table 1, the rock properties for the two sandstone layers and granite are listed [13,14]. It must be noted that the data presented in Tables 1 and 2 are based on the calibration through the field data and discussed in the unpublished works of the MEET project. The sedimentary section has a maximum geothermal gradient of up to >100 K km−1 making the Soultz-sous-Forêts site ideal for geothermal energy extraction [15]. Figure 1 shows that the temperature around the wellbores of Soultz-sous-Forêts is higher than that of the surrounding region. Free convection along the major faults [16–18] is the primary reason causing the increased thermal gradients. For depths greater than 3700 m, the geothermal gradient becomes 10 K/km.

*Geosciences* **2021**, *11*, 464 2 of 19

Soultz-sous-Forêts is located in the central Upper Rhine Graben, France and has a great potential for geothermal energy exploitation. Soultz-sous-Forêts is the most investigated site in terms of geoscientific studies. The top 1.5 km of the geological succession is made of thick Quaternary and Tertiary sediments, Mesozoic to Paleozoic sedimentary rocks above the crystalline basement, which is represented by naturally fractured granite.

**Figure 1.** Temperature distribution at 2 km depth TVD in the Upper Rhine Graben [19]. **Figure 1.** Temperature distribution at 2 km depth TVD in the Upper Rhine Graben [19].


**Table 1.** Rock matrix parameters [13,20–22].


**Table 2.** Fault parameters [13]. Thermal conductivity W·m−1·K−<sup>1</sup> 2.8 2.5 2.5

Porosity - 0.1 0.03 0.03

Figure 2 shows the geothermal gradient at the Soultz-sous-Forêts site. Sausse et al. [23] and Dezayes et al. [24] used borehole image logs and core studies to characterize 3D realistic and static fractures of Soultz granite. Sausse et al. [23] found 53 structures including 39 fracture zones, seven microseismic structures and six vertical seismic profiles (VSP) at the Soultz-sous-Forêts site. In addition, Dezayes et al. [24] also identified 39 fractures aligned with a general strike of N160◦E at the Soultz site. The sedimentary layer above 1400 m is considered for geothermal activity in the literature due to its remoteness from the main fluid circulation, and it is considered as a caprock. Transmissivity m2·s <sup>−</sup><sup>1</sup> 7.3 × 10−<sup>5</sup> 2.55 × 10−<sup>4</sup> 0.4 3 × 10−<sup>4</sup> 6.3 × 10−<sup>5</sup> Figure 2 shows the geothermal gradient at the Soultz-sous-Forêts site. Sausse et al. [23] and Dezayes et al. [24] used borehole image logs and core studies to characterize 3D realistic and static fractures of Soultz granite. Sausse et al. [23] found 53 structures including 39 fracture zones, seven microseismic structures and six vertical seismic profiles (VSP) at the Soultz-sous-Forêts site. In addition, Dezayes et al. [24] also identified 39 fractures aligned with a general strike of N160°E at the Soultz site. The sedimentary layer above 1400 m is considered for geothermal activity in the literature due to its remoteness from the main fluid circulation, and it is considered as a caprock.

**Figure 2.** Geothermal gradient at the Soultz-sous-Forêts site. Here, an anomaly in temperature is observable in the top 3 km section or in the sedimentary layer. We assumed 10 °C temperature at **Figure 2.** Geothermal gradient at the Soultz-sous-Forêts site. Here, an anomaly in temperature is observable in the top 3 km section or in the sedimentary layer. We assumed 10 ◦C temperature at the surface to calculate this geothermal gradient. The initial data up to the depth of 5.1 km is measured alongside GPK-2 by Pribnow and Schellschmidt [25] and further modified by Rolin et al. [13].

The geothermal project was commenced at Soultz-sous-Forêts in 1984 and the drilling started in 1987 [26]. The earliest plan was to create a fractured granite reservoir in the deep crystalline rock at a depth of 5 km to generate electricity. The industrial electricity production at this site started in June 2016. Presently, the Soultz-sous-Forêts site operates three wells with a maximum depth of up to 5000 m (GPK-2, GPK-3 and GPK-4, see Figure 3). These wells follow the main fault along the NNW–SSE direction. The binary geothermal power plant is working on an Organic Rankine Cycle (ORC) for the heat to electricity conversion. The production well is GPK-2 whereas two wells, GPK-3 and GPK-4, are reinjection wells. The hot fluid produced from GPK-2 is fed into the heat exchanger where the heat is transferred to the isobutane of the ORC cycle and reinjected after being cooled. The fluid production temperature at the Soultz plant is >150 ◦C and the injection temperature is 70 ◦C. The production well (GPK-2) and one injection well (GPK-3) indicate fluid leakage in the respective depth intervals at 1431–4170 m measured depth from ground level (MDGL) and 1447–3988 m MDGL, respectively [27]. There is not enough precise data available for the leakage zone and, therefore, it is assumed to be homogeneous over the depth. Both injection wells are cased only at the top, whereas the granitic reservoir section is not completed and in an open-hole condition. The geothermal project was commenced at Soultz-sous-Forêts in 1984 and the drilling started in 1987 [26]. The earliest plan was to create a fractured granite reservoir in the deep crystalline rock at a depth of 5 km to generate electricity. The industrial electricity production at this site started in June 2016. Presently, the Soultz-sous-Forêts site operates three wells with a maximum depth of up to 5000 m (GPK-2, GPK-3 and GPK-4, see Figure 3). These wells follow the main fault along the NNW–SSE direction. The binary geothermal power plant is working on an Organic Rankine Cycle (ORC) for the heat to electricity conversion. The production well is GPK-2 whereas two wells, GPK-3 and GPK-4, are reinjection wells. The hot fluid produced from GPK-2 is fed into the heat exchanger where the heat is transferred to the isobutane of the ORC cycle and reinjected after being cooled. The fluid production temperature at the Soultz plant is >150 °C and the injection temperature is 70 °C. The production well (GPK-2) and one injection well (GPK-3) indicate fluid leakage in the respective depth intervals at 1431–4170 m measured depth from ground level (MDGL) and 1447–3988 m MDGL, respectively [27]. There is not enough precise data available for the leakage zone and, therefore, it is assumed to be homogeneous over the depth. Both injection wells are cased only at the top, whereas the granitic reservoir section is not completed and in an open-hole condition.

the surface to calculate this geothermal gradient. The initial data up to the depth of 5.1 km is measured alongside GPK-2 by Pribnow and Schellschmidt [25] and further modified by Rolin et al. [13].

*Geosciences* **2021**, *11*, 464 4 of 19

**Figure 3.** Geometry for numerical modeling of Soultz-sous-Forêts geothermal site. Elliptic geometries are faults listed in Table 1 (blue color). Open hole sections of the injection wells are denoted by green colors (GPK-3 and GPK-4) whereas open hole section of the production well is denoted by the dark red color (GPK-2). The leakage zone of the production well is denoted by light red whereas the leakage zone of the GPK-3 is shown by the yellow color. **Figure 3.** Geometry for numerical modeling of Soultz-sous-Forêts geothermal site. Elliptic geometries are faults listed in Table 1 (blue color). Open hole sections of the injection wells are denoted by green colors (GPK-3 and GPK-4) whereas open hole section of the production well is denoted by the dark red color (GPK-2). The leakage zone of the production well is denoted by light red whereas the leakage zone of the GPK-3 is shown by the yellow color.

For the model geometry, only the hydraulically active fractures with high permeability, as proven by thermal anomalies, detected microseismicity during stimulation and operation [23], and which are intersecting multiple wells, were included. The model is thus limited to only five major fractures out of 39 faults or fault zones as shown in Figure 3. The properties of these fractures (fault zones) are listed in Table 2. For the model geometry, only the hydraulically active fractures with high permeability, as proven by thermal anomalies, detected microseismicity during stimulation and operation [23], and which are intersecting multiple wells, were included. The model is thus limited to only five major fractures out of 39 faults or fault zones as shown in Figure 3. The properties of these fractures (fault zones) are listed in Table 2.

Although the Soultz-sous-Forêts site has been the focus of more than 60 PhD theses and 300 peer-reviewed articles [19], only a few hydrothermal modeling studies have been conducted to understand the hydro-thermal behavior of the reservoir in detail. These studies were coupled with and validated by field operational data specifically with tracer tests to understand the flow path within the fractured granite [14].

The flow circulation between GPK-3 and GPK-2 wells was addressed by Sanjuan et al. [27] through an analytical dispersive transfer model, whereas Blumenthal et al. [28], Gessner et al. [29] and Egert et al. [30] also used dispersive transport models for the Soultz-sous-Forêts site. They investigated the hydraulic connectivity between the injection well (GPK3) and production wells (GPK2 and GPK4) using a multi-well tracer test. Gentier et al. [31] developed the first discrete fracture network (DFN) model while employing a particle tracking method to consider the hydraulically active parts and fracture sets for both wells. More recent modeling studies include Magnenet et al. [32], where a 2D THM model was developed based on a finite element grid (FEM); Aliyu and Chen [33], where finite element method (FEM) was used to model hydro-thermal (HT) processes of Soultz while using different working fluids; and most recently Vallier et al. [14], where a THM model based on FEM was developed at reservoir scale coupled with gravity measurements.

Previous studies showed that a single-fracture approach is not sufficient to represent the hydraulic flow existing at Soultz and 2D models are limited to represent the site in terms of the complex geometry and interconnection of dominating faults. Thus, this study takes its roots from the developed 3D THM model based on FEM while hosting five fractures (FZ1800, FZ2120, FZ4760, FZ4770 and FZ4925; also see Table 2) [13].

From the above literature, it is clear that cold water is injected at 70 ◦C through both the injection wells. Therefore, injection of cold water below this temperature may enable much higher geothermal energy extraction. However, no numerical studies have been conducted thus far to support this idea. In the presented study, the energy extraction potential from Soultz-Sous-Forêts for 100 years was investigated, allowing the thermal drawdown at the production well to be quantified. The major simplification of this study is neglecting the mechanical behavior. For the short term, as the temperature and pressure development are limited in the wellbore regions, this simplification is relevant and we can use the modeling hydro-thermal simulation result matching with the operational data to better characterize the wellbore effect and reservoir properties. In the ongoing study, we are trying to examine THM behavior of this system for a better prediction for the long term. Another simplification considered here is scaling in the reservoir. Possible scaling effects on the pipelines and heat exchanger devices are beyond the scope of this study. The reservoir size considered for the numerical simulation is large and computational modeling of kinetic controlled reactive fluid flow in such a reservoir requires significantly high computational resources. The possible incompatibility is insignificant because of the reinjection of the same fluid for the entire operation. However, the effect of temperature reduction on the chemical reactions requires experimental work to update the permeability variation.

The manuscript outline is as follows: First, we present a brief geological setting of Soultz-Sous-Forêts, followed by numerical modeling studies for the site. Furthermore, the mathematical and computational technique to model hydro-thermal processes during heat mining from a fractured reservoir is discussed. Next, the wellbore–reservoir coupling is demonstrated and its impact on wellhead temperature is quantified. In the following section, model results and their discussion are followed by final conclusions.

#### **2. Methodology**

In this section, the mathematical modeling is discussed in two stages. In the first part, governing equations for cold water dynamics in the porous media are presented, and in the second part a mathematical model for fluid leakage from the wellbore is discussed.

#### *2.1. Reservoir Flow Modeling*

A constant heat flux of 0.07 W/m<sup>2</sup> [17] was assigned at the bottom boundary of the domain. All other exterior boundaries of the modeled domain are defined as no flow for both fluid and heat transmission. Because the weather conditions of Soultz are not

available, the monthly averaged daily weather fluctuation of Strasbourg, France was used for this study. Strasbourg is approximately 40 km SSE from the Soultz geothermal site. All fractures within the domain are regarded as internal boundaries, implicitly considering the mass and energy exchange between porous media and fractures or fault zones. In the injection well, the diameter of the well is small and can, as a simplification, be represented by a line.

The coupled heat and mass transfer in a fractured rock matrix can be modeled using the mass balance equation integrated with heat transport. The governing equation for heat and mass flow in porous media can be written as [34]:

$$\rho\_1(\phi\_m S\_1 + (1 - \phi\_m) S\_m) \frac{\partial p}{\partial t} - \rho\_1(\alpha\_m(\phi\_m \beta\_1 + (1 - \phi\_m)\beta\_m)) \frac{\partial T}{\partial t} = \nabla . (\frac{\rho\_1 k\_m}{\mu} \nabla p) \tag{1}$$

In the above equation, fluid pressure and temperature in the rock matrix are denoted by *p* and T, respectively. Here, rock porosity is *φm*, and storage coefficients for rock and fluid are *S*<sup>1</sup> and *Sm*. The thermal expansion coefficient of the fluid and rock matrix is denoted by *β*<sup>1</sup> and *βm*, respectively. The fluid density and dynamic viscosity are indicated using *ρ*<sup>1</sup> and *µ*, whereas the reservoir permeability is denoted by *km*.

The fractures are assumed as internal boundaries and the flow along the internal fractures can be denoted by:

$$\rho\_1(\boldsymbol{\phi}\_f \mathbf{S}\_1 + (1 - \boldsymbol{\phi}\_f) \mathbf{S}\_{\text{mf}}) e\_{\mathbf{h}} \frac{\partial p}{\partial t} - \rho\_1(a\_f(\boldsymbol{\phi}\_f \boldsymbol{\theta}\_1 + (1 - \boldsymbol{\phi}\_f) \boldsymbol{\theta}\_f)) e\_{\mathbf{h}} \frac{\partial T}{\partial t} = \nabla\_{\Gamma} \cdot \left(\frac{e\_{\mathbf{h}} \boldsymbol{\rho}\_1 \mathbf{k}\_f}{\mu} \nabla\_{\Gamma} p\right) + n \mathbf{Q}\_{\text{m}} \tag{2}$$

Here, fluid pressure and temperature in the fracture are indicated by *p* and T respectively. Additionally, *φ<sup>f</sup>* , *S<sup>f</sup>* , *β <sup>f</sup>* , *e<sup>h</sup>* and *k <sup>f</sup>* denote the fracture porosity, storage coefficients of the fracture, thermal expansion coefficient of the fracture, hydraulic aperture between the two fracture surfaces, and fracture permeability, respectively. The mass flux exchange between the fracture and matrix are denoted by *n*.*Q<sup>m</sup>* = *n*.(− *ρkm µ*∇*p* ), whereas the gradient operator applicable along the fracture tangential plane is indicated by ∇*T*.

The local thermal non-equilibrium (LTNE) approach to model heat exchange between the rock matrix and water is implemented in this study. The conductive heat transfer between rock matrix and pore fluid is the dominant heat exchange mechanism. For the rock matrix, the heat transfer equation can be written as:

$$(1 - \phi\_m)\rho\_m \mathcal{C}\_{p,m} \frac{\partial T\_m}{\partial t} = \nabla. ((1 - \phi\_m)\lambda\_m \nabla T\_m) + q\_{ml}(T\_l - T\_m) \tag{3}$$

In the above equation, rock matrix and fluid temperatures are denoted by *T<sup>m</sup>* and *T<sup>l</sup>* , respectively. Here, rock density, rock-specific heat capacity, rock thermal conductivity and the rock–fluid heat transfer coefficient are denoted by *ρm*, *Cp*,*m*, *λ<sup>m</sup>* and *qml*, respectively. The heat flux leaving the domain and received by the adjacent fracture can be written as:

$$\rho\_{\mathbf{f}}(1-\phi\_f)e\_{\hbar}\rho\_f\mathbb{C}\_{p,f}\frac{\partial\mathbb{T}\_{\mathbf{m}}}{\partial\mathbf{t}} = \nabla\_{\mathbf{T}}\cdot((1-\phi\_f)e\_{\hbar}\lambda\_f\nabla\_{\mathbf{T}}\mathbb{T}\_{\mathbf{m}}) + e\_{\hbar}q\_{fl}(T\_l-T\_{\mathbf{m}}) + n. (-(1-\phi\_m)\lambda\_m\nabla T\_{\mathbf{m}} \tag{4}$$

where *T<sup>m</sup>* and *T<sup>l</sup>* are the matrix and fluid temperatures in the fracture, respectively; *ρ<sup>f</sup>* is the density of the fracture; *Cp*, *<sup>f</sup>* is the specific heat capacity of the fracture; *λ<sup>f</sup>* is the thermal conductivity of the fracture; and *q f l* represents the rock fracture–fluid interface heat transfer coefficient, related to the fracture aperture. The last term on the right-hand side of Equation (4) represents the heat flux exchange between the rock matrix and the fracture.

The heat convection equation for the pore fluid can be written as:

$$
\rho\_m \rho\_l \mathbf{C}\_{p,l} \frac{\partial T\_l}{\partial t} + \phi\_m \rho\_l \mathbf{C}\_{p,l} (-\frac{k\_m \nabla p}{\mu}), \nabla T\_l = \nabla. (\phi\_m \lambda\_l \nabla T\_l) + q\_{ml} (T\_m - T\_l) \tag{5}
$$

Here *Cp*,*<sup>l</sup>* is the heat capacity of the fluid at a constant pressure and *λ<sup>l</sup>* is the thermal conductivity of the fluid.

The heat flux coupling relationship of the fluid between the domain and the fracture is satisfied by:

$$
\rho\_f e\_h \rho\_l \mathbb{C}\_{p,l} \frac{\partial T\_l}{\partial t} + \phi\_f e\_h \rho\_l \mathbb{C}\_{p,l} (-\frac{k\_f \nabla\_T p}{\mu}) . \nabla\_T T\_l = \nabla\_T (\phi\_f e\_h \lambda\_l \nabla\_T T\_l) + e\_h q\_{fl} (T\_m - T\_l) + n.q\_l \tag{6}
$$

where the heat flux *n*.*q<sup>l</sup>* = *n*.(−*φlλl*∇*Tl*) denotes the heat exchange of the fluid between porous media and the fracture.

Temperature-dependent fluid thermodynamic properties are implemented into the coupled hydrothermal mass and energy balance equations. The thermophysical properties of water as a function of temperature, including dynamic viscosity (*µ*), specific heat capacity (*Cp*), density (*ρ*) and thermal diffusivity (*κ*), are listed below [34]:

$$\begin{array}{cccc} \mu & = 1.38 - 2.12 \times 10^{-2} \times T^1 + 1.36 \times 10^{-4} \times T^2 - 4.65 \times 10^{-7} \times T^3 + 8.90 \times 10^{-10} \times T^4 \\ & - 9.08 \times 10^{-13} \times T^5 + 3.85 \times 10^{-16} \times T^6 & (273.15 - 413.15 \text{ K}) \end{array} \tag{7}$$

$$\begin{aligned} \mu &= 4.01 \times 10^{-3} - 2.11 \times 10^{-5} \times T^1 + 3.86 \times 10^{-8} \times T^2 - 2.40 \times 10^{-11} \times T^3 \\ &\quad (413.15 - 553.15 \text{ K}) \end{aligned} \tag{8}$$

$$\mathcal{C}\_{p} = 1.20 \times 10^{4} - 8.04 \times 10^{1} \times T^{1} + 3.10 \times 10^{-1} \times T^{2} - 5.38 \times 10^{-4} \times T^{3} + 3.63 \times 10^{-7} \times T^{4} \tag{9}$$

$$\rho = 1.03 \times 10^{-5} \times T^3 - 1.34 \times 10^{-2} \times T^2 + 4.97 \times T + 4.32 \times 10^2 \tag{10}$$

$$\kappa = -8.69 \times 10^{-1} + 8.95 \times 10^{-3} \times T^1 - 1.58 \times 10^{-5} \times T^2 + 7.98 \times 10^{-9} \times T^3 \tag{11}$$

We used the commercial software COMSOL Multiphysics, version 5.6 [34] for numerically solving the coupled mass and energy conservation equations listed above. COM-SOL Multiphysics solves general-purpose partial differential equations using the finite element method.

#### *2.2. Wellbore Leakage Modeling*

Understanding the fluid flowing temperature along the wellbore can be useful for an accurate estimation of the overall heat production at the production wellhead temperature, and for estimating any possible leakage caused by heat loss along the wellbore. Several reliable analytical techniques are reported in the literature to calculate the flowing temperature distribution along a wellbore [35–37].

We integrated our reservoir simulation with a wellbore flow model as developed by Hasan et al. [36]. The model constitutes an analytical approach to estimate wellborefluid temperature distribution for steady state flow. The analytical equations are solved sequentially for each section. Figure 4 shows a simplification of a typical geothermal well with one deviation angle. The well is inclined at an angle α with the horizontal plane. The heat transfer between the wellbore fluid and the rock matrix occurs due to the temperature difference between them. A general energy balance equation for single phase fluid flow can be expressed as:

$$\frac{dH}{dz} - \text{g}\,\sin\alpha + \nu \frac{d\nu}{dz} = \pm \frac{Q}{w} \tag{12}$$

**Figure 4.** Wellbore heat loss modeling schematic. **Figure 4.** Wellbore heat loss modeling schematic.

come:

Here, is the fluid enthalpy, is the gravitational constant, is the variable well depth from the surface, is the flow velocity, is the heat flux per unit of well length Here, *H* is the fluid enthalpy, *g* is the gravitational constant, *z* is the variable well depth from the surface, *ν* is the flow velocity, *Q* is the heat flux per unit of well length and *w* is the mass rate. When assuming no-phase change conditions, enthalpy will become:

$$dH = (\frac{\partial H}{\partial T})\_P dT + (\frac{\partial H}{\partial p})\_T dp = c\_p dT - C\_f c\_p dp \tag{13}$$

 = ( ) <sup>+</sup> ( ) <sup>=</sup> <sup>−</sup> (13) In the above equation, *T* is the fluid temperature and *p* is the pressure, *c<sup>p</sup>* is the specific heat capacity of fluid and *C<sup>J</sup>* is the Joule–Thomson coefficient. If *T<sup>f</sup>* is the fluid temperature, the energy balance equation will be:

$$\frac{d\mathbf{T}\_f}{dz} = \mathbf{C}\_f \frac{dp}{dz} + \frac{1}{c\_p} (\pm \frac{\mathbf{Q}}{W} + \mathbf{g}\sin a - \nu \frac{d\nu}{dz}) \tag{14}$$

specific heat capacity of fluid and is the Joule–Thomson coefficient. If is the fluid temperature, the energy balance equation will be: The heat flux per unit wellbore length can be expressed as:

$$Q \equiv -L\_R w c\_p (T\_f - T\_{\text{ei}}) \tag{15}$$

 <sup>=</sup> <sup>+</sup> (± + − ) (14) Here, *Tei* is the rock temperature, and *L<sup>R</sup>* is the relaxation parameter defined as:

$$L\_R \equiv \frac{2\pi}{c\_p w} [\frac{r\_{to} \mathcal{U}\_{to} k\_{to}}{\lambda\_m + (r\_{to} \mathcal{U}\_{to} T\_D)}] \tag{16}$$

$$T\_f = T\_{\dot{e}i} + \frac{1 - \mathbf{e}^{(z-L)L\_R}}{L\_R} [\mathbf{g}\_G \sin \alpha + \Phi - \frac{\mathbf{g} \sin \alpha}{c\_p}] \tag{17}$$

Here, is the rock temperature, and is the relaxation parameter defined as: ≡ 2 [ ] (16) In Equations (16) and (17), *rto* is the tubing outside radius, *Uto* is the overall heat transfer coefficient, *k<sup>e</sup>* is rock thermal conductivity, *T<sup>D</sup>* is the nondimensional temperature, *L* is the measured depth of the wellbore, *g<sup>G</sup>* is the geothermal gradient and Φ is the lumped parameter, which lumps the kinetic energy term and the Joule–Thomson coefficient term.

 + () If *V* is the fluid specific volume and *S* is fluid entropy then from Maxwell identities, we can write:

) <sup>=</sup> <sup>+</sup> (

$$(\frac{\partial H}{\partial p})\_T = V + T(\frac{\partial S}{\partial p})\_T \text{ ét } (\frac{\partial S}{\partial p})\_T = -(\frac{\partial V}{\partial T})\_p \tag{18}$$

$$dH = c\_p dT + [V - T(\frac{\partial V}{\partial T})\_p] dp\tag{19}$$

the lumped parameter, which lumps the kinetic energy term and the Joule–Thomson co-

= + [ − (

If is the fluid specific volume and is fluid entropy then from Maxwell identities,

) & (

) <sup>=</sup> −(

) (18)

)] (19)

( 

efficient term.

we can write:

$$\mathbf{c}\_{p}\mathbf{C}\_{I} = -\left[V - T\left(\frac{\partial V}{\partial T}\right)\_{p}\right] \tag{20}$$

For liquids where *ρ* is the liquid density, volume expansivity (*β*) can be calculated as:

$$\beta \equiv (\frac{1}{V})(\frac{\partial V}{\partial T})\_p \equiv (-\frac{1}{\rho})(\frac{\partial \rho}{\partial T})\_p \tag{21}$$

$$dH = c\_p dT + V(1 - \beta T)dp\tag{22}$$

$$
\mathcal{L}\_p \mathbb{C}\_I = -V(1 - \beta T) \tag{23}
$$

Therefore, the final output temperature from the wellhead will be:

$$T\_{out} = \frac{\int \mathcal{m} \, c\_p \, T \, dz}{\int \, \mathcal{m} \, c\_p \, dz} \tag{24}$$

In this text, we considered three wells: GPK-3 and GPK-4 as two injection wells and GPK-2 as a production well. In GPK-3, the wellbore leakage was assumed between 1282 and 4852 m depth measured from the surface. In the case of GPK-2, the wellbore leakage was modeled between 1264 m to 4244 m depth measured from the surface. The fluid is single phase water flow and the model parameters are constant specific heat capacity of water as 4200 J·kg−1K−<sup>1</sup> , *L<sup>R</sup>* = 0.00001 m−<sup>1</sup> , and Φ = 0.00345 Km−<sup>1</sup> , respectively. Here, *L<sup>R</sup>* and Φ accounts for the casing properties, cement properties and their thicknesses.

The coupling between the reservoir and the wellbore model is achieved through a sequential approach. First, the temperature drop due to heat exchange between the injection wellbore and the rock matrix is calculated through the analytical model. From this, the final wellbore bottom temperature is obtained, which is used as an input for the first iteration of the numerical reservoir model (heat exchange between the rock and the fluid). In the next stage, the wellbore heat exchange effect is implemented through the updated values for the reservoir temperature measured at the production wellbore bottom. The wellbore heat exchange effect is defined analytically and the temperature alongside the wellbore is obtained. Wellbore radius is very small compared to the reservoir size, and is considered as a line with the calculated temperature profile through the analytical model inside the reservoir simulation. The total number of elements in the geometry is 142,051, whereas boundary elements number 8305 and edge elements number 666.

#### **3. Results and Discussions**

In this section, first we present the benchmark for our numerical model. Then, the hydrothermal numerical modeling results are compared with the operational data measured at Soultz-sous-Forêts for three years of operation. Furthermore, new injection scenarios are proposed that can be adopted with the existing industrial setup to enhance the energy extraction capability. Finally, we perform sensitivity analysis on ten governing parameters and estimate their impact on the production temperature.

#### *3.1. Benchmarking*

For benchmarking the numerical model, we used the approach adopted by Cheng et al. [38] and Bongole et al. [39] by using a simplified 1D heat transfer problem for a single fracture system. This approach is used in the previous studies to benchmark the models. The analytical equation for heat transfer considers that the geometry is infinitely extended in both directions (see Figure 5), there is no flow boundary conditions for heat exchange, steady state fluid flow occurs only through the fracture and the rock permeability is zero, and the thermophysical properties of water are constant throughout the simulation. The temperature distribution for the fluid is identical to that of the rock matrix due to the local thermal equilibrium assumption. The analytical solution for the fluid temperature distribution is [38,39]:

*Geosciences* **2021**, *11*, 464 10 of 19

<sup>0</sup> − (,) <sup>0</sup> −

thermal equilibrium assumption. The analytical solution for the fluid temperature distri-

(,) =

*Geosciences* **2021**, *11*, 464 10 of 19

thermal equilibrium assumption. The analytical solution for the fluid temperature distri-

= [(

2 ℎ,

) √

]

,

4( − )

]

**Figure 5.** Geometry for the benchmarking problem. **Figure 5.** Geometry for the benchmarking problem. **Figure 5.** Geometry for the benchmarking problem.

bution is [38,39]:

bution is [38,39]:

We observe a good agreement between the numerical and analytical solutions, as In the above equation, *Tf D* is the nondimensional fracture temperature and *u<sup>f</sup>* is the fluid velocity. We observe a good agreement between the numerical and analytical solutions, as

demonstrated in Figure 6. We observe a good agreement between the numerical and analytical solutions, as demonstrated in Figure 6. demonstrated in Figure 6.

**Figure 6.** Comparison of the numerical solution with the analytical temperature distribution along the fracture length. **Figure 6.** Comparison of the numerical solution with the analytical temperature distribution along the fracture length.

**Figure 6.** Comparison of the numerical solution with the analytical temperature distribution along the fracture length. The operational data for three years was made available for Soultz-sous-Forêts site by the site operators and is used here to calibrate the coupled unsteady hydro-thermal model. Figure 7 shows the injection and production rates at the wellhead for 1163 days from June 2016 to September 2019. The fluid injection temperature is 70 °C for both the The operational data for three years was made available for Soultz-sous-Forêts site by the site operators and is used here to calibrate the coupled unsteady hydro-thermal model. Figure 7 shows the injection and production rates at the wellhead for 1163 days from June 2016 to September 2019. The fluid injection temperature is 70 ◦C for both the injection wells.

The operational data for three years was made available for Soultz-sous-Forêts site

by the site operators and is used here to calibrate the coupled unsteady hydro-thermal model. Figure 7 shows the injection and production rates at the wellhead for 1163 days from June 2016 to September 2019. The fluid injection temperature is 70 °C for both the

injection wells.

injection wells.

**Figure 7.** Injection schedule at (**a**) GPK-3 and (**b**) GPK-4 and (**c**) production schedule at production well GPK-2 for 1163 days of operation from June 2016 to September 2019. Here, the blue lines are the actual injection and production rates. The red dash lines indicate no operation period. **Figure 7.** Injection schedule at (**a**) GPK-3 and (**b**) GPK-4 and (**c**) production schedule at production well GPK-2 for 1163 days of operation from June 2016 to September 2019. Here, the blue lines are the actual injection and production rates. The red dash lines indicate no operation period.

#### *3.2. Validation with Operational Data*

*3.2. Validation with Operational Data* In Figure 8, the numerical model data is validated with operational data for the time period as described above. Unfortunately, it is not possible to publish the exact values of operational data due to concerns of our industrial partners and we can only show the amount of change. These are the actual temperature values shown by different colors for operational and simulations (not the differences). The measured temperature data is the operational data for 1163 days at the production wellhead. The temperature at the production well based on the hydro-thermal model is significantly different compared to the operational data. For most of the operational period, the predicted production well temperature is 15 °C higher than the measured temperature. Only operation onset and termi-In Figure 8, the numerical model data is validated with operational data for the time period as described above. Unfortunately, it is not possible to publish the exact values of operational data due to concerns of our industrial partners and we can only show the amount of change. These are the actual temperature values shown by different colors for operational and simulations (not the differences). The measured temperature data is the operational data for 1163 days at the production wellhead. The temperature at the production well based on the hydro-thermal model is significantly different compared to the operational data. For most of the operational period, the predicted production well temperature is 15 ◦C higher than the measured temperature. Only operation onset and termination stages display smaller deviation in predicted temperature than observed temperature. Because the wellhead temperature measuring device may be affected by the local ambient temperature

nation stages display smaller deviation in predicted temperature than observed temperature. Because the wellhead temperature measuring device may be affected by the local

almost the same for the corresponding months in each operational year, a correction factor to account for the weather impact on the measuring device based on the numerical model and the monthly average temperature near the geothermal site is almost the same for the corresponding months in each operational year, a correction factor to account for the weather impact on the measuring device based on the numerical model is introduced. Two scenarios of seasonal impact on the production fluid temperature are considered: (a) 20% impact of ambient temperature (Teffective=Tsimulation + 0.2 × ambient temperature) and (b) 50% impact of ambient temperature (Teffective =Tsimulation + 0.5 × ambient temperature). is introduced. Two scenarios of seasonal impact on the production fluid temperature are considered: (a) 20% impact of ambient temperature (Teffective=Tsimulation + 0.2 × ambient temperature) and (b) 50% impact of ambient temperature (Teffective =Tsimulation + 0.5 × ambient temperature).

*Geosciences* **2021**, *11*, 464 12 of 19

**Figure 8.** Difference between operational data from June 2016 to September 2019 and the data obtained from the numerical model. **Figure 8.** Difference between operational data from June 2016 to September 2019 and the data obtained from the numerical model.

Figure 8 shows the comparison of the operational data with the coupled reservoirwellbore model and the weather-influenced production fluid temperature. The integrated wellbore–reservoir model has the highest overestimation of production temperature. However, when daily weather fluctuations in the integrated wellbore–reservoir model are considered, the prediction matches very well for most of the operation, as shown in Figure 8. The temperature differences are more relevant to understand its deviation from the actual value rather than the original temperature. The difference between operational and numerical data while considering 50% of the ambient temperature on the production tem-Figure 8 shows the comparison of the operational data with the coupled reservoirwellbore model and the weather-influenced production fluid temperature. The integrated wellbore–reservoir model has the highest overestimation of production temperature. However, when daily weather fluctuations in the integrated wellbore–reservoir model are considered, the prediction matches very well for most of the operation, as shown in Figure 8. The temperature differences are more relevant to understand its deviation from the actual value rather than the original temperature. The difference between operational and numerical data while considering 50% of the ambient temperature on the production temperature of the coupled wellbore–reservoir model has the best matching among all models. However, the model deviates by more than 15 ◦C from the operation data during the periods of 1.8 and 2.4 years. Because no other reasons for these deviations are provided with the operational data set, different measurement procedures or false measurements at the wellhead are assumed as reasons for these deviations.

#### *3.3. Long-Term Operational Behavior*

and 40 m<sup>3</sup>

perature of the coupled wellbore–reservoir model has the best matching among all models. However, the model deviates by more than 15 °C from the operation data during the periods of 1.8 and 2.4 years. Because no other reasons for these deviations are provided with the operational data set, different measurement procedures or false measurements at the wellhead are assumed as reasons for these deviations. *3.3. Long-Term Operational Behavior* In the next study, the model was extended to a simulation period of 100 years of In the next study, the model was extended to a simulation period of 100 years of operation to predict the wellhead temperature development at the production well. In this section, different initial temperatures at the bottom hole section than the operationally measured data were used. The main objective of this study was to estimate the temperature at the production well (GPK-2) for different injection temperatures for long-term operational periods. In both scenarios, the injection rates for the first 1163 days are the same as in the provided operational data set. The recently designed heat exchanger at Soultz-sous-Forêts is capable of cooling the water from 70 to 40 ◦C using a cooling loop at 15 ◦C and 40 m3/h [40]. Therefore, two scenarios were considered, A and B, for different injection temperatures. For the remaining operational period, scenario A considers four different fluid injection temperatures at the injection wellhead (70, 60, 50 and 40 ◦C).

operation to predict the wellhead temperature development at the production well. In this

measured data were used. The main objective of this study was to estimate the temperature at the production well (GPK-2) for different injection temperatures for long-term operational periods. In both scenarios, the injection rates for the first 1163 days are the same as in the provided operational data set. The recently designed heat exchanger at Soultzsous-Forêts is capable of cooling the water from 70 to 40 °C using a cooling loop at 15 °C

temperatures. For the remaining operational period, scenario A considers four different fluid injection temperatures at the injection wellhead (70, 60, 50 and 40 °C). The fluid injection rates are 13.3 and 11 L/s for GPK-3 and GPK-4, respectively, and the production fluid rate of GPK-2 is 24.3 L/s for the remaining operational period. In Scenario B, the injection rates after 1163 days are 19.6 and 9.7 L/s for GPK-3 and GPK-4, respectively, and the production rate of GPK-2 is 29.3 L/s; the same four injection wellhead temperatures as for scenario A were considered: 70, 60, 50 and 40 °C. These values of the injection and

production rates are the operational requirements requested by our industrial partner.

Figure 9a–d shows the temperature along the wellbore for scenarios A and B, respec-

tively, for both injection wells. The wellbore GPK-3 has an open hole section that causes a

/h [40]. Therefore, two scenarios were considered, A and B, for different injection

The fluid injection rates are 13.3 and 11 L/s for GPK-3 and GPK-4, respectively, and the production fluid rate of GPK-2 is 24.3 L/s for the remaining operational period. In Scenario B, the injection rates after 1163 days are 19.6 and 9.7 L/s for GPK-3 and GPK-4, respectively, and the production rate of GPK-2 is 29.3 L/s; the same four injection wellhead temperatures as for scenario A were considered: 70, 60, 50 and 40 ◦C. These values of the injection and production rates are the operational requirements requested by our industrial partner.

Figure 9a–d shows the temperature along the wellbore for scenarios A and B, respectively, for both injection wells. The wellbore GPK-3 has an open hole section that causes a linear temperature drop along the wellbore instead of a nonlinear temperature drop, as shown in Figure 9a,b. It is interesting to note that instead of having different injection-production rates in all three wells, the fluid production temperature at the GPK-2 wellhead is almost similar for both of the scenarios A and B, as shown in Figure 9e,f. The small increase in temperature at the production wellhead is due to the sudden drop in the production wellhead pressure. The contribution in the fluid flow is due to the first pressure shock of the injection that comes from the faulted zones which are located at the bottom of the system with a higher temperature. As time proceeds, the contribution from the matrix and the leakage zone increases and reduces the temperature a few days after the beginning of the injection. To calculate the initial temperature at the wellhead, it is assumed that there is a steady state flow from the combination of the matrix and the fault zones. This initial temperature is slightly lower than that of the unsteady condition at the early time period. The fluid with the lower viscosity shows a delay in the development of the pressure shock resulting from the cold fluid injection. Therefore, the contribution from the matrix and the leakage zone for the fluid with the temperature 40 ◦C happens later and the main fluid flow from the faulted zone in the bottom of the system lasts for a longer time. Moreover, the temperature increase in scenario B is higher compared to that of scenario A due to the fact that scenario B has a higher production rate than scenario A which reduces the time for exchanging heat in the wellbore.

Figure 10 shows the comparison of temperature distribution in the fractures and along the wellbore for scenarios A and B. The higher production rate results in slightly faster thermal drawdown at the production well bottom for scenario B than scenario A. No thermal breakthrough was observed at the production well bottom even after 100 years of operation, as shown in Figure 10e,f.

#### *3.4. Uncertainties*

There are several uncertainties in this model. We considered the wellbore as a line source for the heat flow. The faulted zone is formulated using a fracture. Both of these assumptions are reliable because the size of the wellbore and the fault zone is negligible in comparison to the overall size of the reservoir. Data validation for the short operational period for production confirms this behavior. The matrix zone is considered as homogeneous and isotropic. As the permeability of matrix is lower than faulted zone, its contribution to the heat and mass flux is small. Therefore, this assumption holds true. As we do not know the exact point of the leakage zone alongside the casing area, we considered a homogeneous leakage and tried to compensate for the possible errors by performing a trial-and-error method to find an appropriate lumped parameter that defines the wellbore heat exchange effect. Furthermore, due to the unavailability of the geomechanical and geochemical data, we mainly focused on the hydrothermal behavior of the geothermal system. Short-term validation of this TH model gives an insight regarding the accurate system characterization, including the permeability and porosity distribution, fault placement and its contribution to the overall flow, the wellbore effect on the overall heat exchange, and fluid and rock properties. Therefore, it builds a basis for future THM or THMC (thermo-hydro-mechanical-chemical) simulations. Our expectation regarding the THM behavior is that permeability around the injection would increase (resulting from the localized thermoelastic stress reorientation and increased pore pressure). Therefore, the enhanced permeability will be favorable in the energy extraction. Based on this un-

*Geosciences* **2021**, *11*, 464 13 of 19

derstanding, TH provides a preliminary basis for the thermoelastic and poroelastic stress development in this geothermal site. nario A due to the fact that scenario B has a higher production rate than scenario A which reduces the time for exchanging heat in the wellbore.

linear temperature drop along the wellbore instead of a nonlinear temperature drop, as shown in Figure 9a,b. It is interesting to note that instead of having different injectionproduction rates in all three wells, the fluid production temperature at the GPK-2 wellhead is almost similar for both of the scenarios A and B, as shown in Figure 9e,f. The small increase in temperature at the production wellhead is due to the sudden drop in the production wellhead pressure. The contribution in the fluid flow is due to the first pressure shock of the injection that comes from the faulted zones which are located at the bottom of the system with a higher temperature. As time proceeds, the contribution from the matrix and the leakage zone increases and reduces the temperature a few days after the beginning of the injection. To calculate the initial temperature at the wellhead, it is assumed that there is a steady state flow from the combination of the matrix and the fault zones. This initial temperature is slightly lower than that of the unsteady condition at the early time period. The fluid with the lower viscosity shows a delay in the development of the pressure shock resulting from the cold fluid injection. Therefore, the contribution from the matrix and the leakage zone for the fluid with the temperature 40 °C happens later and the main fluid flow from the faulted zone in the bottom of the system lasts for a longer time. Moreover, the temperature increase in scenario B is higher compared to that of sce-

**Figure 9.** Comparison between scenarios A and B for (**a**,**b**) temperature along the injection well GPK-3, (**c**,**d**) temperature along the injection well GPK-4, and (**e**,**f**) wellhead temperature at the production well GPK-2. **Figure 9.** Comparison between scenarios A and B for (**a**,**b**) temperature along the injection well GPK-3, (**c**,**d**) temperature along the injection well GPK-4, and (**e**,**f**) wellhead temperature at the production well GPK-2.

years of operation, as shown in Figure 10e,f.

Figure 10 shows the comparison of temperature distribution in the fractures and along the wellbore for scenarios A and B. The higher production rate results in slightly faster thermal drawdown at the production well bottom for scenario B than scenario A. No thermal breakthrough was observed at the production well bottom even after 100

**Figure 10.** Comparison of temperature distribution (in SI units) in the fractures for scenarios A and B at time (**a**,**b**) 0 year, (**c**,**d**) 50 years and (**e**,**f**) 100 years. Here, ∆ is the temperature drop in the reservoir from the initial state. **Figure 10.** Comparison of temperature distribution (in SI units) in the fractures for scenarios A and B at time (**a**,**b**) 0 year, (**c**,**d**) 50 years and (**e**,**f**) 100 years. Here, ∆*T* is the temperature drop in the reservoir from the initial state.

#### There are several uncertainties in this model. We considered the wellbore as a line *3.5. Sensitivity Analysis of Hydrothermal Uncertainties*

*3.4. Uncertainties*

source for the heat flow. The faulted zone is formulated using a fracture. Both of these assumptions are reliable because the size of the wellbore and the fault zone is negligible in comparison to the overall size of the reservoir. Data validation for the short operational period for production confirms this behavior. The matrix zone is considered as homogeneous and isotropic. As the permeability of matrix is lower than faulted zone, its contribution to the heat and mass flux is small. Therefore, this assumption holds true. As we do not know the exact point of the leakage zone alongside the casing area, we considered a homogeneous leakage and tried to compensate for the possible errors by performing a trial-and-error method to find an appropriate lumped parameter that defines the wellbore heat exchange effect. Furthermore, due to the unavailability of the geomechanical and geochemical data, we mainly focused on the hydrothermal behavior of the geothermal system. Short-term validation of this TH model gives an insight regarding the accurate system characterization, including the permeability and porosity distribution, fault placement and its contribution to the overall flow, the wellbore effect on the overall heat exchange, and fluid and rock properties. Therefore, it builds a basis for future THM or THMC (thermo-hydro-mechanical-chemical) simulations. Our expectation regarding the To examine the effect of the uncertainty of the involved parameters in hydro-thermal simulations for the Soultz-sous-Forêts geothermal reservoir, a detailed sensitivity analysis was performed, and its results are shown in Figure 11. The base case was selected as scenario A with an injection temperature of 40 ◦C. The range of parameters are mentioned in Table 3. Results show that the hydraulic conductivity of the matrix and fault zone and the wellbore leakage have a considerable effect on the production temperature. This finding is well aligned with the sensitivity analysis of the THM process in the fracture reservoir system [41,42]. However, these values are one order of magnitude lower than the wellbore heat exchange effect, as shown in Figure 9e. The other three parameters—fault thickness, matrix thermal conductivity and the matrix specific heat capacity—have approximately 1 ◦C variation over 100 years of operation. The porosity of the matrix and the fault zone, in addition to the fault zone thermal conductivity, have no impact on the temperature variation. Interestingly, heat flux has no effect on the production temperature at the surface due to the conductive heat flow in the reservoir and because the fault zones are farther away from the bottom boundary considered for the simulation. Important parameters in this sensitivity analysis show a monotonic effect on the production temperature behavior and they cannot explain the sinusoidal temperature fluctuation of more than 10 ◦C in each year. To check our assumption regarding the weather fluctuation impact on the production temperature, we tried to estimate the wellbore heat exchange effect. We found that the wellbore heat exchange is mainly flow-rate dependent parameter and the flow rates for the production data are constant from 41 to 250 days, whereas we can see a fluctuation in the recorded temperature. This indicates that the cyclic variability in the production temperature cannot be supported by the wellbore heat exchange argument. Therefore, the most suitable reason of the periodic production temperature variability is weather fluctuation on the measuring device.

**Figure 11.** Sensitivity analysis for 10 parameters affecting the hydro-thermal processes at Soultz-sous-Forêts for (**a**) matrix hydraulic conductivity, (**b**) heat flux from the bottom boundary, (**c**) matrix specific heat capacity, (**d**) hydraulic conductivity of faults (here , is the fault zone hydraulic conductivity as given in Table 2), (**e**) porosity of fault zone, (**f**) leakage contribution to the total fluid flow, (**g**) matrix porosity, (**h**) matrix thermal conductivity, (**i**) fault thickness (here is the fault thickness as given in Table 2), and (**j**) thermal conductivity of the fault zone. **Figure 11.** Sensitivity analysis for 10 parameters affecting the hydro-thermal processes at Soultz-sous-Forêts for (**a**) matrix hydraulic conductivity, (**b**) heat flux from the bottom boundary, (**c**) matrix specific heat capacity, (**d**) hydraulic conductivity of faults (here *K<sup>f</sup>* ,0 is the fault zone hydraulic conductivity as given in Table 2), (**e**) porosity of fault zone, (**f**) leakage contribution to the total fluid flow, (**g**) matrix porosity, (**h**) matrix thermal conductivity, (**i**) fault thickness (here *F*<sup>0</sup> is the fault thickness as given in Table 2), and (**j**) thermal conductivity of the fault zone.


of 10 to 20 °C. After 100 years of cold fluid injection and hot fluid production, the observed temperature drop at the production wellhead is less than 20 °C. Therefore, our numerical model predicts that 100 years of geothermal energy extraction operation at Soultz-sous-

**4. Conclusions Table 3.** Range of parameters for sensitivity analysis.


**Table 3.** *Cont.*

#### **4. Conclusions**

As part of the MEET project, a coupled reservoir and wellbore model for hydraulic and thermal processes involved during the geothermal energy extraction operation at Soultz Sous Forêts was developed. Operational data from a period of 1163 days of operation was used to validate the numerical model. The validated hydro-thermal numerical model precisely simulates the geothermal energy extraction operation for 3 years. Furthermore, two operational scenarios for 100 years with four different injection wellhead temperatures—70, 60, 50 and 40 ◦C—were analyzed. It can be observed that even after 100 years of operation, the thermal breakthrough at the production well is only in the range of 10 to 20 ◦C. After 100 years of cold fluid injection and hot fluid production, the observed temperature drop at the production wellhead is less than 20 ◦C. Therefore, our numerical model predicts that 100 years of geothermal energy extraction operation at Soultz-sous-Forêts is feasible and will have a sufficiently high production temperature throughout the operation duration.

**Author Contributions:** Conceptualization, S.M. and K.B.; methodology, S.M. and M.S.; software, S.M. and M.S.; validation, S.M. and M.S. writing—original draft preparation, S.M. and M.S.; writing review and editing, K.B., A.T.; visualization, S.M. and M.S.; supervision, K.B. and I.S.; project administration, K.B.; funding acquisition, K.B. All authors have read and agreed to the published version of the manuscript.

**Funding:** The work is conducted as part of the MEET project that has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No 792037. Authors have received support from the Group of Geothermal Science and Technology, Institute of Applied Geosciences, Technische Universität Darmstadt.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Restrictions apply to the availability of these data. Data was obtained from [ÉS-Géothermie] and are available [https://geothermie.es.fr/en/contact/, accessed on 9 November 2021] with the permission of [ÉS-Géothermie].

**Acknowledgments:** Authors would like to thank ÉS-Géothermie for providing Soultz-sous-Forêts operational data.

**Conflicts of Interest:** The authors declare no conflict of interest.

### **References**


**Yassine Abdelfettah 1,\* and Christophe Barnes 1,2**


**Abstract:** We have performed several sensitivity studies to assess the ability of the Full Wave Inversion method to detect, delineate and characterize faults in a crystalline geothermal reservoir from OVSP data. The distant goal is to apply the method to the Soultz-sous-Forêts site (France). Our approach consists of performing synthetic Full Wave 2D Inversion experiments using offset vertical seismic and comparing the estimated fields provided by the inversion, i.e., the estimated underground images, to the initial reference model including the fault target. We first tuned the inversion algorithmic parameters in order to adapt the FWI software, originally dedicated to a sedimentary context, to a crystalline context. In a second step, we studied the sensitivity of the FWI fault imaging results as a function of the acquisition geometry parameters, namely, the number of shots, the intershot distance, the maximum offset and also the antenna length and well deviation. From this study, we suggest rules to design the acquisition geometry in order to improve the fault detection, delineation and characterization. In a third step, we studied the sensitivity of the FWI fault imaging results as a function of the fault or the fault zone characteristics, namely, the fault dip, thickness and the contrast of physical parameters between the fault materials and the surrounding fresh rocks. We have shown that a fault with high dip, between 60 and 90◦ as thin as 10 m (i.e. lower than a tenth of the seismic wavelength of 120 m for Vp and 70 m for Vs) can be imaged by FWI, even in the presence of additive gaussian noise. In summary, for a crystalline geological context, and dealing with acceptable S/N ratio data, the FWI show a high potential for accurately detecting, delineating and characterizing the fault zones.

**Keywords:** geothermal; OVSP; well seismic data; fault; fracture; EGS; geothermal derisking; FWI; numerical modelling; inversion; imaging

#### **1. Introduction**

For any deep georesources exploration project, finding the location of underground resources is an important step. Deep geothermal exploration projects do not go against this rule. The location of the underground thermal anomalies as well as the different physical parameters of the subsurface are key to the success of the project. For instance, the porosity, permeability, heat flux and geomechanical stress field of the reservoir are determining parameters. For the case of an Enhanced Geothermal System (EGS), undoubtedly, the fractures and the faults play a major role for the reservoir quality and increase the geothermal fluid production (e.g., [1]. The surface of rock-to-hot fluid interaction is increasing with the interconnected fractures network. This improves heat exchange by driving the deep hot fluid to shallower and exploitable depths. The presence of an adequate fault network in geothermal fields is crucial. This was observed during the drilling and different hydraulic tests performed in Soultz-sous-Forêts geothermal boreholes (e.g., [2] and included references) that the geothermal brine inflows to the wells at depths where faults are imaged and clearly identified.

**Citation:** Abdelfettah, Y.; Barnes, C. Sensitivity Analysis of FWI Applied to OVSP Synthetic Data for Fault Detection and Characterization in Crystalline Rocks. *Geosciences* **2021**, *11*, 442. https://doi.org/10.3390/ geosciences11110442

Academic Editors: Béatrice A. Ledésert, Ronan L. Hébert, Ghislain Trullenque, Albert Genter, Eléonore Dalmais, Jean Hérisson and Jesus Martinez-Frias

Received: 23 August 2021 Accepted: 24 October 2021 Published: 27 October 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

For geothermal reservoirs deeper than 1500 m, the main fault identification and characterization remains a difficult task, even using efficient geophysical exploration techniques. Using a dataset acquired from the surface, we can merely identify a major fault crossing our study area presenting an important vertical displacement. However, identification and characterization of faults related to the reservoir quality, at the reservoir scale, remains a challenge. These large faults could be identified, from surface, by using, for instance, surface seismic [3] or gravity and magnetotelluric surveys [4,5] However, hectometric faults as well as faults at the reservoir scale (i.e., metric) are more challenging to identify from the surface and their characterization, at depth, remains a difficult task that becomes impossible when their size is lower than the seismic resolution.

Once the first well is drilled, it is possible to identify and characterize the fractures and faults in the reservoir by analyzing the cuttings and the borehole data. We can characterize faults in the vicinity of the well, but not in the whole reservoir. These faults play a key role in the productivity and longevity of the project. One can also use the microseismicity generated during well stimulation or well cleaning to better understand the structure of the fault network located in the reservoir [6] but not to provide their physical parameters.

A Multi-Offset Vertical Seismic Profile (OVSP) or a 3D-VSP, which provide a better data redundancy, could be appropriate geophysical techniques to better identify and characterize these faults in a neighborhood of a few hundred of meters around the well (e.g., [7]. As the seismic waves cross the surface weathered zone (i.e., the near-surface zones presenting velocity variations) only once, and as the receivers located in the reservoir are close to the target, the seismic signal is generally more informative than the one from surface seismic, the frequency bandwidth is higher and the signal to noise ratio is often higher. Another advantage is that the area illuminated by the well seismic is better in the vicinity of the well due to a higher data redundancy. More precisely, the downgoing waves interact with the heterogeneities or faults around the well and therefore generate a complex scattered wavefield. The incident P-wave generates reflected P-waves and converted P-to-S waves (both reflected and transmitted), and the incident S-wave (often P-to-S downgoing conversion from shallower interfaces) generates reflected S-waves and converted S-to-P waves (both reflected and transmitted). This complex wavefield, recorded by the downhole receivers, is very informative for imaging and characterization purposes in the vicinity of the well.

Considering the standard processing techniques for VSP data (e.g., [8], as the receivers record both up and downgoing waves but also laterally incident waves and wave conversions, e.g., P-to-S and S-to-P, the generated and the recorded wavefield is more complex compared to the surface seismic. The crystalline body we consider here is also more complex than the OVSP in a more horizontally structured sedimentary body. In such a case, the classical and standard processing sequence, by separating up and downgoing waves, show some limitations due to several reasons, particularly when increasing the offset of the source. Due to the global velocity trend, increasing with depth, the long to very long offset (from offset equal to target depth up to several times the target depth), the direct P-wave, downgoing in the shallow depths, can propagate laterally when arriving at the well and sometimes even turn into an upgoing wave (diving waves, or refracted waves). For small or zero offset, wave separation still stands (except when lateral velocity variations are high above the target zone). For objects that are not nearly horizontal, such as faults, reflected waves may arrive laterally or with uncommon apparent velocity. The second reason is that when increasing the offset in sedimentary bodies, the scattered field for shear waves generally shows increasing energy, making it difficult to separate P and S waves. In addition, another issue may arise: the presence of P-to-S-to-P converted waves, for example, or other scattered waves of second order which can be energetic under certain conditions. In sedimentary context, is not uncommon to find 3rd order scattered phases, even 4th order in OVSP seismograms as soon as the offset is sufficient. Moreover, when imaging faults, diffracted waves due to point or linear scatters can be observed. The standard processing technique (wave separation, deconvolution and migration) does not take

into account such phases, because the processing has been designed for primaries, i.e., for the first order scattered field. Of course, the 2nd order scattered field is less energetic than the first order, but if the S/N ratio is sufficient, the 2nd order scattered wavefield provides information and one can take advantage of it rather than trying to remove it or neglect it. The third reason is that the deconvolution of the upgoing waves by the downgoing waves is not an accurate process when increasing the offset as the downgoing raypath becomes different from the upgoing raypath. This issue can be important for target not very close to the well and in presence of lateral variations of velocity. As a comparison, the diffractions are considered as a noise for a classical processing approach whereas it carries useful information for FWI (e.g., [9], helping to accurately build an edge or discontinuous surface. In other words, the classical VSP data processing approach reduces the complexity of the recorded complex wavefield by separating the wave field to up and downgoing waves and often removes part of the information contained in the data. This approach provides a good result, but it is subject to limitations for specific and complex cases.

The recent sensitivity study performed on the granite where the data were processed by a classical approach [10] have showed the capability of this technique and pointed out some issues. During their synthetic sensitivity study [10] a systematic analysis optimizing the number of sources was proposed, and the authors showed that the VSP data have a high potential to detect faults in crystalline bodies. They also noted that, for some fault characteristics, even with an increased number of sources, some artefacts remain strong in the final migrated images, given interpretation ambiguities. They also pointed out that the faults with high dips (e.g., 70◦ ) were more complicated to recover than the shallow dipping faults (e.g., 30◦ ). In deep geothermal projects, especially in the granite context, the probability that the well crosses faults with dips around 30◦ is exceptionally low compared to highly dipping faults, and this defines an important limit of the classical processing approach. Other interesting works have also been conducted on the OVSP data of Soultzsous-Forêts recorded in GPK1 and EPS1 wells using the standard approach (e.g., [11]. They used an adapted classical approach for crystalline rocks. The authors of [11] introduced a 3D parametric separation which treated the seismic wavelength in 3D, improving the 3D structural model, especially the faults, and the reservoir knowledge. This study was conducted for VSP 0-offset (<200 m of source-offset) and small sources-offset distance (<600 m), and for shallower targets, located at 2000 m for the EPS1 well and 3000 m for GPK1. A specific data processing queue should be adapted for the crystalline studies (e.g., see also [12]).

Full Wave Inversion (FWI) can deal with primaries, secondary or even higher order scattered phases, including diffractions and multiples issues (water layer or internal multiples). Its informative wavefield can be extracted to constrain the imaging purpose [13,14] We can therefore detect and even characterize faults located hundreds of meters from the well and not only the faults crossing the well. As the OVSP data are acquired in different azimuths, and by a different offset according to the receivers, the target is observed in different and complementary incident angles. The FWI technique applied to well seismic data (OVSP) should provide a better underground image and therefore better identify, delineate and characterize the faults in the well neighborhood. This approach has also been assessed using OVSP data in difficult contexts as subsalt imaging (e.g., [15]. Nevertheless, this technique remains underused, even in the sedimentary context for well seismic data, because the FWI requires building physical models with an adequate rheology (elastic including anisotropy and attenuation) before applying the inversion. Effectively, for well seismic, data redundancy is weak, and the starting model should be sufficiently close to the true one to start the FWI process. In other words, the starting model should reproduce qualitatively the recorded wavefield and the travel times of the major phases should be correct (to avoid the cycle skipping issue). Additionally, it requires a good S/N ratio because the technique is sensitive to noise. All these additional necessary preprocessing tasks are time consuming, which remains the major constraint, especially in industrial applications. As a consequence, data-driven techniques (data processing) are often preferred. Nevertheless, in the industry, FWI is used classically when working with the lower frequencies in order to improve the velocity model used for 3D migration, particularly in difficult geological contexts (e.g., [16]).

Previous works have demonstrated the added value of the FWI method for OVSP data [13,17–21] These studies were performed for oil and gas targets with high challenges, for instance, for subsalt imaging, velocity estimation for pore pressure, sub-basalt imaging, CO<sup>2</sup> sequestration and others, and authors have obtained better results compared to the surface seismic and compared to VSP data processed with a classical approach (e.g., [13]. In Barnes and Charara [13] FWI was applied to North Sea VSP data and recovered accurately the gas reservoir, which is confirmed by the well, whereas a standard VSP processing gave a wrong imaging result, despite the sedimentary context.

More recently, for geothermal purposes and in the Soultz-sous-Forêts geological context, where a granitic basement is located at 1.4 km depth, OVSP synthetic data have been successfully inverted and faults were well identified and characterized around GPK's wells using the FWI and Full Wave Modeling (FWM) [22,23] The obtained results confirm the high imaging potential for this inversion technique and open a new perspective for its geothermal use.

In this paper, we perform a synthetic study for fault delineation and characterization in the crystalline basement using FWM and FWI. No real data will be shown. The study was done in 2D assumption because we need to perform several experiments of different physical models, including different fault geometries and features. A 3D sensitivity analysis needs much more CPU time. The main objective of this paper is to test the ability of the FWI to detect and delineate faults and further characterize them in terms of velocities and density. We aimed first to check the applicability of the FWI in the hard rock. To provide an accurate sensitivity analysis, we have used synthetic experiments, because we can easily control the affecting parameters, e.g., faults characteristics and acquisition geometry, frequency and the receiver's location, etc. We need to know our data exactly to analyze the FWI results accurately and quantitatively. We added noise to the synthetic data to assess the robustness of the method in noisy environments. Nevertheless, we decided to perform the entire experiment without adding noise, except for experiments related to the noisy test where noises are added to the data, to ensure separation of the effects and assessing the FWI capabilities. Important issues such as the effects of a wrong starting model, of anisotropy or attenuation in the data, are not addressed in this paper.

With these purposes in mind, a complete sensitivity study is shown and discussed, including both noise-free data and noisy data. Different fault features as well as acquisition geometry were tested, and the results summarized. We have first introduced the method and tuned the inversion with the adequate parameters (Section 3), examining for instance the effect of the polarization, of the correlation lengths, etc. In a second part (Section 4), we have studied the effect of the acquisition geometry on the inversion results, including the intershot distance, number of shots used in the same run, the maximum offset, etc. Finally, in a third part (Section 5), we have studied the effect of the fault characteristics on the inversion results: fault thickness, dip and distance to the receivers, as well as the P- and S-waves velocities and density contrasts, including the multi-faults experiment and the robustness of the method with respect to the seismic noise.

## **2. Geological Setting**

We performed this study inspired by the geological context of the geothermal site of Soultz-sous-Forêts. This site belongs to the Upper Rhine Graben (URG) and is characterized by an important thermal anomal [24] It is intensively documented by several papers and works, which in the early days studied the site for its oil and gas potential [25] but more recently for its geothermal potential for both electricity and heat co-generation [26,27].

A thick sediment pile overlies the crystalline basement which is located at 1400 m depth beneath GPK1 headwell. Sediment ages filling the graben range from Quaternary to Permia [28] the bedding structures dips shallowly to the south and east. The graben strikes N–S, to NNE–SSW in the northern part of the studied area. Several faults and fractures analyses have been performed on the continuous sample borehole core and or from borehole data in the different geothermal deep well in Soultz, for instance EPS1 and GPK1 to 4. They showed that the fractures are mainly dominated by NNW–SSE strike orientation [29,30] The current stress regime is strike-slip with a NW–SE compression direction in accordance with the general trend in Western Europe, and with the observed faults and fracture [31].

#### **3. Methodology**

#### *3.1. Seismic Imaging Techniques for Well Data*

Well seismic data are used for different purposes. For instance, VSP data can be used to estimate a depth-time relationship and calibrate the velocity model for surface seismic data in order that seismic horizons are located at the correct depth. Walkaway or walkaround seismic data are used for anisotropy estimation and walkaway for AVO analysis (Amplitude Versus Offset). Imaging using well seismic data is less common because the conventional imaging tool, the migration, has to overcome the problem of lack of data redundancy compared to surface seismic. It is an important issue even for dense 3D-VSP. Moreover, for the fault imaging goal, the conventional technique of downgoing and upgoing waves suffer from some limitations when increasing the offset. In principle, the FWI method does not suffer from the above limitations except the weak redundancy which can be overcome by using additional constraints in the inversion process. These constraints can derive from additional observations such as polarization (e.g., [32]) in the data space or for example, the spatial correlation (e.g., [13,33,34]), or the inter parameter correlation in the model space.

#### *3.2. The Inverse Problem Applied to Seismic Data*

The inverse problem can be expressed as the minimization of a misfit function as stated by Tarantola [35] for least squares, this function is a scalar function defined over the model space as:

$$\mathbf{S(m)} = \Delta \mathbf{d}^{\mathrm{T}} \mathbf{C}\_{\mathrm{D}}^{-1} \Delta \mathbf{d} \tag{1}$$

where **m** is a model, ∆**d** = **g**(**m**) − **d***obs* are the residuals with **d***obs* the observed data, and **g**(**m**) the synthetic data obtained by resolution of the wave equation, and where **C<sup>D</sup>** denotes the covariance matrix over the data space. This matrix can be not diagonal as when using the polarization constraint [34] i.e., the constraint given by the azimuth and incidence of the seismic waves. The misfit function measures the discrepancy between observed and calculated seismic data, i.e., between amplitudes of the signals for each trace. Because of the non-linearity and the complexity of the forward modelling, the misfit is reduced iteratively using a local method based on derivatives [35] The descent algorithm is based on the conjugate gradient method proposed by Polack and Ribière [36] The step optimization is defined along the conjugate gradient direction as in Crase [37] FWI software following these procedures has been developed continuously by GIM-labs for more than 15 years.

#### *3.3. Modelling the Seismic Wave Propagation*

The direct problem associated to the present fullwave inverse problem is the propagation of (visco) elastic waves in an (an) isotropic medium. As the imaging target, i.e., the fault network, is one or several 3D objects in a 3D nearly homogeneous medium, we aim at achieving a 3D inversion. However, the sensitivity analysis requires numerous inversions to check all the parameters separately and a 3D inversion cost tens of hours of CPU time (using our resources) even using a well-designed parallelized seismic modelling code. As a consequence, we will consider 2D wave propagation for the synthetic experiments used in the sensitivity analysis (see Section 5).

This assumption allows us to check a major part of the parameters of the sensitivity analysis. However, the main drawback of running 2D seismic modelling rather than 3D modelling is that the fault is always perpendicular to the propagation plane. In other word, the azimuth of the fault (the dip direction) corresponds to the propagation plane. In a 3D world, we need more shots with different azimuths to constrain the 3D FWI. A 3D sensitivity analysis of the dependency to the azimuth of the fault dip has not been performed due to the high cost in CPU time.

The finite differences method is based on the displacement formulation of the wave equation for the viscoelastic rheology (isotropic, VTI and HTI anisotropy). The spatial discretization is using a staggered grid, a 2nd order Taylor explicit scheme in time and 4th order differential operators in space. The FWM corresponding software has been developed continuously by GIM-labs for more than 20 years. It is parallelized (using OpenMP for domain decomposition and MPI for shots) and can be run on large clusters.

#### *3.4. The Rheology Issue*

The actual rheology is elastic for the synthetic FWI experiments in Section 5.1 and viscoelastic for the case of real seismic data FWI. When the data redundancy is weak as for borehole seismic, we need to extract the most information from the data. In order to achieve this goal, we must reduce all the additional noises: numerical, experimental and physical [14] The numerical noise is a trade-off between the calculation cost in time and the accuracy of results, reducing this noise is then easy but has a cost; moreover, this noise is not strongly structured [14] The experimental noise concerns the accuracy of the source and receiver location, the modelling of the source and receiver radiation pattern or the source time function. These parameters can be either better controlled or inverted during the FWI (for instance, the source time function). The physical noise is the most challenging one as it is strongly structured and may produce strong artefacts in results when the physics is not adequate [14] As a rule of thumb, all these noises should be less than the data noise in order to extract information from the data and reduce artefacts [14] Non additive structured noises have the largest impact on the results [14] and reducing the noise due to an inadequate rheology is thus the main issue. For example, using a simplified rheology as acoustic, even for marine data, implies a large artefact in the solution due to the wrong modelled AVO, as shown by Barnes and Charara [19].

Borehole seismic data generally exhibits a highly informative wavefield containing energetic 2nd or even 3rd order scattered waves [13] For example, downgoing P-to-S converted waves can convert back to P-wave after reflection on an interface. P-to-S conversions increase in amplitude according to the offset. Consequently, in most cases for borehole seismic with offset (OVSP, walkaway, 3D-VSP) and in a sedimentary context, once removing the downgoing direct P-wave, 80% of the energy is provided by the S-waves [13] For OVSP data in a crystalline context, S-waves are also present (as for instance the downgoing P-to-S wave converted at the top basement), sometimes more attenuated. The elastic rheology is then required.

Moreover, Equation (1) is based on amplitude, and thus seismic attenuation, often present in the data, should be considered as well, at least in the FW modeling (without inverting for attenuation parameters). Anelastic phenomena can be modeled by viscoelasticity at the scale of the seismic wavelength. One often defines a global Q-factor using a constant Q or a nearly constant Q (NCQ) model [38,39] or even a more general standard linear solid model (SLS). Charara and Barnes [40] have proposed modeling the attenuation by using two Q-factors, the Q<sup>κ</sup> factor related to the bulk incompressibility modulus κ and the Q<sup>µ</sup> factor related to the shear modulus µ. The first one is affected by fluids, in particular, liquid-gas mixing while the latter one is related to microstructures of the solid. In FWI, the viscoelastic parameter fields provide a poor information on the spatial resolution as the seismic attenuation is an integrative phenomenon but, when taking into account the seismic attenuation, we obtain a better resolution on other parameters (e.g., [41]).

The seismic anisotropy is another issue which is important in a sedimentary context. For crystalline rocks with a sedimentary cover, the anisotropy could be taken into account.

We did not address seismic attenuation or seismic anisotropy in the sensitivity study for the sake of simplicity. Of course, for real data, these seismic rheologies have to be taken into account (e.g., [41,42]).

#### *3.5. Aim of the Sensitivity Studies*

The first objective of the conducted sensitivity study is to evaluate the ability of the FWI to detect, delineate and characterize the fault zones in the granite. Some precisions about these goals:


Two major sensitivity analyses have been carried out. The first one concerns the acquisition geometry and the second one concerns the fault characteristics.

We carefully investigated several acquisition parameters affecting the results of fault detection and characterization. The studied parameters are:


We have investigated first the single shot problem for the understanding of the resolution power of the FWI. From that, we investigate the effect of this parameter on the final underground image reconstruction. In the first set of synthetic FWI experiments, the number of sources is varying from 1 to 17, while increasing the maximum offset and decreasing the intershot distance (as we are in 2D, this can apparently appear as a walkaway VSP experiment). For a second set of experiments the intershot distance is varying while the maximum offset is constant, quantifying the intershot distance effect alone.

After having defined the optimal acquisition parameters, we can perform the sensitivity analysis of the fault characteristics. We have considered constant velocity values (P and S) and density contrasts, according to the background, and we mainly investigated the effect of:


#### *3.6. Tuning of the Inversion Algorithm and Definition of the Inversion Parameters*

Our FWI software parameters are those usually used in the sedimentary geological domain, so we spent large time to define the right inversion parameters. Before using them in the granite context, we need to first choose adequate inversion parameters to maximize the likelihood of faults' detection, delineation and characterization. This step was done using several inversion experiments where their results were compared. The best inversion parameters are those which provide better results in term of fault imaging, and then minimize the difference with the true models.

Several inversion algorithmic parameters have been tested and validated. We have tested the data polarization, the physical parameter crosscorrelation, the physical parameter spatial correlation, the frequency content, and the antennae length (illuminated zone according to the receivers) effects. The three first are constraints in the FWI through the covariance matrices in the data space for the polarization and in the model space for both the parameter crosscorrelation and the spatial correlation (see [32,34]). Basically, we have tested the following parameter values:

Spatial correlation range: 20, 50 and 100 m, using the Laplace correlation function and stationary random field assumption. This means that, for each iteration, the perturbation of the parameter field values should be close in these ranges.


We also performed other experiments combining and mixing these parameters. The best results are obtained when used (1) the correlation length of 20 m, corresponding approximately to the fault thickness (or a bit smaller, depending on the considered fault thickness), (2) without using the polarization and (3) using the crosscorrelation between velocities and density (with positive coefficients of 0.9). We decided to use (1) and (2) and do not use (3) in order to evaluate independently the resolving power of FWI for the different physical parameter. Concerning the polarization, it is demonstrated from previous works (e.g., [32] that it provides better results in a sedimentary context, but this is not the case in the granite.

#### *3.7. The Workflow Used for the Sensitivity Analysis*

We run several synthetic FWI experiments with controlled parameters and part of the parameters are varying for the corresponding parametric study. All the used parameters including physical models, source location, receiver locations, the dominant frequency, the noise level, etc., are well known and accurately controlled. The general workflow is: (i) we chose the acquisition geometry parameters, for instance source and receiver locations, etc, (ii) define the target, i.e., the fault characteristics, (iii) generate synthetic data, and then (iv) invert these synthetic data and analyse the results.

The first step is choosing the geometry data acquisition where we define the parameters controlling the data acquisition experiment, for instance the number of sources, shot locations, deviated or vertical well, the receiver locations and their number, and so on.

In the second step, we define the characteristics of the target, i.e., the fault. We define its geometry, shape and area, its depth, thickness and dip. We should also define, for an elastic modelling, its physical parameters, for instance its P- and S- wave velocities and density values. These values depend on the contrast considered between the fault and the background, for instance 5, 10 or 15% (see Section 3.8 for more details on how these values are defined). From the fault definition and the background model, we build the 2D model named "true model" or considered model used in the next step (the FWM).

The last step before inversion, is to model the synthetic data according to the geometry acquisition and the source function (type, frequency), and the true model (including the fault) using the FWM (Figure 1). These synthetic data are calculated according to the maximum recording time. This time should be chosen large enough to record the data in the entire receivers including the time where the waves interact with fault. Once the experiments.

synthetic data are calculated, we can use them as the observed data in the inversion process, directly for free noise experiments, or after adding noise for noisy data experiments. delineation and characterization. The workflow presented in Figure 1 summarizes the main steps during the FWM/FWI process.

are defined). From the fault definition and the background model, we build the 2D model

The last step before inversion, is to model the synthetic data according to the geometry acquisition and the source function (type, frequency), and the true model (including the fault) using the FWM (Figure 1). These synthetic data are calculated according to the maximum recording time. This time should be chosen large enough to record the data in the entire receivers including the time where the waves interact with fault. Once the synthetic data are calculated, we can use them as the observed data in the inversion process, directly for free noise experiments, or after adding noise for noisy data

Finally, we reach the inversion step and so the fault imaging goal. The objective in this step is to use the observed data obtained from the true model and the FWM in the previous step and invert these data to quantify the capability of the FWI for fault detection,

named "true model" or considered model used in the next step (the FWM).

*Geosciences* **2021**, *11*, x FOR PEER REVIEW 9 of 36

**Figure 1.** Workflow of the method used in the feasibility study. (1) From the true model (including the fault), we generate the synthetic data by FWM. (2) Add or not the noise according to the objective of the experiment. This data is then used in the inversion as observed data. (3) Start the inversion process from the starting model (which is the true model without the fault) and the observed data, and (4) once the nonlinear iterative FWI process has converged, we obtain (i) the estimated data that will be directly compared to the observed data, and (ii) the estimated models, which are directly compared to the true models. Here, the term "observed data" should not be confused with the term "real data" because we are dealing only with synthetic data. **Figure 1.** Workflow of the method used in the feasibility study. (1) From the true model (including the fault), we generate the synthetic data by FWM. (2) Add or not the noise according to the objective of the experiment. This data is then used in the inversion as observed data. (3) Start the inversion process from the starting model (which is the true model without the fault) and the observed data, and (4) once the nonlinear iterative FWI process has converged, we obtain (i) the estimated data that will be directly compared to the observed data, and (ii) the estimated models, which are directly compared to the true models. Here, the term "observed data" should not be confused with the term "real data" because we are dealing only with synthetic data.

*3.8. Geological and Physical Models Building and Faults Modelling* In the frame of EGS Alsace project and ANR Cantare programs, a regional 3D structural model was built for Northern Alsace. It is built mainly by reprocessing the old vintage 2D seismic lines [46] which are focused on oil and gas exploration of the Tertiary Finally, we reach the inversion step and so the fault imaging goal. The objective in this step is to use the observed data obtained from the true model and the FWM in the previous step and invert these data to quantify the capability of the FWI for fault detection, delineation and characterization.

layers. This geological model could show high uncertainties because at this time, and as the target is shallower than the geothermal reservoir, the used seismic parameters were not adequate to produce images of the underlying crystalline rocks. These uncertainties The workflow presented in Figure 1 summarizes the main steps during the FWM/FWI process.

#### could mainly be found at the sediments – basement interface which can reach hundreds *3.8. Geological and Physical Models Building and Faults Modelling*

of meters, especially in the deeper part of the graben, for instance the eastern part. A total of five geological interfaces were modelled and included in this model: (1) "schistes à Poissons", (2) Tertiary unconformity, (3) top of Trias, (4) top of Muschelkalk and (5) top of Buntsandstein. In order to build the P- and S-wave velocities as well as the density models from the structural model, we need initial values. For this purpose, we used existing physical, generally 1D, models. These models were obtained from previous studies and from borehole data. These models are good enough for our model building. Once the physical models were chosen, we used them jointly with the stratigraphical 3D model to generate a 3D P-wave, S-wave velocity models and a density model. We defined these parameters In the frame of EGS Alsace project and ANR Cantare programs, a regional 3D structural model was built for Northern Alsace. It is built mainly by reprocessing the old vintage 2D seismic lines [46] which are focused on oil and gas exploration of the Tertiary layers. This geological model could show high uncertainties because at this time, and as the target is shallower than the geothermal reservoir, the used seismic parameters were not adequate to produce images of the underlying crystalline rocks. These uncertainties could mainly be found at the sediments – basement interface which can reach hundreds of meters, especially in the deeper part of the graben, for instance the eastern part. A total of five geological interfaces were modelled and included in this model: (1) "schistes à Poissons", (2) Tertiary unconformity, (3) top of Trias, (4) top of Muschelkalk and (5) top of Buntsandstein.

in the top and at the bottom of our stratigraphical model, and applied a linear gradient in-In order to build the P- and S-wave velocities as well as the density models from the structural model, we need initial values. For this purpose, we used existing physical, generally 1D, models. These models were obtained from previous studies and from borehole data. These models are good enough for our model building. Once the physical models were chosen, we used them jointly with the stratigraphical 3D model to generate a 3D P-wave, S-wave velocity models and a density model. We defined these parameters in the top and at the bottom of our stratigraphical model, and applied a linear gradient in-between. We show on Figure 2 cross-sections of P-wave and S-wave models and density model extracted from the complete 3D models.

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**Figure 2.** Physical models used to perform a sensitivity study of experiments. (**a**,**b**) the P-wave and S-wave velocity models, and (**c**) the density model. (**d**) shows the target area around the receivers where the results will be shown. The inverted triangles are the receivers located in the well and the stars are the source locations on the earth's surface. Note that the inter-shot is variable, 500 m around the well head to 1000 m far away the well head. **Figure 2.** Physical models used to perform a sensitivity study of experiments. (**a**,**b**) the P-wave and S-wave velocity models, and (**c**) the density model. (**d**) shows the target area around the receivers where the results will be shown. The inverted triangles are the receivers located in the well and the stars are the source locations on the earth's surface. Note that the inter-shot is variable, 500 m around the well head to 1000 m far away the well head.

The sources are placed on the topographic surface. The waves propagate down and no reflected and or transmitted waves occur above the surface. As a complete wave field is modelled and the full seismic propagation equation used, several seismic waves have been considered, for instance up and downgoing waves, converted waves and even multiples. values decreased by 10 to 25% for P-wave velocity, between 10 to 20% for S-wave velocity and between 5 to 10% for densities (Figure 3). Consequently, for our synthetic experiments, we considered an average fault characteristics value of the real values. We consider a fault zone with the following

To define the characteristics of the faulted zone, we carefully analysed the available borehole data for the GPK1, 2, 3 and 4 wells. The objective is to define their average thickness and their physical values, i.e., P- and S-wave velocities and density. We showed in Figure 3 the middle part of the GPK1 where we noted the interpreted faulted zones by

During our fault analysis performed on the GPK1 and GPK2 well log data (e.g., Figure 3) we noted that the apparent fault thickness varies between 15 and 80 m. If we consider a dip fault of 75°, which is a realistic value for GPK1 and the closer boreholes [47] we recompute the real fault thickness which varies between 5 and 25 m. More detailed fault and fractures data analysis can be found in Dezayes et al. [29] and Sausse et al. [30]. From the amplitudes, we also computed the amplitude decreases of the P- and Swave velocities and density values according to the background, i.e., according to the mean values. From the well data of GPK1 and GPK2 (e.g., sonic and neutron density), the

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the red arrows.

To define the characteristics of the faulted zone, we carefully analysed the available borehole data for the GPK1, 2, 3 and 4 wells. The objective is to define their average thickness and their physical values, i.e., P- and S-wave velocities and density. We showed in Figure 3 the middle part of the GPK1 where we noted the interpreted faulted zones by the red arrows. characteristics: (i) the faulted zone thickness is 30 m and (ii) the decrease of the physical values is 20% for the P- and S-wave velocities and 7% for density. We show on Figure 2 the reference physical models from which the fault contrast is computed. These models are the background physical models.

**Figure 3.** Middle part of the borehole logs for GPK1 (granite) where the blue profile is the P-wave velocity, the red profile is the S-wave velocity, and the brown profile is the density values. The red arrows show the location of some interpreted fault zones. A good correlation is observed between Pand S-wave velocities and density (especially in the granites). These borehole data are measured on a well crossing the dipping faults. The apparent vertical thickness of these fault zones varies between 15 and 80 m. If we consider a fault dip of 75◦ , we found that their real thickness varies between 5 and 25 m.

During our fault analysis performed on the GPK1 and GPK2 well log data (e.g., Figure 3) we noted that the apparent fault thickness varies between 15 and 80 m. If we consider a dip fault of 75◦ , which is a realistic value for GPK1 and the closer boreholes [47] we recompute the real fault thickness which varies between 5 and 25 m. More detailed fault and fractures data analysis can be found in Dezayes et al. [29] and Sausse et al. [30].

From the amplitudes, we also computed the amplitude decreases of the P- and S-wave velocities and density values according to the background, i.e., according to the mean values. From the well data of GPK1 and GPK2 (e.g., sonic and neutron density), the values decreased by 10% to 25% for P-wave velocity, between 10% to 20% for S-wave velocity and between 5% to 10% for densities (Figure 3).

Consequently, for our synthetic experiments, we considered an average fault characteristics value of the real values. We consider a fault zone with the following characteristics: (i) the faulted zone thickness is 30 m and (ii) the decrease of the physical values is 20% for the P- and S-wave velocities and 7% for density. We show on Figure 2 the reference physical models from which the fault contrast is computed. These models are the background physical models.

#### **4. Sensitivity Analysis of the Parameters Describing the Acquisition Geometry**

We consider an experimental setup which fits as much as possible the real OVSP setup. The sources are located on the Earth's surface, and the locations of the well-head as well as the well trajectory (where geophones are located) are realistic. In addition, we have used the seismic velocities and the density models extracted from the 3D models.

#### *4.1. Single Shot Problem*

We have started our analysis from the FWI results using only one source, located at zero-offset. This numerical experiment helps to understand the resolution power of the FWI. The initial P-wave velocity and S-wave velocity models used as well as the location of the fault are shown in Figure 2 (the density model is not shown). We have used the following acquisition geometry parameters:


The fault characteristics are:


We have also used the algorithmic parameters tuned in Section 3.6. These parameters have been set as follows: (i) FWI performed without polarization, (ii) spatial correlation range is 20 m, (iii) the main frequency is 50 Hz and (iv) without using the inter-correlation between the physical parameters in order to better understand the sensitivity of each parameter separately.

Besides the interest of the single shot problem for the understanding of the FWI method resolution power, we think that it is also remarkably interesting to study this case on a practical point of view. Indeed, due to restricted financial support compared to the oil and gas industry, geothermal project supervisors tend to choose this single-source data acquisition layout. Thus, it is particularly important to quantify the recovered physical fault images especially in the granite geological context.

We compare on Figure 4 seismograms obtained by FW modelling for the model with and without the fault. Recall that this experiment is done without adding noise. If we consider the standard processing, the reflected phase coming from the fault has a slope corresponding to the downgoing field, which leads us to a wrong interpretation. The apparent velocity between the downgoing waves and the reflections arising from the fault are very close, creating an ambiguity in their origin. The FWI method overcomes this problem by dealing with the full wavefield without wave separation. and cannot resolve it when reflection redundancy is weak. From the one-source shot experiment, we conclude that in the granites and using the described acquisition geometry and the fault characteristics, we cannot image the modelled fault accurately enough for a reliable interpretation. We understand from this experiment that in the granite geological context, one zero– offset shot is not sufficient to detect, delineate and characterize faults having the described features.

expected, the result is bad, showing that this parameter is weakly sensitive to the fault

**Figure 4.** Seismograms showing the seismic effect of the fault. (**a**) synthetic VSP data of the model without the fault. (**b**) synthetic VSP data including the fault. We can mainly identify the scattered fields coming from the fault and crossing the first arrivals at ~−2400 m depth. (**c**) difference between (a) and (b). The acquisition geometry is identical to that showed in Figure 2, where we show only the data for source located at 0 m offset. **Figure 4.** Seismograms showing the seismic effect of the fault. (**a**) synthetic VSP data of the model without the fault. (**b**) synthetic VSP data including the fault. We can mainly identify the scattered fields coming from the fault and crossing the first arrivals at ~−2400 m depth. (**c**) difference between (**a**) and (**b**). The acquisition geometry is identical to that showed in Figure 2, where we show only the data for source located at 0 m offset.

We show on Figure 5 the inversion result for a zero-offset single-source VSP experiment after 60 iterations. The result is poor. FWI has recovered a small part of the P-wave velocity field but with artefacts mainly in the upper part of the antenna leading to interpretation difficulties. For the S-wave velocity field, FWI has recovered a small section in the lower part of the antenna, but several artefacts can also be observed. For density, as expected, the result is bad, showing that this parameter is weakly sensitive to the fault and cannot resolve it when reflection redundancy is weak. From the one-source shot experiment, we conclude that in the granites and using the described acquisition geometry and the fault characteristics, we cannot image the modelled fault accurately enough for a reliable interpretation. **Figure 4.** Seismograms showing the seismic effect of the fault. (**a**) synthetic VSP data of the model without the fault. (**b**) synthetic VSP data including the fault. We can mainly identify the scattered fields coming from the fault and crossing the first arrivals at ~−2400 m depth. (**c**) difference between (a) and (b). The acquisition geometry is identical to that showed in Figure 2, where we show only the data for source located at 0 m offset.

effect of the inter-shots, experiments 6 to 9 to quantify only the effect of the maximum offset and experiments 7 to 10 to understand and quantify the effect of the maximum offset. **Table 1.** Geometry data acquisition parameters used in the sensitivity study for fault detection, **Figure 5.** The physical models retrieved from FWI for one shot at zero offset. (**a**) P-wave velocity model shown for the interest area around the receivers (see the white box in Figure 2c). (**b**) and (**c**) recovered S-wave velocity and density models, respectively. The trace of the simulated fault is shown with black polygons. **Figure 5.** The physical models retrieved from FWI for one shot at zero offset. (**a**) P-wave velocity model shown for the interest area around the receivers (see the white box in Figure 2c). (**b**,**c**) recovered S-wave velocity and density models, respectively. The trace of the simulated fault is shown with black polygons.

delineation and characterization. **Expe. Shots Shot Offsets [km] Max Offset [km]** *4.2. Multi-Shots Problem* Several synthetic experiments have been performed for different data acquisition geometries. (Table 1) The goal is to quantify the effects of (i) the maximum offset, (ii) the We understand from this experiment that in the granite geological context, one zero– offset shot is not sufficient to detect, delineate and characterize faults having the described features.

number of sources and iii) the intershot distance effect. Experiment 1 is that discussed in the previous section for a one-source problem. The idea is to compare the experiment

effect of the inter-shots, experiments 6 to 9 to quantify only the effect of the maximum offset and experiments 7 to 10 to understand and quantify the effect of the maximum

**Table 1.** Geometry data acquisition parameters used in the sensitivity study for fault detection,

**[km]**

**Max Offset [km]**

**Expe. Shots Shot Offsets**

offset.

delineation and characterization.

#### *4.2. Multi-Shots Problem*

Several synthetic experiments have been performed for different data acquisition geometries (Table 1). The goal is to quantify the effects of (i) the maximum offset, (ii) the number of sources and iii) the intershot distance effect. Experiment 1 is that discussed in the previous section for a one-source problem. The idea is to compare the experiment results, for instance, to compare the results of experiments 5, 6 and 7 to quantify only the effect of the inter-shots, experiments 6 to 9 to quantify only the effect of the maximum offset and experiments 7 to 10 to understand and quantify the effect of the maximum offset.


**Table 1.** Geometry data acquisition parameters used in the sensitivity study for fault detection, delineation and characterization.

The objective is to change the number of shots used in the same inversion run as well as the intershot and the maximum offset to quantify the FWI ability for faults' detection and characterization. For instance, comparing the results of experiments 5, 6 and 7 to quantify only the effect of the inter-shot spacing, which is 1000 m for experiment 5, and 500 and 250 m for 6 and 7, respectively. The maximum offset of 2000 m remains unchanged for these three experiments. We can also compare the results of experiment 6 and 9 to quantify the effect of the maximum offset alone, which is 2000 m for the experiment 6 and 4000 m for experiment 9, where the inter-shot spacing of 500 m remains unchanged around the well.

10 15 −5, −4, −3, −2, −1.5, −1, −0.5, 0, 0.5, 1, 1.5, 2, 3, 4, 5 ±5.0

Experiment 2 used only three shots distant by 500 m, which is the smallest maximum offset used after the single-shot zero-offset experiment. From experiments 2 to 7, we changed and increased the number of shots, the intershot distance as well as the maximum offset to reach a maximum offset of 2000 m. Experiments 7 to 10 will help us to understand and quantify the effect of the maximum offset. In all these experiments, we used the starting physical models shown in Figure 2 and the fault features are those used in the single-shot problem (Section 4.1).

We show in Figure 6 the results summary of experiments 2, 4, 6, 8 and 10, showing the recovered P- and S-wave velocity fields as well as the recovered density model. In Figure 6a, we show the retrieved models for experiment 2 (Table 1) where only three shots are used with a maximum offset of 500 m. The FWI has partly recovered the upper part of the fault in the P-wave field and density but less in the S-wave field. We note that in the P-wave field, the shape of the fault is nearly completely recovered. The physical values remain lower than those of the real model, however. The lower part of the fault is not well resolved for P velocity because beside the direct P, the only phase is the downgoing P-to-S converted wave. We note also that several significant artefacts are present that would lead to wrong geological interpretations.

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**Figure 6.** In the top panel, a simplified sketch showing the acquisition geometry used for each experiment is indicated by the number in-brackets. The modeled physical models remain unchanged throughout the different experiments whereas **Figure 6.** In the top panel, a simplified sketch showing the acquisition geometry used for each experiment is indicated by the number in-brackets. The modeled physical models remain unchanged throughout the different experiments whereas the number of sources changes. In the bottom panel, the physical models recovered from the sensitivity study of the acquisition geometry. At the top, we show P-wave field, in the middle S-wave field and at the bottom the density model. According to the Table 1, we show the results obtained from experiments 2 (**a**), 4 (**b**), 6 (**c**), 8 (**d**) and 10 (**e**). The inverted triangles are the receivers, and the black polygons follow the fault trace. The results are shown only in the target area.

When we increase the number of shots up to seven and the maximum offset to 1500 m (Table 1 and Figure 6b), the fault is better resolved. The upper part of the fault is better delineated for the three physical parameters. The lower part of the fault remains however not well resolved (better for the S-wave field due to the downgoing P-to-S converted phase). The artefacts remain relatively significant for the three parameters (Figure 6b).

In Figure 6c, we show the retrieved physical models for experiment 6 (Table 1) where nine shots and a maximum offset of 2000 m were used. The retrieved models, compared to experiments 4 and 2, are better resolved, especially for the lower part of the fault. This lower part is less revolved compared to the upper part, and the inverted physical values for the three parameters show underestimated contrasts. We also note the significant improvement of these results, for instance the artefacts present in experiments 1, 2 and 4 are attenuated, except for the density model as expected, because the density is always less resolved then P- and S-wave fields for borehole FWI context.

When increasing the maximum offset to 3000 m (experiment 8) and the number of shots to 11 (Figure 6d), the estimated physical models are improved. These improvements are higher for the P velocity field and the density field than for the S velocity field. Nevertheless, the retrieved density model still exhibits important artefacts.

The last results (Figure 6e) were obtained from experiment 10 (Table 1). The number of shots is 15 and the maximum offset is 5000 m. The fault is accurately retrieved, and the obtained values are compared to those of the real model, except for the lower fault extremity where the values are underestimated. This is mainly true for the P- and S-wave velocity fields, but not for the density. The density model is better recovered except for the area crossing the well, where some artefacts remain visible.

To conclude, the five experiments studied (e.g., experiments 2, 4, 6, 8 and 10) and documented in Table 1 reveal that in the crystalline basement and for a 2D model and seismic modelling):


Note that the inter-shot spacing of the experiments discussed above is 500 m, while the number of shots and the maximum offset is varying. The shots at large offsets clearly provide more information through the scattered field. This is not the case with real data as the shots at large offsets exhibit low S/N ratios.

We would like also to quantify the effects of the number of sources for a constant maximum offset. We set the maximum offset to 2000 m and consider various numbers of shots. The number of shots of experiments 5, 6 and 7 (Table 1) are respectively 5, 9 and 17. This means that the inter-shot spacing is different between these experiments, from 1000 m for experiment 5, to 500 m for experiment 6 and down to 250 m for experiment 7.

Slight or non-negligible improvement can be observed between experiments 5 and 6 in all recovered physical parameters. We recovered better the lower part of the fault in experiment 6. This is the direct effect of the number of shots and the intershot distance. Where a non-negligible effect is observed between the results of experiments 5 and 6, no visible effect was observed between the results of experiments 6 and 7. The reason is that for our target, the minimum inter-shot spacing is already reached in experiment 6 and even if we increase the shots number, and decrease the inter-shot distance, the imaging results are not improved. For real noisy data, a smaller inter-shot spacing distance and more sources should be needed, depending strongly on the noise level and the depth of the target. For a real case, a sensitivity analysis could be performed including different noise types and amplitudes to quantify their effect and then choose the optimizing acquisition geometry.

We conclude from these experiments that the number of shots and the inter-shot spacing are both important. It is not appropriate to use several sources with kilometric inter-shot spacing or inter-shot spacings smaller than 250 m (for a 3 km depth target fault and data main frequency of 50 Hz). We observed that using a small number of shots does not allow us to recover accurately our target fault, especially its lower part (e.g., Figure 6a,b), but also that using more shots with non-adequate inter-shot spacing do not improve the results (e.g., experiment 7, Table 1). We should define an appropriate distance from a sensitivity analysis, which could change according to the depth, thickness, dip, azimuth, and so on, of the target. According to the faults which could be met in the granite of Soultz-sous-Forêts, the best parameters deduced from the sensitivity study are: (i) the optimized number of shots is 9, (ii) the intershot distance is 800 m, and (iii) the maximum offset is 4000 m.

We recall also that these conclusions hold for noise-free data and for a 2D seismic modelling. For noisy data, the number of required shots would increase. And for a 3D model with azimuth coverage, the number of necessary shots N should be around *πn* <sup>2</sup>/4, where n is the number of shots needed for 2D.

#### **5. Sensitivity Analysis of the Fault Parameters**

We now use the best acquisition geometry parameters determined in the previous section and study the seismic effect of the fault features: (i) the fault geometry (length, dip, distance from the receiver) and (ii) the fault physical characteristics (P- and S-wave velocities, density contrasts and thickness). The thickness of the fault zone is a geometrical parameter but as this parameter is related to the ability of the FWI to retrieve the true values of the physical parameters inside the fault zone, we consider it as a physical parameter. The ability to retrieve the true values of the physical parameters (fault characterisation) is also related to the main frequency of the seismic data.

#### *5.1. Fault Geometry Parameters*

We consider a fault with the same features as that described in the single-shot problem (Section 4.1). We vary the fault dip (0◦ , 30◦ , 60◦ , 75◦ , −75◦ and 90◦ )) and the fault distance from the well: fault crossing the well, or horizontally shifted by 600 m or 1000 m from (Figure 7). The same inversion parameters were used: 20 m for the spatial correlation length, and without polarization. Concerning the correlation between the physical parameters contrasts, Vp, Vs and density, we consider two cases: (i) a strong correlation, i.e., crosscorrelation coefficients of 0.9 for the three couples of parameters) and (ii) a moderate to strong correlation, i.e., 0.8 for the (Vp, Vs) couple and 0.6 for the two other couples (Vp, density) and (Vs, density). We used the best geometrical data acquisition recovered in the previous sensitivity study (Section 5.2), namely (i) 800 m for the inter-shot spacing, (ii) maximum offset of 4000 m, and (iii) eleven shots located at the following offsets: −4000, −3200, −2400, −1600, −800, 0, 800, 1600, 2400, 3200 and 4000 m (Figure 7).

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**Figure 7.** Different faults used in the sensitivity analysis with different dips shown on the P-wave velocity model. The center of the fault is at 3000 m depth. The faults are: (1) 75° dip, (2) 75° dip, shifted 600 m to the left (the lower part of the fault is about 200 m from the receivers), (3) 75° dip, shifted 800 m to the left, (4) 60° dip, (5) 60° dip, shifted 700 m to the left, (6) 30° dip, (7) -75° dip, shifted 650 m to the left, (8) vertical, shifted 200 m to the left and (9) horizontal, crossing the well at 3000 m. The stars show source locations and the reverted triangles, the receivers. **Figure 7.** Different faults used in the sensitivity analysis with different dips shown on the P-wave velocity model. The center of the fault is at 3000 m depth. The faults are: (1) 75◦ dip, (2) 75◦ dip, shifted 600 m to the left (the lower part of the fault is about 200 m from the receivers), (3) 75◦ dip, shifted 800 m to the left, (4) 60◦ dip, (5) 60◦ dip, shifted 700 m to the left, (6) 30◦ dip, (7) −75◦ dip, shifted 650 m to the left, (8) vertical, shifted 200 m to the left and (9) horizontal, crossing the well at 3000 m. The stars show source locations and the reverted triangles, the receivers.

We have summarized in Figure 8 the sensitivity to fault dips for the faults crossing the well and the receivers. We can observe that the fault dip is not an issue even at high dips (>75°). Generally, the higher the fault dips the better the FWI retrieves the whole fault shape and contrasts. This is true except for a horizontal fault, where the fault parts close to the receivers are accurately recovered, but not the faraway parts (Figure 8d). Nevertheless, the physical parameters for the parts closest to the receivers are accurately recovered. We note that for high dip faults, i.e., >60° (Figure 8a,b), we recovered accurately the entire upper part of the fault, but not completely the lower part, as in the previous experiments (see Section 5). This is due to the scattered field, as already explained. The worst cases are for shallow dipping faults, probably between 10° to 40° more or less (e.g., Figure 8c). We note also the presence of some artefacts in the recovered density field, but again we can observe that for a horizontal fault (Figure 8d) and for high dip faults (e.g., Figure 8a), the retrieved density field is better than the retrieved P- and S-wave velocity We have summarized in Figure 8 the sensitivity to fault dips for the faults crossing the well and the receivers. We can observe that the fault dip is not an issue even at high dips (>75◦ ). Generally, the higher the fault dips the better the FWI retrieves the whole fault shape and contrasts. This is true except for a horizontal fault, where the fault parts close to the receivers are accurately recovered, but not the faraway parts (Figure 8d). Nevertheless, the physical parameters for the parts closest to the receivers are accurately recovered. We note that for high dip faults, i.e., >60◦ (Figure 8a,b), we recovered accurately the entire upper part of the fault, but not completely the lower part, as in the previous experiments (see Section 5). This is due to the scattered field, as already explained. The worst cases are for shallow dipping faults, probably between 10◦ to 40◦ more or less (e.g., Figure 8c). We note also the presence of some artefacts in the recovered density field, but again we can observe that for a horizontal fault (Figure 8d) and for high dip faults (e.g., Figure 8a), the retrieved density field is better than the retrieved P- and S-wave velocity field.

field. In a second step, we have considered the case of the distance of the fault from the well. What is the maximum distance where a fault could be accurately imaged or even detected? The results of the FWI for the faults 2, 3 and 5 are shown in Figure 9 and for the faults 7 and 8, in Figure 10. The FWI can accurately detect and delineate the fault even when it is far away from the receivers. The maximum distance varies from 500 m for the lower part of the fault to 1000 m for the upper part (e.g., Figure 9). This maximum distance decreases when the dip decreases. When the fault dip decreases from 75◦ to 60◦ , the farthest part of the fault is not detected (compare Figure 9a,c). When the fault dip decreases, we delineate with more accuracy the closest part than the furthest part, this can be noticed when comparing faults 2 and 5. This is expected, because when increasing the fault dip, we increase the distance between the upper part of the fault and the receivers, for the same fault length. We note also that the density field is recovered with some artefacts, and its physical values were recovered accurately. We recall that the inverted data are free of noise, and we expect these maximum distances to be smaller with real noisy data.

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**Figure 8.** Sensitivity analysis results obtained for dip faults crossing the well at 3000 km depth. We show P-wave velocity (left), S-wave velocity (center) and density (right) fields for fault dips of (**a**) 75°, (**b**) 60°, (**c**) 30° and (**d**) 0°. These results correspond to faults 1, 4, 6 and 9 showed in Figure 7. We show only the interest area showed by the white rectangle in Figure 2c. **Figure 8.** Sensitivity analysis results obtained for dip faults crossing the well at 3000 km depth. We show P-wave velocity (left), S-wave velocity (center) and density (right) fields for fault dips of (**a**) 75◦ , (**b**) 60◦ , (**c**) 30◦ and (**d**) 0◦ . These results correspond to faults 1, 4, 6 and 9 showed in Figure 7. We show only the interest area showed by the white rectangle in Figure 2c.

In a second step, we have considered the case of the distance of the fault from the well. What is the maximum distance where a fault could be accurately imaged or even detected? The results of the FWI for the faults 2, 3 and 5 are shown in Figure 9 and for the faults 7 and 8, in Figure 10. The FWI can accurately detect and delineate the fault even when it is far away from the receivers. The maximum distance varies from 500 m for the lower part of the fault to 1000 m for the upper part (e.g., Figure 9). This maximum distance decreases when the dip decreases. When the fault dip decreases from 75° to 60°, the farthest part of the fault is not detected (compare Figure 9a,c). When the fault dip decreases, we delineate with more accuracy the closest part than the furthest part, this can

for the same fault length. We note also that the density field is recovered with some

noisy data.

artefacts, and its physical values were recovered accurately. We recall that the inverted data are free of noise, and we expect these maximum distances to be smaller with real

**Figure 9.** The retrieved P-wave velocity field (left), S-wave velocity field (center) and density field (right) for faults (**a**) 2, (**b**) 3 and (**c**) 5 (Figure 7). The faults 2 and 5 are 200 m far from the closest receivers whereas fault 3 is 500 m far from the closest receivers in the lower part of the fault. We show only the target area showed by the white rectangle in Figure 2c. **Figure 9.** The retrieved P-wave velocity field (left), S-wave velocity field (center) and density field (right) for faults (**a**) 2, (**b**) 3 and (**c**) 5 (Figure 7). The faults 2 and 5 are 200 m far from the closest receivers whereas fault 3 is 500 m far from the closest receivers in the lower part of the fault. We show only the target area showed by the white rectangle in Figure 2c.

The conclusions of the previous section concerning the fault dip remain true. We observed that the higher the fault dips, the better we can delineate the fault and recover the contrasts in the physical parameters. This is the case even for a vertical fault (Figure 10b). In this case, the fault is accurately delineated, and the P-wave velocity and the density fields are recovered with a good precision. The S-wave velocity field show a correct delineation, but the contrasts are not well estimated in the deeper part of the fault. The reason is that in this part, the P-to-S reflected (from right side sources), or the transmitted converted S waves (from left side sources) provide information only at a few receivers (the deepest). Even for a vertical fault, the FWI shows a high potential to accurately recover its shape and the physical contrasts, which is not the case to the classical VSP processing approach (see discussion below). The conclusions of the previous section concerning the fault dip remain true. We observed that the higher the fault dips, the better we can delineate the fault and recover the contrasts in the physical parameters. This is the case even for a vertical fault (Figure 10b). In this case, the fault is accurately delineated, and the P-wave velocity and the density fields are recovered with a good precision. The S-wave velocity field show a correct delineation, but the contrasts are not well estimated in the deeper part of the fault. The reason is that in this part, the P-to-S reflected (from right side sources), or the transmitted converted S waves (from left side sources) provide information only at a few receivers (the deepest). Even for a vertical fault, the FWI shows a high potential to accurately recover its shape and the physical contrasts, which is not the case to the classical VSP processing approach (see discussion below).

The challenging fault shape is for a dip of −75° when the fault is far away from the receivers and when reflected waves cannot reach the receivers. We can notice that for the P-wave velocity field (Figure 10a), only a small upper part is recovered, whereas for both the S-wave velocity and density fields, the whole fault is correctly delineated, but with underestimated contrasts. The S-wave velocity field is better estimated due to the P-to-S converted waves of the scattered field (Figure 11). Notice that in the well vicinity (distance less than 300 m) the FWI has accurately recovered the shape and the physical contrasts of The challenging fault shape is for a dip of −75◦ when the fault is far away from the receivers and when reflected waves cannot reach the receivers. We can notice that for the P-wave velocity field (Figure 10a), only a small upper part is recovered, whereas for both the S-wave velocity and density fields, the whole fault is correctly delineated, but with underestimated contrasts. The S-wave velocity field is better estimated due to the P-to-S converted waves of the scattered field (Figure 11). Notice that in the well vicinity (distance less than 300 m) the FWI has accurately recovered the shape and the physical contrasts of the fault. The tendency is that the physical parameter contrasts are more underestimated when moving down and away from the well.

when moving down and away from the well.

**Figure 10.** The retrieved P-wave velocity field, S-wave velocity field and density field for faults (**a**) 7 and (**b**) 8 (Figure 7). The fault 7 is 200 m far to the closest receivers in its upper part. We show only the interest area showed by the white rectangle in Figure 2c. Even for a vertical fault, the FWI shows a high potential to accurately recover its shape and the physical contrasts. In this case, the fault is accurately delineated, and the P-wave velocity and the density fields are recovered with a high precision. The S-wave velocity model show a correct delineation, but the contrasts are not well estimated in the deeper part of the fault, which could be explained by a low P-to-S reflected or less transmitted converted S-waves. **Figure 10.** The retrieved P-wave velocity field, S-wave velocity field and density field for faults (**a**) 7 and (**b**) 8 (Figure 7). The fault 7 is 200 m far to the closest receivers in its upper part. We show only the interest area showed by the white rectangle in Figure 2c. Even for a vertical fault, the FWI shows a high potential to accurately recover its shape and the physical contrasts. In this case, the fault is accurately delineated, and the P-wave velocity and the density fields are recovered with a high precision. The S-wave velocity model show a correct delineation, but the contrasts are not well estimated in the deeper part of the fault, which could be explained by a low P-to-S reflected or less transmitted converted S-waves.

the fault. The tendency is that the physical parameter contrasts are more underestimated

An interesting comparison could be made between the FWI technique and the standard OVSP data processing technique for their ability to detect and characterize faults in the granites. This sensitivity study shows us that we can fairly to accurately detect, delineate, and characterize fault zones in the granite context (in the well vicinity). Experiments show also that the higher the fault dip, the better is the fault delineation and also the better we characterize the physical parameter contrasts. A standard approach, where OVSP data are processed classically by separating the recorded field to up- and down- going fields and where only the first seismic order (primaries) of the upgoing fields is used, would fail for faults with high dips. Reiser et al. [10] obtained accurate fault imaging for faults, especially those with a shallow dip, and demonstrated that the Kirchhoff migration cannot provide accurate fault imaging for high fault dips: the faults dipping at 30◦ are, for instance, better imaged than those at 70◦ (also in a granite context). The authors have also noted the presence of important artefacts that cannot be removed even when they increase the source number due to the diffraction hyperbola. For the FWI method, the most challenging fault dip could be found for dip angles of 10–40◦ . For fault dips between 45 and 90◦ , which are the most frequently found in deep geothermal crystalline contexts, the FWI show a fully accurate fault imaging result. Very few faults may present this maximum dip (i.e., 90◦ ), but the idea here is to check the ability of the applied method in very steepest contrasts. Additionally, the observed artefacts are removed when increasing the number of shots to seven, and completely removed with nine shots, because the multiple diffractions or high order scattered field constitutes useful information. In other words, as the full wave equation reproduces these phases, we can invert this part of the wavefield, introducing constraining information and helping the inversion to provide an accurate and realistic underground image. However, we recall that these FWI synthetic experiments have been performed for perfect data (noise free) and for a 2D world (i.e., the fault is always perpendicular to the propagation plane). We recall also that the aim of this study is to demonstrate the ability of the FWI to recover accurately faults with realistic parameters and characteristics, *Geosciences* **2021**

besides the real data complications (for instance attenuation, 3D effects, alterations and anthropogenic noise) which could not affect considerably the results of this study, because their effects (e.g., attenuation) do not play a major role in the FWI. , *11*, x FOR PEER REVIEW 23 of 36

**Figure 11.** Seismograms recovered from the FWI of fault number 7 (for location, see Figure 7) for X (horizontal) component (left) and Z (vertical) component (right) obtained for zero offset source location. (**a**) observed X and Z components, (**b**) inverted X and Z components and (**c**) X and Z differences between (**a**) and (**b**). **Figure 11.** Seismograms recovered from the FWI of fault number 7 (for location, see Figure 7) for X (horizontal) component (left) and Z (vertical) component (right) obtained for zero offset source location. (**a**) observed X and Z components, (**b**) inverted X and Z components and (**c**) X and Z differences between (**a**) and (**b**).

An interesting comparison could be made between the FWI technique and the standard OVSP data processing technique for their ability to detect and characterize faults in the granites. This sensitivity study shows us that we can fairly to accurately detect, delineate, and characterize fault zones in the granite context (in the well vicinity). We have performed an additional sensitivity study regarding antennae length. We have found as expected that we recover only the fault part located at the receiver depths. This means that when a fault is detected and delineated, its length could not be the complete length if the recovered fault length and the antennae are comparable.

Experiments show also that the higher the fault dip, the better is the fault delineation and also the better we characterize the physical parameter contrasts. A standard approach, where OVSP data are processed classically by separating the recorded field to up- and The sensitivity analyses described and discussed above have been performed for a fault thickness of 30 m. What is the minimum fault thickness which can be recovered in

down- going fields and where only the first seismic order (primaries) of the upgoing fields

Kirchhoff migration cannot provide accurate fault imaging for high fault dips: the faults dipping at 30° are, for instance, better imaged than those at 70° (also in a granite context). *Geosciences* **2021**

the granites using the FWI technique? Even if the thickness is a geometrical parameter of the fault, its estimation is related to the physical parameter contrasts and the frequency content of the seismic signal (interaction between the wavelength of the P- and the S-wave and the fault thickness); this is why we have considered this parameter separately.

#### *5.2. The Fault Thickness Issue*

We start by analysing the quantitative parameters recovered in the previous experiments. For instance, we focus on the horizontal profile of the estimated physical parameters for fault no. 4 (see Table 1, Figure 8b), which represent a fault crossing the well at 3000 m, showing a dip of 60◦ , a thickness of 30 m and 20, 20 and 7% for P- and S-wave velocity and density contrasts, respectively. Qualitatively, remember that the upper part of this fault was accurately imaged by the three parameters (i.e., P-, S-waves and density), but its lower section was partly imaged. The contrast analysis (Figure 12) provides a quantitative view. The fault contrasts in its upper part before crossing the well is fully recovered where at least 97% of the maximum contrast is retrieved. Some oscillations can be observed for the density. , *11*, x FOR PEER REVIEW <sup>25</sup> of 36

**Figure 12.** The estimated P- (right) and S-wave (middle) velocities and density (right) contrasts for five representative depths; (**a**) at the upper extremity (2200 m), (**b**) at 2600 m, (**c**) crossing the well at 3000 m, (**d**) at 3400 m, and e) the lower fault extremity at 3800 m. The fault no. 4 has been modelled and inverted (Figure 7), where the FWI image is shown in Figure 8b. Note that the true curves has no rectangular shape, because we smoothed the model to reduce diffractions arising from the model pixels. A filter smoothing 4x4 pixels (i.e., 20 × 20 m) have been applied to smooth the final physical, P-, S- waves and density models. The physical parameter contrasts for the lower part of the fault are poorly recovered **Figure 12.** The estimated P- (right) and S-wave (middle) velocities and density (right) contrasts for five representative depths; (**a**) at the upper extremity (2200 m), (**b**) at 2600 m, (**c**) crossing the well at 3000 m, (**d**) at 3400 m and (**e**) the lower fault extremity at 3800 m. The fault no. 4 has been modelled and inverted (Figure 7), where the FWI image is shown in Figure 8b. Note that the true curves has no rectangular shape, because we smoothed the model to reduce diffractions arising from the model pixels. A filter smoothing 4 × 4 pixels (i.e., 20 × 20 m) have been applied to smooth the final physical, P-, S- waves and density models.

in the P-wave velocity field where 400 m below the receivers (i.e., at 3400 m depth), only 40% of the maximum contrast has been recovered (Figure 12d), whereas 70% of the S– wave contrast has been obtained, and an overestimation of 120% for the density.

contrast has been retrieved and around 45% for the S-wave velocity and 75% for the density. Note that the density provides better results for free noise data, and it is more sensitive to noise as the obtained results quality decreases when increasing the noise

To quantitatively address the fault thickness, we consider the geometry data acquisition as that shown in Figure 7, and we consider the fault (1), dip of 75° with different thicknesses. We have studied the following fault thicknesses: 5, 10, 15, 20, 30 and 50 m. Both acquisition geometry and inversion parameters remain unchanged, for

We can notice that the fault contrasts have been accurately estimated by the FWI (Figure 13). Qualitatively, the fault has been accurately retrieved in all experiments. The

comparison with the previous images obtained for a fault thickness of 30 m.

(Figure 12).

The physical parameter contrasts for the lower part of the fault are poorly recovered in the P-wave velocity field where 400 m below the receivers (i.e., at 3400 m depth), only 40% of the maximum contrast has been recovered (Figure 12d), whereas 70% of the S–wave contrast has been obtained, and an overestimation of 120% for the density. Considering the lower fault extremity (Figure 12e), less than 10% of the P-wave velocity contrast has been retrieved and around 45% for the S-wave velocity and 75% for the density. Note that the density provides better results for free noise data, and it is more sensitive to noise as the obtained results quality decreases when increasing the noise (Figure 12).

To quantitatively address the fault thickness, we consider the geometry data acquisition as that shown in Figure 7, and we consider the fault (1), dip of 75◦ with different thicknesses. We have studied the following fault thicknesses: 5, 10, 15, 20, 30 and 50 m. Both acquisition geometry and inversion parameters remain unchanged, for comparison with the previous images obtained for a fault thickness of 30 m.

We can notice that the fault contrasts have been accurately estimated by the FWI (Figure 13). Qualitatively, the fault has been accurately retrieved in all experiments. The fault location was rightly estimated, even for the very narrow fault of 5 m thickness. It is also important to quantitatively assess the FWI estimated contrasts especially for narrow faults, i.e., fault thickness less than 20 m (see discussion below). *Geosciences* **2021**, *11*, x FOR PEER REVIEW 26 of 36 fault location was rightly estimated, even for the very narrow fault of 5 m thickness. It is also important to quantitatively assess the FWI estimated contrasts especially for narrow faults, i.e., fault thickness less than 20 m (see discussion below).

**Figure 13.** P-wave velocity estimated field for faults with different thicknesses: (**a**) 5 m, (**b**) 10 m, (**c**) 15 m, (**d**) 20 m, (**e**) 30 m and (**f**) 50 m. We show only the P-wave velocity in the target area limited by white block in Figure 2c. The quality results of the S-wave velocity and density are comparable to the P-wave velocity results. **Figure 13.** P-wave velocity estimated field for faults with different thicknesses: (**a**) 5 m, (**b**) 10 m, (**c**) 15 m, (**d**) 20 m, (**e**) 30 m and (**f**) 50 m. We show only the P-wave velocity in the target area limited by white block in Figure 2c. The quality results of the S-wave velocity and density are comparable to the P-wave velocity results.

In the granite, the P-wave velocity value is around 6000 m/s as showed by sonic logs acquired in GPK1 borehole (e.g., [48]. For a central frequency of 50 Hz, as is the case for our experiments, the seismic wavelength for P-waves is 120 m (i.e., λ = 120 m) and about half for the S-wave (70 m). Barnes and Charara [13]show that for OVSP data, when the scattered S-wave field is energetic (as often when offset is sufficient), the S-wave velocity estimated field provides a better spatial resolution than the P-wave velocity field, even when S-wave suffer from seismic attenuation because the scattered S-wave field is mainly generated in the well vicinity implying small propagation distances. Moreover, and because it deals with the complete wave equation, the FWI can detect and delineate faults even for thicknesses of λ/10 (i.e., for λp = 12 m, and λs = 7 m). In a sedimentary context, thin beds can also be detected with thicknesses of λ/1 [13] However, as the scattered energy decreases with the fault thickness, in the real world, the scattered energy from a In the granite, the P-wave velocity value is around 6000 m/s as showed by sonic logs acquired in GPK1 borehole (e.g., [48]. For a central frequency of 50 Hz, as is the case for our experiments, the seismic wavelength for P-waves is 120 m (i.e., λ = 120 m) and about half for the S-wave (70 m). Barnes and Charara [13] show that for OVSP data, when the scattered S-wave field is energetic (as often when offset is sufficient), the S-wave velocity estimated field provides a better spatial resolution than the P-wave velocity field, even when S-wave suffer from seismic attenuation because the scattered S-wave field is mainly generated in the well vicinity implying small propagation distances. Moreover, and because it deals with the complete wave equation, the FWI can detect and delineate faults even for thicknesses of λ/10 (i.e., for λp = 12 m, and λs = 7 m). In a sedimentary context, thin beds can also be detected with thicknesses of λ/1 [13] However, as the scattered energy decreases with the fault thickness, in the real world, the scattered energy from a

thin fault can easily be covered by ambient noise. Therefore, for real data, the detection, delineation, and characterization of thin faults depend strongly on the data quality and

either for faults of 5, 10 and 15 m thick (Figure 13a–c), we accurately recovered their

The obtained contrasts compared to the true contrasts are shown on Figure 14 for several experiments, including different fault thicknesses (5, 10, 15, 30 and 50 m) and at a particular depth of 3000 m. It was clear that the FWI will provide precise faults geometries and their characteristics, i.e., velocities and density contrasts, for thick faults (>30 m). Contrasts of these thick faults have been accurately retrieved, especially for P- and S-wave fields but less resolved for density fields, with some artefacts (Figure 14e,f). Surprisingly, precise contrasts have been recovered for very narrow faults of 5 and 10 m (Figure 14a,b). When comparing the FWI estimated contrasts to the true contrasts (Figure 14), precise values have been obtained for all thicknesses (Table 2), where the worst recovered contrast

locations and dips, but what about the recovered contrasts?

on the S/N ratio.

thin fault can easily be covered by ambient noise. Therefore, for real data, the detection, delineation, and characterization of thin faults depend strongly on the data quality and on the S/N ratio.

As the seismic wavelength is around 120 m (70 m for S-waves), we observe also that either for faults of 5, 10 and 15 m thick (Figure 13a–c), we accurately recovered their locations and dips, but what about the recovered contrasts?

The obtained contrasts compared to the true contrasts are shown on Figure 14 for several experiments, including different fault thicknesses (5, 10, 15, 30 and 50 m) and at a particular depth of 3000 m. It was clear that the FWI will provide precise faults geometries and their characteristics, i.e., velocities and density contrasts, for thick faults (>30 m). Contrasts of these thick faults have been accurately retrieved, especially for P- and S-wave fields but less resolved for density fields, with some artefacts (Figure 14e,f). Surprisingly, precise contrasts have been recovered for very narrow faults of 5 and 10 m (Figure 14a,b). When comparing the FWI estimated contrasts to the true contrasts (Figure 14), precise values have been obtained for all thicknesses (Table 2), where the worst recovered contrast is 97% of the maximum true contrast, which is very satisfactory for fault thickness characterization, especially for narrow faults (i.e., fault thickness less than 15 m).

**Table 2.** The recovered contrast according to the maximum true contrasts, where True means the physical parameter contrast for the fault in the reference or True model and FWI means the physical parameter contrast for the fault in the models estimated by the FWI. Note that these contrasts are relative to the background values.


#### *5.3. The Multi-Faults Experiment*

We now consider four faults with different lengths and thicknesses, and a deviated well. We thus mix different challenges in the same inversion experiment to explore the ability of the FWI method to separate and interpret the scattered fields of the different faults. The modelled fault features are shown in Table 3. The faults a, c and d cross the well, whereas fault b is located in the vicinity of the well at the right side, under the receivers.

**Table 3.** Fault features of the multi-fault experiment. The VC. Stand the Velocity Contrast (idem to C). The fault locations are shown in Figure 15.


5 or 10 m (a and b).

receivers.

*5.3. The Multi-Faults Experiment*

C.). The fault locations are shown in Figure 15.

*Geosciences* **2021**, *11*, x FOR PEER REVIEW 28 of 36

**Figure 14.** Estimated physical parameter values as a function of the distance for several fault thickness at 2800 m depth. The estimated P-wave (left), S-wave (middle) and density (right) from FWI for fault thicknesses; (**a**) 5 m, (**b**) 10 m, (**c**) 15 m, (**d**) 20 m, (**e**) 30 m and (**f**) 50 m. The estimations are good to very good but some artefacts are present in density curves, for instance, panels c-e. Surprisingly, the FWI provides accurate and precise fault characterization even for faults as thin as **Figure 14.** Estimated physical parameter values as a function of the distance for several fault thickness at 2800 m depth. The estimated P-wave (left), S-wave (middle) and density (right) from FWI for fault thicknesses; (**a**) 5 m, (**b**) 10 m, (**c**) 15 m, (**d**) 20 m, (**e**) 30 m and (**f**) 50 m. The estimations are good to very good but some artefacts are present in density curves, for instance, panels c-e. Surprisingly, the FWI provides accurate and precise fault characterization even for faults as thin as 5 or 10 m (a and b).

faults. The modelled fault features are shown in Table 3. The faults a, c and d cross the well, whereas fault b is located in the vicinity of the well at the right side, under the

**Table 3.** Fault features of the multi-fault experiment. The VC. Stand the Velocity Contrast (idem to

We now consider four faults with different lengths and thicknesses, and a deviated well. We thus mix different challenges in the same inversion experiment to explore the

For acquisition geometry parameters, a total of 21 sources have been used with increasing inter-shot spacing from 250 m, around the well, to 500 m at intermediate distance (between 1 and 3 km away) to reach 1000 m at large offsets. The maxim offset used is 5000 m. The deviated well is inspired by GPK4 at Soultz-sous-Forêts. We do not add noise. The obtained P- and S-wave velocity and density estimated fields are shown in Figure 15 after 100 iterations. The FWI accurately recovers the fault locations and their shapes except for the deepest part of the faults c and d, as was observed in the previous experiments. These deep parts are better recovered for the S-wave estimated field than for the P-wave field and density as in previous experiments. The main result from the multi-fault experiment is that i) the overall conclusions are the same as for previous synthetic FWI experiments and ii) the presence of several faults does not affect the accuracy of results for each fault independently, at least in 2D and using noise-free data. In addition, we have understood from this experiment, that the FWI can provide a clear underground image of faults network, at least for fault zones having average characteristic values as those modelled here. For instance, fault a, which is only 20 m thick, is recovered in the right location and shape, but its thickness is underestimated. Undoubtedly, the narrow faults, typically with a thickness of less than 20 m, will be more challenging.

*Geosciences* **2021**, *11*, x FOR PEER REVIEW 29 of 36

the P-wave field and density as in previous experiments.

Thickness [m] 20 50 25 40 Dip [°] −60 −60 75 80 P-wave VC. [%] 25 20 25 20 S-wave VC. [%] 25 20 25 20 Density C. [%] 10 7 10 7

For acquisition geometry parameters, a total of 21 sources have been used with increasing inter-shot spacing from 250 m, around the well, to 500 m at intermediate distance (between 1 and 3 km away) to reach 1000 m at large offsets. The maxim offset used is 5000 m. The deviated well is inspired by GPK4 at Soultz-sous-Forêts. We do not add noise. The obtained P- and S-wave velocity and density estimated fields are shown in Figure 15 after 100 iterations. The FWI accurately recovers the fault locations and their shapes except for the deepest part of the faults c and d, as was observed in the previous experiments. These deep parts are better recovered for the S-wave estimated field than for

From the estimated fields, we can observe that the most important parameters affecting the results are the dip and location of the faults according to the receivers (Figure 15). We also notice that even if the fault does not cross the well, the FWI can retrieve accurately the fault characteristics. From the P-wave velocity estimated field, we can notice that the fault b is better resolved, then d, then c and finally a. The major difference between the resulted fault features for fault a and b, which have the same dip, is mainly their thickness, where the fault b thickness is 50 m, and only 20 m for fault a (Table 3).

**Faults a b c d**

**Features**

**Figure 15.** P- and S-wave velocity and density estimated fields from experiment with several faults having different features. The features of the modelled faults are shown in Table 3. The inverted triangles showed the receivers in the deviated well. We show the results only around the faults. The black polygon shows the location of the true modelled faults. **Figure 15.** P- and S-wave velocity and density estimated fields from experiment with several faults having different features. The features of the modelled faults are shown in Table 3. The inverted triangles showed the receivers in the deviated well. We show the results only around the faults. The black polygon shows the location of the true modelled faults.

During the FWM, we can record the waves' propagations through the entire experiment. Figure 16 shows snapshots at times 2 ms, 660 ms, 850 ms and 1050 ms. The P-From the estimated fields, we can observe that the most important parameters affecting the results are the dip and location of the faults according to the receivers (Figure 15). We also notice that even if the fault does not cross the well, the FWI can retrieve accurately the fault characteristics. From the P-wave velocity estimated field, we can notice that the fault b is better resolved, then d, then c and finally a. The major difference between the resulted fault features for fault a and b, which have the same dip, is mainly their thickness, where the fault b thickness is 50 m, and only 20 m for fault a (Table 3).

The main result from the multi-fault experiment is that (i) the overall conclusions are the same as for previous synthetic FWI experiments and (ii) the presence of several faults does not affect the accuracy of results for each fault independently, at least in 2D and using noise-free data. In addition, we have understood from this experiment, that the FWI can provide a clear underground image of faults network, at least for fault zones having average characteristic values as those modelled here. For instance, fault a, which is only 20 m thick, is recovered in the right location and shape, but its thickness is underestimated. Undoubtedly, the narrow faults, typically with a thickness of less than 20 m, will be more challenging.

During the FWM, we can record the waves' propagations through the entire experiment. Figure 16 shows snapshots at times 2 ms, 660 ms, 850 ms and 1050 ms. The P- and S-wave front can be followed and their interactions with the faults are visible. P-to-S and S-to-P wave conversions are also visible. Combining these screen shots, we built a movie (see the Supplementary Material to watch it). Analysing continuously the seismograms and the movie, we better understand the different phases in the seismograms and their origins. seismograms and their origins.

and S-wave front can be followed and their interactions with the faults are visible. P-to-S and S-to-P wave conversions are also visible. Combining these screen shots, we built a

seismograms and the movie, we better understand the different phases in the

**Figure 16.** Representative snapshots for the multi-faults experiment at different times; (**a**) 2 ms, (**b**) 660 ms, (**c**) 850 ms and (**d**) 1050 ms. The divergence of displacements (P-waves) are shown in bleu (negative) and green (positive), and the curl of displacements (S-waves) are shown in red (negative) and yellow (positive). Notice the S-wave generated from the faults (i.e., panels c and d), the reflected and the converted waves from the top basement (e.g., panel b) and the multiples in the sedimentary **Figure 16.** Representative snapshots for the multi-faults experiment at different times; (**a**) 2 ms, (**b**) 660 ms, (**c**) 850 ms and (**d**) 1050 ms. The divergence of displacements (P-waves) are shown in bleu (negative) and green (positive), and the curl of displacements (S-waves) are shown in red (negative) and yellow (positive). Notice the S-wave generated from the faults (i.e., panels c and d), the reflected and the converted waves from the top basement (e.g., panel b) and the multiples in the sedimentary layers (panel c and d), and several other waves.

layers (panel c and d), and several other waves.

Additive Gaussian noise,

characteristics:

#### **6. Results and Discussion on the FWI Robustness for Noisy Data**

data). We now test the FWI performance with moderate and high noise in the data using experiment 5 as a reference (Table 1). We considered the noise with the following

**6. Results and Discussion on the FWI Robustness for Noisy Data** In order to demonstrate the FWI ability for fault delineation and characterization, it is important to separate the data quality issue (information content of the data) and the starting model issue (non-linearity) from the imaging issue. This is why we have performed sensitivity analyses using noise-free data in the above sections (even the numerical noise is negligible as it is the same in the observed data and in the calculated In order to demonstrate the FWI ability for fault delineation and characterization, it is important to separate the data quality issue (information content of the data) and the starting model issue (non-linearity) from the imaging issue. This is why we have performed sensitivity analyses using noise-free data in the above sections (even the numerical noise is negligible as it is the same in the observed data and in the calculated data). We now test the FWI performance with moderate and high noise in the data using experiment 5 as a reference (Table 1). We considered the noise with the following characteristics:


*Geosciences* **2021**, *11*, x FOR PEER REVIEW 31 of 36

Ambient noise is unlocalized,

Noise has the same f-k amplitude spectrum than the data,

Coda noise is localized a few periods after energetic phases.

We show in Figure 17 the Z-components for the three experiments namely Ref, MN and HN (Table 4). We can observe that for free noise data, we identify clearly the arrivals crossing the first arrival from −2000 m, whereas in MN these arrivals are more difficult to


We show in Figure 17 the Z-components for the three experiments namely Ref, MN and HN (Table 4). We can observe that for free noise data, we identify clearly the arrivals crossing the first arrival from −2000 m, whereas in MN these arrivals are more difficult to identify. For HN, these arrivals cannot be identified. We focus on these arrivals, because they are generated from our target (i.e., the fault). **N/S Amplitude Radio Ambient [%] Coda [%]** Noise free (Ref) 0 0 Moderate noise (MN) 15 25 High noise (HN) 30 50

**Figure 17.** Vertical component (Z) for the three experiments showing the free noise data (**left**), MN data (**center**) and HN (**right**). We can notice that for the HN case, the fault scattered field is completely covered by the coda noise. **Figure 17.** Vertical component (Z) for the three experiments showing the free noise data (**left**), MN data (**center**) and HN (**right**). We can notice that for the HN case, the fault scattered field is completely covered by the coda noise.

We have run the FWI for these three experiments, as shown in Figure 2. The outcomes are shown in Figure 18. As expected, the estimated fields are noisy. The FWI detects the **Table 4.** The two noise parameters, ambient and coda, used in the noise study. The reference experiment is experiment 5 (Table 1).


can also be observed implying ambiguities in the interpretation (e.g., Figure 18c).

For the case of the moderate noise experiment (MN), the FWI is able to provide an accurate fault detection, delineation, and characterization (Figure 18b). We have run the FWI for these three experiments, as shown in Figure 2. The outcomes are shown in Figure 18. As expected, the estimated fields are noisy. The FWI detects the fault and retrieve quite accurately the shape and the location of the fault as well as its dip, even for noisy data (e.g., Figure 18b). The contrasts in the physical parameter are not well estimated. As previously observed, the lower part of the fault is partly recovered for both the P- and the S-wave velocity fields. This is due to the short maximum offset used in these experiments (2000 m) which is less than the optimal one (4000 m). Several artefacts can also be observed implying ambiguities in the interpretation (e.g., Figure 18c).

For the case of the moderate noise experiment (MN), the FWI is able to provide an accurate fault detection, delineation, and characterization (Figure 18b).

In the high-noise experiment (HN, Figure 18c), the upper part of the fault in the P-wave velocity field is recovered, but it is less well defined in the S-wave velocity field (and not well retrieved in density field, not shown here). The lower part of the fault is recovered partially in the P- and S-wave velocity fields, the delineation can be obtained but not the physical parameter contrasts. This HN experiment illustrates the capability of the FWI to detect and delineate faults, even for noisy data in the granite context. We recall here that this noise, even high, is structured, additive and Gaussian, which is theoretically compatible with the least square method used in the FWI. The application to real data is not as straightforward as in a sedimentary context. Effectively, the FWI needs a precise starting model including a complex rheology in order to account for the main heterogeneities (structures), the travel times of the main downgoing waves, and potentially, anisotropy or attenuation effects in the data. Some experiment parameters have to be inverted (as the source function for instance). Finally, the noise characteristics, depending on the dataset, *Geosciences* **2021**

should be carefully studied as the seismic data quality is always a key issue when using the FWI technique. All these issues have been already addressed with success in sedimentary contexts for oil and gas applications. The present results prepare the application of the FWI method to real borehole data in a crystalline basement and we hope that they will ease the interpretation of its outcomes. , *11*, x FOR PEER REVIEW 32 of 36

**Figure 18.** P- and S-wave velocity models recovered for; (**a**) the reference experiment (Ref), i.e., data free noise, (**b**) moderately noisy data (MN), and (**c**) highly noisy data (HN). We show only the target area around the fault for P-wave velocity (left) and S-wave velocity (right). The inverted triangles show the receivers and the black polygon show the shape of the fault. **Figure 18.** P- and S-wave velocity models recovered for; (**a**) the reference experiment (Ref), i.e., data free noise, (**b**) moderately noisy data (MN), and (**c**) highly noisy data (HN). We show only the target area around the fault for P-wave velocity (left) and S-wave velocity (right). The inverted triangles show the receivers and the black polygon show the shape of the fault.

In the high-noise experiment (HN, Figure 18c), the upper part of the fault in the Pwave velocity field is recovered, but it is less well defined in the S-wave velocity field (and not well retrieved in density field, not shown here). The lower part of the fault is recovered partially in the P- and S-wave velocity fields, the delineation can be obtained but not the

this noise, even high, is structured, additive and Gaussian, which is theoretically compatible with the least square method used in the FWI. The application to real data is not as straightforward as in a sedimentary context. Effectively, the FWI needs a precise starting model including a complex rheology in order to account for the main heterogeneities (structures), the travel times of the main downgoing waves, and potentially, anisotropy or attenuation effects in the data. Some experiment parameters have to be inverted (as the source function for instance). Finally, the noise characteristics, depending on the dataset, should be carefully studied as the seismic data quality is always

#### **7. Conclusions**

We have performed several sensitivity analyses of the full wave inversion (FWI) method using numerical full wave modelling (FWM) in order to assess the capabilities of the FWI method for the purpose of detection, delineation, and characterization of faults in a crystalline basement. By adopting the following simplifications, we are somehow assessing the maximum capabilities of the FWI:


Most of the experiments are performed using noise-free data, i.e., perfect data. This allows us to check the method independently of the noise characteristics, i.e., the capabilities of the FWI methods when data conditions are perfect.

We have studied several sets of parameters: (i) the inversion algorithmic parameters for the crystalline basement context, (ii) the acquisition geometry parameters, and (iii) the fault characteristics parameters. For algorithmic parameters, the goal was to tune the inversion process in the FWI in order to optimize the results, and improve the final quality of the recovered underground images (i.e., the physical estimated fields). For instance, and contrary to sedimentary contexts, considering the data polarization increases the artefacts in the estimated fields. We have also tested several spatial correlation ranges. We have found that a range of 20 m, i.e., a little less than the fault thickness, yields the best results according to the thickness of the fault target. We have also tested the crosscorrelation between the P-, the S-wave velocities and the density parameters as strong positive correlations are noticeable in well logs, and we have found that the obtained images are improved, and the artefacts are clearly attenuated.

In the second step, we have studied the effect of the acquisition geometry: (i) the number of shots, (ii) the inter-shot distance and (iii) the maximum offset, which could be used to improve the final FWI results. Using a single shot in the granite is more challenging for the FWI to accurately characterize the fault. The presence of important artefacts in the estimated fields creates ambiguities in the interpretation of the fault images. As expected, these artefacts are attenuated when increasing the number of shots. With three shots, the quality of the retrieved images is improved but the estimated fields remain perturbed by artefacts. With five shots, we obtain better estimated fields and from seven shots and up, we accurately retrieve the fault with negligible artefacts. For a given number of shots, small inter-shot spacing (around 250 m) and large inter-shot spacing (around 1000 m) do not give suitable results. A reasonable intershot distance should be defined according to the depth of the target and to the seismic main frequency. Shots at far offsets (once to twice the target depth) provide constraining information to the FWI method. However, the quality of real, noisy data at far offsets is often not sufficient. The optimal acquisition geometry parameters depend on the S/N ratio. Of course, these conclusions have to be adapted when considering a 3D domain.

Considering the fault delineation and characterization goals, we studied the effect of the fault thickness and its dip in both configurations: a fault crossing the receivers in the well, and a fault far away from the well. The obtained spatial resolution is good even for a very thin fault of 5 m, where about 98% of the physical parameter contrasts have been recovered. This result stands for noise-free data but, as the energy of the scattered field decreases with the fault thickness, the S/N ratio is critical for thin fault zones. We can accurately detect, delineate and characterize faults with high dips (60◦ to 90◦ ). Horizontal faults and their features were also retrieved accurately. The dips ranging between 10◦ and 40◦ remain a challenge. This may not be a critical problem because this fault dip range seems uncommon in granite, judging by the Soultz-sous-Forêts and Rittershoffen

geothermal sites (e.g., [26,27,29]. The multi-faults case was also studied and the FWI showed a noticeable robustness and ability for delineation and characterization objectives. The delineation and characterization of a fault network could be considered in future applications. This capability of the FWI method has to be investigated further, especially in 3D, by studying the azimuthal effect for noisy OVSP data.

For a moderate noisy data, the FWI showed a high potential to detect, delineate and even characterize faults in the crystalline context. This opens new perspective for its future application on real data.

**Supplementary Materials:** Supplementary Materials: Video: Seismic wave propagation in a simplified elastic model of Soultz-sous-Forêts. Available online at https://www.mdpi.com/article/10.3390 /geosciences11110442/s1. Description: Seismic wave propagation in a simplified elastic model of Soultz-sous-Forêts: Seismic wave propagation in a 2D earth model extracted from a 3D simplified elastic model of Soultz-sous-Forêts. The divergence of the displacement (P-waves) is indicated in blue/green while the curl of the displacement (S-waves) are in red/yellow. We can notice the complexity of the wavefield and the clear interaction with the faults. The calculation is performed using an elastic fullwave modelling code based on the finite difference method.

**Author Contributions:** Conceptualization, Y.A. and C.B.; methodology, C.B. and Y.A.; validation, Y.A. and C.B.; writing—original draft preparation, Y.A.; writing—review and editing, Y.A. and C.B. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by MEET project, which has received funding from the European Union's Horizon 2020 research and innovation program under grant agreement No. 792037.

**Acknowledgments:** The authors thank EEIG "Heat Mining" for sharing geoscientific and technical data from Soultz-sous-Forêts geothermal site. This work was realized within the MEET project which has received funding from the European Union's Horizon 2020 research and innovation program under grant agreement No. 792037. We also thank Albert Genter, Eléonore Dalmais, Vincent Maurer and Nicolas Cuenot from Electricité de Strasbourg company for their fruitful discussions on various issues. We would like to thank Albert Genter for the first reading of this paper. We thanks Amine Ourabah and Bertrand Maillot for helping us to improve the english language.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


## *Article* **Fluid-Rock Interactions in a Paleo-Geothermal Reservoir (Noble Hills Granite, California, USA). Part 1: Granite Pervasive Alteration Processes away from Fracture Zones**

**Johanne Klee 1,\* , Sébastien Potel <sup>1</sup> , Béatrice A. Ledésert <sup>2</sup> , Ronan L. Hébert <sup>2</sup> , Arezki Chabani <sup>1</sup> , Pascal Barrier <sup>1</sup> and Ghislain Trullenque <sup>1</sup>**


**Abstract:** Only few data from geothermal exploited reservoirs are available due to the restricted accessibility by drilling, which limits the understanding of the entire reservoir. Thus, analogue investigations are needed and were performed in the framework of the H2020 MEET project. The Noble Hills range, located along the southern branch of the Death Valley pull-apart (CA, USA), has been selected as a possible granitic paleo-reservoir. The aim is to characterize the pervasive alteration processes affecting this granite, away from the influence of the faults, in terms of mineralogical, petrophysical and chemical changes. Various methods were used as petrographic, geochemical and petrophysical analyses. Mineral changes, clay mineralogy, bulk rock chemical composition, calcite content and porosity were determined on different granite samples, collected in the Noble Hills granite, far from the faults and in the Owlshead Mountains, north of the Noble Hills, considered as its protolith. In order to complete the granite characterization, the metamorphic grade has been studied through the Noble Hills granite body. This complete characterization has allowed distinguishing the occurrence of three stages of alteration: (1) a pervasive propylitic alteration characterized by calcite-corrensite-epidote-K-white mica assemblage, (2) a more local one, only present in the Noble Hills granite, producing illite, kaolinite, illite/smectite, calcite and oxides, characteristic of the argillic alteration, which overprints the propylitic alteration and (3) weathering evidenced by the presence of montmorillonite in the Owlshead Mountains, which is considered as negligible in both granites. Alteration was also outlined by the correlation of the loss on ignition, representing the hydration rate, to porosity, calcite content and chemical composition. Moreover, the Kübler Index calculated from illite crystals allowed to identify a NW-SE temperature gradient in the Noble Hills.

**Keywords:** Noble Hills granite; Owlshead Mountains granite; metamorphic grade; fluid/rock interactions; newly formed minerals; element variations; geothermal reservoir

### **1. Introduction**

Geothermal systems occur in different geological settings such as active volcanic fields, plutonic provinces, extensional domains, intracratonic basins and orogenic belts, i.e., anywhere with heat and fluids that are able to flow through the rocks [1]. The exploitation of geothermal energy is expanding worldwide due to the abundant resources and the progress of the technology that lead to Enhanced Geothermal Systems (EGS). EGS (1) defines a reservoir where the natural permeability of the rocks needs to be enhanced through stimulations in order to obtain a sufficient temperature/flow rate ratio [2] and (2) aims at transforming efficiently the geothermal resource into heat and electricity for human consumption [3].

**Citation:** Klee, J.; Potel, S.; Ledésert, B.A.; Hébert, R.L.; Chabani, A.; Barrier, P.; Trullenque, G. Fluid-Rock Interactions in a Paleo-Geothermal Reservoir (Noble Hills Granite, California, USA). Part 1: Granite Pervasive Alteration Processes away from Fracture Zones. *Geosciences* **2021**, *11*, 325. https://doi.org/10.3390/ geosciences11080325

Academic Editors: Chris Clark and Jesus Martinez-Frias

Received: 18 June 2021 Accepted: 27 July 2021 Published: 31 July 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

The present study is part of the MEET H2020 project (Multidisciplinary and multicontext demonstration of EGS exploration and Exploitation Techniques and potentials) [4]. One aim of this project is to provide a characterization method of a geothermal granitic reservoir in a geological extensive context, such as the Great Basin region (USA), where normal fault zones also act as the most favorable structural setting for geothermal fluid flow [5]. In the Great Basin, other notable structural settings control fluid flow such as the intersection between normal faults and other structures like strike-slip faults (~22%), as well as pull-apart structures (4%) [5]. The fluid-rock interaction along and inside fracture zones results in hydrothermal alterations. They lead to geochemical, mineralogical and petrophysical (porosity and permeability) modifications of the rocks [6]. In granitic rocks, fluid circulations usually occur through the fracture network at different scales [6,7] involving a pervasive alteration which may influence up to cubic kilometers of rock [8]. Thus, an intense fluid/rock interaction [9] can significantly change the mineralogy, the chemistry and the texture of the bulk-rock [7] among which the common formation of clay minerals, including illite. Exploited geothermal reservoirs are located at depth, and the only and limited available data come from drillings (cores, cuttings) and seismic surveys. Studying exhumed geothermal reservoirs allows better understanding of the 3D features of the reservoir. To do so, the Noble Hills range (NH, Death Valley, CA, USA) has been selected as a possible granitic geothermal reservoir in a trans-tensional context. The NH are located in the southwestern part of the Great Basin region along the Southern Death Valley Fault Zone (SDVFZ), which constitutes the southern branch of the Death Valley pull-apart [10]. They extend over an area of 7 km long and 2 km wide and contain a part of the Cretaceous granitic pluton (~95 Ma) forming the Owlshead Mountains (OM) [11]. The arid climate prevents from a thick vegetal cover and the deep canyons that crosscut the range allow a thorough 3D investigation in order to characterize the evolution of the granite at the kilometer scale.

This paper aims at characterizing the pervasive alteration processes affecting the NH granite. This massif is considered as a possible paleo-geothermal reservoir. The study is based on the analysis of (1) rock mineralogical and related petrophysical properties changes and (2) associated chemical transfers between host rock and percolating fluids. All samples have been collected away from fractures described by [12] (this issue) in order to avoid the influence of strain and massive fluid flow. This sampling strategy ascertains the preservation of the protolith initial magmatic texture and mineralogy. A second paper (Klee et al., this issue) focusses on the role of deformation on hydrothermal alteration close to fractures. Data collected from the NH granite samples are directly compared to those obtained for the granite samples collected in the OM pluton, which is considered as the protolith. Analyses performed on targeted areas include macroscopic and microscopic petrographic studies, mineralogical characterization by X-ray diffraction (XRD) on whole rock and clay minerals, bulk rock chemical characterization by Inductively Coupled Plasma (ICP)—Mass Spectrometry (MS) and—Atomic Emission Spectrometry (AES), Scanning Electron Microscopy coupled with Energy Dispersive Spectrometry (SEM-EDS) for structural observation and local chemical analyses, as well as calcimetry and porosimetry analyses. To help at the granite characterization, the metamorphic evolution can be estimated through the Kübler Index (KI). Indeed, the temperature range of illite formation can be estimated thanks to the KI [13,14] based on illite "crystallinity" (IC). Temperature is thought to be the main factor controlling the IC evolution, but the lithology also has important effects [15–18]. Working at constant lithology, here granitic rock, allows us to avoid this effect. During the NH range formation, minerals could be transformed similarly as diagenetic reactions observed in feldspathic sandstones [19]. Inoue (1995) [9] has also shown that the rock alteration resulting from hot fluid storage during a long geological period, heated in-situ and in equilibrium with the surrounding rock is usually considered as diagenesis or metamorphism. Therefore, the terms defined by [13] for each diagenetic and metamorphic zones are considered in this study as eligible for granitic context.

#### **2. Geological Setting 2. Geological Setting**

*Geosciences* **2021**, *11*, 325 3 of 34

#### *2.1. Death Valley 2.1. Death Valley*

for granitic context.

The area of interest for this study is the southern part of the Death Valley (DV) region, which extends for about 200 km. It is located southwest of the Basin and Range province [20], in the Eastern California Shear Zone/Walker Lane Belt (ECSZ/WLB) [21–23] (Figure 1a). DV is considered as one of the youngest regions where strike-slip deformation contemporaneously occurs with large-scale crustal extension within the Basin and Range province [24–26]. This extensional basin formation accompanying normal and associated strike-slip faulting would be active since 15 Ma according to [24]. It corresponds to a structural depression between the Panamit Range and the Black and Funeral Mountains [27] (Figure 1b), generally NNW-SSE oriented. This depression is related to tension along a segment of two strike-slip faults. Those two strike-slip faults consisting in the Northern Death Valley Fault Zone (NDVFZ) and the Southern Death Valley Fault Zone (SDVFZ), are characterized by en echelon traces [28] (Figure 1b). They have a general right-lateral movement, NW-SE oriented, from which results a "pull-apart" structure forming a N-S oriented basin [10] (Figure 1b). The area of interest for this study is the southern part of the Death Valley (DV) region, which extends for about 200 km. It is located southwest of the Basin and Range province [20], in the Eastern California Shear Zone/Walker Lane Belt (ECSZ/WLB) [21–23] (Figure 1a). DV is considered as one of the youngest regions where strike-slip deformation contemporaneously occurs with large-scale crustal extension within the Basin and Range province [24–26]. This extensional basin formation accompanying normal and associated strike-slip faulting would be active since 15 Ma according to [24]. It corresponds to a structural depression between the Panamit Range and the Black and Funeral Mountains [27] (Figure 1b), generally NNW-SSE oriented. This depression is related to tension along a segment of two strike-slip faults. Those two strike-slip faults consisting in the Northern Death Valley Fault Zone (NDVFZ) and the Southern Death Valley Fault Zone (SDVFZ), are characterized by en echelon traces [28] (Figure 1b). They have a general right-lateral movement, NW-SE oriented, from which results a "pull-apart" structure forming a N-S oriented basin [10] (Figure 1b).

The SDVFZ is composed of several branches. The SDVFZ formed the NH, at its southernmost part, by vertical displacement [29,30] (Figure 2a). It intersects the easttrending left lateral Garlock Fault Zone (GFZ), which ends at its western termination by the northwest-striking San Andreas fault zone [28] (Figure 1a). Recently, [11] suggested a net dextral slip along the SDVFZ of 40–41 km based on the offset positions of the granitebasement contact from the OM to the Avawatz Mountains. Much of the dextral slip, occurring before the deposition of the 6–8 Ma Neogene cover, is indicated by stratigraphic overlaps on fault rocks. This suggests an occurrence of the dextral slip during the main extension. The authors challenge the young feature of the DV pull-apart [25], by opting to a long-lived pull-apart which is consistent with regional evidence of the initiation in the middle Miocene of the dextral trans-tension in the ECSZ/WLB [31]. The SDVFZ is composed of several branches. The SDVFZ formed the NH, at its southernmost part, by vertical displacement [29,30] (Figure 2a). It intersects the easttrending left lateral Garlock Fault Zone (GFZ), which ends at its western termination by the northwest-striking San Andreas fault zone [28] (Figure 1a). Recently, [11] suggested a net dextral slip along the SDVFZ of 40–41 km based on the offset positions of the granitebasement contact from the OM to the Avawatz Mountains. Much of the dextral slip, occurring before the deposition of the 6–8 Ma Neogene cover, is indicated by stratigraphic overlaps on fault rocks. This suggests an occurrence of the dextral slip during the main extension. The authors challenge the young feature of the DV pull-apart [25], by opting to a long-lived pull-apart which is consistent with regional evidence of the initiation in the middle Miocene of the dextral trans-tension in the ECSZ/WLB [31].

**Figure 1.** (**a**) Simplified tectonic map of the Great Basin region (western U.S. Cordillera) showing the tectonic provinces (modified after [32]). WLB—Walker Lane Belt; ECSZ—Eastern California Shear Zone; GFZ—Garlock Fault Zone. The Basin and Range Province is represented in dark grey and the WLB/ECSZ in light grey. The red dashed line marks the limit between these both domains. The dark lines within the Basin and Range Province and in the WLB-ECSZ zone represent the main faults. (**b**) Structural setting of the Death Valley region (modified after [33,34]. AM—Avawatz **Figure 1.** (**a**) Simplified tectonic map of the Great Basin region (western U.S. Cordillera) showing the tectonic provinces (modified after [32]). WLB—Walker Lane Belt; ECSZ—Eastern California Shear Zone; GFZ—Garlock Fault Zone. The Basin and Range Province is represented in dark grey and the WLB/ECSZ in light grey. The red dashed line marks the limit between these both domains. The dark lines within the Basin and Range Province and in the WLB-ECSZ zone represent the main faults. (**b**) Structural setting of the Death Valley region (modified after [33,34]. AM—Avawatz Mountains; BM—Black Mountains; BMF—Black Mountains Fault; CM—Cottonwood Mountain; FM—Funeral Mountains; GM—Grapevine Mountains; OM—Owlshead Mountains; PM—Panamint Mountains; GFZ—Garlock Fault Zone; NDVFZ—Northern Death Valley Fault Zone; SDVFZ—Southern Death Valley Fault Zone.

#### *2.2. Noble Hills*

The NH extend 14 km northwest of the northern Avawatz Mountains [30] (Figure 2a,b). A first general geological map of the NH was provided by [35], and later completed by [29,36–38]. They show that Precambrian gneiss covered by Crystal Spring Formation (CSF), a siliclastic-carbonate unit [39] of the Pahrump Group, were first intruded by 1.1 Ga diabase sills then by Mesozoic granitic rocks. All of these facies form the axial crystalline ridge defined by [29].

The NH granite was poorly studied previously. It is part of the calc-alkaline granitoid intrusion related to the emplacement of the Sierra Nevada batholith, which was formed due to the eastward dipping subduction of the Pacific plate under the North American continent [40]. It was only defined as both quartz monzonite [35] and leucocratic adamellite [41]. Brady (1986) [29] completed the description as a medium to coarse equigranular grained to slightly porphyritic leucocratic rock containing few biotite and little or no hornblende. The presence of sporadic mineralization due to hydrothermal alteration was also raised by [38]. After the emplacement of the granite and its exhumation, ~3.34 Ma Pliocene sediments of the Noble Hills Formation (NHF) were deposited [38]. The NHF consists in interbedded fine-grained clastic and evaporitic rocks, alluvial conglomerates, minor limestone and megabreccia. Recent work done by [42] in the NH has shown a more complex geometry of the axial ridge than described until now (Figure 2c). The undifferentiated Precambrian and Paleozoic rocks facies were described by [42] as a stacking of different CSF series, intruded by the Mesozoic granite. They seem to be dragged and stretched southeastward against the granite following the SDVFZ trend. Tertiary volcanism was also highlighted at the back of the range.

Based on the geology along the SDVFZ trace, Pavlis and Trullenque (2021) [11] suggests that the NH axial crystalline ridge must be a transported part of the Cretaceous granitic pluton (~95 Ma), forming the OM [34], which is relatively weakly deformed internally at its southern part [26]. This piece would have moved a minimum of 8 km according to [29,37] and around 28 km according to [43] along the SDVFZ (Figure 2b). Brittle shearing and large-scale *boudinage* characterize a brittle deformation, showing generally subhorizontal axes, which is prevalent within the Cretaceous granitic intrusion and Precambrian roof pendants (Figure 2c). Contractional deformation involving all members of the NHF is characterized along the NH and increases in intensity southeast toward the intersection with the GFZ [38].

**Figure 2.** (**a**) Map presenting the structural setting of the southern part of the Death Valley region and the location of the Noble Hills range (NH) and the location of samples in the Owlshead Mountains (OM) represented by the white dots. (**b**) A scheme showing the displacement of the NH granite from the OM along the SDVFZ described by [11]. (**c**) The geological map of the Noble Hills range, modified after [38,42]. The quaternary is not displayed but available on [38] map. In (**a**,**b**), samples location for this study are represented by the white dots; the blue star corresponds to a sample from [34]. NHF— Noble Hills Formation. **Figure 2.** (**a**) Map presenting the structural setting of the southern part of the Death Valley region and the location of the Noble Hills range (NH) and the location of samples in the Owlshead Mountains (OM) represented by the white dots. (**b**) A scheme showing the displacement of the NH granite from the OM along the SDVFZ described by [11]. (**c**) The geological map of the Noble Hills range, modified after [38,42]. The quaternary is not displayed but available on [38] map. In (**a**,**b**), samples location for this study are represented by the white dots; the blue star corresponds to a sample from [34]. NHF—Noble Hills Formation.

#### **3. Material and Methods**

#### *3.1. Material and Sampling Strategy*

Fifteen samples from the NH granite and three samples from the OM granite (Figure 2) were collected in order to perform petrographical, mineralogical and geochemical characterizations. Hand specimens of centimetric size were collected in the two granite bodies (OM and NH) in order to characterize their mineralogical changes.

The selection of those samples through the NH was done under one scope, consisting of target zones away from the faults in order to avoid their influence. In that case, the magmatic texture is preserved. These faults are striking mainly NW/SE (SDVFZ direction) ([12], this issue). In order to be more precise in the sample selection, this latter was also based on the degrees of microfracturing defined by [44], from microscopical observations. This scale was improved by attributing a value of fracture density, based on scanlines realized on thin section mosaics, for each degree of microfracturing, which is described in the Methods section.

All the samples are georeferenced for database supply as well as located precisely (Figure 2). The OM being considered as the same batholith as the NH granite [11], samples were collected in an area unaffected by the SDVFZ activity in order to have a reference protolith of the studied area. Thin sections as well as powders were prepared to perform the following analyses.

#### *3.2. Methods*

#### 3.2.1. Microscopic Observations

A petrographical study performed on covered and polished thin-sections of 15 samples from the NH and two samples from the OM (OM\_1 and OM\_3), was realized at Institut Polytechnique UniLaSalle in Beauvais, using a Leica DM4500-P optical microscope equipped with a Leica DFC450C camera. Images were acquired thanks to the software Leica Application Suite (LAS) v4.11.0. The system is also equipped with a multistep acquisition program to perform thin section mosaics. It consists in the acquisition of several photos that follow each other in order to scan the whole thin section. At the end, the pictures are merged to obtain the mosaic. All the mineral abbreviations used in this paper refer to mineral symbols defined by [45]. The degree of mineral transformation into secondary minerals was defined based on optical observations.

#### 3.2.2. Fractures Density

The studied samples were selected away from fracture zones, but also according to a certain degree of microfracturing based on the scale defined by [44]. For this study, fractures density values were calculated for each degree of microfracturing by using thin section mosaics. For each mosaic, two scanlines [46,47] perpendicular to the main fractures were realized by digitalizing fractures along both lines. The P<sup>10</sup> [46] has been calculated for each scanline. It consists in the number of fracture intersects per line length of scanline. The average was calculated to obtain a value of fracture density attributed to each thin section mosaic and corresponding to each microfracturing degree defined by [44]:

Fd0 < 1687 fracs/m—no to very low microfracturing

Fd1 = 1687 fracs/m—microfracturing of order less than the grain size

Fd2 = 2694 fracs/m, with a multiplicator factor of 1.6—microfracturing of grain size order with interconnections

Fd3 = 3549 fracs/m, with a multiplicator factor of 1.3—abundant microfracturing

Fd4 ≥ 5140 fracs/m ([12] this issue), with a multiplicator factor of 1.4—very abundant microfracturing

Samples selected for this study have so a fracture density lower or equal to Fd2.

#### 3.2.3. SEM-EDS

Scanning Electron Microscope (Hitachi S-3400N SEM) equipped with a Thermo Ultradry Energy Dispersive X-ray Spectrometer (EDS) probe was used on two polished

thin sections and one hand specimen at Institut Polytechnique UniLaSalle in Beauvais. It aimed at analyzing the microstructure characteristics and to perform qualitative and semi-quantitative chemical analyses of various selected mineral phases.

A NORAN-type correction (©Thermo Fisher Scientific, Waltham, MA, USA) procedure was used for all data and all Fe was assumed to be ferrous for simplification. Polished thin sections were analyzed using a 50 µA beam current, an accelerating voltage of 20 kV and an acquisition time of 30 s.

#### 3.2.4. X-ray Diffraction (XRD)

#### Experimental Conditions

XRD analyses were performed at Institut UniLaSalle Beauvais on the 15 samples from the NH and one sample from the OM (OM\_2) using a D8-Advance Bruker-AXS (Siemens, Munich, Germany) diffractometer with a Ni-filtered CuKα radiation at 40 kV and 40 mA, a primary soller slit of 2.5◦ , divergence slit of 0.6 mm and a secondary soller slit of 2.5◦ , with a detector slit of 0.1 mm and an antiscattering slit of 0.6 mm. Samples were crushed with an agate pestle and mortar. Quantitative phase analysis based on Reference Intensity Ratio values were performed on randomly oriented bulk rock powders with a step length of 0.5◦ and a scan speed of 0.014◦/s over the range 3◦–70◦2θ for bulk rocks composition. The uncertainty is estimated to be around 5%.

#### Determination of Illite Crystallinity and Kübler Index

XRD investigations were carried out on bulk rock powder specimens and clay fractions of 16 samples in order to identify and determine the relative abundance of mineral phases (semi-quantitative, around 3–5%) observed upstream under the optical microscope and the SEM. Clay mineral separation was conducted using techniques described by [48], following the recommendations of [49], and according to the standard techniques suggested by [50]. It consists into the collection of the <2 µm and 2–6 µm fractions from the sample powders put in suspension into water in decantation tubes. Oriented slides were then prepared by pipetting suspension onto glass slides (5 mg/cm<sup>2</sup> ) and air-drying. XRD measurements were then performed at air dried, solvated with ethylene glycol, and after heating (550 ◦C) conditions with a step length of 0.5◦ and a speed of 0.01◦/s per step over the range 3◦–35◦2θ. The clay minerals identification, which is based on d-values and the relative intensity of their 00*l* peak reflections, was undertaken referring to [51,52]. The illite "crystallinity" (IC), defined as the full width at half maximum (FWHM) of the 10 Å (001) peak of illite, was calculated using the software DIFFRAC EVA v 4.2 (by ©Bruker AXS, Billerica, MA, USA). The obtained values were standardized using the crystallinity index-standard (CIS) samples of [53] in order to calculate the Kübler Index (KI). The KI values of raw data expressed in ∆ ◦2θ, were measured into three slots, corresponding to different campaigns, inducing the three following standardizations:

$$\text{KI}\_{\text{(ULSI)}} = 1.6987 \times \text{IC}\_{\text{measured}} - 0.0842 \text{ (R}^2 = 0.9724) \tag{1}$$

$$\text{KI}\_{\text{(ULS2)}} = 1.5501 \times \text{IC}\_{\text{measured}} - 0.0512 \text{ (R}^2 = 0.9944\text{)}\tag{2}$$

$$\text{KI}\_{\text{(ULS3)}} = 1.5337 \times \text{IC}\_{\text{measured}} - 0.0498 \text{ (R}^2 = 0.9975\text{)}\tag{3}$$

KI was used to define the limits of metamorphic zones [54], following the recommendations for Kübler-Index calibration of [50] and the CIS-KI transformation formalism of [55]. In siliciclastic rocks, the transitions from non-metamorphic to low-grade (referring to the term greenschist facies [56]) and from the very low-grade (chlorite zone [57]) to low-grade metamorphic zone (biotite zone [58]) take place through three zones defined by [13]: the diagenetic zone, the anchizone and the epizone. The zone boundary values are presented in Table 1. The smallest FWHM able to be measured by our diffractometer (limit detection) is 0.08∆ ◦2θ.


**Table 1.** Metamorphic zone boundaries [59] for Kübler Index (KI) values [55] and temperatures [60].

#### 3.2.5. ICP-MS—ICP-AES

The analyses of major, trace and rare earth elements were completed on five selected samples from the NH (NH\_1, NH\_2, NH\_3, NH\_4 and NH\_12) and one from the OM (OM\_3) by Bureau Veritas Minerals (Vancouver, Canada) using ICP-ES and ICP-MS.

Samples were crushed and mixed with LiBO2/LiB4O<sup>7</sup> flux. Crucibles were fused in a furnace at 980 ◦C. Then, the cooled bead was dissolved in ACS grade nitric acid and analyzed by ICP-AES and/or ICP-MS. Loss on ignition (LOI) was determined by igniting the samples split then measuring the weight loss.

#### 3.2.6. Manocalcimetry

Calcite contents were determined using an OFITE 152-95 manocalcimeter. The analyses were performed on 15 samples from the NH and one sample from the OM at CY Cergy Paris University in the Geosciences and Environment Cergy (GEC) laboratory. It provides an indication of the total carbonate content in a sample and allows to assess the influence of calcite on permeability of the fluid pathways. This is achieved by measuring the rate of response of 10% hydrochloric acid on the samples. Calcimetry has also proved to be an efficient, easy and low-cost method to better understand the hydrothermal sealing of a reservoir [61].

Manocalcimetry consists into the measurements of CO<sup>2</sup> partial pressure when calcite is dissolved by HCl. The reaction that occurs is:

$$\text{CaCO}\_{\text{3(s)}} + 2\text{HCl}\_{\text{(l)}} \rightleftharpoons \text{CO}\_{\text{2(g)}} + \text{H}\_2\text{O}\_{\text{(l)}} + \text{CaCl}\_2\tag{4}$$

The calcimeter, composed of a glass flask and a high precision manometer calibrated with pure calcite reduced into fine powder. This allows us to determine the calcimeter coefficient. Variation of temperature and pressure can cause uncertainty on measurements, which was considered to obtain high quality results with a precision around 0.5 wt.%.

Prior to measurements, sample preparation was done according to [61]. The samples were reduced into powder in an agate mortar and put in the oven at 60 ◦C for 24 h. Then, 1.000 g of each sample was weighed and put in a sample holder, itself put in the calcimeter with a little glass filled with HCl. The amount of HCl is in excess in order to dissolve all the calcite present in the sample. The maximum value reached during the measurement was read on the manometer and the CaCO<sup>3</sup> percentage was determined as follows:

$$\% \text{CaCO}\_3 = \text{(Measured value} \times 100)/\text{Calcimeter coefficient} \tag{5}$$

Two replicates were performed for each sample in order to check the reproducibility of the results, which is considered as good when the difference between the two results is lower than 0.5 wt.%, corresponding to the precision interval mentioned above.

#### 3.2.7. Ethanol Saturation Porosimetry

The estimation of available volume for fluid storage is fundamental and can be quantified by porosity measurements [62]. The connected porosity was measured on 6 samples from the NH and one from the OM by the triple weighing method [63] defined by the RILEM standard (test n◦ I.1, 1978). It consists in the saturation of the samples after vacuum degassing. The measurements were carried out at CY Cergy Paris University in the Laboratory of Mechanics and Materials for Civil Engineering (L2MGC).

In this study, ethanol has been chosen instead of water, as used in classical methods, in order to avoid possible clay swelling [64], which could lead to the destruction of the sample and biased results. Even though ethanol (0.469 nm) is a molecule larger than that of water (0.343 nm), the pore volume is not estimated to be under-evaluated, as the pore size is much larger than that of ethanol molecules. The samples were first oven-dried at approximately 40 ◦C until obtaining a constant weight (W1). Samples were then soaked by capillary action with ethanol after staying for 12 h under a vaccum. When the samples were completely immersed, the vacuum was stopped and the samples left in the ethanol for 24 h. Finally, they were weighted twice: (1) weighing of saturated samples, W2; and (2) weighing of samples under "ethanostatic" conditions (suspended into ethanol under the balance), W3. The connected porosity φ is then calculated:

$$
\Phi(\%) = (W2 - W1/W2 - W3) \times 100\tag{6}
$$

#### **4. Results**

*4.1. Petrographic Description*

4.1.1. The Owlshead Granite

Samples of the OM granite appear rather fresh, meaning that primary minerals seem not transformed into secondary ones and present no sign of deformation. They show a light grey/whitish and yellowish granite (Figure 3a) with equant medium-size grains (0.1–1 cm). Primary assemblage is composed of plagioclase, quartz, K-feldspar and biotite. Biotite is generally surrounded by a yellowish oxide halo, showing its incipient alteration.

OM granite microscopic observations (Figure 3b,c, Table 2) confirm the freshness of the rock as well as the very low to absent microfracturing. Figure 3b shows a microfracturing around Fd1 (Table 2). Most of the fractures are open and a few of them are filled by calcite. Calcite is also present at the grain boundaries (Figure 4a,b).

Regarding mineralogical composition, plagioclase (35%, modal composition) occurs subautomorphous crystals, up to 5 mm, of oligoclase composition with an oscillatory zonation [65] (Figure 3b). Quartz (35%) forms up to 2 cm polycrystalline clusters of anhedral crystals which range up to 1 cm and present a slight rolling extinction. K-feldspar (25%) occurs as centimetric subautomorphous crystals of microcline and orthoclase with a Carlsbad twin, rich in perthites (albite vein or braid/patch shape [65] (Figure 4a,b). Kfeldspar crystals can contain plagioclase and biotite inclusions. Biotite (5%) of around 2 mm in length is euhedral. Primary opaque minerals (<1%) are also found in this granite.

The core of plagioclase is slightly transformed into K-white mica (Figures 3c and 4c,d). They will be represented as Wm. Quartz and K-feldspar are not affected by the alteration and are only little undeformed as seen on quartz showing undulatory extinction (Figure 4a). Biotite can be slightly altered. Few epidotes are present nearby the biotite (Figure 4e,f).

Microscopic observations of samples OM\_3 and OM\_1 are consistent with whole rock XRD analyses performed on the sample OM\_2 from the OM granite. The three samples have a similar mineralogical composition and are grouped together in Table 2.

**Figure 3.** Macroscale to microscale photographs illustrating (**a**–**c**) the Owlshead and (**d**–**f**) the Noble Hills granites. (**a**,**d**) Hand specimens for each granite showing their different aspects. (**b**,**e**) Thin section mosaics realized for each granite under optical microscope in polarized—analyzed light and showing the difference in terms of grain size and microfracturing. (**c**,**f**) Thin sections zooms of each granite mosaic in polarized—analyzed light showing the difference in terms of alteration degree. Abbreviations (except for "Wm") after [45]: Bt—Biotite, Kfs—K-feldspar, Wm—K-white mica, Pl—Plagioclase, Qtz—Quartz. **Figure 3.** Macroscale to microscale photographs illustrating (**a**–**c**) the Owlshead and (**d**–**f**) the Noble Hills granites. (**a**,**d**) Hand specimens for each granite showing their different aspects. (**b**,**e**) Thin section mosaics realized for each granite under optical microscope in polarized—analyzed light and showing the difference in terms of grain size and microfracturing. (**c**,**f**) Thin sections zooms of each granite mosaic in polarized—analyzed light showing the difference in terms of alteration degree. Abbreviations (except for "Wm") after [45]: Bt—Biotite, Kfs—K-feldspar, Wm—K-white mica, Pl—Plagioclase, Qtz—Quartz.

OM granite microscopic observations (Figure 3b,c, Table 2) confirm the freshness of the rock as well as the very low to absent microfracturing. Figure 3b shows a microfracturing around Fd1 (Table 2). Most of the fractures are open and a few of them are

filled by calcite. Calcite is also present at the grain boundaries (Figure 4a,b).

*Geosciences* **2021**, *11*, 325

**Table 2.** List of samples collected in the field with their mineralogical composition determined after microscopic observations and XRD analysis (primary minerals, alteration phases for plagioclase, biotite and K-feldspar, other secondary minerals and microfissuring after Castaing and Rabu scale). Abbreviations (except for "Ox and Wm") after [45]: Qtz—Quartz, Pl—Plagioclase, Mc—Microcline, Or—Orthoclase, Bt—Biotite, Kln—Kaolinite, Ep—Epidote, Ox—Oxide (when it could not be determined precisely), Wm—K-white mica, Cal—Calcite, Dol—Dolomite, Hem-Hematite, Gp—Gypsum, Fd—Fracture density.


143

**Figure 4.** Photomicrographs of the Owlshead granite in polarized-analyzed and polarized—nonanalyzed light showing (**a**,**b**) perthitic and unaltered orthoclase, unaltered quartz presenting a slight undulatory extinction and calcite veinlets at grain boundaries. (**c**,**d**) Plagioclase alteration with the formation of K-white mica. (**e**,**f**) Incipient biotite alteration associated to hematite and epidote formation. Abbreviations (except for "Wm") after [45]: Bt—Biotite, Cal—Calcite, Ep—Epidote, Hem—Hematite, Kfs—K-feldspar, Wm—K-white mica, Pl—Plagioclase, Qtz—Quartz. **Figure 4.** Photomicrographs of the Owlshead granite in polarized-analyzed and polarized—nonanalyzed light showing (**a**,**b**) perthitic and unaltered orthoclase, unaltered quartz presenting a slight undulatory extinction and calcite veinlets at grain boundaries. (**c**,**d**) Plagioclase alteration with the formation of K-white mica. (**e**,**f**) Incipient biotite alteration associated to hematite and epidote formation. Abbreviations (except for "Wm") after [45]: Bt—Biotite, Cal—Calcite, Ep—Epidote, Hem—Hematite, Kfs—K-feldspar, Wm—K-white mica, Pl—Plagioclase, Qtz—Quartz.

#### 4.1.2. The Noble Hills Granite

Far from the major faults, the NH granite appears, as a whole, microfractured and altered. with preserved "fresh" zones. The collected hand specimens (Figure 2b) are equant to slightly porphyritic and display a pinkish color (Figure 3d) or a whitish color for the samples with evidences of alteration. Primary assemblage, as for the OM granite, is made of plagioclase, quartz, K-feldspar and biotite.

At the microscale, the degree of microfracturing ranges from Fd0–1 to Fd2 (Table 2). As for the OM granite, the microfractures can be opened or filled by carbonates. As regards mineralogical composition, plagioclase (~35%, oligoclase in composition) occurs as sub-anhedral to euhedral crystals (up to 5 mm in length) showing growth zonation (see Figure 3f and [65]). Quartz (~30%) forms polycrystalline euhedral clusters of around 1 cm in size made of 3-mm-wide crystals with sometimes a slight undulatory extinction linked to low deformation. K-feldspar (~25%) is made of sub-anhedral to euhedral orthoclase

(up to 1 cm in length) with vein shaped perthites [65]. Microcline is only present in the samples NH\_12 and NH\_14, in the southern part of the range (Figure 2 and Table 2). Some K-feldspar crystals contain inclusions of plagioclase or/and biotite. Depending on the samples, the amount of plagioclase can be equivalent to that of K-feldspar (~30% each), but most of the time, plagioclase dominate. Myrmekite can be observed at the interface between plagioclase and K-feldspar. Biotite (~10%) appears euhedral with crystals ~2 mm in length. Accessory minerals (<1%) as apatite are also observed. More rarely, primary muscovite, as well as primary opaque minerals (oxides) are observed in the granite. A comparison between the NH and the OM granites highlights a grain size difference. Quartz and Kfeldspar crystals are smaller in the NH granite (up to 3 mm and 1 cm respectively, Figure 3e) than in the OM granite (up to 1 cm and centimetric crystals respectively, Figure 3b).

Primary minerals, function of their sensitivity to alteration [65], recrystallized into secondary minerals which are shown in Table 2. This is related to differences into chemical properties [66]. In the plagioclase, which is the most altered mineral (Figure 5), recrystallization propagate from the core of the crystal to the more albitic rim (Figure 5a) [67]. When alteration is intense, plagioclase is entirely replaced by newly formed minerals leaving only the pseudomorph of the plagioclase to subsist (Figure 5d). The newly formed minerals are the following:


Illite and kaolinite can be present together in the same sample (Figure 5d).

The K-feldspar remains always unaffected (Figure 5d), but when the alteration is relatively pronounced, perthites can be altered as well as the mineral inclusions like in sample NH\_3 Table 2). Biotite is progressively replaced by K-white mica (illite) as compared to the biotite in the OM granite (Table 2). K-white mica crystallizes along the cleavages and can be associated to the crystallization of oxides, as hematite, also along the cleavages (Figure 6).

**Table 3.** List of samples with their respective clay minerals composition, FWHM and Kübler Index (KI) for the fractions < 2 µm and 2–6 µm. Abbreviations (except for "Cor") after [45]: Ill—Illite, Kln—Kaolinite, Cor—Corrensite, I/S— Illite/Smectite, Vrm—Dioctahedral Vermiculite, Bt—Biotite, Mnt—Montmorillonite, AD—Air-dried.


*Geosciences* **2021**, *11*, 325 14 of 34

**Figure 5.** Photomicrographs showing the plagioclase transformation progress in the Noble Hills granite. (**a**) Progressive illitization of plagioclase initiating in the core of the mineral under optical microscope in polarized—analyzed light. (**b**) Needles shape illite replacing plagioclase in polarized—analyzed light under optical microscope. (**c**) Back-scattered electron image of needles/flakes shape illite replacing plagioclase. (**d**) Plagioclase completely replaced by illite, kaolinite and calcite and non-altered K-feldspar under optical microscope in polarized—analyzed light. (**e**) Back-scattered electron image showing a fan shape kaolinite, calcite and oxide veinlet. (**f**) Back-scattered electron image showing a magnified view of a single mineral of kaolinite under SEM. Abbreviations (except for "Ox") after [45]: Ap—Apatite, Bt—Biotite, Cal—Calcite, Ill—Illite, Kln—Kaolinite, Kfs—K-feldspar, Ox—Oxides, Pl—Plagioclase, Qtz—Quartz. **Figure 5.** Photomicrographs showing the plagioclase transformation progress in the Noble Hills granite. (**a**) Progressive illitization of plagioclase initiating in the core of the mineral under optical microscope in polarized—analyzed light. (**b**) Needles shape illite replacing plagioclase in polarized—analyzed light under optical microscope. (**c**) Back-scattered electron image of needles/flakes shape illite replacing plagioclase. (**d**) Plagioclase completely replaced by illite, kaolinite and calcite and non-altered K-feldspar under optical microscope in polarized—analyzed light. (**e**) Back-scattered electron image showing a fan shape kaolinite, calcite and oxide veinlet. (**f**) Back-scattered electron image showing a magnified view of a single mineral of kaolinite under SEM. Abbreviations (except for "Ox") after [45]: Ap—Apatite, Bt—Biotite, Cal—Calcite, Ill—Illite, Kln—Kaolinite, Kfs—K-feldspar, Ox—Oxides, Pl—Plagioclase, Qtz—Quartz. The K-feldspar remains always unaffected (Figure 5d), but when the alteration is relatively pronounced, perthites can be altered as well as the mineral inclusions like in sample NH\_3 Table 2). Biotite is progressively replaced by K-white mica (illite) as compared to the biotite in the OM granite (Table 2). K-white mica crystallizes along the cleavages and can be associated to the crystallization of oxides, as hematite, also along the cleavages (Figure 6).

*Geosciences* **2021**, *11*, 325 15 of 34

**Table 3.** List of samples with their respective clay minerals composition, FWHM and Kübler Index (KI) for the fractions < 2µm

NH\_7 + + − + + − + 1.01 1.63 0.71 1.13 NH\_8 + + + + ++ + 1.10 1.79 1.18 1.93 NH\_9 + + ++ + + ++ 0.85 1.36 0.56 0.87 NH\_10 + − ++ + − ++ 0.46 0.65 0.51 0.73 NH\_11 ++ − + ++ + + 0.67 1.05 0.62 0.97 **Figure 6.** Photomicrographs showing a biotite completely altered and replaced by oxides and Kwhite mica (essentially illite) according to the cleavage planes (**a**) in polarized—analyzed light under optical microscope and (**b**) in polarized—analyzed light under optical microscope. Abbreviations (except for "Ox and Wm") after [45]: Bt—Biotite, Cal—Calcite, Kfs—K-feldspar, Wm—K-white mica, Ox—Oxides, Pl—Plagioclase, Qtz—Quartz. **Figure 6.** Photomicrographs showing a biotite completely altered and replaced by oxides and Kwhite mica (essentially illite) according to the cleavage planes (**a**) in polarized—analyzed light under optical microscope and (**b**) in polarized—analyzed light under optical microscope. Abbreviations (except for "Ox and Wm") after [45]: Bt—Biotite, Cal—Calcite, Kfs—K-feldspar, Wm—K-white mica, Ox—Oxides, Pl—Plagioclase, Qtz—Quartz.

NH\_13 + − + + − + 0.46 0.69 0.38 0.56 NH\_14 + −− − + + −− − + 0.59 0.92 0.44 0.66 NH\_15 + − + + − − 0.69 1.08 0.50 0.77 All the samples are plotted in the Streckeisen ternary diagram (Figure 7) [68]. The OM and NH granites of this study are both defined as monzogranites. The OM sample analyzed by [34] (Figure 2a, blue star) shows a different composition (Figure 7, blue star). It is rather a monzonite, as defined by [34], than a monzogranite, as defined in this study. All the samples are plotted in the Streckeisen ternary diagram (Figure 7) [68]. The OM and NH granites of this study are both defined as monzogranites. The OM sample analyzed by [34] (Figure 2a, blue star) shows a different composition (Figure 7, blue star). It is rather a monzonite, as defined by [34], than a monzogranite, as defined in this study.

**Figure 7.** Normative composition of one sample from the OM and 4 samples from the NH in a QAP

Clay minerals from the <2 µm and 2–6 µm fractions were separated. The clay composition of both fractions of each studied sample (OM and NH) is given in Table 3,

Illite and kaolinite can be present together in the same sample (Figure 5d).

(Quartz-Alkali-feldspar-Plagioclase) ternary diagram [68].

4.1.3. Clay Minerals Identification and Kübler INDEX

based on [51].

NH\_12 ++ + − ++ + − 0.57 0.89 0.46 0.69

mica, Ox—Oxides, Pl—Plagioclase, Qtz—Quartz.

**Figure 7.** Normative composition of one sample from the OM and 4 samples from the NH in a QAP (Quartz-Alkali-feldspar-Plagioclase) ternary diagram [68]. **Figure 7.** Normative composition of one sample from the OM and 4 samples from the NH in a QAP (Quartz-Alkali-feldspar-Plagioclase) ternary diagram [68].

The K-feldspar remains always unaffected (Figure 5d), but when the alteration is relatively pronounced, perthites can be altered as well as the mineral inclusions like in sample NH\_3 Table 2). Biotite is progressively replaced by K-white mica (illite) as compared to the biotite in the OM granite (Table 2). K-white mica crystallizes along the cleavages and can be associated to the crystallization of oxides, as hematite, also along the

**Figure 6.** Photomicrographs showing a biotite completely altered and replaced by oxides and Kwhite mica (essentially illite) according to the cleavage planes (**a**) in polarized—analyzed light under optical microscope and (**b**) in polarized—analyzed light under optical microscope. Abbreviations (except for "Ox and Wm") after [45]: Bt—Biotite, Cal—Calcite, Kfs—K-feldspar, Wm—K-white

All the samples are plotted in the Streckeisen ternary diagram (Figure 7) [68]. The OM and NH granites of this study are both defined as monzogranites. The OM sample analyzed by [34] (Figure 2a, blue star) shows a different composition (Figure 7, blue star). It is rather a monzonite, as defined by [34], than a monzogranite, as defined in this study.

#### 4.1.3. Clay Minerals Identification and Kübler INDEX 4.1.3. Clay Minerals Identification and Kübler INDEX

Clay minerals from the <2 µm and 2–6 µm fractions were separated. The clay composition of both fractions of each studied sample (OM and NH) is given in Table 3, based on [51]. Clay minerals from the <2 µm and 2–6 µm fractions were separated. The clay composition of both fractions of each studied sample (OM and NH) is given in Table 3, based on [51]. *Geosciences* **2021**, *11*, 325 16 of 34

#### Owlshead Mountains Owlshead Mountains

Noble Hills

< 2 µm fraction (Figure 9):

corrensite after [51].

cleavages (Figure 6).

The OM sample clay analyses confirm the presence of illite observed under optical microscope. They also reveal the pattern of montmorillonite (Mnt) [51], a common smectite (Figure 8). Its very intense 001 peak allows the determination of its amount representing 15% of the clay fraction. This peak is characterized by a shift from 14.87 Å (air-dried) to 16.90 Å after glycol solvation and it collapses at 10.09 Å after heating. After glycol solvation, new peaks appear at 5.61 Å and 8.46 Å. The OM sample clay analyses confirm the presence of illite observed under optical microscope. They also reveal the pattern of montmorillonite (Mnt) [51], a common smectite (Figure 8). Its very intense 001 peak allows the determination of its amount representing 15% of the clay fraction. This peak is characterized by a shift from 14.87 Å (air-dried) to 16.90 Å after glycol solvation and it collapses at 10.09 Å after heating. After glycol solvation, new peaks appear at 5.61 Å and 8.46 Å .

Two typical XRD patterns of clay minerals are identified in the NH samples for the

shifting to 15.62 Å after glycol solvation and collapses to 11.72 Å after heating, and (2) new peaks at 7.78 Å , 5.15 Å and 3.44 Å appear after glycol solvation and disappear after heating. The corrensite found in the NH granite is considered as a low charge

Corrensite, kaolinite and illite are identified in the first pattern, where corrensite is

 Illite/smectite (I/S) mixed-layer, kaolinite and illite (Figure 9b) are identified in the second pattern, where I/S is illite-rich (R3), with more than 90% of illite and R representing the Reichweite parameter [70]. I/S is characterized by a large peak at 10.08 Å in air-dried, becoming narrower when it collapses to 9.93 Å after glycol

solvation and by a peak at 5 Å swelling after glycol solvation.

**Figure 8.** XRD result obtained for the clay fraction < 2 µm in Air-Dried (AD), Glycolated (G) and Heated (H) of the samples in the OM granite and showing a montmorillonite (Mnt) pattern. **Figure 8.** XRD result obtained for the clay fraction < 2 µm in Air-Dried (AD), Glycolated (G) and Heated (H) of the samples in the OM granite and showing a montmorillonite (Mnt) pattern.

#### Noble Hills

Two typical XRD patterns of clay minerals are identified in the NH samples for the <2 µm fraction (Figure 9):


**Figure 9.** XRD patterns obtained for the clay fraction < 2µm in Air-Dried (AD), Glycolated (G) and Heated (H) for the NH granite and showing the clay composition of the samples in the NH granite: (**a**) corrensite (Cor), a chlorite/smectite mixedlayer, and (**b**) illite/smectite mixed-layer (I/S). Abbreviations (except for "Cor and I/S") after [45]: Bt—Biotite, Kln— Kaolinite, Qtz—Quartz, Ill–Illite. **Figure 9.** XRD patterns obtained for the clay fraction < 2µm in Air-Dried (AD), Glycolated (G) and Heated (H) for the NH granite and showing the clay composition of the samples in the NH granite: (**a**) corrensite (Cor), a chlorite/smectite mixed-layer, and (**b**) illite/smectite mixed-layer (I/S). Abbreviations (except for "Cor and I/S") after [45]: Bt—Biotite, Kln—Kaolinite, Qtz—Quartz, Ill–Illite.

In the NH KI values range from 2.25Δ°2θ to 0.43 Δ°2θ for the <2 µm fraction and from 1.93Δ°2θ to 0.44Δ°2θ for the 2–6 µm fraction (Table 3). The spatial distribution of the samples and the KI values are shown in Figure 10. A NW to SE decrease in KI values in the main granitic body is distinguishable in the <2 µm fraction (Figure 10a) and confirmed in the 2–6 µm fraction (Figure 10b). In the NH KI values range from 2.25∆ ◦2θ to 0.43∆ ◦2θ for the <2 µm fraction and from 1.93∆ ◦2θ to 0.44∆ ◦2θ for the 2–6 µm fraction (Table 3). The spatial distribution of the samples and the KI values are shown in Figure 10. A NW to SE decrease in KI values in the main granitic body is distinguishable in the <2 µm fraction (Figure 10a) and confirmed in the 2–6 µm fraction (Figure 10b).

*Geosciences* **2021**, *11*, 325 18 of 34

**Figure 10.** Geological map (see Figure 2b) representing the Kübler Index (KI) in air dried conditions of each sample and the corresponding metamorphic zone showed by the color of the dots for (**a**) the fraction < 2µm and (**b**) the fraction 2–6 µm. **Figure 10.** Geological map (see Figure 2b) representing the Kübler Index (KI) in air dried conditions of each sample and the corresponding metamorphic zone showed by the color of the dots for (**a**) the fraction < 2µm and (**b**) the fraction 2–6 µm.

#### *4.2. Geochemical Analyses 4.2. Geochemical Analyses* 4.2.1. Major Element Bulk Rock Chemistry

4.2.1. Major Element Bulk Rock Chemistry Major element geochemistry (Table 4) allows classifying the granite samples in

Major element geochemistry (Table 4) allows classifying the granite samples in different diagrams (Figures 11 and 12). different diagrams (Figures 11 and 12).


MnO 0.08 0.09 0.08 0.12 0.08

**Table 4.** Major elements of the Owlshead and Noble Hills granites. **Table 4.** Major elements of the Owlshead and Noble Hills granites. **Sample ID OM\_3 NH\_10 NH\_1 NH\_2 NH\_3**

*Geosciences* **2021**, *11*, 325 19 of 34

**Figure 11.** (**a**) Total alkali versus silica diagram ([71] adopted for plutonic rocks by [72]). (**b**) AFM (Alkali-Fe2O3-MgO) classification diagram established by [73]. (**c**) A/CNK (Al2O3/(CaO + Na2O + K2O)) versus silica diagram. The blue star corresponds to a sample from the OM analyzed by [34]. **Figure 11.** (**a**) Total alkali versus silica diagram ([71] adopted for plutonic rocks by [72]). (**b**) AFM (Alkali-Fe2O<sup>3</sup> -MgO) classification diagram established by [73]. (**c**) A/CNK (Al2O3/(CaO + Na2O + K2O)) versus silica diagram. The blue star corresponds to a sample from the OM analyzed by [34].

In the Na2O + K2O versus SiO<sup>2</sup> classification (called TAS) diagram of [71], modified after [72] for plutonic rocks, all the samples plot in the sub-alkalic domain. They all have a granite composition close to the granodiorite zone (Figure 11a). However, the sample from [34] plots in the syenite field, while it plots in the monzonite field in the Streckeisen diagram (Figure 7). The AFM triangular plot classifies all the samples as calc-alkaline In the Na2O + K2O versus SiO<sup>2</sup> classification (called TAS) diagram of [71], modified after [72] for plutonic rocks, all the samples plot in the sub-alkalic domain. They all have a granite composition close to the granodiorite zone (Figure 11a). However, the sample from [34] plots in the syenite field, while it plots in the monzonite field in the Streckeisen diagram (Figure 7). The AFM triangular plot classifies all the samples as calc-alkaline

(Figure 11b). The silica content of the OM granite 74.65 wt.% is higher than that of the NH

(Figure 11b). The silica content of the OM granite 74.65 wt.% is higher than that of the NH granite which ranges from 68.54 to 69.56 wt.%. According to the SiO<sup>2</sup> versus A/CNK diagram (Figure 11c) [74], all the samples are peraluminous rocks, and are found rather far from the boundary with metaluminous S-type granites, with a A/CNK between 1.4 and 1.6 wt.%. Harker diagrams complete the information by showing a high content of K2O ranging from 3.6 to 4.43 wt.%, and plot the samples in the high-K calc-alkaline domain (Figure 12a) which limits where defined by [75]. However, the OM sample has a lower Al2O<sup>3</sup> content (12.9 wt.%) than the NH samples (14.53–15.36 wt.%) forming a separate cluster (Figure 12b). Again, the sample from [45] (DVB-114A—blue star) shows a large difference in composition compared to OM\_3. granite which ranges from 68.54 to 69.56 wt.%. According to the SiO<sup>2</sup> versus A/CNK diagram (Figure 11c) [74], all the samples are peraluminous rocks, and are found rather far from the boundary with metaluminous S-type granites, with a A/CNK between 1.4 and 1.6 wt.%. Harker diagrams complete the information by showing a high content of K2O ranging from 3.6 to 4.43 wt.%, and plot the samples in the high-K calc-alkaline domain (Figure 12a) which limits where defined by [75]. However, the OM sample has a lower Al2O<sup>3</sup> content (12.9 wt.%) than the NH samples (14.53–15.36 wt.%) forming a separate cluster (Figure 12b). Again, the sample from [45] (DVB-114A—blue star) shows a large difference in composition compared to OM\_3.

*Geosciences* **2021**, *11*, 325 20 of 34

**Figure 12.** Harker diagrams showing the variation of (**a**) K2O [75] and (**b**) Al2O<sup>3</sup> in the OM and NH granites. A sample from the OM analyzed by [34] is represented by the blue star **Figure 12.** Harker diagrams showing the variation of (**a**) K2O [75] and (**b**) Al2O<sup>3</sup> in the OM and NH granites. A sample from the OM analyzed by [34] is represented by the blue star.

The loss on ignition (LOI) is of 0.7 wt.% for the OM granite and ranges from 1.1 to 2.8 wt.% for the NH granite (Table 5), showing that the OM granite contains less volatile elements than the NH granite, even for the freshest samples (NH\_10, NH\_1 and NH\_2). By comparing the alteration degree of each sample estimated from optical observations of plagioclase and biotite (Table 5) and the LOI values, we note that a low LOI corresponds to a slight alteration, e.g., OM\_3 or NH\_2 and a high LOI corresponds to a more pronounced alteration, e.g., NH\_3. The loss on ignition (LOI) is of 0.7 wt.% for the OM granite and ranges from 1.1 to 2.8 wt.% for the NH granite (Table 5), showing that the OM granite contains less volatile elements than the NH granite, even for the freshest samples (NH\_10, NH\_1 and NH\_2). By comparing the alteration degree of each sample estimated from optical observations of plagioclase and biotite (Table 5) and the LOI values, we note that a low LOI corresponds to a slight alteration, e.g., OM\_3 or NH\_2 and a high LOI corresponds to a more pronounced alteration, e.g., NH\_3.

**Table 5.** Loss on ignition values compared to the alteration degree of plagioclase and biotite estimated under optical microscope. **Table 5.** Loss on ignition values compared to the alteration degree of plagioclase and biotite estimated under optical microscope.


In diagrams representing selected major elements versus the LOI (Figure 13), LOI values of NH samples show a positive correlation with K2O and a negative correlation with Na2O and CaO. SiO<sup>2</sup> and Al2O<sup>3</sup> contents are approximately constant, 68.54–69.56 wt.% and 14.53–15.36 wt.% respectively. MgO content varies a lot (0.56–1.15 wt.%) showing no clear correlation with the LOI. K2O and Na2O contents of the OM granite are equivalent to those of the freshest NH granites (NH\_2, NH\_10 and NH\_1). However, the OM granite sample presents a higher amount of SiO<sup>2</sup> and a lower amount of Al2O3, CaO and MgO. The chemistry of the OM granite seems different from that of the NH granite regarding Figures 12 and 13 even though, according to [11], the NH granite derived from the OM granite. In diagrams representing selected major elements versus the LOI (Figure 13), LOI values of NH samples show a positive correlation with K2O and a negative correlation with Na2O and CaO. SiO<sup>2</sup> and Al2O<sup>3</sup> contents are approximately constant, 68.54–69.56 wt.% and 14.53–15.36 wt.% respectively. MgO content varies a lot (0.56–1.15 wt.%) showing no clear correlation with the LOI. K2O and Na2O contents of the OM granite are equivalent to those of the freshest NH granites (NH\_2, NH\_10 and NH\_1). However, the OM granite sample presents a higher amount of SiO<sup>2</sup> and a lower amount of Al2O3, CaO and MgO. The chemistry of the OM granite seems different from that of the NH granite regarding Figures12and 13even though, according to [11], the NH granite derived from the OM granite.

*Geosciences* **2021**, *11*, 325 21 of 34

**Figure 13.** Plot of selected major element oxides (SiO2, K2O, Al2O3, Na2O, CaO and MgO) versus LOI (loss on ignition). **Figure 13.** Plot of selected major element oxides (SiO<sup>2</sup> , K2O, Al2O<sup>3</sup> , Na2O, CaO and MgO) versus LOI (loss on ignition).

#### 4.2.2. Trace Element and REE Bulk Chemistry 4.2.2. Trace Element and REE Bulk Chemistry

Trace elements and Rare Earth Elements (REE) (Table 6) analyses were performed on the same samples as for major elements. Trace elements and Rare Earth Elements (REE) (Table 6) analyses were performed on the same samples as for major elements.


Sc 4 5 4 8 4 Cr2O<sup>3</sup> <0.002 <0.002 <0.002 <0.002 <0.002 Be 2 2 2 3 2

La 52.1 28.3 26.2 21.7 26.8 Ce 97.0 53.0 48.1 40.8 52.2 Pr 9.97 5.93 5.31 4.59 5.62 Nd 31.7 20.6 18.8 16.6 19.5 Sm 5.29 3.82 3.51 3.56 3.48

Rare Earth Elements (ppm)

**Table 6.** Trace elements chemical composition of the Owlshead and Noble Hills granites. **Table 6.** Trace elements chemical composition of the Owlshead and Noble Hills granites.


**Table 6.** *Cont.*

Chondrite-normalized REE patterns (Figure 14a) present enriched samples in light rare earth elements (LREE) relative to heavy rare earth elements (HREE) in both granites. However, the OW granite shows a higher abundance of LREE and a stronger negative Eu anomaly than the NH samples. In spite of different degrees of mineral alteration, all the NH samples follow the same trend. The primitive mantle-normalized multi-element diagram (Figure 14b) is characterized by distinct negative anomalies for Nb and Sr and high Th and U contents, typical for upper crustal composition [76]. They also show variable but high Cs, Rb and Ba contents. More generally, samples are relatively rich in large-ion lithophile elements (LILEs) such as Rb, Ba, Th and U, with Sr having the greatest depletion relative to the LILEs. High field strength elements (HFSEs) such as Ta, Nb, Zr and Hf are depleted compared to the LILEs. The OW granite shows, once again, a different trend compared to the NH samples. It has higher Th, Ta, Nb, La, Ce, Nd and Sm contents and a lower Ba content. On both diagrams of Figure 14, the sample DVB-114A [34] shows a different pattern compared to OM\_3. Chondrite-normalized REE patterns (Figure 14a) present enriched samples in light rare earth elements (LREE) relative to heavy rare earth elements (HREE) in both granites. However, the OW granite shows a higher abundance of LREE and a stronger negative Eu anomaly than the NH samples. In spite of different degrees of mineral alteration, all the NH samples follow the same trend. The primitive mantle-normalized multi-element diagram (Figure 14b) is characterized by distinct negative anomalies for Nb and Sr and high Th and U contents, typical for upper crustal composition [76]. They also show variable but high Cs, Rb and Ba contents. More generally, samples are relatively rich in large-ion lithophile elements (LILEs) such as Rb, Ba, Th and U, with Sr having the greatest depletion relative to the LILEs. High field strength elements (HFSEs) such as Ta, Nb, Zr and Hf are depleted compared to the LILEs. The OW granite shows, once again, a different trend compared to the NH samples. It has higher Th, Ta, Nb, La, Ce, Nd and Sm contents and a lower Ba content. On both diagrams of Figure 14, the sample DVB-114A [34] shows a different pattern compared to OM\_3.

Calcite is present in all the samples, essentially linked to the alteration of the plagioclase. The calcite content is of 0.55% for the OM granite and ranges from 0.55 to 6.53% for the NH granite, with an average of 2.2% and a standard deviation of 1.64%. The porosity is of 2.28% for the OM granite and ranges from 2.21 to 5.17% for the NH granite.

the porosity and the calcite content (Figure 15b,c). However, the sample NH\_7 in Figure 15c is different. Having a low calcite content, it presents a higher porosity compared to the others. Those diagrams show that a low LOI corresponds to a low amount of calcite

**Figure 14.** (**a**) Chondrite-normalized (values from [77]) rare earth element (REE) patterns of samples from the OM and the NH. (**b**) Primitive mantle-normalized (values from [78]'s slight revision of [79]) multi-element diagram showing trace element patterns of samples from the OM and the NH. **Figure 14.** (**a**) Chondrite-normalized (values from [77]) rare earth element (REE) patterns of samples from the OM and the NH. (**b**) Primitive mantle-normalized (values from [78]'s slight revision of [79]) multi-element diagram showing trace element patterns of samples from the OM and the NH.

*4.3. Calcimetry and Porosimetry*

#### *4.3. Calcimetry and Porosimetry*

Calcite is present in all the samples, essentially linked to the alteration of the plagioclase. The calcite content is of 0.55% for the OM granite and ranges from 0.55 to 6.53% for the NH granite, with an average of 2.2% and a standard deviation of 1.64%. The porosity is of 2.28% for the OM granite and ranges from 2.21 to 5.17% for the NH granite. A clear positive correlation can be seen between the calcite content and the LOI (Figure 15a). Positive correlations are also visible between the porosity and the LOI and between the porosity and the calcite content (Figure 15b,c). However, the sample NH\_7 in Figure 15c is different. Having a low calcite content, it presents a higher porosity compared to the others. Those diagrams show that a low LOI corresponds to a low amount of calcite and a low porosity and that a low amount of calcite fits with a low porosity except for NH\_7. *Geosciences* **2021**, *11*, 325 23 of 34 and a low porosity and that a low amount of calcite fits with a low porosity except for NH\_7.

**Figure 15.** (**a**) Plot of the porosity versus the calcite content. (**b**) Plot of calcite content versus LOI (Loss on ignition). (**c**) Plot of porosity versus LOI. **Figure 15.** (**a**) Plot of the porosity versus the calcite content. (**b**) Plot of calcite content versus LOI (Loss on ignition). (**c**) Plot of porosity versus LOI.

#### **5. Discussion 5. Discussion**

#### *5.1. Petrogenesis of the OM and NH Granites 5.1. Petrogenesis of the OM and NH Granites*

Bulk rock analyses of the OM and NH granites indicate for both of them a calcalkaline, monzogranite composition, S-type in character (Figure 11). Rämö et al. (2002) [34] also investigated the OM in the same batholith, but south of our sampling area (blue star in Figure 2a). The comparison of geochemical data from their sample with the samples studied here, shows differences in terms of chemical composition (Figures 7, 11, 12 and Bulk rock analyses of the OM and NH granites indicate for both of them a calc-alkaline, monzogranite composition, S-type in character (Figure 11). Rämö et al. (2002) [34] also investigated the OM in the same batholith, but south of our sampling area (blue star in Figure 2a). The comparison of geochemical data from their sample with the samples studied here, shows differences in terms of chemical composition (Figures 7, 11, 12 and 14). The OM seems to be a heterogenous pluton.

14). The OM seems to be a heterogenous pluton. Chondrite-normalized REE patterns for the NH granite samples show the same trend (Figure 14a), but are different from the OM granite one. REE are relatively immobile during low-grade metamorphism and hydrothermal alteration [76]. The enrichment of the LREE and the depletion of Eu indicate the degree of magmatic differentiation the rock underwent. The Eu negative anomaly is attributed to the plagioclase fractionation involved in the setting of granites [80]. However, the breakdown of plagioclase and biotite Chondrite-normalized REE patterns for the NH granite samples show the same trend (Figure 14a), but are different from the OM granite one. REE are relatively immobile during low-grade metamorphism and hydrothermal alteration [76]. The enrichment of the LREE and the depletion of Eu indicate the degree of magmatic differentiation the rock underwent. The Eu negative anomaly is attributed to the plagioclase fractionation involved in the setting of granites [80]. However, the breakdown of plagioclase and biotite can release some REE except Eu, which can be accommodated by illite formation [81].

can release some REE except Eu, which can be accommodated by illite formation [81]. The same observations were done through the primitive mantle-normalized spider diagrams, which shows variations in Ta and Nb contents of the NH samples (Figure 14b). Those variations are in good correlation with the LOI: the higher the LOI, the lower the Nb and Ta contents. Li et al. (2013) [82]observed Nb/Ta ratios in altered domains in granitic rocks due to the Nb and Ta decreasing content during the illitization stage. The LOI is directly related to the percentage of alteration, the same phenomenon is observed in our samples. The depletion of Sr in the NH granite might be due to the alteration of The same observations were done through the primitive mantle-normalized spider diagrams, which shows variations in Ta and Nb contents of the NH samples (Figure 14b). Those variations are in good correlation with the LOI: the higher the LOI, the lower the Nb and Ta contents. Li et al. (2013) [82] observed Nb/Ta ratios in altered domains in granitic rocks due to the Nb and Ta decreasing content during the illitization stage. The LOI is directly related to the percentage of alteration, the same phenomenon is observed in our samples. The depletion of Sr in the NH granite might be due to the alteration of magmatic primary plagioclase [82]. However, Sr content in OM is relatively low.

magmatic primary plagioclase[82]. However, Sr content in OM is relatively low. Those diagrams show and confirm the difference in terms of chemical composition between the NH and the OM, which was suspected during thin sections observations. A comparison between our own chemical data within the OM and the data presented by [34] show substantial differences meaning that the OM granite is not homogeneous. Given Those diagrams show and confirm the difference in terms of chemical composition between the NH and the OM, which was suspected during thin sections observations. A comparison between our own chemical data within the OM and the data presented by [34] show substantial differences meaning that the OM granite is not homogeneous. Given the fact that the NH granite is considered as a transported part of the OM [11], it is therefore

the fact that the NH granite is considered as a transported part of the OM [11], it is therefore not surprising that the NH granite presents local composition variations. The

Microcline was identified in the OM granite and only in the southern part of the NH indicating that this part of the range might have undergone a slower cooling than the

Petrographic investigations have shown that plagioclase and sometimes biotite are replaced by illite. A recent study from [83] has confirmed that IC provides a useful method

transformations identified in the NH granite.

northern part of the range or a warming.

*5.2. Thermal Evolution of the NH Granite*

not surprising that the NH granite presents local composition variations. The OM samples are considered as representing the protolith prior to the mineral transformations identified in the NH granite.

Microcline was identified in the OM granite and only in the southern part of the NH indicating that this part of the range might have undergone a slower cooling than the northern part of the range or a warming.

#### *5.2. Thermal Evolution of the NH Granite*

Petrographic investigations have shown that plagioclase and sometimes biotite are replaced by illite. A recent study from [83] has confirmed that IC provides a useful method for characterizing regional grades of diagenesis and low-grade metamorphism. As already mentioned, in some conditions the alteration of a granite, resulting from fluid circulation, shows similarities with diagenetic reactions present in feldspathic sandstones [19], meaning that it is possible to characterize a regional grade by using the KI values obtained in granitic rocks.

As shown in Figure 2, the NH range is a structure stretched NW-SE. The KI values display a trend following this direction with decreasing values towards the south-east (Figure 10). KI values can be associated to different metamorphic zones corresponding to ranges of temperature (Table 1, [60]). The northwestern part of the range, characterized by high KI values, reveals mostly low-grade diagenesis tending progressively to highgrade diagenesis roughly toward the SE. A decrease of KI values indicates an increase in temperature [59]. Thus, this tendency reflects a temperature gradient increasing from the NW toward the SE. The elevation being higher in the south-east, with a higher temperature in this zone might indicate that the southern part of the range was more buried than the rest of the range and has been exhumed. A northeast-vergent contractional deformation is well expressed along the NH range in addition to the strike-slip deformation. It increases in intensity where the NH range converges with the Avawatz mountains ([38] and references therein), at the intersection between the SDVFZ and the GFZ [30]. Chabani et al. (2021) [12] have identified E-W structures in this area and they suppose that these structures are linked to the activity of the GFZ and the convergence of the Avawatz and the NH range. It is tempting to propose that this convergence implied the elevation of the topography at the southern part of the NH range. A work is in progress about exhumation history reconstruction by means of isotopic dating.

#### *5.3. Alteration Parageneses*

The OM and NH granites characterization reveals the presence of various secondary minerals as oxides, epidote, corrensite, K-white mica, calcite, kaolinite, illite/smectite mixed-layer and montmorillonite. Those minerals are well known as being the product of alteration processes due to the interaction of a circulating fluid with the surrounding rock. They are in equilibrium with the new environment in response to temperature, pressure and composition of the altering fluid [6,84–86]. In the OM and the NH granites, only plagioclase and biotite are affected. In the case of intense circulation, some primary minerals like plagioclase or biotite may be completely replaced. The newly formed minerals consist mainly in clay minerals [9]. According to optical observations, SEM-EDS and XRD analyses, two types of alteration processes have been identified in the OM and NH granites which are classified as (1) propylitic alteration and (2) argillic alteration. The characterization of the paragenesis and the alteration processes of the granites investigated in this study help to refine a part of the history of the OM and NH granitic basements (Figure 16).


for characterizing regional grades of diagenesis and low-grade metamorphism. As already mentioned, in some conditions the alteration of a granite, resulting from fluid circulation, shows similarities with diagenetic reactions present in feldspathic sandstones [19], meaning that it is possible to characterize a regional grade by using the KI values

As shown in Figure 2, the NH range is a structure stretched NW-SE. The KI values display a trend following this direction with decreasing values towards the south-east (Figure 10). KI values can be associated to different metamorphic zones corresponding to ranges of temperature (Table 1, [60]). The northwestern part of the range, characterized by high KI values, reveals mostly low-grade diagenesis tending progressively to highgrade diagenesis roughly toward the SE. A decrease of KI values indicates an increase in temperature [59]. Thus, this tendency reflects a temperature gradient increasing from the NW toward the SE. The elevation being higher in the south-east, with a higher temperature in this zone might indicate that the southern part of the range was more buried than the rest of the range and has been exhumed. A northeast-vergent contractional deformation is well expressed along the NH range in addition to the strike-slip deformation. It increases in intensity where the NH range converges with the Avawatz mountains ([38] and references therein), at the intersection between the SDVFZ and the GFZ [30]. Chabani et al. (2021) [12] have identified E-W structures in this area and they suppose that these structures are linked to the activity of the GFZ and the convergence of the Avawatz and the NH range. It is tempting to propose that this convergence implied the elevation of the topography at the southern part of the NH range. A work is in

progress about exhumation history reconstruction by means of isotopic dating.

The OM and NH granites characterization reveals the presence of various secondary minerals as oxides, epidote, corrensite, K-white mica, calcite, kaolinite, illite/smectite mixed-layer and montmorillonite. Those minerals are well known as being the product of alteration processes due to the interaction of a circulating fluid with the surrounding rock. They are in equilibrium with the new environment in response to temperature, pressure and composition of the altering fluid [6,84–86]. In the OM and the NH granites, only plagioclase and biotite are affected. In the case of intense circulation, some primary minerals like plagioclase or biotite may be completely replaced. The newly formed minerals consist mainly in clay minerals [9]. According to optical observations, SEM-EDS and XRD analyses, two types of alteration processes have been identified in the OM and NH granites which are classified as (1) propylitic alteration and (2) argillic alteration. The characterization of the paragenesis and the alteration processes of the granites investigated in this study help to refine a part of the history of the OM and NH granitic

**Figure 16. Figure 16.**  Paragenesis sequence and alteration evolution in the OM and NH granite. Paragenesis sequence and alteration evolution in the OM and NH granite.

#### 5.3.1. Propylitic Alteration

obtained in granitic rocks.

*5.3. Alteration Parageneses*

basements (Figure 16).

The newly formed minerals depend on the composition of the host mineral. Corrensite, epidote, K-white micas, calcite and iron oxides were identified in the OM and NH granites (Figure 16) by means of optical observations, SEM-EDS and XRD analyses:


All those secondary minerals occur at temperatures between approximately 160 ◦C and 350 ◦C. The presence of corrensite and epidote is the major indicator of a stage of propylitic alteration. The propylitic alteration (Figure 17b) is considered as an earlier pervasive alteration stage. It is common at the margins of alteration zones produced at low fluid/rock ratio [6] and it takes place at the end of the crystallization of the granite [92]. The propylitic alteration results in the partial recrystallization of primary minerals (biotite and plagioclase) in secondary propylitic assemblages by interstitial fluids trapped into the grain boundaries during the cooling of the pluton [88]. Its effects are discrete, but both the OM and NH massifs are affected.

#### 5.3.2. Argillic Alteration

Other newly formed mineral assemblages were identified only in the NH granite. They consist in illite + kaolinite + mixed-layers as illite/smectite (I/S) + calcite and oxide (Figure 16):


advanced product of hydrolysis reaction due to a high H<sup>+</sup> activity in hydrothermal fluids. All those secondary minerals occur at temperatures between approximately 160 °C and 350 °C. The presence of corrensite and epidote is the major indicator of a stage of

The newly formed minerals depend on the composition of the host mineral. Corrensite, epidote, K-white micas, calcite and iron oxides were identified in the OM and NH granites (Figure 16) by means of optical observations, SEM-EDS and XRD analyses: 1. The calcite as in the OM granite occurs as infills of the microcracks without

interacting with the surrounding rock, as well as at grain boundaries.

2. Mixed-layer clay minerals are the intermediate products of reactions involving endmember clays [87]. Corrensite, a chlorite/trioctahedral smectite mixed-layer phyllosicilate is considered as a stable mineral and also as an indicator of propylitic alteration [86,88,89]. It replaces partially biotite and occurs between 160–250 °C in

3. Epidote crystallization occurs around 220 °C [86]. It is also one major indicator of the

4. The presence of K-white mica flakes allows to fix temperatures around 230 °C up to


*Geosciences* **2021**, *11*, 325 25 of 34

5.3.1. Propylitic Alteration

geothermal fields [6,84,90].

350 °C [84,91].

propylitic alteration with corrensite [89].

**Figure 17.** Schematic representation of the different alteration processes which can be observed in the OM and NH granites. (**a**) Fresh granite non-affected by alteration. (**b**) Granite affected by the propylitic alteration showing the slight chloritization of biotite and the crystallization of K-white micas in the core of plagioclase. (**c**) Granite affected by the argillic alteration and localized along fractures where fluid has circulated. Biotite are locally completely transformed into illite and plagioclase into illite, calcite and/or kaolinite. Perthites and inclusions in K-feldspars can also be altered. Abbreviations (except for "Ox and Wm") after [45]: Bt—Biotite, Cal—Calcite, Chl—Chlorite, Ep—Epidote, Ill—Illite, Kln—Kaolinite, Kfs—K-feldspar, Ox—Oxide, Pl—Plagioclase, Qtz—Quartz, Wm—K-white mica. **Figure 17.** Schematic representation of the different alteration processes which can be observed in the OM and NH granites. (**a**) Fresh granite non-affected by alteration. (**b**) Granite affected by the propylitic alteration showing the slight chloritization of biotite and the crystallization of K-white micas in the core of plagioclase. (**c**) Granite affected by the argillic alteration and localized along fractures where fluid has circulated. Biotite are locally completely transformed into illite and plagioclase into illite, calcite and/or kaolinite. Perthites and inclusions in K-feldspars can also be altered. Abbreviations (except for "Ox and Wm") after [45]: Bt—Biotite, Cal—Calcite, Chl—Chlorite, Ep—Epidote, Ill—Illite, Kln—Kaolinite, Kfs—K-feldspar, Ox—Oxide, Pl—Plagioclase, Qtz—Quartz, Wm—K-white mica.

Plagioclase and quartz form an interconnected skeleton through the texture. The difference of physical and chemical behaviors between both minerals results in different types of porosity. Quartz shows microcracks and plagioclase shows dissolution pits (Figure 18). Ref. [95] observed the same in the Soultz-sous-Forêts granite. They also showed that the exchange surface between plagioclase and a fluid is around 20 times higher than in quartz. As a consequence, they assume that all the pores are interconnected in plagioclase. They considered this mineral as the main path for fluid flow. Thus, this can be also available in the NH granite. K-feldspar is not affected by the alteration, but perthites and mineral inclusions present in the K-feldspars can be dissolved.

**Figure 18.** Back-scattered image showing a magnified view of plagioclase dissolution pits under SEM (15 kV 5.3 mm x 1.7 k BSECOMP). **Figure 18.** Back-scattered image showing a magnified view of plagioclase dissolution pits under SEM (15 kV 5.3 mm × 1.7 k BSECOMP).

Other newly formed mineral assemblages were identified only in the NH granite. They consist in illite + kaolinite + mixed-layers as illite/smectite (I/S) + calcite and oxide

1. Illitic minerals are well known to be indicators of fluid circulation as well as paleocirculation systems [93]. [19,94] show that illite crystallization episodes can occur, for example, in a temperature range of 120 to 160 °C, corresponding to the argillic alteration facies. The illitization process mainly develops in plagioclase and biotite. It is a form of alteration product found extensively in granitoids, and felsic rocks,

2. According to [84], the presence of kaolinite in alteration paragenesis indicates a fluid temperature lower than 200–150 °C. Kaolinite is stable under more acidic conditions than illite, with pH values ranging from about 4.5 to 6. It also represents a more advanced product of hydrolysis reaction due to a high H<sup>+</sup> activity in hydrothermal

3. The illite-rich (R3) I/S mixed-layer form around 150 °C [84,87], with more than 90%

4. Plagioclase, oligoclase in composition, presents patches of calcite. Those patches are

5. Oxides can be present along the cleavages of the altered biotite. They are interpreted

Plagioclase and quartz form an interconnected skeleton through the texture. The difference of physical and chemical behaviors between both minerals results in different types of porosity. Quartz shows microcracks and plagioclase shows dissolution pits (Figure 18). [95] observed the same in the Soultz-sous-Forêts granite. They also showed that the exchange surface between plagioclase and a fluid is around 20 times higher than in quartz. As a consequence, they assume that all the pores are interconnected in plagioclase. They considered this mineral as the main path for fluid flow. Thus, this can be also available in the NH granite. K-feldspar is not affected by the alteration, but

interpreted as a product of Ca release due to plagioclase alteration.

perthites and mineral inclusions present in the K-feldspars can be dissolved.

as the result of Mg and Fe release during biotite alteration.

whereas K-feldspar remains relatively unaltered [8,67,85].

The crystallization of these minerals occurs at temperature between 130 and 200 ◦C. This range of temperature corresponds to the stage of argillic alteration [84]. The argillic alteration (Figure 17c) consists into the chemical leaching and clay enrichment processes produced at lower temperatures [19,88,96]. This alteration is known as a vein alteration organized in the vicinity of fractures where fluids have circulated [86,88].

#### 5.3.3. Evidences of Weathering

5.3.2. Argillic Alteration

(Figure 16):

fluids.

of illite based on [51].

XRD analyses on an oriented sample of the clay fraction from the OM reveal the presence of Montmorillonite (Mnt) (Figure 8). Mnt, a common smectite pattern, results either from argillic (vein) alteration [84,89] or from weathering [97,98]. As described above, the OM granite appears as "fresh" from (1) field observations: no veins were observed at outcrop scale and macro-scale and the granite appears competent, (2) thin-section analyzes: no veins or veinlets, calcite crystallizations are only present at grain boundaries, and (3) geochemical analyzes, which indicate a very low LOI (0.7 wt.%). No vein was observed at any scale and secondary minerals are all characteristic of propylitic alteration. Those data show that the Mnt cannot result from argillic alteration. In the case of the OM granite, the Mnt is interpreted as a signature of weathering. As its amount is low (15% of the clay fraction), the global alteration of the granite is considered as being dominated by the propylitic alteration. With the OM being considered as the protolith, weathering can be considered negligible in both OM and NH granites.

#### 5.3.4. Alteration Stage Occurrences

The OM granite presents evidence of propylitic alteration only, while the NH granite presents both propylitic and argillic facies. The argillic facies seems most of the time to overprinting the propylitic facies. However, some samples present only evidence of argillic alteration. In those cases, either the propylitic facies have either completely disappeared, or some zones were not initially affected by the propylitic alteration. Some minerals, such as illite and kaolinite, crystallize during the argillic alteration under different conditions [84]. This suggests that several episodes of alteration could have occurred in the NH granite. Afterward, weathering can occur at ambient temperature, when the granite was exhumed. These alteration overprints result also in a retrograde evolution in terms of temperature (T) withT propylitic > T argillic > T weathering.

In the NH granite, the argillic alteration seems to be associated to fracturing. A fresh granitic rock is not permeable enough to allow fluid circulation [6]. This suggests that the development of fractures is an important factor allowing fluid to circulate [6], the observation that the freshest NH granite is more altered than the one from the OM (Figure 3) can be related to the fact that the NH lie along an important shear corridor. None of NH samples considered in the present study are fracture free, even though they were collected far from the faults, and each of them shows evidences of argillic alteration. In spite of the low fracture density the existing number of microfractures is enough to allow fluid to significantly percolate through the host rocks and chemically interact with it. A second paper (PART 2, this issue) focusses on the role of the fracture system on the granite alteration processes.

#### *5.4. Effects of Alteration on Petrogaphic and Petrophysical Behaviour*

Petrographic observations and the range of LOI (0.7–4.1 wt.%) values confirm that the NH granite experienced alteration. LOI is so directly related to the degree of mineral alteration as done by [99,100]. Mineral changes being related to the propylitic and argillic alterations, the LOI can be defined in this study as a monitor for alteration processes. The effects of alteration on element transfers can be evaluated thanks to the diagrams plotting SiO2, Al2O3, CaO, K2O, Na2O and MgO against LOI (Figure 13). In Figure 13, the K2O, Na2O, CaO and MgO define a broad correlation with LOI, indicating that they may have been mobile during alteration [99]. The NH granite shows that Na2O and CaO have a negative correlation which can be related to the alteration of the plagioclase (oligoclase initial composition). Indeed, plagioclase can be depleted in Na and Ca mobile elements when it interacts with a fluid [101]. Likewise, the K2O is observed in alteration products of plagioclase as illite and shows an enrichment with the LOI increase. Newly formed minerals, as presented above, are related to the recrystallization of the plagioclase as a result of its interaction with the fluid. As for the CaO and MgO contents, they remain high compared to the OM granite. This can be linked to an external contribution. In a whole, the NH granite was affected by an alkali alteration, which results in major compositional changes. Thus, all the elements, Si and Al excepted, have partly left the system, meaning that the system is open. Their content differences in the NH granite compared to the OM granite could be explained by the depletion of the most mobile elements during the alteration of the NH granite. This can so influence the percentage of each element. Otherwise, it can be suggested that the visible variations of SiO<sup>2</sup> and Al2O<sup>3</sup> were controlled by protolith composition rather than alteration processes.

Link alteration degree and amount of calcite is difficult since petrographic analyses of the samples is qualitative. However, Figure 15a shows a positive correlation between LOI and calcite content. Ledésert et al. (2009) [61] show that calcite can be encountered in high amount in altered zones. Thus, in the NH, the correlation shows that the higher the calcite content, the higher the degree of alteration and vice versa. In the same way, LOI can be related to porosity (Figure 15b) with a low LOI linked to low porosity (NH\_1, NH\_2 and NH\_10) and high LOI linked to as high porosity (NH\_3). Therefore, the increase of porosity is also linked to the increase of alteration. Studies [102,103] showed that the porosity increases from unaltered to altered granite. Figure 15c shows a similar correlation between the calcite content and the porosity. Samples having a low calcite content (NH1, NH\_2, NH\_5 and NH\_10) present a low porosity, while NH\_3 has a high calcite content associated with a high porosity. One exception can be observed. The sample NH\_7 presents a low calcite content for a high porosity. This can be explained by the presence of larger microfractures compared to the other samples, which increase the porosity. Thus, it is not always possible to link the porosity to the calcite content. According to [104], the average calcite content of a fresh granite is 0.252 wt.%, and does not exceed 1.8 wt.%. As a consequence, measurements over this last value can be regarded as a calcite anomaly, and so are representative of a granite affected by argillic alteration, which may be a sign of paleo fluid flow [94]. Ten samples out of fifteen from the NH have a calcite content higher

than 1.8 wt.%. This suggests that the OM and some zones of the NH were not affected by the argillic alteration, but only by the propylitic one. By considering the calcite content average of 2.2% for the NH, those data also indicate that even if the samples were collected far from the major faults, the granite can be affected by argillic alteration.

#### *5.5. The NH: A Paleo-Geothermal Reservoir?*

In the present contribution we have given numerous pieces of evidences for a pervasive alteration of the NH granite. Ubiquitous argillic alteration affecting plagioclase and biotite is present. The K-feldspar being unaltered, potassium enrichment by incoming fluids is necessary to produce abundant amount of illite. The high concentration of calcite, in some samples, requires an external input of Ca, which cannot come only from the plagioclase alteration. Due to this alteration, the rock porosity was drastically enhanced by dissolution of the plagioclase. Porosity is also enhanced by the microfracturing well visible in quartz and K-feldspar, which is related to the activity of the SDVFZ. It is believed that this microfracturing drastically enhanced interaction surfaces between minerals and fluids allowing chemical elements exchanges between hydrothermal fluids and the granite. The strain is not homogeneously distributed in the NH. The NH granite is affected either by non-localized deformation (samples from this study) or by strain concentrations along fault zones that will be presented in the accompanying contribution (PART 2, this issue).

Our results have shown that an alteration of vast volumes of rocks is thus possible, even outside localized high strain zones. All these data are in favor of a hydrothermal fluid percolation, which is encountered in an exploited geothermal reservoir [6,19]. A geothermal reservoir consisting into a flow system where a high amount of hot fluid is stored and circulates through the rock, and our results encourage to consider the NH as a paleo-geothermal reservoir.

#### **6. Conclusions**

The NH were chosen in the framework of the H2020 MEET project as being an opportunity to characterize a granitic paleo-geothermal reservoir in a trans-tensional context. Arid conditions and a 3D exposure were important criteria allowing the thorough characterization of the granite. The aim of this study was to characterize the granite pervasive alteration processes, away from the fractures, in terms of changes of mineralogical, geochemical and related petrophysical properties.

Illite was identified by XRD in all the NH samples, allowing to obtain KI values which revealed a NW-SE temperature gradient through the range. This gradient might be considered as a sign of a possible exhumation of the southern part of the range due to the interaction with the Avawatz Mountains.

The partial recrystallization of plagioclase and biotite into newly formed minerals, due to fluid/rock interactions, was identified as reflecting three types of alteration:


The NH granite alteration was highlighted by optical observations. In addition, geochemistry also provided data to support them. Indeed, depletion of Na and Ca was observed with the increase of LOI, considered as a good indicator of the amount of alteration of plagioclase alteration. At the same time, K enrichment was observed with the increase of LOI, and linked to illite crystallization. Calcimetry performed on the NH granite

samples showed a calcite content often higher than the 1.8% value, admitted as being the maximum in a fresh granite. These values tend to increase with the LOI, confirming that the NH granite underwent alteration. Porosity also shows a positive correlation with the LOI indicating that the porosity increases with the amount of alteration. However, its correlation with the calcite content is less obvious, as calcite might crystallize in the porosity and thus reduce it.

The NH granite underwent up to two stages of alteration before being exposed to surface conditions, showing a retrograde evolution. It was observed petrographically that the argillic alteration overprinted the propylitic alteration, until its signature is lost. The weathering signal is low (~15% of the clay fraction) and considered as negligible in the OM. The OM being considered as the protolith of the NH, the contribution of weathering is also considered as negligible in the NH granite, where no montmorillonite was found. The newly formed minerals are thus considered as being the product of hydrothermal alteration and not of weathering.

This study provides multiple evidence allowing the consideration of the NH granite as a paleo-geothermal reservoir.

The activity of a geothermal reservoir is a combination of pervasive circulation within nearly strain-free zones (as shown in the present contribution), as well as fractured domains where high strain is accumulated. Our study is therefore completed by a PART 2 (this issue), in which the same investigation approach is dedicated to samples taken within visibly fractured zones.

**Author Contributions:** Conceptualization, J.K., S.P., B.A.L., R.L.H., A.C. and G.T.; methodology, J.K., S.P., B.A.L., R.L.H., A.C. and G.T.; software, J.K.; validation, S.P., B.A.L., R.L.H., A.C., P.B. and G.T.; formal analysis, J.K.; investigation, J.K., S.P., B.A.L., R.L.H. and G.T.; resources, J.K.; data curation, J.K., S.P., B.A.L., R.L.H., A.C. and G.T.; writing—original draft preparation, J.K.; writing—review and editing, S.P., B.A.L., R.L.H., A.C., G.T. and P.B. and H2020 MEET consortium; visualization, S.P., B.A.L., R.L.H., A.C., G.T. and P.B.; supervision, J.K.; project administration, G.T.; funding acquisition, G.T. and H2020 MEET consortium. All authors have read and agreed to the published version of the manuscript.

**Funding:** This project has received funding from the European Union's Horizon 2020 research and innovation program under grant agreement No 792037 (H2020 MEET project).

**Data Availability Statement:** Not applicable.

**Acknowledgments:** This manuscript was prepared as a contribution to the PhD thesis (Institut Polytechnique UniLaSalle Beauvais) of Johanne Klee, which was funded by the European Union's Horizon 2020 research and innovation program under grant agreement No 792037 (H2020 MEET project). The authors are grateful to Terry Pavlis for his knowledge and helpful discussions about the regional geology of Death Valley and the Noble Hills. We also acknowledge Albert Genter for the fruitful exchanges about granite alteration processes. We thank Thi Tuyen Nguyen, Elena Pavlovskaia, Carl Tixier and Chloé Gindrat for their help for analyses. Helpful comments and the validation of the manuscript by the H2020 MEET consortium are gratefully acknowledged. We finally would like to thank Catherine Lerouge and the anonymous reviewer for their help and remarks to improve this manuscript.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


## *Article* **Fluid-Rock Interactions in a Paleo-Geothermal Reservoir (Noble Hills Granite, California, USA). Part 2: The Influence of Fracturing on Granite Alteration Processes and Fluid Circulation at Low to Moderate Regional Strain**

**Johanne Klee 1,\* , Arezki Chabani <sup>1</sup> , Béatrice A. Ledésert <sup>2</sup> , Sébastien Potel <sup>1</sup> , Ronan L. Hébert <sup>2</sup> and Ghislain Trullenque <sup>1</sup>**


**Citation:** Klee, J.; Chabani, A.; Ledésert, B.A.; Potel, S.; Hébert, R.L.; Trullenque, G. Fluid-Rock Interactions in a Paleo-Geothermal Reservoir (Noble Hills Granite, California, USA). Part 2: The Influence of Fracturing on Granite Alteration Processes and Fluid Circulation at Low to Moderate Regional Strain. *Geosciences* **2021**, *11*, 433. https://doi.org/10.3390/ geosciences11110433

Academic Editors: Michael G. Petterson and Jesus Martinez-Frias

Received: 23 September 2021 Accepted: 18 October 2021 Published: 20 October 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

**Abstract:** Fracture connectivity within fractured granitic basement geothermal reservoirs is an important factor controlling their permeability. This study aims to improve the understanding of fluid–rock interaction processes at low to moderate regional strain. The Noble Hills range (Death Valley, CA, USA) was chosen as a naturally exhumed paleo geothermal reservoir. A series of petrographic, petrophysical, and geochemical investigations, combined with a fracture distribution analysis, were carried out on samples collected across fracture zones. Our results indicate that several generations of fluids have percolated through the reservoir. An increase of (1) the alteration degree; (2) the porosity values; and (3) the calcite content was observed when approaching fracture zones. No correlation was identified among the alteration degree, the porosity, or the calcite content. At a local scale, samples showed that the degree of alteration does not necessarily depend on the fracture density or on the amount of the strain. It is concluded that the combined influence of strain and coeval fluid–rock interaction processes drastically influence the petrophysical properties of fracture zones, which in turn impact geothermal production potential.

**Keywords:** fracturing processes; fluid circulation; granite alteration; low to moderate regional strain; geothermal reservoir

## **1. Introduction**

Long-term exploitation of geothermal resources is closely linked to reservoir rock petrophysical properties and regional geological settings [1]. Due to the low matrix porosity and permeability of granitic rocks, underground granitic units are considered as a reservoir only when fractures are present. These fractures provide the essential reservoir permeability and porosity for fluid flow [2,3] and are therefore of primary importance regarding geothermal exploitation [4–8]. These structures control the deep flow at the reservoir scale, in case of good connectivity [2,3,9–11], which is one of the most important controls on the permeability [12]. Several granitic reservoirs, as Soultz-sous-Forêts in the Upper Rhine Graben, France [6,13] or the Cooper Basin in Australia [14], give invaluable experience in terms of exploration and exploitation feedback. In addition to these datasets gained from data limited to boreholes and indirect geophysical methods, studies of surface reservoir analogues are common [15–17]. The MEET H2020 project (Multidisciplinary and multi-context demonstration of EGS exploration and Exploitation Techniques and potentials) [18] aims to develop enhanced geothermal systems throughout Europe. Within this project, the Noble Hills (NH) range, located in the southern termination of the Death

Valley (DV, CA, USA), has been chosen as an analogue of fractured granitic basements in a context of transtensional deformation [19]. Klee et al. (2021) [19] highlighted numerous evidences of hydrothermal alterations: (1) a propylitic alteration affecting pervasively a large volume of rock during the cooling of the pluton and (2) an argillic alteration, also called vein alteration [19–23], inducing changes of the bulk-rock chemical and mineralogical compositions and of physical properties [7,24].

A vast amount of literature [9,11,25] has proven that increasing amounts of strain within fault zones drastically change their petrophysical properties. The present paper focuses on the influence of fractures on the fluid circulation and alteration processes at low to moderate regional strain.

The present study aims to:


Macroscopic and microscopic petrographic studies, XRD mineralogical characterization of whole rock and clay minerals, bulk rock chemical analyses by inductively coupled plasma (ICP), mass spectrometry (MS), atomic emission spectrometry (AES), scanning electron microscopy coupled with energy dispersive spectrometry (SEM-EDS) for structural observation and local chemical analyses, mass balance calculations, fracture density calculations, calcimetry, and porosimetry, were performed on samples collected in the vicinity of fracture zones within areas of the NH affected by low to moderate regional transcurrent strains. The results will be discussed and compared with the protolith studied by [19].

#### **2. Geological Setting**

The Death Valley (DV, Figure 1a) is located in the core of a Cenozoic distributed system of dextral strike-slips, about 700 km long, comprising the Walker Lane Belt and the Eastern California Shear Zone (ECSZ/WLB) [26–29]. This narrow northwest-trending system, lying between the Basin and Range region to the east and the Sierra Nevada batholith to the west [28], today accommodate ~25% of the Pacific-North America relative motion [26,30]. DV is a structural depression, NNW–SSE oriented, bounded by the Black and Funeral Mountains to the west and by the Panamint Range to the east [31]. It has been formed by a right-lateral movement giving a pull-apart structure [32].

The area of interest for this study is the Noble Hills range (NH, Figure 1b). It is located in the southernmost part of the DV region and trends parallel to the NW-striking SDVFZ at its southern end. Geological markers along the SDVFZ trace [33] suggest that the NH correspond to a transported fragment of the frontal part of the Owlshead Mountains (OM), a Cretaceous (~95 Ma, [34]) granitic pluton at a 40–41 km distance to the SE. Several attempts have been made and discussed in the literature to give insight to the geological setting of the NH and structural relationships between SDVFZ and GFZ [35–37]. Particular emphasis has been given to a detailed description of sedimentary sequence deposits on each side of the NH Crystalline Bedrock Slice (CBS) [38,39]. The CBS is composed of Proterozoic sediments with upward younging direction the Crystal Spring (CS) quartzite, CS dolomite, detrital flysh, and carbonate sequences possibly part of the Pahrump Group, intruded by 1.1 Ga diabase sills, the whole intruded by Mesozoic granite [40]. However, a detailed structural analysis of the CBS itself is missing. Thus, Section 4.1 of this study will give new elements, improving the observations made by [38,41] concerning the NH structure. A precise fracture pattern characterization of the NH was performed by [42], through a wide-ranging analysis scale from the microscopic scale to the regional scale. These authors showed that the NH fracture network geometry has been controlled by the SDVFZ and the GFZ.

**Figure 1.** (**a**) Location of the Noble Hills on the western USA satellite map. SAFZ—San Andreas Fault Zone, GFZ—Garlock fault zone, and DV—Death Valley. (**b**) The geological map of the Noble Hills range, modified after [19,38,41]. The quaternary is not displayed, but available on the map provided by [38]. Sample locations are represented by the white dots. The asterisk shows the samples used as case studies in this work. NHF—Noble Hills Formation.

> The NH granite was poorly studied in terms of microstructure, petrography, and geochemistry. A recent study conducted by Klee et al. (2021) [19] characterized the granite as a leucocratic equigranular monzogranite (S-type), ranging in the high-K calc-alkaline and peraluminous domains. The NH granite is composed of primary plagioclase, quartz, K-feldspar, and biotite. Klee et al. (2021) [19] have also shown that the NH granite underwent two alteration stages, forming secondary minerals that recorded the chemical and paleo-thermal conditions of the system: (1) a pervasive, propylitic alteration linked to the cooling of the pluton; and (2) a more local alteration corresponding to the argillic alteration (illitization and sometimes kaolinitization), which overprints the propylitic alteration. Among the primary minerals, optical observations and geochemical data show that only plagioclase and biotite are affected by those alteration processes.

#### **3. Materials and Methods**

#### *3.1. Material and Sample Selection*

Digital field mapping techniques have been used in the field; these include the use of portable rugged tablet laptop with internal GPS. The QGIS software has been used for sample location, geological digitization, and structural data acquisition. Georeferenced topographic maps and ortho-imagery were the initial input of the database.

A detailed petrographic, mineralogical, geochemical, and petrophysical characterization was conducted on 25 samples from the NH granite, based on fieldwork and laboratory analyses.

Samples were selected by targeting fracture zones located in CBS areas that have been affected by low to moderate strain, aimed at characterizing the influence of fracturing on fluid circulations and the associated argillic alteration, mentioned only by [19] until now. Thus, the collected samples consisted of altered granite presenting open fractures, veins, reactivated veins, and breccias. All samples were georeferenced for precise locations as well as database supply (Figure 1b). The selection took into account ranges of fracture density (Fd) defined by [19] from scanlines realized on thin sections, based on [43]:

F<sup>d</sup> 0 < 1687 fracs/m—no to very low microfracturing;

F<sup>d</sup> 1 = 1687 fracs/m—microfracturing of order less than the grain size;

F<sup>d</sup> 2 = 2694 fracs/m, with a multiplicator factor of 1.6 compared to Fd1—microfracturing of grain size order with interconnections;

F<sup>d</sup> 3 = 3549 fracs/m, with a multiplicator factor of 1.3 compared to Fd2—abundant microfracturing;

F<sup>d</sup> 4 ≥ 5140 fracs/m ([42] this issue), with a multiplicator factor of 1.4 compared to Fd3—very abundant microfracturing.

Samples selected for this study had a fracture density higher than 2694 fracs/m, meaning they fell into categories from Fd2 to Fd4. Fd4 corresponds to highly strained zones in which granite becomes a breccia. In order to correlate the fracture density with the amount of alteration, three hand specimens and seven thin sections, located in the granite body, were used for fracture extraction and analysis. These fracture characterizations are based on the scanline method, described in Section 3.1. Data from Chabani et al. (this issue, under review) [44] will be used to complete the characterization.

#### *3.2. Methods*

#### 3.2.1. Fracture Network Parameters

Fracture networks can be characterized by their spatial arrangements [45]. The fracture network geometry is used to predict fluid circulation [45] and evidence of structural growth processes [46]. Spacing measurements through the 1D-scanline method are widely used to characterize arrangements [47–50]. They consist of the digitization of fractures along those lines, in order to calculate the linear fracture density P<sup>10</sup> characterized by the number of fractures per length calculated along the scanline [47,48]. The Terzaghi correction has been applied [51]. Two parallel scanlines were performed on the hand specimens, perpendicular to a major fracture. For each oriented thin section mosaic, two scanlines were realized perpendicular to the main structures. For each scanline, stick plots and cumulative frequency diagrams were realized to describe the fractures spatial distribution [50]. A coefficient of variation C<sup>v</sup> was computed for each scanline in order to quantify the fracture distribution [48]: C<sup>v</sup> < 1 indicates a regular fracture spacing, Cv~1 indicates a random distribution, and C<sup>v</sup> > 1 indicates a clustered distribution. Fracture density data obtained by [42] on selected samples will be used in this study.

#### 3.2.2. Petrographic Characterization

Twenty-four samples were selected to prepare thirty-one covered and polished thin sections, for petrographic observations. Optical microscopy was used to study the mineralogical assemblage, the alteration paragenesis, the microfabric, and the degree of microfracturing. The thin sections were observed under a Leica DM4500-P optical microscope, equipped with a Leica DFC450C camera at Institut Polytechnique UniLaSalle (ULS, Beauvais, France). Large field area imaging under polarized-analyzed and polarized-nonanalyzed light was conducted using Leica automatized stage facility and Leica Application Suite (LAS) v4.11.0 software [19].

Based on optical microscopical observations, microsites were selected on 9 thin sections for energy dispersive X-ray spectrometry (EDS) analyses [52] performed at ULS. These were conducted with a Hitachi S-3400N scanning electron microscope (SEM) equipped with a Thermo Ultradry EDS [53] and associated with NSS thermal scientific software. These analyses aimed to obtain qualitative and semi-quantitative chemical compositions and to characterize the microstructure of different selected phases. The analytical conditions consisted of a 50 µA beam current, an accelerating voltage of 20 kV, and an acquisition time of 30 s. A NORAN-type correction procedure was used.

In addition, cathodoluminescence (CL) analyses [54] was performed on 8 thin sections from 4 samples. CL imaging was performed (1) at the University of Göttingen using a "hot-cathode" cathodoluminescence microscope HC3-LM apparatus and (2) at CY Cergy Paris University in the Geosciences and Environment Cergy (GEC) laboratory, using a

cathodoluminescence Olympus BX50. CL of minerals is predominantly a "defect luminescence". This allowed the detection of distribution patterns of certain trace elements, such as iron (Fe), which is the most efficient quencher element and manganese (Mn), which is the most important activator element. Many minerals show visible CL colors like quartz (blue-purple), K-feldspar (blue when fresh and brownish when weathered), plagioclase (green and blue–purple when highly affected by hydrothermal alteration), calcite (yellow or yellow–orange when resulting from hydrothermal alteration), dolomite (orange–red), magnesite (red), apatite (yellow), kaolinite (dark blue) [54,55]. Illite shows no luminescence [54,55].

Most of the mineral abbreviations used in this paper refer to [56] mineral symbols and only a few others were defined by the authors.

#### 3.2.3. X-ray Diffraction (XRD)

XRD analyses were carried out to identify and determine the mineral phases (semiquantitative, around 3–5%). The analyses were performed at (1) ULS using a D8-Advance Bruker-AXS (Siemens) diffractometer with a Ni-filtered CuKα radiation at 40 kV and 40 mA, a primary Soller slit of 2.5◦ , divergence slit of 0.6 mm, and a secondary Soller slit of 2.5◦ , with a detector slit of 0.1 mm and an anti-scattering slit of 0.6 mm; and (2) the University of Göttingen, using a PHILIPS PW1800 diffractometer with a Cu-anode and an automatic divergence slit. Whole rock powders and oriented clay fractions (2–6 µm and <2 µm) analyses were performed on 12 samples. Quantitative phase analysis based on reference intensity ratio values were performed on randomly oriented whole-rock powders with a step length of 0.5◦ and a scan speed of 0.014◦/s over the range 3◦–70◦2θ for whole rocks composition. The uncertainty is estimated to be ±5%. Clay mineral separation was conducted using a technique described by [19], based on [57,58], according to the standard techniques suggested by [59]. For the XRD analyses of both fractions, oriented specimens were measured at air-dried (AD), solvated with ethylene glycol (G), and after heating at 550 ◦C (H) conditions. These three analytical steps were routinely used to better determine clay minerals content and swelling properties [7]. The clay minerals identification, which is based on d-values and the relative intensity of their 00*l* reflections, was undertaken, referencing [60,61]. These measurements were performed with a step length of 0.5◦ and a speed of 0.01◦/s per step over the range 3◦–35◦2θ. The interpretations of the data obtained at ULS were performed using the DIFFRAC EVA v4.2 (©Bruker AXS) software. Two fractions were collected in order to (1) separate the last produced or neoformed clay minerals (fraction <2 µm), which could be assimilated to the result of the last fluid circulation event, from the fraction 2–6 µm assimilated to old grain recrystallization or to a possible mix between detrital and neoformed clay mineral; (2) obtain the respective clay composition; and (3) obtain the temperature conditions.

#### *Kübler Index and Kaolinite Crystallinity Index determination*

The Kübler Index (KI) was used to define the limits of metamorphic zones (diagenetic zone, anchizone, and epizone) [19,62], following the recommendations for Kübler Index calibration of [59] and the CIS-KI transformation formalism of [63], as well as the temperature of illite formation [64,65]. The KI was calculated from the illite crystallinity (IC), which is defined as the full width at half maximum (FWHM) of the (001) 10Å peak of illite, on the AD oriented clay fractions. A recent study [66] has confirmed that IC provides a useful method for characterizing regional grades of diagenesis and low-grade metamorphism. Temperature is thought to be the main factor controlling IC, but other parameters, such as lithology, also have important effects [67–69]. Working at constant lithology allows this effect to be avoided. In some conditions, an altered granite shows similarities with diagenetic reactions present in feldspathic sandstones [20]. Thus, it is possible to characterize temperature ranges by using the KI values obtained for granitic rocks. The values obtained by IC were thus standardized using the crystallinity index-standard (CIS) samples provided by [70] in order to calculate the KI. The KI values of raw data expressed in ∆ ◦2θ,

were measured into three slots, corresponding to different campaigns, which induced three standardizations given by [19]. The Kaolinite Crystallinity Index (KCI) was calculated and put in parallel with the KI in order to identify any correlation between both, and to determine temperature evolution as an indicator for samples free of illite. The KCI is defined as the FWHM of the (001) 7Å peak of kaolinite on the AD oriented clay fraction.

### 3.2.4. Manocalcimetry

Manocalcimetry is used as an indicator of the total calcite content in a rock sample and to assess its possible influence on permeability and consequently better understand the hydrothermal sealing of a reservoir [71]. Calcite content was determined using an OFITE 152–95 manocalcimeter composed of a glass flask and a high precision manometer. The analyses were performed on 15 samples at CY-GEC. High quality results were obtained with an accuracy of ±0.5 wt.%. Prior to measurement, sample preparation was conducted according to [71]. Two replicates were performed for each sample, following the protocol described by [19], in order to check the reproducibility of the results. This procedure was considered to be good when the difference between the two results was lower than 0.5 wt.%, corresponding to the precision mentioned above. The CaCO<sup>3</sup> percentage was calculated according to [19]. The average calcite content of a fresh granite is 0.252 wt.% and does not exceed 1.8 wt.% [72]. As a consequence, measurements above this last value can be regarded as a calcite anomaly [71], due to hydrothermal alteration.

#### 3.2.5. Ethanol Saturation Porosimetry

Porosity measurement quantify the available volume for fluid storage [73]. The connected porosity was measured on three samples by the triple weighing method [19,74] defined by the RILEM standard (test n◦ I.1, 1978). The measurements were carried out at CY Cergy Paris University in the Mechanics and Material for Civil Engineering laboratory (L2MGC). They consist in the saturation of the samples after vacuum degassing. The analyses and calculations were conducted using the technique described by [19]. Ethanol has been chosen instead of water in classical methods, in order to avoid possible clay swelling [75], which could lead to the destruction of the sample and bias to porosity values. Even though ethanol (0.469 nm) is a larger molecule than water (0.343 nm), the pore volume is not estimated to be under-evaluated, because the pore size is likely much larger than that of ethanol molecules.

#### 3.2.6. Bulk Rock Geochemical Analyzes

Chemical analyzes of the major element oxides, rare earth elements, and trace elements were conducted on five samples, selected as case studies in this paper. Analyzes were performed at the Bureau Veritas Minerals (Vancouver, BC, Canada) using inductively coupled plasma emission spectrometry or mass spectrometry (ICP-ES and ICP-MS, respectively). Samples were crushed and mixed with LiBO2/LiB4O<sup>7</sup> flux. Crucibles were fused in a furnace at 980 ◦C. The obtained cooled bead was dissolved in ACS grade nitric acid and analyzed. Loss on ignition (LOI) was determined by igniting the samples split then measuring the weight loss. These chemical analyses were performed in order to determine the element transfers and the degree of alteration.

#### 3.2.7. Mass-Balance Using Gresens' Method

Bulk-rock mass-balance were used to establish element transfers during hydrothermal alteration by applying Gresens' mass-balance procedure [76], consisting of the quantification of gains and losses of major elements by comparing unaltered and altered samples. NH\_2 is considered as the reference because it is the freshest sample collected in the area by [19] and 3 altered samples were selected from this study (NH\_20, NH\_28, NH\_32\_3, and NH\_37). The following equation defined by [76] relates the composition and volume of altered rocks to unaltered/fresh rocks:

$$\mathbf{X\_n = F\_v \times (d\_A/d\_F) \times C\_n{n}{A - C\_n{n}}} \tag{1}$$

With X<sup>n</sup> corresponding to the gain or loss of a considered element n (absolute mobility (%)), F<sup>v</sup> the volume factor, d<sup>A</sup> and d<sup>F</sup> the density (in g/cm<sup>3</sup> ) of the altered (A) and the fresh (F) rocks, respectively, and C<sup>n</sup> <sup>A</sup> and C<sup>n</sup> B , the oxide percentage of the element n for the altered (A) and the fresh (F) rocks, respectively, which were given by the bulk geochemical analyses, recalculated without the LOI. The densities were calculated from the sample masses obtained during the porosity measurements. The F<sup>v</sup> was calculated for each altered sample by considering XAl2O3 = 0 following the analysis of the values. Xn was calculated for each element. Then, the obtained Fv values being very close to 1, the Xn values were recalculated by considering F<sup>v</sup> = 1 (constant volume). Hence, X<sup>n</sup> values > 0 (positive values) represent the gains and X<sup>n</sup> values < 0 (negative values) represent the losses for the considered elements. This calculation was applied for the major elements in each sample.

#### **4. Results**

#### *4.1. Noble Hills Structural Overview*

We investigated the geometry of outcropping Proterozoic sequences between Pipeline and Cave Spring washes (Figure 2a) and confirm at first the plutonic nature of the contact at the base of the Proterozoic sequence with the underlying Mesozoic granite by metamorphic halos [40]. The whole architecture of the NH presents signs of deformation affecting both Proterozoic and granitic units. Proterozoic units present much evidence of deformation with (1) several tectonically induced duplications of the stratigraphic sequence (Figure 2b) and (2) a lateral bending, stretching, and boudinage of this Proterozoic cover nappe stack [41]. Boudinage was identified in the field and in map view where progressive dismantling of stratigraphic markers is observed. (Figure 2b,c). Development of synthetic, oblique dextral shears (Figure 2c), offsetting along the CBS strike and accommodating the deformation, have also been identified. The age and tectonic significance of the nappe stack described in (1) is still unclear at present and possibly predates Mesozoic magmatic intrusion, as it does not appear intensively deformed along the basal contacts of the nappes. Lateral bending and stretching mentioned in (2) and depicted in Figure 2b,c are related to SDVFZ activity, since all kinematic indicators are consistent with progressive southeast oriented dextral shearing. This feature is ubiquitous within the NH as described by [33]. Given these new findings dealing with internal CBS structural organization, it is expected that areas along the rear southern limit of the CBS have recorded less transcurrent shear compared to areas situated along its northern front. Thus, the CBS gives an opportunity to study the effects of progressive transcurrent shearing within a granitic geothermal analogue. The above considerations have important implications regarding strain distribution within the NH and, in turn, concerning the sampling strategy. Given the above-mentioned findings, we consider the CBS as an exceptional example of large-scale cataclastic flow in which rock masses of the northern domain are dragged as a continuous body into a transcurrent deformation corridor (Figure 2a). No signs of a discrete, large-scale deformation structure appear on the map presented in Figure 2, where yellow dashed lines show instead a continuous flow accommodated by brittle deformation processes.

#### *4.2. Petrographic Description*

As described by [19], the primary assemblage of the NH granite is made of plagioclase (mainly oligoclase in composition), quartz, K-feldspar (perthitic orthoclase and sometimes microcline), and biotite. The granitic samples collected for this study show strong evidence of intense alteration, especially on plagioclase and biotite. Plagioclase transformed into illite, kaolinite and/or calcite and biotite into illite and oxides. In rare samples, K-feldspar perthite could be partially altered into illite. However, the magmatic texture is almost preserved, except in the case of breccias, which are not necessarily highly altered. For all samples, the alteration product is always the same, but the relative proportions of the different secondary phases might vary. The mineralogical composition and the degree of fracturing of each sample is given in Table 1.

**Figure 2.** (**a**) Satellite view of the NH range showing a deformation gradient increasing southeastward, represented by the yellow dashed lines. (**b**,**c**) Map view zooms on the Proterozoic units along the NH strike showing the strain increase from (**b**) to (**c**), where basal CS sedimentary sequence appears increasingly stretched and boudinated.

> The clay mineral composition of some samples has been precisely determined for the <2 µm and 2–6 µm (Table 1). It reveals the presence of illite/smectite (I/S) mixed-layers in three samples (NH\_17, NH\_24, and NH31\_1\_2) in both fractions when it was measurable. The I/S identified is always illite-rich (R3), with more than 90% of illite [60], where R represents the Reichweite parameter [60]. A small amount of corrensite (trioctahedral variety of regular 50:50 chlorite/smectite mixed-layer (C/S) [77]) was also identified in the samples NH\_16, NH\_27, and NH\_32. Both mixed-layers (I/S and C/S) were already identified by [19] in the sampled granite away from the fracture zones. Two new patterns were identified in this study (Figure 3):


*Geosciences* **2021**, *11*, 433

**Table 1.** List of samples collected in the field with their mineralogical composition determined after microscopic observations (optical-microscope and SEM-EDS) and XRD analysis (primary minerals and secondary minerals), their degree of microfracturing after [43], and their clay mineral composition for the fractions <2 µm and 2–6 µm. Abbreviations after [56], except for the following: Olg—oligoclase, Ox—oxide, I/S—illite/smectite, C/S—corrensite, n.m.—not measured, n.a.—not analyzed.


**Figure 3.** Two examples of XRD patterns obtained for the clay fraction <2 µm in air-dried (AD–dark), after glycol solvation (G-blue) and heated (H-red) conditions for the NH granite, which were not identified in the fresh granite described by [19], and showing different clay compositions. (**a**) Illite, kaolinite, and quartz. (**b**) Vermiculite, illite, kaolinite, and quartz.

The high proportions of illite and kaolinite are characteristic of the argillic alteration [19]. Argillic alteration is prevalent in the vicinity of fracture zones (Table 1). Vermiculite can be interpreted as either hydrothermal alteration or weathering. This will be discussed in Section 5.1.

Microscopic observations and SEM-EDS analyses have shown that, in almost all the samples, carbonates (dolomite, siderite, ankerite, and calcite) and oxides were present as veins and or in replacement of plagioclase. Moreover, XRD analyses revealed the presence of gypsum and/or halite in minor amounts in few samples (Table 1). Halite only occurred in sample NH\_36 and gypsum was found in samples NH\_17, NH31\_3, NH\_34, and NH\_36.

#### *4.3. Fracturing and Fluid Circulation*

The NH granite presents ubiquitous signs of both fracturing and alteration, due to its location along the SDVFZ major fault corridor. The area lies along a deformation corridor governed by transcurrent deformation along the SDVFZ. In addition to the present contribution, Klee et al. [41] argue in favor of a deformation gradient affecting the CBS. At low to moderate strains, the system presents fracture zones composed of a fault core in which fractures are branching and where most of the displacement is concentrated (Figure 4a). These fracture zones affect the surrounding rock, creating an important fracture network (the damage zone, DMZ). Open fractures and veins are observed in this DMZ (Figure 4b).

Fault zones may act as a channel when connected and open fractures are present or as a barrier when fracture are sealed by mineralization. The distinction is made between (1) zones of opening related structures (i.e., where no signs of displacement are recognized between the two borders of the vein, Figure 4b); and (2) zones of lateral displacement (i.e., indicative of a shear displacement is observable) through three samples used as case studies (NH\_31 (Figure 5a), NH\_36, and NH\_23 (Figure 5b)). Note that these samples are spaced at 2 m and are almost perpendicular to each other.

**Figure 4.** (**a**) Photograph and digitization showing representative hydrothermalized fracture zones observed on the field. (**b**) Photograph and digitization of granite crosscutting by multiple carbonate veins (veins network) altering pervasively the rock.

**Figure 5.** (**a**) Photograph and digitization of a brecciated and recrystallized vein also developing a gradient of alteration. Location of the sample NH\_31 used as a case study in this section. (**b**) Photograph and digitization of a mylonitic vein developing a gradient of alteration. Location of the sample NH\_23 used as a case study in this section.

## 4.3.1. Opening Related Structures with Minimum Shear Displacement

A significant number of veins, veinlets, and microfractures were identified in the different samples and outcrops investigated. Veinlets of various mineralization natures (≤100 µm wide) were also identified in the samples. This variety of fracture infills shows different fluid circulation episodes. Rare veinlets of quartz were observed and intersected by illite veinlets (Figure 6a), which can be contemporaneous to kaolinite veinlets. Illite development is dependent on host mineral properties in terms of mechanical resistance and chemical stability. In that sense, quartz and K-feldspar, which remains unaltered, presents sharp open fractures in which illite precipitates (Figure 6b). Plagioclase, which is altered, presents blurred vein borders and start to spread out pervasively, due to the secondary porosity created by the alteration process (Figure 6b). These veinlets are generally intersected by carbonate veins (Figure 6c). These veins, the sizes of which range from 500-µm widths up to centimetric scales, are composed of dolomite, siderite, ankerite, and calcite. Most of the time, dolomite and ankerite appear contemporaneous. When siderite is present, it alters dolomite borders and crystallizes in it or crosscut it (Figure 6d). Then, calcite veins intersect the dolomite/ankerite and siderite veins (Figure 6d). Calcite can crystallize around angular clasts arranged in a fan shape characteristic of hydraulic fracturing (Figure 6e). Open microfractures present in the samples can show altered walls with kaolinite (Figure 6f) and/or illite (Figure 6g) indicating an influence of microfractures on mineral alteration.

**Figure 6.** (**a**) Photomicrograph of a quartz veinlets intersected by an illite veinlets under optical microscope in polarized– analyzed light. (**b**) Photomicrograph showing an illite vein crosscutting K-feldspar and illitized plagioclase under optical microscope in polarized–analyzed light. (**c**) Back-scattered image showing the different phases presented in (**b**). (**c**) Photomicrograph showing dolomite intersecting illite under optical microscope in polarized–analyzed light. (**d**) Back-scattered image of a dolomite, siderite, and calcite showing their chronology. (**e**) Hydraulic fracturing with calcite precipitating around clasts of quartz placed like a fan under optical microscope in polarized–analyzed light. (**f**) Photomicrograph under optical microscope in polarized–analyzed light of a microfracture intersecting an altered plagioclase which borders are made of pure kaolinite, whereas the plagioclase was recrystallized into kaolinite and illite. (**g**) Photomicrograph under an optical microscope in polarized–analyzed light, showing illite developing on the walls of an open microfracture and dolomite filling this open space.

#### 4.3.2. Infill of Fractures Developed with a Confirmed Lateral Shear Displacement

The previous section shows that all of the samples in the area present many fractures where fluid has circulated, precipitating or not various secondary minerals. However, the area is constrained by a shear component. Three samples were selected in order to describe the relationship between the amount of the strain and fluid circulation.

#### **Sample NH\_31**

The outcrop of the sample NH\_31 (Figure 5a) presents a vein around 10 cm thick crosscutting the granite and with a pinkish halo developed on each border. This halo represents the hydrothermalized zone of the granite. The sample NH\_31 (Figure 7a) is composed of (1) a brecciated vein presenting brecciated quartz remnants, which were overprinted by a carbonate matrix and granitic clasts transported by the carbonate matrix; (2) a hydrothermalized zone, which corresponds to the pinkish halo; and (3) the porphyritic granite crosscut by veinlets filled by carbonates coming from the brecciated vein. Quartz veins are scarce in the NH granite. Fractures are dominantly rich in carbonates. It can be observed through this sample that carbonates crosscut the quartz.

• Spatial fracture distribution: two scanlines were realized in the granitic part of the sample (Figure 7a), from the brecciated vein towards the host rock, in order to evaluate the evolution of the fracture density along those two profiles. The spatial analysis is summarized in Table 2.

The cumulative frequency plotted against the fracture-projected position is presented in Figure 7b. The fracture frequency regularly and slowly increases over the first half part of the diagram curve, then increases regularly but more significantly. The Cv of 0.67 and 0.60 for each scanline shows a regular to random fracture arrangement, which is confirmed by the stick plots in Figure 7c. Both scanlines present an equivalent fracture density of 829 and 882 fracs/m.

Moreover, three thin sections were gained from the sample and one scanline was realized for each thin section (Figure 8a,b). As for the sample scanlines, the thin section scanlines were realized perpendicular to the vein and towards the host rock (Figure 8c).

SL\_NH\_31\_1 shows a fracture frequency that increases following a random arrangement (Cv = 1.03) (Figure 8c,d).

The SL\_NH\_31\_2, parallel to the previous scanline, also presents an irregular distribution. The frequency increases slowly at the beginning, followed by a high fracture density zone around 0.7–1.05 (fracture cluster), then a more significant increase comprising a new fracture cluster around 2–2.2 (Figure 8c). The slightly higher Cv compared to the previous scanline (Cv = 1.07) and the fracture distribution (Figure 8c) indicate a random to clustered arrangement of the fractures.

The last scanline SL\_NH\_31\_3, which is the furthest from the vein, shows a greater overall increase of the fracture frequency compared to the two previous scanlines (Figure 8c). Only one fracture cluster was identified around 1.7–1.9 cm even if the Cv is higher (Cv = 1.11). The fracture arrangement is again considered as random to clustered.

Cv values, as well as fracture density values, increase from the vein towards the host rock, from 1.03 to 1.11 and from 2997 to 5084 fracs/m, respectively (Figure 8d).

By comparing fracture analyses between sample scale and thin section scale, a clear difference is observed among P10, the mean spacing, and Cv values (Table 2). At thin section scale, the fracture density is significantly higher (×4.7) than at sample scale and the mean spacing is six times lower. At sample scale, the Cv is lower than 1 indicating an almost regular spacing between the fractures, even if there is a change of the slope (Figure 7c). Whereas, at the thin section scale, the Cv is around 1 or slightly higher, indicating a global random distribution of the fractures along the scanlines with the appearance of a few clusters (Figure 7c). For both, differences in the fracture distribution can be linked to a subjective bias during the data collection [78], but also to the image resolution, which

prevents from seeing all the fractures and so induced a bias. Thin section fracture analyses are, thus, more precise.

**Figure 7.** (**a**) Photo and the respective digitalization of the sample NH\_31, gathering NH\_31\_1\_2 and NH\_31\_3, showing the different compartments that compose it, as well as the two scanlines realized in the host rock of the vein. (**b**) Plots of the cumulative frequency percentage against distance percentage for both scanlines. The diagonal represents a uniform distribution. (**c**) Stick plots showing the fracture position along the scanlines and for which the fracture density (P10) and the coefficient of variation (Cv) are given.


**Table 2.** Spatial fractures analysis. Scanline length: total length of each scanline; fracture number, mean spacing, P10, and Cv value by scanline and fracture distribution tendency by scanline.

> • Petrographic and petrophysical characterization: the brecciated vein presents a large variety of mineralogical phases. As shown in Figure 7a, this zone shows a carbonate matrix containing clasts of granite, which overprints a brecciated quartz vein remnant showing an undulatory extinction but no evidence of dynamic recrystallization. The carbonate matrix is complex, composed of several phases (Figure 9a–g).

> Focusing on the veins crosscutting the quartz porphyroclasts, three phases are identified (Figure 9a–e):


Evidence of hydraulic fracturing, as presented in Figure 6e, have also been observed in this part of the sample.

By focusing in the carbonate matrix, at the contact with the granite, a new phase is observed, composed of dolomite embedding small clasts (mainly quartz). This phase is intersected by the phase 2, which is intersected by the phase 3 (Figure 9e,f). Examining the hydrothermalized granite along the brecciated vein (NH\_31\_1 and NH\_31\_2), the granite shows a preserved magmatic texture with plagioclase fully altered into illite, ± kaolinite, and calcite, completely altered biotite into illite and oxides, and unaltered perthitic K-feldspar (Figure 9h,i). Hematite and numerous dolomite/ankerite and calcite veinlets are present. Moving away from the brecciated vein (NH\_31\_3), the granite appears less affected by the alteration. Plagioclase and biotite are only partially altered and K-feldspar and quartz are unaltered (Figure 9j,k). Unlike the hydrothermalized zone, the granite presents only a few veinlets of calcite.

**Figure 8.** (**a**) Thin sections location on the sample NH\_31. (**b**) Thin section mosaics showing the position and orientation of the scanlines. (**c**) Plots of the cumulative frequency percentage against distance percentage for each scanline. The diagonal represents a uniform distribution. Dashed lines indicate a zone where a rapid increase of the number of fractures is observed (slope threshold >2). (**d**) Stick plots showing the position of the fracture along the scanlines and for which the fracture density (P10) and the coefficient of variation (Cv) are given.

> Bulk chemical analyses were performed on the granitic part of the sample and show a low LOI of 2.5%, a porosity of 10.1%, and a calcite content of 1.86%, close to the brecciated vein (NH\_31\_1\_2), and a calcite content of 1.37% away from it (NH\_31\_3).

#### **Sample NH\_36**

This sample (Figures 1b and 10a) shows a fractured granite with a preserved magmatic texture intersected by brecciated zones. As for sample NH\_31, the fracture distribution analyses, as well as a petrographic description, were realized.

• Spatial fracture distribution: the spatial fracture distribution analysis was realized based on data from [42]. One scanline was realized through the sample in order to evaluate the evolution of the fracture distribution and density (Table 2, Figure 10a). The cumulative frequency against the fractures projected position presented in Figure 10b shows a fracture frequency slowly increasing, as well as a fracture cluster. The Cv of 1.03 indicates a random arrangement of the fractures along the scanline (Figure 10c). A fracture density of 342 fracs/m was compiled (Figure 10c).

Two thin sections were made from the sample (Figure 10a,d). Two perpendicular scanlines were realized on each thin section (Figure 10d).

**Figure 9.** Photomicrographs of the different compartments of the sample NH\_31 and their locations in the sample. (**a**,**b**) Respectively back-scattered image and CL images of calcite veins composed of two phases (Cal A and Cal B) crosscutting quartz, crosscut by a phase made of a carbonate/oxide matrix (calcite, dolomite, ankerite) with barium patches and transported clasts of quartz, K-feldspars, and few biotites, crosscut by later calcite veins (Cal C). (**c**,**d**) Zoom on the first generation of calcite vein and crosscutting quartz under optical microscope in polarized–analyzed light and showing two phases under CL. (**e**) A chemical quantification map realized under SEM of the carbonate/oxide matrix with barium and clasts. Different colors show a relative abundance of specific chemical elements (counts). (**f**,**g**) A photomicrograph under optical microscope in polarized–analyzed and under SEM, respectively, of the contact with the granite showing a dolomite matrix with transported clasts intersected by a calcite vein, the whole intersected by a carbonate/oxide matrix with transported clasts and barium precipitation patches. (**h**) The altered granite close to the brecciated vein showing a completely altered plagioclase replaced by calcite, kaolinite, and illite, a completely altered biotite replaced by illite and oxides and non–altered K-feldspar and quartz under an optical microscope in polarized–analyzed light. (**i**) The altered granite close to the brecciated vein presented in (**h**) under CL showing illite with no luminescence, in light blue an unaltered K-feldspar, in red some calcite and apatite in yellow. (**j**) The altered granite, away from the brecciated vein, showing a plagioclase partially replaced by calcite, kaolinite, and illite, biotites partially replaced by illite, and oxides, and unaltered quartz under optical microscope in polarized–analyzed light. (**k**) The altered granite away from the brecciated vein presented in (**j**) under CL showing kaolinite in dark blue, calcite in red, apatite in yellow and illite, quartz and biotite with no luminescence.

**Figure 10.** (**a**) Photograph of the sample NH\_36 showing the scanline and the emplacement of the two thin sections made in the sample. (**b**) Plot of the cumulative frequency percentage against distance percentage for the scanline. The diagonal line represents a uniform distribution. Dashed lines indicate a cluster, meaning a zone where a rapid increase of the number of fractures is observed (slope threshold >2). (**c**) Stick plot showing the fracture position along the scanline and for which the fracture density (P10) and the coefficient of variation (Cv) are given. (**d**) Thin section mosaics showing the position and the orientation of the scanlines. (**e**) Plots of the cumulative frequency percentage against distance percentage for each scanline. The diagonal line represents a uniform distribution and the dashed lines delimit a fracture cluster. (**f**) Stick plot showing the fracture position along the scanline and for which the fracture density (P10) and the coefficient of variation (Cv) are given. Data were provided by [42].

Regarding the thin section NH\_36\_1, the scanline SLH\_NH\_36\_1, perpendicular to the main fractures, shows a fracture frequency increases slowly the first 30%, then increases more strongly by presenting five fracture clusters (Figure 10e). This fracture distribution is highlighted by a Cv = 1.49, confirming a clustered arrangement of the fractures (Figure 10f). The fracture clusters are respectively comprised between, 0.9–1.2 cm, 1.4–1.5 cm, 1.55–1.6 cm, 1.7–1.85 cm, and 2.05–2.1 cm intervals (Figure 10e,f). The scanline SLV\_NH\_36\_1, parallel to the main fractures, shows a different trend. The fracture frequency increases slowly and irregularly (Figure 10e). This distribution is highlighted by a Cv = 1.01, indicating a random arrangement of the fractures (Figure 10f). Considering both scanlines, the average fracture density is of 5474 fracs/m.

Regarding thin section NH\_36\_2, the scanline SLH\_NH\_36\_2, parallel to the main fractures shows a fracture frequency trending similarly to SLV\_NH\_36\_1. Four fracture clusters were identified (Figure 10e), also visible in the stick plot between 0.95–1.3 cm, 1.85–2.05 cm, 2.5–2.7 cm, and 3.1–3.2 cm (Figure 10f). The Cv = 1.11 confirmed a random to clustered arrangement of the fractures. The scanline SLV\_NH\_36\_2, perpendicular to the main fractures, crosscut the magmatic preserved texture of the granite and a breccia. A change of the curve inclination is visible around 65% of the scanline, where the fracture frequency strongly increases (Figure 10e). It corresponds to the limit between both zones (Figure 10d). The Cv = 0.92 indicates a global regular to random fracture arrangement along this scanline (Figure 10f). Considering both scanlines, the average fracture density is of 4581 fracs/m.

Because fractures are difficult to recognize in the breccia of the sample NH\_36\_2, the fracture density calculated for both thin sections may be underestimated.

As for sample NH\_31, an important difference between the P<sup>10</sup> values of the sample and the thin sections is observed. However, a global random arrangement of the fractures at both scales is observed. Only SLH\_NH\_36\_1 presents a clustered distribution.

• Petrographic and Petrophysical Characterization

The two thin sections (Figure 11a–c) allow petrographic characterization of the sample. The first thin section, NH\_36\_1 (Figure 11a,b), shows a breccia of the granite with significant variations of the grain size. No crystallographic preferential orientation (CPO) is observed. Some zones show brecciated minerals with small precipitation of carbonates as calcite and dolomite in the microfractures (Figure 11d). Primary minerals are only slightly altered but intensively deformed. Quartz shows a pronounced undulatory extinction and starts to dynamically recrystallize by means of sub-grain rotation processes (Figure 11d). Other zones show preserved minerals, but also a significant amount of carbonate, mainly calcite, between the clasts (Figure 11e). The second thin section, NH\_36\_2 (Figure 11c), shows a granite with a preserved magmatic texture, but fractured, and a breccia composed of a carbonate matrix and transported clasts coming from the granite with no CPO. The preserved granite part shows a low alteration degree. Quartz, K-feldspars (orthoclase and microcline), and biotite are fractured and unaltered. Plagioclase is fractured, slightly altered, and replaced by kaolinite (Figure 11f). The breccia shows a matrix composed of dolomite and calcite flowing through transported clasts of unaltered quartz and feldspar and lenses of kaolinite (Figure 11g).

Bulk analyses show a low LOI (2.6%), a calcite content of 5.95%, and a porosity of 11.5%. XRD bulk and clay fraction analyses also reveal the presence of gypsum and halite.

#### **Sample NH\_23**

At outcrop (Figure 5b) and sample (Figure 12a) scales (Figure 1b), three compartments were identified: (1) a vein composed of a microcrystalline quartz-feldspathic unit, showing signs of foliation with clear shear sense indicators, bordered by a calcium rich mylonite and containing clasts of it, (2) a hydrothermalized zone in the granite along the vein, represented by a pinkish halo and (3) the porphyritic granite (Figure 12a).

**Figure 11.** (**a**) Sample NH\_36 collected close to a fault zone showing the location of the two thin sections. (**b**) A mosaic of the thin section NH\_36\_1 showing a breccia. (**c**) A mosaic of the thin section NH\_36\_2 showing the limit between a breccia and the almost preserved granite. (**d**) A microphotograph of the NH\_36\_1 thin section showing a brecciated and slightly altered plagioclase, a brecciated quartz with a significant undulatory extinction, starting to recrystallize into subgrains, a brecciated biotite, and calcite crystallizing in the microfractures. (**e**) A micrograph of thin section NH\_36\_1 showing brecciated and non-altered K-feldspar and quartz with dolomite and calcite deposits between the clasts. (**f**) A microphotograph zooming in the preserved granitic zone visible of the thin section NH\_36\_2 and showing a brecciated and partially replaced plagioclase into kaolinite and brecciated, but unaltered, quartz and biotite. (**g**) A microphotograph zooming in the brecciated part of the thin section NH\_36\_2 and showing a carbonate matrix composed of dolomite and calcite transported clasts from the granite.

> • Spatial fracture distribution: two scanlines were realized in the granitic part of the sample NH\_23 to evaluate the fracture arrangement from the vein towards the host rock (Figure 12a). The spatial analysis is summarized in Table 2. Fracture distributions presented in Figure 12b,c for each scanline show an evolution in two steps of the fracture cumulative frequency (Figure 12b).

> Along the SL1\_NH\_23 scanline, the frequency slowly increases and shows a regular fracture distribution. At 40% of the scanline, the frequency slightly increases, with a regular arrangement of the fractures. The stick plot Figure 12c highlights this distribution. The SL2\_NH\_23 scanline presents a similar evolution as SL1\_NH\_23 scanline, with an increase in the frequency at 3/4 of the scanline. This slope change is expressed at the end by a fracture cluster around 8.7–10 cm, clearly visible on the stick plot (Figure 12c). The Cv of 0.68 and 0.67 for each scanline shows a regular to random arrangement of the fractures

along both scanlines (Figure 12c, Table 2). Both scanlines fracture densities are equivalent, with respectively 1382 and 1322 fracs/m (Figure 12c, Table 2).

**Figure 12.** (**a**) A photo and the corresponding digitalization of the sample NH\_23 showing the different compartments that compose it, as well as the two scanlines realized in the host rock of the vein. (**b**) Plots of the cumulative frequency percentage against distance percentage for both scanlines. The diagonal represents a uniform distribution. Dashed lines indicate a zone where a rapid increase of the number of fractures is observed (slope threshold >2). (**c**) Stick plots showing the fracture position along the scanlines and for which the fracture density (P10) and the coefficient of variation (Cv) are given.

In order to complete the dataset, the method was repeated on two thin sections from the granite. One is at the border of the vein (NH\_23\_1) and the second away from it (NH\_23\_2) (Figure 13a). A scanline was realized in both thin sections (Figure 13b), perpendicular to the major vein. The spatial analysis is presented in Table 2.

Along the SL\_NH\_23\_1 scanline (Figure 13c), a low fracture density zone is present at the beginning of the scanline, then there is an increase of frequency between 0.9–1.4 cm (fracture cluster, Figure 13d), followed by an irregular fracture distribution until the 0.4 last cm where a fracture cluster was identified. Three fracture clusters are present in the SL\_NH\_23\_2 scanline around 1.5 cm, between 1.7–2.1 cm, and around 2.3 cm. From the first fracture cluster, the frequency increases significantly and irregularly. The scanline SL-NH\_23\_1, with the Cv = 0.77, shows a regular to random arrangement of the fractures, while the Cv = 1.19 of the scanline SL\_NH\_23\_2 indicate a random to clustered arrangement (Figure 13c). The fracture distribution varies with the position of the scanline and shows a P<sup>10</sup> slightly higher close to the vein (4798 fracs/m) than away from it (3879 fracs/m) (Figure 13d).

**Figure 13.** (**a**) Thin section location on the sample NH\_23. (**b**) Thin section mosaics showing the position and orientation of the scanlines. (**c**) Plots of the cumulative frequency percentage against distance percentage for each scanline. The diagonal represents a uniform distribution. Dashed lines indicate a zone where a rapid increase of the number of fractures is observed (slope threshold >2). (**d**) Stick plots showing the position of the fractures along the scanlines and for which the fracture density (P10) and the coefficient of variation (Cv) are given.

• Petrographic and petrophysical characterization: the vein of the sample NH\_23 consists of two parts. The major part is mainly composed of quartz, few feldspars, and oxide minerals having no CPO. Ankerite veinlets crosscut it, and are also intersected by calcite veinlets (Figure 14a,b). This vein includes clasts of carbonates having the same characteristics as the carbonate vein at the contact with the granite (Figure 12b). This thin carbonate vein is composed of ankerite layers and granite lenses (Figure 14c). By zooming in on the ankerite layer, some part of it appears as lenses with automorphic crystals in the swell, which are crushed and stretched through the pinches (Figure 14d). Granite is pinched between these ankerite layers. Quartz clasts present in the granite lenses show an undulatory extinction, as well as some evidences of subgrain rotation phenomena. Carbonates can deform plastically and accumulate

large amount of strain at relatively low P–T conditions, from a minimum temperature of 180 ◦C [78–81]. Quartz crystal plastic deformation is dominant from 600 ◦C [82]. Hence, in the present situation, carbonates accommodate large amounts of deformation by means of crystal plasticity, while granite is being deformed by cataclastic flow, i.e., a process accommodated by brittle processes. A localized and significant amount of deformation occurred in this vein. The major vein of this sample is thus composed of (1) a highly deformed zone made of ankerite and granite lenses and (2) a siliceous vein, which contains clasts of similar composition to the carbonate vein. We suggest that the carbonate vein was the first event, which was intensively deformed, and then intersected by the siliceous vein, tearing off pieces of the carbonate vein. Calcite and ankerite veins identified in Figure 14a,b intersect the carbonate vein and the siliceous vein.

**Figure 14.** Photomicrographs of the different compartments of the sample and their location in the sample. (**a**) Veins of ankerite and calcite crosscutting the major quartzitic/feldspathic vein of the sample under optical microscope in polarized–analyzed light. (**b**) Back-scattered electron image of the photomicrograph (**a**). (**c**) Photomicrograph of the ankerite–granite interlayering zone under optical microscope in polarized–analyzed light. (**d**) A zoom image of the ankerite vein, under optical microscope in polarized–analyzed light, presented in (**c**) and showing a sigmoid of ankerite with a swell of automorphic crystals crushed and stretched in the pinches. (**e**) The altered granite close to the vein showing a completely altered plagioclase and biotite both replaced by illite and oxides and partially altered K-feldspar under optical microscope in polarized–analyzed light. (**f**) The altered granite away from the vein showing a completely altered plagioclase replaced by illite and kaolinite, biotite partially replaced by illite and oxides, an unaltered K-feldspar, and calcite veinlets under optical microscope in polarized–analyzed light.

As presented above, the magmatic texture of the granitic part of the sample is preserved. However, a color change of the granite is observed close to the vein. At a sample scale, the granitic part along the vein (NH\_23\_1) shows a pronounced pinkish color (Figure 13a). In the thin section, the granite appears almost completely altered. Plagioclase and biotite are no longer recognizable and are replaced by illite and oxides. Perthitic K-feldspar are not completely affected by the alteration, but are partially replaced by illite (Figure 14e). Away from the vein (NH\_23\_2), the granite appears whitish at a sample scale (Figure 13a). Compared to NH\_23\_1, plagioclase are completely replaced by illite and kaolinite, but biotite are only partially altered and K-feldspar are unaltered (Figure 14f). This indicates that the granite is more affected by the alteration along the vein, in the hydrothermally altered zone. Bulk analyses performed on the granitic part of the sample show a LOI of 5.2%. In all the granite, calcite veinlets are observed coming from the major vein.

### *4.4. Geochemical Analyses*

The geochemistry of major elements, presented in Table 3, allows establishing diagrams representing selected elements versus LOI (Figure 15) in order to study the alteration degree of the selected samples.


**Table 3.** Major elements and loss on ignition (LOI) weight percentage (wt%) for the NH granite.

The LOI ranges from 2.50 to 10.90 wt% with an average around 5 wt%. The LOI values show a negative correlation with Na2O and SiO<sup>2</sup> and a positive one with K2O. The CaO content varies slightly between 1.81 wt% and 3.12 wt%, except for the sample NH\_27, which CaO content is about 9.10 wt%. Al2O3, MgO, and Fe2O<sup>3</sup> content vary more widely in the ranges 14.05–17.31 wt%, 0.24–1.06 wt%, and 2.69–4.61 wt%, respectively. However, a positive correlation is observed between Al2O<sup>3</sup> and LOI if the sample NH\_27 is rejected. These diagrams show that carbonate (represented by Ca and Mg) and oxide (represented by Fe) precipitations do not depend on the LOI.

### *4.5. Calcite Content*

Calcite is present in the majority of the samples. Samples homogeneously distributed in the studied area were selected for calcite content analyses. The calcite content is represented on the map in Figure 16 by the white dots and figures. The values range between 1.2% and 8.7%. Fracture zones, as well as the surrounding granite, present variable calcite content. However, the calcite content appears higher in the southeastern part of the range than in the northwest. All of the samples, except NH\_17, NH\_26, and NH\_31\_3, have a calcite content higher than 1.8%, meaning that they were affected by hydrothermal alteration, according to White et al. (2005) [72].

**Figure 15.** Plot of selected major element oxides (Na2O, K2O, Al2O<sup>3</sup> , CaO, MgO, Fe2O<sup>3</sup> , and SiO<sup>2</sup> ) versus loss on ignition (LOI) of samples from this study in orange and from [19] in grey. The dashed arrows show the different trends observed.

#### *4.6. Porosity and Mass-Balance*

Porosimetry measurement was only performed on samples NH\_27, NH\_31\_3, and NH\_36 (Table 4). NH\_36 is the closest to a fracture zone and has the highest porosity (11.5%). This suggests that the porosity increases with proximity to fracture zones. Porosity measurements were used to better decipher the petrophysical properties of the rock for geothermal purpose and to realize mass-balance calculations. The chemical compositions recalculated after suppression of the LOI, the densities, and volume factors (Fv), assuming XAl2O3 = 0 of the rock samples used for mass balance calculations, are given in Table 4. The F<sup>v</sup> shows values very close to 1, indicating a small change in volume between the freshest sample and the altered ones.

The results of mass-balance calculations, corresponding to the absolute mobility values of each element for each sample, are given in Table 5, by considering a constant volume, F<sup>v</sup> = 1, as exposed by [76]. Positive values represent the gains and negative values the losses of the considered elements. Absolute mobility values indicate almost immobility of Al2O3, TiO2, and MnO. They also show losses of SiO<sup>2</sup> and Na2O, which are three times more important in NH\_27 than in NH\_31-3, and twice that of NH\_36. The losses of Fe2O<sup>3</sup> and MgO are more important in NH\_31\_3 and less important in NH\_36. CaO losses are observed in NH\_31\_3, whereas CaO gains are observed in NH\_36 and a high gain is observed in NH\_27. Finally, the results show a gain of K2O in samples NH\_27 and NH\_31\_3 and a loss in NH\_37.

**Figure 16.** NH geological map showing the location and the associated calcite content of samples from this study represented by the white dots and of samples from [19] by the grey dots.



<sup>1</sup> Geochemical data recalculated from [19].


**Table 5.** Results of mass-balance calculations assuming Fv = 1.

#### *4.7. Temperature Conditions*

The clay composition of the fractions <2 µm and 2–6 µm was given in Table 1. For some of the samples containing enough illite, Kübler Index (KI) was measured for both fractions (Table 6). The fraction <2 µm likely is supposed to represent neoformed clay minerals, thus corresponding to the youngest event. By contrast, the fraction 2–6 µm might contain either more developed illite crystals by inherited grains recrystallization, or a mix of detrital and neoformed minerals. The KI gives information concerning the degree of metamorphism for each fraction. In some fraction, it was not possible to measure the KI due to the too low amount of illite.

**Table 6.** List of samples with their respective FWHM and Kübler Index (KI) values in air-dried (AD) conditions for the fractions <2 µm and 2–6 µm. n.m.—not measured.


KI values range from 1.32∆ ◦2θ to 0.29∆ ◦2θ for the <2 µm fraction and from 1.27∆ ◦2θ to 0.21∆ ◦2θ for the 2–6 µm fraction (Table 6). The spatial distribution of the samples and their associated KI values are shown in Figure 17 by the dots. In both fractions, most of the samples present KI values corresponding to the diagenetic zone, except for two samples (NH\_32 and NH\_34). These samples are located in the northwestern part of the main granitic body (Figure 7a,b), at the contact with the Proterozoic basement. They present lower KI values of low anchizone and epizone. No significant variations in KI or trends are observed between both fractions.

**Figure 17.** Geological map representing the Kübler Index (KI) in air-dried conditions of each sample from this study (dots) and from [19] (triangles) and the corresponding metamorphic zone represented by the different colors indicated in the legend for (**a**) the fraction <2 µm and (**b**) the fraction 2–6 µm.

Some samples contain only kaolinite and no illite. Positive trends have been identified between KI and KCI for both clay fractions <2 µm and 2–6 µm (Figure 18). Samples NH\_6, NH\_8, and NH\_31\_1\_2, with out of range values, due to the presence of I/S and/or corrensite interfering with the 7Å peak, were excluded from the correlation. The trends observed in the two different fractions are similar and give more confidence into the concomitant evolution of KI and KCI. The correlation provides temperature indications for illite-free samples. Thus, samples NH\_26, NH\_33, and NH\_36 show values equivalent to diagenetic zone and anchizone conditions.

**Figure 18.** (**a**) Diagrams showing Kübler Index (KI) values versus the Kaolinite Crystallinity Index (KCI) for the clay fractions <2 µm and 2–6 µm. (**b**) Diagram showing positive correlations between KI and KCI for the clay fractions <2 µm and 2–6 µm, excluding samples NH\_6, NH\_8, and NH\_31\_1\_2.

#### **5. Discussion**

#### *5.1. Argillic Alteration Dominance*

The characterization of the NH granite alteration processes in the vicinity of fracture zones reveals the presence of various secondary minerals, such as clay minerals (kaolinite, illite, I/S mixed layer, corrensite, and vermiculite), carbonates (calcite, dolomite, ankerite, siderite), and oxides. Thus, two successive types of hydrothermal alteration events, characterized by [19] in the protolith, were observed:


However, compared to [19], the samples are more altered and corrensite is not as evident as in the samples from this study. Kaolinite and illite are the prevailing clay minerals. This confirms a significant fluid–rock interaction near fractures and a predominant argillic alteration, which has overprinted almost completely the propylitic alteration. Kaolinite, being the dominant clay mineral, indicates either a more important leaching of the rock or the circulation of a more acidic fluid [90].

The samples NH\_24, NH\_26, and NH\_33 contain a small amount of vermiculite, which can be associated to hydrothermal alteration at low temperature or to weathering. It is commonly thought that most of the vermiculite is formed under supergene conditions [91,92]. In these samples, the amount of vermiculite is low and the weathering contribution already discarded by [19].

#### *5.2. Thermal Evolution toward Fracture Zones*

Studied samples present KI values characteristic of the diagenetic zone, meaning temperatures lower than 200 ◦C [93]. However, KI values of samples NH\_32 and NH\_34 have lower KI values with anchizonal to epizonal conditions, meaning temperatures around 300 ◦C [93]. These two samples present the highest fracture density (Fd4) suggesting that shear heating could contribute to a local increase of temperature [94]. Moreover, KI values are similar between both clay fractions indicating the predominance of neoformed illite crystallization close to fracture zones. It is highlighted by the presence of illite veins observed microscopically. By comparing KI values from this study and from [19], the KI tends to decrease approaching fracture zones. Thus, the greater the fracturing, the higher was the temperature, except for NH\_31\_1\_2 and NH\_24. These two samples present higher KI values, meaning lower temperatures. It can be explained by the presence of I/S and vermiculite, forming at lower temperature than illite and kaolinite [91,92,95]. The samples NH\_26, NH\_33, and NH\_36 present only kaolinite. KCI values correlating with KI values, these samples show temperatures estimated to be around 200 ◦C or less, which correspond to the temperature obtained for the other samples. Likewise, the presence of kaolinite in hydrothermal alteration paragenesis indicates temperature lower than 200 ◦C [90].

### *5.3. A Multi-Stage Paleo-Fluid Circulation*

Hydrothermal alteration in crystalline basement rocks induces the precipitation of secondary minerals that can seal the fractures [2]. The argillic facies, described above, is also characterized by fractures filled by various kinds of secondary minerals, as a result of different fluid generations. Veins are formed from fluids that had reacted with granite [96] and transported various chemical elements. Through the petrographic analyses of the whole samples, a relative chronology between the different veins can be determined. Six vein generations, following each other, were identified (Figures 6 and 9):


Two types of calcite veins and the carbonate vein of phase 5 were, thus, identified through the sample NH\_31, allowing the definition of two generations of calcite. However, they do not allow a decision on if the calcite veins identified in the other samples correspond to the generation 4 or 6. CL analyses are ongoing to identify the type of calcite generation. Sample NH\_31 and the multiple vein generations show how complex the fluid circulation history was in this area.

#### *5.4. Fluid Circulation and Argillic Alteration Effects on Petrographic and Petrophysical Behavior*

The effects of the alteration on the element transfers are described by the diagrams plotting major element oxides against LOI (Figure 15) and by mass-balance calculations (Table 5) using the Gresens method [76] to quantify the losses and gains of elements during hydrothermal alteration. To this end, data from this study and from [19] were used. LOI has been defined as an indicator of the alteration degree [19,98,99] supporting optical observations. In this study, LOI values range from 2.5% to 10.9% (Table 3), whereas, Klee et al. (2021) [19] obtained values from 1.1% to 2.8% for the protolith. These values confirm a more pronounced alteration of the granite in the vicinity of fracture zones.

Concerning element transfers, only minor variations of Al2O<sup>3</sup> were observed compared to the LOI, also confirmed through mass-balance calculations. Al is thus considered as immobile. This study has shown a significant SiO<sup>2</sup> negative correlation with LOI. This loss is confirmed by mass-balance calculations. It indicates the partial silicate alteration, explaining the presence of quartz veins and veinlets through the granite. A negative correlation with LOI was observed for Na2O, confirmed by the loss of Na2O obtained by mass-balance calculation. Indeed, altered plagioclase are depleted in Na2O. No Na-bearing newly formed minerals (except a little I/S and C/S) was encountered. It is likely that Na was exported out of the alteration zone. When the alteration of plagioclase is less pronounced, as in samples NH\_31\_3 and NH\_36 (Table 3), the Na2O depletion is lower. However, a global enrichment of K2O is observed linked to illite crystallization. A positive correlation is observed between the amount of alteration and illite formation. K-feldspar being rarely altered, chemical modelling would be necessary to determine whether the amount of K release by biotite alteration would be sufficient to allow the rather important formation of illite. MgO and Fe2O<sup>3</sup> present no clear correlation with LOI. However, low depletion of Fe2O<sup>3</sup> and MgO compared to the protolith were identified by mass-balance calculations. It is suggested that these depletions are linked to the alteration of biotite but they are compensated by their precipitation as oxides or in carbonates. Thus, it is likely that no Fe or Mg is exported out of the alteration zones. CaO and calcite content present no correlation with the LOI. Samples NH\_19, NH\_36 (this study), and NH\_3 (in [19]) present a similar calcite content, respectively, of 6.3%, 6.0%, and 6.5%, whereas they present different LOI values (4.1%, 2.6%, and 2.8%, respectively). The case of a high calcite content associated to a low LOI can be explained by (1) physicochemical fluid composition bringing Ca, and not allowing a complete alteration of plagioclase and biotite into clay minerals [100]; (2) the residence time of the fluid not being sufficient [101]; or (3) a non-sufficient amount of fluid to allow the transformation of plagioclase and biotite into clay minerals. CaO losses are attributed to the alteration of plagioclase. However, the amount of Ca released by the alteration of plagioclase is certainly not sufficient to explain the crystallization of large amounts of carbonate into the granite veins. We infer that Ca is related to an external source as it is gained by the system (open system). As carbonate veins are related to the SDVFZ activity, we suggest that the source of the Ca is the Proterozoic series, which contain dolomite and carbonate sequences.

Fracture zones created porosity through microfractures and spaces between secondary minerals (Figure 6f) precipitated during primary mineral alteration. When fracturing increases, alteration increases too, as well as porosity [10]. However, the subsequent mineralization and chemical alteration can either decrease or increase the porosity of the rock [2]. For a similar LOI, porosity values vary significantly (e.g., NH\_3 [19], NH\_23, and NH\_31\_3). No correlation is visible between porosity and alteration or calcite content.

#### *5.5. Relation among Fluid Circulation, Alteration, and Fracture Density*

It is expected that areas along the rear southern limit of the CBS have recorded less transcurrent shear than areas situated along its northern front (Section 4.1). Recent work by Chabani et al. (2021) [42] has shown a structural compartmentalization occurring at the NH scale with a varying intensity that may influence fluid flow through the fracture network. Likewise, they identified a complex network of joints at outcrop scale, also

encountered in this study at the sample and thin section scales, playing a key role in the fracture connectivity. The authors identified several fracture sets, among which, the NW/SE and the E/W oriented sets are predominant. The NW/SE trend, following the SDVFZ direction, controls the geometry in the whole range, whereas the E/W set, characterized by several short fractures, is mostly present in the central and southeastern part of the NH. The geometrical analysis of both fracture sets showed that the connectivity is ruled by fractures of different sizes. Regarding the fracture distribution, the highest fracture density is recorded within the rear southern part with values five times higher than in the northern part. This can be explained by the complex tectonic setting and the gradient of deformation observed in the entire NH range, with evidence of extreme shearing in the southern part as already presented. Moreover, through scanline analyses along drone photogrammetric outcrop profiles and ground outcrop profiles, Chabani et al. (this issue, under review) [44] show a clear correlation between fracture density and distance from a fault zone. The closer the fault zone, the greater the fracture density. There is no straightforward correlation between amounts of deformation and fracture density. Fracture density depends on a series of parameters notably rock competence, anisotropy of units and possible presence of detachment zones concentrating deformation in narrow areas.

This study, together with that of Klee et al. (2020) [19], confirm the increase of fracture density towards fault zones through several samples collected at different distances from the faults. Moreover, at the NH scale, the LOI increases as the fracture zones are approached (Section 5.4). The more intense the fracturing, the higher the alteration. Likewise, porosity values obtained for samples from Klee et al. (2021) [19] range from 2.2% to 5.2%, whereas, porosity values for this study samples range from 10.1% to 14.0%. Close to fracture zones, samples have more than twice the porosity than the samples away from them. Calcite content (Figure 16) also show higher values near to fracture zones, highlighting the importance of the presence of fractures allowing fluid circulations and thus carbonate precipitation, which mainly filled and sealed the fractures [71,102]. Carbonate veins are present in the whole range, preferentially orientated following the NH strike, probably related to the SDVFZ activity. However, calcite content is generally higher in the southeastern part of the range. This part is characterized by a high fracture density due to complex tectonic setting, related to the GFZ activity [42]. The connectivity within this part is ruled by the small and large fractures, and an additional complex joint network leading the fluid supply toward the fault zone.

The comparison of the data from Klee et al. (2021) [19] with those in this study at the NH scale shows that the increase in fracture density is correlated with the increases in alteration degree, porosity, and calcite content, respectively. However, no correlation is observed between alteration, porosity, and calcite content all together. The sample NH\_36 (Figure 11) has shown that calcite content is not related to the intensity of alteration (Section 5.4). This highly fractured sample has been characterized by a specific fracture arrangement, composed mainly of fracture clusters, following the SDVFZ direction. It allows the fluid to circulate following these clusters, and then creating a flow anisotropy. However, only a low alteration degree is observed, which can either be due to (1) specific physicochemical fluid composition [100]; (2) an equilibrium between the fluid and the surrounding rock; (3) an insufficient residence time of the fluid [101]; or (4) a non-sufficient amount of fluid. Fracture density increase does not necessarily induce the increase of alteration (Figure 19a,b), whereas at the NH scale, a general correlation between fracture density and alteration was shown. Sample NH\_36 shows that fluid can circulate through a highly fractured granite without necessarily producing alteration (Figure 19b).

Numerous fractures and veins, showing a high fluid–rock ratio, crosscut the granite altering it consequently (Figure 20a,b). Faulkner et al. (2010) [11] have shown that within crystalline rocks, the flow can be ruled by a small number of fractures within the rock surrounding a fracture zone. The fracture interconnections constitute the main parameter, which can enhance the fluid circulation. Samples NH\_31 and NH\_23 showed the relation between fracturing and alteration at local scale (Section 4.3.2). Thin section fracture analyses

showed that the fracture density average is similar in both samples. NH\_31 consists of a brecciated vein developing an alteration gradient but no fracturing gradient (Figure 20c), while NH\_23, perpendicular to NH\_31, consists of a mylonite developing an alteration and a fracturing gradient (Figure 20d). Regarding the stress axis orientation, it is suggested that the main stress axis σ3 is at a very high angle to the NH\_31 initial quartz vein. The close to normal angle between the initial quartz vein and the stress axis σ3 was favorable to reactivation, inducing a brecciated vein without developing a significant additional fracture gradient in the surrounding rock (Figure 20c). It has been shown that remnants of a quartz vein composed the NH\_31 brecciated vein. This quartz vein, developed during a past event of unknown age and origin, possibly magmatic (last crystallization fluids). It is suggested that this vein was reactivated, letting a new fluid rich in Ca circulates. Then carbonates crystallized giving a brecciated vein as a final product. The alteration gradient observed in the wall rock is especially pronounced at the borders of the brecciated vein. The proximity with the main fluid pathway induced an important leaching by the fluid. Within NH\_23 (Figure 20d), it is supposed that the quartz-feldspathic unit was initially a dyke crosscutting the granitic pluton. Such dykes have been observed in the surroundings. During SDVFZ activity, reactivation of this zone of weakness permitted percolation of a Ca-rich fluid. An intensive shearing induced dynamic recrystallization developing a mylonite in the borders and its associated fracturing gradient in the wall rock. In that case, the main stress axis σ1 would be characterized by an intermediate angle to the shear plane. A fracturing gradient is observed in the surrounding rock. The fracture density induced in the surrounding rock does not further increase. Asymmetric clasts and shear bands are observed within this mylonitic layer.

**Figure 19.** Synthetic scheme showing, from low to moderate strain, the interaction between the fluid and the granite in the cases of a very low fluid/rock ratio. (**a**) Open fractures with an incipient alteration of the surrounding rock. (**b**) Brecciated zones with a carbonated matrix and no change of alteration degree. No scale is given for this scheme, because it can represent fracture zones of several order of magnitude.

Fluid circulation and induced fracturing have promoted fluid–rock interactions and the granite alteration, which is more pronounced in NH\_23 than in NH\_31 (Figures 9h–k and 14e,f). Those two samples showed that at sample and outcrop scales, fracturing and alteration are heterogeneous, but also that the alteration degree is not always related to the fracture density (Figure 20c,d).

**Figure 20.** Synthetic scheme showing, from low to moderate strain, the interaction between the fluid and the granite in the cases of a high fluid/rock ratio observed in the field. (**a**) An open fracture with an incipient alteration gradient at the border. (**b**) A sealed fracture with a slight alteration gradient. (**c**) A brecciated vein induced from fracture reactivation and showing an alteration gradient, but no fracturing gradient. (**d**) A mylonite made of carbonates and granitic lenses showing an alteration gradient and a fracturing gradient. NH\_31 and NH\_23 show a similar fracture density (Fd). No scale is given for this scheme, because it can represent fracture zones of several order of magnitude.

> These sample analyses allowed us to study a fault zone development depending on strain, fluid–rock ratio, and material rheology. It is shown that at low to moderate regional strain, incipient local high strain concentration is present (Figure 20). It has been observed that:


At any scales, fracture density promotes fluid flow through the fracture network provided a fluid is present [5,11]. However, the alteration degree is not correlated to the fracture density.

#### *5.6. Implication of Alteration in Terms of Geothermal Reservoir Properties*

Fresh granite has a very low initial matrix porosity (<1%), which "does not allow" the fluid circulation, hence inducing a low permeability [9]. A granitic geothermal reservoir is considered as exploitable when it presents a connected fracture network increasing the permeability and in which a sufficient amount of hot fluid circulates [2,3,9,11]. By flowing through fractures, the fluid interacts with the rock, increasing the matrix porosity and permeability promoted by the dissolution of the primary minerals and crystallization of newly-formed phases [13]. However, newly-formed minerals can also crystallize in the fractures and seal them, reducing the porosity and the permeability [105,106]. Thus, sealed fractures are transformed from conduits into barriers to fluid flow [83,107,108] and impact the geothermal production by decreasing the connectivity between the fractures and hence the permeability [2,109].

The NH altered granite shows an important fracture network and a high matrix porosity, which allowed fluids to circulate and to interact with the surrounding rock. Indeed, numerous veins with various infills crosscut the granite indicating several successive fluid circulation events. Carbonates occupy a prominent part of the fracture system, which can be easily dissolved thanks to acid injections in order to connect the boreholes to major conductive fractures for geothermal exploitation. It is suggested that, when NH were an active reservoir at depth, fractures were only partially filled, and the fluid could flow through the fracture network. It has been seen that the stress field has a major impact on the fluid circulation. Indeed, drilling into fractures at a very high angle from the main stress axis σ1, such as exposed by sample NH\_31, is favorable to allow fluid to circulate. In the event of geothermal exploitation, only minor chemical stimulation, if any, would have been necessary [13,71,110]. Moreover, the alteration amount is not necessarily related to the degree of fracturing and, therefore, the fracture network influence on fluid circulation is hardly predictable. Thus, due to the conduit-barrier role, the deformation gradient, the degree of fracturing, the alteration processes, and the relationship between them, have a large impact on geothermal production [109].

#### **6. Conclusions**

Noble Hills (NH) is a newly studied area, in terms of an exhumed granitic geothermal reservoir. It provides an excellent opportunity to give fundamental scientific input in 3D, allowing for better understanding of granitic reservoir behavior in a trans-tensional context. This analogue shows how complex a granitic reservoir can be, in terms of structures, fluid circulation, and fluid–rock interactions. This study proposes a geometric, petrographic, petrophysical, and geochemical description in order to characterize the influence of fracturing on fluid circulation and alteration processes.

Approaching fracture zones at large scale, the NH granite shows signs of several generations of fluid circulations resulting in successive veins of various mineralization. Fluid circulation being more important in the vicinity of fracture zones, a stronger fluid– rock interaction is observed. Thus, argillic alteration prevails compared to in the protolith. It is highlighted by the increase of the LOI correlated to a Na depletion due to plagioclase alteration and a K enrichment associated to illite precipitation. Likewise, the porosity, the calcite content, and the temperature increase nearer to fracture zones. However, no correlation exists among LOI, porosity, and calcite content altogether. Moreover, a high fracture density does not necessarily imply a strong alteration (e.g., sample NH\_36).

This relation among fluid circulation, alteration, and fracturing is also visible at a sample scale. The higher the fracture density, the more pronounced the alteration. However, samples NH\_31 and NH\_23 showed how complex this relation could be:


These two samples, showing different deformation features as a result of a different orientation within the stress field, present a similar fracture density. Strain was accumulated within a carbonate mylonite within sample NH\_23. The alteration gradient is more pronounced in this sample, but the fracture density does not change. Sample NH\_36, consisting of a granite composed of a cohesive breccia, whose matrix is made of dolomite, shows a low alteration. Even locally, alteration does not always depend on the deformation gradient or on the fracture density.

This study shows that the deformation gradient observed at a large scale is also visible locally in the context of a low to moderate strain. It also highlights the importance of mineral crystallization in a geothermal reservoir. Fluid flow depends on a connected network of open and permeable fractures. In reservoirs at depth, fractures can be sealed and act as a barrier. Stimulation techniques are needed in order to reopen them so that a drain allowing a new fluid circulation is created. The influence of fracture zones on fluid flow and alteration is difficult to predict and yet impacts the production from the reservoir.

In order to complete this work, a future study will focus on the influence of a fault zone on fluid circulation and alteration processes, in the NH, at high strain conditions. Moreover, laboratory investigations could be performed to better understand the controlling parameters of the ongoing processes and fracturing of rocks.

**Author Contributions:** Conceptualization, J.K., A.C., B.A.L., S.P., R.L.H. and G.T.; methodology, J.K., A.C., B.A.L., S.P., R.L.H. and G.T.; software, J.K.; validation, A.C., B.A.L., S.P., R.L.H. and G.T.; formal analysis, J.K.; investigation, J.K., A.C., B.A.L., S.P., R.L.H. and G.T.; resources, J.K.; data curation, J.K., A.C., B.A.L., S.P., R.L.H. and G.T.; writing—original draft preparation, J.K.; writing—review and editing, A.C., B.A.L., S.P., R.L.H. and G.T.; and H2020 MEET consortium; visualization, A.C., B.A.L., S.P., R.L.H. and G.T.; supervision, J.K.; project administration, G.T.; funding acquisition, G.T. and H2020 MEET consortium. All authors have read and agreed to the published version of the manuscript.

**Funding:** This project has received funding from the European Union's Horizon 2020 research and innovation program under grant agreement no. 792037 (H2020 MEET project).

**Data Availability Statement:** Not applicable.

**Acknowledgments:** This manuscript was prepared as a contribution to the PhD thesis (Institut Polytechnique UniLaSalle Beauvais) of Johanne Klee, which was funded by the European Union's Horizon 2020 research and innovation program under grant agreement no. 792037 (H2020 MEET project). The authors greatly thank Terry Pavlis for his support and helpful exchanges about the regional geology of Death Valley and the Noble Hills. Albert Genter is thanked for the helpful discussions and knowledge about fractured granitic reservoirs. We are grateful to Klaus Wemmer for his help on XRD analyses and the fruitful discussions. We also thank Graciela Sosa and Alphonse M. Van den Kerkhof for their help on cathodoluminescence observations and acquisitions. We thank Mahdi Chettabi, Thi Tuyen Nguyen, Elena Pavlovskaia, Carl Tixier, and Chloé Gindrat for their help with the analyses. We acknowledge the H2020 MEET consortium for their helpful comments and the validation of the manuscript. We would like also to thank the Hauts-de-France region for its help in setting up the MEET project, in particular the FRAPPE (Fonds Regional d'Aide aux Porteurs de Projets Euopéens). We finally would like to thank the two anonymous reviewers and the editors for their help and remarks in improving this manuscript.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


## *Article* **Fracture Spacing Variability and the Distribution of Fracture Patterns in Granitic Geothermal Reservoir: A Case Study in the Noble Hills Range (Death Valley, CA, USA)**

**Arezki Chabani 1,\* , Ghislain Trullenque <sup>1</sup> , Johanne Klee <sup>1</sup> and Béatrice A. Ledésert <sup>2</sup>**


**Abstract:** Scanlines constitute a robust method to better understand in 3D the fracture network variability in naturally fractured geothermal reservoirs. This study aims to characterize the spacing variability and the distribution of fracture patterns in a fracture granitic reservoir, and the impact of the major faults on fracture distribution and fluid circulation. The analogue target named the Noble Hills (NH) range is located in Death Valley (DV, USA). It is considered as an analogue of the geothermal reservoir presently exploited in the Upper Rhine Graben (Soultz-sous-Forêts, eastern of France). The methodology undertaken is based on the analyze of 10 scanlines located in the central part of the NH from fieldwork and virtual (photogrammetric models) data. Our main results reveal: (1) NE/SW, E/W, and NW/SE fracture sets are the most recorded orientations along the virtual scanlines; (2) spacing distribution within NH shows that the clustering depends on fracture orientation; and (3) a strong clustering of the fracture system was highlighted in the highly deformed zones and close to the Southern Death Valley fault zone (SDVFZ) and thrust faults. Furthermore, the fracture patterns were controlled by the structural heritage. Two major components should be considered in reservoir modeling: the deformation gradient and the proximity to the regional major faults.

**Keywords:** fracture network variability; Death Valley; granite; spacing distribution; fracture intensity P10; geothermal reservoir characterization

#### **1. Introduction**

In deep geothermal systems, many studies have been undertaken to better understand the importance of the natural fractures in various contexts [1,2]. In granitic basement rocks, the permeability is mostly increased by the fracture network and faults [3–7], while the porosity is increased by both the alteration (e.g., dissolution of primary minerals) and the proximity to fracture zones ([8], this issue). The low rock matrix permeability and porosity allow the fluid flow within fracture networks [9–11]. The understanding of the spatial arrangement of the fracture network constitutes the main issue in fractured reservoirs [1,3,7,12,13].

A fracture network is characterized by geometrical parameters such as lengths, spacings, widths, orientations, fracture distributions, and the relationships between them significantly affect the connectivity within the reservoir [9,14–17]. Among these parameters, spacing between fractures is a well-considered parameter, because it controls the probability of intersecting fractures during drilling [18]. Statistic parameters that describe fracture spacing include: (1) The mean, which characterizes the global expected frequency of fracture intersection, and (2) the standard deviation, which describes the distribution of the fractures around the mean.

**Citation:** Chabani, A.; Trullenque, G.; Klee, J.; Ledésert, B.A. Fracture Spacing Variability and the Distribution of Fracture Patterns in Granitic Geothermal Reservoir: A Case Study in the Noble Hills Range (Death Valley, CA, USA). *Geosciences* **2021**, *11*, 520. https://doi.org/ 10.3390/geosciences11120520

Academic Editors: Giovanni Barreca and Jesus Martinez-Frias

Received: 21 September 2021 Accepted: 12 December 2021 Published: 17 December 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

Regarding the spacing distribution, fractured zones can be classified into: (1) Fracture corridor, a term usually used for a dominant set of fractures displaying an important variation of fracture intensity. It can represent the main drains for fluid circulation in various reservoir contexts such as geothermal fields [19]; (2) fracture arrays, a term generally used to define a dominant set of fractures which forms an angle to the swarm (area in which any kind of fracture appears) [20]; (3) shear zone, which is defined as a continuous deformed zone with a high strain [21], accommodated by a cataclastic process in granitic rocks and crystalline plasticity in (e.g., carbonate rocks); and (4) fault zone characterized by a fault and its associated damage zone which can act as a barrier or a drain for flow, depending on its intrinsic properties [5,20,22]. In crystalline basement rocks, the fracture distribution within the damage zone is influenced by the distance from the fault core and its displacement along the fault plane [23]. Indeed, the strong variation in fracture distribution (fracture densities) is commonly observed near active faults. Ostermeijer et al. [23] add that the pattern is mainly ruled by the distribution of macro-damage induced on shear-accommodating subsidiary fractures.

Spatial organization of fracture systems became an important studied topic in the recent decades because of the necessity to better understand the architecture of fractured reservoirs [7,24–26]. The spatial arrangement can be quantified using statistical laws (e.g., power law, log normal, and exponential law) [24,27,28] or statistical parameters, such as the coefficient of variability (Cv) along 1D [20] and the normalized correlation count method [27]. The main goal is to enhance the fracture distribution understanding (clustered, random, or uniform distribution) and its effects on connectivity [29]. In that case, many studies are focused on fracture networks characterization in various settings and at different scales [3,12,16,20,30,31]. They commonly used field analogues at surface to resolve the challenge of lack of sub-surface information in reservoirs [32]. The characterization of heterogeneity of the fracture spacing and the fracture abundance at any scale may be performed using line sampling method along one dimension (1D) named scanline (e.g., [26]). The present study combines the spacing data of joints (opening-mode fractures), veins (partially or fully filled), and faults to highlight the spatial arrangement of the fracture patterns in granitic rocks and the influence of the regional major faults. In the present study, the measured fractures, whatever their filling have been classified according to their orientation.

The present work is part of the European MEET project (multidisciplinary and multicontext demonstration of EGS exploration and exploitation techniques and potentials, [33]). This study proposes to (1) describe fracture system distribution at outcrop scale, based on fracture network parameters; (2) shows the role of the regional major faults proximity on the fracture patterns evolution in the basement rocks; and (3) highlights the impact of the deformation at outcrop scale. The present study was performed in the desert environment of Noble Hills (NH) fractured granitic basement, located in the southern termination of Death Valley (Death Valley, CA, USA), and is considered as a paleo geothermal analogue of the Upper Rhine Graben (URG, Alsace area situated in the eastern of France) ([25,34,35], this issue) geothermal systems producing electricity, because of the similarities in the basement rock nature (granite), hydrothermal alterations and the trans-tensional tectonic setting [25,34–36]. However, the geological history of the NH range is rather different from that of to those in the URG, but numerous pieces of evidence of analogy have been highlighted by recent work of Klee et al., [37], which addressed a list of similarities between the URG reservoir targets (exploited geothermal present-day reservoir) and the NH ranges:


Based on scanline methodology (e.g., [26]), this work has been performed using a spacing measurement, compiled from four different canyons located in the central part of NH. This central part has been characterized as having a distinct spatial arrangement of fractures at different scales in comparison with the northeast and southeast parts (for additional explanations, see [25]). The scanlines are located in the granitic part of the NH range, the so called crystalline basement slice (CBS) according to Brady et al. [38]. Some of the measures were acquired directly from the field and others from virtual scanlines (method detailed in Section 3.2). Apertures of fractures have also been measured directly in the field. Numerous fractures were filled by newly formed minerals such as carbonates, oxides, and sometimes barite.

In this study, scanline methodology and statistical tools are used to better understand the fracture spacing variability and the distribution of fracture patterns at depth. This allows better characterizing reservoirs in response to the developing geothermal exploration and exploitation by EGS in basement rock context. This study was conducted:


#### **2. Geological Setting**

The NH structurally belongs to the DV region (Figure 1a), which is characterized by a complex tectonic history (e.g., [39]), starting with late Cenozoic extensional and trans-tensional structures which overprint the Mesozoic to Early Cenozoic contractional structures [39–41]. The extensional regime of the DV has begun around 16 Ma [42,43], and is shifted to a trans-tensional regime around 5 Ma [39,44–46]. Recent work by Pavlis and Trullenque, [36] reconsider the age of the transcurrent deformation in DV around 12 Ma.

The NH ranges forms the principal physiographic feature aligned with segments of the right-lateral Southern Death Valley Fault Zone (SDVFZ) [25,47] (Figure 1b). The SDVFZ net dextral strike-slip displacement has been estimated around 40–41 km [36]. A whole compressional region was created by the interaction between the SDVFZ and the Garlock Fault (GF) system (see Figure 1b for location), which leads to shortening within the Avawatz Mountains (Figure 1b) [48–50].

The exhumation history of NH range is poorly described in the literature. Based on KI/temperature of illite crystals, recent work by Klee et al. [37] highlighted that the southeastern of NH is much elevated, with a higher temperature which could indicate that the south-eastern part of NH was buried deeper than its north-western part and has been exhumed.

Recent work by Chabani et al., [25] highlights the structural organization of the NH range according to the orders of fault magnitude classification by analyzing 2D maps at different scales. These orders consist in (1) second order scale, referring to the faults comprised between 20 and 30 km length; (2) third order scale, referring to faults around 10 km length; and (3) fourth order, referring to the faults under 1 km length. The first order referring to the crustal faults (higher than 100 km length) is not observed within the NH range.

**Figure 1.** (**a**,**b**) Location and geological setting of DV and NH studied area modified after [50], NDVFZ: Northern Death Valley Fault Zone, SDVFZ: Southern Death Valley Fault Zone, GFZ: Garlock fault zone, CA: California, NV: Nevada, IH: Ibex Hills, SPH: Saddle Peak Hills. (**c**) Structural scheme of the NH range performed thanks to high-resolution digital mapping techniques (see below) modified after [34,47]. Additional digitized fractures were obtained using orthophotos. NHFs: Noble Hills formations.

The SDVFZ trending NW/SE and the GFZ trending E/W controlled NH range geometry. Indeed, the SDVFZ controls the NH geometry at large scale within the second order scale, while the GFZ trending E/W controls the NH geometry within the third order scale. Chabani et al., [25] add that the NH are divided into three internal structural domains: (1) Domain A, to the north, is characterized by the dominance of the NW/SE direction at the fourth order scale; (2) domain B, central, is marked by the dominance of the E/W and the NW/SE directions at respectively the fourth and third order scales; and (3) domain C, to the south, is also characterized by the E/W and NW/SE directions dominance but at the third and fourth order scales, respectively.

Numerous episodes of deformations have been highlighted during the fieldwork campaigns. Indeed, the SDVFZ fault segments act with a dextral movement (black lines in Figure 2b), highlighting an intense deformation with local evidences of extreme shearing. These structures are contemporaneous with the syn-kinematic dextral strike faults (orange lines in Figure 2b), highlighted in the recent work done by Klee et al. [8]. In addition, compressional structures like thrust faults crosscut outcrops 6 and 8 (red lines in Figure 2b). A clear overprinting has been recognized between SDVFZ (which also crosscut the OT2, OT6, and OT7) and the compressive structures are due to the GFZ, which acts with a sinistral movement. Furthermore, the thrusting highlighted in the present study postdates the activity of the SDVFZ. According to Chabani et al. [25], it is tempting to relate the thrust structures to the activity along the frontal termination of GFZ. Furthermore, the compressive structures are related to the interaction of the NH ranges with the Avawatz mountains during the GFZ movement.

**Figure 2.** (**a**) Map highlighting the structural position of the central part of NH, including the outcrops (OT) location and (**b**) SDVFZ segments position in black, syn-kinematic dextral strike slip faults in orange, sinistral strike-slip faults in green lines, and thrust faults in red. Dextral strike slip faults are syn-kinematic with SDVFZ episode, those systems are followed by thrust faults, which are contemporaneous with the GFZ orientated globally E/W.

A gradient of deformation has been highlighted in the central part of NH, with evidence of extreme shearing, close to OT6 and OT7. Boudinage structures and brittle shearing are highlighted within the Crystal Spring series (pCu, Figure 1c). In that case, the new geological map (Figure 1c) built using the high-resolution mapping techniques on the ground, using a tablet and QGIS software by Klee et al. [34] revealed a stacking of the Crystal Spring series, intruded by the Mesozoic granite (Mzla, Figure 1c). Laterally, the thickness of Crystal Spring series was reduced, as they were dragged and stretched against the granite due to the SDVFZ activity, especially in OT6 to OT8 areas.

Cenozoic volcanic series have also been highlighted in the southeastern end of the NH [47]. Cenozoic formations have been characterized by Niles, [47] outside the center part of the NH. They are mainly composed of fanglomerate, alluvial fan deposits, lacustrine deposits, sabkha, evaporitic rocks, carbonate units, and megabreccia.

#### **3. Methodology**

Scanlines are commonly used to describe the reservoir properties and the fracture systems from analogues of hydrocarbon and groundwater reservoirs [20,30,51–54], and of geothermal reservoirs [55]. The scanline methodology, widely described in the literature [2,26,54,56], helps the understanding of the fractured reservoir geometry.

#### *3.1. Scanline Data Acquisition*

In the present work, the geometrical parameters of fractures, such as orientation, spacing, and aperture, were acquired directly from scanlines in the field. A decameter was installed horizontally along the outcrop (Figure 2a). Note that data about every fracture (e.g., joint, vein or fault) intersected by the scanline were collected, whatever its orientation class or filling. The cross-cutting relationships between the studied fractures are difficult to observe in the field, as intersections rarely occur along the scanline. Then, the fracture parameters were acquired by reporting the successive position of each fracture along the scanline. The projected positions were then collected and reported in Excel software v.2019. The spacing between two consecutive fractures is given by [20]:

$$\mathbf{S\_A = P\_n - P\_{n-1}} \tag{1}$$

S<sup>A</sup> is the apparent spacing of fractures calculated from the fracture positions measured from field, P<sup>n</sup> refers to the position of fracture n, and Pn–1 refers to the position of fracture n–1, both expressed in meters, the location of the beginning of the measurement line being the reference. During the data analysis step, the fractures were filtered by orientation classes in order to discuss the effect of the regional directions on the local fracturing heterogeneity. One to two scanlines were acquired from each outcrop. Five scanlines were performed

along the outcrops OT 1, OT2, and OT3.

Fracture spacings were also calculated from virtual scanlines based on photogrammetric models and on fracture maps. The photogrammetric models were performed using two drones: 3DR Solo drone and DJI Phantom. These drones were loaned by University of Texas at El Paso (UTEP), TX, USA. The videos were recorded between the late morning and the early afternoon during seven consecutive days using a manual mode camera setting to reduce the effects of lighting condition. Then, pictures were extracted from the recorded videos. To provide a sufficient overlapping, pictures were extracted every second using ffmpeg software v.4.5 (Grenoble, France). The alignment of the pictures was done in Agisoft Metashape software 2020, v.1.6.5. (Saint Petersburg, Russia). Regarding the picture resolution, we ensured that every picture had a resolution of 300 dpi (300 pixels per 300 pixels). That permitted us to digitize the maximum number of fractures of decimeter length. The size of the pixel is 10 cm per pixel.

Several processing steps were needed to build the 3D models, starting by sky removal to reduce the noises, and the creation of different picture chunks (Figure 3). The 3D models were georeferenced and then imported in open access QGIS® software 2018, v.2.18.17 (Beaverton, OR, USA) to start the fracture extraction process. To improve the accuracy,

ground control points (GCP) put in the field, using differential global positioning system (DGPS) and global positioning system (GPS) integrated directly in the drones, have been used. The georeferencing of each outcrop was realized independently using DGPS. The extraction of fractures was done manually by tracing every plane from the 3D outcrop. The orientation of every extracted trace plane was done automatically, and then compiled. For further explanation, the methodology of the modeling and the fracture extraction is detailed in Chabani et al. [35]. The digitized fractures were projected on a 2D map in order to keep data consistent among the whole datasets.

**Figure 3.** Workflow illustrating the different steps to build the 3D photogrammetric models, georeferencing, and fractures detection and extraction. Modified after Chabani et al. [35].

Two-dimensional fracture maps OT4 and OT5 (Figure 2) were performed from the field using a DSLR high resolution camera, with fixed focal (50 mm) in order to reduce the distortion. Furthermore, to avoid light effects, pictures were taken in the absence of direct sunlight (e.g., [16]). Several pictures were taken vertically, with the same distance, and with a sufficient overlapping. These pictures were then aligned using Agisoft Metashape software 2020 v.1.6.5 with the procedure detailed in Chabani et al. [35]. Outcrops OT6 to OT8, also located in the central part of NH, were analyzed by photogrammetric technology, and are also located in the central part of NH. In total, five scanlines were performed (Figure 4e–i).

**Figure 4.** Visualization of the eight outcrops studied in this work, including the scanlines (SL) location. (**a**) Outcrop 1 trending SW/NE shows heterogeneity of fracture orientation distribution. (**b**,**c**) Outcrop 2 trending E/W shows large NE/SW and NW/SE fracture planes crosscut by SL2a and SL2b. (**d**) Outcrop 3 trending NW/SE shows large E/W fracture planes crosscutting SL3a and SL3b. (**e**) Outcrop 4 consists in a fracture map; 2 scanlines were traced perpendicular to the main structures, recording then large E/W and N/S fracture planes for SL4 and SL5 respectively. (**f**) Outcrop 5 also consists in a fracture map; 2 scanlines were traced perpendicular to the main structures, crosscutting mainly fracture planes orientated NW/SE for SL6 and E/W for SL7. (**g**) Outcrop 6 consists in a canyon perpendicular to the SDVFZ segments, which crosscuts a large E/W fracture plane. This outcrop shows the transition between granitic basement and Crystal Spring sedimentary rocks. (**h**) Outcrop 7 trending NE/SW records a several fracture plane orientations. (**i**) Outcrop 8 trending NW/SE highlights mainly NE/SW and E/W fracture planes. SDVFZ: Southern Death Valley Fault Zone. For outcrops location, see Figure 2. Note that the OT6, 7 and 8 cross some major talus slopes. These outcrops have been modeled in 3D, making the fracture digitation possible to do in CloudCompare software. Then, the planes have been projected in 2D to keep data homogeneous from all fracture sets.

The fracture maps and the photogrammetric models were georeferenced and then used to extract the fractures in QGIS® software 2018, v.2.18.17. In this study, the fracture digitization was performed manually by tracing every detected fracture because of insufficient contrast between the fractures and the surrounding rock. Each digitized fracture became a georeferenced lineament in QGIS®. In the case of fracture maps, note that the fractures extending out of the sampling area were considered as one continuous feature [57–59] (Figure 2b). In QGIS®, the procedure of digitization consisted in an extraction of the end point coordinates of each fracture. Each fracture contained X and Y coordinates of each of the two end points, which helped to compute the spacings along a virtual scanline according to the following procedure:


$$\parallel \mid \mathbf{AB} \parallel \mid = \sqrt{(\mathbf{x\_b} - \mathbf{x\_a})^2 + (\mathbf{y\_b} - \mathbf{y\_a})^2} \tag{2}$$

The calculated spacing in Equation (2) is not adjusted by Terzaghi correction. According to the scanline orientation, fracture orientations, and the position of scanline intersections for each fracture set, the fractures spacing were adjusted by applying the Terzaghi correction following [60]:

$$\mathbf{S} = \mathbf{S}\_{\mathbf{A}} \times \cos \theta \tag{3}$$

S is the true mean spacing of fractures in a set, S<sup>A</sup> is the apparent mean spacing of fractures in a set and θ is the acute angle between the direction normal to fractures and the scanline.

Orientation bias can be minimized by drawing a scanline parallel to the normal to a fracture set, such that θ is close to 0◦ . All fractures intersected by scanlines were acquired. Then, all measured fractures were filtered by orientations during the analysis in order to describe the patterns of spacing according to each fracture set.

#### *3.2. Fracture Orientation Analysis*

In this study, the orientation is the first parameter analyzed to classify the fractures into fracture sets. As described before, from virtual scanlines, the fracture dip was not obtained from virtual scanlines, while it was measured for each fracture on field scanlines. The fracture dip has been measured for each fracture. Here, the classification into fracture sets is based only on strike orientation without considering the variation in dip to preserve data homogeneity. Note that, from field scanlines, the dip direction for each fracture is however provided in the Schmidt canvas.

Several software packages such as Win-tensor [61], Stereonet [62], and Digifrac [63] have been developed in order to project the structural data. Fisher distribution [64], Fisher-Bingham distribution [65], and von Mises distribution [66] are commonly used to describe symmetrical distributions of orientations in 2D, and sometimes in 3D in case of Fisher distribution. However, these distributions do not describe complex asymmetrical data. Then, the classification was performed using the mixture of von Mises distribution (MvM) [67], which is adapted to describe complex circular data and then seem relevant to model larger complex fracture networks. The methodology consists in a semi-automated approach based on appraisal tests to avoid any subjectivity in fracture set analysis. This distribution is based on three parameters: (1) Mean orientation (µ ◦ ), around which the

distribution is centered; (2) kappa (κ), which controls the concentration of the orientation values around the mean; and (3) weight (ω), corresponding to the relative contribution of each fracture set to the model. In addition, the best number of fracture sets is approved using the goodness of fit parameters (e.g., likelihood). The degree of precision of each mean fracture orientation is computed using the standard deviation (SD), which is of +/−10◦ . For further explanations, see Chabani et al., [68], which described and adapted the MvM methodology for structural data. To plot the orientation data in the current study, we used a rose diagram for describing data which only contain dip direction measurements, and Schmidt canvas for describing data which contain strike and dip measurements.

#### *3.3. Analysis of Spacing*

Numerous statistical tools have been developed in the recent decades specially to analyze the facture parameters such as spacing, width, length, orientation [26,51–53], and its spatial distribution (e.g., clustered, random, or uniform distribution) [26]. For spacing parameter, a coefficient of variability (Cv) has been widely described in the literature, that provides an indication of the fracture distribution [20,26,54,69]. It is given as:

$$\mathbf{C}\mathbf{v} = \sigma\_{\mathbf{s}/} \mathbf{S} \tag{4}$$

σ<sup>s</sup> and S represent, respectively, the standard deviation and the mean spacing. When Cv ≈ 1, the fractures intersected by the scanline are distributed randomly. When Cv < 1, fractures are more regularly spaced, while Cv = 0 represents uniformly spaced fractures, and Cv > 1 indicates fractures that are more irregularly spaced. Each Cv value can provide information about the degree of fracture clustering [26].

The heterogeneity of fracture distribution based on cumulative distribution has also been quantified using the V0 statistic of [70], applied to structural geology by [20,30,31]. Indeed, the heterogeneity of distribution of the fractures and associated parameters (aperture, spacing, thickness, etc.) may be characterized from the cumulative frequency using the method described by [70]. Then, V0 is defined as the measure of the heterogeneity within the scanline, which is given as:

$$\mathbf{V}' = \mathsf{ID}\_{\text{max}}\,\mathsf{l} + \mathsf{ID}\_{\text{min}}\,\mathsf{l} \,\mathsf{/A} \,\mathsf{A} \tag{5}$$

Dmax and Dmin are the cumulative frequency at that point if the fracture parameter was uniformly distributed [30]. Dmax and Dmin are positive and negative respectively. A is the total cumulative frequency of the analyzed parameter. In the present study, the V0 will be used on aperture parameter in order to evaluate the strain heterogeneity. This strain heterogeneity depends on the amount of displacement (aperture or heave) and the spatial distribution of the fractures [31]. Analogical tests have been illustrated by Putz-Perrier and Sanderson [31] for two examples of the same population of extensional fractures, with different spatial arrangement, but with same strain. They obtained a fracture network uniformly distributed for the first example, and strongly clustered for the second one. Then, aperture parameter helps us to better characterize the degree of heterogeneity of every analyzed area. A perfect regular fracture distribution produces a V<sup>0</sup> ≈ 0 as fracture sizes decrease, while the maximum heterogeneity of fractures distribution would produce a V 0 = 1 value. For further explanations, see Putz-Perrier and Sanderson [31].

## *3.4. Fracture Density P<sup>10</sup>*

The position and spacing of a set of fractures are considered whatever of their type (e.g., normal, reverse, etc.) [20]. A scanline normal to a set of fractures would intersect N fractures (number of fractures) over a length. The fracture density (P10) is defined as the number of fracture intersections (N) per unit length (L) [58], following:

$$\mathbf{P}\_{10} = \mathbf{N}/\mathbf{L} \tag{6}$$

#### *3.5. Cumulative Frequency Diagrams*

The spacing distribution and arrangement were analyzed by using cumulative frequency. As recommended by [20,26], stick plots were used, in which the location of each fracture intersected by the scanline is mentioned. This allows to better visualize the fracture distribution. Furthermore, a plot of cumulative frequency versus distance along the scanline (from the beginning to the end) was used, in which P<sup>10</sup> is proportional to the slope of the cumulative curve. The cumulative plot is normed by the maximum value, expressed in percentage (%) and it always starts at the origin (0, 0) and ends at (d<sup>N</sup> − d1), (N − 1). The parameters d<sup>1</sup> and d<sup>N</sup> represents respectively the first and the last fracture. The cumulative frequency (%) against distance along the scanline provides a rapid visual comparison between datasets for each scanline and between those scanlines whatever their lengths [71].

#### **4. Results**

#### *4.1. Description of Fracture Systems Acquired from NH Range*

The studied outcrops reported in the Figure 2 were distributed homogenously within the entire central part of the NH (CBS). The structural position of each outcrop is described below.

#### 4.1.1. Fieldwork Scanlines

The fracture network parameters were compiled from the field (Figure 2). The measurements were performed within OT1 using a scanline 1 (SL1 orientated N010) of 13.45 m length (Figure 4a), intersecting a total of 324 fractures, with a mean space of 0.04 m (Table 1). The orientation, spacing and aperture data were acquired along two scanlines with different orientations in OT2 (Figure 4b,c). The SL2a (orientated N160) of 7.5 m length intersected 109 fractures, with a mean space of 0.07 m, while the SL2b (orientated N070) of 1.64 m length intersected 37 fractures, with a mean space of 0.04 m. Within OT3, the fracture spacing and aperture were also acquired along two different orientation scanlines: SL3a and SL3b orientated N055 and N160 respectively (Figure 4d). Both scanlines intersected respectively 31 and 47 fractures, with a mean space of 0.03 and 0.06 m.

**Table 1.** Characteristics of the fractures acquired from each studied outcrop, along the scanlines. Outcrop 1 to 3 (without asterisk) show the characteristics of the fractures acquired directly from field scanlines. Outcrop 4 to 8 (with asterisk) show the data extracted from aligned photographs using Metashape Software v.1.6.5, with a virtual scanline. For each outcrop, number of scanlines are indicated with: Number of fractures intersected, orientation and length of scanlines, mean fractures space, density (frac/m), coefficient of variability (Cv), and V0 statistic fom [70]. The proximity to the major faults is mentioned. Mean spacing and Cv are computed with Terzaghi correction. Sgmt: segments.


#### 4.1.2. Virtual Scanlines

The fracture variability analysis was further conducted by creating, fracture maps with a resolution of 2 <sup>×</sup> <sup>10</sup>−<sup>4</sup> m, OT4 and OT5. OT4 is sized 1.7 m per 1.6 m and is located in the granitic facies close to the SDVFZ segments (Figure 4e). Two scanlines: SL4 and SL5, orientated, respectively, N163 and N073, were traced perpendicular to each other in order to intersect the maximum number of fractures and avoid angular bias (e.g., [26]). In total, 28 fractures were intersected along SL4 of 0.80 m length, with a mean space of 0.02 m. Regarding the SL5, 46 fractures were intersected, with a mean space of 0.04 m (Table 1). OT5 is sized 1.8 per 1.7 m and is also located in the granitic facies, close to the SDVFZ segments (Figure 4f). Here again, two scanlines: SL6 and SL7 were traced, orientated respectively N074 and N157. They intersected, respectively, 26 and 31 fractures. The mean spacing is of 0.05 and 0.02 m for SL6 and SL7, respectively.

To perform the fracture variability study in 1D, three photogrammetric models localized only in the granitic facies were added to the present work. They are located close to the major fault segments. The fractures extracted from these models ranged from 10−<sup>2</sup> to 20 m in length.

The drone photogrammetric model displayed in OT6 is sized approximately 110 per 45 m (Figure 4g); 171 fractures were traced and are intersected by the SL8. Note that OT6 presents various lithologies including granitic rocks, gneiss, gabbro, and sedimentary rocks. This may influence the spatial variability of the fractures in this area, as it will be discussed below. The drone photogrammetric model presented in OT7 is sized approximately 82 per 45 m. In this model, 188 fractures were traced and intersected by the SL9 (Figure 4h). Finally, drone photogrammetric model displayed in OT8 is sized approximatively 100 per 25 m. In total, 258 fractures were traced and intersected by SL10 (Figure 4i).

#### *4.2. Fracture Orientation Distributions*

The data acquired from scanlines in the central part of the NH show a heterogenous fracture distribution. SL1 is located near (around 10 m) a SDVFZ major segment (bold black line in Figure 2b), which acts following dextral strike-slip movement. Several lineaments are identified from the high-resolution field mapping, striking E/W (GFZ signature) to NW/SE (SDVFZ signature). From the SL1, the mean fracture orientations (µ) are striking N026, N062, N092, N130, and N171 (Figure 5a, Table 2). Fracture abundances for each fracture set are characterized by a slight dominance of the N062 and N092 fracture set with, respectively, 21% and 37% (Table 2). N026, N130, and N171 fracture sets represent, respectively, 17%, 15%, and 10% of the whole fracture set. Then, NE/SW trend appears at outcrop scale and is equivalent to E/W fractures in term of density. However, SL2a crosscut by SDVFZ major segment and close to thrust fault (Figure 2b), and a significant difference was observed in terms of fracture abundance with respectively 80 fractures in comparison with SL1 (261 fractures). The most recorded fracture sets are striking N014, N025, and N102 with, respectively, 18%, 46%, and 27%. The other fracture sets do not exceed 10% (Figure 5b, Table 2). N152 is the most dominant fracture orientation highlighted along the SL2b, representing 38%. N003 and N112 both represent 31% (Figure 5c, Table 2). Both SL3 scanlines are located far from the influence of the SDVFZ segments, thrust faults and sinistral strike-slip faults (Figure 2b). Then, SL3a, much smaller in length, intersected three fracture sets: N077, N098, and N135 with, respectively, 49%, 25%, and 26% abundances (Figure 5d, Table 2). Three fracture sets were also highlighted from the SL3b striking N040 (24%), N081 (65%), and N150 (11%). The orientations of fractures detected in SL3 scanlines are less heterogenous than in SL2 and SL1. The structural position of SL3 far from major faults (around 40 m in distance) very likely impacts the fracturing at outcrop scale.

**Figure 5.** Fracture orientation distributions of the NH studied outcrops (**a**–**l**). (**a**–**e**) The fracture orientation distributions are represented into Schmidt canvas, lower hemisphere because they contain strike and dip measurements. (**f**–**l**) Fracture orientation distributions are represented by rose diagrams because they contain only dip direction measurements. Each direction rose diagram of direction is expressed with classes of 5◦ . The dashed lines indicate the direction of the scanline. n: Number of data. See legend in the figure for colors.

Regarding the virtual scanlines, the structural position of SL4 (OT4 orientated N163) and SL5 (orientated N073) is the same as SL1. Indeed, both scanlines are located near SDVFZ major segment (around 6 and 4 m in distance, respectively), highlighted by dominance of NW/SE and E/W structures. SL4 intersected much less fractures in comparison with the perpendicular SL5 (Table 1). SL4 displayed three fracture sets striking N034 (34%) and N086 (53%), and N123 (13%), while SL5 highlighted five fracture sets striking: N001 (39%), N018 (12%), N040 (14%), N113 (9%), and N144 (26%) (Figure 5f,g, Table 2). SL6 and SL7 orientated, respectively, N074 and N157, acquired from OT5, showed a heterogeneous fracture set, and are located near SDVFZ segments (4 m distance). Indeed, SL6 highlighted three fracture sets striking N004, N100, N161 with, respectively, 35%, 49%, and 16%, while SL7 highlighted N053, N087, and N116 fracture sets with, respectively, 13%, 81%, and 6% (Figure 5h,i, Table 2).



Crosscutting the NW/SE thrust faults (in red lines, Figure 2b) and SDVFZ segment faults (in black bold lines, Figure 2b), the OT6 to OT8 displayed heterogeneous fracture orientation distribution from scanline measurements. SL8 scanline acquired within OT6 is characterized by a special geological setting. Indeed, compressional structures like thrust faults crosscut this outcrop (Figure 2b), close to the Canadian Club Wash (Figure 1c). SL7 is however crosscut by 2 SDVFZ major segments. Regarding the orientation distributions, SL8 of 109 m length, orientated N020, recorded three fracture sets, striking N058, N090, and N132 with an equivalent fracture abundance (between 32% and 36%) (Figure 5j, Table 2). However, five fracture sets were highlighted from SL9, striking N029 (20%), N060 (27%), N096 (9%), N132 (22%), and N176 (22%) (Figure 5k,l). SL10 recorded N004 (3%), N040 (7%),

N091 (73%), and N118 (17%) fracture sets. This scanline crosscut a thrust fault and several secondary SDVFZ segments (Figure 2b).

#### *4.3. Spatial Distribution of Fractures*

The spatial organization of fractures was highlighted from scanlines, whatever the fracture orientation, and is summarized in Table 1. In addition, the spatial organization was also studied following the fracture orientations in order to determine the impact of some regional directions on the NH structural organization.

From SL1, fracture density (P10) and Cv are around, respectively, 19.4 frac/m and 1.2, indicating a random fracture distribution. Equivalent P<sup>10</sup> and Cv were measured from SL2b with, respectively, 19.5 frac/m and 1.1, also indicating a random distribution. While SL2a recorded a P<sup>10</sup> of 10.6 frac/m and Cv of 14.4, indicating a less abundant and highly clustered fracture system. Values of P<sup>10</sup> of 31.8 and of 8.4 frac/m, Cv of 0.7 and 1.7 were highlighted from SL3a and SL3b, respectively, (Table 1), indicating very abundant fractures with a random distribution.

Three different spacing organizations were identified from fracture sets in SL1 (Table 2):


The fracture distribution presented in Figure 6 shows the layout of fractures and their location along each scanline. For SL1, the fracture distribution is showed using a cumulative frequency plot against the position of fractures along the scanline for each fracture set (Figure 6a). Two major trends are distinguished: (1) Regular fracture distribution from the beginning to the end of the scanline especially for fracture sets N026 and N171 (respectively in black and orange colors with diamond and square symbols in Figure 6a); and (2) a regular fracture distribution at the beginning, then clustered (increased frequency), followed by another regular distribution at the end for fracture sets N062, N092, and N130 (respectively in red, green and purple colors in Figure 6a). Three fracture clusters having a slope higher than 2 are highlighted in N062 fracture set, around 5.5, 8, and 10 m (Figure 6a), highlighting a clustered spacing. Note that, this slope corresponds to the shape of the cumulative frequency compared to the uniform distribution highlighted in the plots below (Figure 6). The cumulative frequency plot highlighted one fracture cluster around 12–13 m in the N092 fracture set. Within the N130 fracture set, two fracture clusters are characterized around 3–4 and 10 m.

SL1 is in moderate deformation zone, affected mainly by SDVFZ major segment and some E/W fault segments. The position of SL1 close to SDVFZ major segment, trending NW/SE creates these irregularities in fracture distribution. Indeed, the NW/SE (N130) fracture set is one of the most clustered fracture sets. The intermediate (in term of length) E/W segments shown in the Figure 2b have a strong impact on N092 fracture set distribution, making it the more clustered distribution with Cv = 1.44.

A high fracture density is observed in the central part of the SL2a profile (Figure 6b). Indeed, five fracture clusters were identified in which the fracture density is increased around 3–4 m in N143 fracture set (purple color in Figure 6b), 4.5 m in N014 and N025 fracture sets (black and orange colors, respectively, for N014 and N025 in Figure 6b), and around 6 m in N014 and N050 fracture sets, displayed, respectively, in black and red colors for N014 and N050 in Figure 6b. The SDVFZ crosscuts the SL2a profile and introduces some irregularities in fracture distribution since the beginning, mainly in N143 and N014 fracture sets, highlighting then an anisotropy following some directions.

**Figure 6.** Cumulative frequency diagram along each scanline and following each fracture set (in colors). Plot of cumulative frequency expressed in % versus distance along scanline for: (**a**) SL1, (**b**) SL2a, and (**c**) SL2b. Dashed lines indicate a potential cluster for each fracture distribution, indicating a rapid increase in the number of fractures with slope threshold > 2. The diagonal line in each plot of cumulative frequency defines a uniform or regular distribution. Visual location of fractures expressed in stick plots for each fracture set distribution, highlighting the fracture position along the scanline, including the fracture density (P10) and the coefficient of variation (Cv) values. The structural position is done in each diagram. See the color legend for the orientation of fracture sets.

Fractures intersected by the SL2b are distributed randomly whatever the direction with Cv close to 1 (Table 2). N098 and N0135 fracture sets intersected by SL3a displayed a Cv of 0.6 and 0.8, indicating a uniform spacing organization, while Cv of 1.07 measured from the N077 fracture set indicates a clustered organization. However, the beginning and the end of the SL2a profile showed a regular fracture distribution. Along SL2b, a random fracture distribution was observed whatever the fracture orientation with Cv around 1 (Figure 6c). Three fracture clusters are, however, detected within N003, N112, and N152 fracture sets (displayed respectively in black, green, and purple colors), respectively, around 0.4–0.6, 0.8–1, and 1.2 m (Figure 6c).

A regular fracture distribution was highlighted within fracture orientations N098 and N135 along SL3a profile, with Cv of 0.6 and 0.8, respectively (Figure 7a). For N077 fracture set (red color with triangle symbol), a clustered distribution was shown with two fracture clusters around 0.3–0.4 and 0.7–0.8 m. However, along SL3b scanline profile, one fracture cluster which corresponds to an increase in fracture density was shown around 2 and 2.25 m, respectively, in N040 and N150 fracture sets (respectively in red and purple colors in Figure 7b). Only three fracture clusters were identified around 1.5, 2.5–3, and 4 m in N081 fracture set (green color). A regular fracture distribution was characterized outside these fracture clusters. Located away from major fault segments, around 40 m distance, the SL3a and SL3b profiles displayed a very poor fracture system organization and fracture density. In addition, these profiles are in a moderate deformation zone, which can impact drastically the fracture distribution and density. Boudinage structures and brittle shearing are not observed within this area.

OT4 and OT5 are in a moderate deformation zone, affected mainly by SDVFZ major segment and some E/W fault segments. From virtual scanlines, three fracture sets were recorded in SL4. The N034 fracture set highlighted one fracture cluster around 0.5–0.6 m (red rectangle in Figure 8a). However, four fracture clusters were highlighted at the beginning and at the end of the SL4 profile within N086 fracture set (green color with cross mark symbol in Figure 8a), around 0.01, 0.25, 0.65, and 0.7–0.8 m. The rest of the intervals are characterized by a regular fracture distribution. The SL5 scanline recorded five fracture sets and are characterized by a regular fracture distribution whatever the fracture set (Figure 8b). An increased fracture density is identified within the N001 fracture set (black color) around 0.7 and 1.2 m.

Fractures detected within SL6 are mainly distributed regularly for N004 and N161 fracture sets (displayed respectively in black and purple colors in Figure 8c), with Cv of 0.88 and 0.84, respectively. Cv of 1.35 was, however, computed from the N090 fracture orientation (green color with cross mark symbol, Figure 8c), indicating highly clustered fractures. Then, one fracture cluster was identified around 0.5–0.6 m (Figure 8c). The three fracture sets striking N053, N087, and N132 are recorded mainly with fractures regularly distributed along the SL7, with Cv ranging from 0.83 to 0.84 (Figure 8d). Two fracture clusters are then identified within the N087 fracture set (green color with cross mark symbol in Figure 8d) around 0.5 and 0.6–0.7 m.

The influence of the regional directions was observed on E/W fractures orientation, with a higher density and clustering within this fracture set (Table 2). However, the NW/SE direction is less expressed in comparison with SL1 and SL2. The small length of OT4 and OT5 scanlines may influence the result and then introduce some bias to the analysis.

**Figure 7.** Cumulative frequency diagram along each scanline and following each fracture set (in colors). Plot of cumulative frequency expressed in % versus distance along scanline for: (**a**) SL3, and (**b**) SL3a. Dashed lines indicate a potential cluster for each fracture distribution, indicating a rapid increase in the number of fractures with slope threshold > 2. The diagonal line in each plot of cumulative frequency defines a uniform or regular distribution. Visual location of fractures expressed in stick plots for each fracture set distribution, highlighting the fracture position along the scanline, including the fracture density (P10) and the coefficient of variation (Cv) values. See the color legend in Figure 6.

Near the Canadian wash (see Figure 1c for location), OT6 is located close to the highly deformed zone (for location, see Figure 2). Two major faults crosscut this outcrop: SDVFZ major fault segment and thrust fault. SL8 intersected three fracture sets with a high fracture density interval (Figure 9a). Three fracture clusters were identified in N058 fracture sets, respectively, around 10–20, 40, and 75 m (red color with triangle symbol legend, Figure 9a). The fracture clusters in N090 fracture set (green color with cross mark symbol, Figure 9a) are around 40, 50–60, 75, and 80 m. Finally, within N132 fracture set (purple color with strikethrough cross, Figure 9a), two fracture clusters comprised between 10–15 and 50–70 m were identified. We are fully aware that the canyon presents a complex structuration due to various lithologies and the overprinting faults.

**Figure 8.** Cumulative frequency diagram along each scanline and following each fracture set (in colors). Plot of cumulative frequency expressed in % versus distance along scanline for: (**a**) SL4, (**b**) SL5, (**c**) SL6, and (**d**) SL6. Dashed lines indicate a potential cluster for each fracture distribution, indicating a rapid increase in the number of fractures with slope threshold > 2. The diagonal line in each plot of cumulative frequency defines a uniform or regular distribution. Visual location of fractures expressed in stick plots for each fracture set distribution, indicating the fracture position along the scanline, including the fracture density (P10) and the coefficient of variation (Cv) values. The structural position is done in each diagram. See the color legend in Figure 6.

**Figure 9.** Cumulative frequency diagram along each scanline and following each fracture set (in colors). Plot of cumulative frequency expressed in % versus distance along scanline for: (**a**) SL8, (**b**) SL9, and (**c**) SL10. Dashed lines indicate a potential cluster for each fracture distribution, indicating a rapid increase in the number of fractures with slope threshold > 2. The diagonal line in each plot of cumulative frequency defines a uniform or regular distribution. Visual location of fractures expressed in stick plots for each fracture set distribution, showing the fracture position along the scanline, including the fracture density (P10) and the coefficient of variation (Cv) values. See the color legend in Figure 6.

Additionally located in the highly deformed zone, SL9 is crosscut by two SDVFZ major segments. Several fracture clusters are observed as following (Figure 9b):


SL10 scanline crosscuts several secondary SDVFZ segments and a thrust fault, in moderate deformation domain. A regular distribution of fractures was encountered in N004 fracture set (black color with diamond symbol legend in Figure 9c). Three fracture clusters were detected around 30–40, 55–65, and 80–90 m in N040 fracture set (data in red with triangle symbol legend, Figure 9c), while in N091 fracture set, the fracture clusters are around 10–20, 28, 40, 60–70, and 90 m (green color with cross mark symbol, Figure 9c). The E/W and NE/SW fractures orientations are more expressed in terms of fracture density which can be enhanced by the position of the major faults in this area.

#### *4.4. Fracture Aperture Distribution*

The heterogeneity of the fractures distribution and associated parameters (e.g., aperture, spacing, etc.) can be determined using the Kuiper's method [20,30,31,70]. In this study, the V0 is used to better precise the degree of heterogeneity of aperture distribution along scanlines. V0 values are summarized in Table 1 for only data acquired from the fieldwork. Confidence interval of 95% was used to compile V0 . Then, a cumulative aperture was plotted against fracture location along the scanline (Figure 10). Application of the Kuiper test shows V0 = 0.29 for SL1, meaning that the apertures are distributed randomly (Figure 10a). For SL2a and SL2b, V0 is, respectively, 0.42 and 0.50 despite the difference in term of scanline length and orientation (Table 1, Figure 10b,c). These values indicate that the apertures are distributed randomly along each scanline. The same result of aperture distribution is shown along the SL3a and SL3b (Figure 10d,e), with V0 of 0.32 and 0.57, respectively. The fracture aperture distribution is more heterogeneous in SL3b and SL2b, than in SL1, SL2a, and SL3a.

The possibility of any correlation between the fracture orientation and the aperture was tested using a plot of aperture against fracture set for each scanline (Figure 11). The mean fracture aperture in SL1 is about 2.5 mm and, therefore, lower than in fractures of SL2a and SL2b at, respectively, 2 and 1.7 mm. In SL1, the widest fracture apertures are around 10 mm, and occurred in fractures orientated N092 (Figure 11a). The most common observed fractures in the field were affected by mineralization of carbonates mostly (Figure 12). The widest fracture apertures detected in fracture orientation N092 are classified as fully sealed by carbonates (Figure 12a). In SL2a, the maximum fracture aperture is also 10 mm and belongs to the N050, N150, and N170 striking sets (Figure 11b). The widest fracture apertures are classified as fully sealed by carbonates and oxides (Figure 12a,b). In SL2b, the maximum fracture aperture does not exceed 8 mm, and occurred in fractures striking N009 and N090 (Figure 11c) and classified as fully sealed by carbonates and oxides.

**Figure 10.** Plot of the sum of all apertures (cumulative fracture aperture) intersected along a scanline to show V0 for (**a**) SL1, (**b**) SL2a, (**c**) SL2b, (**d**) SL3a, and (**e**) SL3b. The diagonal of each plot (black line) represents the uniform distribution linking the origin to the cumulative aperture to the end of the scanline (for further explanations, see [20,30]). Dmax and Dmin correspond to the maximum and minimum difference between the cumulative aperture and the uniform strain line, respectively. V0 quantifies the heterogeneity of the strain distribution, varying from 0 (uniform distribution) to 1 (maximum possible hetrogeneity).

**Figure 11.** Half circular diagram showing the relation between fracture strike and apertures. (**a**) SL1, (**b**) SL2a, (**c**) SL2b, (**d**) SL3a, and (**e**) SL3b. Apertures from SL4 to SL10 are not available. Rose diagram scaled for mean aperture with classes of 5◦ .

**Figure 12.** Illustration of the observed fractures observed in the field, mostly affected by mineralization. (**a**) Picture taken near OT6 illustrating veins fully sealed by carbonates. (**b**) Picture taken near the Canadian Wash illustrating open and partially open fractures. The carbonates are ubiquitous following SDVFZ trend (i.e., NW/SE). The fractures striking E/W have been observed with a wider aperture and were filled by barite and oxides.

The mean fracture aperture in SL3a and SL3b is about 0.9 and 2.8 mm, respectively. The maximum fracture apertures are around 10 mm. They occur in fractures striking N162 and N150 for SL3a and SL3b, respectively (Figure 11d,e). The maximum fracture apertures identified in SL3a occurred in fractures classified as partially open (Figure 12b), while in SL3b, the maximum fracture apertures occurred in fractures classified as fully sealed by carbonates and oxides. The fracture aperture distribution are more heterogenous in SL3b than in SL3a, in which apertures are generally lower than 2 mm.

As a summary, the distribution of the apertures in the central part of NH is ruled by a random behavior. Regarding the relationship between apertures and the orientations, an anisotropy was observed following E/W trend, which presents fractures with a wider aperture.

#### **5. Discussion**

#### *5.1. Representativness of the Fieldwork and Virtual Scanlines*

The present study covers a sampled fracture network from fieldwork and virtual scanlines obtained from photogrammetry. The moderate linear density compiled from the virtual scanlines, especially in SL8, SL9, and SL10, does not exceed 3 frac/m. The highest linear density is detected in SL4 and SL7 with, respectively, 42.1 and 44 frac/m. From fieldwork scanlines, the linear densities ranged between 8.4 frac/m in SL3b and 31.8 frac/m in SL3a.

Regarding the sampling resolution, in case of virtual scanlines, the shorter fracture measurement is around the decimeter to meter and depends on the photogrammetric image resolution, while in the case of fieldwork scanlines, the measurement resolution is around the millimeter. The difference in resolution strongly impacts the fracture density and its representativeness. The low density of the fractures detected from virtual scanlines might not be fully considered as representative of the whole granitic rock. However, it is very useful in zones with difficult access.

In the case of sampling in 1D, a scanline perpendicular to the fractures will detect a maximum of sub-set of all fractures. Then, the probability that a fracture is detected within a scanline is proportional to the fracture surface area [72]. In basement rocks, fractures that span the sampling study area limits whatever its lengths and heights will reflect 3D sampling. The same case is observed in sedimentary rocks when fractures span the layers and the limits of the studied area [72].

#### *5.2. Consistency of the Recorded Fracture Sets*

The main dominant orientations recorded from the different scanlines displayed in the central part of the NH highlight the fact that NH geometry is controlled by NE/SW, E/W, and NW/SE trends (Figure 13). From fieldwork scanlines, the E/W and NW/SE fracture sets are the most consistent orientations whatever the scanline. The N/S, NNE/SSW, and NE/SW fracture sets are only recorded in the SL1 and SL2a fieldwork scanlines (Figure 13). SL2b, SL3a, and SL3b detected mostly E/W and NW/SE directions with a heterogeneous recording (Figure 13). The E/W is the most dominant trend within SL3b, while the NW/SE trend dominates within SL2b, and constitutes the second and third dominant fracture sets within SL3a and SL3b, respectively. The variability in fracture orientation may be related to the influence of the major faults. Indeed, as showed in Figure 2, the position of SL1 and SL2a close to the SDVFZ segment interfering with the thrust fault induces an additional complexity in the structural signature. As mentioned before, a clear overprinting has been recognized between primary SDVFZ and syn-kinematic dextral strike slip faults related to the transcurrent movements followed in time by compressive structures. Thrusting is postdating the activity of the SDVFZ, and it is tempting to relate the thrust structures to activity along the frontal termination of GFZ which acts with a sinistral strike slip movement.

**Figure 13.** Plot displaying the mean orientation with arrows of each collected fracture set from NH scanlines. Each arrow was characterized by its own length, which corresponds to the fracture set abundance. The horizontal line above each arrow corresponds to the standard deviation of each fracture set, using an interval of confidence of 75% (see [68] for more explanations). Each color arrow corresponds to a fracture set. Orange arrow: NNE/SSW fracture set, red arrow: NE/SW fracture set, green arrow: E/W fracture set, yellow arrow: NNW/SSE fracture set, purple arrow: NW/SE fracture set, and black arrow: N/S fracture set.

In the southern end of the NH central area, E/W trending structures showing evidences of compression again possibly related to GFZ activity are even clearer.

Regarding the fracture orientations highlighted from the virtual scanlines, a reproducible and consistent NE/SW, E/W, and NW/SE fracture sets are encountered (Figure 13). The GFZ is confirmed as a major fault which influences the NH geometry and induces the E/W fractures which are more expressed in SL4, SL6, SL7, SL8, and SL10. According to Chabani et al. [25], who describe the spatial organization of a NH fracture network at different scales from 2D maps and previous works [47–49,73], the compression episode at the southeastern end of the NH and at the front of the Avawatz mountains plays a key role in the increase of the fracture intensity in the central domain of NH, and can explain the consistency of the E/W direction in the whole internal NH domain.

The NW/SE direction is the second most reproducible direction recorded along the internal part of NH (Figure 13), related to SDVFZ activity, which acts with a dextral movement. This direction is more expressed especially near the Canadian wash, where the deformation is important, following a second order scale as described by Chabani et al. [25].

The N/S and NE/SW fracture sets are also highlighted from the virtual scanlines but are less consistent than the E/W and NW/SE directions. These directions are heterogeneous with more than 25◦ (dispersion of the mean orientation) of variability in case of the NE/SW fracture set (Figure 13). These trends are highly dependent on the scale of observation and have no influence on the NH geometry [25].

As mentioned before, a recent study by Chabani et al., [25] revealed the same influence of the E/W and NW/SE fracture sets in the central part of NH. Indeed, E/W and NW/SE trends control the NH geometry within the third and fourth order scale. In addition, the major faults played a key role in the fracture density increase following different areas inside the central part of NH. The gradient of deformation shown in Klee et al. [34] and Chabani et al. [25] induced fracturing notably near OT6 and OT7, in which the strain gradient is the highest.

#### *5.3. Clustering of Fractures in Central Part of NH*

Figure 14a highlighted the Cv for the relative spaces between adjacent fractures for each studied scanline, by plotting the values against the overall fracture intensity. This correlation helps to better compare the Cv values and assess the spatial organization of the fractures. A large range of behaviors were observed. A regular spacing distribution (Cv < 1) was highlighted especially from SL3a, SL4, SL5, SL6, and SL7 (Figure 14a, Table 1). However, a more clustered distributions (Cv > 1) was observed in the SL1, SL2a, SL2b, SL8, SL9, and SL10. This large variation is probably related to the prominent influence of the thrust faults and the SDVFZ major segments close to SL8, SL9, and SL10, and only the influence of the SDVFZ major segments in the case of SL1 and SL2 profiles. However, the location in moderate deformation zone and away from major faults of SL3 scanlines highlight the absence of any organization in the fracture systems. They confirm the key role of the structural heritage (regional directions) in fracture patterns at outcrop scale. Recent study by Franklin et al. [74] highlighted and confirmed that the clustered spacing distribution is pronounced at the outcrop scale and is related to the influence of the major faulting.

From all the analyzed datasets, note that the outcrops with the greatest numbers of fractures are most usually characterized by random patterns. This observed relationship could be interpreted as the result of the increasing spatial heterogeneity of the fracture pattern with increasing strain. In that case, OT6 to OT8 highlighted that the greatest number of fractures, the fracture density, and the strong clustering within fracture sets can be related to the intensity of deformation in this area and the proximity to the SDVFZ major segments and thrust faults. Indeed, the new geological map displayed in Figure 2b highlighted a stacking of the Crystal Spring series, intruded by the Mesozoic granite. In addition, the thickness of Crystal Spring series was reduced, as they were dragged, and stretched laterally against the granite due to the SDVFZ activity, especially in OT6 to OT8 areas. This intense deformation affected the entire NH range with local evidences of extreme shearing. However, we are aware that the presence of several different lithologies with varying competences within OT6 may bias the fracture distribution and its interpretation. In addition, the structural architecture of this area is the most complex within NH range as it includes overprinting deformation phases. A future publication dedicated to these overprinting issues is in preparation.

**Figure 14.** (**a**) Coefficient of variability (Cv) plotted against fracture intensity (P10) of the NH studied outcrops. SD: Standard of deviation of spacing measured from each scanline; mean: Mean spacing measured from each scanline. (**b**) Coefficient of variability (Cv) plotted against fracture number normalized by the scanline length.

Another approach approved by Hooker et al. [30] consists of cross-examining the low number N of datasets. Cv values are commonly indistinguishable from random for low-N sets. Then, Cv increases with increasing fracture abundance (Figure 14b). This observation reflects an increase in fracture clustering with fracture abundance only in case of fracture sets detected from virtual scanlines (SL8, SL9, and SL10, Figure 14b). In case of fractures detected from fieldwork scanlines, the trend is more unclear since the Cv evolution is still comprised between 0.5 and 1.5, whatever the fracture abundance (Figure 14b). Once again, the proximity to major faults in case of SL8, SL9, and SL10 may play a key role in the fracture patterns growth. For SL1 to SL7, the fracture organization may be perturbed by the abundance of the E/W facture orientation, which can increase drastically the fracture abundance following E/W fracture set trend. This may be related to the scanline orientation which cannot intersect the rest of the fracture sets. From SL1 to SL7, fracture set trending E/W is more expressed than the rest of the sets except for SL2a, SL2b, and SL5 (Table 2). Then, the complexity in fracture orientation recording has a strong impact on the spacing variability and fracture patterns evolution, evolving a random state. In case of SL8, SL9, and SL10, the fractures are distributed homogenously following the orientations outside the fracture clusters (see Table 2 for proportion).

Regarding the clustering, relative spacing analysis shows that fracture clusters have been detected in the whole profiles, except for SL3 profiles, in which very few clusters were detected (Figure 8). Clustering depends on the fracture orientation. Two major factors are responsible for this clustering:


The regular spacing distribution exist whatever the analyzed direction. This observation is more highlighted within SL4, SL5, and SL7 profiles (Figure 8a,b,d). In these cases, clustering depends on the orientation. Few fracture clusters were detected within the E/W direction (data in green color with cross mark symbol, Figure 8).

However, the lower fracture density compiled from SL8, SL9, and SL10, due to the sampling bias relative to the virtual scanlines, nuances the real influence of this clustering on the anisotropy of the possible flow.

To summarize, clustering is mostly observed for scanlines orthogonal to the observed fractures close to the major faults, such as SDVFZ and thrust faults, except for SL3 profiles which can be biased due to their small length and their location away from major faults (Figure 14a). In contrast, scanlines sub-parallel to the main trend of the major faults have a rather random distribution pattern (Figure 14a).

#### *5.4. Conceptual Model of NH Paleo Geothermal Analogue*

In fractured reservoirs, the main challenge is to understand the fracture variability from only 1D data obtained from wells. The 3D fracture networks commonly show a strong spatial heterogeneity, related in several cases to geological features, such as faults, folds, stress fields, or lithological trends, which impact large scale fracture networks [75]. The central part NH studied here is an appropriate case study to test these assumptions, such as size distribution (e.g., length, spacing, aperture etc.), fracture trends record, and the relationship between them. In the present study, the 1D measurements which can be assimilated to synthetic well data revealed the same density results as those obtained by 2D measurements in the central part of NH. Note that, the 2D study has been published in previous work [25] for the entire NH range. This previous study concluded that the center part of NH is ruled by fracture networks dominated by E/W (GFZ trend) and NW/SE (SDVFZ trend) directions. This result is also observed in this present study based on 1D measurements. Indeed, the main dominant directions (e.g., E/W and NW/SE) are also recorded at outcrop scale, meaning that independently of well measurement, whatever any sampling bias and statistic uncertainties resulting from the data measurements, the well (in case of a reservoir) or the scanline (in case of an analogue) is representative of the heterogeneity at outcrop scale and reservoir scale.

The main directions that follow the regional trend and then control the NH geometry are commonly characterized by clustered fractures. Close to the major faults, the fracture network arrangement is more clustered, especially in the high strain zone near OT6, OT7, and OT8. Then, the fracture system is marked by a strong clustering within its organization following most of the recorded fracture sets, except for NW/SE and N/S fracture sets of OT8. This clustering impacts the reservoir behavior in that fluid circulation is influenced by the role of the major faults. Outside these major faults and their associated fracture clusters, a secondary fracture network was characterized by a random distribution, which plays a key role in the fracture connectivity leading to the fluid supply toward the fractured zone.

Evidences of fluid circulations have been identified by Klee et al. (2021a) [37] and Klee et al., 2021b [8] through (1) the alteration processes that occurred in the whole granite

body (propylitic and argillic), and (2) the fracture infills. Among the different natures of fractures infills that have been identified in the granite, carbonates are omnipresent [8]. They mainly filled the fracture following the SDVFZ direction (i.e., NW/SE), which is the main fracture orientation in the area. However, as presented above, E/W-oriented fractures have also been observed with a wider aperture. These fractures, related to the activity of the GFZ [25], are often filled with barite and oxides, especially at the southern rear part of the range, close to the Avawatz Mountains. This difference of infills according to two different fracture sets shows two different episodes of fluid circulation through the granite body.

Furthermore, fluid–rock interactions investigations through the NH area, by collecting samples according to profiles approaching major fault segments, have been conducted in recent previous works [8,37]. These major segments consist of the SDVFZ segments, the same ones considered in this present study, since we considered the same faults interpretation in both works based on fieldwork mapping. Porosity measurements were realized on five samples away from fracture zones and on three samples in the vicinity of fracture zones. It aimed at evaluating a possible correlation with the amount of alteration. The authors showed that the porosity increases with proximity to fracture zones. It is known that alteration can create some porosity by the dissolution of primary minerals like plagioclase and biotite. However, these studies have shown that porosity does not always correlates with the amount of alteration. Indeed, microfracturing also creates porosity.

The argillic alteration related to hydrothermal fluid circulations through the fracture network affects dominantly the NH granite [8,37]. During this fluid–rock interaction process, plagioclase and biotite are replaced by secondary minerals, such as illite and kaolinite, which crystallize between 120 and 200 ◦C [8]. Such temperatures are also confirmed by the Kübler Index measured from the illite crystallinity. To know more precisely the fluid temperature that has circulated, fluid inclusions measurements are required, which will be published in the future work.

As introduced before, NH is considered as an exhumed analogue for Soultz-sous-Forêts and Rittershoffen geothermal reservoirs. Both sites display a similar alteration and hydrothermal activity [8,76]. For example, the reservoir volume in Soultz-sous-Forêts is around 12 km<sup>3</sup> [77], and is crosscut by regional faults following the second and third orders scale according to Morrelato et al. [78] classification. The order of faults magnitude highlighted in the central part of NH is the same as that detected in the subsurface reservoirs at Soultz-sous-Forêts and Rittershoffen. Indeed, the second and third order scales control the geometry of the internal part of NH [25]. Then, the reservoir volume in case of NH paleo geothermal analogue can be equivalent to that at those of Soultz-sous-Forêts reservoir. Furthermore, during the Rittershoffen reservoir stimulation, a repercussion has been recorded in the Soultz-sous-Forêts reservoir and confirmed the kilometer faults orders (personal communication).

To further characterize a geothermal reservoir, it is important to determine the geothermal gradient and temperature at the targeted exploitation depth. However, the geothermal gradient in the NH context is difficult to highlight. Some additional data likely provided by fluid inclusion micro-thermometry and stable isotope analyses are needed to determine this gradient. In addition, it would be important to take in consideration the present-day stress field according to their orientation, the fractures might be open or closed and thus favorable or not to fluid circulation.

#### **6. Conclusions**

The present work is part of MEET project and focused on the NH range, considered as a paleo geothermal reservoir analogue, which offers a general overview of the structural organization of the fracture networks at outcrop and wider scales. This study aims at understanding the fracture spacing variability and the distribution of fracture patterns in granitic rocks, and the impact of the proximity of major faults on fracture distribution and fluid circulation. In the NH case study, the fracture patterns are controlled by the

structural heritage. This heritage results from the activity of the SDFVZ and GFZ faults, which strongly control the geometry of the entire ranges. The evidence of fluid circulations has been highlighted in previous studies and consist in the granite hydrothermal alteration (propylitic and argillic), and the fracture infills. The carbonate infill is associated to the fractures striking NW/SE (SDVFZ direction), while the barite infill is related to the fractures striking E/W (GFZ direction). Hence, at least, two episodes of fluid circulation have occurred within NH ranges.

From fieldwork scanlines, the main dominant trends within the central part of NH are the NW/SE and the E/W directions, well expressed whatever the scanline. The variability between fracture orientations was probably related to the influence of the major faults. From virtual scanlines, NE/SW, E/W, and NW/SE fracture sets were the most consistent orientations. However, some sampling bias previously discussed, such as the absence of dip in case of virtual scanlines and image resolution, which can impact the fracture detection should be reconsidered in the methodological development of the future work.

The spatial organization of the NH fracture network reveals that fracture clustering increases with fracture abundance only in the case of fracture sets detected from virtual scanlines (SL8, SL9, and SL10) due to the proximity of major faults. However, from fieldwork scanlines, the correlation seems not so clear. Furthermore, clustering depends on the strike of the fractures:


The most reproducible trends in the NH range are characterized by a clustered spacing distribution. The most clustered systems were identified close to or crosscutting the major faults which control the NH geometry. These faults are SDVFZ major segments and thrust faults. In addition, the deformation gradient impacts strongly the fracture patterns. The present paper highlighted that in a high deformation context, the spatial distribution of fracture become clustered, while in moderate deformation context, the fracture patterns are distributed randomly or regularly. These distributions considerably impact the fluid flow within the reservoir. The forthcoming reservoir modeling should consider the deformation gradient and the evolution of fracture patterns toward to major fault zones, as well as present-day stress field.

**Author Contributions:** Conceptualization, A.C., G.T., J.K. and B.A.L.; methodology, A.C.; software, A.C.; validation, G.T., B.A.L. and J.K.; formal analysis, A.C.; investigation, A.C., G.T., J.K., B.A.L.; resources, A.C.; data curation, A.C.; writing—original draft preparation, A.C.; writing—review and editing, G.T., B.A.L. and H2020 MEET consortium; visualization, G.T., B.A.L. and J.K.; supervision, G.T.; project administration, G.T.; funding acquisition, G.T. and H2020 MEET consortium. All authors have read and agreed to the published version of the manuscript.

**Funding:** This project has received funding from the European Union's Horizon 2020 research and innovation program under grant agreement No 792037 (MEET project).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** This work is part of postdoctoral contribution, prepared at Institut Polytechnique UniLaSalle Beauvais, which was funded by European Union's Horizon 2020 research (H2020 MEET project, grant agreement No 792037). We are grateful to Terry Pavlis for fruitful discussions. We also wish to thank the H2020 MEET consortium for helpful comments and manuscript validation.

**Conflicts of Interest:** The authors declare no conflict of interest.

### **References**


## *Article* **Multiscale Characterization of Fracture Patterns: A Case Study of the Noble Hills Range (Death Valley, CA, USA), Application to Geothermal Reservoirs**

**Arezki Chabani 1,\* , Ghislain Trullenque <sup>1</sup> , Béatrice A. Ledésert <sup>2</sup> and Johanne Klee <sup>1</sup>**


**Abstract:** In the basement fractured reservoirs, geometric parameters of fractures constitute the main properties for modeling and prediction of reservoir behavior and then fluid flow. This study aims to propose geometric description and quantify the multiscale network organization and its effect on connectivity using a wide-ranging scale analysis and orders scale classification. This work takes place in the Noble Hills (NH) range, located in the Death Valley (DV, USA). The statistical analyses were performed from regional maps to thin sections. The combination of the length datasets has led to compute a power law exponent around −2, meaning that the connectivity is ruled by the small and the large fractures. Three domains have been highlighted in the NH: (1) domain A is characterized by a dominance of the NW/SE direction at the fourth order scale; (2) domain B is characterized by a dominance of the E/W and the NW/SE directions at respectively the fourth and third order scales; (3) domain C is also marked by the E/W direction dominance followed by the NW/SE direction respectively at the fourth and third order scale. The numerical simulations should consider that the orientation depends on scale observation, while the length is independent of scale observation.

**Keywords:** fracture network; Death Valley; Noble Hills; power law distribution; multiscale analysis; geothermal reservoir characterization

### **1. Introduction**

Fluid flow in fractured rocks of very low matrix permeability is localized mainly in few fractures [1]. The complex geometry of fracture and fault patterns is the main cause of the complexity of fluid flow. In that case, numerous studies have been undertaken worldwide to show the control of the fracture network on the fluid circulations especially in hydrocarbon and aquifers reservoirs [2–5], in heat transfer [6], and thus also in geothermal reservoirs [7–9].

A fracture system is characterized by geometrical parameters as fracture lengths, spacings, orientations, and relations between them [1,10–12]. In order to access hierarchical and mechanical relationships between fracture systems, many authors undertook a multiscale approach, in sedimentary [2,12–15], and in Crystalline [16–20] rocks. This approach allows to model and predict hydraulic reservoir properties, by studying several geometric attributes, such as the distribution of orientations, lengths, widths, spacings and densities classically considered in spatial arrangement analysis [21–24].

The geometric parameters are commonly collected for (1) explicitly constructing deterministic models (Discrete Fracture Network: DFNs, [2]) or (2) ensuring inputs of stochastic simulations by determining fracture distribution functions from sampled fracture networks [23,25–27]. The main goal is to better understand the fracture network connectivity and then the fluid flow patterns [3,22,28]. Subsequently, the main question is whether

**Citation:** Chabani, A.; Trullenque, G.; Ledésert, B.A.; Klee, J. Multiscale Characterization of Fracture Patterns: A Case Study of the Noble Hills Range (Death Valley, CA, USA), Application to Geothermal Reservoirs. *Geosciences* **2021**, *11*, 280. https:// doi.org/10.3390/geosciences11070280

Academic Editors: Jesus Martinez-Frias and Gianluca Groppelli

Received: 10 June 2021 Accepted: 30 June 2021 Published: 3 July 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

data correspond to scale-limited lognormal or exponential distributions, or scale-invariant power laws, corresponding to fractal patterns? Several orders of magnitude based on length and spacing characteristics are thus mandatory to establish scaling laws from statistical distributions [29]. These orders of magnitude have been widely described in the literature in extensional [17,20,30] and trans-tensional [17] contexts. It consists of: (1) first order scale related to the crustal faults larger than 100 km length, (2) second order scale refers to the faults comprised between 20 and 30 km length, (3) third order scale refers to faults around 10 km length, (4) and the fourth order refers to faults under 1 km length [20]. In the extensional regime, [30] having defined a spacing characteristic for the two first order scales, with a 10 to 15 km spacing for first order and 3 to 8 km for the second order scale; while [20] have defined 0.8 to 1.5 km spacing for the third order scale. However, the fourth order spacing characteristic is not defined in the literature.

Fracture networks impact the fluid flow in reservoirs [23]. The 2D/3D seismic lines and 1D borehole data cannot detect respectively the fracture geometries and the spatial arrangement at the reservoir scale due to the lack of information [31]. Then, the spatial arrangement of fracture networks are widely studied from field analogues [16,23,29,32], as they give access to 2D and 3D distributions. In geothermal basement setting, the analogues are chosen according to the lithology and geological context to get closer to the reservoir conditions. Sometimes, the analogue is chosen in desert conditions, without vegetation, perfectly suited for realistic multiscale fracture network reconstructions in 2D, and in 3D in case of modeling canyons with photogrammetric [33] or lidar [34] approaches.

The present work is part of the MEET project (Multidisciplinary and multi-context demonstration of EGS exploration and Exploitation Techniques and potentials, [35]), which aims to develop geothermal exploitation at European scale by applying Enhanced Geothermal System (EGS) technology to different geological contexts. This study aims to propose geometric description and quantify the multiscale network organization and its effect on connectivity. A wide-ranging scale analysis from the microscopic scale to the regional scale was conducted in the desert environment of Noble Hills (NH) fractured granitic basement. It is located in the southern termination of Death Valley (DV, California, USA) and assimilated to a paleo geothermal analogue. The NH range is considered as analogue to the Soultz-sous-Forêts (SsF) geothermal electricity producing system, due to the granitic nature, the alteration and the trans-tensional tectonic setting of the DV region [36,37].

Measurements have been performed at various scales using the DV regional map [38] at 1:250,000, NH regional map based on previous studies undertaken by [37,39] and orthophoto images taken for the present day. At outcrop scale, fractures are digitized thanks to the photogrammetric models. Several 2D fracture maps are also used, as well as additional scales on samples and in thin sections. This allows to integrate fracture lengths ranging from micrometer to kilometer scales.

In this study, the multiscale approach is used to better understand the spatial arrangement of the fracture networks which aims at producing the necessary data for DFN modeling. This helps to better characterize reservoirs in response to the developing geothermal exploration and exploitation by EGS. This study is conducted through:


#### **2. Geological Setting**

The present study takes place in the NH fractured granitic zone, located at the southern termination of the Death Valley (DV, California, USA) (Figure 1a). The NH range is assimilated to a paleo geothermal analogue [37]. Indeed, Reference [37] confirmed the analogy between the DV region and Soultz-sous-Forêts reservoir (Rhine graben, East of France), with many similarities, especially: (1) the trans-tensional tectonic setting of the DV, and (2) the granitic nature and hydrothermal alteration of the central part of the NH range. Furthermore, the desert conditions of the NH range make this analogue perfectly suited for multiscale characterization of fracture networks dedicated to the global understanding of the spatial arrangement in granitic reservoir affected by trans-tensional tectonics [35].

**Figure 1.** (**a**,**b**) Location and geological setting of DV, NDVFZ: Northern Death Valley Fault Zone, SDVFZ: Southern Death Valley Fault Zone; (**c**) Structural scheme of the NH range built using high-resolution digital mapping techniques modified after [37,39]. Additional digitized fractures were performed using orthophotos. The aerial picture in (**b**) was extracted from Google Earth®. The samples location was reported in the structural scheme. FM: fracture map.

The DV region has been characterized by a complex structural and tectonic history which includes the overprinting of Mesozoic to early Cenozoic contractional structures by late Cenozoic extensional and trans-tensional features [40–42]. The northwest trending contractional structures of the DV are at the origin of the Cordilleran orogenic belt of North America, which extends more than 6000 km from southern Mexico to the Canadian Arctic and Alaska [43]. Their age is estimated around 100 Ma and coincides with the Sevier orogenic belt [43,44]. The northeast trend is related to a thrust faults system [41].

The Mesozoic period was marked by the beginning of pluton emplacement in DV along the development of contractional structures. Then, during the Cenozoic period, the DV extension episode occurred [45,46], but there is no general agreement about its timing, e.g. [45,47]. The Miocene period was characterized by a trans-tensional regime. The opening of the DV region as a pull-apart basin began around 5 Ma [41,48–50]. A recent study done by [51] challenges this, mentioning that the opening of DV region into pull-apart basin started around 12 Ma ago.

Located in the southernmost part of the DV, the NH range trends parallel to, and then forms, the main topographic features aligned with components of the right-lateral Southern Death Valley Fault Zone (SDVFZ) [37] (Figure 1b). This SDVFZ is part of the Death Valley fault system (DVFS) [52], and its net dextral strike-slip displacement has been estimated around 40–41 km [51]. The northeast-vergent contractional deformation has been characterized along the length of the NH and constitutes the dominant structural style [48,53,54]. In the NH foreland basin, compressional structures have been characterized by [39] near the Canadian Club Wash (Figure 1c). An entire compressional region has also been created by the interaction between the SDVFZ and the GF zone, which is responsible for shortening within the Avawatz Mountains [55,56]. Furthermore, the reverse displacement of the GF was identified in the front of the Avawatz [57]. The E/W fractures observed mainly in the southeast end of the NH show an identical orientation to GF. Given this similarity in orientation and the close vicinity to the GF, it is tempting to relate the E/W trending fracturing to GF zone activity.

Recent work by [37] using high-resolution digital mapping techniques reveals the dominance of basement rocks in the central part of the NH (Figure 1c). Indeed, the granitic rocks are mostly represented and related to the Mesozoic granitic intrusion (Mzla, Figure 1c) [58]. Proterozoic formations characterized by gneiss in the bottom have been defined in the center part and the southeast end of the NH (pCgn, Figure 1c). The Proterozoic Crystal Spring sedimentary series defined in the northwestern part of the NH are mainly composed of carbonates and quartzites facies (pCu, Figure 1c). Some tertiary volcanic series have also been mapped in the southeastern end of the NH.

Outside the center part, Reference [39] has widely studied the Cenozoic NH formations mainly composed of Fanglomerate and alluvial fan deposits.

#### **3. Materials and Methods**

#### *3.1. Materials*

3.1.1. Large Scale Characterization

The analysis of large scale fracture attributes was performed on fractures digitized from DV regional map at 1:250,000 scale (geological map of California, Trona Sheet [38]) (Figure 2a). In the central part of the NH range, the main structures were mapped during 2018 and 2019 field campaigns published by Klee et al. [37]. In addition, in this present study, orthophoto images of 1 m resolution were used to digitalize and then complete the fractures sampling (Figure 2b).

**Figure 2.** Fracture traces, orientation, and boxplot distributions from (**a**) DV geological map and (**b**) NH range map (in red rectangle for large scale location). The order of fractures magnitude were referred to the classification detailed in [30]. The first order referred to the faults larger 100 km length is not detected in this study. Each fracture map dataset is expressed in histogram for orientation distribution, and into boxplot for length distribution, according to the fracture orientations. Two scanlines (SL) were taken for every map.

With the aim of pinpointing the likely fracture variability, the NH range map has been divided into three domains (Figure 3). The sampling strategy along domains is detailed below. In total, 1013 fractures are extracted from the DV geological map, 1434 fractures from the NH map with 306 from domain A, 522 from domain B, and 606 from domain C.

**Figure 3.** Fracture traces from the NH range divided into 3 domains. (**a**) NH domains: A, B, and C, (**b**) orientation distributions, and (**c**) boxplot of length distributions according to the fracture orientations. Two scanlines (SL) were taken for every domain. For boxplot and orientation distribution legend, see Figure 2.

Orientation and length distributions were collected and 1D/2D densities were calculated from them. All of these data are summarized in Table 1.


**Table 1.** Spatial statistics of 2D samples acquired at large scale (DV and NH regional maps) and outcrop scale (Drone models). Two Scanlines (SL) at least were generated for calculating the fracture density (P10). The length average is provided.

#### 3.1.2. Photogrammetric Study/Analysis

In order to combine the widest fracture network analysis, three photogrammetric models, localized only in the granitic facies and alongside the major faults that structure the NH range (see Figure 1 for the location), are considered in this study to extract the fractures ranging approximatively from 10−<sup>2</sup> m to 20 m. A photogrammetric campaign was carried out in October 2018 with a high-resolution 3D point cloud and large collection of photographs.

Drone model 1 is sized approximately 350 m per 46 m and is located in the granitic facies (Figure 1); 1271 fractures are traced. Drone model 2 is located in the granitic facies within a high deformation zone, and is sized approximately 172 m per 44 m (Figure 1). In total, 4196 fractures are traced. Finally, drone model 3 is located in the southeast termination of NH, and is sized approximately 280 m per 70 m. 15,594 fractures are traced.

The main statistical characteristics are summarized in Table 1.

#### 3.1.3. Fracture Map Characterization

To complete the multiscale analysis with the small fractures, fracture maps were created with a resolution of 2 <sup>×</sup> <sup>10</sup>−<sup>4</sup> m. The fracture map 1 (see Figure 1c for location) is sized at 3.4 m per 3.1 m and is located between the granitic facies and the tertiary sediments, near the influence of the SDVFZ (see Figure 1b for the SDVFZ location). It is composed of quartzite boudin facies (part of Crystal Spring series) and granitic rocks, which respectively represent approximately 20% and 80% of occurrences.

In order to include the very small fractures in this study, additional fracture sets were collected from this fracture map with sample 1-1 sized 17 cm per 12 cm (resolution of 10−<sup>4</sup> m) and thin sections 1-1 and 1-2 (resolution of 10−<sup>5</sup> m), both sized 3.5 per 2.5 cm (see Figure 1c for location). Both sections are composed mainly of Plagioclase, Quartz, K-Feldspar, and Biotite representing respectively 35%, 30%, 25%, and 10% of occurrences.

Fracture map 2 (Figure 1c) is sized 1.7 m per 1.6 m and is located in the granitic facies, near the SDVFZ deformation corridor. This map includes sample 2-1 and thin section 2-1 which size respectively 15 cm per 5.2 cm and 3.5 cm per 2.5 cm. Thin section 2-1 represents the same mineral composition as thin sections 1-1 and 1-2 with approximately the same occurrences. Fracture map 3 (Figure 1c) is sized 1.8 m per 1.7 m and is located also in the granitic facies.

Table 2 summarizes the main statistical characteristics.


**Table 2.** Spatial statistics of 2D samples acquired from outcrop scale (fracture maps) to thin section scale. Two Scanlines (SL) at least were generated for calculating the fracture density (P10); the length average is provided.


**Table 2.** *Cont.*

#### *3.2. Methods*

3.2.1. Fractures Acquisition

In this study, fracture digitization was performed manually by tracing every fracture segment from entire 2D maps in QGIS® software v.2.18.17. Only fractures reported as full solid lines on the DV geological map were considered for statistical analysis (Figure 2a).

Regarding the procedure of fracture digitization, the fractures extending out of the sampling domain were considered as one continuous feature [16,23,59] (Figure 2b). The digitization of fractures consists of an extraction of the end point coordinates of each fracture using the QGIS® software v.2.18.17. Each extracted fracture is characterized by the X and Y coordinates of each of the two end points, which help to compute the orientations and the length of segments. In case of curved fractures, a straight segment line was automatically traced between the end of point coordinates, and then the mean directions and lengths were computed.

As described above, the NH fracture data were acquired during the field mapping campaign and then completed by orthophoto image analysis. The data were analyzed in the entire area (Figure 2b). However, the complexity in loading history within NH widely discussed in the literature [48,54,60] makes the analysis of the fracture geometries difficult. Furthermore, the field observations and the new geological map done by [37] reveal additional complexities inside this area, and show a stacking of different Crystal Spring series (pCu, Figure 1c), intruded by the Mesozoic granite (Mzla, Figure 1c). This observation was highlighted in the northwest part of the NH. In center part, Crystal Spring series thicknesses were reduced, dragged, and stretched against the granite due to the SDVFZ activity (pCu, Figure 1c). The southeast of the NH is characterized by the absence of the Crystal Spring series. To better characterize the fracture variability, it is prime of interest to consider the facies variability and the deformation intensity within NH, because they influence the fracture evolution [23,59]. In this sense, we decided to divide the NH range into three domains according to the facies variability and change in range trend orientation variation (Figure 3): (1) Domain A is located northwestward, highlighted by thick Crystal Spring sediments and granitic rocks; (2) Domain B is in the central part of NH, highlighted by reduced thickness of Crystal Spring sediments, granitic and gneissic rocks, and (3) Domain C is located in the southeastern part of the NH and is characterized by granite, gneiss, and Tertiary volcanism. Note that Domain B and C are composed approximately of the same facies. However, range orientation in domain B is NW/SE, while in domain C it is toward E/W. This general E/W trend is puzzling as it is similar to the GF (see Figure 1b for location). Therefore, this difference in orientation constitutes an additional argument to better delimitate domain B and C. Figure 3 shows the fracture

distributions within each domain. Some more work based on field analyses could more precisely delimitate the domains.

The photogrammetric models undertaken in this work were performed using a 3DR Solo drone with 4k cameras and DJI Phantom drone provided by University of Texas at El Paso (UTEP), Texas, USA. The videos were recorded between the late morning and the early afternoon during seven days with a manual mode camera setting to reduce the effects of lighting condition. Pictures were then extracted every second from the recorded drone videos using ffmpeg software v.4.5. The extracted pictures with a sufficient overlapping were aligned in Agisoft Metashape software (2020, Version 1.6.5). The obtained 3D models are georeferenced and then imported in CloudCompare software (version 2.9.1; [GPL software] (2017)) to begin the fracture extraction process. A workflow explaining the procedure of the models construction and the fractures extraction is detailed in [36]. In this study, the digitized fractures are projected on a 2D map to make the work only in 2D in order to keep data homogenous at different scales.

The 2D fracture maps at outcrop scale were performed in the field using a DSLR high resolution camera provided by UniLaSalle (Beauvais, France), with a 50 mm focal lens to minimize distortion. Pictures were taken vertically, with the same distance, and in the absence of sunlight to avoid the light effects in the fracture digitization [12]. From each fracture map, several pictures were taken with a sufficient overlapping. Then, pictures were aligned using the Agisoft Metashape software with the same procedure detailed in [36]. The maps are georeferenced and then used to extract the fractures in QGIS® with the same technique as for large scale maps.

Additional fracture datasets are used in this study by adding samples. These samples were taken directly from fracture maps. Then, a high-resolution picture was taken for each sample using a DSLR camera. With the same procedure as large-scale fractures acquisition, the sample was added in QGIS® to extract the fractures.

Thin section mosaics are also added to this study, made from samples as described earlier to keep a consistent sampling strategy. These mosaics were taken under an optical microscope Leica DM4500-P provided also by UniLaSalle (Beauvais, France), using a ×5 magnification and polarized non-analyzed light mode. A Leica DFC450C high resolution camera provided also by UniLaSalle (Beauvais, France) and Leica application Suite v.4.11.0 were used to take pictures. Every mosaic was relatively oriented using the corresponding sample. Then, with the same fracture digitization procedure described earlier, fracture parameters were extracted under QGIS® v.2.18.17.

#### 3.2.2. Fractures Analysis

Different geometrical parameters were then collected from each fracture database at different scales. Detailed orientation distributions and classification into fracture sets were performed using the mixture of von Mises distribution (MvM) [61]. This approach consists of a semi-automated procedure based on appraisal tests in order to avoid any subjectivity in fracture sets analysis. For each fracture set, three output parameters were considered: (1) mean orientation (µ) around which the distribution is centered, (2) kappa (κ) which controls the concentration of the orientation's values around the mean, and (3) weight (ω) corresponding to the relative contribution of each fracture set to the model. Then, we are able to check the best number of fracture sets from the distributions using the goodness of fit parameters (e.g., Likelihood). For more details, see [62] who describe and adapt the methodology for structural data. The standard of deviation of +/−10◦ was calculated for each given mean orientation value in this study.

Fracture length is the most used geometrical parameter to characterize the spatial organization in the natural fracture networks [4,25,63]. This characterization is performed using a statistical distribution as the Power law distributions widely used in structural data from field analogue [4,25,26,63,64]. The power law is often used to describe the distribution of fracture parameters such as length and aperture [25]. It is recognized that power law and fractal geometry provide widely applicable descriptive tools for fracture system

characterization. This is due to the absence of characteristic length scales in the fracture growth process. The power law exponent α provides a real significance on the fracture connectivity. Indeed, for an exponent comprised between 2 and 3, fracture connectivity is ruled by both small and large fractures [65]. In addition, fractal analyses using Cantor's dust method allow the quantification of fracture distribution in clusters or, in the opposite, with a homogeneous distribution [66] and prediction of the fracture occurrence [7]. The exponential law is also used to describe the size of discontinuities in rocks [67–69], and to incorporate a characteristic scale that reflects a physical length in the system, such as thickness of a sedimentary layer [70].

However, fitting the geometric attributes to the statistical distributions suffers from a lot of biases, such as truncation and censoring biases [25]. Truncation effects are caused by resolution limitations of a field observation such as from satellite images, the human eye, or microscopes [63]. Censoring effects are associated with the probability that a long fracture intersecting the boundary of the sampling area is not sampled, and to the subjective choice of the sampling area which tends to exclude very long fractures [63,71]. Then, censoring effects cause an overestimation of fracture density. In this study, the truncation and censoring effects were automatically excluded from the distributions. Length distribution in Figure 4 shows the data excluded from the distribution (grey color) due to the impact of truncation and censoring effects.

The fracture length distributions are analyzed using the cumulative distribution. Statistical distributions used in this study were adjusted after corrections from the truncated and censoring effects. Research for truncation and censoring thresholds was performed using the « poweRlaw: Analysis of Heavy Tailed Distributions » package from Rstudio® v.1.3.1056 [72]. We also used the coefficient of determination (R<sup>2</sup> ) to estimate the goodness of fit of the power law to the length distribution. This coefficient is comprised between 0 and 1. A high R<sup>2</sup> for a given number of degrees of freedom means that the regression is a statistically meaningful description of the data.

Fracture densities are computed in this study. They consist of fracture density (P10), defined as the number of fracture intersections along a 1D virtual scanline traced on every analyzed 2D map [59,73]. The scanline methodology is widely used to describe the fracture variability in 1D [73]. In this study, the linear fracture density P<sup>10</sup> was obtained from two virtual scanlines, orientated perpendicular to the main structures.

Finally, the surface fracture density (P21) is defined as the total sum of fracture lengths within the area [59,73].

**Figure 4.** Fracture traces, orientation, boxplot length distributions from (**a**) drone model 1 and (**b**) drone model 2. Each fracture map data is expressed into histogram for orientation distribution, boxplot of length distribution according to the fracture orientations, and cumulative distribution function (CDF) of lengths. Two scanlines (SL) were taken along the left and the right side of the canyon. For the boxplots and orientation distributions legend, see Figure 2.

#### **4. Results**

#### *4.1. Large Scale Domains*

The mean orientation (µ) N095◦ (E/W trend) and N132◦ (NW/SE trend) trending fractures occur at the largest length scale, with a 20 and 24% of whole fractures, and about 3300 to 4400 m mean length (Figure 2a). Both directions are well expressed following the DV and Garlock strike slip trend faults (See Figure 1b for location) [39,48]. The largest fracture length is recorded within the NE/SW fracture set with 65 km length. The other recorded fracture sets are relatively equivalent (around 20%), except for the N025◦ fracture set which is less dominant, with 13% and 1900 m mean length.

At NH scale, the same dominance of N090◦ and N126◦ fracture sets with respectively 37% and 31% are observed (Figure 2b). The other fracture sets are poorly expressed (<15%). The boxplot distribution in Figure 2b showed also the dominance of the E/W and NW/SE fracture sets with respectively 80 m and 125 m mean length. The other fracture sets did not exceed the 50 m mean length.

The occurrence of two prominent fracture sets is shown in the NH domains A and B (Figure 3a,b). Domain A is characterized by two main fracture sets striking N091◦ and N132◦ representing respectively 29% and 55% of occurrences (Figure 3b). The N091◦ fracture set lengths range from 30 m to 300 m, while the N132◦ fracture set length ranges from 5 m to 800 m, meaning that the NW/SE is the most dominant fracture set in domain A (Figure 3b).

Orientation and length data of domain B shows an equivalent distribution as in domain A (Figure 3b). Indeed, two main fracture sets striking also N088◦ and N128◦ are mostly representative with respectively 45% and 31%. The fractures are much longer within NW/SE trend, ranging from 2 m to 1300 m (mean is of 108 m). The other fracture sets show an intermediate length with a 50 m mean value.

Fracture geometry in Domain C shows immediately a different distribution with four main fracture sets striking N050◦ (19%), N085◦ (31%), N111◦ (20%), and N141◦ (17%) (Figure 3b). The NW/SE fracture set mainly sampled and representative in the domain A and B is split into N111◦ and N141◦ fracture sets in domain C, with respective lengths ranging from 3 to 1600 m (mean is 190 m) and from 8 m to 730 m (mean is 65 m).

The fracture densities are increasing considerably from domain A to C with <sup>2</sup> <sup>×</sup> <sup>10</sup>−2/3 <sup>×</sup> <sup>10</sup>−<sup>2</sup> m/m<sup>2</sup> in the domain A and B, and 5 <sup>×</sup> <sup>10</sup>−<sup>2</sup> m/m<sup>2</sup> in the domain C.

#### *4.2. Photogrammetric Models*

NH canyons modeled with photogrammetric method provide fractures from centimetric to decametric scale. Fracture distributions are displayed by drone model 1 for both sides of the canyon walls (Figure 4a). Six fracture sets are recorded and strike N025◦ , N055◦ , N085◦ , N115◦ , N142◦ , and N174◦ . The N142◦ is also the most dominated fracture set with 22%. The E/W fracture set is the less expressed (14%) at outcrop scale. An equivalent mean length of fractures is shown by the boxplot distribution graphic with 2.3 m, whatever the fracture set (Figure 4a).

The exponent of power law (red line in the length distribution, Figure 4) is of α = −2.4 for length distribution of the drone model 1, outside lengths affected by truncation and censoring bias (data mentioned in the length distribution graphic with grey color, Figure 4). The range of length values performed by the power law is 1.85 m to 25 m.

Finally, fracture densities P<sup>21</sup> and P<sup>10</sup> are of respectively 2 <sup>×</sup> <sup>10</sup>−<sup>1</sup> m/m<sup>2</sup> and 6.5 <sup>×</sup> <sup>10</sup>−<sup>1</sup> frac/m.

Fractures from drone model 2 are mainly distributed along the left side of the canyon (Figure 4b). The same fracture sets as drone model 1 are recorded with an equivalent percentage (between 15 and 18%) (Figure 4b). Fracture lengths are highlighted by the boxplot distribution and are also equivalent with 1 m mean length, whatever the fracture set. The largest fractures are recorded within the NW/SE fracture set (maximum of 8.5 m), and then confirm the consistency of the NW/SE direction at outcrop scale.

The fracture length range modeled by the power law is of 0.69 m to 8.5 m, for exponent <sup>α</sup> <sup>=</sup> <sup>−</sup>2.5 and R<sup>2</sup> = 0.97 (Figure 4b). Fracture lengths under 0.69 m are excluded automatically from the distribution (truncation effects).

Fracture densities are quite high in comparison with Drone model 1, with <sup>7</sup> <sup>×</sup> <sup>10</sup>−<sup>1</sup> m/m<sup>2</sup> and 1.28 frac/m for respectively P<sup>21</sup> and P10.

Drone model 3 is the largest studied model with 15594 traced fractures (Figure 5). Six fracture sets are highlighted also in this canyon. Their proportions range from 13% (N079◦ and N109◦ ), 14–16% (N140◦ and N038◦ ), to 19–20% (N018 and N169◦ ). The fracture lengths are equivalent, once again, with a 1.2 m mean length.

**Figure 5.** Fracture traces, orientation, boxplot length distributions from drone model 3. Different Datasets are expressed into histogram for orientation distribution, boxplot of length distribution according to the fracture orientations, and cumulative distribution function (CDF) of lengths. Two scanlines (SL) were taken along the left and the right side of the canyon. For Boxplot and orientation distribution legend, see Figure 2.

The power law exponent for drone model 3 length distribution is of α = −2, outside lengths affected by truncation and censoring effects (Figure 5). R<sup>2</sup> value is of 0.97, indicating a good fit of the power law to the data. Fracture density P<sup>21</sup> is of 1 m/m<sup>2</sup> , increasing by a factor 5 compared to drone model 1 fracture density.

#### *4.3. Fracture Maps*

Fracture map 1 is characterized by intense fracture areas, especially along the center part (Highly fractured area, Figure 6). The high fracture density is located mainly in the quartzite boudin, while the less fractured zone is related to the granitic rocks.

**Figure 6.** Fracture traces, orientation and length distributions from fracture map 1. Different datasets are expressed into histogram for orientations distribution, and into cumulative distribution function (CDF) of lengths. Two scanlines (SL) were taken for every domain. For orientation distribution legend, see Figure 2.

For the rest of the fracture map, average P<sup>10</sup> of 12 frac/m is computed from two scanlines (SL1\_map1 and SL2\_map 2, Figure 6), while P<sup>21</sup> is of 10 m/m<sup>2</sup> . Two main fracture sets are highlighted: N005◦ and N083◦ , with respectively 57% and 32% (Figure 6). Outside fracture lengths affected by truncation and censoring bias, the power law exponent is of <sup>α</sup> <sup>=</sup> <sup>−</sup>1.7 for values ranging from 6 <sup>×</sup> <sup>10</sup>−<sup>2</sup> m to 1.2 m.

Sample 1-1 is characterized by homogeneous fracture distribution with four main fracture sets: N018◦ , N053◦ , N090◦ , and N126◦ representing respectively 27%, 30%, 30%, and 13% (Figure 7a). The largest veins visible in the sample map are characterized by carbonate mineralizations in two directions: N053◦ and N126◦ . P<sup>10</sup> and P<sup>21</sup> fracture densities are of 184 frac/m and 118 m/m<sup>2</sup> respectively. Regarding the length distribution, the power law exponent is of <sup>α</sup> <sup>=</sup> <sup>−</sup>1.43, with thresholds of 3 <sup>×</sup> <sup>10</sup>−<sup>3</sup> m and 7 <sup>×</sup> <sup>10</sup>−<sup>2</sup> m.

Four main fracture sets are highlighted in thin section 1-1: N018◦ , N053◦ , N090◦ , and N126◦ with a comparable fracture proportion (around 25%). Additional fracture set is detected in thin section 1-2: N162◦ . Regarding the densities, P<sup>21</sup> is of 715 m/m<sup>2</sup> and 702 m/m<sup>2</sup> , while P<sup>10</sup> is of 5140 frac/m and 4525 frac/m respectively for thin section 1-1 and 1-2 (Figure 7b,c). The power law exponents are quite higher with α = −1.95 (modeled range from 2.2 <sup>×</sup> <sup>10</sup>−<sup>4</sup> m to 4.63 <sup>×</sup> <sup>10</sup>−<sup>3</sup> m) and <sup>α</sup> <sup>=</sup> <sup>−</sup>1.7 (modeled range from 2.2 <sup>×</sup> <sup>10</sup>−<sup>4</sup> <sup>m</sup> to <sup>7</sup> <sup>×</sup> <sup>10</sup>−<sup>3</sup> m) respectively for thin section 1-1 and 1-2.

**Figure 7.** Fracture traces, orientation and length distributions from (**a**) sample 1-1, (**b**) thin section 1-1, and (**c**) thin section 1-2 sampled from fracture map 1. Different datasets are expressed into histograms for orientations distribution, and into cumulative distribution function (CDF) of lengths. Two scanlines (SL) were taken for each map. For orientation distribution legend, see Figure 2.

Fracture densities of fracture map 2 are comparable with fracture map 1 with average P<sup>10</sup> = 18 frac/m and P<sup>21</sup> = 13 m/m<sup>2</sup> (Figure 8a). Five fracture sets are highlighted: N005◦ , N038◦ , N070◦ , N110◦ , and N145◦ . The N070◦ and N145◦ are the most recorded fracture sets with respectively 32% and 27%.

**Figure 8.** Fracture traces, orientation, and length distributions from (**a**) fracture map 2, (**b**) sample 2-1, and (**c**) thin section 2-1, located in sample 2-1. Different datasets are expressed into histogram for orientations distribution, and into cumulative distribution function (CDF) of lengths. Two scanlines (SL) were taken for each map. For orientation distribution legend, see Figure 2.

The power law exponent is also comparable to that of fracture map 1 (α = −1.59), with the thresholds of 8 <sup>×</sup> <sup>10</sup>−<sup>2</sup> m and 1.43 m (Figure 8a).

Sample 2-1 is characterized by a fracture density of P<sup>10</sup> = 177 frac/m and P<sup>21</sup> = 240 m/m<sup>2</sup> (Figure 8b). In total, five fracture sets are highlighted: N017◦ , N057◦ , N092◦ , N130◦ , and N157◦ . Three fracture sets are the most recorded: N057◦ , N130◦ and N157◦ , with 20% to 25%. The power law exponent is of <sup>α</sup> <sup>=</sup> <sup>−</sup>1.66, thresholds from 1.6 <sup>×</sup> <sup>10</sup>−<sup>3</sup> m to 3.33 <sup>×</sup> <sup>10</sup>−<sup>2</sup> m.

Thin section 2-1 trans-cutting a large carbonate vein in the central part (Figure 8c), is characterized by a fracture density P<sup>21</sup> = 1064 m/m<sup>2</sup> higher than in thin section 1-1 and 1-2. Only four fracture sets are highlighted: N014◦ , N059◦ , N097◦ and N140◦ , with an equivalent fracture proportion. Outside the lengths affected by sampling bias, the exponent is of <sup>α</sup> <sup>=</sup> <sup>−</sup>2, thresholds of 7 <sup>×</sup> <sup>10</sup>−<sup>4</sup> m to 3.5 <sup>×</sup> <sup>10</sup>−<sup>2</sup> m.

Finally, fracture map 3 is characterized by a comparable fracture density as in fracture map 2 with P<sup>10</sup> = 20 frac/m and P<sup>21</sup> = 12 m/m<sup>2</sup> (Figure 9). Five fracture sets are also detected with a high proportion of 26% for N009◦ and N149◦ . Fracture sets N033◦ , N077◦ , N104◦ showed an abundance of 15%, 21%, and 12% respectively. The power law exponent is of <sup>α</sup> <sup>=</sup> <sup>−</sup>1.53 for lengths data ranging from 4 <sup>×</sup> <sup>10</sup>−<sup>2</sup> m to 1.21 m.

**Figure 9.** Fracture traces, orientation and length distributions from fracture map 3. The computed dataset is expressed into histogram for orientations distribution, and into cumulative distribution function (CDF) of lengths. Two scanlines (SL) were taken. For orientation distribution legend, see Figure 2.

#### **5. Discussion**

The combination of data at various scales in this study allowed to propose a new interpretation of the fracture network in the NH range, based on multiscale evolution of fractures length and orientation. A conceptual scheme of the NH structuration is created and discussed in terms of fracture network connectivity and its influence of fluid flow.

#### *5.1. Multiscale Length Characterization*

The cumulative length distributions of each fracture map from the DV regional map scale to thin section scale are plotted in Figure 10. All length datasets have been fitted to the power law distribution, outside lengths affected by truncation and censoring bias.

**Figure 10.** Fracture length distribution from (**a**) DV geological map, (**b**) NH range, (**c**) NH map domain A, (**d**) NH map domain B, and (**e**) NH map domain C, and (**f**) Multiscale length distribution obtained from the combination of the whole data.

DV regional map exponent is quite low, around α = −1.40, and gradually increase to around α = −1.62 in NH map (Figure 10a,b). The division of the NH into 3 domains according to the facies variability and the change in range trend orientation showed a disparity in power law exponent values. Indeed, the exponent α = −0.83 in the domain A (values ranging from 21 m to 230 m), while α = −1.42 (values ranging from 25 m to 1283 m) and α = −1.52 (values ranging from 70 m to 1500 m) respectively in domain B and C (Figure 10c–e). The lowest α value in domain A can be explained by the dependence of fracture lengths on scale of observation for fractures ranging from 5 m to 870 m. In addition, the domain A is composed of granitic rocks and Crystal Spring sedimentary series with carbonates and quartzites (Figure 1), meaning that the sedimentary rocks can

have a different behavior from that of basement rocks during the fracture growth and propagation process.

Cumulative distribution of fracture lengths in the domain A showed also two different trend slopes (Figure 10c), with a failure slope quantified around 230 m. Distribution into two slopes has been largely discussed in the literature [25,67,70], and can be explained by the fracture growth process which has been divided into two trends. However, this result and interpretation cannot allow to determine if these two trends correspond to a single or to two different regional directions. Cumulative distribution of fracture lengths according to their orientations and the nature of rocks could help to resolve the episodes of deformation challenge, together with some more work in the field (e.g., looking for evidences of displacement).

The cumulative fracture length from all maps has been plotted in a single graphic, normalized by surface area of each map [63] (Figure 10f). The power law distribution included fracture lengths from 2.2 <sup>×</sup> <sup>10</sup>−<sup>4</sup> m to 65 km scale. Power law distribution was performed over 6 orders of magnitude. Two length ranges were not represented in this study. The first one corresponds to the fracture lengths over 100 km and related to the first order fracture defined by [30]. This absence can be explained by: (1) a different evolution stage and opening mechanism of faults [30,74], (2) a structural heritage which controls the reactivation during the DV trans-tensional tectonic setting. The second one corresponds to the length ranging from 1 km to 5 km length (Figure 10f). The Basin and Range regional map and the geological map at 1:25,000 scale could help to resolve both gaps.

The power law distribution gives an exponent α = −2 for the whole 2D fracture lengths analyzed in this study (Figure 10f), which suggests the 2D representation is selfsimilar [4,16,23,26]. The probability to detect fracture of the size of the sampling window is the same at all scales. Then, the fracture connectivity is ruled by the small and large fractures [65], meaning that the large fractures detected and studied at large scale in the NH play the same role as any fracture at millimeter scale in fracture network connectivity.

#### *5.2. Spatial Organization of NH Fracture Network*

The fracture densities and the main dominant orientations on the regional maps show the control of NH geometry by NW/SE and E/W trends. Both trends are associated to the second order scale faults over 20 km length, well expressed in terms of abundance (DV regional map, Figure 11). The third order scale detected along NE/SW trend is characterized by faults around 10 km length. Spacing values were computed and correspond to 5 km and 1 km respectively for the second and the third order scale (Figure 12a). The same geometrical characteristics (detailed in the introduction) were approved in the extensional regime [20,30], meaning that the second and third order scale spacing classification can be generalized to the trans-tensional regime studied in the present work.

At NH scale, the fracture densities and the main dominant orientations approve the separation of the NH into three domains:


fracture of 100 m mean length (Figure 11). Then, NW/SE and E/W directions control the NH geometry respectively following the third and fourth order scale length. In this case, the spacing related to the third order scale is around 1 km between the SDVFZ bordering faults and regularly spaced at 0.2 km (Figure 12b). A spacing of 0.05 km is defined along the E/W fracture set (Figure 12b).

3. The southeastern end area corresponding to the domain C (Figure 3) highlights a specific spatial arrangement with an additional fracture set (yellow color, Figure 11), the longest one with 200 m mean length. Indeed, the NW/SE direction is split into N111◦ and N141◦ fracture sets thus highlighting the influence of both NW/SE and E/W deformation episodes in this area. Once again, the E/W direction is more expressed, with a 100 m mean length (Figure 11). The ENE/WSW, E/W and also NW/SE directions control the NH geometry and structuration respectively following the third and fourth order scale. The spacing of 0.3 km defined for the third order scale in domain C between the SDVFZ bordering faults is under the third order spacing characteristic. Indeed, the NW/SE direction has been deviated and then the relative spacing is reduced. Regarding the internal organization, the NW/SE and E/W fractures are also regularly spaced with 0.1–0.2 km and 0.05 km, respectively (Figure 12b).

**Figure 11.** Orientation plot representing mean orientation of each fracture set from DV regional map, NH regional map, NH domains and drone models at outcrop scale. Each arrow corresponds to the mean orientation. The length of each arrow corresponds to the fracture set abundance. The horizontal line above each arrow corresponds to the fracture set standard deviation within an interval of confidence of 75% (see [62] for more explanations). Each color arrow corresponds to fracture set: Blue arrow corresponds to NNE/SSW fracture set, red arrow corresponds to the NE/SW fracture set, green arrow corresponds to the E/W fracture set, yellow arrow corresponds to the NNW/SSE fracture set, purple arrow corresponds to the NW/SE fracture set, and marron arrow corresponds to the N/S fracture set.

**Figure 12.** Conceptual scheme presenting the spatial arrangement of the NH fracture network at (**a**) regional scale, (**b**) NH scale, and (**c**) outcrop scale. The organization is based on scale orders referring to the [16,17,20,30] classification, and their associated spacing characteristics referring to [20,30]. The picture presented in (**c**) is provided by GoogleEarth®.

In the present work, the spacing characteristics of 0.05 km to 0.1–0.2 km computed in the three internal domains are attributed to the fourth order scale (Figure 12b). These values vary according to their directions and also lengths. Two spacing characteristics can be highlighted from this study: (1) spacing of 0.05 km corresponding to the fractures comprised between 0.1 and 0.35 km (percentile 90 values), (2) spacing of 0.1–0.2 m corresponding to the fractures comprised between 0.35 and 0.5 km. Further work on the fourth order scale spacing characteristics will obviously be needed in order to generalize them to the trans-tensional regime.

At outcrop scale, the drone models highlighted the reproducibility and the consistency of the whole fracture sets defined at large scale (Figure 11). However, N111◦ fracture set, detected only in domain C, is less expressed in domain A (drone model 1, 9%) (Figure 11). The E/W direction trend is more expressed in the drone models 2 and 3 respectively in the domain B and C. This observation is confirmed by the fracture maps 2 and 3, sample 2-1 and thin section 2-1 (Figures 8 and 9), highlighting a consistent fracturing episode. In the previous works, [39,55–57] mentioned the presence of the compression signature at the southeastern end of the NH and the front of the Avawatz mountains. According to these studies and our current observations, a hypothesis of fracturing intensity which affected up to the internal domain can explain the consistency of the E/W direction.

A special fracture arrangement was observed in fracture map 1 (Figure 6). The length distribution is characterized by a high density of short fractures in the quartzite boudin rocks, while the granitic part is characterized by a lower density of long fractures. This leads to a change in the power law and orientation distributions and then makes a bias. Indeed, only N/S and E/W directions are recorded, while the sample 1-1, thin sections 1-1 and 1-2 have recorded the whole fracture sets.

Fractures are organized along SDVFZ direction as fault zone segments with a highly mineralized (clay minerals) fault core (FC) which can act as a barrier and damage zone (DZ), acting as a conduit (Figure 12c). A complex joint network that can play a key role in the fracture connectivity is highlighted in the host rock. A petrographic study focusing on these fault zones is required to better characterize the fluid circulation potential.

The N/S to NNE/SSW and the NE/SW fracture sets are less expressed and are attributed to the fourth order scale with 40 m mean length on NH map, while they are still very important and consistent at outcrop, sample, and thin section scales, regardless of domain (Figures 2–5). These trends are highly dependent on the scale of observation and have no influence on the NH geometry.

To summarize, a new spatial organization of the NH range based on second, third, and fourth order scales has been proposed with length, spacing, density, and orientation distributions. Each NH domain shows its own internal organization. Variability in between recorded fracture sets from different areas is a marker of a complex tectonic and geometrical setting. One main deformation episode played a key role in the NH structuration: SDVFZ trending NW/SE affected whole NH and then controlled its geometry. The second main deformation episode is in the GF system trending E/W, likely responsible for E/W fracturing episode, and controlled the NH geometry mostly in its internal part and the southeastern end.

The identical orientation of GF and the E/W structures could suggest that the GF was responsible for the E/W fracturing in the internal and southeastern end domains (Figure 12b). Furthermore, the E/W structures are characterized by a sinistral strike-slip displacement, highlighted by the movement of the tertiary volcanic blocks in the back of the NH. This sinistral strike-slip movement has been characterized along the GF zone, widely described in the literature [55,57]. The similarities on the strike-slip nature can help to consider that the E/W fractures are related to GF activity which plays a key role on the NH geometry. In addition, the lower dominance of the NW/SE direction in the central and the southeastern end of the NH can be explained by the overprinting of the E/W fracturing, highlighting that these structures are posterior to the SDVFZ system (Figure 12c).

Regarding the fracture distributions, the fracture density is higher in the domain C with a factor 2.5 and 1.5, in comparison respectively with domain A and B (Figure 3). At outcrop scale, fracture densities raise from domains A and B to domain C with a factor 05 and 1.4, approving the localization of the fracture intensity in this area due to the complex tectonic setting [39]. Furthermore, a gradient of deformation has been observed in the field along the entire NH length with evidence of extreme shearing, notably in the internal domain. Boudinage structures and brittle shearing are prevalent within Crystal Spring series. A future publication will be planned to better characterize this deformation.

#### *5.3. Fracture Network Impact on Flow*

The deformation occurred with a different intensity at the whole NH scale. This can influence the fluid circulation through the fracture network following the domains. Even if the connectivity in the reservoir analogue is ruled by the large and small fractures (Figure 10f), some domains, such as domain A, had a different behavior insofar as the connectivity was ruled by only the large fractures. A complex joint network is highlighted at outcrop scale in the host rock and plays a key role in the fracture connectivity leading the fluid supply toward the fault zone.

The fluid flow modeling in this reservoir analogue should consider that the orientation parameter depends on scale observation and then should be modeled differently at each scale, while the length parameter is independent of the observation scale in the case of NH geothermal reservoir analogue.

Flow simulations will be planned in the future publications, based on photogrammetric models acquired from different NH domains. This study can help to approve the sensitivity of the fluid circulations to the gradient of strike-slip deformation and the spatial arrangement of NH fracture network. The sensitivity of the deterministic models on resulting permeability will be tested according to the directional dependence and their corresponding length distribution.

#### **6. Conclusions**

This study is part of the MEET project (Multidisciplinary and multi-context demonstration of EGS exploration and Exploitation Techniques and potentials), aiming at developing geothermal exploitation at European scale by applying Enhanced Geothermal System (EGS) technology to different geological settings. NH range, assimilated to a paleo geothermal reservoir analogue, gives an opportunity to study the basement rocks in trans-tensional context. This study proposes geometric description and quantifies the multiscale network organization and its effect on connectivity using a wide-ranging analysis scale from the microscopic scale to the regional scale. We used 2D fracture maps at different scales. We have shown a power law distribution for six orders of scales. Then, a power law exponent of α = −2 was computed by combining the whole datasets, meaning that the connectivity is ruled by the small and the large fractures.

A new spatial arrangement of the fracture network at different scales has been proposed for the NH range, based on densities, spacings, orientations, and length distributions. The SDVFZ controls the NH geometry at large scale within the second order scale, while the E/W directions—whose origin remains to be determined—controls the NH geometry within the third order scale. The spacing characteristics are of 5 and 1 km for respectively the second and the third order scale, and correspond to the spacings highlighted in the extensional regime.

The division into three domains according to the facies variability and the change in range trend orientation has been approved by statistical analysis. Indeed, domain A is characterized by a dominance of the NW/SE direction in terms of length and abundance at the fourth order scale with a regular fracture spacing of 0.1–0.2 km. Then, NW/SE direction controls the internal structuration of this domain. Domain B is structured by the second and third orders of fractures scales following the E/W and NW/SE direction with regular spacing of 0.2 km and 0.005 km, respectively. Domain C was also characterized by

the structuration of a specific spatial arrangement with the dominance of short fractures following E/W direction, which highlight the persistence of the E/W fracturing episode. The ENE/WSW, E/W, and also NW/SE directions control the NH geometry and structuration in this area. A regular spacing of 0.2 km and 0.005 km is computed inside the domain at fourth order scale. Therefore, two spacing characteristics have been highlighted in this study at fourth order scale: 0.1–0.2 km and 0.05 km spacing for fractures length of 0.1–0.35 km and 0.005 km, respectively.

Each internal domain described in this study proposes its own spatial arrangement of fracture network. Indeed, two main deformation episodes referring to the SDVFZ striking NW/SE and fractures system striking E/W play a key role in the structuration of the NH range. However, the SDVFZ deformation affected the whole NH, whereas the E/W fracturing affected only the central and the southeastern area.

Fluid flow modeling will be planned and will take into consideration that orientation parameters should be modelled differently at each scale, while length parameters modelled by the power law should be considered as homogenous at different scales.

**Author Contributions:** Conceptualization, A.C., G.T. and B.A.L.; methodology, A.C.; software, A.C.; validation, G.T., B.A.L. and J.K.; formal analysis, A.C.; investigation, A.C., G.T., B.A.L. and J.K.; resources, A.C.; data curation, A.C.; writing—original draft preparation, A.C.; writing—review and editing, G.T., B.A.L. and H2020 MEET consortium; visualization, G.T., B.A.L. and J.K.; supervision, G.T.; project administration, G.T.; funding acquisition, G.T. and H2020 MEET consortium. All authors have read and agreed to the published version of the manuscript.

**Funding:** This project has received funding from the European Union's Horizon 2020 research and innovation program under grant agreement No 792037 (MEET project).

**Data Availability Statement:** Not applicable.

**Acknowledgments:** This work is part of postdoctoral contribution, prepared at Institut Polytechnique UniLaSalle Beauvais, which was funded by European Union's Horizon 2020 research (H2020 MEET project). We are grateful to Armand Pomart and Ruben Attali for their help for analyses. We also wish to thank the H2020 MEET consortium for their helpful comments and manuscript validation. We also thank the Assistant Editor Sorin Hadrian Petrescu and the anonymous reviewers for the relevant remarks that significantly approved the article.

**Conflicts of Interest:** The authors declare no conflict of interest.

### **References**


## *Article* **Lab-Scale Permeability Enhancement by Chemical Treatment in Fractured Granite (Cornubian Batholith) for the United Downs Deep Geothermal Power Project, Cornwall (UK)**

**Katja E. Schulz \*, Kristian Bär \* and Ingo Sass**

Department of Geothermal Science and Technology, Technische Universität Darmstadt, Schnittspahnstraße 9, 64287 Darmstadt, Germany; sass@geo.tu-darmstadt.de

**\*** Correspondence: kontakt@schulzks.de (K.E.S.); baer@geo.tu-darmstadt.de (K.B.)

**Abstract:** A hydrothermal doublet system was drilled in a fault-related granitic reservoir in Cornwall. It targets the Porthtowan Fault Zone (PTF), which transects the Carnmenellis granite, one of the onshore plutons of the Cornubian Batholith in SW England. At 5058 m depth (TVD, 5275 m MD) up to 190 ◦C were reached in the dedicated production well. The injection well is aligned vertically above the production well and reaches a depth of 2393 m MD. As part of the design process for potential chemical stimulation of the open-hole sections of the hydrothermal doublet, lab-scale acidification experiments were performed on outcrop analogue samples from the Cornubian Batholith, which include mineralised veins. The experimental setup comprised autoclave experiments on sample powder and plugs, and core flooding tests on sample plugs to investigate to what degree the permeability of natural and artificial (saw-cut) fractures can be enhanced. All samples were petrologically and petrophysically analysed before and after the acidification experiments to track all changes resulting from the acidification. Based on the comparison of the mineralogical composition of the OAS samples with the drill cuttings from the production well, the results can be transferred to the hydrothermally altered zones around the faults and fractures of the PTF. Core Flooding Tests and Autoclave Experiments result in permeability enhancement factors of 4 to >20 and 0.1 to 40, respectively. Mineral reprecipitation can be avoided in the stimulated samples by sufficient post-flushing.

**Keywords:** enhanced geothermal systems (EGS); fractured granite; core flooding experiments; autoclave experiments; Cornubian Batholith

#### **1. Introduction**

The geothermal doublet at United Downs in Redruth, Cornwall, consists of the production well UD-1 and the injection well UD-2. UD-1 reaches a depth of 5058 m TVD (true vertical depth)/5275 m MD (measured depth), with an approximately 1.2 km long open-hole section, while the injection well UD-2 reaches 2214 m TVD/2393 m MD, with an approximately 550 m long open-hole section. Geothermal Engineering Limited (GEL) plans the establishment of a geothermal power plant with 1 to 3 MWel net energy production [1]. The reservoir rock is the fractured Carnmenellis granite, which is one of the onshore plutons comprising the Cornubian Batholith. It is characterised by a strong geothermal anomaly caused by radioactive decay of U, Th and K in the granite [2]. The geological target structure is the Porthtowan fault zone (PTF), which vertically links the two wells [1]. Since a sufficient reservoir temperature of ~190 ◦C was reached in the production well, the limiting factor for the project is the hydraulic productivity of the reservoir. For this reason, the analysis of permeability enhancement by chemical treatment in the fractured Cornish granite is the prerequisite for an assessment of the potential effectivity of such stimulation in the pilot project United Downs Deep Geothermal Power (UDDGP).

**Citation:** Schulz, K.E.; Bär, K.; Sass, I. Lab-Scale Permeability Enhancement by Chemical Treatment in Fractured Granite (Cornubian Batholith) for the United Downs Deep Geothermal Power Project, Cornwall (UK). *Geosciences* **2022**, *12*, 35. https:// doi.org/10.3390/geosciences12010035

Academic Editors: Béatrice A. Ledésert, Ronan L. Hébert, Ghislain Trullenque, Albert Genter, Eléonore Dalmais, Jean Hérisson and Jesús Martínez-Frías

Received: 29 September 2021 Accepted: 10 January 2022 Published: 12 January 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

Around fault zones, a complex permeability pattern develops, which is determined by the characteristics of the fracture network. Permeability can vary by up to five orders of magnitude between unaffected granite and fractured and altered granite [3]. Under reservoir conditions, open fractures will be filled with secondary minerals over time if no tectonic reactivation occurs. These (partly) mineralised fractures can be a relevant target for chemical treatment.

Within the scope of the EU-Horizon2020-project Multidisciplinary and multi-context demonstration of EGS exploration and Exploitation Techniques and potentials (MEET), the elaborated results will be applied at transfer sites in similar geological settings within the Variscan basement of Europe.

#### *Geological Setting*

The geology of Cornwall is dominated by the Cornubian Batholith, which intruded into metasediments during the late phase of the Variscan orogeny in the Early Permian period. The metasediments consist in Devonian and Carboniferous passive continental margin successions, locally termed 'Killas', which were affected by regional low-grade metamorphosis during Variscan shortening in early Carboniferous (prehnite–pumpellyite facies [4]). During the succeeding post-collisional extension 292–270 Ma ago (Early Permian period) the Cornubian Batholith was emplaced in at least two major phases. It is a peraluminous S-type granite. The source rock of the melt is a meta-greywacke [5]. The emplacement occurred mainly along preexisting fault- and weakness zones, possibly including fault zones related to the extensional reactivation of the Rhenohercynian suture [6]. Whereas the rock exposed at the surface was mapped in detail during the intense Cornish mining activity of the last few centuries [7], the composition and fracturation of the granite in the subsurface are the subject of current investigations. Detailed information can be found, e.g., in the work of Beamish and Busby, Shail and Leveridge, Willis-Richards, Edmunds et al., Yeomans et al., and Ghosh [2,6,8–12].

Simons et al. [5] have classified the intrusion stages of the Cornubian Batholith and provide detailed information about the general mineralogical composition, possible accessory minerals and grain size distribution of the respective granite types (Figure 1). The rock samples analysed in the present study were therefore classified according to Simons et al. [5], although the samples are hydrothermally influenced. Information on the mineralogical composition of the relevant samples is provided in Table 1 and Figure 1.


**Table 1.** Origin of the six analysed samples.

Cornwall is intersected by several fault systems, such as the Porthtowan Fault Zone (PTF), which are mainly strike slip faults, roughly trending NW–SE (NNW–SSE) and locally referred to as 'cross courses' [9], connecting ENE–WSW-striking extensional faults [13] or dykes, called 'Elvans'. Cornwall is intersected by several fault systems, such as the Porthtowan Fault Zone (PTF), which are mainly strike slip faults, roughly trending NW–SE (NNW–SSE) and lo‐ cally referred to as 'cross courses' [9], connecting ENE–WSW‐striking extensional faults [13] or dykes, called 'Elvans'.

The PTF is a NNW–SSE striking strike–slip fault zone (Figure 1). It consists of several fault strands and thus is 200 to 500 m wide at the surface and assumed to be more than 15 km long [1]. The northwestern part was mapped geologically [14] and remotely [11], while the southeastern part is not exposed at the surface and its extent is only presumed from indirect hints (e.g., morphology). The PTF is a NNW–SSE striking strike–slip fault zone (Figure 1). It consists of several fault strands and thus is 200 to 500 m wide at the surface and assumed to be more than 15 km long [1]. The northwestern part was mapped geologically [14] and remotely [11], while the southeastern part is not exposed at the surface and its extent is only presumed from indirect hints (e.g., morphology).

Along the PTF, hydrothermal alteration has affected the mineralogical composition of the reservoir rocks. Two main phases of alteration can be distinguished: younger alteration related to circulation of (partly) meteoric water in structural discontinuities and older alteration related to hydrothermal convection cells around the cooling granitic bodies, with: (a) fluids possibly linked with the first marine incursions in late Triassic and (b) fluids with magmatic origin [4]. Along the PTF, hydrothermal alteration has affected the mineralogical composition of the reservoir rocks. Two main phases of alteration can be distinguished: younger alter‐ ation related to circulation of (partly) meteoric water in structural discontinuities and older alteration related to hydrothermal convection cells around the cooling granitic bod‐ ies, with: (a) fluids possibly linked with the first marine incursions in late Triassic and (b) fluids with magmatic origin [4].

Products of hydrothermal alteration are present, such as Kaolinite (likely Dickite at reservoir depth [15–18], greisenisation (paired with tourmalinisation and cassiterite veins [19], Tourmaline veins (related to the circulation of boron-enriched fluids in hydrothermal convection cells [20], Chlorite [20], hydrothermal W/Sn/Cu/As/Zn ore minerals (mainly in the metasediments [4,13] and Quartz, Fluorite or Barite veins [15,21]. Products of hydrothermal alteration are present, such as Kaolinite (likely Dickite at reservoir depth [15–18], greisenisation (paired with tourmalinisation and cassiterite veins [19], Tourmaline veins (related to the circulation of boron‐enriched fluids in hydrothermal convection cells [20], Chlorite [20], hydrothermal W/Sn/Cu/As/Zn ore minerals (mainly in the metasediments [4,13] and Quartz, Fluorite or Barite veins [15,21].

**Figure 1.** Simplified geological map of Cornwall, showing granite types after Simons et al. [5], sam‐ pling locations and relevant project locations; PTF simplified after Reinecker et al. [22]; meta sedi‐ ments, dykes and non‐magmatic geological units in grey. **Figure 1.** Simplified geological map of Cornwall, showing granite types after Simons et al. [5], sampling locations and relevant project locations; PTF simplified after Reinecker et al. [22]; meta sediments, dykes and non-magmatic geological units in grey.

#### **2. Materials and Methods 2. Materials and Methods**

The analysed rock samples are outcrop analogue samples (OAS). They were collected during fieldwork in June 2019 from six different locations of the Cornubian Batholith (selected from a total of 47 samples from 35 different locations—sea cliffs, major and minor natural outcrops, rock dumps and active and abandoned quarries) [23]. They have a relatively high geochemical conformity with the Carnmenellis Granite (based on data from Simons et al. [5]) and include mineralised veins, which allow analogies with hydrothermally altered zones around the faults and fractures of the PTF encountered in UD-1. As a result of a lack of sampling material from the granites of the Carnmenellis, Carn Marth or Carn Brea plutons, which contain veins, the representativity for the Carnmenellis granite is limited to far-field analogues (Land's End, Tregonning Godolphin, Cligga and St. Austell plutons). Nevertheless, the present samples display an analogy to the fault and fracture zone itself. For analysis, the samples were cored into plugs 40 mm in diameter and ranging in length from 20 to 80 mm. Each core targets a vein, with the core axis drilled parallel to the vein (Figure 2). Cutoffs were ground to powder finer than 63 µm for chemical and mineralogical analysis. The analysed rock samples are outcrop analogue samples (OAS). They were collected during fieldwork in June 2019 from six different locations of the Cornubian Batholith (se‐ lected from a total of 47 samples from 35 different locations—sea cliffs, major and minor natural outcrops, rock dumps and active and abandoned quarries) [23]. They have a rela‐ tively high geochemical conformity with the Carnmenellis Granite (based on data from Simons et al. [5]) and include mineralised veins, which allow analogies with hydrother‐ mally altered zones around the faults and fractures of the PTF encountered in UD‐1. As a result of a lack of sampling material from the granites of the Carnmenellis, Carn Marth or Carn Brea plutons, which contain veins, the representativity for the Carnmenellis granite is limited to far‐field analogues (Land's End, Tregonning Godolphin, Cligga and St. Aus‐ tell plutons). Nevertheless, the present samples display an analogy to the fault and frac‐ ture zone itself. For analysis, the samples were cored into plugs 40 mm in diameter and ranging in length from 20 to 80 mm. Each core targets a vein, with the core axis drilled parallel to the vein (Figure 2). Cutoffs were ground to powder finer than 63 μm for chem‐ ical and mineralogical analysis.

For comparison, drill cuttings from production well UD-1 from the open-hole section between 4 and 5 km MD are analysed. The cuttings, which were sampled by GEL/ Geosciences Limited, represent 44 depth intervals of 10 m in length, between 4050 m TVD and 4930 m MD. For comparison, drill cuttings from production well UD‐1 from the open‐hole section between 4 and 5 km MD are analysed. The cuttings, which were sampled by GEL/Geosci‐ ences Limited, represent 44 depth intervals of 10 m in length, between 4050 m TVD and 4930 m MD.

**Figure 2.** Top view on representative cores (40 mm diameter) from the six samples; the mineralogi‐ cal composition of the sample and the veins is given in Table 1. **Figure 2.** Top view on representative cores (40 mm diameter) from the six samples; the mineralogical composition of the sample and the veins is given in Table 1.

Besides an accompanying petrophysical analysis, the effect of chemical treatment on the permeability of the rock matrix and fracture systems due to acidification is investi‐ gated under approximation of reservoir conditions. This implies the acidification of sam‐ ples using two methods (Core Flooding Tests, CFT; Autoclave Experiments, AE), a petro‐ physical before/after comparison and a geochemical analysis of the fluid–rock interaction. Besides an accompanying petrophysical analysis, the effect of chemical treatment on the permeability of the rock matrix and fracture systems due to acidification is investigated under approximation of reservoir conditions. This implies the acidification of samples using two methods (Core Flooding Tests, CFT; Autoclave Experiments, AE), a petrophysical before/after comparison and a geochemical analysis of the fluid–rock interaction.

A set of different analytical methods, such as XRF, XRD, AAS, IC, ICP‐MS, thermos‐ canning, helium pycnometry, helium permeametry, water permeametry and sonic veloc‐ ity, is used to characterise the samples petrologically and petrophysically before and after chemical treatment in AEs and CFTs at reservoir temperatures and pressures, as well as the spent acids from the AEs (Table 2, Figure 3). A set of different analytical methods, such as XRF, XRD, AAS, IC, ICP-MS, thermoscanning, helium pycnometry, helium permeametry, water permeametry and sonic velocity, is used to characterise the samples petrologically and petrophysically before and after chemical treatment in AEs and CFTs at reservoir temperatures and pressures, as well as the spent acids from the AEs (Table 2, Figure 3).

In the chemical treatment experiments (AEs), the samples are placed in autoclaves together with acids at 150 °C for 24 h. The utilised acids are: (a) 15% HCl and (b) 'white acid', which consists of 12% HCl and 3% HF and resembles Regular Mud Acid (RMA), which is commonly employed in chemical well stimulation. In the CFTs, which were conducted at the labs of Fangmann Energy Services (FES), In the chemical treatment experiments (AEs), the samples are placed in autoclaves together with acids at 150 ◦C for 24 h. The utilised acids are: (a) 15% HCl and (b) 'white acid', which consists of 12% HCl and 3% HF and resembles Regular Mud Acid (RMA), which is commonly employed in chemical well stimulation.

the chemical blends SSB‐007 and SFB‐007 were circulated through the cores at a tempera‐ ture of 150 °C and a confining pressure of 172 bar (2500 psi). During the flow rate‐con‐ trolled tests, the differential pressure is logged to calculate the permeability development over time [24]. SSB‐007 and SFB‐007 have relatively similar characteristics to the fluids

used in the autoclave experiments.

**Figure 3.** Flow chart of the lab work. **Figure 3.** Flow chart of the lab work.

*2.1. Sample‐Preparation* All samples were dried to mass constancy (cuttings at 105° for 24 h, OAS at 65 °C for > 48 h to avoid low‐temperature alteration processes of clay minerals) and stored in closed containers at ~ 20 °C with silica gel. OAS were cored, sawn and burnished at the Institute of Applied Geosciences in Darmstadt. All cores have a diameter of 40 mm and include In the CFTs, which were conducted at the labs of Fangmann Energy Services (FES), the chemical blends SSB-007 and SFB-007 were circulated through the cores at a temperature of 150 ◦C and a confining pressure of 172 bar (2500 psi). During the flow rate-controlled tests, the differential pressure is logged to calculate the permeability development over time [24]. SSB-007 and SFB-007 have relatively similar characteristics to the fluids used in the autoclave experiments.

veins of different mineralogical composition. The initial length of the 'cores' was set to 80 mm (optimum: 2:1 length to width ratio), which had to be reduced to 20 mm 'plugs' for further experiments. The core axis was oriented parallel to the strike of the vein; the cores had plan‐parallel surfaces. Grinding was performed in a tungsten carbide disc mill (two minutes at a speed of 1000 rpm) following Ferreiro Mählmann and Frey [25]. Grinding was performed on cuttings and core‐cutoffs from sawing, which allow best comparability

water through a 63 μm sieve without containment).


**Table 2.** Applied methods and analysed sample sets. Abbreviations: CFT = core flooding tests; AE = autoclave experiments; PEF = permeability enhancement factor; OAS = outcrop analogue samples.

#### *2.1. Sample-Preparation*

All samples were dried to mass constancy (cuttings at 105◦ for 24 h, OAS at 65 ◦C for >48 h to avoid low-temperature alteration processes of clay minerals) and stored in closed containers at ~20 ◦C with silica gel. OAS were cored, sawn and burnished at the Institute of Applied Geosciences in Darmstadt. All cores have a diameter of 40 mm and include veins of different mineralogical composition. The initial length of the 'cores' was set to 80 mm (optimum: 2:1 length to width ratio), which had to be reduced to 20 mm 'plugs' for further experiments. The core axis was oriented parallel to the strike of the vein; the cores had plan-parallel surfaces. Grinding was performed in a tungsten carbide disc mill (two minutes at a speed of 1000 rpm) following Ferreiro Mählmann and Frey [25]. Grinding was performed on cuttings and core-cutoffs from sawing, which allow best comparability with OAS cores. The cutting samples lack the sub-63 µm-fraction, which includes the clay minerals (due to washing at the project site: rinsing 2–3 times and decantation of excess water through a 63 µm sieve without containment).

#### *2.2. Petrophysical Methods*

Gas pycnometry (determination of the effective porosity, which is an approximation of the total porosity, due to He diffusion) was conducted on all samples according to the recommendations of Micromeritics [26] as described in Weydt et al. [27] with the two-chamber systems AccuPyc 1330, AccuPyc II 1340 and CorePyc 1360 (Micromeritics, Germany) using He. The bulk volume was calculated from the geometry of the cylindrical cores.

Sonic measurements were conducted as described in Weinert et al. [28] with an ultrasonic pulse generator (USG40) (Geotron-Elektronik, Germany), a PicoScope Detector and a UPG-S/UPE-S emitter/receiver set (pushed against the sample with a pressure of 1 bar, coupled by Magnaflux 54-T04 shear gel) on 80 mm cores and 20 mm plugs to calculate the dynamic Poisson ratio and dynamic Young's Modulus.

Thermal conductivity and thermal diffusivity were measured as described by Mielke et al. [29] on the 80 mm cores before treatment and on 20 mm plugs after treatment with a Thermal Conductivity Scanner (Lippmann and Rauen, Germany), using gabbro standards (TC) and Quartz/Titan and Titan/Steel standards (TD) [30]).

The permeability was analysed with a column gas permeameter (stationary air permeameter with a Hassler type cell [31]). A verification of the results was performed with a water permeameter.

The gas permeameter measurements were conducted according to Filomena et al. [31], using the different pressure levels 1050–1250–1500–2000–3000–5000 mbar and a mantle pressure of 10 bar for each experiment. The pressure difference was set between up to 1000 mbar (samples with permeabilities in the range of 10−<sup>17</sup> m<sup>2</sup> ) and only 50 mbar (permeabilities below 10−<sup>14</sup> m<sup>2</sup> ). Further information about the method is provided by Weydt et al. [27]. Since the sample axis was parallel to the vein, the measured permeability was a combined vein and matrix permeability and the permeability of the whole sample was highly anisotropic.

### *2.3. Acidification*

CFTs were conducted at the labs of Fangmann Energy Services, using a Manual Reservoir Permeability Tester (OFI Testing Equipment) to induce and analyse changes to the sample properties caused by acidification (Figure 4). The relative permeability changes over time were analysed by the measurement of the pressure difference at the in- and outlet of the sample (constant flow rate; measurement similar to a permeameter). The CFT procedure can be summarised in the following steps:


The NH4Cl-brine was used because it has relatively similar flow properties compared to the applied acids and does not react with the acids, cores or the device. Besides, since NH<sup>4</sup> + is not included in the geochemical analysis (and would be falsified anyway by the use of ammonium bifluoride as a constituent for the preparation of HF), the falsification of the analytical results was limited to Cl−.

The composition of Fangmann's acid blends SSB-007 and SFB-007 is confidential. According to general information from Fangmann, SSB-007 is based on HCl or on a Strong Organic Acid (SOA) with comparable reaction kinetics. SFB-007 contains additional HF and is relatively similar to Regular Mud Acid (RMA) [24]. RMA is a common acid used for sandstone matrix acidising [32]. Recalde Lummer and Rauf [24] state the applicability of Fangmann's product SFB-007 as well for granite.

for sandstone matrix acidising [32]. Recalde Lummer and Rauf [24] state the applicability

The applied test conditions were temperatures of 150 °C, confining pressure (mantle pressure, prevents lateral flow around the sample) of 172.4 bar and back pressure (system pressure, prevents boiling of the fluids) of 34.5 bar. A drive pressure pushed the fluid through the core and depended on the flow rate (sample 010006004: 0.9 mL/min through artificial fissure; 017001005: 1.36 mL/min through artificial fissure; 23001002: 0.665 mL/min through natural vein) and the permeability of the sample [24]. As the initial per‐ meability of two samples was too low for the circulation of the brine, those samples were sawn along the original vein. This joint was compressed by the confining pressure. Fur‐ ther information on the permeability measurement before and after the CFTs is given in

Due to cost‐ and time‐intensity and unknown composition of the acids, only three

During the AEs, the acid and sample were encased in high‐pressure autoclaves (Parr Acid Digestion Bombs, 302AC T304, Bomb No. 4748, stainless‐steel autoclave system with a cylindrical Teflon (PTFE) container) and heated at 150 °C for 24 h (closed system). In contrast to the CFTs, no circulation of fluids though the sample was realised, implying that no pre‐ or post‐flush was conducted to cleanse the samples of any reaction products

cores were analysed in CFTs and AEs were used to resemble the CFTs.

of Fangmann's product SFB‐007 as well for granite.

Appendix A.

after reaction (Figure 4).

**Figure 4. S**implified sketch of the setup and conditions of core flooding tests (**A**) and autoclave experiments (**B**). **Figure 4.** Simplified sketch of the setup and conditions of core flooding tests (**A**) and autoclave experiments (**B**).

In the autoclave experiments, two different acids were used to resemble Fangmann's acid blends SSB‐007 and SFB‐007: 15% HCl. 12% HCl with 3% HF (White acid, common basis for RMA, produced by mixing 1000 mL HCl (15%) and 50 g ammonium bifluoride (ammonium hydrogen fluoride, F2H5N, purchased as granulate) [33]. HF in a concentration range between 1 and 7% is dangerous to life in case of skin contact, among other hazards, and is class 2 in the German Water Hazard Classification The applied test conditions were temperatures of 150 ◦C, confining pressure (mantle pressure, prevents lateral flow around the sample) of 172.4 bar and back pressure (system pressure, prevents boiling of the fluids) of 34.5 bar. A drive pressure pushed the fluid through the core and depended on the flow rate (sample 010006004: 0.9 mL/min through artificial fissure; 017001005: 1.36 mL/min through artificial fissure; 23001002: 0.665 mL/min through natural vein) and the permeability of the sample [24]. As the initial permeability of two samples was too low for the circulation of the brine, those samples were sawn along the original vein. This joint was compressed by the confining pressure. Further information on the permeability measurement before and after the CFTs is given in Appendix A.

System [34]. It is not biodegradable. For powder acidification experiments (set 1: 12% HCl + 3% HF) the autoclaves were Due to cost- and time-intensity and unknown composition of the acids, only three cores were analysed in CFTs and AEs were used to resemble the CFTs.

loaded with 6 g of powder (from ground OAS) and 60 mL of acid (ratio of powder During the AEs, the acid and sample were encased in high-pressure autoclaves (Parr Acid Digestion Bombs, 302AC T304, Bomb No. 4748, stainless-steel autoclave system with a cylindrical Teflon (PTFE) container) and heated at 150 ◦C for 24 h (closed system). In contrast to the CFTs, no circulation of fluids though the sample was realised, implying that no pre- or post-flush was conducted to cleanse the samples of any reaction products after reaction (Figure 4).

In the autoclave experiments, two different acids were used to resemble Fangmann's acid blends SSB-007 and SFB-007:


HF in a concentration range between 1 and 7% is dangerous to life in case of skin contact, among other hazards, and is class 2 in the German Water Hazard Classification System [34]. It is not biodegradable.


a volume of acid corresponding to the surface area of the plug in a ratio 1:1. This approach assumed that mainly the sample surface, plus permeable parts of the sample, mainly along the vein–rock matrix interface, would contribute to chemical reactions.

• To saturate the samples with the acids, the loaded Teflon cylinders were evacuated in a desiccator with a water-jet vacuum pump for 30 min.

After the heating phase, the autoclaves were cooled with wet tissue until they were cold enough to be touched and opened (approximately one hour, but as short a time as possible, to reduce precipitation). The liquid (spent acid) was then separated from the solid sample remnants for AAS and IC analysis via pipetting. The plugs were then rinsed with deionised water to allow safe handling and to reduce precipitation. For the powder samples, the non-dissolved solid fraction of the sample was repeatedly centrifugated with deionised water to increase the pH from pH < 1 to pH > 5, to allow safe handling of the sample and enable further analysis.

The following bullet points summarise the most important conditions of the autoclave experiments:


As the applied acids, especially at high temperatures, are very corrosive, the materials of the autoclaves and the Manual Reservoir Permeability Tester, as well as any used lab equipment in contact with the acids, had to be chosen accordingly and all devices and tools were visually controlled before and after use. With respect to the CFTs, the used acids contained corrosion inhibitors.

#### *2.4. Fluid Chemistry*

Atomic Absorption Spectroscopy (AAS) was conducted with a ContrAA 300 (Analytic Jena, Germany, Xenon continuum source lamp plus monochromator, PTFE impact bead; acetylene/air-flame (2200 ◦C) or N2O/acetylene flame (2750 ◦C), measurement duration (3 to 4 s), flame height and the characteristic lines used for analysis depend on the element and are selected according to Analytic Jena recommendations, based on the software database; software Aspect CS, version 1.5.6.0). Further details on the method can be found in Broekaert, Skoog and Leary as well as Welz and Sperling [35–37]. The spent acids from the autoclave experiments were diluted by a factor of 50 or 100 as a reasonable compromise between the fitting with the calibration range and a reduction in the dilution error. This affects the measurement quality for Si, Al, Fe and partly Ca, K and Na. A six (or seven) point calibration was conducted, with calibration standards from single-element standards (Carl Roth) and a LaCl-CsCl-solution (Merck KGaA, Germany) in a 2% HCl (supra quality) matrix.

Ion exchange chromatography was conducted with a Compact IC (Metrohm, Germany; Compact IC autosampler plus, two separation columns for an- and cations with organic polymer resin (both Compact IC plus; software MagIC Net™; cation-eluents: Pyridine-2,6-dicarboxylic acid (C7H5NO4) and nitric acid (HNO3), anion eluent: Sodium carbonate (Na2CO3)/Sodium hydrogen carbonate (NaHCO3). A 16-point calibration of the device is performed every three to four months, a control measurement is conducted within the analysis.

The silica content of the spent acid was determined with a Photometer Specord 200+ (Analytik Jena, Germany), and the reagents 'Merck 14,794 (Silicate Test)' using the software WinAspect+, according to DIN 38405-21 [38]. A nine-point calibration (0, 0.5, 1, 2, 3, 4, 5, 6 and 7 mg/L) was performed. Although the spent acid had a yellowish colour, the optical measurement was possible for set 1 and 3, as these samples were diluted by a factor of 1000; set 2 was not measured because the required dilution factor was too high, as the silicate content is very low.

#### *2.5. Mineralogy and Geochemistry*

X-ray diffractometry (XRD) was conducted on powder tablets (low-texture samples) by Dr. R. Petschick (Goethe University of Frankfurt) with a Panalytical X'Pert Pro Powder Xray-diffractometer (Kassel, Germany; Cu-ray tube with Cu radiation: 40 kV, 30 mA; Ni-filter with λ(CuKα) = 1.542 Å (no separate α-peaks), automatic divergence slits, X'Cellerator line counter) with the following goniometer settings: two hours per sample with a detection angle from 2.5–70◦ 2θ, emitter and detector circuit step length of 0.0083◦ 2θ and 100 s measurement time. The software X'Pert Data Collector (Panalytical, German<), X'Pert Highscore Pro (Panalytical, Germany) and MacDiff [39] were used to evaluate the measurements; measured intensities were normalised with an external standard (Corundum), approximating the natural concentration. Fluorescence effects were reduced by a baseline correction and a peak-position correction was conducted based on the Quartz peaks. Further details on the method are described by Petschick [40].

For geochemical analysis the internal method 'Quant Express, Best Detection' (wavelengthdispersive, no external standards) of the X-ray-fluorescence-spectrometer S8 Tiger 4 kW (Bruker, Karlsruhe, Germany, scintillation counter for heavy elements, proportional counter for light elements (Bruker [41]) was used. For the evaluation, the total sum of measured elements was normalised to 100%.

For the powder tablets, a ground <63 µm sample was combined with Hoechst wax C micro powder (C38H76N2O2) (Merck, Germany) in a ratio 1:4, homogenised in a rotator mixer for 30 min and pressed to tablets in a stainless-steel cylinder under pressure of 160 bar.

#### **3. Results**

Both acidification methods, CFTs and AEs, were used to analyse the permeability enhancement by chemical treatment (Appendix B, Figure A1) in samples from the Cornubian Batholith. Additionally, mineralogical, geochemical, petro- and thermophysical rock properties were determined, allowing before–after comparison and the quantification of the acidification effects. The OAS from the Cornubian Batholith were selected with focus on their comparability with the Carnmenellis granite and the presence of veins. The veins allowed comparison with hydrothermally altered zones in the well. Additionally, cuttings from the geothermal well UD-1 were used for a preliminary transfer of results from lab scale to the reservoir.

#### *3.1. Sample Composition*

All six sampled outcrops or quarries were granitic. However, as veins (mainly filled with Quartz) were targeted for sampling, all samples had elevated Quartz content compared to the cuttings from UD-1 and the regional chemistry, as described by Simons et al., (2016). In three cases the sample composition was classified as quartzolitic, as the volumetric overrepresentation of the veins caused elevated Quartz (and Tourmaline) content (Table 3). In relation to Plagioclase, the K-Feldspar content was also slightly elevated. As the resilience of Plagioclase is usually lower, compared to K-Feldspar, this may be an indicator for weathering effects on the samples. Macroscopically, Muscovite and Biotite were detected in all samples (Ms ≥ Bt). As accessory minerals, Tourmaline, Chlorite and Cassiterite were identified in the OAS and Hornblende and Chlorite in the cuttings. All veins consisted of Quartz, plus Tourmaline in most cases and rarely ore minerals. The general mineralogical evaluation of the samples with XRD confirms the macroscopically detected minerals, except for Biotite, which is underrepresented in the XRD results. The conducted REE analysis [42] generally correlates with the trends described by Simons et al. [5]. Detected deviations in REE may also be explained by weathering processes in the samples, because an inverse

Europium anomaly could be related to weathering of plagioclase. The REE evaluation might thus be useable as a tool to detect weathering.



#### *3.2. Acidification*

The CFTs, conducted and evaluated by Fangmann Energy Services [44], resulted in a significant increase in permeability. To quantify the effectivity of the acidification, we defined the permeability enhancement factor (PEF), which is the ratio between the permeability before (Kpre) and after (Kpost) treatment:

$$\text{PEF} = \mathbf{K}\_{\text{post}} / \mathbf{K}\_{\text{pre}} \tag{1}$$

The CFTs resulted in a PEF between 4 and 50. On the treated samples, a white precipitate was visible after the acidification.

In contrast to the CFTs, the trend in permeability variation was more ambiguous in the AEs. The AEs induced a permeability variation by a PEF between 0.1 and 40 (for 15% HCl: 0.8–39.44; for 12% HCl + 3% HF: 0.13–40.48). A permeability decrease (PEF < 1) was, in most cases, accompanied by (and likely caused by) the precipitation of a yellowish and a white mineral, which were macroscopically visible on the plugs (Figure 5). After treatment with HCl + HF, the bottom of the samples showed more intense changes: a relief was created, which was especially visible in samples 2, 3, 5 and 6 (Figure 5). In this relief, the Quartz veins acted as the resistant parts and remained almost unaffected. In sample 3, this effect was visible for the Quartz grains in the matrix. On the top of the sample, these effects were less intense. In addition, samples 2 to 6 showed yellow or white precipitation, also mainly on the bottom of the samples. After treatment with HCl, a relief was only created in sample 2, 5 and 6, mainly close to the veins. No white precipitates were visible, but yellow precipitates occurred on sample 2 to 6.

The yellow mineral does not resemble any original crystal structures and can partially be dissolved or washed away, but reprecipitates during the drying process (65 ◦C). This is most likely caused by the evaporation of the remaining pore fluid and indicates that the acid penetrated the sample surface. This was confirmed by a reaction front, which was visible in most samples in the cross section of the plugs after sawing them vertically. This reaction front was commonly located around the vein (sample 1, 4, 5 and 6) or in the entire sample (sample 2 and 3), but with a gradual increase towards the vein. The white mineral mainly occurred on or along pre-existing minerals (Feldspars and Quartz), especially on the bottom of the plugs. In difference to the yellow reaction front, it did not seem to be related to the veins and occurred only on the outside of the samples. The precipitate occurred in spent 15% HCl as well as 12% HCl + 3% HF.

**Figure 5.** Photomontage of the plugs after acidification, combined with the permeability enhance‐ ment factor resulting from treatment with the respective acids 15% HCl or 12% HCl + 3% HF in autoclave experiments: Top (**left**) and bottom (**right**) view of the sawn plugs after the autoclave experiments illustrating the stronger degree of precipitation on the samples bottom surfaces. **Figure 5.** Photomontage of the plugs after acidification, combined with the permeability enhancement factor resulting from treatment with the respective acids 15% HCl or 12% HCl + 3% HF in autoclave experiments: top and bottom view of the sawn plugs after the autoclave experiments illustrating the stronger degree of precipitation on the samples bottom surfaces.

The yellow mineral does not resemble any original crystal structures and can par‐ tially be dissolved or washed away, but reprecipitates during the drying process (65 °C). This is most likely caused by the evaporation of the remaining pore fluid and indicates that the acid penetrated the sample surface. This was confirmed by a reaction front, which was visible in most samples in the cross section of the plugs after sawing them vertically. This reaction front was commonly located around the vein (sample 1, 4, 5 and 6) or in the entire sample (sample 2 and 3), but with a gradual increase towards the vein. The white mineral mainly occurred on or along pre‐existing minerals (Feldspars and Quartz), espe‐ cially on the bottom of the plugs. In difference to the yellow reaction front, it did not seem to be related to the veins and occurred only on the outside of the samples. The precipitate occurred in spent 15% HCl as well as 12% HCl + 3% HF. In the fluid samples, no precipitation processes were observed, even after several weeks of storage. During the AEs, the acid colour changed from clear transparent to an In the fluid samples, no precipitation processes were observed, even after several weeks of storage. During the AEs, the acid colour changed from clear transparent to an intense yellow. Based on the hydrochemical analysis of the spent acid, showing elevated iron concentrations, most likely these minerals were partly iron hydroxides (FeO(OH), Goethite or Limonite). Macroscopically this was indicated by the yellowish colour of the fluids, which could be interpreted as an indicator for hydrated trivalent iron, as the iron(III)complex [FeCl(H2O)5] 2+(aq) (ligand Cl−) was yellow [45]. The precipitate may also include silica gel. According to Portier and Vuataz [46] this is formed by a secondary substitutionary reaction of hexafluorosilicic acid (high solubility) (which is formed from HF-acidification of Quartz) where Si ions are exchanged by Al3+ and precipitate as SiO2, while the fluoaluminates remain in the solution. This reaction is triggered when HF is nearly consumed. As clays or Micas are the main source for the Al3+, they increase the probability of silica gel precipitation.

intense yellow. Based on the hydrochemical analysis of the spent acid, showing elevated iron concentrations, most likely these minerals were partly iron hydroxides (FeO(OH), Goethite or Limonite). Macroscopically this was indicated by the yellowish colour of the fluids, which could be interpreted as an indicator for hydrated trivalent iron, as the iron(III)complex [FeCl(H2O)5]2+(aq) (ligand Cl−) was yellow [45]. The precipitate may also include silica gel. According to Portier and Vuataz [46] this is formed by a secondary sub‐ stitutionary reaction of hexafluorosilicic acid (high solubility) (which is formed from HF‐ acidification of Quartz) where Si ions are exchanged by Al3+ and precipitate as SiO2, while the fluoaluminates remain in the solution. This reaction is triggered when HF is nearly consumed. As clays or Micas are the main source for the Al3+, they increase the probability of silica gel precipitation. Permeability tracking during the CFTs, as displayed in Figure 6, shows the processes during the acidification. Regarding the evaluation of the CFTs, the tracked pore volume can be considered proportional to time, since the flow rate was constant. As visible in Equation (A1) in Appendix A, the pressure difference was inversely proportional to the permeability and the maximum measurement range of the device is approx. 19 bar. The sudden drop in measured pressure difference at the transitions between the different flu‐ ids, which was visible in all three CFTs, was caused by an inlet pressure drop when the Permeability tracking during the CFTs, as displayed in Figure 6, shows the processes during the acidification. Regarding the evaluation of the CFTs, the tracked pore volume can be considered proportional to time, since the flow rate was constant. As visible in Equation (A1) in Appendix A, the pressure difference was inversely proportional to the permeability and the maximum measurement range of the device is approx. 19 bar. The sudden drop in measured pressure difference at the transitions between the different fluids, which was visible in all three CFTs, was caused by an inlet pressure drop when the fluid valves were changed. Regarding sample 6 (Figure 6), the effect of SSB-007 was insignificant in the sample (no calcite or well-soluble minerals), as the differential pressure did not vary before and after SSB-007. During the application of SSB-007, differential pressure decreased, implying a high efficiency of HF in this sample. The shape of the curve resembled an exponential decrease, implying a fast efficiency decrease in HF. In the sample this effect could be due to an initial dissolution phase, which mainly affects pore throats and macropore contaminants. Combined with the flushing of the macropores and smaller pores, now with extended pore throats, the removal of particles increases the permeability with high effectivity in this initial phase. Another explanation might be that the exponential decrease was an effect of grain integrity and grain size distribution. Because this samples showed signs of weathering, the trend could express a significant reaction with fine- to

very fine pre-damaged grains. After this, the grains with higher integrity showed a lower reactivity with SFB-007. In the post-flush phase, the pressure difference increased after the circulation of 22 pore volumes. This behaviour might indicate the collapse of a fracture under the applied confining pressure during the flushing process. This implies the risk of a permeability decrease by the reduction in rock stability during chemical treatment. In further CFTs, permeability increased during the post-flush phase displayed the relevance of the post-flush, which seemed to mobilise particles that cause pore clogging. ples showed signs of weathering, the trend could express a significant reaction with fine‐ to very fine pre‐damaged grains. After this, the grains with higher integrity showed a lower reactivity with SFB‐007. In the post‐flush phase, the pressure difference increased after the circulation of 22 pore volumes. This behaviour might indicate the collapse of a fracture under the applied confining pressure during the flushing process. This implies the risk of a permeability decrease by the reduction in rock stability during chemical treat‐ ment. In further CFTs, permeability increased during the post‐flush phase displayed the relevance of the post‐flush, which seemed to mobilise particles that cause pore clogging.

fluid valves were changed. Regarding sample 6 (Figure 6), the effect of SSB‐007 was insig‐ nificant in the sample (no calcite or well‐soluble minerals), as the differential pressure did not vary before and after SSB‐007. During the application of SSB‐007, differential pressure decreased, implying a high efficiency of HF in this sample. The shape of the curve resem‐ bled an exponential decrease, implying a fast efficiency decrease in HF. In the sample this effect could be due to an initial dissolution phase, which mainly affects pore throats and macropore contaminants. Combined with the flushing of the macropores and smaller pores, now with extended pore throats, the removal of particles increases the permeability with high effectivity in this initial phase. Another explanation might be that the exponen‐ tial decrease was an effect of grain integrity and grain size distribution. Because this sam‐

*Geosciences* **2022**, *12*, x FOR PEER REVIEW 13 of 24

**Figure 6.** Pore volume—differential pressure diagram showing the development of the CFT on sample 6, applied flow rate: 0.665 mL/min; modified after [44]. **Figure 6.** Pore volume—differential pressure diagram showing the development of the CFT on sample 6, applied flow rate: 0.665 mL/min; modified after [44].

In difference to sample 6, the samples 5 (Figure 7) and 3 (Figure 8) were sawn verti‐ cally along the natural vein to increase the permeability, because the execution of the CFTs was not possible as the initial permeability was too low for circulation of ammonium chlo‐ In difference to sample 6, the samples 5 (Figure 7) and 3 (Figure 8) were sawn vertically along the natural vein to increase the permeability, because the execution of the CFTs was not possible as the initial permeability was too low for circulation of ammonium chloride.

ride. The documented pressure differences in the CFT on sample 5 resemble sample 6. A major difference is that during the long post-flush period, the pressure difference decreased significantly after a total of approximately 275 PV of circulated fluids and the permeability increased, respectively (doubling of the permeability from 1 mD (9.87 <sup>×</sup> <sup>10</sup>−<sup>16</sup> <sup>m</sup><sup>2</sup> ) to 4 mD (3.95 <sup>×</sup> <sup>10</sup>−<sup>15</sup> <sup>m</sup><sup>2</sup> )). This implies a high relevance of the post-flush, which seems to mobilise particles, that cause pore clogging.

The evaluation of sample 3 shows major difficulties during the CFT. The permeability of the sample, even after sawing an artificial vein, was too low to allow the analysis of the pressure differences, because the device's measurement range is exceeded. The given diagram cannot be analysed with regard to the effectivity of the acid blends, but a general statement about the acidification is still possible: the permeability increases significantly, since a low-rate circulation of ammonium chloride becomes possible after the acidification.

*Geosciences* **2022**, *12*, x FOR PEER REVIEW 14 of 24

**Figure 7.** Pore volume—differential pressure diagram showing the development of the CFT on sam‐ ple 5, applied flow rate: 1.360 mL/min; modified after [44]. **Figure 7.** Pore volume—differential pressure diagram showing the development of the CFT on sample 5, applied flow rate: 1.360 mL/min; modified after [44]. **Figure 7.** Pore volume—differential pressure diagram showing the development of the CFT on sam‐ ple 5, applied flow rate: 1.360 mL/min; modified after [44].

sample 3, applied flow rate: 0.900 mL/min; modified after [44]. **Figure 8.** Pore volume—differential pressure diagram showing the development of the CFT on sample 3, applied flow rate: 0.900 mL/min; modified after [44]. **Figure 8.** Pore volume—differential pressure diagram showing the development of the CFT on sample 3, applied flow rate: 0.900 mL/min; modified after [44].

**Figure 8.** Pore volume—differential pressure diagram showing the development of the CFT on

The documented pressure differences in the CFT on sample 5 resemble sample 6. A major difference is that during the long post‐flush period, the pressure difference de‐ creased significantly after a total of approximately 275 PV of circulated fluids and the per‐ meability increased, respectively (doubling of the permeability from 1 mD (9.87 ∙ 10–16 m2) to 4 mD (3.95 ∙ 10–15 m2)). This implies a high relevance of the post‐flush, which seems to The documented pressure differences in the CFT on sample 5 resemble sample 6. A major difference is that during the long post‐flush period, the pressure difference de‐ creased significantly after a total of approximately 275 PV of circulated fluids and the per‐ meability increased, respectively (doubling of the permeability from 1 mD (9.87 ∙ 10–16 m2) This implies a significant permeability increase in all three cases, which is almost exclusively caused by SFB-007. The flushing of the pores was identified as an important factor to increase the permeability after the acidification but may result in a pore collapse due to the confining pressure.

mobilise particles, that cause pore clogging. The evaluation of sample 3 shows major difficulties during the CFT. The permeability to 4 mD (3.95 ∙ 10–15 m2)). This implies a high relevance of the post‐flush, which seems to mobilise particles, that cause pore clogging. The three CFT diagrams show that the permeability increase could account for the HF-bearing acid blend SFB-007, while the effect of SSB-007 was insignificant in the samples.

of the sample, even after sawing an artificial vein, was too low to allow the analysis of the

The evaluation of sample 3 shows major difficulties during the CFT. The permeability of the sample, even after sawing an artificial vein, was too low to allow the analysis of the

The relevance of SSB-007 was mainly as a pre-treatment to avoid unwanted chemical reactions with HF, such as the precipitation of CaF2. In the AEs, the PEF was higher if HF was involved, but the number of cases with permeability decreased as well. Hydrochemical analyses, using AAS, IC and Si-Photometry, show that the total ion load of the spent HF-based acid was far higher compared to spent 15% HCl. The precipitation of the iron hydroxide was most intense in samples with the highest ion load in the fluid.

#### *3.3. Petrophysical Methods*

Permeametry, Sonic, Thermoscanning and Pycnometry were used to assess the petroand thermophysical rock properties before and after treatment. The initial gas-permeabilities of the untreated samples ranged between 1.3 <sup>×</sup> <sup>10</sup>−<sup>18</sup> and 3.1 <sup>×</sup> <sup>10</sup>−<sup>14</sup> <sup>m</sup><sup>2</sup> . After treatment, the gas permeabilities ranged between 1.2 <sup>×</sup> <sup>10</sup>−<sup>17</sup> <sup>m</sup><sup>2</sup> and 1.8 <sup>×</sup> <sup>10</sup>−<sup>14</sup> <sup>m</sup><sup>2</sup> . The permeability correlated with the porosities, which ranged between 0 and 12.02% before treatment and increased to 0.92 to 14.52% after treatment. The largest porosity increase was achieved during the CFTs (max. plus 5.03%). In the AEs the treatment 12% HCl + 3% HF was more effective than 15% HCl. Thermal conductivity (2.5–4.5 W·m−<sup>1</sup> ·K−<sup>1</sup> )) and thermal diffusivity (1.2–3.9 <sup>×</sup> <sup>10</sup>−<sup>6</sup> <sup>m</sup>2/s) resulted in specific heat capacities between 572 and 827 J·kg−<sup>1</sup> ·K −1 ) and were not significantly affected by acidification. Sonic velocities (p-wave velocities between 3095 and 6360 m/s, s-wave velocities between 1909 and 4447 m/s, mean value per sample before treatment) resulted in high Young's moduli and low Poisson ratios. These deviated from the literature, possibly because Quartz veins provide preferential wave propagation paths. While the Poisson ratio decreased after acidification, Young's modulus increased, indicating that precipitation might have increased the mineral interconnectivity.

#### **4. Discussion**

As a major difference between the CFTs and the AEs, in the CFTs the applied acids SSB-007 (based on a strong organic acid), followed by SFB-007 (based on hydrochloric acid plus hydrofluoric acid) were circulated through up to 80 mm long cores for up to 2.5 h under approximation of reservoir conditions (150 ◦C, 172.4 bar confining pressure). In contrast, in the AEs, the acids 15% HCl or 12% HCl + 3% HF, together with 20 mm long rock plugs or powder from ground samples, were heated to 150 ◦C for 24 h without circulation. This implies that no pre- or post-flush was conducted.

The analysis of the effectivity of the acids regarding different minerals, quantified by using XRD and XRF as well as AAS, IC and Si-Photometry on the spent acids, displayed similar trends, which generally correlate with earlier studies [46,47] as well as with results from Economides and Nolte [48].

The most relevant chemical equations for reactions with HCl + HF are listed below to give a preliminary understanding of the results discussed in the following section. Chemical reactions with only HCl are not displayed separately since, chemically, Cl- has comparable characteristics to F- and can therefore be involved in similar chemical reactions, but with reaction rates that are several magnitudes lower. The following chemical equations were documented by Economides and Nolte [48]:


Depending on the respective stoichiometry, clay minerals reacted with HF + H+ under the creation of AlF<sup>2</sup> + , SiF<sup>4</sup> and H2O in different ratios. As the composition of Tourmaline is extremely variable, no chemical reaction was provided.

While the reactions between HF and silicates generally resulted in the creation of liquid hexafluorosilicic acid, which, depending on the pH of the resulting fluid, could precipitate as amorphous silica gel, a reaction between HF and Calcite would immediately result in the precipitation of CaF<sup>2</sup> and cause pore clogging.

The XRD results show that on ground samples 12% HCl + 3% HF, the Quartz content in the treated samples increased to up to 100%. This implies that every other mineral reacted entirely. An exception is Tourmaline (Schorl), which was partly persistent in samples with an initial concentration above 5.5%. As a product of the HF acidification, Hieratite (K2[SiF6]) crystallised in several samples. In accordance with results from Sclar and Fahey [49], it was most likely a product of the acidification of K-Feldspars, since it contains K and F and was found in the samples with initially highest K-Feldspar concentrations. In the powder samples, Micas and Plagioclase were dissolved completely, but no correlation reaction products could be identified. The crystallisation of further minerals is indicated with additional spectral peaks in the XRD-results, but those minerals could not be identified, as well as amorphous phases. In the acidified rock samples (plugs) trends were less distinctive. For 12% HCl + 3% HF as well as 15% HCl, Quartz and Tourmaline were least affected, while Micas, especially Fe-Chlorite, were statistically most affected. The Feldspar contents did not display clear trends, but in relative numbers Plagioclase seemed to be less affected than K-Feldspar. If 15% HCl was applied, the effect on Quartz was insignificant. In all samples the effectivity of the acidification regarding the relative mineral concentrations increased if HF was involved. Comparing the SSB-007 plus SFB-007 acidification in CFTs with 12% HCl + 3% HF in AEs, the trends were similar, except for Muscovite, which seemed to be less affected. This may be related to additives with the purpose of inhibiting the participation of clay minerals.

The XRD results were generally confirmed by the XRF results, which displayed low to no effectivity regarding Quartz, depending on the acid, (relative SiO<sup>2</sup> increase) and higher effectivity regarding Micas and Feldspars or other Al-bearing silicates (relative Al2O3, K2O or Na2O decrease). The effectivity regarding Schorl was low to intermediate (Fe2O<sup>3</sup> concentration decreased or did not change in samples without Fe-Chlorite and Biotite). Again, the trends accounted for 15% HCl as well as for 12% HCl + 3% HF, but the magnitude was larger for 12% HCl + 3% HF. Further trends in other main elements (TiO2, MnO, MgO, CaO, Na2O, K2O, P2O5) or trace elements cannot be generalised.

In sample 6 (023001, Cligga granite), as an exception, indicators for Cassiterite, Galena, Pyrite or other ore minerals were detected. This confirms the XRD results and macroscopic observations for the specific sample.

The chemical analysis of the spent acids, using AAS, IC and Si-Photometry also confirmed the trends from XRD and XRF. In most cases, relative concentrations can be generalised as trends for the respective acidification set:


Regarding 12% HCl + 3% HF as well as 15% HCl acidification on plugs, the relative participation rates of Feldspars are low (relatively low K<sup>+</sup> , Na<sup>+</sup> and Ca2+ concentrations), while Micas, especially Muscovite, are strongly affected (relatively high Al3+-concentrations). Tourmaline and other Fe-bearing minerals have intermediate relative participation rates, if present (relatively high Mn2+ and Fe2+/3+ concentrations). If 15% HCl is used, Si is absent in the fluid, implying zero participation of silicates. This is a contradiction to the abovementioned results unless assuming precipitation of silica gel, as described above. In contrast, applying 12% HCl + 3% HF (comparable trends on plugs as on powder), the participation of Feldspars and Micas, as well as mafic minerals, is magnitudes higher compared to 15% HCl (extremely high Al3+, high Si and high Fe2+/3+, Mg2+, Ca2+, Na<sup>+</sup> and K<sup>+</sup> concentrations). Total ion loads reach up to approx. 11,000 mg/L in spent 12% HCl + 3% HF, but only approx. 550 mg/L in spent 15% HCl.

Comparing the acidification on plugs and powder (with 12% HCl + 3% HF in both cases), the data show similar trends. In relative numbers, the ratio of the dissolved elements fits quite well between acidised OAS powder and plugs. The main difference is an extremely low Fe2+/3+ concentration in the fluid from powder acidification experiments (maximum Fe2+/3+ concentration in powder experiment: 16 mg/L; in plug experiment: 1355 mg/L). This might indicate the precipitation of an iron mineral on the large powder surface and separation during centrifugation of the powder sample. In XRD, the respective mineral would likely not be detected as the precipitate would most likely precipitate as an amorphous mineral. No XRF measurements of the powder samples were performed, because the remaining material mass was too small for the method.

Summarising the effects on specific minerals, the effectivity of the acidification depends primarily on the composition of the spent acid. Theoretically, the effect of the temperature is relevant, but since all experiments were conducted at the same temperature, this cannot be validated by the data. The effect of the grainsize is minor, as powder and plug acidification had comparable effectivities regarding different minerals, although the grainsize was homogenised by pulverisation. It also depends on geochemical variations in the sample, such as varying concentrations of ore minerals, Chlorite, Muscovite and Biotite or Tourmaline. Feldspars and Mica are mainly affected by the chemical reactions. The effect on Quartz is far lower, even if HF is involved. Since the AEs last 24 h and near-equilibrium conditions are established, reaction kinetics are not as important for the resulting effects on the samples as they would be in a real stimulation or in CFTs, in which the reaction time is much lower (0.5 to 6 h). However, since all relevant reactions imply an activation energy threshold, reaction kinetics still influence the results. Equilibrium constants in a multi-phase—multi-component system can be derived from reaction rate constants. Portier and Vuataz [46] use respective parameters for a granite system and state that, using 12% HCl + 3% HF, the reaction rates for Feldspars and Micas are two magnitudes higher than for Quartz. Their results also confirm a higher reactivity of K-Feldspar compared to Plagioclase. Reaction rates for HCl and HCl + HF in varying concentrations are also provided by Economides and Nolte [48] and confirm the present results. If the effectiveness of the acids is summarised in terms of the estimated solubility of the minerals, which are predominantly involved in the analysed samples, the following order can be derived:

## • Micas (especially Fe-Chlorite) > K-Feldspar > Plagioclase > Tourmaline > Quartz

Further quantifications of the reaction kinetics in the autoclave experiments would require a larger dataset and more detailed analysis. Regarding SSB-007 and SFB-007, reaction kinetics are influenced by the addition of retardants and corrosion inhibitors. As the exact composition of the acid blends has not been provided, no further interpretation of the reaction processes during the CFTs is possible.

Regarding the comparability of the acidification methods (CFTs versus AEs; 15% HCl versus SSB-007; SFB-007 versus 12% HCl + 3% HF), it is very important to consider the different reaction times, as the SSB-007 flush lasted less than one hour in the CFTs, while the AEs were conducted during 24 h. As a summarising comparison, 15% HCl has a weak, but evident effect on the AE samples and in the fluid samples, while SSB-007 did not cause any effect on permeability that could be identified during the CFTs. All effects related to geochemical variations induced by the CFTs could solely account for SFB-007. Comparing SFB-007 and 12% HCl + 3% HF, the effects seem to be quite comparable, except for the slightly lower effectivity of SFB-007 on Micas, detected in the XRF data. From several papers published by Fangmann Energy Services, only Recalde Lummer and Rauf [24] unambiguously describe the application of SFB-007, stating that K-Feldspars of the analysed samples are not affected by conducted experiments. This is not confirmed by the present results. The absolute effectivity of both methods is not comparable due to the differences in duration, pressure and the acid circulation in the CFTs.

The most important limitations of methods are related to the acidification experiments: in the CFTs, no absolute permeability is measured since the fluid properties (viscosity of the acid, as well as the exact composition of the acid blends) are unknown and likely change during the experiment. Thus, unfortunately, the permeability determination is only reliable during the ammonium chloride flush. The dynamic viscosity of ammonium chloride under test conditions would need to be determined, as well as the fluid properties of SSB-007 and SFB-007, which are required for hydraulic modelling. The flow behaviour, and thus also the retardation and reaction behaviour, is highly dependent on viscosity and density. In the

AEs, the quantification of the mineral dissolution is corrupted by precipitates, which do not occur in the CFTs to a comparable extent and would not occur in the near-well regions of the reservoir (metres to tens of metres), if an adequate post-flush is conducted to displace the reaction products deeper into the formation. This displays the main limitation of the AEs.

Indicators for the relevance of ore minerals in acidification are found in sample 6 (023001), where precipitates are most abundant. The thickness and the extent of the yellow to white precipitate is highest. Uniquely, sample 6 contains macroscopically visible finegrained ore minerals. Cassiterite was identified by XRD; further ore minerals (possibly Galena and Pyrite) are indicated in XRF data. The AEs on sample 6 result in a PEF of 0.8 for 15% HCl and 0.59 for 12% HCl + 3% HF. It is the only sample with a permeability decrease after acidification with 15% HCl. Fe was identified to cause the yellow precipitate, which occurs not only in the presence of ore minerals but also in samples that contain mafic or Fe-rich minerals, such as Schorl, Hornblende or Fe-Chlorite. Assuming the presence of Pyrite, the abundance of the precipitate can be explained. In the XRF data, the relative Fe2O<sup>3</sup> content increases, indicating that Fe-ions reprecipitate. To assess the presence of ore minerals for a chemical stimulation, XRF is recommended instead of XRD, as XRD is not a well-suited method to identify ore minerals.

Comparing OASs and cuttings, only limited transferability is given between the two sample types. This highlights the significant effect of surface weathering or alteration processes on the samples, which can be excluded by the drilling of Side Wall Cores for a high-quality assessment of the reservoir. The reduced normalised Plagioclase content in the OAS, in comparison to the cuttings, could be another indicator—besides the REE pattern—for weathering, because Plagioclase has higher weathering rates than K-Feldspars. Nevertheless, the mineralogical composition of the OAS resembles hydrothermally altered fracture zones and is therefore a relevant approach for deep geothermal systems in fractured granite.

#### **5. Conclusions**

Regarding the results of the present study, the most efficient acid for United Downs is clearly HF-based. In other wells, when calcite is present in veins, HCl or an Organic Acid is usually sufficient for stimulation, but this is not the case in UDDGP. In case chemical treatment is not an option, e.g., due to due to regulatory requirements regarding the applied acids, pulse fracturing treatment—as described by Tariq et al. [50]—might be an option. Thermochemical acid fracturing, as described by Tariq et al. [51], which is based on the pressure increase during specific chemical reactions and can be based on less hazardous chemicals, may also display an alternative. HF is not biodegradable and not environmentally friendly, although Recalde Lummer and Rauf state that the treatment system SSB-007 + SFB-007 is biodegradable [24], which is confirmed by the safety sheets of the single components. To reduce safety and environmental risks, the HF-based acid is prepared on site from ammonium bifluoride and strong organic acids, which are less hazardous. This allows safer handling and a demand-controlled preparation of the required acid volume. Technical restrictions regarding the project site, such as swelling of clays and compatibility with borehole and reservoir fluids, as well as casing steel and cements were analysed and show no signs of incompatibility. Technical constraints from the environmental side include the presence of a hydraulic barrier, such as a customised barrier (e.g., inert, impermeable textiles or foils) on top of a concrete pad of sufficient extent around the well, the integrity of the well cementation, the exclusion of any leaks in or around the well or project site and the exclusion of any other hydraulic links between the reservoir and non-target areas.

The CFTs were conducted to approximate a chemical reservoir stimulation on lab scale. A major difference between the lab-scale experiments and a reservoir stimulation is that in a reservoir stimulation, chemical stimulation is accompanied by hydraulic and thermal stimulation effects.

As relatively cold fluids, compared to the reservoir temperature, are injected, thermoelastic effects may cause fracture opening or fracturing as well, as significant contraction effects may occur due to the large reservoir volume and will strongly be influenced by injection volume and the duration of injection. In the CFTs, the sample is heated to 150 ◦C, while the fluid is at room temperature before the contact with the sample. For the small core volume, thermal contraction is not relevant. Effects of thermal contraction would most likely occur during the ammonium chloride pre-flush but have not been detected.

The hydraulic pressure is at least the hydrostatic pressure of the fluid column in the well, but may be artificially increased, depending on the stimulation approach.

Regarding the pressure conditions, the applied confining pressure in the CFTs was set to 172.4 bar and a back pressure of 34.5 bar was applied to prevent boiling of the fluids. The pore pressure was in a dynamic relation with the measured differential pressure and depended on the pump pressure, which varied to maintain a constant flow rate (OFITE 2019). In comparison, the stress conditions in the production well were strike–slip stress conditions (max. horizontal pressure > vertical pressure > min. horizontal pressure), critically stressed for shearing on pre-existing fractures with matching orientation [22]. Indicators for a change of stress regime in the open-hole sections were found and are described by Reinecker et al. [22].

While the CFTs affect a specific fissure or vein, a reservoir stimulation is conducted with packers or coiled tubing, affecting entire well sections. The fluid follows preferential flow paths, which implies the risk of creating wormholes along the most permeable fractures, while closed fractures might only be affected by the acid to a very low degree. This issue should be investigated in further studies, e.g., by digital rock imaging, as well as quantification of the changes in roughness.

In the CFTs, during the flushing process under the applied confining pressure, a fracture collapse was detected, as described in Section 3.2. This risk is transferable to the reservoir, as it implies the risk of a permeability decrease by the reduction in vein or fissure stability by particle washout or during chemical treatment. In hydraulic stimulations, proppants are commonly used to avoid fracture collapse. In the case of the granitic reservoir rocks, the Quartz grains, however, might act as natural proppants and keep the fractures open, while Micas and ore minerals in the fractures are preferentially dissolved.

The dissolution characteristics for a HF based acid are good, but imply the precipitation of pore-clogging minerals. A post-flush needs to be executed, which ensures that precipitation occurs only in the reservoir at greater distance of the well, minimising negative hydraulic effects to the well productivity. As an attempt to quantify the required post-flush volume for chemical treatment, it should correspond to at least one times the pore volume of the sample. With respect to the possible fracture collapse and pressure limitations due to technical and safety constraints, the maximum post-flush volume is limited as well. In view of these limitations, a post-flush of three to five times the pore volume is recommended.

Chemical stimulation with HF is common in petroleum projects and has also been applied in geothermal projects [52–54], but open-access datasets are scarce. HF-treatment involves severe risks for human health and the environment. The company and operator have to ensure that during chemical treatment, all risks to health and the environment are considered. Procedures to handle the fluids have to be designed accordingly and countermeasures need to be in place to be applied immediately if needed. The acid blend SFB-007 has already been applied in geothermal projects with granitic reservoir rocks as Soultz sous Forêts, Rittershoffen and Vendenheim [24]. An intense pre-stimulation assessment of the reservoir is required to search for the optimum acid blends and to define required volumes or technical alternatives. The presented research contributes to the optimisation of stimulation pre-assessment, which is transferable to other projects in fractured crystalline rock. The present work contributes significantly to the stimulation preassessment for the United Downs Deep Geothermal Power project and therefore improves the planning process of the reservoir treatment. It complies with the MEET project objective to optimise chemical treatment and reservoir assessment. SSB-007 + SFB-007 are innovative, state of the art acid blends, which are applied internationally. The approximation of these acid blends with 15% HCl and 12% HCl + 3% HF has proven to be a suitable approach. Elaborated results from the selected samples can be transferred to further project sites in a fractured granitic basement. The applied methods in the compiled workflow are an innovative, well-suited tool set for a generalised approach to the lab scale assessment of rock acidification, particularly for application in a crystalline basement.

Using a set of laboratory tests that, to our knowledge, have never before been performed with similar acid combinations on granitic rocks for geothermal purposes, the present study provides new insights into the efficiency as well as possible difficulties of chemical stimulation in such rock types.

**Supplementary Materials:** The following are available online at https://doi.org/10.48328/tudatalib-629 and https://www.mdpi.com/article/10.3390/geosciences12010035/s1, Table S1: Pn2MEET\_ KSchulz: petrophysical and petrological characterisation of outcrop analogue samples before and after acidification; Table S2: Fluid Chemistry-AAS\_IC\_Photometry: chemical characterisation of spent acids after autoclave experiments, Table S3: Core Flooding Tests: permeability tracking during Core Floodings Tests.

**Author Contributions:** Conceptualisation, K.B. and K.E.S.; methodology, K.E.S.; validation, K.B. and K.E.S.; writing—original draft preparation, K.E.S.; writing—draft review, K.B., I.S.; visualisation, K.E.S.; supervision, K.B., I.S.; project administration, K.B.; funding acquisition, K.B., I.S. All authors have read and agreed to the published version of the manuscript.

**Funding:** The work is conducted as part of the MEET project that has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No 792037.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Supplementary Materials are published by Schulz et al. [42] and can be found at https://doi.org/10.48328/tudatalib-629 (access date: 25 November 2021).

**Acknowledgments:** The present work was elaborated at the Institute of Applied Geosciences, Technical University of Darmstadt in the framework of the projects MEET (grant agreement No. 792037) and UDDGP. We would like to thank the supporting staff from the Department of Geothermal Science and Technology, namely G. Schubert, S. Schmidt, R. Seehaus, D. Scheuvens and R. Petschik from Goethe University of Frankfurt for the XRD measurements, as well as our project partners related to MEET/UDDGP, to mention A. Genter, A. Turan, J. Reinecker, J. Gutmanis, R. Shail, B. Simons, C. Dalby. We would also like to acknowledge the editorial support of Mayes Nie and Aleksandar Pavlovic, as well as two anonymous reviewers, who allowed us to substantially improve our manuscript.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Appendix A**

Calculation of permeability from the measured pressure difference before and after the CFTs: the differential pressure and the runtime, which—under constant flow rate—can be expressed as multiples of the pore volume, are measured automatically during the CFTs. The evaluation of the measured pressure difference (given in psi) is based on Darcy's law. An additional multiplication factor, which depends on the device and on the conversion from bar (or Pa) to psi (1 bar = 14,504 psi), is used to calculate the permeability (OFITE, 2019). With k: permeability (mD); µ: viscosity of fluid (cP); Q: flow rate (cm3/s); l: core length (cm); A: cross sectional area of the core (cm<sup>2</sup> ); ∆p: differential pressure (psi), the resulting equation is:

$$\mathbf{k} = 14\text{\textdegree } 700 \cdot \mu \text{\textdegree Q} \cdot \text{l} / (\text{A} \cdot \Delta \text{p}) \tag{A1}$$

As described in Section 3.2, the permeability can only be measured during the preand post-flush. Since the viscosity of the brine (NH4Cl) is temperature dependent, it had

to be determined in additional experiments, conducted by Fangmann Energy Services. Nevertheless, to our knowledge, in the data provided by Fangmann Energy Services, which are included in the Supplementary Materials, the viscosity of the fluid was set to 1 cP.

To avoid falsification of the results, our evaluation of the CFTs is based on the PEF, which is introduced in Section 3.2 and allows a relative quantification of the permeability increase. The permeability changes were verified by additional gas permeability measurements, as described in Section 3.3.

The viscosity of the acids, considering the chemical reactions of the acids and under the applied temperatures, is unknown. Therefore, the tracking of the differential pressure which is inversely proportional to the permeability—during the CFTs, as discussed in Section 3.2, is only a qualitative approach to the permeability changes during the CFTs. *Geosciences* **2022**, *12*, x FOR PEER REVIEW 22 of 24

#### **Appendix B**

**References**

**Appendix B**


relative increase (↑), decrease (↓) or no significant changes (variation < 0,3 %) (o) after acidification

**Figure A1.** Comparison of the relative mineralogical composition before and after chemical treat‐ ment in AEs and CFTs. **Figure A1.** Comparison of the relative mineralogical composition before and after chemical treatment in AEs and CFTs.

11. Yeomans, C.M.; Middleton, M.; Shail, R.K.; Grebby, S.; Lusty, P.A. J. Integrated Object‐Based Image Analysis for semi‐auto‐ mated geological lineament detection in southwest England. *Comput. Geosci.* **2019**, *123*, 137–148,

14. British Geological Survey. BGS Geology 625k|DiGMapGB‐625: Digital Geology Data. BGS. 2007. Available online:

12. Ghosh, P.K. The Carnmenellis Granite: Its Petrology, Metamorphism and Tectonics. *Q. J. Geol. Soc.* **1934**, *90*, 240–276.

#### **References**


https://www.bgs.ac.uk/datasets/bgs‐geology‐625k‐digmapgb/ (accessed on 25 November 2021).

https://doi.org/10.1016/j.cageo.2018.11.005.


## *Article* **Hydrothermal Numerical Simulation of Injection Operations at United Downs, Cornwall, UK**

**Saeed Mahmoodpour 1,\* , Mrityunjay Singh 2,\* , Christian Obaje <sup>3</sup> , Sri Kalyan Tangirala <sup>4</sup> , John Reinecker <sup>5</sup> , Kristian Bär <sup>5</sup> and Ingo Sass 2,6**


**Abstract:** The United Downs Deep Geothermal Project (UDDGP) is designed to utilize a presumably permeable steep dipping fault damage zone (constituting the hydrothermal reservoir in a very low permeability granitic host rock) for fluid circulation and heat extraction between an injection well at 2.2 km depth (UD−2) and a production well at 5 km depth (UD−1). Soft hydraulic stimulation was performed to increase the permeability of the reservoir. Numerical simulations are performed to analyze the hydraulic stimulation results and evaluate the increase in permeability of the reservoir. Experimental and field data are used to characterize the initial reservoir static model. The reservoir is highly fractured, and two distinct fracture networks constitute the equivalent porous matrix and fault zone, respectively. Based on experimental and field data, stochastic discrete fracture networks (DFN) are developed to mimic the reservoir permeability behavior. Due to the large number of fractures involved in the stochastic model, equivalent permeability fields are calculated to create a model which is computationally feasible. Hydraulic test and stimulation data from UD−1 are used to modify the equivalent permeability field based on the observed difference between the real fractured reservoir and the stochastic DFN model. Additional hydraulic test and stimulation data from UD−2 are used to validate this modified permeability. Results reveal that the equivalent permeability field model derived from observations made in UD−1 is a good representation of the actual overall reservoir permeability, and it is useful for future studies. The numerical simulation results show the amount of permeability changes due to the soft hydraulic stimulation operation. Based on the validated permeability field, different flow rate scenarios of the petrothermal doublet and their respective pressure evolution are examined. Higher flow rates have a strong impact on the pressure evolution. Simulations are performed in the acidized enhanced permeability region to make a connection between the ongoing laboratory works on the acid injection and field response to the possible acidizing stimulation.

**Keywords:** United Downs; EGS; hydraulic stimulation; equivalent permeability field

#### **1. Introduction**

Petrothermal systems are reservoirs with preferably high heat flow, geothermal gradient, and temperature, but lack sufficient natural fluid flow (in most cases) and permeability to accommodate flow rates required for economic geothermal systems. In such geothermal play types, enhanced geothermal systems (EGS) can be implemented by creating new fractures or stimulating naturally existing ones to achieve the permeabilities needed for economical fluid flow. This is essential to create a connected network of pathways between

**Citation:** Mahmoodpour, S.; Singh, M.; Obaje, C.; Tangirala, S.K.; Reinecker, J.; Bär, K.; Sass, I. Hydrothermal Numerical Simulation of Injection Operations at United Downs, Cornwall, UK. *Geosciences* **2022**, *12*, 296. https://doi.org/ 10.3390/geosciences12080296

Academic Editors: Béatrice A. Ledésert, Ronan L. Hébert, Ghislain Trullenque, Albert Genter, Eléonore Dalmais, Jean Hérisson and Jesus Martinez-Frias

Received: 17 May 2022 Accepted: 27 July 2022 Published: 29 July 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

the injection well and production well [1]. Achieving economic flow rates at wellhead is the goal of any stimulation operation [2]. There are different techniques of stimulating fractures: (i) hydraulic stimulation, where water is injected at high pressure to enhance the permeability; (ii) chemical stimulation, where acids are injected to dissolve fracture mineralization and thus increase the permeability; and (iii) thermal stimulation, where cold water injection creates thermal stress in the reservoir rock which helps in increasing the permeability of the fracture network [3]. The latter is usually best applicable in very high-temperature reservoirs. In this paper, the impact of hydraulic stimulation on the permeability enhancement of naturally occurring fractures in the fault zone through Thermo-Hydraulic (TH) modeling of the United Down Deep Geothermal Project (UDDGP) at Cornwall, UK, is discussed.

UDDGP is geographically located near Redruth in Cornwall, southwest England. This project is the first in the UK where both injection and production wells are drilled into the highly fractured and steeply dipping Porthtowan Fault Zone (PTF), cross-cutting the Carnmenellis Granite of the Cornubian Batholith. For selecting the geological targets of UDDGP, previous experiences from Rosemanowes HDR wells are considered where the hydraulically active fractures are mainly oriented parallel or at an oblique angle to the maximum horizontal stress direction (*SHmax*) oriented in the NW-SE direction. To use these favorable flow paths, the geological target selection is focused on faults oriented more or less parallel to *SHmax*. Furthermore, hot springs in mines confirm this fracture permeability in the NW-SE direction [4]. Evidence from mining activities in the area of interest covered only the top 400 m, but it provides insights regarding fault dip, direction, damage zone thickness, displacement, and hydraulic activity. Combining these data with surface geological maps, the fault model is generated [5]. For the well trajectories, two criteria are considered: first, longer-length and larger displacement faults, because they are most likely to penetrate to the deeper zones, and second, the selected area should be underlain by granite with high heat production. Given the lack of available significant geophysical data to detect the fault structures at depth, the combination of the surface geology, mining data, few seismic profiles, and analog structures are used to make a drilling prognosis [6–10]. The injection well UD−2 was drilled to a depth of 2393 m MD (2214 m TVD), and the production well UD−1 was drilled to 5275 m MD (5058 m TVD) with a horizontal spacing of 8 m between the two wellheads and a vertical spacing of around 2000 m between the ends of the wells (to prevent thermal short-circuiting). The production well UD−1 is the deepest onshore well drilled in the UK. Both wells were directionally drilled towards the WSW of the well heads to intersect the NW-SE striking PTF (Figure 1). The bottom hole temperature at a depth of 5 km was found to be > 180 ◦C. The open fractures in the PTF are considered to be the main pathways for fluid flow. However, only a small group of fractures were proven to be hydraulically active by indicators, e.g., mud losses during drilling, geothermal gradient anomalies, induced seismic events, and borehole image analysis [11].

The geology of Cornwall is characterized by the Cornubian batholith, which can be distinguished into several plutons. The Carnmenellis granite is one such pluton that formed around 293 Ma ago [12]. The region also comprises metamorphosed Devonian sediments, which are locally known as "killas". Granites in this region have high contents of uranium (U), thorium (Th), and potassium (K), which result in high heat flow values and the high geothermal gradient. There are a few thermal springs in the vicinity of the site. The granitic outcrops, mines with U deposits, and thermal springs, along with faults, are shown in Figure 2. The Carnmenellis granite was estimated to be about 10 km deep, and the temperature at that depth was 650 ◦C [11,13].

The PTF is a set of strike-slip structures with the strike in the NW-SE direction and a width of around 300 m which can be traced as various fault segments on the surface (Figure 1). The PTF accommodates periods of extensional (Devonian, Permo-Trias) and compressional (Variscan, Alpine) tectonics of both dextral and sinistral movements. More information on regional geology and tectonics is given in Reinecker et al. [11].

**Figure 1.** Structural model of UDDGP with injection (UD−2, blue) and production (UD−1, red) wells and their intersection with the Porthtowan Fault Zone (PTF) constituting the two branches of Great **Figure 1.** Structural model of UDDGP with injection (UD−2, blue) and production (UD−1, red) wells and their intersection with the Porthtowan Fault Zone (PTF) constituting the two branches of Great Western cross-courses (xc) and Great Eastern cross-courses (xc).

Western cross-courses (xc) and Great Eastern cross-courses (xc). The geology of Cornwall is characterized by the Cornubian batholith, which can be distinguished into several plutons. The Carnmenellis granite is one such pluton that formed around 293 Ma ago [12]. The region also comprises metamorphosed Devonian sediments, which are locally known as "killas". Granites in this region have high contents of uranium (U), thorium (Th), and potassium (K), which result in high heat flow values and the high geothermal gradient. There are a few thermal springs in the vicinity of the site. The granitic outcrops, mines with U deposits, and thermal springs, along with faults, are shown in Figure 2. The Carnmenellis granite was estimated to be about 10 km deep, and the temperature at that depth was 650 ℃ [11,13]. Ultrasonic imaging of the wellbore has given a very reliable understanding of the natural fracture distribution in UD−1 from 906 m to 5206 m MD (see Figure 3). The fractures can be divided into two sets: fractures trending in the NW-NNW direction and the ENE striking fractures. For more geological details, readers are suggested to read Reinecker et al. [11]. Both these sets consist of mineralized and open fractures (a few of them are hydraulically active). The probable number of fractures in the former set is higher than that of the latter set (based on possible geometrical sampling bias from the log data). The intensity of both the fracture sets generally decreases with depth, a behavior which has also been demonstrated for comparably deep wells in the Upper Rhine Graben by Afshari et al. (2022) [14]. Fractures favorably oriented with the in-situ stress field are critically stressed, and their permeability can be enhanced by slip initiated through fluid-driven stimulation. The fracture sets were further divided on the basis of orientation, intensity, and depth into four domains [11]. Additionally, two large-scale fractures were detected based on a combination of fluid losses during drilling, geothermal anomalies in the temperature logs, by the borehole image logs, and induced seismic events during drilling and subsequent hydraulic testing. Both fractures are oriented more or less in parallel to another, but slightly oblique to the PTF, and are critically stressed in the in-situ stress field [11].

In this study, the thermo-hydraulic process is numerically simulated based on the reported fracture and hydraulic testing/stimulation data. The fractured reservoir for this study is represented by a stochastic DFN-based equivalent continuum model with both homogeneous and anisotropic units representing the host rock and the fault zone, respectively. This study was conducted within the framework of the EU-funded Horizon 2020 project MEET (Multidisciplinary and multi-contact demonstration of EGS exploration and Exploitation Techniques and potentials), which is described in general by Trullenque et al. [15]. The fluid flow and heat transfer during the hydraulic testing and stimulation operations were numerically simulated to estimate the permeability field. Furthermore, the pressure dependency on different injection flow rates is presented and analyzed. Finally, a preliminary model based on the conceptual impact of chemical stimulation on the reservoir permeability is developed, and consequently, its impact on reservoir pressure development is estimated.

*Geosciences* **2022**, *12*, x FOR PEER REVIEW 5 of 20

Due to confidentiality clauses from the industrial partner, all data are reported based on a function of *x*. *Geosciences* **2022**, *12*, x FOR PEER REVIEW 4 of 20

**Figure 2.** Geological map of the region. Isolines of top granite are not displayed on the western and northern sides of the Carnmenellis granite. The red square indicates the UDDGP model outline. Ptn: Porthtowan Formation, MrSl: Mylor Slate Formation, PBr: Porthleven Breccia Member, Pto: Portscatho Formation, all Devonian in age. Towns: T: Truro, F: Falmouth, R: Redruth, C: Camborne, H: Helston [11]. The PTF is a set of strike-slip structures with the strike in the NW-SE direction and a width of around 300 m which can be traced as various fault segments on the surface (Fig-**Figure 2.** Geological map of the region. Isolines of top granite are not displayed on the western and northern sides of the Carnmenellis granite. The red square indicates the UDDGP model outline. Ptn: Porthtowan Formation, MrSl: Mylor Slate Formation, PBr: Porthleven Breccia Member, Pto: Portscatho Formation, all Devonian in age. Towns: T: Truro, F: Falmouth, R: Redruth, C: Camborne, H: Helston [11]. detected based on a combination of fluid losses during drilling, geothermal anomalies in the temperature logs, by the borehole image logs, and induced seismic events during drilling and subsequent hydraulic testing. Both fractures are oriented more or less in parallel to another, but slightly oblique to the PTF, and are critically stressed in the in-situ stress field [11].

ure 1). The PTF accommodates periods of extensional (Devonian, Permo-Trias) and com-

**Figure 3.** Fracture distribution interpreted from ultrasonic logs in UD−1. Note that the depth scale of the structural profile is the true vertical depth below sea level. Cumulative fracture distribution and lithology log originally in measured depth below ground level are shifted and stretched to fit the true vertical depth scale [11]. Two large-scale fractures were detected by induced seismic events during drilling and subsequent injection testing. In this study, the thermo-hydraulic process is numerically simulated based on the reported fracture and hydraulic testing/stimulation data. The fractured reservoir for this **Figure 3.** Fracture distribution interpreted from ultrasonic logs in UD−1. Note that the depth scale of the structural profile is the true vertical depth below sea level. Cumulative fracture distribution and lithology log originally in measured depth below ground level are shifted and stretched to fit the true vertical depth scale [11]. Two large-scale fractures were detected by induced seismic events during drilling and subsequent injection testing.

study is represented by a stochastic DFN-based equivalent continuum model with both homogeneous and anisotropic units representing the host rock and the fault zone, respectively. This study was conducted within the framework of the EU-funded Horizon 2020 project MEET (Multidisciplinary and multi-contact demonstration of EGS exploration and Exploitation Techniques and potentials), which is described in general by Trullenque et

pressure dependency on different injection flow rates is presented and analyzed. Finally, a preliminary model based on the conceptual impact of chemical stimulation on the reservoir permeability is developed, and consequently, its impact on reservoir pressure development is estimated. Due to confidentiality clauses from the industrial partner, all data

Well data, seismological data, surface mapping, data from nearby mines, outcrop analysis, and data from the Rosemanowes project, along with gravity analysis, are all used

are reported based on a function of .

**2. Methodology** 

#### **2. Methodology**

Well data, seismological data, surface mapping, data from nearby mines, outcrop analysis, and data from the Rosemanowes project, along with gravity analysis, are all used to define the target faults, well trajectories, and fractures. For setting up a static structural reservoir model, the Move 2018 software [16] developed by Midland Valley Explorations Ltd. was used [11]. Fracture network data obtained from fieldwork, borehole logging, and literature are summarized in Tables 1 and 2 for the unfaulted host rock zone and the fault zone, respectively. Discrete fracture networks (DFNs) are generated for the host rock zone and the fault zone using the FracMan 7 [17] software. Due to unavailability of mean fracture half-length and mean hydraulic fracture aperture data for the fracture set 2, corresponding data from fracture set 1 is assumed in Tables 1 and 2. Furthermore, this geometrical model (see Figure 4) is imported into COMSOL Multiphysics [18] for the hydraulic stimulation simulation.

To enhance the hydraulic connection of the open hole sections of both wells to the fault-bounded reservoir, hydraulic stimulation operations have been performed on UD−1 and UD−2. The injectivity of UD−2 is within the targets set for the power plant operation. To increase the hydraulic connectivity of UD−1 to the reservoir and the near wellbore reservoir hydraulic conductivity, three stages of hydraulic stimulation were performed [11]: (a) Phase 1—step rate injection testing during August 2020, (b) Phase 2—extended injection testing between September and October 2020 and (c) Phase 3—low pressure extended injection testing between October 2020 and February 2021. All phases can be characterized as soft hydraulic stimulation operations due to the low injection volumes and flow rates but sufficient pressures to induce micro-seismic events. Figure 5 shows the operational details of phase 3 hydraulic stimulation for UD−1. This data is used to validate and adjust the anisotropic permeability field of the stochastic DFN models based on the fracture network characteristics for the UDDGP geothermal field. In this data, some changes need to be highlighted: (i) in the first part, from steps 0 to 15, the injection volumes were increased while flow rates and pressures were kept at a low level, followed by (ii) a set of injections with significantly higher injection pressures and considerably higher flow rates from step 16 until step 21 accompanied by increasing induced micro-seismicity (not shown due to confidentiality) leading into (iii) a third part where flow rates increase further with significantly lower injection pressures. These changes indicate that the hydraulic injections are increasing the reservoir injectivity and prove that they can be defined as soft hydraulic stimulation.



Furthermore, the hydraulic testing/stimulation operational data for UD−2, conducted from the 17th until the 20th of November 2020, is used to validate the calculated permeability field (Figure 6). Based on this validated permeability field, different operational scenarios of flow conditions were simulated to evaluate reservoir performance. and the fault zone using the FracMan 7 [17] software. Due to unavailability of mean fracture half-length and mean hydraulic fracture aperture data for the fracture set 2, corresponding data from fracture set 1 is assumed in Tables 1 and 2. Furthermore, this geometrical model (see Figure 4) is imported into COMSOL Multiphysics [18] for the hydraulic stimulation simulation.

to define the target faults, well trajectories, and fractures. For setting up a static structural reservoir model, the Move 2018 software [16] developed by Midland Valley Explorations Ltd. was used [11]. Fracture network data obtained from fieldwork, borehole logging, and literature are summarized in Tables 1 and 2 for the unfaulted host rock zone and the fault zone, respectively. Discrete fracture networks (DFNs) are generated for the host rock zone

*Geosciences* **2022**, *12*, x FOR PEER REVIEW 6 of 20

**Figure 4.** Schematic geometry used to simulate a cubic space of the UDDGP geothermal system. The hydraulically stimulated region is depicted by a cylinder around UD−1. Two critically stressed large-scale fractures, subparallel to the PTF, are implemented based on the seismic events as documented by, e.g., [11] and indicated with a disc shape. **Figure 4.** Schematic geometry used to simulate a cubic space of the UDDGP geothermal system. The hydraulically stimulated region is depicted by a cylinder around UD−1. Two critically stressed largescale fractures, subparallel to the PTF, are implemented based on the seismic events as documented by, e.g., [11] and indicated with a disc shape. Furthermore, the hydraulic testing/stimulation operational data for UD−2, conducted from the 17th until the 20th of November 2020, is used to validate the calculated permeability field (Figure 6). Based on this validated permeability field, different operational scenarios of flow conditions were simulated to evaluate reservoir performance.

To enhance the hydraulic connection of the open hole sections of both wells to the

**Figure 5.** Daily flow rate, injection pressure, and injected volume of the hydraulic testing/stimulation operation on UD−1 from September 2020 until January 2021. Here flow rate, pressure, and injection volume are hidden for commercial issues. The black and blue colors indicate the pressure and volume of the injected fluid. **Figure 5.** Daily flow rate, injection pressure, and injected volume of the hydraulic testing/stimulation operation on UD−1 from September 2020 until January 2021. Here flow rate, pressure, and injection volume are hidden for commercial issues. The black and blue colors indicate the pressure and volume of the injected fluid.

**Figure 6.** Pressure and flow rates of the four days of hydraulic testing/stimulation operation performed in UD−2 from 17th to 20th November 2020. Due to confidentiality, exact flow rate and pressure values are hidden and are shown only in terms of multiplication of *x*. **Figure 6.** Pressure and flow rates of the four days of hydraulic testing/stimulation operation performed in UD−2 from 17th to 20th November 2020. Due to confidentiality, exact flow rate and pressure values are hidden and are shown only in terms of multiplication of *x*.



Producing fracture spacing [m] 10 Spacing between producing fractures is in the order of 10 m [21] Fracture area density [m−1] 0.9 0.2 Only 10–15% of the fractures carry Using the following equation [18], heat and mass transfer in a porous media is coupled to simulate the fluid flow during the hydraulic stimulation operation:

$$\rho\_1(\phi\_m S\_1 + (1 - \phi\_m) S\_m) \frac{\partial p}{\partial t} - \rho\_1(a\_m(\phi\_m \beta\_1 + (1 - \phi\_m)\beta\_m)) \frac{\partial T}{\partial t} = \nabla \cdot \left(\frac{\rho\_1 k\_m}{\mu} \nabla p\right) \tag{1}$$

In this equation, *p*, *T*, *φm*, *km*, *S*1, *Sm*, *αm*, *β*<sup>1</sup> and *β<sup>m</sup>* are pressure, temperature, porous media porosity, permeability, storage coefficient of rock, storage coefficient of fluid, Biot's coefficient of porous media, the thermal expansion coefficient of fluid, and thermal expansion coefficient of the porous medium, respectively. The fluid dynamic viscosity and density are denoted by *ρ*<sup>1</sup> and *µ*, respectively.

Heat exchange between the rock matrix and water is modeled based on the local thermal non-equilibrium approach, and the governing equation for the rock can be written as:

$$(1 - \phi\_m)\rho\_m \mathcal{C}\_{p,m} \frac{\partial T\_m}{\partial t} = \nabla. ((1 - \phi\_m)\lambda\_m \nabla T\_m) + q\_{ml}(T\_l - T\_m) \tag{2}$$

Here, *Tm*, *T<sup>l</sup>* , *ρm*, *Cp*,*m*, *λ<sup>m</sup>* and *qml* are rock temperature, fluid temperature, rock density, rock-specific heat capacity, rock thermal conductivity, and the rock-fluid heat transfer coefficient, respectively. If *Cp*,*<sup>l</sup>* and *λ<sup>l</sup>* are the heat capacity and thermal conductivity of fluid, then the governing equation of heat transfer for the fluid is:

$$
\rho\_m \rho\_l \mathbb{C}\_{p,l} \frac{\partial T\_l}{\partial t} + \phi\_m \rho\_l \mathbb{C}\_{p,l} \left(-\frac{k\_m \nabla p}{\mu}\right) . \nabla T\_l = \nabla. (\phi\_m \lambda\_l \nabla T\_l) + q\_{ml} (T\_m - T\_l) \tag{3}
$$

These equations are fully coupled and solved in COMSOL Multiphysics [18], where the necessary thermophysical properties of water (dynamic viscosity (*µ*), specific heat capacity (*Cp*), density (*ρ*), and thermal diffusivity (*κ*)) are given below:

$$\begin{aligned} \mu &= 1.38 - 2.12 \times 10^{-2} \times \left(T + 273.15\right)^{1} + 1.36 \times 10^{-4} \times \left(T + 273.15\right)^{2} - 4.65 \times 10^{-7} \times \left(T + 273.15\right)^{3} \\ &+ 8.90 \times 10^{-10} \times \left(T + 273.15\right)^{4} - 9.08 \times 10^{-13} \times \left(T + 273.15\right)^{5} + 3.85 \\ &\times 10^{-16} \times \left(T + 273.15\right)^{6} \left(0 - 140 \text{ } ^{\circ}\text{C}\right) \end{aligned} \tag{4}$$

$$\begin{array}{c} \mu = 4.01 \times 10^{-3} - 2.11 \times 10^{-5} \times \left(T + 273.15\right)^{1} + 3.86 \times 10^{-8} \times \left(T + 273.15\right)^{2} \\\ \quad - 2.40 \times 10^{-11} \times \left(T + 273.15\right)^{3} \left(140 - 280 \text{ }^{\circ}\text{C}\right) \end{array} \tag{5}$$

$$\begin{array}{c} \text{C}\_{p} = 1.20 \times 10^{4} - 8.04 \times 10^{1} \times \left(T + 273.15\right)^{1} + 3.10 \times 10^{-1} \times \left(T + 273.15\right)^{2} \\ \quad - 5.38 \times 10^{-4} \times \left(T + 273.15\right)^{3} + 3.63 \times 10^{-7} \times \left(T + 273.15\right)^{4} \end{array} \tag{6}$$

$$\rho = 1.03 \times 10^{-5} \times \left(T + 273.15\right)^3 - 1.34 \times 10^{-2} \times \left(T + 273.15\right)^2 + 4.97 \times \left(T + 273.15\right) + 4.32 \times 10^2 \tag{7}$$

$$\begin{aligned} \text{rk} &= -8.69 \times 10^{-1} + 8.95 \times 10^{-3} \times \left(T + 273.15\right)^{1} - 1.58 \times 10^{-5} \times \left(T + 273.15\right)^{2} \\ &+ 7.98 \times 10^{-9} \times \left(T + 273.15\right)^{3} \end{aligned} \tag{8}$$

A finite element discretization approach is adopted for this simulation. The complete mesh consists of 135,748 domain elements, 14,320 boundary elements, and 670 edge elements. Backward Differential Formula (BDF) with variable time step is used. The hydrothermal model used here is validated against Bai [24] in previous works by the authors [25,26].

Table 3 shows the rock properties and operational conditions for the numerical simulations of this study. These parameters are obtained from the experimental tests and field works.

**Table 3.** Rock and fluid properties for the United Downs geothermal system, as defined for the numerical simulations.


#### **3. Results and Discussions**

The present section is organized in the following approach: initially, the equivalent permeability field is calculated from the discrete fracture network, followed by updating the permeability field with the operational data from UD−1. The reason behind this step is to compensate for the permeability loss due to closed fractures or uneven morphology of the fracture surfaces, or resulting error from the stochastic approach (from FracMan). Next, the obtained permeability field is validated with the operation data from UD−2, assuming a constant fracture density in the fault zone. Finally, simulations for the cold-water injection for a longer time period are shown to capture the pressure evolution and temperature reduction for different flow rates.

Within the fault zone, 10 million fractures were produced with FracMan based on the fracture network characteristics presented in Tables 1 and 2. This output is difficult to present in a DFN framework included in numerical simulation software. Hence the upscaling of the permeability of the single fractures of the corresponding networks into an equivalent permeability field becomes a necessity. To calculate the equivalent permeability field, the Oda approach [27], as implemented in FracMan, was used. Oda [27] employed the geometry of fractures to calculate effective permeability for a given grid with a given pressure gradient. Inside the FracMan, Poiseuille law is used to calculate the fracture permeability from the fracture aperture. The roughness of the fracture is considered one. Using the orientation of individual fractures present in a grid cell and assigning each fracture as a unit normal vector *n*, a tensor depicting the mass moment of inertia of fractures normally distributed over a unit sphere was obtained through integration of the fractures over all of the unit normal [17]. Figure 7 shows the equivalent permeability field estimation using the Oda method, and it is obvious that the heterogeneity of the final permeability field is a function of the grid size. A smaller grid size results in a more accurate representation of the heterogeneous permeability distribution of the fractured rock mass than a large grid size, where single permeable fractures are less well represented. However, reducing the grid size increases the computational cost. While the permeability range of the permeability field created with the fine grid size is larger than for the coarse grid size, the mean permeability value is approximately the same. Therefore, the coarse grid size, which still provides a sufficiently accurate representation of the fractured reservoir, is used in this study to minimize the computational cost. The permeability field resulting from the Oda methodology for the fault zone is a heterogeneous field that is implemented through the TH calculations in the COMSOL. Consider that meshing for the equivalent permeability from FracMan (structured rectangular mesh) is different than the simulation meshes in the COMSOL (unstructured tetrahedral meshes). Therefore, permeability values mapped from the structural rectangular to the unstructured tetrahedral inside the COMSOL. The average value of the permeability field in anisotropic matrix is reported as below with the highest value in the *z* direction and the second highest value in the *y*-direction, both subparallel to the fault zone strike, which shows the effect of the fracture set orientation (see Table 2):

$$
\begin{bmatrix}
5.5 \times 10^{-15} & 0 & 0 \\
0 & 1.7 \times 10^{-14} & 0 \\
0 & 0 & 2 \times 10^{-14}
\end{bmatrix}
$$

The reported data from the field work, logging and literature (see Table 2) shows that fractures are mainly vertically oriented, which aligns with higher permeability in the *z*-direction. Strike values with the fracture orientation in the *x*-*y* space indicate that their tendency towards the *y*-axis is greater, resulting in a higher permeability in the *y*-direction. While the fracture density slightly decreases with depth, a single averaged fracture density is used to simplify reservoir permeability for the entire fault zone. A similar approach is used to obtain the host rock permeability, and the resulting value is two orders of magnitude smaller than those of the fault zone. This limits the host rock's contribution to the convective heat and mass flux while its effects are still considered in the numerical simulation. The possible discrepancy between actual field and simulated permeability fields is solved with a correction factor to the permeability fields of the Oda methodology based on the hydraulic testing data. Technically, the permeability obtained from the hydraulic test data could have been directly matched with the numerical model to obtain a realistic value, but in this case, the resultant reservoir permeability from the Oda method is heterogeneous. The DFN generation and Oda upscaling were chosen specifically to better reflect the anisotropic permeability field for the faulted reservoir. From Figure 8, it is clear that the pressure increases at a higher rate by increasing the peak flow rate until step 21. The obtained permeability field till step 21 is:


The above permeability field is thus 38 times smaller compared to the permeability obtained by the Oda approach. Possible differences between the actual fractures and the stochastic fractures can be attributed to differences in the fracture aperture caused by chemical reactions, physical precipitations, rough fracture surfaces, and stress reorientation or the general share of open vs. closed fractures.

After reaching the maximum injection pressure at step 21, Figure 5 indicates that the flow rates beyond step 21 do not increase the pressure in a similar magnitude with respect to steps prior to 21. This suggests that some pre-existing fractures are propagated to reduce the incremental pressure rate with increasing the peak flow rate. The initiation of new fractures can be ruled out due to the injection pressure being too small to exceed the tensile strength of the granite and due to the high fracture density of the formation. Therefore, step 22 is seen as proof of a significant hydraulic stimulation of the reservoir. Data matching is performed as shown in Figure 8 for two periods (before and after step 21), and the permeability tensor obtained by averaging the permeability field is 1.7 times higher than the initial rock permeability:

$$1.7 \times \begin{bmatrix} \frac{5.5 \times 10^{-15}}{38} & 0 & 0\\ 0 & \frac{1.7 \times 10^{-14}}{38} & 0\\ 0 & 0 & \frac{2 \times 10^{-14}}{38} \end{bmatrix}$$

The obtained permeability field through the UD−1 well data is validated with the hydraulic testing and stimulation data of well UD−2. Figure 9 demonstrates a good match between the operational data and numerical simulation of UD−2 for the first three stages of injection. However, there is a discrepancy between the measured and modeled data, as shown in Figure 6 for 20 November. Based on this figure, the flow rate decreases to zero in the middle of the test and increases afterward. The operational data shows that the injection pressure increases following the initial trend without experiencing an impact due to the intermittent flow rate breaks. The numerical simulation for UD−2, on the contrary, shows that if the flow rate decreases only for a short time interval, pressure decreases for the rest of the entire injection step and does not reach the previous pressure level. The observed low pressure after a short gap in the injection is not due to the permeability change. Rather the pressure diffuses inside the system leading to pressure drop. It, therefore, seems likely that the flow rate stops and pressure drops are rather a measurement error while reporting the pressure and flow rate data or that the wellbore effect [26] between the wellhead and the reservoir section mitigates the flow rate and pressure drops.

It should be noted that these short-term hydraulic stimulation results are restricted to the near wellbore area, and do not influence the far-field of the reservoir. Therefore, uncertainty remains regarding the volume of the reservoir, which is affected by this operation. To examine the near wellbore effect, a cylindrical zone around UD−1 is considered in which the permeability is changed by hydraulic stimulation. Two radii of 25 and 50 m are considered for this zone, and the behavior of the system is modeled at three fluid rates of *x*,

2*x*, and 3*x* L/s. Figure 10 shows the resulting pressure data on the bottom of the UD−1 and UD−2 based on different flow rates and hydraulically affected area radius. There is no data to show which radius around the wellbore is affected by the hydraulic stimulation. By comparing 25 and 50 m, it is shown that the region size is not important for the studied time periods, but the amount of permeability changes is important. Another model without considering this cylindrical region is run, and the results are different than the operational observations (see Figure 8). This permeability variation importance around the production wellbore is not exactly for this studied short time period, but for the long-term operation, authors showed in another study that permeability around the production wellbore is an important factor [26]. *Geosciences* **2022**, *12*, x FOR PEER REVIEW 12 of 20

**Figure 7.** Oda methodology [27] to calculate the equivalent permeability field and its sensitivity to the two different mesh sizes (17 and 85 m, respectively). Upper left: first, a stochastic DFN of the fault zone and host rock is created based on the fracture network characteristics; Upper middle: then, using the Oda approach, a permeability field is calculated for each cell of a given grid (upper right) separately. The bottom panels show the heterogeneous permeability field for the matrix zone for two different mesh sizes for the equivalent permeability estimation (lower right and lower left). The unit of permeability is m2. **Figure 7.** Oda methodology [27] to calculate the equivalent permeability field and its sensitivity to the two different mesh sizes (17 and 85 m, respectively). Upper left: first, a stochastic DFN of the fault zone and host rock is created based on the fracture network characteristics; Upper middle: then, using the Oda approach, a permeability field is calculated for each cell of a given grid (upper right) separately. The bottom panels show the heterogeneous permeability field for the matrix zone for two different mesh sizes for the equivalent permeability estimation (lower right and lower left). The unit of permeability is m<sup>2</sup> .

obtained by the Oda approach. Possible differences between the actual fractures and the stochastic fractures can be attributed to differences in the fracture aperture caused by chemical reactions, physical precipitations, rough fracture surfaces, and stress reorienta-Initially, the simulated pressures of the UD−1 are higher than UD−2 due to the hydrostatic pressure. By injecting fluid at UD−2 and producing from UD−1, they experience pressure buildup and drawdown, respectively. Obviously, by increasing the flow rate, the

The above permeability field is thus 38 times smaller compared to the permeability

tion or the general share of open vs. closed fractures.

pressure separation between the two wells increases at later times. Pressure changes are greater at early times, and as time goes on, pressure show semi-steady behavior, and the operator can decide regarding the optimal flow rate. For example, for the cases with 25 m of hydraulically stimulated area, the pressure after ten days reaches 4.78*x*, 7.39*x*, and 10.05*x* MPa with flow rates of *x*, 2*x*, and 3*x* L/s, respectively, whereas after 150 days it becomes 5.8*x*, 9*x* and 12.1*x* MPa respectively. However, there is not much change between 150 and 300 days, where in the latter case, the final pressure values are 6.1*x*, 9.34*x*, and 12.6*x* MPa for the flow rates of x, 2x, and 3x L/s, respectively. Correspondingly for UD−1, a decreasing trend is observed at a gentle gradient. For the flow rates of *x*, 2*x*, and 3*x* L/s, observed pressure values after ten days are 4.05*x*, 3.72*x* and 3.38*x* MPa, respectively, which becomes 3.38*x*, 2.86*x* and 2.35*x* MPa, respectively, after 150 days which finally reaches to 3.08*x*, 2.51*x* and 1.93*x* MPa, respectively, after 300 days. This analysis shows that pressure differences between the two wells are 3.02*x*, 6.83*x*, and 10.67*x* MPa after 300 days for three flow rates, *x*, 2*x*, and 3*x* L/s, respectively. It is interesting to note that from an economical point of view, the higher flow rate is attractive, but it may eventuate the seismic events. During the examined period, the radius of the hydraulically stimulated area near the UD−1 has a negligible effect on the pressure profiles in comparison to the flow rate. The pressure differences between the wellbore for a 50 m radius of hydraulically stimulated zone reach 2.97*x*, 6.71*x*, and 10.56*x* MPa after 300 days for *x*, 2*x*, and 3*x* L/s injection rates, respectively. Therefore, in the remaining parts, a small radius of 25 m is examined. Similar behavior is recognized by Mahmoodpour et al. [26] that the permeability field in the vicinity of the production well is an important factor. *Geosciences* **2022**, *12*, x FOR PEER REVIEW 13 of 20

**Figure 8.** Matching operational and simulation pressure data to obtain the permeability field before and after the hydraulic stimulation process. The pink dotted line marks the occurrence of a microseismic event, which significantly changed reservoir injectivity. **Figure 8.** Matching operational and simulation pressure data to obtain the permeability field before and after the hydraulic stimulation process. The pink dotted line marks the occurrence of a microseismic event, which significantly changed reservoir injectivity.

After reaching the maximum injection pressure at step 21, Figure 5 indicates that the flow rates beyond step 21 do not increase the pressure in a similar magnitude with respect to steps prior to 21. This suggests that some pre-existing fractures are propagated to reduce the incremental pressure rate with increasing the peak flow rate. The initiation of new fractures can be ruled out due to the injection pressure being too small to exceed the tensile strength of the granite and due to the high fracture density of the formation. Therefore, step 22 is seen as proof of a significant hydraulic stimulation of the reservoir. Data matching is performed as shown in Figure 8 for two periods (before and after step 21), and the permeability tensor obtained by averaging the permeability field is 1.7 times higher than the initial rock permeability: 5.5 × 10ିଵହ <sup>38</sup> ൗ 0 0 Figure 11 shows the pressure plume development at iso-surface of 3.5*x* MPa after 100, 200, and 300 days of the injection. At the early time, the pressure around the UD−2 is lower than 3.5*x* MPa, and around the UD−1, pressure is higher than 3.5*x* MPa. Therefore, small pressure iso-surfaces around the wells being observed. As time goes on, the pressure near UD−2 increases and near the UD−1 decrease, and the trend of these changes in Figure 11 is clearly obvious. Obviously, with increasing the injection and production flow rates, the plume size increases. Furthermore, due to the higher permeability of the fault zone, pressure changes mainly happen inside the fault zone and two large-scale fractures, which are detected through seismic events. These sharp pressure changes (and consequently the stress changes not discussed in this paper) inside the fault zone requires special attention to examine the possibility of the seismic events.

<sup>0</sup> 1.7 × 10ିଵସ

The obtained permeability field through the UD−1 well data is validated with the hydraulic testing and stimulation data of well UD−2. Figure 9 demonstrates a good match between the operational data and numerical simulation of UD−2 for the first three stages of injection. However, there is a discrepancy between the measured and modeled data, as shown in Figure 6 for 20 November. Based on this figure, the flow rate decreases to zero in the middle of the test and increases afterward. The operational data shows that the injection pressure increases following the initial trend without experiencing an impact due to the intermittent flow rate breaks. The numerical simulation for UD−2, on the contrary, shows that if the flow rate decreases only for a short time interval, pressure decreases for the rest of the entire injection step and does not reach the previous pressure level. The observed low pressure after a short gap in the injection is not due to the permeability change. Rather the pressure diffuses inside the system leading to pressure drop. It, therefore, seems likely that the flow rate stops and pressure drops are rather a measurement error while reporting the pressure and flow rate data or that the wellbore effect [26] between the wellhead and the reservoir section mitigates the flow rate and pressure drops.

<sup>38</sup> ൗ <sup>0</sup>

<sup>38</sup> ൗ <sup>⎦</sup> ⎥ ⎥ ⎥ ⎤

1.7×

⎣ ⎢ ⎢ ⎢ ⎡

**Figure 9.** Matching of the operational and simulation pressure data of the UD−2 hydraulic injection/Stimulation tests to validate the simulated permeability field obtained from the UD−1 operational data. **Figure 9.** Matching of the operational and simulation pressure data of the UD−2 hydraulic injection/Stimulation tests to validate the simulated permeability field obtained from the UD−1 operational data.

It should be noted that these short-term hydraulic stimulation results are restricted to the near wellbore area, and do not influence the far-field of the reservoir. Therefore, uncertainty remains regarding the volume of the reservoir, which is affected by this operation. To examine the near wellbore effect, a cylindrical zone around UD−1 is considered in which the permeability is changed by hydraulic stimulation. Two radii of 25 and 50 m are considered for this zone, and the behavior of the system is modeled at three fluid rates of , 2, and 3 L/s. Figure 10 shows the resulting pressure data on the bottom of the UD−1 and UD−2 based on different flow rates and hydraulically affected area radius. There is no data to show which radius around the wellbore is affected by the hydraulic stimulation. By comparing 25 and 50 m, it is shown that the region size is not important for the studied time periods, but the amount of permeability changes is important. Another model without considering this cylindrical region is run, and the results are different than the operational observations (see Figure 8). This permeability variation importance During the 300 days, the temperature changes are limited near the injection well. Therefore, to examine the effects of different flow rates on the temperature, temperaturechanges alongside the open hole section of the injection well and inside the fault zone are being considered, which is very close to the wellbore in Figure 12 for different flow rates. On the horizontal axis, 0 m shows the top point of the open hole section of the injectionwell, and 300 m shows the bottom point of this section. Initially (0 days in the graphs), thetemperature distribution follows up the temperature gradient of the system. As time goes on, the cold front propagates to the deeper zones of the reservoir. An increase in the flow rate increase the speed of the temperature front propagation in the farther regions, and it shows that the heat transfer process is mainly controlled by the convective mechanism. The possibility of higher fluid injection should be examined through the techno-economic aspects. The increasing flow rate will increase the heat extraction rate at early times. On the other hand, it increases the possibility of seismic events and early breakthrough time [25].

around the production wellbore is not exactly for this studied short time period, but for the long-term operation, authors showed in another study that permeability around the production wellbore is an important factor [26]. Initially, the simulated pressures of the UD−1 are higher than UD−2 due to the hydrostatic pressure. By injecting fluid at UD−2 and producing from UD−1, they experience pressure buildup and drawdown, respectively. Obviously, by increasing the flow rate, the pressure separation between the two wells increases at later times. Pressure changes are greater at early times, and as time goes on, pressure show semi-steady behavior, and the operator can decide regarding the optimal flow rate. For example, for the cases with 25 m of hydraulically stimulated area, the pressure after ten days reaches 4.78, 7.39, and 10.05 MPa with flow rates of , 2, and 3 L/s, respectively, whereas after 150 days it becomes 5.8, 9 and 12.1 MPa respectively. However, there is not much change between 150 and 300 days, where in the latter case, the final pressure values are 6.1, 9.34, and 12.6 MPa for the flow rates of x, 2x, and 3x L/s, respectively. Correspondingly for UD−1, a decreasing trend is observed at a gentle gradient. For the flow rates of , 2, and 3 L/s, observed pressure values after ten days are 4.05, 3.72 and 3.38 MPa, respectively, which becomes 3.38, 2.86 and 2.35 MPa, respectively, after 150 days which finally reaches to 3.08, 2.51 and 1.93 MPa, respectively, after 300 days. This analysis shows that pressure differences between the two wells are 3.02, 6.83, and 10.67 MPa The acid injection may increase the permeability to a higher extent than the hydraulic stimulation. Preliminary studies in the core scale samples from the rocks of this reservoir show a good outcome of the acid injection and the possibility of permeability increase between 4 and 50 times in core-flooding tests, but the autoclave experiments show this increment between 0.1 (this shows that permeability decreases up to the 10 % of the initial value and it explains the possible precipitation which is visible in the microscopic scale) and 40 times [28]. Therefore, we assumed imaginary cases of permeability alteration by ten times, and 100 times in comparison to the initial state due to the possible acid injection process at the reservoir scale using a cylindrically affected region surrounding the wellbore with a radius of 25 m. Figure 13 (left column) shows the results for ten times of the permeability enhancement where the pressure of UD−2 after ten days reaches 2.92*x*, 3.22*x* and 3.51*x* MPa with flow rates of *x*, 2*x* and 3*x* L/s, respectively, whereas after 150 days it becomes 3.6*x*, 3.93*x* and 4.26*x* MPa, respectively. While, there is not much change between 150 and 300 days, where in the latter case, the final pressure values are 3.06*x*, 4*x*, and 43.3*x* MPa for the flow rates of *x*, 2*x*, and 3*x* L/s, respectively. Correspondingly for UD−1, these values are 4.02*x*, 3.96*x*, and 3.9*x* MPa for the flow rates of *x*, 2*x*, and 3*x* L/s. After 150 days, pressure values are 3.32*x*, 3.26*x*, and 3.2*x* MPa, respectively, which becomes 3.34*x*, 3.28*x*, 3.22*x* and 3.22*x* MPa, respectively, after 300 days. Therefore, the pressure difference between the two wells is 0.32*x*, 0.72*x*, and 1.11*x* MPa after 300 days for three flow rates,

*x*, 2*x*, and 3*x* L/s. From this pressure behavior, it is clear that the acidizing process for ten times permeability increment has a great potential to increase the flow rate with a huge decrease in the pressure gradient between the two wells, compared to only hydraulic stimulation. Experimental studies show that this permeability enhancement is attainable at the core level [26]. For the case of 100 times in the permeability enhancement, all flow rates show the same pressure behavior indicating the presence of a highly conductive region between the injection and production wells, which has a significant impact on the pressure gradient. At later times for both permeability enhancement scenarios, the pressure of UD−1 increases, demonstrating the production of injected fluid rather than the production of fluid initially residing in the fault zone. that from an economical point of view, the higher flow rate is attractive, but it may eventuate the seismic events. During the examined period, the radius of the hydraulically stimulated area near the UD−1 has a negligible effect on the pressure profiles in comparison to the flow rate. The pressure differences between the wellbore for a 50 m radius of hydraulically stimulated zone reach 2.97, 6.71, and 10.56 MPa after 300 days for , 2, and 3 L/s injection rates, respectively. Therefore, in the remaining parts, a small radius of 25 m is examined. Similar behavior is recognized by Mahmoodpour et al. [26] that the permeability field in the vicinity of the production well is an important factor.

after 300 days for three flow rates, , 2, and 3 L/s, respectively. It is interesting to note

region that spans over 25 m, whereas it is 50 m for the right panel.

*Geosciences* **2022**, *12*, x FOR PEER REVIEW 15 of 20

**Figure 10.** Simulated pressures at the injection and production wells for injection flow rate of (**a1**, **a2**) L/s, (**b1**, **b2**) 2 L/s and (**c1**, **c2**) 3 L/s. The left panels are plotted for a hydraulically stimulated **Figure 10.** Simulated pressures at the injection and production wells for injection flow rate of (**a1**,**a2**) *x* L/s, (**b1**,**b2**) 2*x* L/s and (**c1**,**c2**) 3*x* L/s. The left panels are plotted for a hydraulically stimulated region that spans over 25 m, whereas it is 50 m for the right panel.

Figure 11 shows the pressure plume development at iso-surface of 3.5 MPa after 100, 200, and 300 days of the injection. At the early time, the pressure around the UD−2 is lower than 3.5 MPa, and around the UD−1, pressure is higher than 3.5 MPa. Therefore, small pressure iso-surfaces around the wells being observed. As time goes on, the pressure near UD−2 increases and near the UD−1 decrease, and the trend of these changes in Figure 11 is clearly obvious. Obviously, with increasing the injection and production flow rates, the plume size increases. Furthermore, due to the higher permeability of the fault zone, pressure changes mainly happen inside the fault zone and two large-scale fractures, which are detected through seismic events. These sharp pressure changes (and consequently the stress changes not discussed in this paper) inside the fault zone requires spe-

cial attention to examine the possibility of the seismic events.

*Geosciences* **2022**, *12*, x FOR PEER REVIEW 16 of 20

**Figure 11.** Pressure plume development for three different injection rates at three different times. The iso-surfaces are plotted for 3.5 MPa. **Figure 11.** Pressure plume development for three different injection rates at three different times. The iso-surfaces are plotted for 3.5*x* MPa. *Geosciences* **2022**, *12*, x FOR PEER REVIEW 17 of 20

During the 300 days, the temperature changes are limited near the injection well.

**Figure 12.** Simulated temperature alongside the open hole section of the injection well UD−2 for the injection flow rates (**a**) L/s, (**b**) 2 L/s, and (**c**) 3 L/s. The arc length is measured from the top of the open hole section of the well that falls inside the Porthtowan Fault zone. **Figure 12.** Simulated temperature alongside the open hole section of the injection well UD−2 for the injection flow rates (**a**) *x* L/s, (**b**) 2*x* L/s, and (**c**) 3*x* L/s. The arc length is measured from the top of the open hole section of the well that falls inside the Porthtowan Fault zone.

The acid injection may increase the permeability to a higher extent than the hydraulic stimulation. Preliminary studies in the core scale samples from the rocks of this reservoir show a good outcome of the acid injection and the possibility of permeability increase between 4 and 50 times in core-flooding tests, but the autoclave experiments show this

and 40 times [28]. Therefore, we assumed imaginary cases of permeability alteration by ten times, and 100 times in comparison to the initial state due to the possible acid injection process at the reservoir scale using a cylindrically affected region surrounding the wellbore with a radius of 25 m. Figure 13 (left column) shows the results for ten times of the permeability enhancement where the pressure of UD−2 after ten days reaches 2.92, 3.22 and 3.51 MPa with flow rates of , 2 and 3 L/s, respectively, whereas after 150 days it becomes 3.6, 3.93 and 4.26 MPa, respectively. While, there is not much change between 150 and 300 days, where in the latter case, the final pressure values are 3.06, 4, and 43.3 MPa for the flow rates of , 2, and 3 L/s, respectively. Correspondingly for UD−1, these values are 4.02, 3.96, and 3.9 MPa for the flow rates of , 2, and 3 L/s. After 150 days, pressure values are 3.32, 3.26, and 3.2 MPa, respectively, which becomes 3.34, 3.28, and 3.22 3.22 MPa, respectively, after 300 days. Therefore, the pressure difference between the two wells is 0.32, 0.72, and 1.11 MPa after 300 days for three flow rates, , 2, and 3 L/s. From this pressure behavior, it is clear that the acidizing process for ten times permeability increment has a great potential to increase the flow rate with a huge decrease in the pressure gradient between the two wells, compared

**Figure 13.** Simulated pressures at the injection and production wells for the injection flow rate of (**a1**, **a2**) L/s, (**b1**, **b2**) 2 L/s, and (**c1**, **c2**) 3 L/s after the permeability enhancement through the considered chemical stimulation. The left column shows a permeability enhancement by a factor of 10, and the right column shows a permeability enhancement by a factor of 100 with respect to the initial values. **Figure 13.** Simulated pressures at the injection and production wells for the injection flow rate of (**a1**,**a2**) *x* L/s, (**b1**,**b2**) 2*x* L/s, and (**c1**,**c2**) 3*x* L/s after the permeability enhancement through the considered chemical stimulation. The left column shows a permeability enhancement by a factor of 10, and the right column shows a permeability enhancement by a factor of 100 with respect to the initial values.

to only hydraulic stimulation. Experimental studies show that this permeability enhancement is attainable at the core level [26]. For the case of 100 times in the permeability enhancement, all flow rates show the same pressure behavior indicating the presence of a highly conductive region between the injection and production wells, which has a significant impact on the pressure gradient. At later times for both permeability enhancement scenarios, the pressure of UD−1 increases, demonstrating the production of injected fluid

rather than the production of fluid initially residing in the fault zone.

#### **4. Conclusions 4. Conclusions**

In this study, hydraulic injection testing/stimulation operations for both the wells of UDDGP are numerically simulated. Results are used to characterize the permeability field of the system and examine pressure development based on different injection flow rates. Results show that pressure changes are occurring primarily in the early time, with later time showing a semi-steady pressure increase. With the current permeability field after the hydraulic stimulation operation, huge pressure differences develop by increasing the flow rates. The possible effect of chemical stimulation operation on the permeability is considered through the data obtained from the lab-scale models, and reservoir response after the permeability modification is numerically simulated. Results for the permeability enhancement of the 10-time compared to the initial value due to the chemical stimulation (it is attainable as shown by experiments) enable us to triple the flow rate with one-third of the initial pressure difference without chemical stimulation. The reported values and In this study, hydraulic injection testing/stimulation operations for both the wells of UDDGP are numerically simulated. Results are used to characterize the permeability field of the system and examine pressure development based on different injection flow rates. Results show that pressure changes are occurring primarily in the early time, with later time showing a semi-steady pressure increase. With the current permeability field after the hydraulic stimulation operation, huge pressure differences develop by increasing the flow rates. The possible effect of chemical stimulation operation on the permeability is considered through the data obtained from the lab-scale models, and reservoir response after the permeability modification is numerically simulated. Results for the permeability enhancement of the 10-time compared to the initial value due to the chemical stimulation (it is attainable as shown by experiments) enable us to triple the flow rate with one-third of the initial pressure difference without chemical stimulation. The reported values and the reservoir characterization performed during this study will build a basis for future numerical simulations for the United Down geothermal site.

**Author Contributions:** Conceptualization, S.M., M.S. and K.B.; methodology, S.M. and M.S.; software, S.M. and M.S.; validation, S.M. and M.S. writing—original draft preparation, S.M., M.S., C.O. and S.K.T.; writing—review and editing, J.R. and K.B.; visualization, S.M., M.S. and C.O.; supervision, K.B. and I.S.; project administration, K.B. and I.S.; funding acquisition, K.B. and I.S. All authors have read and agreed to the published version of the manuscript.

**Funding:** The work is conducted as part of the MEET project that has received funding from the European Union's Horizon 2020 research and innovation program under grant agreement No 792037.

**Data Availability Statement:** Due to the confidential nature of the field data, the exact units of the data are hidden.

**Acknowledgments:** Group of Geothermal Science and Technology, Institute of Applied Geosciences, Technische Universität Darmstadt has provided institutional support to the authors. The authors would like to acknowledge Geothermal Engineering Limited (Ryan Law and Hazel Farndale) for providing the well-testing data for the hydraulic stimulation operations conducted from September 2020 until February 2021. Additionally, we would like to thank two anonymous reviewers for their helpful and constructive remarks, which greatly helped to improve the manuscript. Additionally, we would like to acknowledge Golder Associate Inc for providing academic licenses of FracMan v7.

**Conflicts of Interest:** The authors declare no conflict of interest.

## **References**


## *Article* **Use of Analogue Exposures of Fractured Rock for Enhanced Geothermal Systems**

**D. C. P. Peacock 1,2,\*, David J. Sanderson <sup>3</sup> and Bernd Leiss 1,2**


**Abstract:** Field exposures are often used to provide useful information about sub-surface reservoirs. This paper discusses general lessons learnt about the use of deformed Devonian and Carboniferous meta-sedimentary rocks in the Harz Mountains, Germany, as analogues for a proposed enhanced geothermal reservoir (EGS) at Göttingen. The aims of any analogue study must be clarified, including agreeing with people from other disciplines (especially reservoir modellers) about the information that can and cannot be obtained from surface exposures. Choice of an analogue may not simply involve selection of the nearest exposures of rocks of a similar age and type, but should involve consideration of such factors as the quality and geological setting of the analogue and reservoir, and of any processes that need to be understood. Fieldwork should focus on solving particular problems relating to understanding the EGS, with care being needed to avoid becoming distracted by broader geological issues. It is suggested that appropriate questions should be asked and appropriate analyses used when planning a study of a geothermal reservoir, including studies of exposed analogues.

**Keywords:** exposed analogue; enhanced geothermal system; fractures

### **1. Introduction**

Rock exposures are commonly used as analogues to understand and make predictions about sub-surface geology. Exposed analogues have been used for a range of applications, including in the geothermal (e.g., [1]), mining (e.g., [2]), petroleum (e.g., [3]), hydrogeology (e.g., [4]), nuclear waste disposal (e.g., [5]) and carbon sequestration (e.g., [6]) industries. Many of these applications require understanding or prediction of fluid flow in the subsurface, which may be either through pores or through fractures within the rock.

Use of exposed analogues is relatively simple in cases in which there are not significant differences between rocks at the surface and sub-surface. For example, sedimentological analogues relate to depositional processes. While compaction and diagenesis during burial may produce changes in the fabrics and thicknesses of sedimentary rocks, the arrangement of depositional facies are largely unchanged. This means that sequence stratigraphy (e.g., [7]), building on simple principles such as Steno's "Law of Superposition" (e.g., [8]) and Walther's "Law of Facies Adjacency" (e.g., [9]) still apply. Sedimentary analogues are therefore routinely used to understand sub-surface sedimentary and reservoir geology (e.g., [10]). Exposed analogues can be useful to study aspects of structural geology that are not affected by significant changes as the rocks are exhumed. For example, exposed analogues have been used to analyse fault geometries, kinematics and mechanics (e.g., [11]), and to characterise vein networks (e.g., [12]). There are, however, problems in using exposed analogues in situations where there are significant changes to key aspects of the structural geology as the rocks are exhumed (e.g., [13]). This is particularly the case with

**Citation:** Peacock, D.C.P.; Sanderson, D.J.; Leiss, B. Use of Analogue Exposures of Fractured Rock for Enhanced Geothermal Systems. *Geosciences* **2022**, *12*, 318. https://doi.org/10.3390/ geosciences12090318

Academic Editors: Ronan L. Hébert, Ghislain Trullenque, Albert Genter, Eléonore Dalmais and Jean Hérisson

Received: 30 June 2022 Accepted: 25 August 2022 Published: 26 August 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

joints, which are commonly created during exhumation (e.g., [14]). This means that joints seen at the surface do not necessarily occur in the sub-surface.

This paper describes lessons we have learnt, while undertaking an analogue study in the Harz Mountains as part of the EU-Horizon project MEET (Multidisciplinary and multicontext demonstration of Enhanced Geothermal Systems exploration and Exploitation Techniques and potentials). MEET was aimed at developing cost-effective techniques for Enhanced Geothermal Systems (EGS) in a variety of geological settings across Europe. The western Harz Mountains were selected as an analogue for a proposed EGS project at Göttingen (Lower Saxony, Germany), where the reservoir rocks are expected to be folded and thrusted Devonian and Carboniferous metasedimentary rocks. EGS involves stimulation, which is the artificial increase in fluid flow through the reservoir rocks. Our fieldwork therefore focussed on collecting structural data that would help model the effects of hydraulic [15] and thermal stimulation on the Devonian and Carboniferous rocks beneath Göttingen. During the MEET project, we attempted to use analogue exposures of fractures constrain flow models and make predictions about enhanced geothermal systems.

The aim of this paper is to pass on our experiences and the knowledge gained. While scientific papers tend to highlight successes, here we pass on some of the problems we encountered, lessons we learnt and advice on how to avoid such problems.

#### **2. Rationale for Using the Harz Mountains as an Analogue**

This section explains the rationale behind the use of the Harz Mountains as an analogue for the proposed EGS at Göttingen, gives an introduction to the geology of the region, and compares the analogue with the sub-surface geology we expect at Göttingen. In the absence of well data and with limited seismic data for the sub-Zechstein rocks, the rocks beneath the Permian Zechstein evaporites at Göttingen must be predicted. Devonian quartzitic sandstones and slates, and Carboniferous greywackes and slates (predominantly Culm flysch deposits) are exposed in the western Harz Mountains ~40 km to the NE and in the Rhenish Massif ~70 km to the SW (e.g., [16–18]), as shown in Figure 1. We have selected analogue sites in the Oberharz Anticline and the Culm Fold Zone, which belong to the parautochthonous domain of the Harz Mountains (e.g., [19]) because we consider these to be areas to have the best exposures of the sub-Zechstein rocks that are most likely to occur beneath Göttingen [20].

The Devonian and Carboniferous rocks of the region are part of the Variscan foldthrust belt (e.g., [21]). Later deformation events in the region include Late Cretaceous and Cenozoic uplift and exhumation in the Harz Mountains (e.g., [22]) and Cenozoic rifting in the Göttingen area (the Leinetal Graben, e.g., [23]). The fractures visible in the exposures of the Harz Mountains include veins and joints [24,25], with cleavage being well-developed in the slates [26]. Thrusts that appear to have displacements of up to a few metres are exposed [27], but larger thrusts are not well-exposed. The north-eastern boundary the Harz Mountains is marked by the Harznordrand Fault, which was active during the Late Cretaceous and Tertiary (e.g., [28]). NW-SE striking Mesozoic normal and oblique-slip faults occur in the Harz Mountains, some of which contained economic Pb-Zn and Ba-F deposits [29].

Table 1 shows seven key parameters that control deformation of rocks and our predictions for the Variscan rocks that occur beneath Göttingen. Table 1 also includes comments on what can and cannot be learnt from the Harz Mountains. While the exposed analogues give useful information about lithologies, the conditions that existed during the Variscan Orogeny and about Variscan structures, they tend to give less information about subsequent conditions and deformation. For example, it is difficult to determine absolute ages of joints and to determine the tectonic conditions under which they formed. Differences between the rocks exposed in the Harz Mountains and those at a depth of more than 1.5 km beneath Göttingen include:

1. The Göttingen area has undergone post-Variscan rifting (the Leinetal Graben) and still has a cover sequence of Permian and Triassic sedimentary rocks about 1.5 km thick. The Harz Mountains, however, have undergone several kilometres of exhumation since the Late Cretaceous and have been fully exhumed (i.e., there is no cover sequence).


**Figure 1.** Geological map showing the location of the Harz Mountains, where the exposed Devonian and Carboniferous rocks are used as an analogue for a proposed EGS at Göttingen. Additionally, shown is the Rhenish Massif, which also shows exposures of Devonian and Carboniferous rocks. Göttingen along strike of the Variscan belt between the Harz Mountains and the Rhenish Massif. The dominant lithologies are as follows. Lower Palaeozoic, Devonian and Carboniferous: metasedimentary sandstones, slates and carbonates. Permian: sandstones, marls and evaporites. Mesozoic: shales, sandstones and limestones. Cenozoic: unconsolidated siliciclastic sediments. Data source: GK1000© BGR, Hannover, 2013. Downloaded on 6 June 2022, from https://gdk.gdi-de.org/geonetwork/srv/api/records/5f77d681-b7e4-4dd0-8f15-7b93744450b0.

**Table 1.** Key parameters that control rock deformation with predictions for the Variscan rocks beneath Göttingen and comments on what can and cannot be learnt from the exposed analogues in the Harz Mountains. For a list of parameters to be characterised in a geothermal reservoir, see [30].



#### **Table 1.** *Cont.*

### **3. Lessons Learnt about the Use of Analogues**

We experienced the following problems and learnt the following lessons about the use of analogues for fractured geothermal reservoir rocks during the course of the MEET project.

#### *3.1. Aims of Using an Exposed Analogue*

A problem we had with the fieldwork in the Harz Mountains arose because it was undertaken for several different reasons. Although at the start of the project the aim was to develop a numerical model for fluid flow through the rocks [31], various other aims were introduced. These included: to create general and conceptional structural models for the Harz Mountains, to determine the histories of deformation and fluid flow, to make predictions about the sub-surface at Göttingen, and to provide data that could be used by colleagues to perform discrete fracture network (DFN) modelling of fluid flow in the sub-surface. While these different aims were not necessarily conflicting, they did lead to some confusion in deciding what types of structures were important to analyse, how best to analyse them, and what data were needed. For example, one of the methods used was to map traces of veins, joints and other fractures exposed on rock surfaces to provide inputs into DFN models. We realised, however, that these maps lacked vital information that would enable realistic DFN models for the sub-surface at Göttingen to be created (Section 3.3), although they did help us interpret the histories of deformation and fluid flow in the Harz Mountains.

A study of an exposed analogue needs to be set up carefully, including definition of the problems being addressed and the aims of the work. These aims then need to be translated into specific objectives, with careful consideration of the priorities of each, determination of the data needed, and establishment of the appropriate methods. It is also important to keep evaluating the work, to determine whether the approach is working, and to make changes as needed. General questions that may typically be asked about a potential exposed analogue include:


• Is there information about active fluid flow in the sub-surface, such as evidence of hydrothermal fluids in spring water?

An important lesson from our fieldwork in the Harz Mountains was not just that we needed to be clear at the start of the work what problems were being addressed, but that we needed to frequently review our progress in solving (and ability to solve) those problems and be prepared to adjust the approaches used.

#### *3.2. Choice of Exposed Analogue*

The Harz Mountains were an obvious choice for an analogue study because similar rocks are expected to occur in the sub-surface at Göttingen and are likely to have similar structures and deformation histories (Section 2 and Table 1). Furthermore, geographical proximity meant that long journeys and overnight accommodation were not needed for fieldwork. There are, however, two main problems with the Harz Mountains as an analogue study area. Firstly, the exposure quality is commonly poor, being restricted to steep roadcuts, abandoned quarries and natural exposures that are typically up to a few tens of metres long and a few metres high. Many of the best exposures are cliff faces formed by the dominant set of joints, which are steeply dipping and strike at a high angle to the Variscan folds, thrusts and cleavage. While these exposure surfaces are ideal for analysing the Variscan structures, they are poor for analysing the fracture networks, especially the joint systems, because it is difficult to analyse those structures in three dimensions. Secondly, while the Harz Mountains have undergone several kilometres of exhumation since the Late Cretaceous, the Göttingen area is in a Late Cretaceous and Cenozoic rift and has undergone far less exhumation (Table 1). Both areas, however, underwent post-Variscan, pre-Zechstein exhumation.

Lessons learnt about the choice of field areas from use of the Harz Mountains include the following:


observations could have been made on slates in other regions. Indeed, observations from a range of slates of different compositions, of different ages and subjected to different deformation histories, are likely to have improved knowledge about the reservoir properties of slates, thereby improving predictions for the sub-surface of Göttingen.

**Figure 2.** Photograph of a syncline in Upper Palaeozoic slates at Schulenberg im Oberharz, Harz Mountains, Germany. Most of the exposure surface is defined by a set of steeply dipping joints that strike at a high angle to the fold.

#### *3.3. What Exposed Analogues Can and Cannot Tell You*

One of the main aims of the fieldwork in the Harz Mountains was to provide data about fracture networks and their relationships to folds to create a conceptual model that could be used in DFN modelling to predict fluid flow rates in the sub-surface at Göttingen. Such modelling requires such data as the in situ stresses as well as the apertures and connectivities of open fractures in the sub-surface (e.g., [33]). This information cannot be provided from rocks exposed at the surface. For example, joints commonly develop during exhumation (e.g., [34]), with the apertures, frequencies, sets and patterns of joints seen at the surface not necessarily being the same as those at reservoir depths. While the joints analysed in the Harz Mountains may give some indications about open fractures in the sub-surface at Göttingen, such as whether open fractures may be expected to occur in slates, they did not provide sufficient information about sub-surface fractures to enable meaningful DFN modelling to be undertaken.

Exposed analogues may provide information about such characteristics of sub-surface geology as lithologies, the geometries and kinematics of certain structures (e.g., folds, faults, veins), the histories of deformation and fluid flow, and aspects of mechanical behaviour (e.g., mechanical stratigraphy). Exposed analogues cannot, however, provide with much certainty information that is important for reservoir modelling, such as the presence and geometries of open fractures, fracture porosity, stresses, temperatures and fluid flow. Some certainty about conditions in the sub-surface will only be obtained when well data become available.

Fieldwork in the Harz Mountains, and our subsequent attempts to use the data to make predictions about the sub-surface geology at Göttingen taught us the importance of understanding what you can and cannot do with field data, and of conveying that information clearly to other people who may rely on those data. Both field geologists and reservoir modellers need to be aware of the limitations of field data, as to be aware of the uncertainty limitations of subsequent models. We found that field data are useful for developing initial models and for testing concepts (e.g., [35]), and we used data and observations from the field to make simple predictions about the effects of hydraulic stimulation in the potential geothermal reservoir rocks at Göttingen [15].

An important consideration in the comparison between an exposed analogue and a reservoir is that they have different histories, especially their burial and exhumation histories. Many of the structures that occur in the surface exposures in the Harz Mountains that are likely to be important in a geothermal reservoir at Göttingen probably post-date the Variscan Orogeny. These include the joints, many of which are likely to have been caused by exhumation (e.g., [36]). Such differences must be considered when comparing an exposed analogue with a reservoir.

#### *3.4. Avoid Distracting Topics*

Fieldwork in the Harz Mountains taught us the importance of focussing on the key aims of the study and of being careful to avoid spending too much time on by other interesting topics. Two aims of the project were: (1) discovering the ways and methods to use an exposed analogue for predicting the properties of enhanced geothermal systems, and (2) to use the exposures in the Harz Mountains to help us predict the characteristics and behaviour of the reservoir rocks beneath Göttingen. Fieldwork often leads to new, unexpected discoveries, and these should not be ignored. It is important, however, that such discoveries do not cause too much distraction from the aims of the field study. We were occasionally distracted by discussions about Variscan tectonics, which were not directly related to the aims of the fieldwork but did lead us towards new research projects. While an academic environment provides freedom to follow new ideas and research interests, it is still important to do the work expected by academic partners and by funding bodies. The need to stay focused on solving particular problems is more intense in industry, where managers and clients will expect particular outcomes from a study.

While the Harz Mountains were selected as an analogue because they show similar rocks and structures that are expected to occur beneath Göttingen, and these were compared with exposures in the Rhenish Massif, a more distant analogue site could have been selected, for example if the more distance analogue has better exposure. Key factors to consider in the choice of an analogue site include how well the lithologies and structures match the geothermal reservoir, and the quality of the exposure. As such, the ages of the rocks and of the deformation may be irrelevant.

#### *3.5. Use of the Term "Fracture"*

Our work in the Harz Mountains, and the subsequent attempts to use this work to make predictions about the sub-surface at Göttingen, showed the importance of specifying fracture types in the field. Reservoir modellers commonly use the general term "fracture", and often do not distinguish between faults, veins, joints and other types of fracture. When field geologists also use "fracture", they cannot properly understand the geometries, age relationships, tectonics, mechanics and fluid flow histories of the rocks and the fractures they contain [37,38]. Different fracture types have different origins, distributions and properties, hence different significance in predicting the engineering behaviour of a reservoir. For example, veins are fractures that are partly or completely sealed by minerals, while joints are not mineralised (Figure 3). Thus, veins will tend to have greater mechanical cohesion and are less likely to be conduits for present-day fluid flow, than joints. Veins also tend to be clustered, such as in fold hinges (e.g., [39]) and around faults (e.g., [40]), whilst joints tend to be more widely distributed in a rock mass (e.g., [41,42]). Such differences have significance for the properties of an EGS and on the ways the reservoir rocks respond to stimulation. Merging these different types of structures together as "fractures" during initial fieldwork in the Harz Mountains meant that important interpretations about the histories and significance of those structures could not be made.

**Figure 3.** Photographs of different types of "fractures" in the Harz Mountains. (**a**) Partly filled quartz vein in a sandstone, which resulted from and gives information about palaeo fluid flow. The vein was either never completely cemented or has been subjected to weathering. The quartz will hinder present-day fluid flow through the vein. (**b**) Joints in sandstones and slates. Veins are (by definition) not mineralised, so are potential pathways for present-day fluid flow in the sub-surface.

Whilst geologists are generally well-aware of the significance of different types of fracture, engineers are more likely to think of a fracture simply as a surface across which the rock mass may lose cohesion or frictional resistance. To a reservoir engineer, a fracture may assume the role of a large void that facilitates fluid flow. A major problem occurs when these different groups start to communicate referring to everything as a "fracture", mainly in the interest of finding a common language. In the MEET project, geologists investigating faults, veins, joints and other types of fracture would present their field data as measurements of the geometries and topologies of "fractures". This can easily result in vein data being used to estimate fluid flow in DFNs (i.e., treated as "open" fractures, modelled by flow between parallel plates; see Section 3.7).

#### *3.6. Palaeo Fluid Flow vs. Present-Day Fluid Flow*

The fieldwork in the Harz Mountains taught us the importance of differentiating between studies of palaeo fluids and studies to make predictions about present-day fluid flow. This issue is related to use of the term "fracture" (Section 3.5), because the minerals within veins tend to give information about palaeo fluid flow (e.g., [43]), while knowledge about joints and other open fractures helps in predicting present-day fluid flow (Figure 3). For example, while the maps of fracture traces we created (Section 3.1) turned out to be of little use for DFN modelling, they did provide a basis for understanding the palaeo fluid flow through veins and the potential for present-day fluid flow through joints.

When the aims of the fieldwork are decided, it is important to study the appropriate fractures using appropriate methods. For example, a study of an ancient hydrothermal system should focus on veins and the minerals they contain, while a study to predict present-day fluid flow would tend to focus on joints and other open fractures.

#### *3.7. Understanding the Needs of Other Disciplines*

One of the original aims of the fieldwork in the Harz Mountains (and of other analogue areas used in the MEET project) was to obtain field data that could be used to create models to predict fluid flow in the sub-surface. A particular problem, however, was that the field geologists were not able to collect key data that the modellers, who were not geologists, needed to make realistic DFN models (Section 3.3). Such data included information about the apertures and connectivities of open fractures (e.g., joints) in the sub-surface. This led to mutual frustration. It is therefore important that field geologists are clear about what can and cannot be learnt from analogues, including what data can be collected. Another problem was that the field geologists would use terminology that the reservoir modellers did not understand and vice versa. An example of such miscommunication was the use of "fracture" by the reservoir modellers to mean a discontinuity along which fluids can flow in the present-day, while the geologists would use the term for any brittle discontinuity, regardless of the potential for fluid flow (Section 3.5). For example, if a field geologist reports an abundance of veins with apertures of 1–10 mm, this does not justify a modeller using open fractures with apertures of 1–10 mm in a DFN model.

Lessons from our experience of working with reservoir modellers to make predictions about the sub-surface at Göttingen include: (1) it is important to understand the data they need to develop their models; (2) modellers must be informed about what data can and cannot be provided from field data, and this should include information about the uncertainties in the field data; (3) a common understanding of the terms used by both geologists and non-geologists must be established.

#### **4. Integration of Exposed Analogues in the Analysis of Geothermal Reservoirs**

This section discusses how exposed analogue studies may be best integrated in the analysis of geothermal reservoirs.

#### *4.1. Improved Understanding of the Contribution of Exposed Analogue Studies*

The starting point of any scientific study is generally a question or problem that needs to be solved. The initial aims of the use of exposed analogues in the MEET project are described by [31]. Table 2 shows some of the questions that should be asked when setting up a study, either of a geothermal reservoir or an exposed analogue, along with elements that need to be considered in such studies. It also shows how exposed analogues may help answer those questions. Table 2 aims to show the importance of deciding what problems are to be addressed and determining the appropriate ways to solve those problems. We suggest four steps in determining how best to use an exposed analogue:


**Table 2.** Examples of questions that should be asked when planning a study of a geothermal reservoir or of an exposed analogue. Additionally, shown are typical elements that need to be considered and comments about how exposed analogues can be used to study these elements.


#### *4.2. Modelling Techniques*

As discussed in Section 3.3, exposed analogues cannot provide some information that reservoir modellers may need to create realistic DFN models. To make predictions about the sub-surface at Göttingen before well data are available, we therefore had to use modelling techniques. We used Mohr diagrams with realistic ranges of input parameters (mostly using data from the exposed analogues in the Harz Mountains) to make predictions about how the Devonian and Carboniferous rocks expected to occur beneath Göttingen will respond to stimulation [15]. Modelling techniques need to be used that are suited to answering the right questions at early stages of geothermal assessment, and that are feasible based on the data available at the pre-drilling stage.

#### *4.3. Ranges and Variabilities of Parameters*

The modelling approach we used to predict the response of rocks in the sub-surface at Göttingen used information obtained from the exposed analogues in the Harz Mountains (Section 4.2; [15]). This included information about the ranges and variabilities of such factors as rock mechanical properties and the geometries of structures (e.g., folds, veins and joints). Exposed analogues are therefore useful for providing realistic ranges of input parameters for modelling. In our experience, non-geologists tend to want a single value or answer for any given parameter. Exposed analogues are therefore particularly useful for informing people from other disciplines (such as reservoir modellers and drilling engineers) about such geological variabilities.

#### *4.4. Knowledge Transfer*

Another way exposed analogues can be used in the analysis of geothermal reservoirs is in improved communication and knowledge transfer between scientists from different disciplines (e.g., between geologists, reservoir modellers and drilling engineers). Discussions about exposed analogues, especially when undertaken in the field, can help geologists and non-geologists appreciate potential and actual links between surface and sub-surface geology, and between geology and other disciplines. Exposed analogues can be used to help answer a series of key questions, such as:


Expressing a model purely in terms of black-box equations will not usually help a geologist understand what the model does or how different parameters are used. Similarly, field data fed to modellers needs to be accompanied by information that captures potential factors that are important in its use (e.g., "open" vs. "closed" fractures, scale ranges over which data were collected).

#### **5. Discussion of Other Uses of Analogue Exposures of Fractured Rock**

Although we have used exposures in the Harz Mountains as analogues to make predictions about a proposed EGS, our experiences can give useful insights into the use of exposed analogues for other situations in which it may be important to predict fluid flow through fractures in the sub-surface. This includes use of analogues for studies on other types of geothermal systems (e.g., [44]), hydrogeology (e.g., [45]), nuclear waste storage (e.g., [46]), CO<sup>2</sup> sequestration (e.g., [47]), mineral extraction (e.g., [48]), and petroleum resources (e.g., [49]). Any study using analogues has to be carefully planned and focussed so that specific questions about the sub-surface can be answered. The fieldwork must be of use to, and understandable by end-users from other disciplines.

As discussed in Section 3.3, it is important to understand what can and cannot be learnt from exposed analogues, and this will change based on the intended use of the analogue. For example, if the fieldwork is to collect information about veins that formed during particular time periods or tectonic events, then this information is likely to be directly applicable to understanding those vein systems that occur in the sub-surface (e.g., [50]). Note that certain minerals can be utilised for chemical stimulation (e.g., [51]). More care is needed, however, if the exposed analogue is used to map joint systems for direct use in DFN models of the sub-surface, especially if those joints formed during exhumation. For example, while the Devonian and Carboniferous rocks beneath Göttingen may have joints related to exhumation during and immediately after the Variscan Orogeny, they are less likely than the Harz Mountains to have joints related to Late Cretaceous and Cenozoic exhumation. Joints exposed at the surface may therefore not equate in a simple way to open fractures in the sub-surface.

## **6. Conclusions**

While exposed analogues can provide critical information that can be used to make predictions about the sub-surface, including the behaviour of enhanced geothermal systems (EGS), care is needed in planning and executing fieldwork. We highlight key learning gained during our use of the Harz Mountains (Germany) as an analogue for an EGS at Göttingen, which will be applicable to studying analogues elsewhere:


We make several suggestions for how studies of exposed analogue studies can be better integrated into the analysis of geothermal reservoirs:


While we focus on the use of exposed analogues for EGS, much of this paper is applicable to other situations in which it is important to make predictions about fluid flow in the sub-surface. For example, understanding the behaviour of rocks, the structures within those rocks and their effects on fluid flow is vital to nuclear waste storage, CO<sup>2</sup> sequestration, hydrogeology and the petroleum industry. In each of these applications, an appropriate exposed analogue should be studied in suitable ways to answer key questions that will enable predictions to be made about the sub-surface.

**Author Contributions:** Conceptualization, D.C.P.P., D.J.S. and B.L.; methodology, D.C.P.P., D.J.S. and B.L.; validation, D.C.P.P., D.J.S. and B.L.; resources, B.L.; data curation, B.L.; writing—original draft preparation, D.C.P.P.; writing—review and editing, D.J.S. and B.L.; supervision, B.L.; project administration, B.L.; funding acquisition, B.L. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work has received funding from the European Union's Horizon 2020 research and innovation programme (grant agreement No. 792037-MEET Project).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** No new data were created or analysed in this study. Data sharing is not applicable to this article.

**Acknowledgments:** Carl-Heinz Friedel is thanked for his helpful advice and discussions. We thank Paolo Pace and two anonymous reviewers for their helpful comments.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


## *Article* **Long-Term Evolution of Fracture Permeability in Slate: An Experimental Study with Implications for Enhanced Geothermal Systems (EGS)**

**Chaojie Cheng 1,\* , Johannes Herrmann <sup>2</sup> , Bianca Wagner 3,4, Bernd Leiss 3,4 , Jessica A. Stammeier <sup>1</sup> , Erik Rybacki <sup>1</sup> and Harald Milsch <sup>1</sup>**


**Citation:** Cheng, C.; Herrmann, J.; Wagner, B.; Leiss, B.; Stammeier, J.A.; Rybacki, E.; Milsch, H. Long-Term Evolution of Fracture Permeability in Slate: An Experimental Study with Implications for Enhanced Geothermal Systems (EGS). *Geosciences* **2021**, *11*, 443. https:// doi.org/10.3390/geosciences11110443

Academic Editors: Béatrice A. Ledésert, Ronan L. Hébert, Ghislain Trullenque, Albert Genter, Eléonore Dalmais, Jean Hérisson and Jesus Martinez-Frias

Received: 30 September 2021 Accepted: 26 October 2021 Published: 28 October 2021

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**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

**Abstract:** The long-term sustainability of fractures within rocks determines whether it is reasonable to utilize such formations as potential EGS reservoirs. Representative for reservoirs in Variscan metamorphic rocks, three long-term (one month each) fracture permeability experiments on saw-cut slate core samples from the Hahnenklee well (Harz Mountains, Germany) were performed. The purpose was to investigate fracture permeability evolution at temperatures up to 90 ◦C using both deionized water (DI) and a 0.5 M NaCl solution as the pore fluid. Flow with DI resulted in a fracture permeability decline that is more pronounced at 90 ◦C, but permeability slightly increased with the NaCl fluid. Microstructural observations and analyses of the effluent composition suggest that fracture permeability evolution is governed by an interplay of free-face dissolution and pressure solution. It is concluded that newly introduced fractures may be subject to a certain permeability reduction due to pressure solution that is unlikely to be mitigated. However, long-term fracture permeability may be sustainable or even increase by free-face dissolution when the injection fluid possesses a certain (NaCl) salinity.

**Keywords:** fracture; permeability; fluid–rock interactions; slate; temperature; time-dependent; pressure solution; dissolution

## **1. Introduction**

Geothermal energy is ubiquitous at a certain depth of the Earth's crust and may provide great potential to meet the energy demand [1]. To utilize such hot formations for district heating or electricity generation, a sufficient amount of fluid needs to be injected and extracted into/from the reservoirs. Therefore, high hydraulic conductivity of the reservoir determines the success and economic efficiency of such utilization. However, often deep hot reservoirs are of low or no hydraulic conductivity, and thus need to be stimulated to increase their permeability by creating new fracture networks or by activating pre-existing fractures, denoted as Enhanced Geothermal Systems (EGS) [2]. Sustainable fractures, acting as the main pathways for fluid flow, are most important in this context.

Fracture permeability changes associated with, e.g., effective stress, fracture surface roughness, fracture offset/shear displacement, and the mechanical properties of the rock matrix have been widely investigated in experiments e.g., [3–11]. Such short-term experiments mainly focused on the stress-dependent permeability variation to shed light on the critical factors (e.g., shear displacement, surface roughness, mechanical properties of the

reservoir rock) that determine the sustainability of fracture permeability. Most rock fractures, once created, are always conductive for fluid flow and difficult to close completely by mechanical loading [11,12], which is favorable for EGS. However, a decline in fracture permeability with time has been observed in the field and in laboratory experiments. For example, the productivity index of the geothermal reservoir in Groß Schönebeck, Germany, decreased by about one order of magnitude within two and a half years [13], which was believed to be induced by fluid–rock interactions [14]. Time-dependent fracture permeability reduction in core samples under constant pressure and temperature conditions was also documented in some previous studies e.g., [4,8,15–18], including various rock types, such as novaculite [15,17], granite [4,19–21], shale [21,22], limestone [16], dolomitic anhydrite [18], sandstone, and mudstone [23].

Typically, such permeability reduction occurs at the early stage of an experiment after pressure build-up and progressively towards a steady state with time. The mechanisms governing the fracture permeability evolution are expected to be an interplay of pressure solution, stress corrosion, and mineral dissolution/precipitation [15,17,20,24–29], which are often referred to as sealing/healing for macroscopic fracture strengthening or strength recovery [30]. Pressure solution and stress corrosion cracking are driven by the imposed (effective) stress on the fracture plane. The former is a three-step process that involves dissolution at the fracture contacts (i.e., asperities), diffusion along the contact interface, and precipitation within the unstressed fracture void space [31]. The latter mainly results in subcritical crack propagation due to fluid–rock interaction at the stressed crack tips [32–34]. Mineral dissolution/precipitation under hydrostatic pore fluid pressure is driven by chemical potential gradients and independent of the applied effective stress on the solid phases. All of the former processes imply a change in the fracture void space, i.e., the fracture aperture, available for fluid flow and thereby yield either a decrease (pressure solution, stress corrosion, and precipitation) or increase (free-face dissolution) in fracture permeability. In addition, fine particle migration-induced permeability reduction was commonly observed in porous media, where fines/clay particles attached to grain surfaces are susceptible to fluid flow [35]. Fines migration may also occur in (re-)activated rock fractures, where gouge material may lead to clogging of the main flow pathways, resulting in permeability reduction [5].

Depending on the dominating mechanisms, the overall process of fracture evolution, permeability may change differently. For example, for the dissolution/precipitationdominated processes, open fractures can be sealed by mineral deposits within months to hours depending on temperature [29,36,37]. Supersaturated alkaline fluids result in permeability reduction in granite due to promoted precipitation of clay minerals, but under-saturated alkaline fluids can create cavities along the fractures by dissolution, generating sustainable and pressure-independent fracture permeability [38]. Reactive flow experiments with high and low flow rates show significant fracture permeability reduction and unchanged permeability over time, respectively, indicating that equilibrium of fluid– rock interaction processes is important [18]. By using an injection fluid close to chemical equilibrium with the rock matrix, precipitation-induced permeability reduction can be minimized [39]. In some cases, permeability can persist to hundreds of days at intermittent flow of deionized water (DI), where fluid–rock interactions tend to equilibrium during the stopped flow stages [23,24]. Even for substantial mineral precipitation in fractures, permeability can remain almost unchanged up to two months duration if the deposition is mainly located behind contact asperities with respect to the flow direction [30]. Interestingly, limestone permeability can even increase with time if flowing DI produces "wormholes" that develop due to dissolution and mass transfer [16].These findings suggest that mineral dissolution/precipitation effects on fracture permeability evolution are closely related to the fluid/rock compositions, the reaction kinetics, and how the reactive components reshape the flow channel patterns [40–42].

In addition to pure chemical effects, stress-induced fracture deformation is also an important process leading to time-dependent permeability reduction. A high fracture closure rate occurs under high effective stress, indicating the contribution of pressure solution [20,43]. The permeability reduction with time can be described by a powerlaw relation under constant differential stress conditions [21,22], which may result from decreasing normal stress acting on an increasing area of the contact asperities [17,19,44–46]. In the presence of stress, subcritical crack growth by stress corrosion may also contribute to the mechano-chemical processes that affect permeability evolution [28], but the effect on fluid chemistry is small [17].

In the aforementioned mechanisms, temperature plays an important role since it determines the reaction kinetics and the solubility of minerals [15,27,43,47]. Fracture permeability evolution, either increase or reduction, depends on the coupled process of mechano-chemical compaction and free mineral dissolution/precipitation under specific pressure and temperature conditions [48]. Therefore, the thermodynamic boundary conditions (pressure, temperature), fluid composition, and rock composition are important for predicting fracture permeability evolution with time.

This experimental study is part of the 'MEET' project (Multidisciplinary and multicontext demonstration of EGS exploration and Exploitation Techniques and potentials) within the framework of the European Union's Horizon 2020. With the aim of evaluating the potential of Variscan metamorphic rocks for EGS in the future, this study focuses on slate material, which is one of the target rocks for a planned EGS at the Göttingen University campus, Germany. We investigated the time-dependent fracture permeability evolution in slates, considering the effects of flow operations (continuous or intermittent flow), fluid composition (deionized water (DI) or brine), and temperature (up to 90 ◦C as the expected upper bound fluid reinjection temperature after energetic use of the geothermal fluid).

#### **2. Materials and Methods**

#### *2.1. Rock Samples*

The samples were extracted from a drill core made up of dark grey to black Middle Devonian Wissenbach slate from the Hahnenklee well, Harz Mountains, Germany. The original drill core was taken about 40 years ago, is 80 mm in diameter and 320 mm in length, and originates from a well depth between 1156 and 1156.32 m. The core has no macroscopic veins (i.e., a distinct sheet-like body of crystallized minerals within a rock) or obvious fractures (i.e., separated voids in rocks). It should be noted that the choice of well analogue rocks may not fully represent the rock encountered in the reservoir to be accessed and used later for geothermal energy provision. However, in the absence of an exploration well at a particular site, this is the closest one can get and, consequently, has become a standard in experimental reservoir assessment. The sample material used in this study was carefully selected in this regard and originates from a well that is located in geologically close vicinity to the well to be drilled later at the Göttingen University campus, Germany. Regarding possible aging or alteration of the cores during storage in the repository, based on our experiences, there is no indication that this were the case to a degree that would impede any conclusions drawn on the corresponding behavior of the rock encountered in situ.

To prepare three cylindrical samples, SM1, SM2, and SM3, the drill core was first cut with a saw perpendicular to its longitudinal axis to create a macroscopic fracture. Subsequently, smaller cores with a diameter of 25 mm were drilled with maintaining the saw-cut fracture in its center. The two ends of each core were cut and polished to obtain a cylinder with a length of 50 mm. Finally, the saw-cut fracture surfaces were ground using rolling grains of a defined diameter to obtain closely identical surface roughness spectra and thereby ensure comparability between the samples. Some leftover material was used for X-ray powder diffraction (XRD) analysis at the University of Göttingen, Germany, to determine the mineral composition. The main constituents are quartz, muscovite, chlorite, and feldspar (Table 1). This table also evidences the excellent mineralogical homogeneity of the samples. As sample SM3 was located in the original drill core at a cm scale distance to both SM1 and SM2, there is no reason to believe that its composition should differ significantly and thereby impede any comparability. The matrix permeability of the sample

material is on the order of 10−<sup>19</sup> m<sup>2</sup> , determined by a gas permeameter at TU Darmstadt, Germany, using a fourth (neighboring) sample and argon gas and applying the Klinkenberg correction. material is on the order of 10−<sup>19</sup> m<sup>2</sup> , determined by a gas permeameter at TU Darmstadt, Germany, using a fourth (neighboring) sample and argon gas and applying the Klinkenberg correction.

**Table 1.** Mineral composition of slate samples. **Table 1.** Mineral composition of slate samples.

determine the mineral composition. The main constituents are quartz, muscovite, chlorite, and feldspar (Table 1). This table also evidences the excellent mineralogical homogeneity

to both SM1 and SM2, there is no reason to believe that its composition should differ significantly and thereby impede any comparability. The matrix permeability of the sample


#### *2.2. Experimental Procedures 2.2. Experimental Procedures*

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The two halves of the prepared specimens were assembled, jacketed with a heatshrink tube (Figure 1a,b), and vacuum-saturated with DI in a desiccator for more than 24 h. The experiments were performed using three different flow-through apparatuses. For experiments with saline fluids, a device made of Hastelloy C-276 was used, while the other two devices made of stainless steel were used for tests with DI as the fluid medium. All apparatuses can apply pore fluid pressures up to *P*<sup>p</sup> = 50 MPa at hydrostatic confining pressure up to *P*<sup>c</sup> = 100 MPa and temperatures between room temperature and *T* = 200 ◦C (for details, see Milsch et al. [49]). Fracture permeability can be determined by monitoring the differential pressure (using a 0~0.6 MPa differential pressure transducer) between the sample's ends at a constant flow rate. The upstream pump maintains a constant flow rate, while the downstream pump is set to a constant pressure to receive the fluid volume (Figure 1c). A relief valve is connected in parallel to the downstream side, allowing sampling of the effluents for chemistry analysis under constant pore pressure. The two halves of the prepared specimens were assembled, jacketed with a heatshrink tube (Figure 1a,b), and vacuum-saturated with DI in a desiccator for more than 24 hrs. The experiments were performed using three different flow-through apparatuses. For experiments with saline fluids, a device made of Hastelloy C-276 was used, while the other two devices made of stainless steel were used for tests with DI as the fluid medium. All apparatuses can apply pore fluid pressures up to *P*p = 50 MPa at hydrostatic confining pressure up to *P*c = 100 MPa and temperatures between room temperature and *T* = 200 °C (for details, see Milsch et al. [49]). Fracture permeability can be determined by monitoring the differential pressure (using a 0~0.6 MPa differential pressure transducer) between the sample's ends at a constant flow rate. The upstream pump maintains a constant flow rate, while the downstream pump is set to a constant pressure to receive the fluid volume (Figure 1c). A relief valve is connected in parallel to the downstream side, allowing sampling of the effluents for chemistry analysis under constant pore pressure.

**Figure 1.** Workflow for the long-term flow-through experiments, (**a**) two halves of prepared slate specimens, (**b**) the assembled sample jacketed with heat-shrink tubing, and (**c**) the flow-through apparatus. **Figure 1.** Workflow for the long-term flow-through experiments, (**a**) two halves of prepared slate specimens, (**b**) the assembled sample jacketed with heat-shrink tubing, and (**c**) the flow-through apparatus.

Here, all experiments were conducted at constant effective pressure (*P*c = 10 MPa and *P*<sup>p</sup> = 1 MPa). Each experiment included three stages: (1) initially, continuous flow-through tests after pressurization at room temperature, (2) temperature cycles between room temperature and up to 70 or 90 °C, and (3) long-term permeability measurements with the intermittent flow at 70 or 90 °C. In two flow-through experiments (SM1 and SM2), DI was Here, all experiments were conducted at constant effective pressure (*P*<sup>c</sup> = 10 MPa and *P*<sup>p</sup> = 1 MPa). Each experiment included three stages: (1) initially, continuous flowthrough tests after pressurization at room temperature, (2) temperature cycles between room temperature and up to 70 or 90 ◦C, and (3) long-term permeability measurements with the intermittent flow at 70 or 90 ◦C. In two flow-through experiments (SM1 and SM2), DI was used as fluid medium, and in one test (SM3), a 0.5 M NaCl solution was used to investigate the effect of fluid type on fracture permeability evolution. The salinity was chosen since fluid inclusions within the slates contain mainly water with low salinity NaCl. Note, however, that in some cases, fluid inclusions also contain CaCl2. Details about applied temperatures, flow rates, duration of each stage, experimental conditions, and

permeating fluid types for the three samples are listed in Table 2. The intention to divide each experiment into three different stages was the following:



<sup>a</sup> Flow rate used for permeability measurements, the flow rate during effluent sampling is always *Q* = 0.1 mL/min. <sup>b</sup> Elapsed time during the corresponding stages.

> The experiments target the evaluation of a medium enthalpy EGS system with a reservoir or (fluid) production temperature of about 150 ◦C. After the heat exchanger, the fluid, typically, has a temperature of approximately 70 ◦C (lower bound experimental temperature), which increases to around 90 ◦C (upper bound experimental temperature) before being reinjected into the formation. Due to technical constraints, the temperature of the sample and the one of the fluid, when being injected into the sample, are identical (Figure 1c). The experiments thus replicate a reservoir scenario, where, when starting from the well-to-formation interface, rock and fluid are in thermal equilibrium. As fluid is

continuously injected and transported further into the reservoir, the volume where rock and fluid are in thermal equilibrium expands. This study thus investigates processes that may alter fracture permeability in the vicinity of an injection well, where the formation is at fluid injection temperature.

During fluid flow (i.e., fracture permeability measurements and effluent sampling), the differential pressure between the sample ends was limited to ∆*p* ≤ 0.5 MPa (i.e., the maximum upstream pore fluid pressure is below 1.5 MPa) to ensure to not exceed the measurable range of the differential pressure transducer and to avoid changing effective stress beyond critical values.

Sample permeability *k* is calculated based on Darcy's law assuming steady-state conditions as

$$Q = \frac{k \Delta pA}{\mu L} \tag{1}$$

where *Q* is the flow rate, *L* is the sample length, *A* = *πr* 2 is the cross-sectional area of the cylindrical sample, ∆*p* is the differential pressure over the sample length *L*, and *µ* is the dynamic fluid viscosity, which depends on the fluid type, salinity, temperature, and pore pressure [50,51] and was adjusted according to tabulated values in the cited literature when calculating permeability. By ignoring fluid flow in the rock matrix because of the low matrix permeability (*k* ~10−<sup>19</sup> m<sup>2</sup> ), the "cubic law", assuming laminar flow through a fracture between parallel plates, gives the expression of the separation distance, *b*h, between the two smooth plates during flow-through tests as [52,53]

$$Q = \frac{b\_{\rm h} \, ^3W \Delta p}{12 \mu L} \tag{2}$$

where *W* is the width of the fracture (sample diameter). *b*<sup>h</sup> can be considered an equivalent aperture (hydraulic aperture) in case of rough fractures. Using this approximation and assuming that all fluid flow through the fracture (*A* = *Wb*h), fracture permeability, *k*<sup>f</sup> , can be expressed by combining Equations (1) and (2) as

$$k\_{\mathbf{f}} = \frac{b\_{\mathbf{h}}^2}{12} \tag{3}$$

### *2.3. Analytical Methods*

2.3.1. Effluent Element Concentrations

Effluent element concentrations of Al, Ca, Fe, K, Mg, Na, Si, and Zn were determined by Inductively Coupled Plasma-Optical Emission Spectrometry (ICP-OES) analyses performed at the ElMiE Lab at the German Centre for Geosciences (GFZ, Potsdam, Germany) using a 5110 spectrometer (Agilent, Santa Clara, CA, USA). The analytical precision and reproducibility are generally better than 2%, regularly tested using certified reference material and in-house standards. Effluent samples were diluted with HNO3.

#### 2.3.2. Fracture Surface Topographies

The fracture surface topographies were measured before and after the experiments using white light interferometry (Keyence VR 3000). The resolution of the in-plane coordinates was 23.5 µm, and the vertical resolution was 1.0 µm. Statistical parameters, the peak height difference *R*p, the mean *R*m, and the root-mean-square *R*rms, of fracture surfaces were used to compare the changes of surface roughness, expressed as

$$R\_{\mathbf{P}} = \max |z\_{\mathbf{i}} - z\_{\mathbf{a}}| \tag{4}$$

$$R\_{\mathbf{m}} = \frac{1}{n} \sum\_{i=1}^{n} |z\_{\mathbf{i}} - z\_{\mathbf{a}}| \tag{5}$$

$$R\_{\rm rms} = \sqrt{\frac{1}{n} \sum\_{i=1}^{n} (z\_i - z\_a)^2} \tag{6}$$

where *z*<sup>i</sup> is the height of the *i* th point, and *z*<sup>a</sup> is the mean height of the elevation plane, which is discretized by *n* points.

#### 2.3.3. SEM-EDX

After the experiments were conducted, the fracture surfaces were coated with carbon and observed by performing scanning electron microscopy (SEM) using both the backscattered electron (BSE) and the secondary electron (SE) mode. Combined energy dispersive X-ray analysis (EDX) was performed to identify the elemental composition of representative locations.

#### **3. Results**

Fracture permeability (Equation (3)) evolution was explored upon continuous fluid flow after pressurization at ambient temperature, heating–cooling cycles, and intermittent flow over a long-time duration (Section 3.1). Effluent element concentrations were used to qualitatively analyze potential mineral reactions in rock fractures (Section 3.2). We compared fracture surface topographies before and after the experiments (Section 3.3) and explored the mechanisms governing fracture permeability evolution using microstructural observations (Section 3.4).

#### *3.1. Variations of Fracture Permeability*

#### 3.1.1. Initial Fracture Permeability Decline with Continuous Flow (Stage 1)

All samples exhibited a progressive fracture permeability decline with time during fluid flow, particularly pronounced for SM3 with NaCl solution as permeating fluid (Figure 2). Samples SM1 and SM2 showed nearly identical fracture permeability degradation, which slowly converged over time/reaching a minimum value. After the fluid flow was stopped for about 65 h, the fracture permeability of SM1 remained unchanged (i.e., *<sup>k</sup>*<sup>f</sup> = 3.7 <sup>×</sup> <sup>10</sup>−<sup>12</sup> <sup>m</sup><sup>2</sup> ). Fracture permeability of sample SM3 was first continuously measured for 41 hours and subsequently measured again after flow was stopped for about 28 h and 16 h (see two lower right panels in Figure 2). Compared to samples SM1 and SM2, fracture permeability was more strongly reduced in the first 2 hours and progressively converged from initial 3.5 <sup>×</sup> <sup>10</sup>−<sup>12</sup> <sup>m</sup><sup>2</sup> to 7 <sup>×</sup> <sup>10</sup>−<sup>13</sup> <sup>m</sup><sup>2</sup> at the end of continuous flow. Fracture permeability slightly declined further to 6.7 <sup>×</sup> <sup>10</sup>−<sup>13</sup> <sup>m</sup><sup>2</sup> and 6.6 <sup>×</sup> <sup>10</sup>−<sup>13</sup> <sup>m</sup><sup>2</sup> after interrupting fluid flow for 28 h and 16 h, respectively.

The evolution of fracture permeability with cumulative fluid flow volume is shown in Figure 3. Samples SM1 and SM2 presented almost similar permeability decay with flow volume, independent of flow rate. In contrast, the permeability of sample SM3 decreased more drastically with the same amount of NaCl solution. Again, the flow rate was adjusted during the flow tests to ensure that the differential pressure did not reach the maximum range of the transducer, but had no effect on permeability evolution. We expect that the total flow volume determines permeability variations by interaction with the fracture surface rather than flow dynamics.

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surface rather than flow dynamics.

surface rather than flow dynamics.

justed during the flow tests to ensure that the differential pressure did not reach the maximum range of the transducer, but had no effect on permeability evolution. We expect that the total flow volume determines permeability variations by interaction with the fracture

justed during the flow tests to ensure that the differential pressure did not reach the maximum range of the transducer, but had no effect on permeability evolution. We expect that the total flow volume determines permeability variations by interaction with the fracture

**Figure 2.** Fracture permeability determined by continuous flow tests after pressure build-up (*P*c: 10 MPa and *P*p: 1 MPa) as a function of elapsed time at room temperature. The large fluctuation of SM3 permeability (blue line) between 13 and 27 h is because the upstream pump pressure reached a set limit, and the flow rate was automatically adjusted. Panels at the bottom show measurements after fluid flow was interrupted for certain time intervals. **Figure 2.** Fracture permeability determined by continuous flow tests after pressure build-up (*P*c: 10 MPa and *P*p: 1 MPa) as a function of elapsed time at room temperature. The large fluctuation of SM3 permeability (blue line) between 13 and 27 h is because the upstream pump pressure reached a set limit, and the flow rate was automatically adjusted. Panels at the bottom show measurements after fluid flow was interrupted for certain time intervals. **Figure 2.** Fracture permeability determined by continuous flow tests after pressure build-up (*P*c: 10 MPa and *P*p: 1 MPa) as a function of elapsed time at room temperature. The large fluctuation of SM3 permeability (blue line) between 13 and 27 h is because the upstream pump pressure reached a set limit, and the flow rate was automatically adjusted. Panels at the bottom show measurements after fluid flow was interrupted for certain time intervals.

**Figure 3.** Fracture permeability evolution in stage 1 after pressure build-up (*P*c: 10 MPa and *P*p: 1 MPa) versus cumulative flow volume. Temperature is 25 °C. Flow rates are indicated. **Figure 3.** Fracture permeability evolution in stage 1 after pressure build-up (*P*c: 10 MPa and *P*p: 1 MPa) versus cumulative flow volume. Temperature is 25 °C. Flow rates are indicated. **Figure 3.** Fracture permeability evolution in stage 1 after pressure build-up (*P*c: 10 MPa and *P*p: 1 MPa) versus cumulative flow volume. Temperature is 25 ◦C. Flow rates are indicated.

#### 3.1.2. Temperature Effects (Stage 2)

Using DI as permeating fluid, increasing the temperature stepwise resulted in a slight fracture permeability reduction from 3.7 <sup>×</sup> <sup>10</sup>−<sup>12</sup> <sup>m</sup><sup>2</sup> (at 25 ◦C) to 3.4 <sup>×</sup> <sup>10</sup>−<sup>12</sup> <sup>m</sup><sup>2</sup> (at 85 ◦C) in sample SM1, and from 4.5 <sup>×</sup> <sup>10</sup>−<sup>12</sup> <sup>m</sup><sup>2</sup> (at 25 ◦C) to 3.8 <sup>×</sup> <sup>10</sup>−<sup>12</sup> <sup>m</sup><sup>2</sup> (at 70 ◦C) in SM2, respectively (Figure 4). The permeability decline was not recovered after cooling to room temperature. After re-heating, the permeability of samples SM1 and SM2 was slightly reduced by about 3~6% at peak temperature (Figure 4, right-hand panels), indicating a time-dependent permeability reduction. A temperature increase from room temperature to <sup>90</sup> ◦C caused an irreversible permeability increase from 6.6 <sup>×</sup> <sup>10</sup>−<sup>13</sup> <sup>m</sup><sup>2</sup> to 1.3 <sup>×</sup> <sup>10</sup>−<sup>12</sup> <sup>m</sup><sup>2</sup> in sample SM3, in particular between 70 and 90◦C (Figure 4). Opposite to the behaviors of the other two samples, the permeability of SM3 slightly increased after re-heating to 90 ◦C. sample SM1, and from 4.5 × 10−<sup>12</sup> m<sup>2</sup> (at 25°C) to 3.8 × 10−<sup>12</sup> m<sup>2</sup> (at 70 °C) in SM2, respectively (Figure 4). The permeability decline was not recovered after cooling to room temperature. After re-heating, the permeability of samples SM1 and SM2 was slightly reduced by about 3~6% at peak temperature (Figure 4, right-hand panels), indicating a time-dependent permeability reduction. A temperature increase from room temperature to 90 °C caused an irreversible permeability increase from 6.6 × 10−<sup>13</sup> m<sup>2</sup> to 1.3 × 10−<sup>12</sup> m<sup>2</sup> in sample SM3, in particular between 70 and 90°C (Figure 4). Opposite to the behaviors of the other two samples, the permeability of SM3 slightly increased after re-heating to 90 °C.

Using DI as permeating fluid, increasing the temperature stepwise resulted in a slight

(at 25 °C) to 3.4 × 10−<sup>12</sup> m<sup>2</sup>

(at 85 °C) in

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fracture permeability reduction from 3.7 × 10−<sup>12</sup> m<sup>2</sup>

3.1.2. Temperature Effects (Stage 2)

**Figure 4.** Fracture permeability variations during the temperature cycles between room temperature and up to 90 °C (SM1 and SM3) and 70 °C (SM2) (left panel). The arrows indicate the heating and cooling sequences. All tests started at approximately 25 °C. Details of permeability variations at the respective target temperatures (grey boxes) after first and second heating are shown in the three panels on the right. Sample SM2 was measured twice (No.1 and No.2) at 70 °C after first heating within a time interval of 15 h, indicating a time-dependent permeability reduction at constant temperature. After second heating of this sample, the respective permeability value is therefore labelled No. 3. Error bars are in the range of ±2 × 10<sup>−</sup><sup>14</sup> m<sup>2</sup> and hence not visible on the logarithmic y-axis. 3.1.3. Time dependence of Permeability with Intermittent Flow (Stage 3) **Figure 4.** Fracture permeability variations during the temperature cycles between room temperature and up to 90 ◦C (SM1 and SM3) and 70 ◦C (SM2) (left panel). The arrows indicate the heating and cooling sequences. All tests started at approximately 25 ◦C. Details of permeability variations at the respective target temperatures (grey boxes) after first and second heating are shown in the three panels on the right. Sample SM2 was measured twice (No. 1 and No. 2) at 70 ◦C after first heating within a time interval of 15 h, indicating a time-dependent permeability reduction at constant temperature. After second heating of this sample, the respective permeability value is therefore labelled No. 3. Error bars are in the range of <sup>±</sup><sup>2</sup> <sup>×</sup> <sup>10</sup>−<sup>14</sup> <sup>m</sup><sup>2</sup> and hence not visible on the logarithmic y-axis.

#### For intermittent flow of DI through samples SM1 and SM2, fracture permeability 3.1.3. Time Dependence of Permeability with Intermittent Flow (Stage 3)

progressively reduced over time, slightly more at T = 90 °C (SM1) than at T = 70 °C (SM2) (Figure 5). However, such time-dependent permeability reduction of both samples was likely to vanish or slowed down after cooling the sample to room temperature. For sample SM3 with a NaCl solution as permeating fluid, the permeability showed a 1.5-fold increase by over 34 days duration that remained constant after cooling down to 25 °C. In comparison to the initial permeability measured at room temperature in stage 1, all samples, subjected to the three test stages (i.e., the initial continuous flow, temperature cycles, and the intermittent flow), show at 25 °C fracture permeability reductions between 42 and 78% after a total test period of about 40 days (Table 3). For intermittent flow of DI through samples SM1 and SM2, fracture permeability progressively reduced over time, slightly more at T = 90 ◦C (SM1) than at T = 70 ◦C (SM2) (Figure 5). However, such time-dependent permeability reduction of both samples was likely to vanish or slowed down after cooling the sample to room temperature. For sample SM3 with a NaCl solution as permeating fluid, the permeability showed a 1.5-fold increase by over 34 days duration that remained constant after cooling down to 25 ◦C. In comparison to the initial permeability measured at room temperature in stage 1, all samples, subjected to the three test stages (i.e., the initial continuous flow, temperature cycles, and the intermittent flow), show at 25 ◦C fracture permeability reductions between 42 and 78% after a total test period of about 40 days (Table 3).

**Figure 5.** Time-dependent fracture permeability evolution with intermittent flow at 90 °C (SM1 and SM3) and 70 °C (SM2). Each symbol represents a steady-state permeability measurement. The open symbols indicate permeability measured at room temperature at the beginning and end of the experiments, respectively. **Figure 5.** Time-dependent fracture permeability evolution with intermittent flow at 90 ◦C (SM1 and SM3) and 70 ◦C (SM2). Each symbol represents a steady-state permeability measurement. The open symbols indicate permeability measured at room temperature at the beginning and end of the experiments, respectively.



The initial and final permeability indicate the first permeability after pressure buildup and the end permeability at room temperature (see open symbols in Figure 5). The initial and final permeability indicate the first permeability after pressure build-up and the end permeability at room temperature (see open symbols in Figure 5).

#### *3.2. Fluid Chemistry Evolution 3.2. Fluid Chemistry Evolution*

The element concentrations of Al and Zn in all effluent samples were negligible (<0.1 mg/L). Ca, Fe, K, Mg, Na, and Si concentration changed within a set of subsamples that were collected on day 7 after the first time interval of 6 days (Figure 6). This and each subsequent sampling sequence took approximately 1.5 h. It is implied that fluid–rock reactions occurred along the fracture and that dissolved matter diffused from the fracture aperture to the capillaries connected to the sample within the semi-closed pore fluid system. We interpret the subsample with peak element concentrations as the fluid representative of the composition in the fracture aperture during the 6-day interval. Because the fracture volume (on the order of ~0.01 mL) is significantly smaller than 1.0 mL (i.e., the volume of each effluent subsample), the absolute element concentrations of the fluid within the fracture aperture may be significantly larger than the measured peak values, depending on the dissolution and diffusion rates. Therefore, the measured element concentrations indicate the degree of fluid–rock reactions, but may represent a lower bound. For samples SM1 and SM2 with DI, all element concentrations of SM1 are slightly The element concentrations of Al and Zn in all effluent samples were negligible (<0.1 mg/L). Ca, Fe, K, Mg, Na, and Si concentration changed within a set of subsamples that were collected on day 7 after the first time interval of 6 days (Figure 6). This and each subsequent sampling sequence took approximately 1.5 h. It is implied that fluid–rock reactions occurred along the fracture and that dissolved matter diffused from the fracture aperture to the capillaries connected to the sample within the semi-closed pore fluid system. We interpret the subsample with peak element concentrations as the fluid representative of the composition in the fracture aperture during the 6-day interval. Because the fracture volume (on the order of ~0.01 mL) is significantly smaller than 1.0 mL (i.e., the volume of each effluent subsample), the absolute element concentrations of the fluid within the fracture aperture may be significantly larger than the measured peak values, depending on the dissolution and diffusion rates. Therefore, the measured element concentrations indicate the degree of fluid–rock reactions, but may represent a lower bound.

higher than that of SM2, which is likely due to enhanced reaction rates at the higher temperature applied to sample SM1. Strikingly, the Na concentrations of both samples are about one order of magnitude higher than that of the other elements, revealing relatively strong reactions of Na-rich minerals in DI (e.g., plagioclase, c.f., Table 1). In sample SM3 with 0.5 M NaCl solution, the concentrations of Ca, K, and Mg are about one order of

**Figure 6.** Effluent element concentrations of subsamples after the first time interval of 6 days in SM1 (**a**,**b**), SM2 (**c**,**d**), SM3 (**e**,**f**). Peak values indicate fluid composition extracted from the fracture aperture, while the other subsamples include fluid **Figure 6.** Effluent element concentrations of subsamples after the first time interval of 6 days in SM1 (**a**,**b**), SM2 (**c**,**d**), SM3 (**e**,**f**). Peak values indicate fluid composition extracted from the fracture aperture, while the other subsamples include fluid within the capillaries adjacent to the sample. Note the different scales of Na concentrations.

within the capillaries adjacent to the sample. Note the different scales of Na concentrations.

By comparing all peak concentrations obtained after each time interval, we were able to evaluate the reaction rate evolution of the fluid–rock system under constant pressure and temperature conditions (Figure 7). For samples SM1 and SM2, the maximum concentrations occurred after the first time interval on day 7. Subsequently, all element concentrations progressively reduced with time, implying a reduction of fluid–rock interactions. In particular, Fe concentration reduced to nearly zero, which may manifest the reaction termination of Fe-containing minerals or the disappearance of such minerals after dissolution. In contrast, for sample SM3, the concentrations of all elements, except K, showed minor reduction after each week (Figure 7f), indicating that fluid–rock interactions in SM3 For samples SM1 and SM2 with DI, all element concentrations of SM1 are slightly higher than that of SM2, which is likely due to enhanced reaction rates at the higher temperature applied to sample SM1. Strikingly, the Na concentrations of both samples are about one order of magnitude higher than that of the other elements, revealing relatively strong reactions of Na-rich minerals in DI (e.g., plagioclase, c.f., Table 1). In sample SM3 with 0.5 M NaCl solution, the concentrations of Ca, K, and Mg are about one order of magnitude larger than those in SM1 and SM2 (Figure 6), and the Si concentration is ≈1.5–2 times higher than in SM1 and SM2. For sample SM3, the Fe concentration is negligible in all subsamples, possibly due to the dissolution limit of Fe-contained minerals or the lack of Fe-contained minerals (e.g., Ankerite and Chlorite) on the SM3 fracture surfaces.

magnitude larger than those in SM1 and SM2 (Figure 6), and the Si concentration is ≈1.5– 2 times higher than in SM1 and SM2. For sample SM3, the Fe concentration is negligible in all subsamples, possibly due to the dissolution limit of Fe-contained minerals or the lack of Fe-contained minerals (e.g., Ankerite and Chlorite) on the SM3 fracture surfaces.

were relatively stable, although the dissolution reaction rates were faster than those in SM1 and SM2. By comparing all peak concentrations obtained after each time interval, we were ableto evaluate the reaction rate evolution of the fluid–rock system under constant pressure and temperature conditions (Figure 7). For samples SM1 and SM2, the maximum concentrations occurred after the first time interval on day 7. Subsequently, all element concentrations progressively reduced with time, implying a reduction of fluid–rock interactions. In particular, Fe concentration reduced to nearly zero, which may manifest the reaction termination of Fe-containing minerals or the disappearance of such minerals after dissolution. In contrast, for sample SM3, the concentrations of all elements, except K, showed minor reduction after each week (Figure 7f), indicating that fluid–rock interactions in SM3 were relatively stable, although the dissolution reaction rates were faster than those in SM1 and SM2.

**Figure 7.** Peak effluent element concentrations extracted from each set of subsamples of sample SM1 (**a**,**b**), SM2 (**c**,**d**), SM3 (**e**,**f**), after prescribed time intervals. The data on day zero present the element concentrations of the injected fluid and data on day 1 (for SM1 and SM2) indicate the effluent sampled right after increasing the temperature to the targets. Note the different scales of Na concentrations. **Figure 7.** Peak effluent element concentrations extracted from each set of subsamples of sample SM1 (**a**,**b**), SM2 (**c**,**d**), SM3 (**e**,**f**), after prescribed time intervals. The data on day zero present the element concentrations of the injected fluid and data on day 1 (for SM1 and SM2) indicate the effluent sampled right after increasing the temperature to the targets. Note the different scales of Na concentrations.

#### *3.3. Fracture Surface Topography 3.3. Fracture Surface Topography*

Fracture surface topographies before and after the experiments are shown in Figures A1–A3 (in the Appendix A) for samples SM1, SM2, and SM3, respectively. The topography of both fracture surfaces changed due to fluid flow, particularly in areas close to the fluid injection side (i.e., dark areas in maps measured after testing), and in most cases resulted in a slightly wider height distribution compared to the initial surface (Figure 8). The removal of surface heights (dark areas in Figures A1–A3), where stresses are expected to be high (stress concentrations at the tips of the surface asperities), indicates that the mass loss is induced by pressure solution of contact asperities. However, the peak height difference *R*p, the mean height *R*m, and the root mean square height *R*rms of the whole surface before and after the experiments show that fracture surface roughness remains nearly unchanged or slightly increased (Table 4), which indicates that the global statistical values cannot easily reveal some localized solution/dissolution processes. It can be assumed that such fracture surface roughness changes may result from a combination of pressure solution and dissolution/precipitation reactions, which, in turn, might counteract each other to a certain degree. Fracture surface topographies before and after the experiments are shown in Figures A1–A3 (in the Appendix A) for samples SM1, SM2, and SM3, respectively. The topography of both fracture surfaces changed due to fluid flow, particularly in areas close to the fluid injection side (i.e., dark areas in maps measured after testing), and in most cases resulted in a slightly wider height distribution compared to the initial surface (Figure 8). The removal of surface heights (dark areas in Figures A1–A3), where stresses are expected to be high (stress concentrations at the tips of the surface asperities), indicates that the mass loss is induced by pressure solution of contact asperities. However, the peak height difference *R*p, the mean height *R*m, and the root mean square height *R*rms of the whole surface before and after the experiments show that fracture surface roughness remains nearly unchanged or slightly increased (Table 4), which indicates that the global statistical values cannot easily reveal some localized solution/dissolution processes. It can be assumed that such fracture surface roughness changes may result from a combination of pressure solution and dissolution/precipitation reactions, which, in turn, might counteract each other to a certain degree.

**Figure 8.** Comparison of fracture surface height distribution before and after the experiments, SM1 (**a**,**b**), SM2 (**c**,**d**), SM3 (**e**,**f**). **Figure 8.** Comparison of fracture surface height distribution before and after the experiments, two surfaces (**a**,**b**) for sample SM1, (**c**,**d**) for sample SM2, (**e**,**f**) for sample SM3, respectively.



4.33 2.44 13.69 4.93 2.60 16.27 After

#### *3.4. Microstructures*

The post-experimental backscattered electron (BSE) micrograph and the EDX map of sample SM1 (Figure 9) taken as an example, indicate a complex mineral distribution, where pyrite and ankerite are normally located as a cluster, and other minerals are mixed without clear boundaries. Fracture surfaces are rough and attached with various particles (e.g., pyrite, plagioclase, muscovite) that are authigenic (Figure 10). The particle size is in general within 10 µm. Mineral dissolution and secondary mineral formation (precipitation) are hard to distinguish based on the micrographs. However, we observed some fiber-like texture at the edge of some crystals (Figure 10d) in sample SM3, which may imply strong reactions on the mineral surfaces. *3.4. Microstructures* The post-experimental backscattered electron (BSE) micrograph and the EDX map of sample SM1 (Figure 9) taken as an example, indicate a complex mineral distribution, where pyrite and ankerite are normally located as a cluster, and other minerals are mixed without clear boundaries. Fracture surfaces are rough and attached with various particles (e.g., pyrite, plagioclase, muscovite) that are authigenic (Figure 10). The particle size is in general within 10 µm. Mineral dissolution and secondary mineral formation (precipitation) are hard to distinguish based on the micrographs. However, we observed some fiberlike texture at the edge of some crystals (Figure 10d) in sample SM3, which may imply strong reactions on the mineral surfaces. *3.4. Microstructures* The post-experimental backscattered electron (BSE) micrograph and the EDX map of sample SM1 (Figure 9) taken as an example, indicate a complex mineral distribution, where pyrite and ankerite are normally located as a cluster, and other minerals are mixed without clear boundaries. Fracture surfaces are rough and attached with various particles (e.g., pyrite, plagioclase, muscovite) that are authigenic (Figure 10). The particle size is in general within 10 µm. Mineral dissolution and secondary mineral formation (precipitation) are hard to distinguish based on the micrographs. However, we observed some fiberlike texture at the edge of some crystals (Figure 10d) in sample SM3, which may imply

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strong reactions on the mineral surfaces.

**Figure 9.** (**a**) Backscattered electron (BSE) micrograph and (**b**) EDX map of the fracture surface of sample SM1 after experiments. **Figure 9.** (**a**) Backscattered electron (BSE) micrograph and (**b**) EDX map of the fracture surface ofsample SM1 after experiments. **Figure 9.** (**a**) Backscattered electron (BSE) micrograph and (**b**) EDX map of the fracture surface of sample SM1 after experiments.

**Figure 10.** Scanning electron (SE) micrographs of the fracture surface of sample SM2 (**a**,**b**) and sample SM3 (**c**,**d**) after the experiments. **Figure 10.** Scanning electron (SE) micrographs of the fracture surface of sample SM2 (**a**,**b**) and sample SM3 (**c**,**d**) after the experiments. **Figure 10.** Scanning electron (SE) micrographs of the fracture surface of sample SM2 (**a**,**b**) and sample SM3 (**c**,**d**) after the experiments.

The observed evolution of fracture permeability with time and temperature in addition to the associated change of the effluent chemistry may be explained by one or more

The observed evolution of fracture permeability with time and temperature in addition to the associated change of the effluent chemistry may be explained by one or more

**4. Discussion**

**4. Discussion**

#### **4. Discussion**

The observed evolution of fracture permeability with time and temperature in addition to the associated change of the effluent chemistry may be explained by one or more of the following mechanisms: pressure solution, stress corrosion, free-face dissolution, and fines migration. We discuss if these mechanisms may have contributed to permeability evolution in the separated experimental stages.

#### *4.1. Mechanism of Initial Permeability Decline under Constant Conditions*

Time-dependent fracture permeability decrease was observed with DI flow under static stress conditions [15,17,21,22]. The degradation was explained by pressure solution, a continuous sealing process of the macroscopic fracture. Im et al. [21] found that fracture permeability decay during hold periods over dozens of hours in slide-hold-slide experiments can be well described by power-law compaction coupled with the "cubic law". Power-law compaction was established in indentation experiments, where the timedependent displacement of the indenter into the crystalline mineral matrix can be described by a power-law function, induced by pressure solution [54]. Because of indentation of the contact asperities into the matrix, it is assumed that the overall fracture closure (∆*b*, geometrical aperture changes) also follows a power law with respect to time as

$$
\Delta b = \mathfrak{a}t^n\tag{7}
$$

where *n* is the power-law exponent, *t* is the elapsed time, and *α* is the aperture change when *t* = 1. Further, by substituting Equation (1) into Equation (2), sample permeability *k* can be expressed with hydraulic aperture *b*<sup>h</sup> as,

$$k = \frac{b\_{\rm h}^3}{6\pi r} \tag{8}$$

Assuming equivalent hydraulic and geometrical aperture *b*, sample permeability evolution can be correlated to fracture closure ∆*b* [21,52,55] as

$$k = k\_0 \left( 1 - \frac{\Delta b}{b\_0} \right)^3 \tag{9}$$

where *k*<sup>0</sup> and *b*<sup>0</sup> are the initial permeability and aperture, respectively. Substituting Equation (7) into Equation (9) yields

$$k = k\_0 \left(1 - \frac{\alpha}{b\_0} t^{\alpha}\right)^3 \tag{10}$$

We used the measured permeability data during continuous flow (Figure 2) to parameterize *k*0, *α*/*b*0, and *n* by using the least-squares method. The resulting values, provided in Table 5, fit very well to the data (Figure 11). We observed a similar permeability degradation trend but with a larger range of power exponents in comparison to similar permeability measurements in granite with saw-cut fractures under effective pressure of 3 MPa (*n* = 0.3~0.4) described in [21]. The power exponent *n* measured for sample SM3 is distinctly lower than of samples SM1 and SM2, which may imply that the permeability changes are not solely controlled by pressure solution. Because the indenter experiments indicate that pressure solution-controlled indenting displacement yields a power-law function with exponents normally larger than 0.3 [54]. Our results imply other processes (free-face dissolution) also play an important role in the overall fracture aperture variation, which will be discussed below. Evidently, when the flow was stopped for some time, measured permeability showed much less reduction than predicted for continuous flow (c.f., samples SM1 and SM3 in Figure 11). This suggests that a chemical equilibrium within the fracture aperture was attained during no flow periods leading to a high concentration

of the pore fluid and less efficient pressure solution, resulting from limiting the diffusion from contacts to the pore fluids. perature are 889.9 and 928.6 µPa\*s, respectively [50,51]. For particles of similar size, this would lead to a difference of drag forces between the two fluid compositions of about 4%, which is unlikely to explain the lower permeability obtained with NaCl compared to DI.

**Sample** *k***<sup>0</sup> α/***b***<sup>0</sup> n Adjusted** *R***<sup>2</sup>** SM1 1.95×10−<sup>15</sup> 7.3×10−<sup>2</sup> 0.43 0.99 SM2 2.0×10−<sup>15</sup> 4.5×10−<sup>2</sup> 0.61 0.99 SM3 1.13×10−<sup>14</sup> 0.6 0.072 0.98

Another possibility is fines migration-induced permeability decline, commonly occurring in porous media [35]. In our samples, fine particles are attached to the fracture surfaces (Figure 10), which may have been transported upon fluid flow, causing permeability to decrease. During no flow periods, particles may not migrate and clog the flow pathways, mitigating permeability reduction. The drag force *F*d, causing the particle to move, is proportional to the fluid dynamic viscosity *μ*, flow rate *U*, and particle radius *r*s: <sup>d</sup> ∝ [56,57]. We found that permeability reduction is relatively independent of flow rates (Figure 3). For DI and the 0.5 M NaCl solution, the dynamic viscosities at room tem-

**Table 5.** Fitting parameters. In addition, high-salinity fluid would increase the stability of mobile particles due to the

**Table 5.** Fitting parameters.


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**Figure 11.** Sample permeability (Equation (1)) variations with time under constant pressure (*P*c: 10 MPa and *P*p: 1 MPa) and room temperature conditions. Fitting curves (in green) are derived based on Equation (10). **Figure 11.** Sample permeability (Equation (1)) variations with time under constant pressure (*P*c: 10 MPa and *P*p: 1 MPa) and room temperature conditions. Fitting curves (in green) are derived based on Equation (10).

Assuming that the initial fracture aperture *b*<sup>0</sup> is equivalent to the initial hydraulic aperture *b*h0, *b*<sup>0</sup> can be expressed based on Equation (8) as <sup>0</sup> = √6<sup>0</sup> 3 (11) Using fitted parameters, *k*<sup>0</sup> and *α*/*b*<sup>0</sup> (Figure 11 and Table 5), we can determine the aperture change as a function of time, ∆ = (Figure 12a). We noticed that the initial aperture changes of sample SM3 were significantly larger than that of the other two samples. However, the aperture closure rate ∆̇ = −1 , of sample SM3 decreased much faster and was smaller than that of SM1 and SM2 after about 10 hours duration (Figure Another possibility is fines migration-induced permeability decline, commonly occurring in porous media [35]. In our samples, fine particles are attached to the fracture surfaces (Figure 10), which may have been transported upon fluid flow, causing permeability to decrease. During no flow periods, particles may not migrate and clog the flow pathways, mitigating permeability reduction. The drag force *F*d, causing the particle to move, is proportional to the fluid dynamic viscosity *µ*, flow rate *U*, and particle radius *r*s: *F*<sup>d</sup> ∝ *µrsU* [56,57]. We found that permeability reduction is relatively independent of flow rates (Figure 3). For DI and the 0.5 M NaCl solution, the dynamic viscosities at room temperature are 889.9 and 928.6 µPa\*s, respectively [50,51]. For particles of similar size, this would lead to a difference of drag forces between the two fluid compositions of about 4%, which is unlikely to explain the lower permeability obtained with NaCl compared to DI. In addition, high-salinity fluid would increase the stability of mobile particles due to the increase in the electrostatic force [35]. In this case, with the assumption of fines migration, permeability should present less reduction upon fluid flow with NaCl, which is opposite to our experimental results. Therefore, fines migration is expected to be not the dominant factor in flow-dependent permeability reduction.

Assuming that the initial fracture aperture *b*<sup>0</sup> is equivalent to the initial hydraulic aperture *b*h0, *b*<sup>0</sup> can be expressed based on Equation (8) as

$$b\_0 = \sqrt[3]{6\pi r k\_0} \tag{11}$$

Using fitted parameters, *k*<sup>0</sup> and *α*/*b*<sup>0</sup> (Figure 11 and Table 5), we can determine the aperture change as a function of time, ∆*b* = *αt n* (Figure 12a). We noticed that the initial aperture changes of sample SM3 were significantly larger than that of the other two samples.

However, the aperture closure rate ∆ . *b* = *nαt n*−1 , of sample SM3 decreased much faster and was smaller than that of SM1 and SM2 after about 10 hours duration (Figure 12b). This implies that at the beginning of the experiments, the NaCl solution accelerated the pressure solution rate by increasing the dissolution kinetics of some minerals, e.g., quartz [58,59] and calcite [60]. Due to an increasing rate of free-face dissolution, which has a contrasting (i.e., enlarging) effect on fracture aperture, the total aperture closure rate may significantly reduce if pressure solution rate slows down or terminate eventually due to the continuous increase in contact areas. Therefore, we expect that the initial permeability decline observed in stage 1 of our experiments was mainly governed by pressure solution with a relatively increasing contribution of free-face dissolution with increasing time. 12b). This implies that at the beginning of the experiments, the NaCl solution accelerated the pressure solution rate by increasing the dissolution kinetics of some minerals, e.g., quartz [58,59] and calcite [60]. Due to an increasing rate of free-face dissolution, which has a contrasting (i.e., enlarging) effect on fracture aperture, the total aperture closure rate may significantly reduce if pressure solution rate slows down or terminate eventually due to the continuous increase in contact areas. Therefore, we expect that the initial permeability decline observed in stage 1 of our experiments was mainly governed by pressure solution with a relatively increasing contribution of free-face dissolution with increasing time.

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**Figure 12.** Measured and calculated (with Equation (7)) aperture change with time in log-log plot (**a**), where all parameters are derived based on the fitting curves in Figure 11, and (**b**) fracture aperture change rate as a function of time. **Figure 12.** Measured and calculated (with Equation (7)) aperture change with time in log-log plot (**a**), where all parameters are derived based on the fitting curves in Figure 11, and (**b**) fracture aperture change rate as a function of time.

#### *4.2. Thermal Effects on Permeability 4.2. Thermal Effects on Permeability*

Thermally driven hydraulic aperture reduction is believed to be induced by thermal dilation, mechanical creep, and pressure solution [19,43]. However, in our experiments, temperature cycles resulted in opposite irreversible permeability changes (i.e., decrease in sample SM1 and SM2 with DI and increase in sample SM3 with the NaCl solution) (Figure 4). Therefore, thermal dilation or thermal stress effects cannot solely control the process, otherwise similar permeability changes are expected. In addition, we observed time-dependent permeability changes at peak temperatures and after temperatures cycling (Figure 4). Thermally driven hydraulic aperture reduction is believed to be induced by thermal dilation, mechanical creep, and pressure solution [19,43]. However, in our experiments, temperature cycles resulted in opposite irreversible permeability changes (i.e., decrease in sample SM1 and SM2 with DI and increase in sample SM3 with the NaCl solution) (Figure 4). Therefore, thermal dilation or thermal stress effects cannot solely control the process, otherwise similar permeability changes are expected. In addition, we observed time-dependent permeability changes at peak temperatures and after temperatures cycling (Figure 4).

In general, increasing temperature enhances fluid–rock reaction rates [17,24,61–64], leading to enhanced pore space or permeability changes. The continuous flow tests in stage 1 demonstrated an interplay of pressure solution and free-face dissolution, where the initial pressure solution rate in sample SM3 with the NaCl solution was much faster than that of the other two samples. Obviously, the rate-limiting process of pressure solution (dissolution, transport, or precipitation) was different for DI and NaCl solutions and strongly temperature-dependent between 70 and 90 °C. Although we measured the amount of species diluted in the effluent, which strongly differed if using DI or NaCl solution as permeating fluid (Figure 7), we were not able to quantify the element concentrations. We expect that temperature-dependent solubilities and reaction rates, as well as time, control the permeability evolution, but cannot specify the relative contribution based on the available data. Nevertheless, the slight permeability reduction with time of samples SM1 and SM2 after temperature cycling, and the slight increase with time for sample SM3 In general, increasing temperature enhances fluid–rock reaction rates [17,24,61–64], leading to enhanced pore space or permeability changes. The continuous flow tests in stage 1 demonstrated an interplay of pressure solution and free-face dissolution, where the initial pressure solution rate in sample SM3 with the NaCl solution was much faster than that of the other two samples. Obviously, the rate-limiting process of pressure solution (dissolution, transport, or precipitation) was different for DI and NaCl solutions and strongly temperature-dependent between 70 and 90 ◦C. Although we measured the amount of species diluted in the effluent, which strongly differed if using DI or NaCl solution as permeating fluid (Figure 7), we were not able to quantify the element concentrations. We expect that temperature-dependent solubilities and reaction rates, as well as time, control the permeability evolution, but cannot specify the relative contribution based on the available data. Nevertheless, the slight permeability reduction with time of samples SM1 and SM2 after temperature cycling, and the slight increase with time for sample

may be explained by the cross-over from dominantly pressure solution controlled to free-

face dissolution-controlled permeability evolution (c.f., Figure 12).

SM3 may be explained by the cross-over from dominantly pressure solution controlled to free-face dissolution-controlled permeability evolution (c.f., Figure 12). *Geosciences* **2021**, *11*, x FOR PEER REVIEW 18 of 24

#### *4.3. Potential Fluid–Rock Interactions on Time-Dependent Permeability Changes 4.3. Potential Fluid–Rock Interactions on Time-Dependent Permeability Changes*

Figure 13 shows potential processes that cause permeability changes with time. They may occur solely or simultaneously depending on the pressure, temperature, fluid, and rock compositions [16,17,24]. Despite fluid chemistry, pressure solution and stress corrosion require normal stress acting on the solid contacts as the driving force. Thus, they occur predominantly at the early stage when the effective stress on the contacts is relatively high. In this case, fracture permeability reduction is always accompanied by obvious fracture deformation [22]. In addition, sufficient dissolved components can be detected in the effluents due to pressure solution-enhanced solubility [17,19,24,43]. For the other mechanisms, i.e., free-face dissolution, precipitation [25,61], and fines migration [35], no obvious deformation is required in conjunction with fracture permeability changes at a relatively small scale. Figure 13 shows potential processes that cause permeability changes with time. They may occur solely or simultaneously depending on the pressure, temperature, fluid, and rock compositions [16,17,24]. Despite fluid chemistry, pressure solution and stress corrosion require normal stress acting on the solid contacts as the driving force. Thus, they occur predominantly at the early stage when the effective stress on the contacts is relatively high. In this case, fracture permeability reduction is always accompanied by obvious fracture deformation [22]. In addition, sufficient dissolved components can be detected in the effluents due to pressure solution-enhanced solubility [17,19,24,43]. For the other mechanisms, i.e., free-face dissolution, precipitation [25,61], and fines migration [35], no obvious deformation is required in conjunction with fracture permeability changes at a relatively small scale.

**Figure 13.** Potential fluid–rock interactions occurring during the long-term experiments and their effects on fracture permeability and fracture deformation. Both (**b**,**c**) involve dissolution of solid matter into a fluid phase, where the former is taking place within the contact area of stressed asperities and the latter occurs on the free faces of the mineral grains. (**a**) Stress corrosion cracking; (**b**) Pressure solution; (**c**) Dissolution; (**d**) Precipitaion; (**e**) Fines migration. **Figure 13.** Potential fluid—rock interactions occurring during the long-term experiments and their effects on fracture permeability and fracture deformation. (**a**) Stress corrosion cracking, (**b**) pressure solution, (**c**) dissolution, (**d**) precipitation, and (**e**) fines migration, in which both (**b**,**c**) involve dissolution of solid matter into a fluid phase, where the former is taking place within the contact area of stressed asperities and the latter occurs on the free faces of the mineral grains.

> We were not able to identify if stress corrosion cracking played a role in our experiments, but fines migration appeared to terminate towards the end of stage 1 (Figure 2) and hence to play a subordinate role during stage 2 and stage 3. Since we did not measure strain data to evaluate which mechanisms contribute to the overall process, we relied on analyses of measured permeability changes and effluent concentration variations. The element concentrations in sample SM3 were significantly larger than those of the other two samples (Figure 6), supporting the hypothesis that the NaCl solution could increase mineral reaction rates in SM3. Sodium cations would accelerate the dissolution rate of, for example, quartz [58,59] and calcite [60]. The enhanced concentrations of Ca and K in sample SM3 are possibly due to the dissolution of plagioclase (NaAlSi2O8 to CaAl2Si2O8) and muscovite (KAl2(AlSi3O8)(OH)2). The large Fe concentrations in samples SM1 and SM2 may result from Ankerite (Ca(Fe2+, Mg)(CO3)2) dissolution. We were not able to identify if stress corrosion cracking played a role in our experiments, but fines migration appeared to terminate towards the end of stage 1 (Figure 2) and hence to play a subordinate role during stage 2 and stage 3. Since we did not measure strain data to evaluate which mechanisms contribute to the overall process, we relied on analyses of measured permeability changes and effluent concentration variations. The element concentrations in sample SM3 were significantly larger than those of the other two samples (Figure 6), supporting the hypothesis that the NaCl solution could increase mineral reaction rates in SM3. Sodium cations would accelerate the dissolution rate of, for example, quartz [58,59] and calcite [60]. The enhanced concentrations of Ca and K in sample SM3 are possibly due to the dissolution of plagioclase (NaAlSi2O<sup>8</sup> to CaAl2Si2O8) and muscovite (KAl2(AlSi3O8)(OH)2). The large Fe concentrations in samples SM1 and SM2 may result from Ankerite (Ca(Fe2+, Mg)(CO3)2) dissolution.

> The element concentrations of sample SM1 at 90 °C were slightly higher than those of sample SM2 tested at 70 °C (Figure 7). This supports the hypothesis that increasing temperature enhances the fluid–rock interactions. The fact that all element concentrations of samples SM1 and SM2 showed a maximum after the first time interval and declines The element concentrations of sample SM1 at 90 ◦C were slightly higher than those of sample SM2 tested at 70 ◦C (Figure 7). This supports the hypothesis that increasing temperature enhances the fluid–rock interactions. The fact that all element concentrations of samples SM1 and SM2 showed a maximum after the first time interval and declines

> afterwards indicates that pressure solution was dominant at the early stage of long-term intermittent flow, but was progressively less effective in later stages when contact areas

afterwards indicates that pressure solution was dominant at the early stage of long-term intermittent flow, but was progressively less effective in later stages when contact areas expanded. The changes in the effluent concentration (SM1 and SM2) are consistent with pressure solution evolution. Temperature-dependent kinetics is in line with our observation of stronger fracture permeability reduction with time at 90 ◦C compared to 70 ◦C (Figure 5). For sample SM3, the element concentrations (except Na) also increased after the first time interval, but remained relatively stable afterwards (Figure 7). This implies permeability changes are first mainly controlled by pressure solution and then by free-face dissolution, because the latter is directly correlated to the reactive surface areas that did not change dramatically. The increase in permeability with time for sample SM3 reveals the contribution of mass transfer forming voids.

We noticed that the stopped flow within the semi-closed pore fluid system mitigated permeability decline at room temperature (Figure 11), but the intermittent flow still led to substantial permeability changes at elevated temperatures (Figure 5). This discrepancy is likely also related to thermally enhanced fluid–rock interactions as permeability changes with the intermittent flow significantly slow down after cooling to room temperature.

In our experiments, the initial hydraulic aperture of saw-cut fractures was in the range of 6~7 µm (calculated from Equation (2)) under low-stress conditions (effective stress of 9 MPa), which is in the same order of magnitude as the fracture surface roughness (Table 4). This indicates that the fracture surface roughness is strongly correlated to the initial fracture aperture and thus represents a defining parameter with respect to fracture permeability. The surface height distributions remain unchanged or slightly rougher after the experiments (Figure 8), likely resulting in the dissolved mass on some localized areas (dark areas on the fracture surface topographies, Figures A1–A3). However, we were not able to quantify if such height reduction resulted from dissolution or pressures solution, because both mechanisms led to local mass removal from the fracture surface. In addition, we expect that the effect of mass transfer (caused by pressure solution or mineral dissolution) in such narrow fracture apertures are drastic, whereas larger fractures with high surface roughness or fractures under high-stress conditions may lead to different evolutions of fracture aperture, which need to be further investigated.

#### *4.4. Implications for EGS*

The long-term sustainability of rock fracture permeability is crucial to guarantee the lifespan of a successful EGS. Our experimental results demonstrate that newly generated fractures in slates (e.g., artificially prepared, injection created, and sheared) may be subject to large and fast permeability reduction with time under constant effective stress conditions. Such time-dependent fracture permeability reduction was also observed in granite, shale, and novaculite [4,15,17,19,21,22]. Similarly, fracture permeability reduction can slow down at the late stage during fluid flow. Moreover, the governed mechanisms in our experiments are pressure solution and free-face dissolution, where the former may slow down and terminate at some point, and the latter plays a more important role in the late stage. In the sample with NaCl solutions as the permeating fluid, permeability showed a slight increase at the late stage, where we expect that pressure solution is nearly stopped because of the enlargement of contact areas, and mineral dissolution may increase the voids. This behavior was also found in a flow-through experiment of a fractured limestone with distilled water, where free-face dissolution overtakes pressure solution, generating a "wormhole" for fluid flow [16]. Therefore, we infer that the pre-existing fractures, if hydraulically conductive, may persist for a very long term, but newly generated fractures will yield a certain reduction with time due to the initial high-stress concentration on the self-propping contacts. For assessing the performance of geothermal reservoirs after stimulation, such time-dependent permeability reduction must be borne in mind.

To reach the economic utilization of geothermal reservoirs, some indicators, such as production temperature, injection temperature, and the flow rate, have to be set within a certain range. Our laboratory investigation found that elevated temperatures lead to en-

hanced fluid–rock interactions, causing fracture permeability to change drastically, but such high reaction rates may be conducive to permeability enhancement if mineral dissolution dominates. Slates containing fractures, subjected to time-dependent closure, can possibly be mitigated by controlling injected fluid compositions. On the other hand, precipitation was not observed in our experiments, either due to permanent fluid under-saturation or as a result of the pore fluid exchange during the last permeability measurement before final cooling. This, however, may not be true in the field [13,14]. Dissolved minerals may increase the local permeability, where they dissolved, but may cause permeability reduction in far-field flow owing to precipitation at a large scale. Running an EGS in such metamorphic strata requires an understanding of the long-term evolution of the fractures in the host rocks, to which this study aimed to contribute. How to mitigate any fracture permeability reduction observed here, however, needs to be elucidated further.

#### **5. Conclusions**

To evaluate sustainability of fractures within slates, three long-term flow-through experiments with Wissenbach slate samples containing a macroscopic saw-cut fracture were conducted under constant pressures (i.e., *P*<sup>c</sup> = 10 MPa and *P*<sup>p</sup> = 1 MPa) and varying temperatures (room temperature up to 90 ◦C). Fracture permeability and effluent element concentrations were measured throughout the experiments. The results show that after applying effective pressure, the initial permeability reduction follows a power-law function during continuous flow, but this decrease slows down or terminates when flow is stopped. Temperature cycling causes an irreversible permeability decline when DI is used as the pore fluid, but permeability increases when the pore fluid is a 0.5 M NaCl solution. When fluid flow is intermittent, permeability shows a time-dependent reduction with DI as the permeating fluid, which is more pronounced at 90 ◦C compared to 70 ◦C. Again, permeability slightly increases when the sample is saturated with the NaCl solution. Ultimately, all samples yielded a certain and time-dependent permeability reduction. It is demonstrated that fracture permeability evolution in slates is controlled by pressure solution and free-face dissolution. Temperature cycles may affect fracture permeability by thermally enhanced fluid–rock interactions. NaCl accelerates the dissolution kinetics such that pressure solution is faster. However, pressure solution slows down drastically as the driving force (i.e., the normal stress on the contact asperities) decreases with time. The permeability degradation of fractured slates is similar to that of saw-cut granite fractures, which implies that slate reservoirs may be equally suitable for EGS as those in granites. However, for comparable effective pressures, the initial fracture aperture associated with the fracture surface roughness may determine how sensitive the aperture is to fluid–rock interactions in the long term.

**Author Contributions:** Conceptualization, C.C., J.H., E.R. and H.M.; methodology, C.C. and H.M.; investigation, C.C., J.H., J.A.S., E.R. and H.M.; experiments and measurements, C.C., J.A.S. and B.L.; writing-original draft preparation, C.C., B.W. and H.M.; writing-review and editing, J.H., B.L., J.A.S. and E.R.; supervision, E.R. and H.M. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by EU—European Union's Horizon 2020 research and innovation program (MEET project, grant number: 792037).

**Data Availability Statement:** All data related to this study can be obtained from the corresponding author upon request.

**Acknowledgments:** The authors would like to thank Stefan Gehrmann for rock sample preparation, Sabine Tonn for fluid chemistry measurements with ICP-OES, Ilona Schäpan and Valerian Schuster for SEM measurements. Furthermore, Tanja Ballerstedt and Jasper Florian Zimmermann are acknowledged for their assistance with the apparatus preparation and updates. We are also grateful to David Charles Peter Peacock as well as three anonymous reviewers for their thoughtful and constructive comments that helped to improve the manuscript.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Appendix A**

Fracture surface topographies before and after the entire experiments are shown below. Fracture surface topographies before and after the entire experiments are shown below. Fracture surface topographies before and after the entire experiments are shown below.

*Geosciences* **2021**, *11*, x FOR PEER REVIEW 21 of 24

*Geosciences* **2021**, *11*, x FOR PEER REVIEW 21 of 24

**Figure A1.** Fracture surface topographies and the central profiles of sample SM1 before (**a**,**b**) and after (**c**,**d**) the entire experiments, where the arrows indicate the flow direction. **Figure A1.** Fracture surface topographies and the central profiles of sample SM1 before (**a**,**b**) and after (**c**,**d**) the entire experiments, where the arrows indicate the flow direction. **Figure A1.** Fracture surface topographies and the central profiles of sample SM1 before (**a**,**b**) and after (**c**,**d**) the entire experiments, where the arrows indicate the flow direction.

**Figure A2.** Fracture surface topographies and the central profiles of sample SM2 before (**a**,**b**) and after (**c**,**d**) the entire experiments, where the arrows indicate the flow direction. **Figure A2.** Fracture surface topographies and the central profiles of sample SM2 before (**a**,**b**) and after (**c**,**d**) the entire experiments, where the arrows indicate the flow direction. **Figure A2.** Fracture surface topographies and the central profiles of sample SM2 before (**a**,**b**) and after (**c**,**d**) the entire experiments, where the arrows indicate the flow direction.

**Figure A3.** Fracture surface topographies and the central profiles of sample SM3 before (**a**,**b**) and after (**c**,**d**) the entire experiments, where the arrows indicate the flow direction. **Figure A3.** Fracture surface topographies and the central profiles of sample SM3 before (**a**,**b**) and after (**c**,**d**) the entire experiments, where the arrows indicate the flow direction.

#### **References References**

	- Enhanced Geothermal Systems: Experimental and modeling constraints*. J. Energy Res. Tech.* **2020**, *143*, 1–37, doi:10.1115/1.4049181. 9. Phillips, T.; Bultreys, T.; Bisdom, K.; Kampman, N.; Van Offenwert, S.; Mascini, A.; Cnudde, V.; Busch, A. A systematic investigation into the control of roughness on the flow properties of 3D-printed fractures. *Water Resour. Res.* **2021**, *57*, 4. [CrossRef]

## *Article* **Spring Water Geochemistry: A Geothermal Exploration Tool in the Rhenohercynian Fold-and-Thrust Belt in Belgium**

**Marina Cabidoche 1,\*, Yves Vanbrabant 1,\*, Serge Brouyère <sup>2</sup> , Vinciane Stenmans <sup>3</sup> , Bruno Meyvis <sup>1</sup> , Thomas Goovaerts <sup>1</sup> , Estelle Petitclerc <sup>1</sup> and Christian Burlet <sup>1</sup>**


**Abstract:** Spring water geochemistry is applied here to evaluate the geothermal potential in Rheno-


hercynian fold and thrust belt around the deepest borehole in Belgium (Havelange borehole: 5648 m MD). Fifty springs and (few) wells around Havelange borehole were chosen according to a multicriteria approach including the hydrothermal source of "Chaudfontaine" (T ≈ 36 ◦C) taken as a reference for the area. The waters sampled, except Chaudfontaine present an in-situ T range of 3.66–14.04 ◦C (mean 9.83 ◦C) and a TDS (dry residue) salinity range of 46–498 mg/L. The processing methods applied to the results are: hierarchical clustering, Piper and Stiff diagrams, TIS, heat map, boxplots, and geothermometry. Seven clusters are found and allow us to define three main water types. The first type, locally called "pouhon", is rich in Fe and Mn. The second type contains an interesting concentration of the geothermal indicators: Li, Sr, Rb. Chaudfontaine and Moressée (≈5 km East from the borehole) belong to this group. This last locality is identified as a geothermal target for further investigations. The third group represents superficial waters with frequently high NO<sup>3</sup> concentration. The application of conventional geothermometers in this context indicates very different reservoir temperatures. The field of applications of these geothermometers need to be review in these geological conditions.

**Keywords:** blind geothermal system; compositional anomalies; hierarchical clustering; self-organizing maps; unconventional reservoirs

#### **1. Introduction**

Geothermal exploration, as any subsurface resource evaluation, requires a multidisciplinary approach (e.g., geological mapping, geophysics, geochemistry) and usually follows a downscaling approach starting from a regional scale toward a shortlist of potential sites for more detailed investigations [1,2]. These sites usually show surface indicators of the presence of a geothermal resource at depth. The nature of these indicators varies in the shape of hydrothermal springs, vapor exhalation, or sinter deposition. These indicators can even take the shape of biological manifestations as bacterial mats (e.g., [3–5], presence of bacterial community on travertine deposits [6] or even saline water tolerant plant and animal concentrations (e.g., eels) [7]). Even if such indicators are interesting clues in evaluating the geothermal fields, not all of them show obvious indicators at ground surface of their presence. An example of such blind geothermal fields is the Great Basin region in Nevada, which was recognized as a high-enthalpy important geothermal field without surface indicators [2,8]. Other blind geothermal systems were explored and/or developed in New Zealand, Hawaii, Indonesia [9,10]. Some of these blind geothermal systems were

**Citation:** Cabidoche, M.; Vanbrabant, Y.; Brouyère, S.; Stenmans, V.; Meyvis, B.; Goovaerts, T.; Petitclerc, E.; Burlet, C. Spring Water Geochemistry: A Geothermal Exploration Tool in the Rhenohercynian Fold-and-Thrust Belt in Belgium. *Geosciences* **2021**, *11*, 437. https://doi.org/10.3390/ geosciences11110437

Academic Editors: Béatrice A. Ledésert, Ronan L. Hébert, Ghislain Trullenque, Albert Genter, Eléonore Dalmais, Jean Hérisson and Jesús Martínez-Frías

Received: 20 September 2021 Accepted: 15 October 2021 Published: 22 October 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

even discovered while targeting other resources (oil and gas, coal, minerals) for example in southern California [11], in Nevada [12], or in Belgium [13,14]. A common denominator of these blind geothermal systems is the presence of a cap formation, which hides many indicators of the presence of the geothermal resource.

The specificities and challenges to evaluate the geothermal potential of deep metasedimentary formations such as those encountered by the Havelange borehole (Belgium) are numerous: the Havelange borehole was drilled for gas exploration, hence, some important tasks/parameters for geothermal exploration were not conducted or recorded. The borehole site location is, therefore, fixed and not necessarily located in the most promising location for the development of a geothermal system in the region. The aforementioned downscaling approach frequently used in geothermal exploration cannot be applied. Another issue is the lack of information regarding the deep fluid flows and fluid composition since formation water inflows were thwarted by drilling mud injections as usual in drilling operation. It is important to note that two thick aquifer formations were encountered in this borehole [15]: (i) limestones and dolomites of Frasnian-Givetian ages (MD: 606–1595 m) and calcareous-sandstones of Eifelian (MD: 1610–1700 m); (ii) the fractured continuous quartzites of the Upper Praguian (MD: 4365–4554 m and 4639–4778 m). These two aquifers are separated from each other by more than 2000 m of aquiclude shales and slates of Emsian and Upper Praguian ages (from MD 1920 m to 4300 m). The aquifer character of the carbonate formations of Frasnian and Givetian is attested by significant mud losses during drilling and by few artesian events while adding drill rods. With regard to the aquifer and fractured Pragian quartzites, there are indirect indications that support this hypothesis: significant losses of drilling mud, sudden increases of mud temperature, poor Dipmeter log not showing consistent dips, Sonic log showing low speed peaks (fractures). The quarzitic Praguian, host rock for the geothermal reservoir, must be regarded as tight but permeable fracture zones that could represent potential geothermal targets. The logging data (gammaray, sonic, dipmeter) acquired during the 1980s provide only partial information regarding fracture networks, especially in comparison with modern logging data.

The punctual bottom hole temperature measurements indicate a mean moderate geothermal gradient of 22 ◦C/km but a sudden increase to 30 ◦C/km from 4400 m to the deepest parts of the borehole to reach a corrected value of 126 ◦C at 5369 m (MD-5277 VD) [15,16]. If the geothermal resource exists, it corresponds to a blind geothermal system with no obvious surface indicator of the resource.

Besides all these challenges, the existence of a deep borehole cross cutting a full (meta-)sedimentary sequence is not so common. All the cores, the cuttings, and most of the documents (e.g., logs) are still available and conserved by the Geological Survey of Belgium. The observations conducted thanks to this borehole provide important control to build a model of the deep structure of the region. Finally, the observation of significant mud losses during the drilling operations through Lower Devonian quartzite units and in the absence of borehole wall collapses, as indicated by the Caliper log, provides a promising key indication of the existence of deep fluid flows within the metasedimentary units in the region of the Havelange borehole. In this regard, the main target for the development of a deep geothermal reservoir is, therefore, these lower Devonian quarzitic units and a secondary target at shallower depth could be represented by Givetian/Frasnian limestone formations.

In this study, we apply one of the geothermal exploration tools to extend the investigation area surrounding the Havelange borehole by collecting spring and shallow borehole water samples. The geochemical composition of these samples aims to detect compositional anomalies as markers of deep fluid flows. The notion of anomaly is addressed in this paper. The signal of such flows requires, however, detecting a small anomaly, since deep-origin water is more likely mixed with superficial water during its ascending path. Our paper includes, first, the regional geological setting and key information regarding the Havelange borehole. The field sampling protocol and the analysed chemical compounds and physicochemical parameters are then listed. The data treatment and the main results

are in turn presented by applying various clustering technics. Finally, we discuss the results through the application of common geothermometers to evaluate the potential reservoir temperature. This discussion also focuses on the applicability of these geothermometers in our study case; those thick meta-sedimentary formations in a fold-and-thrust belt.

#### **2. Geological Setting**

The study area and the Havelange borehole are located on the Eastern part of the Dinant Synclinorium, a sub-unit of the Ardenne Allochthon. These units compose the Belgian segment of the Rhenohercynian fold-and-thrust belt, which results from the accretion of the Rhenohercynian passive margin during the Variscan orogeny between the end of the Visean age to the Upper Carboniferous period (330–300 Ma) [17–20]. The Dinant Synclinorium (Figure 1) is bordered to the North by the trace of the Midi Thrust, which separates the Ardenne Allochthon from the Brabant Parautochthon [21].

**Figure 1.** Simplified regional geological map around Havelange's borehole in Dinant synclinorium, Wallonia region (Eastern Belgium) and location of sampling sites for the water springs study. The Brabant Massif (BM) and Malmedy Graben (MG) are also visible in this map. The study near field (see text) is represented by a circle.

The main lithologies composing the Dinant Synclinorium are thick detrital Devonian formations combined with carbonate formations of Givetian, Frasnian, and Dinantian ages. These Devono-Carboniferous formations underwent during their evolution high diagenetic conditions and even green-schist facies conditions for the deepest formations (Lower Devonian) [22].

The Dinant Synclinorium passes eastward to the Lower Palaeozoic Stavelot Massif inlier. The contact between the metasedimentary units of the Stavelot Massif and the Lower Devonian formation of the Dinant Synclinorium is marked by an unconformity reflecting the action of a branch of the Caledonian Orogeny. The rock of the Stavelot Massif underwent, therefore, the Caledonian and Variscan orogenies.

The main faults in the region are South- to South-East dipping longitudinal thrust faults, as well as bulged faults forming the Theux and Gileppe windows to the North of

the Stavelot Massif [23]. The fold structures are oriented NE-SW or even E-W depending of local conditions. Transversal or oblique faults crosscutting the folds and longitudinal thrust faults were formed either at the end of the Variscan orogeny or even during the poorly controlled age post-Variscan events. Some of these transversal and oblique fractures were filled by significant Pb-Zn deposits. Other transversal fractures are frequent targets as conduits for superficial groundwater resources, especially in carbonate formations.

Since the end of the Variscan orogeny, the tectonic activity in the study area has been quite limited. In the Stavelot Massif, the narrow Malmedy graben was formed, probably during the Permo-Triassic period. The whole region underwent a global uplift during the Quaternary. The current seismic activity in Southern Belgium is mainly located along the rim of the Brabant Parautochthon and in the Stavelot Massif [24]. Only a very limited number low magnitude events (Local Magnitude (ML) < 3.0) were recorded in the study area and the probabilistic model for a return period of 475 years predicts a maximum ground acceleration ranging between 0.04 and 0.06 g.

Following its geological characteristics, the Havelange borehole was selected in the framework of the H2020 MEET project as a demo-site to evaluate the geothermal potential of EGS development in a setting of Variscan meta-sedimentary units not affected by a younger extension period.

The Havelange borehole [16] was drilled for the Geological Survey of Belgium between January 1981 and November 1984 and reached a depth of 5648 m (MD). It aimed to investigate the potential natural gas resources under the Midi Thrust and, therefore, to drill through the Dinant Synclinorium to reach the deeply rooted Brabant Parautochthon southern extension. The site selection for the Havelange borehole results from the gas detection in another deep borehole (Focant) and the results of a seismic reflection campaign conducted in 1978. This seismic campaign indicates the presence of deep bulge-like reflectors interpreted as the presence of a local dome of the southern extension of the Midi Thrust. The methane gas inflows were too limited for any economic development program.

Briefly, the Havelange borehole encountered from top to bottom:


The borehole allowed the detection of several thrust faults indicated by the repetition of stratigraphic units especially in the lower part of the borehole.

The main mineralogical phases encountered are: quartz > illite/muscovite > clinochlore > calcite > dolomite > pyrophyllite > feldspar > garnet > hematite > ilmenite, with obviously major variations according to the lithostratigraphic units. Another important property to mention is the high level of lithification of the studied formation. Even if Rhenohercynian fold-and-thrust resulted from the accretion of sedimentary basin, the involved lithology underwent a major lithification, reducing the porosity to a few percent and, hence, the connate water content is more likely very limited. This context differs, therefore, significantly from oil-gas sedimentary basins associated with significant brine contents.

The study area was the object of several studies to evaluate the subsurface temperature and heat flow conditions at a regional scale. The temperature values recorded in the Havelange borehole frequently serve as input data to calibrate the models [16].

Vandenberghe and Fock [25] reviewed the existing temperature measurements in wells from Belgium. They established a series of temperature distribution maps for a set of depths. They observed some trends such as the presence of a cold anomaly located in the northern part of the Stavelot Massif, while high temperature halos (~40 ◦C/km) are present in Western and Northern Belgium. According to their study, the Havelange borehole is located in an average geothermal gradient zone. The main limitation of such maps is that isotherms are based on widely spread data from boreholes separated to each other by a few tens of kilometres. The determined isotherms are extrapolated on a large scale without taking in consideration any thermal parameters. As a result, the isotherms are smooth and obliterate the presence of any potential thermal anomalies at a local scale (few km).

More recent approaches applied 2D numerical models to compute the subsurface temperature and the surface heat flows again at a regional scale. These studies [26,27] consider the thermal properties (i.e., thermal conductivity and radiogenic heat production) and other parameters such as the density and porosity from reference rock samples or from published data for crustal horizons located at great depth. These models also rely on a selection of published deep cross-sections to establish the structure and the composition of the upper crust. The comparison of the works of Rogiers et al. [26] and Schintgen et al. [27] is a complicated exercise since the models follow very different numerical approaches and try to answer different scientific questions. Rogiers et al.'s. [26] study aims to understand the presence of low heat flow anomaly detected in the shallow part of some boreholes in Belgium (Soumagne, Grand-Halleux, and Havelange). They consider the influence of groundwater flow at a shallow depth through various heat transfer mechanisms: conduction vs. heat advection. The influence of Quaternary paleoclimate changes is also applied through temperature variation of the model top boundary condition leading to a transient model. The lower part of the model is associated with a homogeneous and constant heat flow at depths ranging from 20 to 10 km. In the case of the Havelange site, the estimated basal heat flow would be 90 mW/m<sup>2</sup> at 14 km deep.

By contrast, the model by Schintgen et al. [27] aims to evaluate the heat flow with a specific focus on the situation in the Great-Duchy of Luxembourg, but the studied sections extend to the Stavelot Massif and in the neighbourhood of the Havelange borehole. Their model is a 2D steady-state conductive model. The model dimensions are also very different, since the lower boundary condition correspond to lithosphere–asthenosphere boundary (LAB) located at a depth ranging from 80 to 130 km and with a temperature of 1300 ◦C. The model of Schintgen et al. [27] also consider the presence of an Eifel plume in Germanym resulting in a LAB depth reduced between 40 and 60 km. The lateral extension of this plume would reach the Eastern border of Belgium [28,29]. The model results evaluate the heat flow at 1 km deep in the South-East part of the Dinant Synclinorium to a value of c. 80 mW/m<sup>2</sup> , while in Rogiers et al. [26], the heat flow at a shallow depth of the Havelange borehole is smaller, c. 55 mW/m<sup>2</sup> . This low value would result from a downward water flow at a shallow depth in the Havelange borehole. Besides the numerous differences between the approaches of Rogiers et al. [26] and Schintgen [30], both modelling predict significant heat flow variations at a local scale in the shallow part of the studied areas. In the approach of Schintgen et al. [27], these variations result from strong thermal conductivity contrasts observed for the rocks composing the upper crust, whereas the forced water advection in the shallow crust is the driving mechanisms of Rogiers et al.'s [26] model.

Recently, a review work on the origin of CO<sup>2</sup> content of Fe-rich soda springs, mainly located in the Stavelot Massif, indicates that the water is of meteoritic origin, but the CO2-content results from the mixing of sources from hypothetic carbonate dissolution and from magmatic origins [31]. Their study focuses mainly on the isotopic signature of H, O, C, and He. The CO<sup>2</sup> magmatic source is regarded by Barros et al. [31] to be linked to the Eifel plume.

Most of the previous models rely on old observations acquired during the 1960s and 1980s, thanks to the exploration deep well campaigns led by the Geological Survey of Belgium. Some debate points between models result frequently because of the very limited numbers of information. An example of this issue is the use of a specific cross-section as a base for the numerical thermal models. However, these cross-sections are matter of debates and the choice of another section will fundamentally modify the results of the numerical models.

The approach followed in our paper aims to acquire new information using a costeffective approach for the geothermal exploration thanks to the geochemical analyses of spring waters. The collected samples were acquired in two distinct regions. A first group of water samples was collected in a 5 km perimeter around the Havelange borehole head. The subsurface composition of these springs is considered very similar to the geological formations observed in the shallow part of the borehole, that is, the mid- and upper-Devonian geological formations. This zone is referred to here as the "near field". The second group of samples were mainly acquired in the South and East borders of the Dinant Synclinorium where mid- and mainly lower-Devonian formations outcrops. The analogue formations were encountered in the deep part of the Havelange borehole. This second sampling zone is named, here, "the far field".

#### **3. Materials and Methods**

#### *3.1. Sampling Campaign*

The sampling campaign started with an initial deskwork phase for selecting potential target sites. This pre-selection includes the analysis of topographic, geological, and hydrogeological maps. A series of priorities were established based on the spring elevation, their position in a valley (e.g., lower part of the valley bank or at the valley head) or their vicinity with a fault. Springs located at an elevation lower than +250 m (Z) were considered as a priority, since this elevation corresponds to the static level of the Praguian and Lochkovian aquifer(s) in the non-cased section of the Havelange borehole. A site in the village of Moressée was also selected based on the toponymy of a spring: "La chaude Fontaine" (translated in English by "the hot fountain").

An additional site located at the north end of the study zone in the city of Chaudfontaine was chosen to collect a reference sample of hydrothermal water. The natural mineral water source (Source Astrid) captured in the Frasnian limestone at a depth of 396 m reaches a temperature of 36 ◦C.

The 50 samples were collected and conditioned by the team of the Geological Survey of Belgium (GSB) between the 13 November 2019 and the 5 March 2020. The ISO 5668– 11 recommendations and the OFEFP guide [32] were followed during the actual water sampling. Each site was also the object a detailed description regarding its environment, its precise location, the water flow magnitude, the presence of infrastructures (e.g., metallic pipes, concrete walls, etc.). Physicochemical parameters of spring water (pH, EC, T) were also measured in each site using a multiparameter meters from Hanna Instruments.

During the field campaign, some of the pre-selected sites were not sampled as some springs were dry. The region underwent a series of drought periods especially during the three previous summers. Conversely, the field reality led us to samples other sites discovered during the campaign.

All the observations, field measurements, and analytical results were included in a relational database designed for this campaign. A total of 20 samples were collected in the far field study zone and 30 samples in the near field. A table with the data used in this article are retrievable in Supplementary Materials (Table S1).

#### *3.2. Laboratory Analyses*

The central laboratory of the "Société Wallonne des Eaux (SWDE)" performed the analyses on the water spring samples on behalf of the GSB. The following parameters were measured: pH, electrical conductivity at 20 ◦C (EC), colour (ISO 7887 (C Method)), turbidity (NTU) (nephelometric method), dry residue (TDS), and suspended solids (SSC) (ISO 11923).

The major and minor anions (SO<sup>4</sup> <sup>2</sup>−, Cl−, NO<sup>3</sup> <sup>−</sup>, o-PO<sup>4</sup> <sup>3</sup>−, NO2−, F−, Br−) were analysed by ion chromatography methods (ISO 10304-1, ISO 10304-4). The major and minor cations (Na<sup>+</sup> , K<sup>+</sup> , Ca2+, Mg2+, Ba2+, Fe (total), U, Mn<sup>+</sup> , Si4+, Sr2+), trace metals (Ag, Al, As, B, Be, Cd, Co, Cr, Cu, Hg, Li, Mo, Ni, Pb, Rb, Sb, Se, Sn, V, Zn) on unfiltered and filtered water were measured by Inductively Coupled Plasma Mass Spectrometry (ICP-MS) (ISO 17294-2). The concentrations of NH<sup>4</sup> <sup>+</sup> and the complete alkalimetric strength (TAC) were analysed by Spectrophotometry.

Other parameters such as the Total Hardness (TH) and the TOC (Total Organic Carbon) (ISO 8245) were also acquired. The presence and the distribution between

HCO<sup>3</sup> −/CO<sup>3</sup> <sup>2</sup>−/dissolved CO<sup>2</sup> are deduced from the values of the Alkalimetric strength (TA) = (OH−) + (CO<sup>3</sup> <sup>2</sup>−), the TAC = TA + (HCO3−), and pH. The details of the laboratory parameters and LOQ are presented in the additional material (Table S2).

#### *3.3. Data Treatment Methods*

The interpretation of the water spring analyses made in this paper is based on the filtered water results. The use of filtered water (filtration at 0.45 microns) allows to concentrate the interpretation on the dissolved element in water and avoid the micro particles present in non-filtered water (e.g., clay).

Before statistically processing the data, the charge balance equilibrium (CBE) of the analytical values of the 50 water samples (converted from mg/L to meq/L) were calculated, using the formula: (CBE(%) = ((Scat − San)/(Scat + San)) × 100; S, cat, and an mean total, cation and anion, respectively [33]. Applied on one hand to major ions only (those used for Piper Diagram) and on the other hand to major and some minor ions (those mentioned in annual report of SPW-Agriculture, Ressources Naturelles et Environnement: F, PO4, NO2–Sr, Ba, Al, Fe, Mn [34], the resulting CBE are ranging as follows: (0.02–9.89%) with an average of 3.47% for MAJOR and some MINOR ions of 49/50 water samples; only one sample with CBE > 10% sample 32 at 28.10%.

The Piper diagrams [35] and the Stiff diagrams (e.g., [36]) were also made in this unit of measurement. The total ionic salinity (TIS) with Na + K vs. Ca + Mg is expressed in meq/kg [37]. The nitrate concentration values due to potential anthropic contamination of the water composition, from superficial water samples especially, are not included in the Piper diagrams. Finally, a hierarchical clustering method was applied and specifics elements of hydrogeological or geothermal interest (Li, Rb, pH, NO3, etc.) were selected to be represented as boxplots. In addition, several maps were made to show the locations of the clusters and the concentration in particular elements with the use of the Jenks natural breaks classification methods.

#### 3.3.1. Hierarchical Clustering Methods

The geochemical analyses acquired during this campaign are the results of several cases of the water evolution during its subsurface transit. The latter can be short (e.g., superficial water in and out-flow during a brief period) or long (deep fluid circulation or shallow low-permeable system). The geological setting of each spring can also be influenced by numerous parameters, such as the mineralogical composition of the rocks and the specific dissolution rate of their mineral, the physicochemical parameters of water during its interactions with the minerals, amongst others. The mixing of water masses that followed different subsurface paths certainly represent a key factor influencing the spring water composition. Finally, external parameters influencing the spring water composition are the climatic conditions (rain precipitation regime) or possible natural or anthropic contaminations (e.g., mineral deposit interactions, road de-icing, or agricultural spreading). Hence, the challenge is to detect the key trends and key parameters allowing us to detect trends in a multivariate system. In this study, we have chosen to apply the hierarchical clustering method to discover a structure in the data set. The hierarchical clustering method was applied on all 50 samples and for a set 37 parameters, including the physicochemical parameters (e.g., pH, EC, TAC), the concentration of the major anions, and trace metal cations. The data set is organized in a matrix of 50 rows and 37 columns. In a first step, the Euclidean distance is computed between each row (i.e., sample) of the matrix in a m-dimension space, with m equals to 37. The output of this first operation is a distance matrix, which represents the input data for the hierarchical clustering. Concretely, the distance matrix and the hierarchical clustering were computed by applying the dist and the hclust functions from the base 'Stats' Package from the R language [38]. The hierarchical clustering outputs are commonly represented by a dendrogram where the distances between the samples is represented by a difference of height between the tree limbs.

#### 3.3.2. Jenks Natural Breaks Classification Methods

The Jenks natural breaks classification method is used to create a map based on any kind of data with spatial attribute. This method conducts natural groupings (clusters) inherent to the chosen data (e.g., the concentration in one element). The breaks are determined to find the best group with similar values and with a marked difference between classes. This method pursued to minimize the variance within classes and maximize the variance between classes [39]. In the GIS application, the number of desired classes in a result set for the Jenks method must be added before the algorithm is applied on the dataset. In this paper, the reference separation was chosen at five, after different tests.

The Jenks method is applied in this study to create thematic maps based on the element concentration (Li, Rb and Sr) with QGIS software. It allows us to see the natural break in the concentration dataset for each element.

#### **4. Results**

#### *4.1. Hierarchical Clustering of Water Analyses*

The application of the hierarchical clustering on the spring water dataset (Figure 2) indicates that seven clusters can be reasonably distinguished. Cluster 1 contains only one sample (n◦33) collected in the lower Palaeozoic Stavelot Massif in the vicinity of the Permian graben of Malmedy. This sample in the dendrogram occupies its own limb with a significant distance with all other samples. Clusters 2 to 4 include two samples each, whereas cluster 5 has only one sample (n◦25). As we move down in the dendrogram, the height between the limbs is decreasing, reflecting tighter clusters or, in other words, samples with compositions more and more similar. The last two clusters (6 and 7) include 14 and 28 samples, respectively, and encompass the bulk (84%) of the collected samples.

**Figure 2.** Dendrogram representing the result of the hierarchical clustering (R program). The colours represent the attribution of samples to their cluster. Note that the hydrothermal water from Chaudfontaine (n◦50) belongs to cluster 6.

In this analysis, the hydrothermal reference sample (n◦50) from Chaudfontaine is classified within cluster 6 along with 13 other samples, which show, therefore, a degree of affinity in their chemical composition with the hydrothermal reference one. A corollary of this observation is that the composition of samples from clusters 1 to 4 clearly deviates from the bulk of collected samples and from the hydrothermal reference sample. At this stage of the analysis, the results indicate that in terms of anomalies, the study area is, thus, characterized by several types of springs with "abnormal" compositions.

The samples from clusters 1 to 3 and cluster 5 (Figure 3) come from sites located in the Stavelot Massif and mainly the Eastern rim of the Dinant Synclinorium, which is the study zone "far field". In this region, the surface and subsurface formations consist primarily of Lower Palaeozoic and Lower Devonian detrital meta-sedimentary rocks (phyllite/slate, sandstone, and quartzite). By contrast, samples from cluster 4 originate from a very limited zone located 4 km to the East of the Havelange borehole site. The samples of cluster 6 were collected mainly in the near field with two other samples located on the west edge of the far field. As already stated, the reference hydrothermal water from Chaudfontaine is located at the north end of the study zone. Finally, the samples of cluster 7 cover indiscriminately the entire study zone with a common characteristic of a low salinity (TDS ranging from 46 to 276 mg/L and TIS < 9.25 meq/kg (see Figure 8 in point 4.3).

**Figure 3.** (**a**) Geological map located the samples in the entire study zone according to their cluster attribution; (**b**) Zoom on the location of the samples with their cluster attribution in the near field around the Havelange borehole.

#### *4.2. Heat Map and Boxplots*

Even if the hierarchical cluster provides valuable information to detect compositional affinities/dissimilarities between samples, it does not directly provide the key compositional characteristics of each cluster. Regarding cluster 1, the examination of laboratory results indicates a very high concentration of iron (45,052.0 mg/L) and manganese (4321.3 mg/L), while the mean iron concentration for the dataset reaches 1462.7 mg/L and 189.5 mg/L for manganese and the median values are only 5 mg/L for Fe and 1.25 mg/L for Mn.

For the other clusters, the set of elements characterizing them is less obvious to detect. Figure 4 presents a heatmap on the same dataset as for the hierarchical clustering. Note that parameter values or concentrations for each column are normalized to avoid the predominance of very high values (e.g., iron or manganese concentration) with respect to lower values as those of trace elements. The study of the heatmap indicates three broad horizons of values. From bottom to top, one can distinguish a lower horizon gathering

samples from clusters 1 to 5 that are characterised by high concentration of numerous elements, such as Fe, Mn, Ni, Be, Mg, Li. These samples have usually a low concentration of NO3, Se, Sb. The EC and TDS are usually high, and the pH level is variable. Some sub-horizons can be distinguished with for instance the samples from cluster 4 (sample n ◦41 and 42), which show higher levels of Sr, Mo, and Sb. The central horizon of the heatmap (from samples 30 to 2 along the sample index axis) contrasts with, globally, a low concentration in several elements: Li, Rb, Ca, Na, K, Mo, U, HCO3. These low levels are also reflected by low EC and TDS values. At least a part of these samples is also affected by high nitrate levels. This central horizon is occupied by samples from cluster 7. Finally, the top heatmap horizon, which corresponds to cluster 6, shows, again, higher levels in numerous elements, but not the same as in the lower horizon. The high levels of the top horizon include Bromide, Mo, U, V, Se, Sb, Cu, TOC. The EC, TDS, and pH levels are usually higher than in the central horizon.

**Figure 4.** Cluster heatmap of the dataset of §4.2. The water samples are organized according to the hierarchical clustering along the vertical axis. Light yellow colours represent low-value parameters/concentrations, whereas the high concentrations/parameters are expressed as darker colours (orange, red, brown). Note that the parameter/concentration list is also reshuffled to highlight the similarities between the variables.

The high nitrate levels from spring water in areas with intense agricultural activities such as in the study area are commonly regarded as a signal of anthropic contamination of the aquifers. For our study, we can consider that high NO<sup>3</sup> levels is a good indicator of important influx of superficial water within the aquifers drained by the springs. Clusters 5 to 7 (Figure 5a) gathers, therefore, springs with water from superficial flow or at least a mix of superficial water with deeper aquifers. Interestingly, the water from Chaudfontaine well occupies the minimum quartile (Q1) of cluster 6, indicating the absence of any significant nitrate input in this hydrothermal system.

**Figure 5.** Boxplots presenting the concentration of (**a**) NO<sup>3</sup> ; (**b**) Li; (**c**) Rb; (**d**) Si; (**e**) Sr/Ca; (**f**) Mg/Ca; (**g**) pH; (**h**) EC according to the clusters. The geothermal reference water sample (n◦50) is pointed by a cyan cercle in cluster 6 and a horizontal line marked the neutral pH.

Li, Rb, and Si are amongst the numerous elements that are commonly analysed to detect and to characterize the presence of geothermal water. In our dataset, the higher levels of lithium (Figure 5b) are observed in Clusters 1, 2, 4, 5, and the upper part of cluster 6. By contrast, water samples from cluster 3 and mainly 7 are lacking significant Li concentrations. A similar observation can be applied for the Rb concentration (Figure 5c). Even if the Li and Rb levels observed in cluster 3 are quite similar with those of clusters 6 and 7, the Si concentration of samples from cluster 3 is clearly larger than in the other two clusters (Figure 5d).

Element level ratios are also frequently evaluated to characterize the aquifers, such as [Sr]/[Ca] and [Mg]/[Ca] (Figure 5e,f). The results indicate that cluster 4 is characterized by high values of [Sr]/[Ca] with respect to all other clusters, while it is more difficult to detect a clear trend for the ratio [Mg]/[Ca].

The analysis of the pH levels (Figure 5g) shows that water from clusters 4 and 6 is mainly composed by water with a pH above 7, while the other clusters are primarily associated with slightly acidic water. Finally, the EC of clusters 1, 2, 4, to 6 have high values, while clusters 3 and 7 exhibit low or intermediate electrical conductivity (Figure 5h).

#### *4.3. Water Composition*

The Piper diagram of the filtered samples (Figure 6) shows that 86% of the spring water samples can be classified into three main categories, namely the "Magnesian Calcium", "Calcium and Magnesian bi-carbonate", and "Chlorinated and sulphated calcium and magnesian" types. It is observed that the samples rarely belong to a type containing high concentration of sodium and none of them are of "magnesium" type or in "sulfate" type.

**Figure 6.** Piper diagram of filtered water spring analyses combined with the surface geology.

A total of 23 water samples were collected from sites where the Famennian detrital formations outcrop. Their major dissolved constituents exhibit a broad spectrum of compositions, including the three aforementioned main water types (i.e., Ca + Mg, Ca(Mg)HCO<sup>3</sup> and Ca(Mg)Cl(SO4)). The dominant cation is Ca or there is no dominant cation, whereas the bicarbonate anion is dominant or no dominant anion can be identified. The nine samples from the outcropping zone of carbonate and shale formations of Frasnian age are characterized by a composition of mainly Ca + Mg type with Ca and HCO<sup>3</sup> as the dominant ions. The three samples from Emsian formation indicate a sulphated composition.

The Praguian meta-sedimentary rocks (phyllite, siltstone, sandstone, and quartzite) are of great interest in this study since they represent the main target for the geothermal development of the Havelange demo-site and they represent a cumulative apparent thickness by tectonic staking of 1565 m in the borehole. The six spring water samples from the Praguian Stage show a much broader distribution of compositions with bicarbonate as the main anion, but without any dominant cation. However, three samples from the Praguian and one from the Permian are located on the lower triangles (Na-K-HCO<sup>3</sup> type). This type can indicate a cation exchange (Na, Ca) carried out by a deep-water circulation over a long period in clay facies. It is hazardous for the other Geological Stages to detect a clear trend or to evaluate the composition coverage due to the very limited number of samples per stage.

This broad distribution of compositions and their rather weak relationships with the Geological stages reflect the difficulty to associate the composition of a spring water with its surface geology. As we will discuss in the following parts of this paper, numerous springs discharge superficial water masses with a short subsurface transit period from the recharge zone and without enough time to reach a real equilibrium with their host rocks. On the other hand, water volumes flowing from deep units are likely to be in contact with several formations of different lithologies. The attempt to link the spring water composition of the main elements with the surface geology must be regarded as an oversimplification.

The second Piper diagram represent the 50 water samples according to the defined clusters (Figure 7). For samples from clusters 1 to 5, it is not possible to define a trend due to the very limited number of samples per cluster (e.g., 1 or 2). However, samples from clusters 1, 2, and 5 are located close to perimeter of HCO<sup>3</sup> + CO<sup>3</sup> type water. By contrast, many samples from cluster 6 are located along the Ca + Mg water type or within the Ca(Mg)HCO<sup>3</sup> domain. Finally, the water samples for which there is an indication of superficial subsurface flow (cluster 7) spread over a broad zone, including Ca(Mg)HCO<sup>3</sup> and Ca(Mg)Cl(SO4) water types.

**Figure 7.** Piper diagram of filtered water spring analysis with hierarchical clusters (mEq) (R program).

If we compare the Piper diagram of surface geology (Figure 6) with the one of clusters (Figure 7), two relationships can be detected. First, the spring water samples collected from sites where the surface geology belongs to Famennian formations are frequently attributed to cluster 7, namely the group of superficial waters. This relationship indicates that the shale formations of Famennian age act as aquiclude leading springs discharging only very superficial water masses. A corollary of this statement is that the same shale act as a cap rock for the deeper water masses. The second relationship is indicated by a degree of correlation between water samples from cluster 6 with samples collected in the outcrop zones of the Frasnian carbonate and shale formations.

Furthermore, the spring waters show low total ionic salinity (TIS) values between 1 and 16.25 meq/kg (Figure 8). More specifically, the lowest TIS < 9.25 meq/kg are associated with cluster 7 (identified as superficial water). All the other samples, except one from cluster 6, have a TIS > 9.25 meq/kg. In addition, cluster 6 (which contains hydrothermal water) presents a higher concentration in Ca + Mg than in Na + K. On the other hand, one sample from cluster 2 and one from cluster 6 show higher concentrations in Na + K than in Ca + Mg.

**Figure 8.** Correlation plot of Na + K vs. Ca + Mg (meq/kg) of filtered water spring analysis with hierarchical clusters also presenting iso-ionic-salinity (TIS) lines for reference (R program).

#### *4.4. Stiff Diagrams and Clusters*

The Stiff diagrams presented in this paper are built with the median values of the main constituents from each cluster expressed in meq/L (Figure 9).

The clusters 4 and 6 are the ones that show the most typical shapes for bicarbonate calcic groundwaters. However, cluster 4 shows enrichment in SO<sup>4</sup> compared to cluster 6. The clusters 1, 5 (one sample each), and the cluster 2 are characterised by an asymmetric polygon due to an elevated concentration of bicarbonate (around 7 meq/L) in comparison to cluster 4 and 6. This might reflect a deeper source of CO<sup>2</sup> in these waters. Moreover, cluster 2 shows a relative depletion of Ca compared to Na + K and Mg. This probably reflects the occurrence of cation exchange processes affecting groundwater, which has circulated deeper, in contact with clay materials. Cluster 3 presents intermediate mineralization with low indication of anthropic contamination (low Na, Cl and NO3). This might be the result of groundwater circulation through geological units that contain a relatively low level of potassium. Finally, the cluster 7 displays the lowest global mineralization, reflecting surface waters or very shallow groundwaters.

The Stiff diagrams of all the samples are available in additional material (Figure S1).

#### *4.5. Anomalies and Elementary Maps*

The previous heatmap (see Figure 4) highlights three main horizons in the dataset. Each horizon reflects a group of samples with similar constituents' concentration and/or similar physicochemical parameters. At the scale of a single sample the concentration in a specific element can be regarded in some cases as an anomaly within its heatmap horizon. Sample n◦5 has for instance a higher Se level with respect to all other samples in the central heatmap horizon. Such deviation from the trend/horizon, that is an anomaly, can result from a water transit through a specific subsurface environment such as the presence of mineral concentration. The evaluation of anomalies in the composition of water can be

conducted in different ways. For this study, the first approach consists of the application of the Jenks natural breaks with five classes for a set of 16 elements. A sample is considered with anomalous concentration in a given element if its concentration belongs to the two upper Jenks classes. Table 1 presents the results of detected anomalies.

**Figure 9.** (**a**) Stiff diagrams of spring water sampling interpretation made with the free software "diagrams" created by Roland Simler in the hydrogeology laboratory of Avignon (France); (**b**) Picture of Jalna site (M. Cabidoche) (Sample n◦27) illustrating a superficial water flowing from a spring located at the interface between the colluvium and Famennian shale and siltstone units. This interface is shown by red dashed line.

> Nearly half (22) of the collected samples exhibit a least one element with a concentration anomaly. In this analysis, samples n◦39, 33, 40, and 45 show the highest number of anomalies and the elements reported more frequently as anomalies are Li, Si, Mn, and Mo.

> Surprisingly, some anomalies are detected even in samples related to superficial water (cluster 7). The explanation for those particular cases are not easy to address, but at least in one case (sample n◦15), its copper anomaly can be linked to the presence of a former Pb-Zn-Cu mine near the village of Heure [40,41].

> Another approach to evaluate the presence of abnormal compositions is to compare the measured concentrations with literature values of element concentration in aquifers. For instance, six samples in the dataset have a Co concentration > 0.33 µg/L, which is a level well above the average value generally reported for spring waters [42]. In the same way, five samples have a Ba concentration > 100 µg/L [43] and seven samples have a concentration Mn > 200 µg/L [44]. In this paper, the focus is made on Li, Rb, and Sr concentrations in the water spring samples (Figure 10).

#### 4.5.1. Lithium

The concentration of lithium in fresh waters usually ranges between 1 µg/L and 20 µg/L [45]. In this study, 11 samples (Table 2) have a concentration of Li above 20 µg/L. Lithium deposits or concentration are usually found in salars or in pegmatites and less frequently they are found in clays and Li-rich micas. There is no observation of salars or pegmatites in the region and, hence, the Li source comes probably from clay minerals. However, mineral occurrences of Lithiophorite ((Al,Li)MnO2(OH)2) with possible traces of

Co, Ni, Cu, and Zn are reported in the mines of Rahier, Bihain, Vielsalm, and Malempré in the Stavelot massif. No similar occurrence has been reported so far in the Devonian formations. One of the hypotheses is that the high concentration of lithium in the MEET samples could come from deep fluids that crossed Devonian formation.

**Table 1.** Summary table of samples showing anomalies (higher than the Jenks mean concentration value for each chemical element).


**Table 2.** Table of MEET samples with the concentration Li, Sr, Rb: [Rb] > 7.6 µg/, [Li] > 20 µg/L or [Sr] > 1000 µg/L.


4.5.2. Rubidium

Rubidium is usually found in potassium minerals such as lepidolite, biotite, and feldspar. In natural groundwater, the Rb concentration is around 0.1 to 100 µg/L [46]. In this study, all the samples are below the highest reference values for spring water 100 µg/L. The referential sample n◦50 (hydrothermal spring) shows only 7.6 µg/L of Rb. Six samples are above the referential sample n◦50 and three of them (samples n◦42, n◦39, and n◦41) are higher than 10 µg/L (Table 2). Four sampled sites are located in the near field (samples n ◦17, n◦39, n◦41, n◦42) to the East of the Havelange borehole and two others are in the far field (samples n◦38 and n◦45). These samples are mostly located in shale, siltstone, and sandstone formations.

**Figure 10.** Maps representing the concentration in (**a**) Li, (**b**) Rb, and (**c**) Sr, following a separation in five classes with the Jenks natural breaks. The high lithium levels are observed in a few sites located in the far field, but also in a zone located 4 km to the East of the Havelange borehole (near field) near the villages of Moressée and Heure. Very similar observations can be conducted for the Rb and Sr concentrations.

#### 4.5.3. Strontium

Strontium enters into the groundwater composition during the leaching of limestone, igneous and metamorphic rocks, especially in granites and sedimentary rocks, as hydrated Sr2+ [47]. The concentration of strontium in fresh water is generally present as traces below 1000 µg/L [48]. The referential sample n◦50 (hydrothermal spring) shows only 455.1 µg/L of Sr.

In the spring water from this study, two samples (n◦41 and n◦42) are above 1000 µg/L (Table 2). The high concentration of strontium for these samples could come from the leaching of Givetian or Frasnian limestone formations. Moreover, a strontium occurrence (Celestine) has been described in the literature near the village of Verdenne, on the East of Marche-en-Famenne city.

#### **5. Geothermometry**

One of the main goals of geochemical exploration through the evaluation of spring water composition aims to quantify or at least to estimate the thermodynamic conditions encountered by water during its path from the recharge area to the potential geothermal reservoir and in turn in discharge zone. Numerous equations are published to derive the geothermal reservoir temperature, but all these equations are based on a series of assumptions leading to a specific field of applications. This field of application includes some restrictions with the main ones that are the range of temperature values within the geothermal reservoir, the assumption that the thermodynamic conditions are satisfied for a reaction equilibrium between the water and the reservoir rocks, but also the geological setting (volcanic zone, sedimentary basin, metamorphic terranes. . . ). The available papers on the subject usually discuss the field of applications, but even in these cases it is not always straightforward to decide if a particular equation can or cannot be applied. For instance, even if we have detected geochemical anomalies of subsurface water on the East side of the study near field, we must assume that the reservoir temperature fits with the temperature range of the applied geothermometers. For our study case, the temperature constraints within the Havelange borehole are known to be limited with a maximum bottom temperature of 126 ◦C (after correction) measured at 5369 MD (5277 m VD) [15]. Another temperature value is related to the Chaudfontaine site where the temperature of 36 ◦C was recorded during the sample collection, while for the other sites the spring temperature ranges between 3.7 ◦C and 14 ◦C. As a result, the geothermometers developed for the very high temperature conditions are not necessary the most appropriate for our study.

Some geothermometers were developed for geochemical reaction of minerals as feldspars, which are present in the Havelange borehole subsurface, but in a limited proportion. The available literature abounds with geothermometer evaluations for high-enthalpy geothermal systems in magmatic and volcanic contexts, but the number of geothermometer research in fold-and-thrust belt setting is quite limited. The closest domain of such evaluation to fold-and-thrust belt corresponds to sedimentary basins, with the main source of information on the reservoir water composition and temperature coming from oil fields. In this setting, the temperature ranges are usually quite low, but the conditions are not identical to those of fold-and-thrust. Amongst the differences the rocks of the Rhenohercynian Variscan orogen are strongly lithified, the diagenetic and metamorphic reactions are completed, and the porosity/permeability is mainly controlled by fracture networks, since the primary porosity is strongly reduced. From a lithological point of view, geothermometers were published by Chiodini et al. [49] for a geological setting, including limestone and evaporite formations. Their study led to a good correlation between a theoretical model and water samples collected in the Etruscan Swell (Italy). The occurrence of Givetian-Frasnian limestones in our study area could represent a promising target for the application of the Chiodini et al.'s model [49]. However, evaporite deposits were not recognized in the subsurface of the Havelange demo-site. Hence, our water samples are strongly undersaturated in SO<sup>4</sup> concentration (between 0.03 and 3.41 meq/L), which is between three orders of magnitude and at best a factor 3 lower than samples from the Etruscan Swell. This SO<sup>4</sup>

deficit induces an overestimation of the reservoir temperature (~>100 and 150 ◦C) even for samples of superficial waters.

Despite these unknown parameters and uncertainties on the field of application of the geothermometers, we attempt and discuss some of the published geothermometers. The most widely used geothermometer is the one based on silica concentration in water. Different equations are available according to the silica forms [50]. It is usually considered that the quartz phase is controlling the silica dissolved concentration for water temperature above 180 ◦C, while chalcedony is the main phase governing the water silica content for a temperature below 110 ◦C. Between these values, the main controlling phase is undetermined. If we applied the equations developed by Fournier [50] for the dataset of this study, several problems are encountered: firstly, the ranges of computed temperatures for amorphous quartz, α-cristobalite, β-cristobalite include only negative temperature values. If chalcedony is considered as the controlling phase of dissolved silica, negative temperatures are computed for most of the superficial waters associated with cluster 7 of the hierarchical clustering. Some negative temperatures are also evaluated for samples of cluster 6. For the other cluster, the temperature values are quite small. Secondly, another problem in this approach is that the computed temperature for the Chaudfontaine hydrothermal reservoir is only 29.9 ◦C, while the recorded temperature at the sampling site is 36 ◦C. For similar reasons, Graulich [51] applied the equation of quartz and evaluate a temperature of 50 ◦C for the reservoir of Chaudfontaine. If we apply the equation for quartz to the dataset of our study, we can observe that the computed temperature values vary according to the clusters (Figure 11a). Computed values for clusters 1, 3, and 4 are located near a temperature of 50 ◦C. The two points belonging to cluster 2 exhibit different values: 33.5 and 79.1 ◦C. Cluster 6 corresponds to temperatures stretching between 17.9 and 62.0 ◦C. The last value equals the computed temperature of the reservoir of Chaudfontaine. Finally, the superficial water samples (cluster 7) are associated with the lowest temperature except two outliners.

**Figure 11.** Computed temperature ranges for the different clusters from the geothermometers: (**a**) using the equation for quartz [50]; (**b**) lithium for a low Cl content (<0.2 M) [52]. The geothermometer equations are reported in the lower left corners. *t* is the temperature expressed in ◦C, SiO<sup>2</sup> concentration in mg/L and Li concentration in mol/kgw considering a low salinity (Cl < 0.2 M). The geothermal water sample (n◦50) is pointed by a green circle in cluster 6. For the sake of clarity, computed temperatures below 0 ◦C are not plotted.

The question of the application of the quartz phase equation for our dataset remains. It seems surprizing that the widely used silica geothermometers lead to unrealistic values if chalcedony is considered and if the quartz phase equation is applied the computed temperatures seem closer to conceivable values, but we apply an equation far below its lower temperature limit (180 ◦C) that is the equation is applied out of its field of application. Several remarks need to be addressed. First, Brook et al. [53] consider that in granitic massifs, the quartz is still the controlling phase for the dissolved silica down to a temperature of 90 ◦C. An assumption would be, therefore, to extend this lower limit even

below 90 ◦C in the case of the rock assemblage like the one of Havelange in a setting of a fold-and-thrust belt, but the thermodynamic explanation will need to be addressed in the future. Another explanation of such paradoxical situation is that all silica geothermometers are directly related to the silica concentration. Hence, the unrealistic temperature observed with the chalcedony equation is related to abnormal low SiO<sup>2</sup> concentrations in the collected samples. In this case, the reasons of this SiO<sup>2</sup> apparent deficit are manyfold: the amount of chalcedony available for reaction with water in the Havelange subsurface is too small. Another possibility could be by the admixture of water with another water mass with a low SiO<sup>2</sup> concentration (e.g., superficial water). The water flow in the subsurface is too high to allow a full equilibrium between the water and the reservoir rocks. Finally, the potentially SiO2-rich water in the near field that would flow at great depth are likely to encounter carbonate rocks during the ascending phase. The flow through the carbonate formations is likely to be associated with several reactions associated with the change in physicochemical conditions. The last two assumptions (fast flow, carbonate reactions) seem, however, unlikely since the abnormal computed temperatures are observed in both the near and far field. In this last zone, some of the geochemical anomalies are related to sites where the presence of limestone in the subsurface has never been recognized. Finally, the assumption of a fast-ascending flow is incompatible with the low temperature recorded in the springs.

The geothermometer analyses are rarely conducted with just one method, but it is common to compare the results of several methods. Another method based on a single element is associated with the Li concentration [52]. If applied on the Havelange dataset, it comes out that the computed temperature for clusters 1, 2, 4, and 5 are significantly higher than with the quartz geothermometer (Figure 11b). The computed temperature values for this group range between 80.4 and 108.3 ◦C. Cluster 6 includes values covering the full interval between 100 and 0 ◦C with the reservoir temperature in Chaudfontaine reaching a temperature of 76 ◦C. The lack or very low Li concentration in samples of cluster 7 (superficial waters) leads to very low or even negative value for this group.

If the observations based on lithium concentrations are crossed with the assumption of the SiO<sup>2</sup> concentration too low due to the admixture with superficial waters, the lithium concentrations in clusters 1 to 6 are, therefore, underestimated and as a result the computed temperatures with the Li geothermometer would be underestimated. In this approach, the computed temperatures presented in Figure 11b need to be regarded as minimum values for the reservoir.

Another widely applied geothermometer is based on the ratio Na/K and its development results from a series of empirical observations combined with experimental and thermodynamics modelling. As such, the Na/K-based geothermometers cannot be directly applied since they are valid only for high temperature conditions (>180 ◦C) [54–56] likely to be above the temperature conditions in the Havelange demo-site case. Furthermore, the computations are based on feldspar stability conditions, which are not the main mineralogical phases in the studied part of the Rhenohercynian fold-and-thrust belt. To extend the field of application of such geothermometer, Fournier and Truesdell [54] includes in the equation the Ca concentration. The range of temperatures covered by their geothermometer range between 4 and 340 ◦C. The Figure 12a shows the computed temperatures with the Fournier and Truesdell geothermometer [54]. The bulk of values is located below 60 ◦C with the higher temperatures for samples of clusters 1, 2, and 5. The composition of samples from cluster 3 leads to apparent temperature close to zero. The computed temperatures in cluster 6 are shifted towards low and even negative values, while the superficial water from cluster 7 is promoted to higher and more likely unrealistic values.

The Na-K-Ca geothermometer of Fournier and Truesdell [54] was criticized due to deviation for low temperature and modifications, or new geothermometers were published. Giggenbach [55] proposes the application of a K-Mg geothermometer for low temperatures. The computed temperatures based on the equation of Giggenbach on our dataset (Figure 12b) show, globally, the same trend that the Na-K-Ca geothermometer, but the

temperature for samples are less spread and negative values are absent. Finally, Kharaka and Mariner [57] proposed an equation based on the ratio Mg/Li (Figure 12c). Following this model, the computed temperatures for clusters 1, 2, 4, and 5 are between 31 and 49 ◦C. Some of the samples from cluster 6 drops to negative values and the very low Li-content from superficial waters of cluster 7 lead to only negative values.

**Figure 12.** Computed temperature ranges for the different clusters from the geothermometers: (**a**) using the equation for the ion Na-K-Ca [54]—concentrations expressed in mol/L; (**b**) K-Mg [55]—concentrations expressed in mg/L and (**c**) Mg-Li [57]—concentrations expressed in mg/L. The geothermometer equations are reported to the right. *t* is the temperature expressed in ◦C. The geothermal water sample (n◦50) is pointed out by a cyan circle in cluster 6.

The previous three geothermometers predict a reservoir temperature for the Chaudfontaine of 27.6 ◦C for Na-K-Ca, 32.5 ◦C for K-Mg, and 28.9 ◦C for Mg-Li. These values are below the recorded temperature during the sampling site (36 ◦C), indicating that these geothermometers predicts too low values for the reservoir. A possible interpretation for such uncertainties is the impact of high-Ca and high-Mg concentrations in the studied samples. More specifically, the Ca, Mg contents in clusters 4 and 6 tends to draw downward the values for these groups. Giggenbach [55] evaluate the impact of calcium in the reactions and concluded that the problems of the Na-K-Ca geothermometers result from sensitivity on variations on CO2-content in the geothermal waters. For the case of the Na-K-Ca geothermometer, one of the assumptions (excess in silica) for the establishment of the equation is probably not met (see the silica geothermometer).

The last geothermometers to be considered here were developed to evaluate the behaviour of, and trace elements from, major hot water reservoirs in granitic terranes [58]. This study covers several domains in Europe and showed that the concentrations in the studied elements are not significantly affected during the flow from the reservoir to the surface for alkaline water conditions (pH > 9–9.5). The water samples collected during the Havelange demo-site campaign show that alkaline conditions are encountered for samples of clusters 4 and 6, while the other clusters gather slightly acidic water. The geothermometer equation for the Rb/Na ratio corresponds to a low temperature aquifer from Bulgaria. If this geothermometer is applied to the Havelange demo-site dataset, it comes out that the computed temperatures are significantly higher than those predicted by the previous geothermometers (Figure 13a). For all clusters, except the last one, all temperatures are largely higher than 50 ◦C and in the case of cluster 4, temperature estimations even reach values above 200 ◦C. Similar observations can be conducted for some outliner values of cluster 6. For this geothermometer, the reservoir temperature in Chaudfontaine would be 110.8 ◦C. Interestingly, these higher temperatures are associated with the clusters of alkaline waters, which are closer to the field of application of this geothermometer. On the other hand, the evaluated temperatures for the superficial waters of cluster 7 are clearly too high.

**Figure 13.** Computed temperature ranges for the different clusters from the geothermometers: (**a**) using the equation for the ratio Rb/Na [58]—concentrations expressed in mol/L; (**b**) the ratio Sr/K [58]—concentrations expressed in mol/L. The geothermometer equations are reported in the lower left corners. *t* is the temperature expressed in ◦C. The geothermal water sample (n◦50) is pointed by a green circle in cluster 6.

The Sr/K geothermometer also indicates high values: c. 100 ◦C for samples from clusters 1, 2, 4, and some outliners of cluster 6. By contrast, temperatures for cluster 3 and 4 show a more reduced values around 50 ◦C (Figure 13b).

If we compare all computed temperatures with the different geothermometers, it is challenging to identify a clear trend since the temperature ranges are very broad. In a general sense, the temperatures evaluated from the concentrations of major elements (SiO2, Ca, K, Na, Mg) indicate low temperatures for the geothermal reservoirs. Some of these values are clearly underestimated as indicated by the reservoir temperature that would be inferior to the recorded value at the collecting point (Chaudfontaine). Numerous assumptions can be considered, but a likely feature is the global low concentrations in many of these major elements, with respect to geothermal water. This deficit in major elements was already developed for the silica concentration. The values Lkm (log(K2/Mg)) and Lkc (log(K2/Ca)), as defined by Giggenbach [55], are very low (<0), indicating that the potassium concentration is larger than the square root of Mg and Ca. When reported into a triangle plot of Na, Mg, and K concentration, all points from the current study plot in the Mg corner correspond to immature waters, that is, far from the fully equilibrated waters.

The second category of tested geothermometers are based on the concentration of minor element (Li) or the ratio of a minor elements (Li, Rb, Sr) and a major element (Na, K, Mg). For those cases, the evaluated temperatures are usually higher than for the major element-only methods. The presence of a major element in low concentration associated

with a minor element in the geothermometer equations has probably the reverse effect of overestimating the reservoir temperature. The unrealistic temperatures of superficial waters (cluster 7) are clearly the sign of this overestimation. Qualitatively, the real temperatures are probably between the two categories of geothermometer.

#### **6. Discussion**

The geothermal exploration must follow a multidisciplinary approach, especially in an unconventional and mainly blind geothermal system. This study case uses the geochemistry of spring water for leading an investigation around the gas exploration well of Havelange, which is here under investigation for a reconversion in a deep geothermal development project. As a result, the common procedure of first conduct exploration at the regional scale followed by a downscaling approach towards sweet spots for the evaluation and development of geothermal cannot be followed, since the borehole was already implemented and drilled in the 800 s without any geothermal objective. It is, therefore, difficult to answer fundamental questions such as: are there significant deep fluid flows? Or if another borehole needs to be drilled to develop a geothermal doublet, where is the best place to intersect the deep fluid flow(s)?

On the other hand, the presence of such deep borehole crosscutting a whole sequence of Devonian metasedimentary formations is relatively unique. It allows us to investigate the geothermal potential of an unconventional reservoir, which consists of fracture tight metamorphic units in a fossil fold-and-thrust belt and in a zone where the presence of post-Variscan extensional fractures is absent or very-limited. The Havelange borehole is, therefore, a good candidate for exploring and evaluating the development of a geothermal system in such unconventional conditions. The success of such a project would unlock new possibilities for the development of the geothermal industry in regions where conventional targets are not available. These regions include many places in the Rhenish Massif in Germany, Northern Luxembourg, a large portion of southern Belgium, and the buried basement under the London–Paris basin.

In this paper, the various subsurface fluid flows around the Havelange deep borehole were analysed by studying the groundwater geochemistry composition from mainly springs and a few other infrastructures (wells, a drainage gallery). The dataset includes physicochemical parameters recorded in a laboratory and in the field of 50 sites in the near field (NF) (< 5 km from Havelange borehole) and the far field (FF). The Lower Devonian rocks from the FF represent the ground surface analogue formations to those observed in the deep part of the Havelange borehole. One of the samples was also acquired from a water catchment in the city of Chaudfontaine and is used here as a hydrothermal reference.

The analysis results treatment includes conventional data representations of aquifer composition in hydrogeology such as the Piper and Stiff diagrams along with a multivariate approach to define compositional affinities/dissimilarities between the samples. Several geothermometers such as chalcedony, quartz, lithium, Na-K-Ca, K-Mg, Mg-Li, Rb-Na, and Sr-K were also used to evaluate reservoirs temperatures.

The results show a broad variability of the compositions and various clusters, or groups can be identified. The number of clusters is, however, dependant of the applied method and of the analyst choice. For this study, seven clusters were identified with the hierarchical clustering method; the heat map representation indicates three main horizons of compositions. Even if the data-treatment methods provide different numbers of clusters, they globally tend to similar groupings with marginal variation for intermediate composition.

The largest group from the hierarchical clustering corresponds to superficial water, slightly acidic and with frequent high NO<sup>3</sup> levels more likely related to agricultural activities. This group is also characterised by a low electrical conductivity, a low TDS level and, hence, a narrow Stiff polygon. A strong relationship is observed between these superficial water discharges and the presence of detrital formation of Famennian age in surface geology. The known barrier or cap rock behaviour of the Famennian formations, especially the lower Famennian shale, is here confirmed.

At the other end of the composition spectrum, a few springs in the FF show acidic water and a high mineral charge. These springs are known in the region as 'pouhons' or carbogaseous springs and they are associated with detrital metasedimentary rock of either the Lower Devonian or Lower Palaeozoic age. The iron and manganese contents are very high and indicators of thermal water such as Li, Sr, and Rb are also observed in high concentration. The NO<sup>3</sup> levels in this group is very low.

A third important group corresponds to slightly alkaline water with a significant mineral charge and high levels of the Li, Sr, and Rb indicators. The mineral composition is, however, different from the previous carbogaseous group. Samples from this third group are acquired in the NF and especially in an area located about 4 km to the East of the Havelange borehole in the villages of Moressée and Heure. Such composition of water in the region was not yet coined and provide new valuable information. In addition, during the field campaign several springs in the NF shown the presence of gas. Besides these occurrences in the NF, the reference hydrothermal water from Chaudfontaine also belongs to this group. In other words, water samples from this group in the Havelange borehole NF have, therefore, affinities with the hydrothermal water of Chaudfontaine. The water composition of this group is interpreted as water discharges from a deep, partly confined, aquifer developed in either Givetian or Frasnian limestone formations. The discharge of this aquifer at ground surface and, thus, through the confining beds of Famennian formations is probably the result from the presence of a draining fracture zone.

Besides these three large groups of composition, other springs are characterized by intermediate composition that reflects transitions; either a local specificity (e.g., mineral deposits) or the mixing of water from different composition groups.

At this stage of the exploration, it is delicate to evaluate the significance of the fluid flow between the aquifer located in the Givetian and Frasnian limestones and those located deeper in the detrital Lower and Mid-Devonian formations observed in the deep part of the Havelange borehole. As a first approach and following the spring water composition observed in similar rocks in the FF, it is likely that the water in the deepest part of the Havelange borehole is acidic with a significant mineral charge, include significant concentration in Fe, Mn. In a hypothesis of a water flow upward from the deep subsurface, it will reach the limestone beds and their associated aquifer, and a series of reactions will take place, such as a dissolution of the limestone and the production of dissolved CO2. The presence of gas in several springs from the NF is a probable indicator of such reactions.

The application of geothermometers in a metasedimentary context of a fold-and-thrust belt indicates various results and shows different limits. In fact, the use of one type of geothermometer rather than another is based on a supposed reservoir temperature and on the phase equilibrium. In this study, we considered that the reservoir is around 100 ◦C. Of the nine geothermometers used, only two seems to show convincing results (quartz and lithium). Indeed, if the Chaudfontaine site is taken as a reference (temperature of 36 ◦C at the surface), the results obtained with the use of chalcedony (29.9 ◦C), Na-K-Ca (27.6 ◦C), K-Mg (32.5 ◦C), and Mg-Li (28.9 ◦C) geothermometers do not seem realistic (not to mention the negative values in some clusters). The higher concentration of Ca and Mg in some clusters may explain the calculated low temperature and the presence of CO<sup>2</sup> and silica deficiency may interfere with the use of the Na-K-Ca geothermometer. Geothermometers based on major and trace elements indicate very high temperatures (Chaudfontaine temperature 110.8 ◦C (Rb-Na)). Moreover, the superficial water reservoirs would be at more than 50 ◦C due to the higher concentration of major elements than trace elements.

Regarding geothermometers, which seems to indicate more consistent results, quartz can be used for reservoirs above 180 ◦C and research in granite massifs has shown that it remains applicable below 90 ◦C in this environment. It would be necessary to conduct a study to verify the applicability of this method to a geological context like the Havelange. If the quartz-based calculations are applied to Chaudfontaine, the reservoir temperature calculated in this paper is about 62 ◦C instead of 50 ◦C found by Graulich in the 1980s.

The geothermometer based on the lithium concentration also shows values that seem consistent although overestimated. However, the application of this tool should only be done when the clusters contain a significant content of Li, otherwise negative temperatures are calculated.

In view of these diverging results, the questions would be: is it possible to use these geothermometers in the geological context of the Havelange, namely meta-sediments in fold-and-thrust belt? Are these variations due to dilution effects or to the unavailability of the necessary mineral phases in the water?

#### **7. Conclusions**

In this study, the geochemical composition analysis of spring water is applied as a surface tool for deep geothermal potential exploration. It aims to detect the geochemical indications of the impact of ascending deep-water flow on the composition of spring water samples. This approach is of particular interest in blind geothermal systems where there are no clear surface manifestations of the presence of a deep geothermal system. The technique is here applied to water samples collected in the near and far field around the Havelange borehole. This site is the selected H2020 MEET project demo-site for the evaluation of the geothermal potential of the unconventional reservoirs in the Variscan metasedimentary system, unaffected later by an extensional deformation phase.

The results show that the water samples can be separated into different clusters of compositions revealing different water evolutions. The number of clusters is dependent on the statistical method applied for the data treatment. Using the hierarchical clustering, seven clusters can be evaluated and related to different combination of concentrations/values of elements or parameters such as Li, Rb, Sr, pH, and EC. The application of the heat map technique demonstrates the presence of at least three types of water. The first group consisting of water sources locally known under the name of "Pouhon", is characterized by an acidic pH, a high EC, and TDS and by the frequent presence of anomalies in Fe, Mn, Ni, Be, Mg, and Li. The second group is represented primarily by carbonate water compositions with neutral to basic pH as well as high EC and TDS. Bromide, Mo, U, V, Se, Sb, Li, Rb, Sr, and Cu anomalies are frequently observed in this category. The Chaudfontaine reference hydrothermal site and the samples located in Eastern neighbourhood (near the village of Moressée) belong to this second type. Waters from this category constitute the targets for future geothermal studies. In fact, the water samples around the village of Moressée show higher concentrations of Li, Sr, and Rb than in Chaudfontaine. The third and last group contains superficial waters with a low conductivity and TDS. They exhibit a high concentration of NO<sup>3</sup> and low concentrations of Li, Rb, Ca, Na, K, Mo, and HCO3. These superficial waters are frequently associated with the outcropping zone of lower Famennian formations that represent an aquiclude and act as a cap rock for the deep-water reservoir. Future investigations will need to focus on other categories of analyses such as the isotopic and gas content.

In addition, this paper shows that the use of geothermometers in the Havelange context, and probably more broadly in metasedimentary fold-and-thrust belt domains, need to be considerate with caution. In fact, the low temperature presupposed (around 100 ◦C) and the lack of knowledge on the phase balance in the reservoir suggest that the method can hardly directly be applied with commonly used geothermometers (chalcedony, quartz, Li, Na-K-Ca, K-Mg, and Mg-Li). A hydrogeochemical model of the reservoir would possibly provide indication of the water composition evolution in our system and to develop geothermometers usable in this geological context.

To conclude, the indication of deep fluid flow in the region of the Havelange borehole is a significant information, but at this stage it is difficult to evaluate if such phenomenon is restricted to a small zone around the study site and if it can be extrapolated to numerous zones of occurrence of Variscan meta-sedimentary formations. If this second option could

be verified, it would open new opportunities for the development of deep geothermal projects in numerous regions of North-West Europe, such as the Rheinische Schiefergebirge in Germany, the Oesling in the Great Duchy of Luxembourg, the Ardenne in Belgium to even Devon and Cornwall in SW-England.

**Supplementary Materials:** The following are available online at https://www.mdpi.com/article/10 .3390/geosciences11110437/s1, Figure S1: Stiff diagrams of all the water springs samples classified by clusters, Table S1: Coordinates of the spring water samples and results of analyses of the physicochemical parameters used in this article, Table S2: Detailed list of the SWDE laboratory parameters and LOQ.

**Author Contributions:** Conceptualization, Y.V. and M.C.; methodology Y.V., M.C., V.S., T.G., B.M., E.P. and C.B.; software, Y.V. and M.C.; validation, Y.V., M.C., S.B. and V.S.; formal analysis, Y.V., M.C., S.B. and V.S.; investigation, Y.V., M.C., S.B. and V.S.; resources, Y.V., T.G., V.S., C.B. and SWDE; data curation, Y.V. and M.C.; writing—original draft preparation, Y.V. and M.C.; writing—review and editing, Y.V., M.C., S.B., V.S. and H2020 MEET consortium; visualization, Y.V. and M.C.; supervision, Y.V.; project administration, Y.V.; funding acquisition, Y.V., E.P. and H2020 MEET consortium. All authors have read and agreed to the published version of the manuscript.

**Funding:** This project has received funding from the European Union's Horizon 2020 research and innovation program under grant agreement No 792037 (H2020 MEET project).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** The authors greatly thank, Jean-Louis Cornet for his contribution on Chaudfontaine's hydrogeology, Jean-Benoit Charlier and Jennifer Defoux for their advice and explanations on analysis made in the SWDE laboratory. We want to thank Jean Goffaux from AIEC for is help during the sampling campaign. Thanks to Renata Barros for her help on Piper diagrams and water analyses interpretation. We are grateful to de Woot and the owners who have authorized us to sample the water on their land. Also, we wish to thank the MEET project partners and particularly Albert Genter for his help on geothermometers methods reflexion. The authors thank the reviewers who gave their time for critical reading of the manuscript and the improvement of it.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


## *Article* **Use of Mohr Diagrams to Predict Fracturing in a Potential Geothermal Reservoir**

**D.C.P. Peacock 1,2,\*, David J. Sanderson <sup>3</sup> and Bernd Leiss 1,2**


**\*** Correspondence: peacock@uni-goettingen.de

**Abstract:** Inferences have to be made about likely structures and their effects on fluid flow in a geothermal reservoir at the pre-drilling stage. Simple mechanical modelling, using reasonable ranges of values for rock properties, stresses and fluid pressures, is used here to predict the range of possible structures that are likely to exist in the sub-surface and that may be generated during stimulation of a potential geothermal reservoir. In particular, Mohr diagrams are used to show under what fluid pressures and stresses different types and orientations of fractures are likely to be reactivated or generated. The approach enables the effects of parameters to be modelled individually, and for the types and orientations of fractures to be considered. This modelling is useful for helping geoscientists consider, model, and predict the ranges of mechanical properties of rock, stresses, fluid pressures, and the resultant fractures that are likely to occur in the sub-surface. Here, the modelling is applied to folded and thrusted greywackes and slates, which are planned to be developed as an Enhanced Geothermal System beneath Göttingen.

**Keywords:** stress; fluid pressure; Mohr diagrams; fracturing; geothermal; greywackes; slates

## **1. Introduction**

A study is being undertaken to predict the structures and fluid flow behaviour in the sub-surface as part of a proposed geothermal project at Göttingen in Germany [1–3]. The reservoir rocks are the Devonian and Carboniferous metasedimentary sequence thought to occur at a depth of ~1.5 km, beneath a cover of Permian and Mesozoic sedimentary rocks [4]. Göttingen is one of the sites within the European funded project Multidisciplinary and multi-context demonstration of EGS exploration and Exploitation Techniques and potentials (MEET) to develop enhanced geothermal systems (EGS) across Europe (e.g., [5–7]). The Triassic Bunter Sandstone is also being considered as a potential medium-deep geothermal reservoir (i.e., at depths between about 200 m and 1000 m; e.g., [8]), including heat storage options [2], and this is also discussed here.

Only two wells have yet penetrated the metasedimentary rocks in the Göttingen area, these not extending far below the base Zechstein, and so limited well data are available. Additionally, the limited seismic data available show poor resolution beneath the Zechstein salt (e.g., [9,10]). Two seismic lines were shot in 2015, these being 10 km and 11 km long and to about 5 km deep. These seismic lines allow interpretation of the post-Carboniferous sedimentary rocks in the north-south striking Leinetal Graben [3], but do not enable reliable interpretation of the sub-Zechstein rocks. The metasedimentary rocks exposed in the Harz Mountains, ~40 km NE of Göttingen, are being used to predict the rocks and structures that may occur in the sub-surface at Göttingen, and to gain data input for discrete fracture network (DFN) modelling. Exposures of the Bunter Sandstone occur in the area around Göttingen (e.g., [11–13]).

**Citation:** Peacock, D.C.P.; Sanderson, D.J.; Leiss, B. Use of Mohr Diagrams to Predict Fracturing in a Potential Geothermal Reservoir. *Geosciences* **2021**, *11*, 501. https://doi.org/ 10.3390/geosciences11120501

Academic Editors: Béatrice A. Ledésert, Ronan L. Hébert, Ghislain Trullenque, Albert Genter, Eléonore Dalmais, Jean Hérisson and Jesus Martinez-Frias

Received: 24 September 2021 Accepted: 2 December 2021 Published: 9 December 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

There are significant uncertainties involved in evaluating the characteristics and mechanical properties of the rocks beneath Göttingen. Although field analogues indicate many different types of natural fractures occur (faults, veins, joints, etc.), their intensity, geometry, topology and spatial variation in the sub-surface are unknown. Many of the fractures, especially the joints, may not exist at reservoir depths (e.g., [14,15]). The proposed EGS project would involve stimulation of intensely-deformed Upper Palaeozoic rocks, and there are significant uncertainties involved in predicting the hydraulic fracturing of such anisotropic and pre-fractured rocks (e.g., [16]).

Because there is limited knowledge of the reservoir rocks in the sub-surface, including such parameters as fracture types, orientations, apertures, and connectivity, there is need for an early-stage (pre-drilling) assessment that will enable reasonable predictions to be made about natural and induced fractures in the sub-surface. Here, we use simple modelling and reasonable values of stress states, fluid pressures and rock failure criteria to make predictions about the conditions under which rocks will fracture.

The aim of this paper is to develop a simple workflow in which we assess the likely stress states, fluid pressures, and failure conditions in the sub-surface. We then use Mohr diagrams (Figure 1; e.g., [17,18]) to make predictions of the behaviour of rocks and fluids within potential reservoir rocks. The approach uses information about rock types and structures obtained from exposed analogues and rock deformation tests to predict the effects of changes in effective stresses on natural and induced fractures. In the absence of information on the geometry and topology of the fracture networks and on the conductivity of the fractures, this represents an early-stage approach and a necessary prerequisite to more detailed analysis of the contribution of fractures to fluid flow, such as through the use of DFN modelling (e.g., [19]).

Although the approach is simple, it provides understanding of the relationships between key factors controlling rock behaviour. It helps us identify uncertainties and their possible effects. It can also be considered as a "dynamic" analysis for fracturing, because it can be used to predict the reactivation and generation of fractures as fluid pressures and stresses change. Here, *reactivation* is used to mean renewed shear and/or opening displacement on a pre-existing fracture.

The methods presented here have general applicability to making predictions about fractures in the sub-surface, but here we focus on several key questions about the proposed geothermal reservoir at Göttingen:


#### **2. Predictions about the Pre-Permian Geology beneath Göttingen**

In the absence of well data or high-quality seismic data for the sub-Zechstein rocks, the rocks beneath the Permian Zechstein evaporites at Göttingen are predicted to be Devonian quartzitic sandstones and slates, and Carboniferous greywackes and slates (mainly Culm flysch deposits). Such rocks are exposed in the western Harz Mountains ~40 km to the NE, in the Oberharz Anticline and the Culm Fold Zone, which belong to the par-autochthonous domain of the Harz Mountains (e.g., [3,20]) and in the Rhenish Massif ~70 km to the SW (e.g., [21–23]). The fractures visible in these exposures include veins and joints [24], with cleavage being well-developed in the slates [25]. Small thrusts that appear to have displacements of up to a few metres are exposed [26], but larger thrusts are not wellexposed. The north-eastern boundary the Harz Mountains is marked by the Harznordrand

Fault, which was active during the Late Cretaceous and Tertiary [27]. NW-SE striking Mesozoic normal and oblique-slip faults occur in the Harz Mountains, some of which contained economic Pb-Zn and Ba-F deposits [28]. well‐exposed. The north‐eastern boundary the Harz Mountains is marked by the Harznordrand Fault, which was active during the Late Cretaceous and Tertiary [27]. NW‐ SE striking Mesozoic normal and oblique‐slip faults occur in the Harz Mountains, some of which contained economic Pb‐Zn and Ba‐F deposits [28]. SE striking Mesozoic normal and oblique‐slip faults occur in the Harz Mountains, some of which contained economic Pb‐Zn and Ba‐F deposits [28]. well‐exposed. The north‐eastern boundary the Harz Mountains is marked by the Harznordrand Fault, which was active during the Late Cretaceous and Tertiary [27]. NW‐ SE striking Mesozoic normal and oblique‐slip faults occur in the Harz Mountains, some Harznordrand Fault, which was active during the Late Cretaceous and Tertiary [27]. NW‐ SE striking Mesozoic normal and oblique‐slip faults occur in the Harz Mountains,some of which contained economic Pb‐Zn and Ba‐F deposits [28]. well‐exposed. The north‐eastern boundary the Harz Mountains is marked by the Harznordrand Fault, which was active during the Late Cretaceous and Tertiary [27]. NW‐ striking Mesozoic oblique‐ faults the Harz Mountains, some to have displacements of up to a few metres are exposed [26], but larger thrusts are not well‐exposed. The north‐eastern boundary the Harz Mountains is markedby the Harznordrand Fault, which was active during the Late Cretaceous and Tertiary [27]. NW‐ well‐exposed. The north‐eastern boundary the Harz Mountains is marked by the Harznordrand Fault, which was active during the Late Cretaceousand Tertiary [27]. NW‐ SE striking Mesozoic normal and oblique‐slip faults occur in the Harz Mountains, some

joints [24], with cleavage being well‐developed in the slates [25]. Small thrusts that appear to have displacements of up to a few metres are exposed [26], but larger thrusts are not

joints [24], with cleavage being well‐developed in the slates [25]. Small thrusts that appear

SE striking Mesozoic normal and oblique‐slip faults occur in the Harz Mountains, some

joints [24], with cleavage being well‐developed in the slates [25]. Small thrusts that appear to have displacements of up to a few metres are exposed [26], but larger thrusts are not well‐exposed. The north‐eastern boundary the Harz Mountains is marked by the

joints [24], with cleavage being well‐developed in the slates [25]. Small thrusts that appear to have displacements of up to a few metres are exposed [26], but larger thrusts are not

joints [24], with cleavage being well‐developed in the slates [25]. Small thrusts that appear to have displacements of up to a few metres are exposed [26], but larger thrustsare not

*Geosciences* **2021**, *11*, x FOR PEER REVIEW 3 of 27

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joints [24], with cleavage being well‐developed in the slates [25]. Small thrusts that appear to have displacements of up to a few metres are exposed [26], but larger thrusts are not well‐exposed. The north‐eastern boundary the Harz Mountains is marked by the Harznordrand Fault, which was active during the Late Cretaceous and Tertiary [27]. NW‐

geothermal energy. These predictions are expressed in terms of seven parameters that we

*Geosciences* **2021**, *11*, x FOR PEER REVIEW 3 of 27

*Geosciences* **2021**, *11*, x FOR PEER REVIEW 3 of 27

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of which contained economic Pb‐Zn and Ba‐F deposits [28].

of whichcontainedeconomicPb‐ZnandBa‐Fdeposits[28].

of which contained economic Pb‐Zn and Ba‐F deposits [28].

**Figure 1.** (**a**) Generalised Mohr diagram of shear stress (τ) against normal effective stress (σ'N) show‐ ing failure envelopes. Continuous line ("Cohesional") = Mohr failure envelope for intact rock, with tensile strength (T = 2 MPa), cohesion (SO = 4 MPa) and coefficient of internal friction (μ = 0.75). Dotted (parabolic) line ("Griffith") = Griffith criterion. Dashed line ("Cohesionless") = cohesionless failure (μ = 0.75) typical of slip on faults. Three stress states are shown, representing stable (), shear failure on cohesionless fractures () and extension fracturing (). (**b**) Mohr diagram showing the fields in which extension (), hybrid () and shear () fractures occur [29]. **Figure 1.** (**a**) Generalised Mohr diagram of shear stress (τ) against normal effective stress (σ 0 N) showing failure envelopes. Continuous line ("Cohesional") = Mohr failure envelope for intact rock, with tensile strength (T = 2 MPa), cohesion (S<sup>0</sup> = 4 MPa) and coefficient of internal friction (µ = 0.75). Dotted (parabolic) line ("Griffith") = Griffith criterion. Dashed line ("Cohesionless") = cohesionless failure (µ = 0.75) typical of slip on faults. Three stress states are shown, representing stable ( ing failure envelopes. Continuous line ("Cohesional") = Mohr failure envelope for intact rock, with tensile strength (T = 2 MPa), cohesion (SO = 4 MPa) and coefficient of internal friction (μ = 0.75). Dotted (parabolic) line ("Griffith") = Griffith criterion. Dashed line ("Cohesionless") = cohesionless failure (μ = 0.75) typical of slip on faults. Three stress states are shown, representing stable (), shear failure on cohesionless fractures () and extension fracturing (). (**b**) Mohr diagram showing the fields in which extension (), hybrid () and shear () fractures occur [29]. Table 1 shows features of these "basement" rocks that are likely to be important for ), shear failure on cohesionless fractures ( **Figure 1.** (**a**) Generalised Mohr diagram of shear stress (τ) against normal effective stress (σ'N) show‐ ing failure envelopes. Continuous line ("Cohesional") = Mohr failure envelope for intact rock, with tensile strength (T = 2 MPa), cohesion (SO = 4 MPa) and coefficient of internal friction (μ = 0.75). Dotted (parabolic) line ("Griffith") = Griffith criterion. Dashed line ("Cohesionless") = cohesionless failure (μ = 0.75) typical of slip on faults. Three stress states are shown, representing stable (), shear failure on cohesionless fractures () and extension fracturing (). (**b**) Mohr diagram showing the fields in which extension (), hybrid () and shear () fractures occur [29]. ) and extension fracturing ( **Figure 1.** (**a**) Generalised Mohr diagram of shear stress (τ) against normal effective stress (σ'N) show‐ ing failure envelopes. Continuous line ("Cohesional") = Mohr failure envelope for intact rock, with tensile strength (T = 2 MPa), cohesion (SO = 4 MPa) and coefficient of internal friction (μ = 0.75). Dotted (parabolic) line ("Griffith") = Griffith criterion. Dashed line ("Cohesionless") = cohesionless failure (μ = 0.75) typical of slip on faults. Three stress states are shown, representing stable (), shear failure on cohesionless fractures () and extension fracturing (). (**b**) Mohr diagram showing the fields in which extension (), hybrid () and shear ) fractures occur [29]. ). (**b**) Mohr diagram showing the fields in which extension ( **Figure 1.**(**a**) GeneralisedMohr diagramof shearstress(τ)againstnormaleffective stress(σ'N)show‐ing envelopes. = failure for rock, with tensilestrength(T =2MPa),cohesion (SO =4 MPa) and coefficientofinternal friction (μ <sup>=</sup> 0.75).Dotted ("Griffith") <sup>=</sup> Griffith criterion. Dashed line <sup>=</sup> failure (μ = 0.75) typical of slip on faults. Three stress states are shown, representing stable (), shear failure on cohesionless fractures () and extension fracturing (). (**b**) Mohr diagram showing the fields in which extension (), hybrid () and shear () fractures occur [29]. ), hybrid ( **Figure 1.** (**a**) Generalised Mohr diagram of shear stress (τ) against normal effective stress (σ'N) show‐ ing failure envelopes. Continuous line ("Cohesional") = Mohr failure envelope for intact rock, with tensile strength (T = 2 MPa), cohesion (SO = 4 MPa) and coefficient of internalfriction (μ = 0.75). Dotted(parabolic) line ("Griffith") = Griffith criterion. Dashed line ("Cohesionless") = cohesionless failure (μ = 0.75) typical of slip on faults. Three stress states are shown, representing stable (), shear failure on cohesionless fractures ()andextension fracturing (). (**b**) Mohr diagram showing the ) and shear ( **Figure 1.** (**a**) Generalised Mohr diagram of shear stress (τ) against normal effective stress (σ'N) show‐ ing failure envelopes. Continuous line ("Cohesional") = Mohrfailure envelope for intact rock, with tensile strength (T = 2 MPa), cohesion(SO = 4 MPa) and coefficient of internal friction (μ = 0.75). Dotted (parabolic) line("Griffith") = Griffith criterion. Dashed line ("Cohesionless") = cohesionless failure (μ = 0.75) typical of slip on faults. Three stress states are shown, representing stable (), shear failure on cohesionless fractures () and extension fracturing (). (**b**) Mohr diagram showing the fields in which extension (), hybrid () and shear ()fractures occur [29]. ) fractures occur [29].

Table 1 shows features of these "basement" rocks that are likely to be important for geothermal energy. These predictions are expressed in terms of seven parameters that we consider important in describing a geothermal reservoir: lithology and inferred rheologi‐ cal behaviour, fluid type, stresses, fluid pressure, temperature, strains and existing struc‐ tures, and geological history (cf. [30]). More information is available about the Bunter Sandstone, which is exposed in the consider important in describing a geothermal reservoir: lithology and inferred rheologi‐ cal behaviour, fluid type, stresses, fluid pressure, temperature, strains and existing struc‐ tures, and geological history (cf. [30]). More information is available about the Bunter Sandstone, which is exposed in the Göttingen area (e.g., [11,12]). Fractures exposed include normal faults [31], strike‐slip Table 1 shows features of these "basement" rocks that are likely to be important for geothermal energy. These predictions are expressed in terms of seven parameters that we consider important in describing a geothermal reservoir: lithology and inferred rheologi‐ cal behaviour, fluid type, stresses, fluid pressure, temperature, strains and existing struc‐ tures, and geological history (cf. [30]). geothermal energy. These predictions are expressed in terms of seven parameters that we consider important in describing a geothermal reservoir: lithology and inferred rheologi‐ cal behaviour, fluid type, stresses, fluid pressure, temperature, strains and existing struc‐ tures, and geological history (cf. [30]). More information is available about the Bunter Sandstone, which is exposed in the Table 1 shows features of these "basement" rocks that are likely to be important for geothermal energy. These predictions are expressed in terms of seven parameters that we consider important in describing a geothermal reservoir: lithology and inferred rheologi‐ behaviour, stresses, fluid pressure, existing struc‐ Table 1 shows features of these "basement" rocks thatare likely to be important for geothermal energy. These predictions are expressed in terms of seven parameters that we consider important in describing a geothermal reservoir: lithology and inferred rheologi‐ cal behaviour, fluid type, stresses, fluid pressure, temperature,strains and existing struc‐ Table 1 shows features of these "basement" rocks that are likely to be important for geothermal energy. These predictions are expressed in terms of seven parameters that we consider important in describing a geothermal reservoir: lithology and inferred rheologi‐ cal behaviour, fluid type, stresses, fluid pressure, temperature, strains and existing struc‐ tures, and geological history (cf. [30]). Table 1 shows features of these "basement" rocks that are likely to be important for geothermal energy. These predictions are expressed in terms of seven parameters that we consider important in describing a geothermal reservoir: lithology and inferred rheological behaviour, fluid type, stresses, fluid pressure, temperature, strains and existing structures, and geological history (cf. [30]).

fields in which extension (), hybrid () and shear () fractures occur [29].

Table 1 shows features of these "basement" rocks that are likely to be important for

Göttingen area (e.g., [11,12]). Fractures exposed include normal faults [31], strike‐slip faults [32], veins [33], sedimentary dykes [34], and joints [35]. There is limited well data, which suggests that the Bunter Sandstone has been affected by halokinesis of the Zech‐ stein evaporites [1,36,37]. faults [32], veins [33], sedimentary dykes [34], and joints [35]. There is limited well data, which suggests that the Bunter Sandstone has been affected by halokinesis of the Zech‐ stein evaporites [1,36,37]. More information is available about the Bunter Sandstone, which is exposed in the Göttingen area (e.g., [11,12]). Fractures exposed include normal faults [31], strike‐slip faults [32], veins [33], sedimentary dykes [34], and joints [35]. There is limited well data, which suggests that the Bunter Sandstone has been affected by halokinesis of the Zech‐ stein evaporites [1,36,37]. Göttingen area (e.g., [11,12]). Fractures exposed include normal faults [31], strike‐slip faults [32], veins [33], sedimentary dykes [34], and joints [35]. There is limited well data, which suggests that the Bunter Sandstone has been affected by halokinesis of the Zech‐ stein evaporites [1,36,37]. tures, and geologicalhistory(cf.[30]).More information is available about the Bunter Sandstone, which is exposed in the Göttingen area (e.g., [11,12]). Fractures exposed include normal faults [31], strike‐slip faults [32], veins [33], sedimentary dykes[34], and joints [35]. There is limited well data, which suggests that the Bunter Sandstone has been affected by halokinesis of the Zech‐ stein evaporites [1,36,37]. tures, and geological history (cf. [30]). More information is available about the Bunter Sandstone, which is exposed in the Göttingen area (e.g., [11,12]). Fractures exposed include normal faults [31], strike‐slip faults [32], veins[33], sedimentary dykes [34], and joints [35]. There is limited well data, which suggests that the Bunter Sandstone has been affected by halokinesis of the Zech‐ More information isavailable about the Bunter Sandstone, which is exposed in the Göttingen area (e.g., [11,12]). Fractures exposed include normal faults [31], strike‐slip faults [32], veins [33], sedimentary dykes [34], and joints [35]. There is limited well data, which suggests that the Bunter Sandstone has been affected by halokinesis of the Zech‐ stein evaporites [1,36,37]. More information is available about the Bunter Sandstone, which is exposed in the Göttingen area (e.g., [11,12]). Fractures exposed include normal faults [31], strike-slip faults [32], veins [33], sedimentary dykes [34], and joints [35]. There is limited well data, which suggests that the Bunter Sandstone has been affected by halokinesis of the Zechstein evaporites [1,36,37].

stein evaporites [1,36,37].

**Table 1.** Predictions about the geology of the potential geothermal reservoirs at Göttingen. See, for example, [38] for full information about deformation of the Bunter Sandstone in the Leinetal Graben. See [20,39] for further information about the geology of the Devonian and Carboniferous rocks of the Harz Mountains.


**Table 2.** Parameters used in the modelling. \* Geostatic stress ratios are calculated from the Poisson ratios. \*\* Representative values of the coefficient of internal friction are used here, using the approximate median value of the range of internal angles of friction.


#### **3. Model Set-Up**

A Microsoft Excel spreadsheet has been created to make the necessary calculations and to plot Mohr diagrams (e.g., Figure 2). For simplicity, we keep the Mohr diagram analysis two-dimensional, considering just the vertical stress and the horizontal stress in one direction. This approach is taken both because it simplifies the analysis and because the orientations and magnitudes of the horizontal stresses are presently unconstrained. We start with a reference state where the horizontal strains are zero, which is the uniaxial strain condition (e.g., [58]) and the horizontal effective stress (σ 0 <sup>H</sup>) is given by:

$$
\sigma'\_{\rm H} = \mathbf{k}\_0 \ \sigma'\_{\rm V} \tag{1}
$$

where k<sup>0</sup> is the geostatic stress ratio [59] or coefficient of lateral earth pressure [60]. The geostatic stress ratio is the ratio of the horizontal effective stress to the vertical effective stress (i.e., k<sup>0</sup> = σ 0 <sup>H</sup>/σ 0 <sup>V</sup>). For an isotropic elastic material:

$$\mathbf{k}\_0 = \mathbf{v}/(\mathbf{1} - \mathbf{v})\tag{2}$$

where ν is Poisson's ratio, which is generally in the range 0 to 0.5 (where 0.5 is incompressible). For most water-saturated rocks, is in the range 0.15 < ν < 0.4 (e.g., [61]).

We consider the vertical stress to result from the weight of the overlying material and the horizontal stresses to result from the combined effects of the geostatic stress ratio and the applied tectonic stresses. We start the analysis with a base-case, in which fluid pressure is hydrostatic and there are no applied tectonic stresses. We then consider how changes in fluid pressure and/or apply tensile or compressional horizontal ("tectonic") stresses might lead to fracturing.

#### *3.1. Mohr Diagrams, Stresses and Failure Envelopes*

Mohr diagrams are commonly used to show the relationships between stresses, fluid pressure, and fractures (Figure 1a; e.g., [62]). They provide a convenient graphic representation of the effective stress states and of failure (e.g., [17]). Normal stress (σN) is plotted on the *x*-axis and shear stress (τ) on the *y*-axis, with the principal axes of stress (σ<sup>1</sup> = maximum compressive stress, σ<sup>2</sup> = intermediate compressive stress, σ<sup>3</sup> = minimum compressive stress) or principal axes of effective stress (σ 0 <sup>1</sup> = maximum effective compressive stress, etc., where σ <sup>0</sup> = σ − B.PF, where P<sup>F</sup> = fluid pressure and B is Biot's constant, which we will assume to be approximately 1). Since the magnitudes and orientations of the horizontal stresses are currently unknown, we consider stress in 2D, with σ<sup>2</sup> being ignored (e.g., [63]). We assume an Andersonian stress regime with one principal stress vertical (the overburden stress, σV) and the other horizontal stress (σh) [64]. In the base case models used here, the starting point is that there are no applied tectonic stresses, so σ<sup>V</sup> = σ1, and σ<sup>h</sup> = σ<sup>3</sup> (Figure 2).

*Geosciences* **2021**, *11*, x FOR PEER REVIEW 7 of 27

**Figure 2.** Base case Mohr diagrams, with Mohr circles for end‐member geostatic stress ratios (k0) shown (see Table 3 for parameters used). Representative dips of structures are shown to illustrate which of these structures might be reactivated under different stress conditions. (**a**) The Bunter Sandstone. (**b**) Devonian and Carboniferous greywackes at a depth of 2 km. (**c**) Devonian and Carboniferous slates at a depth of 2 km. (**d**) Devonian and Carboniferous greywackes at a depth of 4.5 km. (**e**) Devonian and Carboniferous slates at a depth of 4.5 km. **Figure 2.** Base case Mohr diagrams, with Mohr circles for end-member geostatic stress ratios (k<sup>0</sup> ) shown (see Table 3 for parameters used). Representative dips of structures are shown to illustrate which of these structures might be reactivated under different stress conditions. (**a**) The Bunter Sandstone. (**b**) Devonian and Carboniferous greywackes at a depth of 2 km. (**c**) Devonian and Carboniferous slates at a depth of 2 km. (**d**) Devonian and Carboniferous greywackes at a depth of 4.5 km. (**e**) Devonian and Carboniferous slates at a depth of 4.5 km.

**Table 3.** Parameters used to model the base case scenarios for the Bunter Sandstone and the Devonian and Carboniferous greywackes and slates, with stresses and fluid pressures rounded to one decimal place. Values that depend on different geostatic stress ratios (k<sup>0</sup> ) are shown in different colours (red for lower k<sup>0</sup> values in range, blue for upper k<sup>0</sup> values). Values specific to a modelled depth of 2 km are shown in bold, and values specific to a modelled depth of 4.5 km are shown in italics. Representative structures are shown for the dips of structures in both the SE- and NW-dipping limbs of folds in the greywackes and slates. Effective stresses are calculated assuming a Biot coefficient of 1.


Any 2D state of effective stress can be represented by a circle that intersects the *x*-axis at σ 0 <sup>1</sup> and σ 0 <sup>3</sup>, with the centre of the circle representing the mean stress (σ 0 Mean = (σ 0 <sup>1</sup> + σ 0 <sup>3</sup>)/2). Mohr diagrams are useful for illustrating the conditions under which fracturing may occur in a particular rock under specific conditions (i.e., the failure envelope), but only if the effective stresses are plotted.

Fracturing is classically attributed to conditions where the effective stress components exceed some critical value, usually termed the strength, which is thought to be a property of the material (e.g., [65]). Tensile failure occurs if:

$$
\sigma'\_3 \le \Upsilon \tag{3}
$$

where T is the tensile strength. Compressive stresses are positive. Shear failure occurs if:

$$
\pi \ge \mathcal{S}\_0 + \mu \left. \sigma\_{\mathcal{N}} \right| \tag{4}
$$

where µ is the coefficient of (internal) friction and S<sup>0</sup> is the cohesion. These conditions are usually linked to produce a failure envelope (e.g., [66,67]), as in Figure 1a.

The composite failure criteria used in this work (e.g., Figures 1 and 2) combine a linear, Mohr–Coulomb envelope for shear fracture under compressive effective stresses, with a parabolic, plane Griffith envelope for tensile/hybrid fractures under tensile stress conditions. The two envelopes join at the τ-axis (σ 0 = 0), where there is a discontinuity in the slopes of the failure envelopes. Continuity in the slope could be achieved by using the methods outlined in [68]. This type of composite failure envelope is consistent with a modification of the Griffith theory to account for closure and frictional behaviour under compression [69,70].

Following [71], the plane Griffith failure envelope in Mohr space (τ, σ 0 ) is given by:

$$
\pi^2 = 4\text{ T (}\sigma' + \text{T)}\tag{5}
$$

of which contained economic Pb‐Zn and Ba‐F deposits [28].

*Geosciences* **2021**, *11*, x FOR PEER REVIEW 3 of 27

*Geosciences* **2021**, *11*, x FOR PEER REVIEW 3 of 27

of which contained economic Pb‐Zn and Ba‐F deposits [28].

*Geosciences* **2021**, *11*, x FOR PEER REVIEW 3 of 27

of which contained economic Pb‐Zn and Ba‐F deposits [28].

joints [24], with cleavage being well‐developed in the slates [25]. Small thrusts that appear to have displacements of up to a few metres are exposed [26], but larger thrusts are not well‐exposed. The north‐eastern boundary the Harz Mountains is marked by the Harznordrand Fault, which was active during the Late Cretaceous and Tertiary [27]. NW‐ SE striking Mesozoic normal and oblique‐slip faults occur in the Harz Mountains, some

joints [24], with cleavage being well‐developed in the slates [25]. Small thrusts that appear to have displacements of up to a few metres are exposed [26], but larger thrusts are not well‐exposed. The north‐eastern boundary the Harz Mountains is marked by the Harznordrand Fault, which was active during the Late Cretaceous and Tertiary [27]. NW‐ SE striking Mesozoic normal and oblique‐slip faults occur in the Harz Mountains, some

joints [24], with cleavage being well‐developed in the slates [25]. Small thrusts that appear to have displacements of up to a few metres are exposed [26], but larger thrusts are not well‐exposed. The north‐eastern boundary the Harz Mountains is marked by the Harznordrand Fault, which was active during the Late Cretaceous and Tertiary [27]. NW‐ SE striking Mesozoic normal and oblique‐slip faults occur in the Harz Mountains, some

and the Mohr–Coulomb envelope by:

joints [24], with cleavage being well‐developed in the slates [25]. Small thrusts that appear to have displacements of up to a few metres are exposed [26], but larger thrusts are not well‐exposed. The north‐eastern boundary the Harz Mountains is marked by the

SE striking Mesozoic normal and oblique‐slip faults occur in the Harz Mountains, some

*Geosciences* **2021**, *11*, x FOR PEER REVIEW 3 of 27

of which contained economic Pb‐Zn and Ba‐F deposits [28].

$$
\pi = \mathbf{S}\_0 + \boldsymbol{\mu} \ \boldsymbol{\sigma}' \tag{6}
$$

where T = Tensile strength, S<sup>0</sup> = cohesion, and µ = coefficient of internal friction. Putting σ 0 = 0 in both Equations (5) and (6) gives:

$$
\boldsymbol{\pi} = \mathbf{S}\_0 = \mathbf{2} \,\mathrm{T} \tag{7}
$$

Hence, the cohesion would be simply twice the tensile strength. The unconfined compressive strength (C0), is a widely measured parameter representing the stress required for failure when σ<sup>3</sup> <sup>0</sup> = 0 which for Mohr–Coulomb failure is given by:

$$\mathbf{C}\_{0} = \mathbf{2S}\_{0} \left[ (\mu^{2} + 1)^{1/2} + \mu \right] \tag{8}$$

Substituting Equation (7) in Equation (8) gives:

$$\mathbf{C}\_0 = 4\mathbf{T} \left[ (\mu^2 + \mathbf{1})^{1/2} + \mu \right] \tag{9}$$

Using a value of µ ≈ 1, gives the following approximations for rocks: (1) S<sup>0</sup> ≈ 0.2 C0; (2) T ≈ 0.5 S0; so (3) T ≈ 0.1 C<sup>0</sup> [71]. Sedimentary rocks typically show an exponential increase in C<sup>0</sup> with decreasing porosity [72]. **Figure 1.** (**a**) Generalised Mohr diagram of shear stress (τ) against normal effective stress (σ'N) show‐ ing failure envelopes. Continuous line ("Cohesional") = Mohr failure envelope for intact rock, with

We assume a lower bound to likely failure envelopes is given by the failure envelope shown by the "Cohesionless" line in Figure 1a, which is typical of slip on pre-existing cohesionless fractures (e.g., joints) (e.g., [73]). Such failure envelopes typically have coefficients of friction of 0.6 to 0.9 (average 0.75; e.g., [74]). tensile strength (T = 2 MPa), cohesion (SO = 4 MPa) and coefficient of internal friction (μ = 0.75). Dotted (parabolic) line ("Griffith") = Griffith criterion. Dashed line ("Cohesionless") = cohesionless failure (μ = 0.75) typical of slip on faults. Three stress states are shown, representing stable (), shear failure on cohesionless fractures () and extension fracturing (). (**b**) Mohr diagram showing the

In Figure 1a, the effective stress state shown by Mohr circle fields in which extension (), hybrid () and shear () fractures occur [29]. Table 1 shows features of these "basement" rocks that are likely to be important for geothermal energy. These predictions are expressed in terms of seven parameters that we consider important in describing a geothermal reservoir: lithology and inferred rheologi‐ cal behaviour, fluid type, stresses, fluid pressure, temperature, strains and existing struc‐ tures, and geological history (cf. [30]). More information is available about the Bunter Sandstone, which is exposed in the Göttingen area (e.g., [11,12]). Fractures exposed include normal faults [31], strike‐slip is typical of a rock at depth of ~2 km, with the maximum compressive stress being vertical (σV) and caused by the weight of the overlying material. The rock is under a hydrostatic fluid pressure (where PF/σ<sup>V</sup> = ~0.4, based on the assumption that P<sup>F</sup> ~ 20 MPa and σV~50 MPa at 2 km) and a tectonic stress (−2 MPa, as may occur during regional extension). Note that this is in the stable region, but within ~5 MPa of the failure envelope for rocks with cohesionless fractures. Figure 1a shows stress states that are stable ( **Figure 1.** (**a**) Generalised Mohr diagram of shear stress (τ) against normal effective stress (σ'N) show‐ ing failure envelopes. Continuous line ("Cohesional") = Mohr failure envelope for intact rock, with tensile strength (T = 2 MPa), cohesion (SO = 4 MPa) and coefficient of internal friction (μ = 0.75). Dotted (parabolic) line ("Griffith") = Griffith criterion. Dashed line ("Cohesionless") = cohesionless failure (μ = 0.75) typical of slip on faults. Three stress states are shown, representing stable (), shear failure on cohesionless fractures () and extension fracturing (). (**b**) Mohr diagram showing the fields in which extension (), hybrid () and shear () fractures occur [29]. Table 1 shows features of these "basement" rocks that are likely to be important for ), that would cause slip on a suitably orientated pre-existing cohesionless fractures ( **Figure 1.** (**a**) Generalised Mohr diagram of shear stress (τ) against normal effective stress (σ'N) show‐ ing failure envelopes. Continuous line ("Cohesional") = Mohr failure envelope for intact rock, with tensile strength (T = 2 MPa), cohesion (SO = 4 MPa) and coefficient of internal friction (μ = 0.75). Dotted (parabolic) line ("Griffith") = Griffith criterion. Dashed line ("Cohesionless") = cohesionless failure (μ = 0.75) typical of slip on faults. Three stress states are shown, representing stable (), shear failure on cohesionless fractures () and extension fracturing (). (**b**) Mohrdiagram showing the fields in which extension (), hybrid () and shear () fractures occur [29]. ), and that would create tensile failure of the intact rock ( **Figure 1.** (**a**) Generalised Mohr diagram of shear stress (τ) against normal effective stress (σ'N) show‐ ing failure envelopes. Continuous line ("Cohesional") = Mohr failure envelope for intact rock, with tensile strength (T = 2 MPa), cohesion (SO = 4 MPa) and coefficient of internal friction (μ = 0.75). Dotted (parabolic) line ("Griffith") = Griffith criterion. Dashed line ("Cohesionless") = cohesionless failure (μ = 0.75) typical of slip on faults. Three stress states are shown, representing stable (), shear failure on cohesionless fractures () and extension fracturing (). (**b**) Mohr diagram showing the fields in which extension (), hybrid () and shear () fractures occur [29]. ).

faults [32], veins [33], sedimentary dykes [34], and joints [35]. There is limited well data, which suggests that the Bunter Sandstone has been affected by halokinesis of the Zech‐ stein evaporites [1,36,37]. geothermal energy. These predictions are expressed in terms of seven parameters that we consider important in describing a geothermal reservoir: lithology and inferred rheologi‐ cal behaviour, fluid type, stresses, fluid pressure, temperature, strains and existing struc‐ Table 1 shows features of these "basement" rocks that are likely to be important for geothermal energy. These predictions are expressed in terms of seven parameters that we Table 1 shows features of these "basement" rocks that are likely to be important for geothermal energy. These predictions are expressed in terms of seven parameters that we In this paper, we use Mohr diagrams to illustrate the conditions under which a rock can go from a stable stress system (i.e., no active fracturing occurs) to an unstable stress system (i.e., fracturing occurs). The change from stable to unstable condition depends upon:

	- 3. In the upper crust, fluid pressure in the pores and cracks combines with the applied stresses to produce an effective stress, where σ <sup>0</sup> = σ − P<sup>F</sup> (e.g., [79–81]). In the absence of specific information, we use a Biot coefficient (B) of 1, where σ <sup>0</sup> = σ − B.P<sup>F</sup> [82]. Changes in fluid pressure that can lead to fracturing can either be an increase in fluid pressure (e.g., [83]) or a reduction in fluid pressure, which can cause pore collapse (e.g., [84,85]). Pore collapse is not considered further in this paper.

The type and orientation of fractures developed can be predicted from the relationship between the Mohr circle for effective stress and the failure envelope (Figure 1b). Extension fractures typically develop perpendicular to the direction of σ 0 <sup>3</sup> if σ 0 <sup>3</sup> touches the failure envelope on the τ = 0 axis (Figure 1b tensile strength (T = 2 MPa), cohesion (SO = 4 MPa) and coefficient of internal friction (μ = 0.75). Dotted (parabolic) line ("Griffith") = Griffith criterion. Dashed line ("Cohesionless") = cohesionless failure (μ = 0.75) typical of slip on faults. Three stress states are shown, representing stable (), shear failure on cohesionless fractures () and extension fracturing (). (**b**) Mohr diagram showing the fields in which extension (), hybrid () and shear () fractures occur [29]. Table 1 shows features of these "basement" rocks that are likely to be important for geothermal energy. These predictions are expressed in terms of seven parameters that we consider important in describing a geothermal reservoir: lithology and inferred rheologi‐ cal behaviour, fluid type, stresses, fluid pressure, temperature, strains and existing struc‐ ), which generally requires a relatively low differential effective stress (σ 0 Diff = σ 0 <sup>1</sup> − σ 0 <sup>3</sup>). Shear fractures are predicted to develop if the Mohr circle touches the failure envelope in the compressive field (Figure 1b **Figure 1.** (**a**) Generalised Mohr diagram of shear stress (τ) against normal effective stress (σ'N) show‐ ing failure envelopes. Continuous line ("Cohesional") = Mohr failure envelope for intact rock, with tensile strength (T = 2 MPa), cohesion (SO = 4 MPa) and coefficient of internal friction (μ = 0.75). Dotted (parabolic) line ("Griffith") = Griffith criterion. Dashed line ("Cohesionless") = cohesionless failure (μ = 0.75) typical of slip on faults. Three stress states are shown, representing stable (), shear failure on cohesionless fractures () and extension fracturing (). (**b**) Mohr diagram showing the fields in which extension (), hybrid () and shear () fractures occur [29]. Table 1 shows features of these "basement" rocks that are likely to be important for geothermal energy. These predictions are expressed in terms of seven parameters that we ), this typically requiring a relatively high σ 0 Diff. Hybrid fractures develop by synchronous extension and shear (e.g., [29]), and occur if the Mohr circle touches curved part of the failure envelope within the tensile field of the Mohr diagram (Figure 1b **Figure 1.** (**a**) Generalised Mohr diagram of shear stress (τ) against normal effective stress (σ'N) show‐ ing failure envelopes. Continuous line ("Cohesional") = Mohr failure envelope for intact rock, with tensile strength (T = 2 MPa), cohesion (SO = 4 MPa) and coefficient of internal friction (μ = 0.75). Dotted (parabolic) line ("Griffith") = Griffith criterion. Dashed line ("Cohesionless") = cohesionless failure (μ = 0.75) typical of slip on faults. Three stress states are shown, representing stable (), shear failure on cohesionless fractures () andextension fracturing (). (**b**)Mohr diagram showing the ).

**Figure 1.** (**a**) Generalised Mohr diagram of shear stress (τ) against normal effective stress (σ'N) show‐ ing failure envelopes. Continuous line ("Cohesional") = Mohr failure envelope for intact rock, with

*Geosciences* **2021**, *11*, x FOR PEER REVIEW 3 of 27

of which contained economic Pb‐Zn and Ba‐F deposits [28].

joints [24], with cleavage being well‐developed in the slates [25]. Small thrusts that appear to have displacements of up to a few metres are exposed [26], but larger thrusts are not well‐exposed. The north‐eastern boundary the Harz Mountains is marked by the Harznordrand Fault, which was active during the Late Cretaceous and Tertiary [27]. NW‐ SE striking Mesozoic normal and oblique‐slip faults occur in the Harz Mountains, some

joints [24], with cleavage being well‐developed in the slates [25]. Small thrusts that appear to have displacements of up to a few metres are exposed [26], but larger thrusts are not well‐exposed. The north‐eastern boundary the Harz Mountains is marked by the Harznordrand Fault, which was active during the Late Cretaceous and Tertiary [27]. NW‐ SE striking Mesozoic normal and oblique‐slip faults occur in the Harz Mountains, some

joints [24], with cleavage being well‐developed in the slates [25]. Small thrusts that appear to have displacements of up to a few metres are exposed [26], but larger thrusts are not well‐exposed. The north‐eastern boundary the Harz Mountains is marked by the Harznordrand Fault, which was active during the Late Cretaceous and Tertiary [27]. NW‐ SE striking Mesozoic normal and oblique‐slip faults occur in the Harz Mountains, some

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*Geosciences* **2021**, *11*, x FOR PEER REVIEW 3 of 27

of which contained economic Pb‐Zn and Ba‐F deposits [28].

of which contained economic Pb‐Zn and Ba‐F deposits [28].

#### tures, and geological history (cf. [30]). consider importantin describing a geothermal reservoir: lithology and inferred rheologi‐ fields in which extension (), hybrid () and shear () fractures occur [29]. *3.2. Input Data, Assumptions, and Uncertainties*

More information is available about the Bunter Sandstone, which is exposed in the Göttingen area (e.g., [11,12]). Fractures exposed include normal faults [31], strike‐slip faults [32], veins [33], sedimentary dykes [34], and joints [35]. There is limited well data, which suggests that the Bunter Sandstone has been affected by halokinesis of the Zech‐ stein evaporites [1,36,37]. cal behaviour, fluid type, stresses, fluid pressure, temperature, strains and existing struc‐ tures, and geological history (cf. [30]). More information is available about the Bunter Sandstone, which is exposed in the Göttingen area (e.g., [11,12]). Fractures exposed include normal faults [31], strike‐slip faults [32], veins [33], sedimentary dykes [34], and joints [35]. There is limited well data, which suggests that the Bunter Sandstone has been affected by halokinesis of the Zech‐ stein evaporites [1,36,37]. Table 1 shows features of these "basement" rocks that are likely to be important for geothermal energy. These predictions are expressed in terms of seven parameters that we consider important in describing a geothermal reservoir: lithology and inferred rheologi‐ cal behaviour, fluid type, stresses, fluid pressure, temperature, strains and existing struc‐ tures, and geological history (cf. [30]). More information is available about the Bunter Sandstone, which is exposed in the Göttingen area (e.g., [11,12]). Fractures exposed include normal faults [31], strike‐slip faults [32], veins [33], sedimentary dykes [34], and joints [35]. There is limited well data, which suggests that the Bunter Sandstone has been affected by halokinesis of the Zech‐ stein evaporites [1,36,37]. Table 2 shows values from the literature for various rock mechanical parameters for the Bunter Sandstone, greywackes, and slates derived from triaxial tests. Table 2 also gives definitions and the significance of each parameter. Triaxial tests typically use intact hand specimen sized rock samples with no pre-existing fractures visible. As such, these values almost certainly over-estimate the strengths of the larger rock masses in the sub-surface, which generally have pre-existing fractures (e.g., [86]), and should be considered as upperlimit values of rock strength. We, therefore, use lower values for rock strength as inputs into the models (Table 3). The failure envelope (e.g., Figure 2) for each rock type is controlled by the tensile strength (T), cohesion (S0) and coefficient of internal friction (µ = tan ϕ, where ϕ = angle of internal friction) (Equations (3) and (4)). The most widely available rock strength parameter is the uniaxial compressive strength (UCS or C0), determined directly from triaxial tests or estimated from geophysical log data [72,73].

Note that the values presented in Table 3 are generally within the ranges of values for Devonian and Carboniferous greywackes and slates in the Harz Mountains and Belgium presented by [87]. Exceptions are the porosity (greywackes, mean value = 2.42%, range 0.04 to 7.35%, *n* = 88; slates, mean value = 2.21%, range 0.17 to 5.51%, *n* = 20), and the cohesion of the greywackes (mean value = 26.57 MPa, range 10.5 to 45.9 MPa, *n* = 5).

The Mohr circle for effective stress is controlled by the applied stresses and the fluid pressure. The vertical stress can be calculated from the densities of the overlying rocks (e.g., [73,88]). The magnitudes and orientations of these horizontal stresses are much harder to calculate (e.g., from well data; [89]) or predict (e.g., from tectonic stress tensors; [90]). Similarly, pore fluid pressure in rocks in the sub-surface is difficult to predict without well data. For example, [91] use sediment consolidation experiments and numerical models to predict fluid pressures.

In the absence of appropriate sub-surface data, the magnitudes of the horizontal stresses are considered in terms of the geostatic stress ratio of the rock (e.g., [92]). The pore pressures are discussed in terms of the hydrostatic pressure and any assumed overpressure.

The modelling presented here makes several assumptions. These assumptions are made to act as a starting point, to simplify the analysis and because of the various uncertainties:


#### *3.3. Base Case Models*

We start with base case models (Figure 2) to derive threshold conditions for the reactivation of fractures or the generation of new fractures. These base cases use the uniaxial strain condition (e.g., [58]), with no applied tectonic stresses. The fluids in pore spaces and open fractures are hydrostatically pressured, with the water table being at the ground surface. In such circumstances, the vertical effective stress creates a horizontal effective stress that is given by the geostatic stress ratio (Figure 2), with the input parameters used shown in Table 3. The base case models are used as a starting point for experiments in which fluid pressure is increased (as would occur either by natural overpressure or by hydraulic stimulation), and the horizontal (tectonic) stress either decreased or increased, until the model predicts either the reactivation of existing cohesionless fractures (hydraulic stimulation) or the generation of new fractures.

For most rocks, T << 100 MPa, with poorly-consolidated sediments having T → 0, whereas for shear failure 0.5 < µ < 1.5 (generally) and 0 < S<sup>0</sup> < 50 MPa. In this paper, we use ranges of T, S0, and µ that are appropriate for the rocks being considered.

An important point illustrated by Figure 2 is that, at typical K<sup>0</sup> values (0.3–0.5), the stress state is stable and no fracturing would be expected. This means that low K<sup>0</sup> values are needed to allow failure in the base case model, which simulates simple burial, with hydrostatic fluid pressure and no applied tectonic stresses. Any failure would largely be by shearing of pre-existing fractures, which may occur in the Devonian and Carboniferous rocks that are considered to occur beneath Göttingen.

#### *3.4. A Range of Stress States for Fracturing*

We consider a range of states of effective stress, seven of which are shown in Figure 3, together with their effect on fracturing. Note that the discussion is of changes in effective stresses, which can be caused by changes in applied stresses and/or fluid pressure. These states of stress have been modelled for the Bunter Sandstone and the Devonian and Carboniferous greywackes and slates by increasing the fluid pressure and by applying "tectonic" stresses to the base case models.

#### **4. Effects of Key Parameters**

A definition and the significance of each of the input parameters, along with representative values, are given in Table 2. For a given overburden stress, higher geostatic stress ratios produce larger horizontal stress and, hence, lower differential stress (Figure 2). The effects of other key parameters are illustrated in Figure 4. The position and shape of the failure envelope is controlled by the tensile strength, cohesion, and coefficient of internal friction of the rock (Figure 4a). Vertical, and therefore horizontal, stress increases with depth as the overburden increases (Figure 4b). High values of compressional tectonic stress can cause the horizontal stress to exceed the vertical stress, tending to lead to shear failure, while tensile tectonic stress will increase the differential stress and may lead to the development of extension fractures (Figure 4c). Increases in fluid pressure move the Mohr circle for effective stress to the left, towards more tensile parts of the Mohr diagram (Figure 4d). Note, however, that a change in fluid pressure will cause a change in differential stress that is proportional to the geostatic stress ratio, and it is a common mistake to show a constant differential stress with changing fluid pressure (e.g., [94,95]). The base cases are close to cohesionless failure if lower K<sup>0</sup> values are used, which implies that fracturing will generally require some tectonic stress and/or overpressure, especially to initiate the development of new fractures.

velopment of new fractures.

depth as the overburden increases (Figure 4b). High values of compressional tectonic stress can cause the horizontal stress to exceed the vertical stress, tending to lead to shear failure, while tensile tectonic stress will increase the differential stress and may lead to the development of extension fractures (Figure 4c). Increases in fluid pressure move the Mohr circle for effective stress to the left, towards more tensile parts of the Mohr diagram (Fig‐ ure 4d). Note, however, that a change in fluid pressure will cause a change in differential stress that is proportional to the geostatic stress ratio, and it is a common mistake to show a constant differential stress with changing fluid pressure (e.g., [94,95]). The base cases are close to cohesionless failure if lower K0 values are used, which implies that fracturing will generally require some tectonic stress and/or overpressure, especially to initiate the de‐

**Figure 3.** A range of effective stress states for fracturing illustrated using Mohr diagrams and sketch cross‐sections with cohesive fractures (e.g., veins) and non‐cohesive fractures (e.g., joints) dipping at 90°, 45°, and 0°. σ<sup>V</sup> = vertical stress, σ<sup>h</sup> = horizontal stress. (**a**) Stable stress state, in which the effective stresses are insufficient to reactivate existing fractures or create new fractures. (**b**) Reduced effective stresses, such that favourably‐orientated pre‐existing cohesionless fractures can be reactivated as shear fractures. (**c**) Reduced effective stresses, such that favourably‐orientated pre‐existing cohesion‐ less fractures can be reactivated as shear fractures. (**d**) Reduced effective stresses, such that new extension fractures are created perpendicular to the least effective stress. (**e**) Reduced effective stresses (e.g., as fluid pressure increases), such that new extension fractures with any orientation can be created. (**f**) Increased effective stresses, such that favourably‐orien‐ tated pre‐existing cohesionless fractures are reactivated as shear fractures. (**g**) Increased effective stresses, such that new shear fractures are generated. **Figure 3.** A range of effective stress states for fracturing illustrated using Mohr diagrams and sketch cross-sections with cohesive fractures (e.g., veins) and non-cohesive fractures (e.g., joints) dipping at 90◦ , 45◦ , and 0◦ . σ<sup>V</sup> = vertical stress, σ<sup>h</sup> = horizontal stress. (**a**) Stable stress state, in which the effective stresses are insufficient to reactivate existing fractures or create new fractures. (**b**) Reduced effective stresses, such that favourably-orientated pre-existing cohesionless fractures can be reactivated as shear fractures. (**c**) Reduced effective stresses, such that favourably-orientated pre-existing cohesionless fractures can be reactivated as shear fractures. (**d**) Reduced effective stresses, such that new extension fractures are created perpendicular to the least effective stress. (**e**) Reduced effective stresses (e.g., as fluid pressure increases), such that new extension fractures with any orientation can be created. (**f**) Increased effective stresses, such that favourably-orientated pre-existing cohesionless fractures are reactivated as shear fractures. (**g**) Increased effective stresses, such that new shear fractures are generated.

*Geosciences* **2021**, *11*, x FOR PEER REVIEW 13 of 27

**Figure 4.** Mohr diagrams showing the effects of key parameters on the failure envelope and state of effective stress, all shown using the model for the Devonian and Carboniferous greywackes with a geostatic stress ratio of 0.125. The param‐ eters used are shown in Table 3. (**a**) The base case Mohr circle (depth of 2 km, hydrostatic fluid pressure and no applied tectonic stress), with a representative cohesional failure envelope shown (Table 3, "Greywacke" and "Slate" columns). "Friction angle" refers to the slope the failure envelope. (**b**) Mohr circles for effective stress at different depths (hydrostatic fluid pressure and no applied tectonic stress). The magnitudes of the effective stresses increase with depth. (**c**) Mohr circles for a depth of 2 km, hydrostatic fluid pressure and different applied tectonic stresses. (**d**) Mohr circles for a depth of 2 km, different fluid pressures and zero applied tectonic stresses. The Mohr diagrams presented in Figures 2–4 show two types of failure envelope. The **Figure 4.** Mohr diagrams showing the effects of key parameters on the failure envelope and state of effective stress, all shown using the model for the Devonian and Carboniferous greywackes with a geostatic stress ratio of 0.125. The parameters used are shown in Table 3. (**a**) The base case Mohr circle (depth of 2 km, hydrostatic fluid pressure and no applied tectonic stress), with a representative cohesional failure envelope shown (Table 3, "Greywacke" and "Slate" columns). "Friction angle" refers to the slope the failure envelope. (**b**) Mohr circles for effective stress at different depths (hydrostatic fluid pressure and no applied tectonic stress). The magnitudes of the effective stresses increase with depth. (**c**) Mohr circles for a depth of 2 km, hydrostatic fluid pressure and different applied tectonic stresses. (**d**) Mohr circles for a depth of 2 km, different fluid pressures and zero applied tectonic stresses.

> "Cohesionless" lines on the Mohr diagrams are typical of slip on pre‐existing unfilled fractures (e.g., joints; Figure 5a), while the "Cohesional" lines represent the behaviour of intact rock or fractures that are filled by cohesive material (e.g., veins or faults with cohe‐ sive gouge; Figure 5b). These different failure envelopes illustrate the different mechanical behaviours of such cohesionless fractures as joints and such cohesional fractures as fully‐ filled veins and faults with clay gouge, highlighting the importance of distinguishing be‐ tween different fracture types when using a field analogue for a geothermal reservoir. **5. Potential for Reactivating and Generating Fractures** The Mohr diagrams presented in Figures 2–4 show two types of failure envelope. The "Cohesionless" lines on the Mohr diagrams are typical of slip on pre-existing unfilled fractures (e.g., joints; Figure 5a), while the "Cohesional" lines represent the behaviour of intact rock or fractures that are filled by cohesive material (e.g., veins or faults with cohesive gouge; Figure 5b). These different failure envelopes illustrate the different mechanical behaviours of such cohesionless fractures as joints and such cohesional fractures as fullyfilled veins and faults with clay gouge, highlighting the importance of distinguishing between different fracture types when using a field analogue for a geothermal reservoir.

#### or horizontal (tectonic) stresses needed to reactivate existing cohesionless fractures, or to **5. Potential for Reactivating and Generating Fractures**

generate new fractures (Table 4). Note that these are simply the results of the model, which is based on poorly constrained parameters and should only be taken as suggestions of what may occur under the conditions stated. Results of the models can be expressed in terms of the critical values of fluid pressure or horizontal (tectonic) stresses needed to reactivate existing cohesionless fractures, or to generate new fractures (Table 4). Note that these are simply the results of the model, which is based on poorly constrained parameters and should only be taken as suggestions of what may occur under the conditions stated.

Results of the models can be expressed in terms of the critical values of fluid pressure

### *5.1. Bunter Sandstone*

Critical values predicted by the modelling for the Bunter Sandstone at a depth of 1 km are presented in Table 4, from which the following predictions can be made. (1) Favourablyorientated cohesionless fractures in the Bunter Sandstone may be critically stressed without fluid overpressure or applied tectonic stresses (i.e., the base-case model) if the geostatic stress ratio is low (e.g., 0.2). (2) Shear may therefore occur on favourably-orientated cohesionless fractures (e.g., joints) if the fluid is hydrostatically pressured (i.e., fluid pressure ~10 MPa; e.g., Figure 3b) for a geostatic stress ratio ~0.2, but a fluid pressure of about 24 MPa would be needed to reactivate cohesionless fractures if the geostatic stress ratio is ~0.54. (3) Gently-dipping extension fractures would start to develop at fluid pressures of about 30 MPa. (4) Steeply-dipping extension fractures will develop if there is a tensile tectonic stress of about 8.2 to 13.5 MPa (e.g., Figure 3d). (5) Extension fractures may develop in all directions if the fluid pressure is about 34 to 54 MPa (e.g., Figure 3e). (6) Favourably-orientated cohesionless fractures may be reactivated in shear (normal faulting) in the greywackes if there is a tensile tectonic stress of 0 to 3.7 MPa (e.g., Figure 3b). (7) Favourably-orientated cohesionless fractures may be reactivated as thrusts if there is a compressive tectonic stress of 43 to 48 MPa (e.g., Figure 3f). (8) New thrusts will develop if there is a compressive tectonic stress of about 90 to 95 MPa (e.g., Figure 3g). *5.1. Bunter Sandstone* Critical values predicted by the modelling for the Bunter Sandstone at a depth of 1 km are presented in Table 4, from which the following predictions can be made. (1) Fa‐ vourably‐orientated cohesionless fractures in the Bunter Sandstone may be critically stressed without fluid overpressure or applied tectonic stresses (i.e., the base‐case model) if the geostatic stress ratio is low (e.g., 0.2). (2) Shear may therefore occur on favourably‐ orientated cohesionless fractures (e.g., joints) if the fluid is hydrostatically pressured (i.e., fluid pressure ~10 MPa; e.g., Figure 3b) for a geostatic stress ratio ~0.2, but a fluid pressure of about 24 MPa would be needed to reactivate cohesionless fractures if the geostatic stress ratio is ~0.54. (3) Gently‐dipping extension fractures would start to develop at fluid pres‐ sures of about 30 MPa. (4) Steeply‐dipping extension fractures will develop if there is a tensile tectonic stress of about 8.2 to 13.5 MPa (e.g., Figure 3d). (5) Extension fractures may develop in all directions if the fluid pressure is about 34 to 54 MPa (e.g., Figure 3e). (6) Favourably‐orientated cohesionless fractures may be reactivated in shear (normal fault‐ ing) in the greywackes if there is a tensile tectonic stress of 0 to 3.7 MPa (e.g., Figure 3b). (7) Favourably‐orientated cohesionless fractures may be reactivated as thrusts if there is a compressive tectonic stress of 43 to 48 MPa (e.g., Figure 3f). (8) New thrusts will develop if there is a compressive tectonic stress of about 90 to 95 MPa (e.g., Figure 3g).

*Geosciences* **2021**, *11*, x FOR PEER REVIEW 14 of 27

**Figure 5.** Examples of fractures in Carboniferous greywackes, cherts and slates in the Harz Mountains. (**a**) Joints (cohe‐ sionless) in thinly‐bedded greywackes and slates at Okerstausee, Niedersachsen. (**b**) Example of cohesional fractures at Lautenthal, Niedersachsen. Clay has been injected along faults with centimetre‐scale displacements, related to block rota‐ tion in a chert bed accommodated by thickness variations in a slate layer. **Figure 5.** Examples of fractures in Carboniferous greywackes, cherts and slates in the Harz Mountains. (**a**) Joints (cohesionless) in thinly-bedded greywackes and slates at Okerstausee, Niedersachsen. (**b**) Example of cohesional fractures at Lautenthal, Niedersachsen. Clay has been injected along faults with centimetre-scale displacements, related to block rotation in a chert bed accommodated by thickness variations in a slate layer.

**Table 4.** Results of the modelling for the Bunter Sandstone and the Lower Palaeozoic greywackes and slates, showing the calculated critical values. Values specific to a modelled depth of 2 km are shown in bold, and values specific to a modelled depth of 4.5 km are shown in italics. \* Shear or hybrid fractures, rather than extension fractures, may develop in the slates under these conditions.


#### *5.2. Devonian and Carboniferous Greywackes and Slates*

Critical values predicted by the modelling for the Devonian and Carboniferous greywackes and slates at depths of 2 km and 4.5 km are presented in Table 4. These depths are used because they represent the proposed depths for an initial research well and an exploitation well, respectively. The results of the modelling enable the following predictions to be made.


The different critical values for the greywackes and slates predicted by the modelling are caused by the different physical properties that have been used for these rock types. The different geostatic stress ratios and failure criteria (especially cohesion and tensile strengths) are particularly important. The different geostatic stress ratios of different rock types may explain variations of fractures with lithology. This is commonly seen in greywacke/slate and sandstone/mudstone sequences (e.g., [96]). The tensile strengths of slates tend to be lower than that of greywackes, so extension fractures may develop in the slates at lower fluid pressures and lower tensile tectonic stresses than in the greywackes. Although this suggests that fractures will be created in slates before fracturing occurs in greywackes during stimulation (Section 6.1), it does not necessarily mean that there will be more, wider or better-connected fractures in the slates than in the greywackes. The model cannot predict the fluid flow properties of the slates or greywackes.

#### *5.3. Possible Effects of Exhumation on the Bunter Sandstone*

Here, we use simple modelling to determine at what depth joints are likely to have developed in the Bunter Sandstone of the Leinetal Graben, based on the changes in stresses and temperatures the rocks are likely to have experienced during exhumation. The Bunter

Sandstone is currently exposed on the flanks of the Leinetal Graben but at depths of between ≈300 m and ≈850 m in Borehole Sudhein II in the Graben [37]. Note that the top of the Bunter Sandstone has been faulted out and the base is mixed with Zechstein Salt in Borehole Sudhein II [37]. The values used in the modelling are shown in Table 5, with the Mohr diagrams shown in Figure 6. The vertical stress changes as the thickness and, therefore, weight of the overlying material changes during burial or exhumation, and this causes a change in the horizontal stresses that is proportional to the geostatic stress ratio (Figure 4b). A change in depth typically causes a change in temperature that is related to the geothermal gradient (e.g., [97]). A decrease in temperature will tend to cause contraction of rock, determined by the coefficient of thermal expansion, and this will tend to cause a reduction in compressional stresses in the rock (e.g., [98]). The Bunter Sandstone is currently exposed on the flanks of the Leinetal Graben but at depths of between ≈300 m and ≈850 m in Borehole Sudhein II in the Graben [37]. Note that the top of the Bunter Sandstone has been faulted out and the base is mixed with Zechstein Salt in Borehole Sudhein II [37]. The values used in the modelling are shown in Table 5, with the Mohr diagrams shown in Figure 6. The vertical stress changes as the thickness and, therefore, weight of the overlying material changes during burial or exhumation, and this causes a change in the horizontal stresses that is proportional to the geostatic stress ratio (Figure 4b). A change in depth typically causes a change in temperature that is re‐ lated to the geothermal gradient (e.g., [97]). A decrease in temperature will tend to cause contraction of rock, determined by the coefficient of thermal expansion, and this will tend to cause a reduction in compressional stresses in the rock (e.g., [98]).

Here, we use simple modelling to determine at what depth joints are likely to have developed in the Bunter Sandstone of the Leinetal Graben, based on the changes in stresses and temperatures the rocks are likely to have experienced during exhumation.

*Geosciences* **2021**, *11*, x FOR PEER REVIEW 17 of 27

*5.3. Possible Effects of Exhumation on the Bunter Sandstone*

**Figure 6.** Mohr diagrams illustrating the possible effects of exhumation and cooling on the Bunter Sandstone. See Table 5 for parameters used in the model. (**a**) Model for the base of the Bunter Sand‐ stone at a depth of 2 km and the top of the Bunter Sandstone at 1.4 km. The model predicts the rock is in a stable stress state. (**b**) Model for the Bunter Sandstone after 0.9 km exhumation. The top of the Bunter Sandstone is now at a depth of 0.5 km, and the stress state promotes the development of steeply‐dipping extension fractures. Notice that the differential effecting stresses in (**a**,**b**) are similar, because cooling during exhumation tends to generate horizontal tensile stresses. **Figure 6.** Mohr diagrams illustrating the possible effects of exhumation and cooling on the Bunter Sandstone. See Table 5 for parameters used in the model. (**a**) Model for the base of the Bunter Sandstone at a depth of 2 km and the top of the Bunter Sandstone at 1.4 km. The model predicts the rock is in a stable stress state. (**b**) Model for the Bunter Sandstone after 0.9 km exhumation. The top of the Bunter Sandstone is now at a depth of 0.5 km, and the stress state promotes the development of steeply-dipping extension fractures. Notice that the differential effecting stresses in (**a**,**b**) are similar, because cooling during exhumation tends to generate horizontal tensile stresses.

The model presented in Figure 6 includes reductions in horizontal stresses caused by decreases in overburden and temperature to predict at what depth extension fractures (e.g., joints) may develop in the Bunter Sandstone. We use a geothermal gradient of 30 ◦C per km, which is similar to that modelled by [99]. The model assumes, for simplicity, an initial 1.4 km depth for the top of the Bunter Sandstone, and an initial depth of 2 km for the base of the Bunter Sandstone (Figure 6a). Vertical and horizontal stresses reduce during exhumation, with the model predicting the development of joints beginning after 0.9 km exhumation, with the top of the Bunter at a depth of 0.5 km (Figure 6b). Note, however, that this base case model assumes hydrostatically-pressured pore fluids and no applied tectonic stresses. Joints would form at greater depths if the fluids are over-pressured, if there is a tensile tectonic stress, or if the geothermal gradient were higher.

**Table 5.** Initial values used for modelling the effects of exhumation and cooling on the Bunter Sandstone.


#### **6. Discussion**

#### *6.1. Possible Effects of Stimulation on Devonian and Carboniferous Rocks at 2 km Depth*

Here, we consider the possible effects of stimulation by increasing fluid pressure on the folded, cleaved and veined Devonian and Carboniferous greywackes and slates, based on the modelling discussed in Section 5 and using a simple schematic figure for these rocks (Figure 7a). The modelling suggests the following sequence of events as fluid pressure is gradually increased (Figure 7):


#### *6.2. Possible Effects of Stimulation on Devonian and Carboniferous Rocks at 4.5 km Depth*

The critical values for deformation predicted by the modelling for the greywackes and slates at a depth of 4.5 km are shown in Table 4. These critical values are higher than predicted for a depth of 2 km, but suggest that stimulation would have similar effects

as at a depth of 2 km. One notable difference is that higher differential stresses at depth would mean that stimulation is more likely to reactivate fractures in shear, or to create shear fractures, at greater depths. The modelling predicts that the slates will be particularly likely to develop shear fractures during stimulation.

Figure 8 highlights the effects of the different fluid pressures needed to stimulate reservoirs at different depths. The difference in fluid pressure between the top and bottom of a 2500 m column of water would be approximately 25 MPa. If fluid pressure is increased at a depth of 4.5 km such that it exceeds the horizontal stress, this may cause the fluid pressure at 2 km to exceed the vertical stress, if these different depths are hydraulicallyconnected (Figure 8). This suggests that care will be needed during stimulation if it is not intended to fracture rocks at shallower levels. We note that the Zechstein salts are likely to act as an effective top-seal (e.g., [101]) during stimulation.

#### *6.3. Possibility of Open Fractures in the Devonian and Carboniferous Rocks below Göttingen*

Although we have carried out simple modelling of joint development in the Bunter Sandstone, we have not performed so for the Devonian and Carboniferous rocks that are inferred to occur below about 1.5 km under Göttingen. This is because we consider there to be too many uncertainties for meaningful analysis of the effects of Late Cretaceous to Tertiary exhumation and cooling on these deeper and older rocks. There are, however, two arguments for the occurrence of open fractures in the Devonian and Carboniferous rocks. Firstly, joints will have developed in those rocks as they were exhumed at the end of the Variscan Orogeny, before deposition of the Permian and Mesozoic rocks unconformably above. It is possible, however, that these late- or post-Variscan joints will have subsequently been mineralised. Secondly, there is evidence that joints and other open fractures can occur at the depths of the proposed geothermal reservoir at Göttingen. For example, joints have been reported at depths of >2 km in tunnels (e.g., [102]) and in mines (e.g., [103,104]). Similarly, open fractures have been reported in fractured "basement" petroleum fields at depths of >4 km (e.g., [105]).

*Geosciences* **2021**, *11*, x. https://doi.org/10.3390/xxxxx www.mdpi.com/journal/geosciences

**Figure 7**. (previous page). Schematic figure for likely effects of stimulation on the folded and cleaved Devonian and Carboniferous greywackes and slates, based on the results presented in Table 4. The fold has an amplitude of a few metres to tens of metres. The model is for a depth of 2 km, at which hydrostatic fluid pressure would be 19.62 MPa. Veins are shown in the greywackes in the outer arcs of folds, and a fanning axial planar cleavage is shown. Joints are drawn approximately perpendicular to bedding. We predict the following sequence of events as fluid pressure is increased. (**a**) Favourably-orientated cohesionless fractures (joints) may be critically-stressed in greywackes with very low geostatic stress ratios, so may undergo normal faulting even at hydrostatic fluid pressure. (**b**) Shear can occur along favourably-orientated joints in the slates at fluid pressures of about 50 MPa. (**c**) Gently-dipping extension fractures can be generated in the slates at fluid pressures at about 68 MPa, and gently-dipping joints in the greywackes may be reactivated as extension fractures. (**d**) Extension fractures with any orientation may develop in the slates at fluid pressure between about 90 and 105 MPa. (**e**) Gently-dipping extension fractures can be generated in the greywackes at fluid pressures of about 72 MPa. (**f**) Extension fractures with any orientation may develop in the greywackes if the fluid pressure is between about 100 and 210 MPa. boniferous greywackes and slates, based on the results presented in Table 4. The fold has an amplitude of a few metres to tens of metres. The model is for a depth of 2 km, at which hydrostatic fluid pressure would be 19.62 MPa. Veins are shown in the greywackes in the outer arcs of folds, and a fanning axial planar cleavage is shown (e.g., Stephan et al., 2016). Joints are drawn approximately perpendicular to bedding. We predict the following sequence of events as fluid pressure is increased. (**a**) Favourably‐orientated cohesionless fractures (joints) may be critically‐stressed in greywackes with very low geostatic stress ratios, so may undergo normal faulting even at hydrostatic fluid pressure. (**b**) Shear can occur along fa‐ vourably‐orientated joints in the slates at fluid pressures of about 50 MPa. (**c**) Gently‐dipping extension fractures can be generated in the slates at fluid pressures at about 68 MPa, and gently‐dipping joints in the greywackes may be reactivated as extension fractures. (**d**) Extension fractures with any orientation may develop in the slates at fluid pressure between about 90 and 105 MPa. (**e**) Gently‐dipping extension fractures can be generated in the greywackes at fluid pressures of about 72 MPa. (**f**) Extension fractures with any orientation may develop in the greywackes if the fluid pressure is between about 100 and 210 MPa.

**Figure 7.** (previous page). Schematic figure for likely effects of stimulation on the folded and cleaved Devonian and Car‐

**Figure 8.** Possible effects of stimulation at a depth of 4.5 km on the rocks at a depth of 2 km, modelled for a greywackes and slates with a geostatic stress ratio of 0.41. (**a**) Graph of pressure against depth. (**b**) Schematic cross‐section. At a depth of 4.5 km, hydrostatic fluid pressure = 44.15 MPa, σ<sup>V</sup> = 118.31 MPa and σ<sup>h</sup> = 74.55 MPa. At a depth of 2 km, hydrostatic fluid pressure = 19.62 MPa, σ<sup>V</sup> = 52.58 MPa and σ<sup>h</sup> = 33.14 MPa. If there is hydraulic connectivity through the greywackes and slates, increasing fluid pressure at 4.5 km to above 77 MPa, such that it exceeds σh, would increase fluid pressure at 2 km 52.58 MPa, at which point it will equal σV. **Figure 8.** Possible effects of stimulation at a depth of 4.5 km on the rocks at a depth of 2 km, modelled for a greywackes and slates with a geostatic stress ratio of 0.41. (**a**) Graph of pressure against depth. (**b**) Schematic cross-section. At a depth of 4.5 km, hydrostatic fluid pressure = 44.15 MPa, σ<sup>V</sup> = 118.31 MPa and σ<sup>h</sup> = 74.55 MPa. At a depth of 2 km, hydrostatic fluid pressure = 19.62 MPa, σ<sup>V</sup> = 52.58 MPa and σ<sup>h</sup> = 33.14 MPa. If there is hydraulic connectivity through the greywackes and slates, increasing fluid pressure at 4.5 km to above 77 MPa, such that it exceeds σh, would increase fluid pressure at 2 km 52.58 MPa, at which point it will equal σV.

#### *6.4. Potential Benefits, Problems, and Improvements 6.4. Potential Benefits, Problems, and Improvements*

Although the modelling presented in this paper is simple, it has several uses when attempting to predict what is likely to occur in the sub‐surface. Firstly, constructing the models requires consideration of the range of the conditions that are likely to occur, in‐ cluding the lithologies and their mechanical properties, stresses, fluid types and fluid pressures, and the presence of different types of fractures. Secondly, predictions can be made about whether natural open fractures (e.g., joints) may occur, and whether exhuma‐ tion might have created joints at reservoir depths. Thirdly, it enables predictions to be made about the orientations and types of induced fractures that are likely to occur under a range of possible conditions (Figure 7). It may also enable predictions to be made about whether there will be induced seismicity during stimulation. Although the modelling presented in this paper is simple, it has several uses when attempting to predict what is likely to occur in the sub-surface. Firstly, constructing the models requires consideration of the range of the conditions that are likely to occur, including the lithologies and their mechanical properties, stresses, fluid types and fluid pressures, and the presence of different types of fractures. Secondly, predictions can be made about whether natural open fractures (e.g., joints) may occur, and whether exhumation might have created joints at reservoir depths. Thirdly, it enables predictions to be made about the orientations and types of induced fractures that are likely to occur under a range of possible conditions (Figure 7). It may also enable predictions to be made about whether there will be induced seismicity during stimulation.

There are various potential problems with the simplicity of the approach presented here, but these suggest ways in which the models can be improved. For example: There are various potential problems with the simplicity of the approach presented here, but these suggest ways in which the models can be improved. For example:

1. The Mohr diagram models used give little direct information about potential fluid flow in the sub‐surface. The approach could, however, be used in combination with 1. The Mohr diagram models used give little direct information about potential fluid flow in the sub-surface. The approach could, however, be used in combination with

other modelling approaches. For example, it would be useful to compare predictions of critically stressed fractures from Mohr diagrams with distinct element analysis of fracture networks (e.g., [106,107]);


### **7. Conclusions**

This paper shows how simple mechanical modelling, using Mohr diagrams and reasonable ranges of values for rock properties, stresses, and fluid pressures, can be used to predict fracturing in a potential geothermal reservoir. Inferences can be made about the range of structures likely to exist in the sub-surface and that may be generated during stimulation. Critical values of fluid pressure and applied tectonic stresses determine under what conditions different types and orientations of fractures are likely to occur or be generated during stimulation.

A model is presented for the development of shear and extension fractures in the Devonian and Carboniferous greywackes and slates as fluid pressure increases, as would occur during hydraulic stimulation (Figure 7). For a depth of 2 km, this involves: (a) shear on favourably-orientated cohesionless fractures in greywackes with a very low geostatic stress ratio under hydrostatic fluid pressure (Figure 7a); (b) shear along favourablyorientated joints in the slates at fluid pressures of about 50 MPa (Figure 7b); (c) generation of gently-dipping extension fractures in the slates at fluid pressures between about 68 MPa (Figure 7c); (d) development of gently-dipping extension fractures in the greywackes at fluid pressures of about 72 MPa (Figure 7d); (e) creation of extension fractures with any orientation in the slates at fluid pressure between about 90 and 105 MPa (Figure 7e); (f) Generation of fractures with any orientation in the greywackes at fluid pressures between about 100 and 210 MPa (Figure 7f). A similar sequence is predicted for a modelled depth of 4.5 km, although higher differential stresses at greater depths imply that hybrid or shear fractures are more likely to form than are extension fractures as fluid pressure increases.

The modelling addresses many key questions asked in Section 1. (1) The tensile strengths of slates tend to be lower than those of greywackes, suggesting lower fluid pressure or lower tensile tectonic stresses are needed to hydraulically fracture slates than greywackes. (2) Critical values of fluid pressure and tectonic stresses for fracturing can be predicted (Table 4). (3) Steeply-dipping cohesionless fractures (e.g., joints) are most likely to be reactivated first, as shear fractures. (4) Existing cohesionless fractures (e.g., joints) may initially reactivate in shear while cohesional fractures (e.g., veins) will tend to reactivate as extension fractures. (5) Shear fracturing generally requires the reactivation of cohesionless fractures as tensile tectonic stresses are applied, or the application of compressive tectonic stresses to generate new shear fractures. (6) Exhumation and related cooling may be responsible for the creation of joints in the Bunter Sandstone and the Variscan rocks beneath Göttingen. It is likely that joints developed in the Variscan rocks prior to deposition of the Permian rocks, but these may have subsequently been mineralised.

The relationships between stresses, fluid pressure and the types and orientations of fractures are important inputs for more detailed modelling techniques (e.g., DFN modelling [110]), and can be used to test the mechanical implications of those detailed modelling techniques. Not only does this modelling help geoscientists consider and model the ranges of mechanical properties of rock, stresses, fluid pressures and the resultant fractures that are likely to occur in the sub-surface, it encourages them to consider the ranges of key parameters and their effects.

**Author Contributions:** Conceptualization, D.C.P.P. and D.J.S.; methodology, D.C.P.P. and D.J.S.; software, D.J.S.; validation, D.C.P.P., D.J.S. and B.L.; resources, B.L.; data curation, B.L.; writing original draft preparation, D.C.P.P.; writing—review and editing, D.J.S. and B.L.; supervision, B.L.; project administration, B.L.; funding acquisition, B.L. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work has received funding from the European Union's Horizon 2020 research and innovation programme (grant agreement № 792037-MEET Project).

**Data Availability Statement:** No new data were created or analysed in this study. Data sharing is not applicable to this article.

**Acknowledgments:** Carl-Heinz Friedel is thanked for helpful advice and discussions. We are grateful to John Reinecker and three anonymous reviewers, whose comments greatly improved this manuscript.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


## *Article* **Fracture Transmissivity in Prospective Host Rocks for Enhanced Geothermal Systems (EGS)**

**Johannes Herrmann 1,\* , Valerian Schuster <sup>2</sup> , Chaojie Cheng <sup>2</sup> , Harald Milsch <sup>2</sup> and Erik Rybacki <sup>2</sup>**


**Abstract:** We experimentally determined the hydraulic properties of fractures within various rock types, focusing on a variety of Variscan rocks. Flow-through experiments were performed on slate, graywacke, quartzite, granite, natural fault gouge, and claystone samples containing an artificial fracture with a given roughness. For slate samples, the hydraulic transmissivity of the fractures was measured at confining pressures, pc, at up to 50 MPa, temperatures, T, between 25 and 100 ◦C, and differential stress, *σ*, acting perpendicular to the fracture surface of up to 45 MPa. Fracture transmissivity decreases non-linearly and irreversibly by about an order of magnitude with increasing confining pressure and differential stress, with a slightly stronger influence of pc than of *σ*. Increasing temperature reduces fracture transmissivity only at high confining pressures when the fracture aperture is already low. An increase in the fracture surface roughness by about three times yields an initial fracture transmissivity of almost one order of magnitude higher. Fractures with similar surface roughness display the highest initial transmissivity within slate, graywacke, quartzite and granite samples, whereas the transmissivity in claystone and granitic gouge material is up to several orders of magnitude lower. The reduction in transmissivity with increasing stress at room temperature varies with composition and uniaxial strength, where the deduction is lowest for rocks with a high fraction of strong minerals and associated high brittleness and strength. Microstructural investigations suggest that the reduction is induced by the compaction of the matrix and crushing of strong asperities. Our results suggest that for a given surface roughness, the fracture transmissivity of slate as an example of a target reservoir for unconventional EGS, is comparable to that of other hard rocks, e.g., granite, whereas highly altered and/or clay-bearing rocks display poor potential for extracting geothermal energy from discrete fractures.

**Keywords:** Enhanced Geothermal Systems (EGS); Variscan rocks; slate; quartzite; granite; claystone; graywacke; gouge; fracture transmissivity; effective stress

## **1. Introduction**

Extracting geothermal energy from underground is of major interest in the transition from energy recovered from conventional resources such as coal or oil towards renewable energies [1]. Geothermal energy is expected to have a great potential to meet future energy demands. However, exploitation is highly dependent on the presence of accessible hot fluids within the reservoir formation to ensure sufficient energy extraction. In contrast to hydrothermal geothermal systems, where steam or hot water is extracted from the subsurface, hot (>150 ◦C) and deep (>3 km), but low permeable, reservoir rocks represent the largest geothermal energy resources [2–5]. To facilitate the extraction of geothermal energy from tight reservoirs, a network of highly conductive fractures is required that serves as heat exchanger [6–8] in Enhanced Geothermal Systems (EGS). An EGS typically

**Citation:** Herrmann, J.; Schuster, V.; Cheng, C.; Milsch, H.; Rybacki, E. Fracture Transmissivity in Prospective Host Rocks for Enhanced Geothermal Systems (EGS). *Geosciences* **2022**, *12*, 195. https://doi.org/10.3390/ geosciences12050195

Academic Editors: Béatrice A. Ledésert, Ronan L. Hébert, Ghislain Trullenque, Albert Genter, Eléonore Dalmais, Jean Hérisson and Jesus Martinez-Frias

Received: 8 April 2022 Accepted: 27 April 2022 Published: 3 May 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

relies on two wells, an injection and a production well, which are connected by a network of open (conductive to fluid flow) fractures. In order to create such a fracture network, artificial fractures are often generated by hydraulic fracturing (HF). These are believed to be connected to pre-existing natural fractures in the reservoir [9]. The efficiency and sustainability of an EGS are critically dependent on sufficient water flow through the fracture network and on the conductive properties of the separate fractures [1]. This prerequisite, in addition to a relatively high geothermal gradient, is necessary to successfully run an EGS over several years [10,11].

Fluid flow within rough natural fractures is a complex process, influenced by many parameters, for example thermodynamic boundary conditions, surface roughness and chemical processes, such as mineral precipitation [12]. In addition, the bedding and cleavage orientation of anisotropic rocks such as shale or slate can have a strong effect on the development and permeability of fractures [13–15]. The surface roughness of natural and artificially created fractures has a strong impact on the (hydraulic) aperture [12,16–18]. Fracture transmissivity can rapidly decrease with increasing confining pressure (pc) [12,16] and increasing effective stress, *σ*, oriented perpendicular to the fracture surface (e.g., [19]). Increasing temperature, T, may (completely) seal fractures in sediments by thermal expansion [17]. Fracture sealing may be also induced by mineral precipitation processes, depending on fluid and rock composition [10,12,20]. Injecting fluid into a fluid-bearing fracture with a different composition may lead to dissolution-precipitation reactions due to local changes in the chemical equilibrium, which typically results in a decrease in fracture transmissivity [10,17,21,22]. The transmissivity may be also reduced by the clogging of flow channels due to the migration of fine particles, e.g., clay [1,13,23,24] or by the production of a fine-grained gouge layer resulting from shear displacement [19]. On the other hand, fracture transmissivity may be enhanced with low effective normal stress acting on the fracture due to shear-induced dilatancy, resulting in self-propping of the fracture surfaces [1,12,16,20,25]. The transmissivity of the propped fractures may be influenced by proppant embedment (e.g., [24]).

Many existing EGS are located in granitic rocks, which often exhibit a relatively large amount of natural, highly permeable, open fractures and have a high potential for successfully creating fracture networks with stimulation techniques [26,27]. However, metamorphic rocks may also be considered as potential host rocks for EGS. Within the European initiative 'Multidisciplinary and multi-context demonstration of Enhanced Geothermal Systems Exploration and Exploitation Techniques and potentials (MEET)', the suitability of Variscan rocks, such as granites [27], quartzites [28], slates and graywacke [29–31] were investigated to assess their potential for extracting geothermal energy. In this study, we focused on the influence of confining pressure, stress, temperature, and surface roughness on the fracture transmissivity of Wissenbach slate which is the expected target rock for a planned EGS in Göttingen, Germany, dedicated to heating the University Campus [31]. Since the productivity of fractured rocks may be influenced by their composition, as well as their metamorphic and alteration grade, we additionally performed flow through experiments at elevated stress on fractured graywacke, quartzite, fresh and altered (gouge) granite, and claystone, where the latter may be regarded as an end-member rock type of highly altered formations. This may help to assess the potential of different geological settings for future EGS.

#### **2. Materials and Methods**

#### *2.1. Sample Material*

Most of the experiments were performed on slates derived from the Middle Devonian (Eifelian age) Wissenbach Slate (WBS) Formation, one of the intended reservoir target horizons for the planned EGS in Göttingen. Because only a few existing wells in the Göttingen area penetrate the Paleozoic rock units below the Permian and Mesozoic sedimentary cover [29,31], rock samples were taken from an analogue site in the Western Harz Mountains. Samples were prepared from cores collected at a depth of 1134–1210 m from the

scientific well 'Hahnenklee', which was drilled in the northwestern part of the Harz mountains in the early 1980's [32–36]. On macroscopic scale, WBS appears as black, homogeneous, argillaceous rock with sporadically distributed pyrite aggregates (<0.25 mm). The very few carbonate layers that occur are aligned parallel to the visible and characteristic cleavage, which is rarely interrupted by carbonate-filled veins (<0.5 mm). An X-Ray diffraction (XRD) analysis revealed that this metamorphic rock is mainly composed of quartz (Qtz), calcite (Ca), dolomite (Dol), muscovite (Ms), illite (Ill), chlorite (Chl), and feldspar (Fsp) with minor amounts of apatite (Ap), pyrite (Py), and organic matter (Om). The bulk composition was categorized into three main groups consisting of mechanically weak (Phyl = phyllosilicates), intermediate strong (Cb = carbonates), and strong (QFSO = Qtz + Fsp + Sulfides + Oxides) minerals (Table 1) and plotted in a ternary diagram (Figure 1). *Geosciences* **2022**, *12*, x FOR PEER REVIEW 6 of 34

**Figure 1.** Ternary plot displaying mineral composition of investigated samples. Composition is separated into mechanically strong (QFSOP = Qtz + Fsp + Sulfides + Oxides), intermediate strong (Cb = Carbonates), and weak (Phyl = Phyllosilicates) fractions. Mineral data given in wt%., WBS = Wissenbach slate, GRW = Graywacke, QTZ\_HV = Quartzite Havelange, GRA\_DV = Granite Death Valley, GOU\_DV = Gouge Death Valley, OPA\_SD = Opalinus clay, sandy facies, OPA\_SH = Opal-**Figure 1.** Ternary plot displaying mineral composition of investigated samples. Composition is separated into mechanically strong (QFSOP = Qtz + Fsp + Sulfides + Oxides), intermediate strong (Cb = Carbonates), and weak (Phyl = Phyllosilicates) fractions. Mineral data given in wt%., WBS = Wissenbach slate, GRW = Graywacke, QTZ\_HV = Quartzite Havelange, GRA\_DV = Granite Death Valley, GOU\_DV = Gouge Death Valley, OPA\_SD = Opalinus clay, sandy facies, OPA\_SH = Opalinus clay, shaly facies.

inus clay, shaly facies. Optical and electron microscopy revealed a complex (expressed by a large range of mineral types and grain sizes), fine-grained microstructure of the starting material (Figure 2a,b), with quartz, feldspar, chlorite and carbonates making up the largest mineral grains (<50 µm) that are dispersed in the phyllosilicate-rich matrix. Cleavage planes are characterized by phyllosilicates whose longest axes are oriented subparallel to each other. The bulk density of dried (110 °C for >48 h) WBS is in the range of around 2.8 g/cm<sup>3</sup> Optical and electron microscopy revealed a complex (expressed by a large range of mineral types and grain sizes), fine-grained microstructure of the starting material (Figure 2a,b), with quartz, feldspar, chlorite and carbonates making up the largest mineral grains (<50 µm) that are dispersed in the phyllosilicate-rich matrix. Cleavage planes are characterized by phyllosilicates whose longest axes are oriented subparallel to each other. The bulk density of dried (110 ◦C for >48 h) WBS is in the range of around 2.8 g/cm<sup>3</sup> with a respective porosity measured with He-pycnometry (Micrometrics, AccuPyc 1340) of *<sup>φ</sup>*He <sup>≈</sup> 2 vol% (including micro pores). Matrix permeability, kmatrix, is less than 10−<sup>19</sup> <sup>m</sup><sup>2</sup> , which is the detection limit of the gas permeameter used at TU Darmstadt (K. Bär, personal communication).

, respectively.

tested materials and ranges around He ≈ 0.2 vol%.

with a respective porosity measured with He-pycnometry (Micrometrics, AccuPyc 1340) of He ≈ 2 vol% (including micro pores). Matrix permeability, kmatrix, is less than 10−1<sup>9</sup> m<sup>2</sup>

which is the detection limit of the gas permeameter used at TU Darmstadt (K. Bär, per-

Göttingen site are Lower Carboniferous (Kulm facies) graywacke-successions [31].

in the 1980′s [32]. This grey to light-green marine psammite shows angular detrital quartz and feldspar grains (<200 µm) embedded in a fine-grained matrix made up of chlorite, feldspar and mica (Figure 2c,d). The samples were taken from a relatively homogeneous part without any obvious grading. Larger, planar aligned biotite grains (<400 µm) indicate the macroscopically visible bedding orientation. The main mineral components determined by the XRD analysis show dominantly quartz, feldspar and micas with minor amounts of carbonates. Porosity and bulk density of dried samples are

A further demonstration site studied in the frame of the MEET-project is the Have-

lange deep borehole in Belgium (Wallonia). Here, Variscan quartzite formations are being considered for the development of potential EGS. Therefore, we also studied the fracture transmissivity of quartzite samples (QTZ\_HV) obtained from a depth of z = 4732 m of the Havelange well, drilled in the Dinant Synclinorium in the early 1980′s [28]. The grey to light-green samples are characterized by a granoblastic fabric of fine-grained (<150 µm) quartz with illite and sparsely appearing dolomite (Figure 2e,f). The Lower Devonian (Pragian) samples contain roughly 77 wt% quartz and 20 wt% clays and micas with minor amounts of dolomite. The porosity of the used samples was lowest off all the

Another potential unit that has sufficient thickness for developing an EGS at the

,

sonal communication).

0.7 vol% and 2.67 g/cm<sup>3</sup>


**Table 1.** Petrophysical and mechanical properties.

*Geosciences* **2022**, *12*, 195



Sq\_ini = initial fracture surface roughness, Sq\_def = fracture surface roughness of the deformed sample (after testing), Phyl = phyllosilicates, Cb = carbonates, QFSO = quartz + feldspar + sulfides + oxides, pc = confining pressure, T = temperature, *σ* = axial stress perpendicular to fracture surface, Sq = root mean square value of frac-

ture surface roughness, H2O = distilled water, Ar = Argon gas.

Another potential unit that has sufficient thickness for developing an EGS at the Göttingen site are Lower Carboniferous (Kulm facies) graywacke-successions [31]. Graywacke (GRW) samples also originate from an analogue site in the Western Harz Mountains and were taken at a depth of 843 m from the well 'Wulpke-20 that was drilled in the 19800 s [32]. This grey to light-green marine psammite shows angular detrital quartz and feldspar grains (<200 µm) embedded in a fine-grained matrix made up of chlorite, feldspar and mica (Figure 2c,d). The samples were taken from a relatively homogeneous part without any obvious grading. Larger, planar aligned biotite grains (<400 µm) indicate the macroscopically visible bedding orientation. The main mineral components determined by the XRD analysis show dominantly quartz, feldspar and micas with minor amounts of carbonates. Porosity and bulk density of dried samples are 0.7 vol% and 2.67 g/cm<sup>3</sup> , respectively.

A further demonstration site studied in the frame of the MEET-project is the Havelange deep borehole in Belgium (Wallonia). Here, Variscan quartzite formations are being considered for the development of potential EGS. Therefore, we also studied the fracture transmissivity of quartzite samples (QTZ\_HV) obtained from a depth of z = 4732 m of the Havelange well, drilled in the Dinant Synclinorium in the early 19800 s [28]. The grey to light-green samples are characterized by a granoblastic fabric of fine-grained (<150 µm) quartz with illite and sparsely appearing dolomite (Figure 2e,f). The Lower Devonian (Pragian) samples contain roughly 77 wt% quartz and 20 wt% clays and micas with minor amounts of dolomite. The porosity of the used samples was lowest off all the tested materials and ranges around *φ*He ≈ 0.2 vol%.

To capture the influence of alteration on fracture transmissivity, tests were performed on fresh (GRA\_DV), altered and sheared granite gouge (GOU\_DV) samples recovered from an exposure located in the Noble Hills area in the southern part of the Death Valley (US) as an easily accessible analogue material to Variscan granites [37,38]. The light-reddish to pinkish, equigranular Noble Hill granite (Figure 2g,h) is mainly composed of medium to coarse grained (<3 mm) plagioclase (35 wt%), quartz (30 wt%), K-feldspar (30 wt%) and biotite (10 wt%) [38] with an initial porosity of 1.3 vol%. On the other hand, the light-yellowish to orange gouge (Figure 2i,j), which was highly altered due to multiple shearing events and weathering processes, is characterized by granite clasts (<5 mm) and brecciated quartz veins (<1 cm) embedded in a carbonate- and clay-rich matrix [37]. In contrast to the granite, the gouge displays a high porosity of 12.6 vol%.

In addition, we performed measurements on claystone samples to shed light on the influence of consolidation and metamorphic grades on fracture transmissivity in clayrich formations, which may result from alteration processes in hard rocks. Claystone material was recovered from the Opalinus Clay Formation (OPA), whose mechanical properties have been well-studied in the context of nuclear waste disposal (e.g., [39–41]). Compared to WBS, these rocks exhibited a much lower burial depth and temperature [42]. We investigated samples from the sandy (OPA\_SD) (Figure 2k,l) and shaly facies (OPA\_SH) (Figure 2m,n), both collected from the Underground Research Laboratory (URL) 'Mont Terri' (Switzerland, St. Ursanne), gratefully provided by the Swiss Federal Office of Topography–swisstopo. The fine-grained OPA\_SD is mainly composed of Qtz (48 wt%), carbonates (20 wt%), and Fsp (9 wt%), but contains a distinctly lower amount of weak sample constituents (30 wt%), such as clay and mica, compared to WBS samples (Figure 1). Note that these values may vary by about 10 wt% because of the compositional heterogeneity of this facies (e.g., [41]). The matrix permeability of OPA\_SD is in the same range compared to WBS (kmatrix\_OPA\_SD = 10−19–10−<sup>21</sup> m−<sup>2</sup> ) [43], whereas the porosity of OPA\_SD (*φ*He\_OPS\_SD = 11.8 vol%) is significantly higher. In comparison to the sandy facies of OPA, the shaly facies contain less quartz (9 wt%) and more clay minerals (74 wt%). The main constituents of OPA\_SH are clay minerals, quartz, carbonates, feldspar, pyrite, and organic matter. The permeability of OPA\_SH is similar to that of OPA\_SD (kmatrix\_OPA\_SH = 10−19–10−<sup>21</sup> m−<sup>2</sup> , [43]), but with a slightly higher porosity of 13.8 vol%.

**Figure 2.** Optical micrographs (left column) and SEM-backscattered (BSE) images (right column) of investigated starting materials showing different composition and grain size (see text for de-**Figure 2.** Optical micrographs (left column) and SEM-backscattered (BSE) images (right column) of investigated starting materials showing different composition and grain size (see text for details).

(**a**,**b**) Wissenbach slate, (**c**,**d**) graywacke, (**e**,**f**) quartzite, (**g**,**h**) granite, (**i**,**j**) altered granitic gouge, (**k**,**l**) Opalinus clay—sandy facies, and (**m**,**n**) Opalinus clay—shaly facies. Note different scales. Dol = Dolomite, Cal = Calcite, Chl = Chlorite, Qtz = Quartz, Om = Organic Matter, Fsp = Feldspar, Py = Pyrite, Bt = Biotite, Zn = Zinc, Kfs = Kalifeldspar, Ap = Apatite, Ill = Illite, Pl = Plagioclase, Hem = Hematite, Sd = Siderite. tails). (**a**,**b**) Wissenbach slate, (**c**,**d**) graywacke, (**e**,**f**) quartzite, (**g**,**h**) granite, (I, j) altered granitic gouge, (**k**,**l**) Opalinus clay—sandy facies, and (**m**,**n**) Opalinus clay—shaly facies. Note different scales. Dol = Dolomite, Cal = Calcite, Chl = Chlorite, Qtz = Quartz, Om = Organic Matter, Fsp = Feldspar, Py = Pyrite, Bt = Biotite, Zn = Zinc, Kfs = Kalifeldspar, Ap = Apatite, Ill = Illite, Pl = Plagioclase, Hem = Hematite, Sd = Siderite.

#### *2.2. Methods 2.2. Methods*

Flow through experiments were performed on cm scale specimens at various pc, T, *σ*-conditions using a modified MuSPIS (multiple sample production and injection simulator, [10]) apparatus for long-term petrophysical investigations. The sample assembly consists of two separate cylindrical objects with a thickness of t\* = 10 mm (Figure 3a,b, Table A1), which were isolated by rubber (neoprene) jackets from the confining medium (hydraulic oil) inside the pressure vessel. Flow through experiments were performed on cm scale specimens at various pc, T, -conditions using a modified MuSPIS (multiple sample production and injection simulator, [10]) apparatus for long-term petrophysical investigations. The sample assembly consists of two separate cylindrical objects with a thickness of t\* = 10 mm (Figure 3a,b, Table A1), which were isolated by rubber (neoprene) jackets from the confining medium (hydraulic oil) inside the pressure vessel.

**Figure 3.** Schematic experimental setup of performed flow through experiments (**a**) and an example of a Wissenbach slate sample (**b**). Flow direction (dashed lines) is upstream borehole to downstream borehole. Differential pore pressure, ∆pp, for the determination of fracture transmissivity is measured using a highly accurate pressure transducer by utilizing two additional boreholes. d = diameter, t\* = thickness. **Figure 3.** Schematic experimental setup of performed flow through experiments (**a**) and an example of a Wissenbach slate sample (**b**). Flow direction (dashed lines) is upstream borehole to downstream borehole. Differential pore pressure, ∆pp, for the determination of fracture transmissivity is measured using a highly accurate pressure transducer by utilizing two additional boreholes. d = diameter, t\* = thickness.

The confining pressure is controlled by a syringe pump (Isco 65D, max p<sup>c</sup> = 138 MPa). The maximum temperature is T = 200 °C, using a resistance-heating element (Thermocoax) mounted on a cylindrical stainless-steel tube placed inside the pressure vessel. To measure the transmissivity of the surface between the two disks, a continuous fluid flow at a pre-defined constant fluid pressure can be generated using two syringe pumps (Isco 100DM), which are connected to the surface via boreholes (up- and downstream boreholes in Figure 3a). The maximum pore (fluid) pressure is p<sup>p</sup> = 70 MPa at flowrates of Q = 2.5 × 10−2 − 1 × 10−6 l/min. The fluid pressure is measured separately across two additional boreholes with an additional pressure transducer (Siemens Sitrans P DS III), which is capable of measuring differential pressures of ∆p<sup>p</sup> = ± 10 mbar (1000 Pa). This was so that we could measure very low-pressure differences at low flow rates within the fracture. As our experiments were performed on low permeable rocks (matrix permeability <10−<sup>17</sup> m<sup>2</sup> ), we assumed the contribution of fluid flow through the matrix to be negligible. Deviatoric stresses up to = 100 MPa perpendicular to the interface can be applied using an axial piston driven by another syringe pump (Isco 65D). The axial load is measured using an internally mounted load cell (200 kN). The displacement of the axial piston is measured by Linear Variable Differential Transformers (LVDT) with an uncertainty of ±1 µm, allowing to correlate fracture transmissivity with changing fracture aperture and sample deformation induced by variations in axial stress, confining pres-The confining pressure is controlled by a syringe pump (Isco 65D, max p<sup>c</sup> = 138 MPa). The maximum temperature is T = 200 ◦C, using a resistance-heating element (Thermocoax) mounted on a cylindrical stainless-steel tube placed inside the pressure vessel. To measure the transmissivity of the surface between the two disks, a continuous fluid flow at a pre-defined constant fluid pressure can be generated using two syringe pumps (Isco 100DM), which are connected to the surface via boreholes (up- and downstream boreholes in Figure 3a). The maximum pore (fluid) pressure is p<sup>p</sup> = 70 MPa at flowrates of Q = 2.5 <sup>×</sup> <sup>10</sup>−<sup>2</sup> <sup>−</sup> <sup>1</sup> <sup>×</sup> <sup>10</sup>−<sup>6</sup> L/min. The fluid pressure is measured separately across two additional boreholes with an additional pressure transducer (Siemens Sitrans P DS III), which is capable of measuring differential pressures of ∆p<sup>p</sup> = ± 10 mbar (1000 Pa). This was so that we could measure very low-pressure differences at low flow rates within the fracture. As our experiments were performed on low permeable rocks (matrix permeability <10−<sup>17</sup> m<sup>2</sup> ), we assumed the contribution of fluid flow through the matrix to be negligible. Deviatoric stresses up to *σ* = 100 MPa perpendicular to the interface can be applied using an axial piston driven by another syringe pump (Isco 65D). The axial load is measured using an internally mounted load cell (200 kN). The displacement of the axial piston is measured by Linear Variable Differential Transformers (LVDT) with an uncertainty of ±1 µm, allowing to correlate fracture transmissivity with changing fracture aperture and sample deformation induced by variations in axial stress, confining pressure, and temperature.

sure, and temperature. For anisotropic rocks, the disks were prepared with the cylinder axis oriented perpendicular to bedding. The surface roughness of the artificial fracture, represented by For anisotropic rocks, the disks were prepared with the cylinder axis oriented perpendicular to bedding. The surface roughness of the artificial fracture, represented by the interface of the two sample disks, was controlled by grinding the flat saw-cut surfaces using

SiC-grains of a defined diameter (Kl60 ≈ 260 µm). The resulting initial fracture surface roughness, S<sup>q</sup> (root mean square value), prior to testing was Sq\_ini = 0.016 ± 0.003 mm, except for the granitic gouge that revealed a considerably higher initial roughness of Sq\_ini = 0.247 mm (Table 1), which was measured with a surface scanner (white light profilometer, Keyence VR3200, accuracy ≈ 3µm). Since we also tested the influence of roughness on fracture transmissivity, an additional sample of Wissenbach slate was roughened with K600 SiC-grains (diameter ≈ 9 µm) resulting in lower Sq\_ini of 0.006 mm.

Experiments on Wissenbach slate, Havelange quartzite, graywacke and the fresh Noble Hill granite from the Death Valley were performed using distilled water at a constant fluid pressure of p<sup>p</sup> = 1 MPa (downstream borehole in Figure 3) as fluid flowing through the artificial fracture. Samples prepared from Opalinus Clay, and the gouge material from the Death Valley were tested using Argon gas to avoid sample disintegration during fluid flow. For comparison, one additional test on slate was also performed with Argon. Due to the high compressibility of the Argon gas, these experiments were performed at elevated p<sup>p</sup> = 10 MPa to reduce the apparent permeability enhancement through the Klinkenberg effect (e.g., [44]). The effective confining pressure peff = p<sup>c</sup> − p<sup>p</sup> was kept constant (4 MPa) throughout most experiments so as to compare results gained with either distilled water or Argon gas. In a few cases, peff could not be held constant, for example, during tests with step-wise increasing confining pressure. Here, p<sup>p</sup> was kept below p<sup>c</sup> to avoid a 'blow-up' of the fracture.

Fracture transmissivity was calculated by assuming the fluid flow pattern within the fracture to be comparable to the flow of electric current through a resistive solid within an insulating medium (dashed lines in Figure 3a). Assuming that the up- and downstream borehole form the dipole of a magnetic field and comparing Ohm's law with Darcy's law for steady fluid flow to characterize the transmissivity of thin cracks in various rocks, Ohm's law may be rewritten as [19,45]:

$$k \ast t = \frac{Q \ast \eta \ast \ln\left(\frac{2a}{r\_0} - 1\right)}{\Delta p\_p \ast B \ast \pi} \tag{1}$$

where the term k∗t is the transmissivity of the fracture, with k and t representing fracture permeability and fracture thickness, respectively. Q is the volumetric flow rate, *η* is the (temperature-dependent) dynamic viscosity of the fluid, 2a is the distance between up- and downstream borehole with radius r0, ∆p<sup>p</sup> is the pressure difference within the fracture, and B (=0.75 for our geometry) is a geometry factor accounting for the aspect ratio of the fracture [19]. Here, we assumed single-phase fluid flow within the fracture, which is certainly a simplification compared to multi-phase fluid flow that may occur in natural fractures and the surrounding matrix [12].

A detailed microstructural analysis of the starting and the post-experimental samples was performed on mechanically as well as broad ion-beam polished, carbon-coated thin sections using a scanning electron microscope (SEM FEI Quanta 3D dual beam). SEM sections were prepared perpendicularly to the fracture surface. Broad ion-beam (BIB JEOL IB-19520CCP) polishing was used for the gouge and OPA samples to avoid preparationinduced damage of clay minerals. Due to its fragile character, the gouge was additionally solidified using epoxy resin prior to broad ion beam-milling.

In addition, we performed uniaxial compression (UCS) tests to determine the basic mechanical properties such as the uniaxial compressive strength (*σ*UCS) and tangent Young's Modulus (E) of each sample material. The tests were performed according to the suggested ISRM method [46] using cylindrical specimens with a length-to-diameter ratio of 2:1. Results from UCS tests (Table 1) indicate that despite the high content of weak mineral phases, the strength and stiffness of WBS are comparable to granite, quartzite and graywacke samples that contain significantly more strong minerals. Furthermore, triaxial compressive strength (*σ*TCS) and static secant Young's modulus of WBS were determined in constant strain rate tests of . <sup>ε</sup> = 5 <sup>×</sup> <sup>10</sup>−<sup>4</sup> s <sup>−</sup><sup>1</sup> at simulated reservoir conditions with a

confining pressure of p<sup>c</sup> = 50 MPa and temperature of T = 100 ◦C using a Paterson-type deformation apparatus [47]. and stresses up to 45 MPa were conducted on the other rock types to evaluate the influence of composition on fracture transmissivity. The experimental duration for most of the experiments was between one and two weeks. Fracture transmissivity was deter-

ditions with a confining pressure of p<sup>c</sup> = 50 MPa and temperature of T = 100 °C using a

In total, we performed five flow through experiments on Wissenbach slate to investigate the evolution of fracture transmissivity with changing confining pressure, differential stress oriented perpendicular to the fracture interface, temperature, and surface roughness. In addition, six tests under room temperature, constant confining pressure

−1 at simulated reservoir con-

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were determined in constant strain rate tests of ε̇ = 5 × 10−4 s

Paterson-type deformation apparatus [47].

#### **3. Results** mined after reaching steady-state flow conditions at the different thermodynamic

**3. Results**

In total, we performed five flow through experiments on Wissenbach slate to investigate the evolution of fracture transmissivity with changing confining pressure, differential stress oriented perpendicular to the fracture interface, temperature, and surface roughness. In addition, six tests under room temperature, constant confining pressure and stresses up to 45 MPa were conducted on the other rock types to evaluate the influence of composition on fracture transmissivity. The experimental duration for most of the experiments was between one and two weeks. Fracture transmissivity was determined after reaching steady-state flow conditions at the different thermodynamic boundary conditions. boundary conditions. Previously performed triaxial tests reveal TCS = 498 ± 20 MPa and E = 69 ± 14 GPa (Table 1) that are comparable to the mechanical data of Westerly granite, Panzhihua gabbro or Novaculite [48] obtained at the same conditions. *3.1. Effect of Thermodynamic Boundary Conditions* Fracture fluid flow experiments at elevated pc, T and -conditions were performed

Previously performed triaxial tests reveal *σ*TCS = 498 ± 20 MPa and E = 69 ± 14 GPa (Table 1) that are comparable to the mechanical data of Westerly granite, Panzhihua gabbro or Novaculite [48] obtained at the same conditions. on Wissenbach slate samples with an average initial fracture surface roughness of S<sup>q</sup> = 0.019 mm. The influence of temperature on fracture transmissivity was evaluated at a confin-

#### *3.1. Effect of Thermodynamic Boundary Conditions* ing pressure of p<sup>c</sup> = 5 MPa and pore pressure of p<sup>p</sup> = 1 MPa in the range of T = 20–100 °C

Fracture fluid flow experiments at elevated pc, T and *σ*-conditions were performed on Wissenbach slate samples with an average initial fracture surface roughness of S<sup>q</sup> = 0.019 mm. (Table 2).

The influence of temperature on fracture transmissivity was evaluated at a confining pressure of p<sup>c</sup> = 5 MPa and pore pressure of p<sup>p</sup> = 1 MPa in the range of T = 20–100 ◦C (Table 2). **Table 2.** Fracture transmissivity in Wissenbach slate at elevated temperatures (p<sup>c</sup> = 5 MPa, = 0 MPa)

**Table 2.** Fracture transmissivity in Wissenbach slate at elevated temperatures (pc = 5 MPa, *σ* = 0 MPa). **T [ °C] p<sup>p</sup> [MPa] k\*t [m<sup>3</sup> ]** 25 1 1.33 × 10−1<sup>4</sup>


T = temperature, p<sup>p</sup> = pore pressure, k∗t = fracture transmissivity. Except for a moderate decrease from T = 20 °C to T = 40 °C, fracture transmissivity

Except for a moderate decrease from T = 20 ◦C to T = 40 ◦C, fracture transmissivity does not change significantly at up to 100 ◦C (Figure 4), showing that the fracture transmissivity of Wissenbach slate is insensitive to changes in temperature at a low confining pressure. does not change significantly at up to 100 °C (Figure 4), showing that the fracture transmissivity of Wissenbach slate is insensitive to changes in temperature at a low confining pressure.

**Figure 4.** Effect of temperature, T, on fracture transmissivity, k∗t, in Wissenbach slate. Fracture transmissivity decreases only slightly from T = 20 ◦C towards T = 40 ◦C and remains almost constant with increasing temperature up to 100 ◦C. Experimental conditions are indicated.

Hydrostatic tests with confining pressures ranging from p<sup>c</sup> = 2–25 MPa and p<sup>p</sup> = 1 MPa were performed at a constant temperature of T = 25 ◦C (Table 3). Hydrostatic tests with confining pressures ranging from p<sup>c</sup> = 2–25 MPa and p<sup>p</sup> = 1 MPa were performed at a constant temperature of T = 25 °C (Table 3).

**Figure 4.** Effect of temperature, T, on fracture transmissivity, k\*t, in Wissenbach slate. Fracture transmissivity decreases only slightly from T = 20 °C towards T = 40 °C and remains almost con-

stant with increasing temperature up to 100 °C. Experimental conditions are indicated.

**Table 3.** Fracture transmissivity in Wissenbach slate at elevated confining pressures (*σ* = 0 MPa, T = 25 ◦C). **Table 3.** Fracture transmissivity in Wissenbach slate at elevated confining pressures ( = 0 MPa, T = 25 °C)


p<sup>c</sup> = confining pressure, p<sup>p</sup> = pore pressure, k∗t = fracture transmissivity. p<sup>c</sup> = confining pressure, p<sup>p</sup> = pore pressure, k\*t = fracture transmissivity.

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Fracture transmissivity decreased non-linearly by about one order of magnitude from <sup>≈</sup>1.5 <sup>×</sup> <sup>10</sup>−<sup>14</sup> <sup>m</sup><sup>3</sup> to 1.7 <sup>×</sup> <sup>10</sup>−<sup>15</sup> <sup>m</sup><sup>3</sup> with increasing confining pressures, approaching almost constant values at high p<sup>c</sup> (Figure 5a). Fracture transmissivity decreased non-linearly by about one order of magnitude from ≈1.5 × 10−1<sup>4</sup> m<sup>3</sup> to 1.7 × 10−1<sup>5</sup> m<sup>3</sup> with increasing confining pressures, approaching almost constant values at high p<sup>c</sup> (Figure 5a).

**Figure 5.** Effect of confining pressure, pc, on fracture transmissivity, k\*t, in Wissenbach slate with high (S<sup>q</sup> = 0.0196 mm) (**a**) and low (S<sup>q</sup> = 0.006 mm) initial roughness (**b**). Fracture transmissivity is decreasing with increasing confining pressure. At relatively low p<sup>c</sup> (≤5 MPa), fracture transmissivity is up to one order of magnitude lower for the sample with low initial roughness. **Figure 5.** Effect of confining pressure, pc, on fracture transmissivity, k∗t, in Wissenbach slate with high (Sq = 0.0196 mm) (**a**) and low (Sq = 0.006 mm) initial roughness (**b**). Fracture transmissivity is decreasing with increasing confining pressure. At relatively low p<sup>c</sup> (≤5 MPa), fracture transmissivity is up to one order of magnitude lower for the sample with low initial roughness.

Experiments performed at p<sup>c</sup> = 5 MPa, p<sup>p</sup> = 1 MPa and T = 25 °C reveal a similar decrease in fracture transmissivity with increasing axial differential stress of = 0–45 MPa, but with a roughly 2-fold higher transmissivity than measured at similar p<sup>c</sup> values (Table 4, Figure 6a). Experiments performed at p<sup>c</sup> = 5 MPa, p<sup>p</sup> = 1 MPa and T = 25 ◦C reveal a similar decrease in fracture transmissivity with increasing axial differential stress of *σ* = 0–45 MPa, but with a roughly 2-fold higher transmissivity than measured at similar p<sup>c</sup> values (Table 4, Figure 6a).

**Table 4.** Fracture transmissivity in Wissenbach slate at elevated differential stress (p<sup>c</sup> = 5 MPa, T = 25 °C) using water as flow medium. **Table 4.** Fracture transmissivity in Wissenbach slate at elevated differential stress (p<sup>c</sup> = 5 MPa, T = 25 ◦C) using water as flow medium.



**Table 4.** *Cont.*

*σ* = differential stress, p<sup>p</sup> = pore pressure, k∗t = fracture transmissivity.

Interestingly, upon unloading, the fracture transmissivity did not recover and remained considerably lower than the initial transmissivity. For comparison, we performed a second test on the WBS slate using Argon gas as fluid medium at p<sup>c</sup> = 14 MPa, p<sup>p</sup> = 10 MPa, i.e., a similar effective pressure of pc\_eff = p<sup>c</sup> − p<sup>p</sup> = 4 MPa, assuming that Terzaghi's principle [49] is valid. For this sample, the initial transmissivity was found to be distinctly lower than of the sample with water as the fluid medium (Table 5, small symbols in Figure 6a), but approaching similar values at high *σ* (≥40 MPa) and showing similar residual transmissivity upon unloading.


**Table 5.** Fracture transmissivity in Wissenbach slate at elevated differential stress (p<sup>c</sup> = 14 MPa, T = 25 ◦C) using Argon gas as flow medium.

*σ* = differential stress, p<sup>p</sup> = pore pressure, k∗t = fracture transmissivity.

For the sample tested with water, after the axial loading (phase I) and unloading (phase II) steps, we subsequently increased p<sup>c</sup> from 5 to 50 MPa (phase III), resulting in a fracture transmissivity slightly lower than that measured at *σ* = 45 MPa (Table 6, Figure 7), confirming the stronger influence of p<sup>c</sup> on transmissivity reduction than of *σ* as described above.

**Figure 6.** Effect of differential stress, , on fracture transmissivity, k\*t, in Wissenbach slate (**a**), Graywacke (**b**), Quartzite-Havelange (**c**), Granite-Death Valley (**d**), Gouge-Death Valley (**e**), Opalinus clay-sandy facies (**f**), and Opalinus clay-shaly facies (**g**). Experiments conducted at p<sup>c</sup> = 14 MPa were performed using Argon gas as flow medium (gouge, OPA), all other with distilled water. The effective pressure (pc–pp) is 4 MPa in all cases. Experimental conditions are indicated. Note different scales. **Figure 6.** Effect of differential stress, *σ*, on fracture transmissivity, k∗t, in Wissenbach slate (**a**), Graywacke (**b**), Quartzite-Havelange (**c**), Granite-Death Valley (**d**), Gouge-Death Valley (**e**), Opalinus clay-sandy facies (**f**), and Opalinus clay-shaly facies (**g**). Experiments conducted at pc = 14 MPa were performed using Argon gas as flow medium (gouge, OPA), all other with distilled water. The effective pressure (p<sup>c</sup> − pp) is 4 MPa in all cases. Experimental conditions are indicated. Note different scales.

Interestingly, upon unloading, the fracture transmissivity did not recover and re-

p<sup>p</sup> = 10 MPa, i.e., a similar effective pressure of pc\_eff = p<sup>c</sup> − p<sup>p</sup> = 4 MPa, assuming that Terzaghi's principle [49] is valid. For this sample, the initial transmissivity was found to be


**Table 6.** Fracture transmissivity in Wissenbach slate at elevated differential stress, confining pressures and temperatures.

*σ* = differential stress, p<sup>c</sup> = confining pressure, T = temperature, p<sup>p</sup> = pore pressure, k∗t = fracture transmissivity.

**Figure 7.** Combined effect of differential stress, , confining pressure, pc, and temperature, T, on fracture transmissivity, k\*t, plotted versus effective normal stress, n\_eff, acting on the fracture surface in Wissenbach slate. Fracture transmissivity decreases along -loading path (I) and recovers only partly during unloading (II). Increasing p<sup>c</sup> (III), (IV) and T (V) further decreases fracture **Figure 7.** Combined effect of differential stress, *σ*, confining pressure, pc, and temperature, T, on fracture transmissivity, k∗t, plotted versus effective normal stress, *σ* n\_eff, acting on the fracture surface in Wissenbach slate. Fracture transmissivity decreases along *σ*-loading path (I) and recovers only partly during unloading (II). Increasing pc (III), *σ* (IV) and T (V) further decreases fracture transmissivity.

transmissivity. Note that for comparison we plotted the transmissivity data which are presented in Figure 7 as a function of the effective normal stress n\_eff = + p<sup>c</sup> − pp, acting normal to the fracture surface. In phase IV, axial stress was increased again to = 30 MPa at a constant p<sup>c</sup> of 50 MPa (n\_eff = 79 MPa), which yields a further transmissivity reduction, again with a lower gradient than observed in phase III (Figure 7). Finally, we increased Note that for comparison we plotted the transmissivity data which are presented in Figure 7 as a function of the effective normal stress *σ*n\_eff = *σ* + p<sup>c</sup> − pp, acting normal to the fracture surface. In phase IV, axial stress was increased again to *σ* = 30 MPa at a constant p<sup>c</sup> of 50 MPa (*σ*n\_eff = 79 MPa), which yields a further transmissivity reduction, again with a lower gradient than observed in phase III (Figure 7). Finally, we increased temperature from 25 to 90 ◦C at constant *σ* and p<sup>c</sup> (phase V), which induced a strong transmissivity reduction of almost one order of magnitude.

#### temperature from 25 to 90 °C at constant and p<sup>c</sup> (phase V), which induced a strong *3.2. Effect of Fracture Surface Roughness*

sures ( = 0 MPa, T = 25 °C)

issues (below measurable range).

*3.3. Effect of Sample Composition*

transmissivity reduction of almost one order of magnitude. The influence of reduced fracture surface roughness on the change of fracture transmissivity with increasing confining pressure of up to 5 MPa was measured on the Wissenbach slate at T = 25 ◦C (Table 7).

*3.2. Effect of Fracture Surface Roughness* The influence of reduced fracture surface roughness on the change of fracture transmissivity with increasing confining pressure of up to 5 MPa was measured on the Wissenbach slate at T = 25 °C (Table 7). **Table 7.** Low-roughness-fracture transmissivity in Wissenbach slate at elevated confining pres-The initial fracture surface roughness of this sample was Sq\_ini\_low = 0.006 mm, which is roughly three times smaller than the surface roughness of previously examined samples (Sq\_ini= 0.019 mm). Comparable to the rough surface, fracture transmissivity decreases nonlinearly with increasing confining pressure (Figure 5b), but at a similar p<sup>c</sup> the transmissivity values are about one order of magnitude lower (Table 3). At higher confining pressures (p<sup>c</sup> > 5 MPa), we were not able to resolve transmissivity due to technical issues (below measurable range).

**..p<sup>c</sup> [MPa] p<sup>p</sup> [MPa] k\*t [m<sup>3</sup>**

1.5 0.5 8.44 × 10−1<sup>6</sup> 2 0.5 7.63 × 10−1<sup>6</sup> 5 1 4.65 × 10−1<sup>6</sup>

The initial fracture surface roughness of this sample was Sq\_ini\_low = 0.006 mm, which

is roughly three times smaller than the surface roughness of previously examined samples (Sq\_ini= 0.019 mm). Comparable to the rough surface, fracture transmissivity decreases non-linearly with increasing confining pressure (Figure 5b), but at a similar p<sup>c</sup> the transmissivity values are about one order of magnitude lower (Table 3). At higher confining pressures (p<sup>c</sup> > 5 MPa), we were not able to resolve transmissivity due to technical

**]**

p<sup>c</sup> = confining pressure, p<sup>p</sup> = pore pressure, k\*t = fracture transmissivity.


**Table 7.** Low-roughness-fracture transmissivity in Wissenbach slate at elevated confining pressures (*σ* = 0 MPa, T = 25 ◦C).

p<sup>c</sup> = confining pressure, p<sup>p</sup> = pore pressure, k∗t = fracture transmissivity.

#### *3.3. Effect of Sample Composition*

To determine the impact of composition on fracture transmissivity, we performed flow through experiments at T = 25 ◦C, with an effective pressure of pc\_eff = 4 MPa, and by increasing differential stress up to 45 MPa. Tests were conducted at p<sup>c</sup> = 5 MPa, pp= 1 MPa using water as fluid medium for samples WBS, GRW, QTZ\_HV and GRA\_DV. For the clay-rich samples GOU\_DV, OPA\_SD and OPA\_SH, we used Argon at p<sup>c</sup> =14 MPa and p<sup>p</sup> = 10 MPa to avoid disintegration and swelling of the samples. As observed for WBS (Figure 6a), in all other rocks, fracture transmissivity decreased non-linearly with increasing *σ* and demonstrated limited recovery upon unloading (Figure 6, Table 8).

**Table 8.** Fracture transmissivity of and Graywacke (GRW), Quartzite-Havelange (QTZ\_HV), Granite Death-Valley (GRA\_DV), Gouge-Death Valley (GOU\_DV), Opalinus clay-sandy facies (OPA\_SD), Opalinus clay-shaly facies (OPA\_SH) at elevated differential stress and T = 25 ◦C.





**Table 8.** *Cont.*

p<sup>c</sup> = confining pressure, *σ* = differential stress, p<sup>p</sup> = pore pressure, k∗t = fracture transmissivity.

The initial transmissivity of the graywacke sample (Figure 6b) is comparable to that of Havelange quartzite (Figure 6c) and Noble Hill granite (Figure 6d). However, the fracture transmissivity of the graywacke decreases at a higher rate upon differential loading, whereas the transmissivity of quartzite and granite decreases almost at the same point. The permanent reduction in transmissivity after unloading is lowest for the quartzite followed by the granite. On the other hand, the graywacke shows a reduction in transmissivity almost threefold that of the quartzite. Compared to WBS, the quartzite and granite were less sensitive to increasing stress, while the graywacke demonstrated a comparable sensitivity (Figure 6). The Death Valley gouge shows a very strong transmissivity reduction already at low stress and almost no recovery after unloading (Figure 6e), which is likely related to the relatively high preparation-related initial roughness, almost an order of magnitude higher than of the other rocks. For Opalinus Clay, transmissivity within the sandy facies (Figure 6f) is about one order of magnitude higher than for the shaly facies (Figure 6g). Interestingly, the non-linearity of transmissivity with increasing stress is least pronounced for OPA\_SH. Note that the maximum stress on OPA\_SH and GOU\_DV samples was less than for the other rocks to avoid potential major creep deformation of these weak rocks.

For comparison, all data are shown in Figure 8 in a semi-logarithmic scale, revealing that hard rocks such as granite and quartzite display transmissivity of several orders of magnitude higher at high *σ* and less irreversible damage than relatively weak OPA and gouge. Moreover, slate and graywacke transmissivity is also relatively high (in the same range as of granite and quartzite transmissivity) at high *σ* but shows much less reversibility upon unloading. Note, however, that the initial roughness of the gouge sample is higher than of the other tested rocks, which may obscure the systematics to some extent.

**Figure 8.** Comparison of the influence of effective normal stress, n\_eff, acting on the fracture surface on fracture transmissivity, k\*t. Data are the same as shown in Figure 6, but plotted in semilogarithmic scale. α and β indicate the linear slopes for fitting of the loading and unloading path to an exponential relationship (c.f., Equation (2)). Note that for unloading the slope is deviating from linearity at low stress. **Figure 8.** Comparison of the influence of effective normal stress, *σ*n\_eff, acting on the fracture surface on fracture transmissivity, k∗t. Data are the same as shown in Figure 6, but plotted in semi-logarithmic scale. *α* and *β* indicate the linear slopes for fitting of the loading and unloading path to an exponential relationship (c.f., Equation (2)). Note that for unloading the slope is deviating from linearity at low stress.

#### *3.4. Microstructures*

*3.4. Microstructures* After each experiment, the topography of the fracture surface of each sample was measured again with a white light profilometer in order to quantify changes due the applied experimental procedures. Thin sections of the tested specimens were then pre-After each experiment, the topography of the fracture surface of each sample was measured again with a white light profilometer in order to quantify changes due the applied experimental procedures. Thin sections of the tested specimens were then prepared for a subsequent SEM analysis.

pared for a subsequent SEM analysis. In order to compare the surface topographies before and after the experiments, we show surface height distribution of the lower sample half (without injection/production holes, see Figure 3a) of each sample in Figures A1 and A2. In comparison to the initial surface, the height distribution of WBS samples (Figure A1) measured after testing at increasing pc, or T became slightly wider but remained more or less unaffected. This is also reflected by the determined surface roughness measurements, which are relatively similar to the initial roughness values (Table 1). The same applies to the other samples, showing slight widening of height distributions after deformation (Figure A2). However, height distributions of the quartzite and granite samples show the least changes (Figure A2b,c), indicating no obvious change in the topography after loading. On the other hand, the distribution and fracture roughness of the gouge (Figure A2d, Table 1) display In order to compare the surface topographies before and after the experiments, we show surface height distribution of the lower sample half (without injection/production holes, see Figure 3a) of each sample in Figures A1 and A2. In comparison to the initial surface, the height distribution of WBS samples (Figure A1) measured after testing at increasing pc, *σ* or T became slightly wider but remained more or less unaffected. This is also reflected by the determined surface roughness measurements, which are relatively similar to the initial roughness values (Table 1). The same applies to the other samples, showing slight widening of height distributions after deformation (Figure A2). However, height distributions of the quartzite and granite samples show the least changes (Figure A2b,c), indicating no obvious change in the topography after loading. On the other hand, the distribution and fracture roughness of the gouge (Figure A2d, Table 1) display the highest grade of asperity degradation, although the maximum applied stress did not exceed 20 MPa. Independent of the facies, the surface of fractures within the Opalinus Clay (Figure A2e,f) exhibit a moderate alteration due to axial loading.

the highest grade of asperity degradation, although the maximum applied stress did not exceed 20 MPa. Independent of the facies, the surface of fractures within the Opalinus SEM micrographs of the Wissenbach slate and of the other rocks prepared perpendicular to the fracture surface are shown in Figures 9 and 10, respectively.

SEM micrographs of the Wissenbach slate and of the other rocks prepared perpen-

Clay (Figure A2e,f) exhibit a moderate alteration due to axial loading.

dicular to the fracture surface are shown in Figures 9 and 10, respectively.

**Figure 9.** Scanning electron microscope-back scattered electron (SEM-BSE) photographs of sections prepared from Wissenbach slate (WBS) samples. All thin sections have been prepared perpendicular to the artificially prepared macro fracture located at the top of each image. Panel (**a**) shows the initial (ini\_rough) fracture prior to testing. Subscripts 'T', 'pc', and 'pc\_\_T' refer to tests performed at increasing temperature (**b**), confining pressures (**c**), a combination of pressure, stress, and temperature (**d**,**e**). Panel (**f)** shows the post-experimental profile of the sample with initial low roughness. Arrows indicate microfracturing and intracrystalline plasticity (see text for details). **Figure 9.** Scanning electron microscope-back scattered electron (SEM-BSE) photographs of sections prepared from Wissenbach slate (WBS) samples. All thin sections have been prepared perpendicular to the artificially prepared macro fracture located at the top of each image. Panel (**a**) shows the initial (ini\_rough) fracture prior to testing. Subscripts 'T', 'pc', and 'pc\_*σ*\_T' refer to tests performed at increasing temperature (**b**), confining pressures (**c**), a combination of pressure, stress, and temperature (**d**,**e**). Panel (**f**) shows the post-experimental profile of the sample with initial low roughness. Arrows indicate microfracturing and intracrystalline plasticity (see text for details). Note the different scales.

For WBS, in comparison to the intact initial rough artificial fracture surface (Figure

9a), the matrix close to the surface of samples after testing is severely damaged (Figure 9b–e). Samples being step-wisely exposed to increasing temperature locally displayed a slightly flattened fracture surface profile (Figure 9b, white arrow). Sporadically, quartz,

tration. On the other hand, small intergranular fractures (<5 µm opening; black arrow in Figure 9b) oriented subparallel to the macroscopic artificial fracture can be frequently observed, which may be partially induced by unloading and/or cooling and follows a cleavage orientation. Deformation microstructures of the sample deformed at varying confining pressure of up to 25 MPa are similar compared to the previously described sample. However, the density of intergranular, cleavage-parallel fractures is higher in comparison (Figure 9c). Damage of the sample subjected to combined pressure, axial stress, and temperature variations was highest when a large number of intra- and trans-

Note the different scales.

finement.

damage zone is limited to <150 µm.

granular cracks in calcite, dolomite and quartz mineral grains (white arrow in Figure 9d) were detected. In addition, this sample shows several bent, kinked and delaminated micas (black arrows in Figure 9d,e), indicative for crystal plasticity. Furthermore, we observed boudinage micas suggesting shear motion at grain boundary surfaces (white arrows in Figure 9e). For all samples, the maximum damage zone is limited to <150 µm below the fracture surface profile line. As expected, the surface of the sample with a low initial roughness was considerably smoother compared to the other samples (Figure 9f). Except for the subparallel fractures with a small aperture, damage of the surface by the applied pressure was hardly visible, likely because of the relatively low applied con-

The damage near the fracture surface of the other rocks after stress stepping varies

with composition. The graywacke sample shows some spalling microfractures in quartz and feldspar grains close to the fracture interface (white and black arrow in Figure 10a). Rarely, minor intergranular fractures (aperture < 5 µm) propagate into the rock. The

**Figure 10.** Scanning electron microscope-back scattered electron (SEM-BSE) photographs of sections prepared from samples of various formations after applying differential stress normal to the **Figure 10.** Scanning electron microscope-back scattered electron (SEM-BSE) photographs of sections prepared from samples of various formations after applying differential stress normal to the fracture surface. All thin sections have been prepared perpendicular to the artificially prepared macro fracture (located at the top of each figure). (**a**) Graywacke (GRW), (**b**) quartzite recovered from the Havelange borehole (QTZ\_HV), (**c**) granite recovered from the Death Valley (GRA\_DV), (**d**) gouge like material recovered from the Death Valley (GOU\_DV), (**e**) Opalinus clay material recovered from the sandy facies (OPA\_SD), (**f**) Opalinus Clay recovered from the shaly facies (OPA\_SH). Arrows indicate testing-induced damage (see text for details). Note different scales.

For WBS, in comparison to the intact initial rough artificial fracture surface (Figure 9a), the matrix close to the surface of samples after testing is severely damaged (Figure 9b–e). Samples being step-wisely exposed to increasing temperature locally displayed a slightly flattened fracture surface profile (Figure 9b, white arrow). Sporadically, quartz, carbonate and dolomite grains are fractured, potentially induced by local stress concentration. On the other hand, small intergranular fractures (<5 µm opening; black arrow in Figure 9b) oriented subparallel to the macroscopic artificial fracture can be frequently observed, which may be partially induced by unloading and/or cooling and follows a cleavage orientation. Deformation microstructures of the sample deformed at varying confining pressure of up to 25 MPa are similar compared to the previously described sample. However, the density of intergranular, cleavage-parallel fractures is higher in comparison (Figure 9c). Damage of the sample subjected to combined pressure, axial stress, and temperature variations was highest when a large number of intra- and transgranular cracks in calcite, dolomite and quartz mineral grains (white arrow in Figure 9d) were detected. In addition, this sample shows several bent, kinked and delaminated micas (black arrows in Figure 9d,e), indicative for crystal plasticity. Furthermore, we observed boudinage micas suggesting shear motion at grain boundary surfaces (white arrows in Figure 9e). For all samples, the maximum damage zone is limited to <150 µm below the fracture surface profile line. As expected, the surface of the sample with a low initial roughness was considerably smoother compared to the other samples (Figure 9f). Except for the subparallel fractures with a small aperture, damage of the surface by the applied pressure was hardly visible, likely because of the relatively low applied confinement.

The damage near the fracture surface of the other rocks after stress stepping varies with composition. The graywacke sample shows some spalling microfractures in quartz and feldspar grains close to the fracture interface (white and black arrow in Figure 10a). Rarely, minor intergranular fractures (aperture < 5 µm) propagate into the rock. The damage zone is limited to <150 µm.

In the Havelange quartzite, microfractures in quartz are confined to single grains. The intragranular cracks form near the surface and lead to the spalling of grain fragments, indicative of small grain contact areas during differential loading (white arrow in Figure 10b). Despite the high number of fractures, the grain shape still remains relatively intact, resulting in a recognizable topography of asperities on the fracture surface. The damage zone below the fracture surface does not exceed 150 µm and is limited to the first layer of grains below the fracture boundary. The Noble Hill granite also exhibited spalling in quartz and feldspar grains at the contact to the fracture surface (white arrow in Figure 10c). In addition, we observed several intra- and trans-granular fractures opening subparallel to the loading direction (black arrow in Figure 10c) as well as the refracturing of previously healed, pre-existing fractures. Compared to the quartzite, the damage zone in the granite sample was found to be significantly larger. Single fractures extend up to 700 µm below the surface. Due to the high alteration and tectonic overprint [37], deformation structures that were generated by our experimental procedure were difficult to identify in the gouge from the Death Valley. Besides the cataclastic fabric and alteration of minerals (e.g., siderite, white arrow Figure 10d), we identified deformation features such as strongly bent phyllosilicates, the collapse of pore space and altered mineral grains (area between dashed white lines in Figure 10d). Clastic mineral grains (quartz, carbonates, feldspars) and mineral fragments show rare evidence of experimentally induced fractures. We observed several intergranular fractures that potentially opened during unloading (black arrow in Figure 10d). Note that the milling artefacts at the fracture surface are caused by the partly remaining resin, which was applied after testing to avoid preparation-induced damage. Opalinus Clay of the sandy (Figure 10e) and shaly (Figure 10f) facies typically displayed matrix deformation by the bending of phyllosilicates (open arrow in Figure 10e) and small fractures opening subparallel to the fracture surface (black arrows in Figure 10e,f). Clastic mineral grains in the sandy facies display several transgranular microfractures (white arrow in Figure 10e). On the other hand, the shaly facies show a significantly lower amount of fractured mineral

grains compared to the sandy facies. Furthermore, these are limited to calcite grains and fossil shells, whereas quartz grains remained unfractured (white arrows in Figure 10f). In both facies, the "card house" structure of the clay matrix observed in the undeformed material collapsed with clay minerals being reoriented, with their longest axis parallel to the facture surface and perpendicular to the maximum principal stress direction. The damage zone extends up to 150 µm below the surface in the sandy facies and up to 300 µm in the shaly facies.

#### **4. Discussion**

Our set of flow through experiments demonstrated that at given fracture surface roughness increasing confining pressure, differential stress, and temperature at elevated pressure reduces the fracture transmissivity of slates (Figures 4–7). Furthermore, the initial transmissivity reduced considerably for smooth surfaces compared to rough surfaces (Figure 5). A strong influence of sample composition and associated mechanical properties on transmissivity is also evident (Figures 6 and 8). These effects will be discussed in the following paragraphs.

#### *4.1. Influence of Thermodynamic Boundary Conditions (T, pc, σ) on Fracture Transmissivity of Wissenbach Slate*

Temperature has a strong effect on the interaction between the fluid transported through the fracture and the adjacent host rock [50–53]. The rate of dissolution of asperities is often enhanced at high temperatures and can reduce the mean fracture aperture due to mineral precipitation [52–55]. For WBS flushed with water, [22] observed a slight (few %), time-dependent fracture permeability decline in long-term flow through tests at p<sup>c</sup> = 10 MPa, *σ* = 0 MPa and elevated temperatures up to 90 ◦C due to pressure solution and free face dissolution. However, using saline fluids, the authors measured an increase in permeability with increasing T, probably related to enhanced dissolution kinetics. In our tests with distilled water, we observed that at p<sup>c</sup> = 5 MPa and *σ* = 0 MPa the fracture transmissivity of WBS was hardly affected by temperature between 25 and 100 ◦C (Figure 4), except a small decrease (≈23%) between 25 and 40 ◦C. This confirms that temperature sensitive processes, like chemical dissolution-precipitation processes or stress corrosion at areas of high stress concentration were not very effective within the relatively short time span of our experiments. In contrast, transmissivity dropped considerably more (≈93%) at p<sup>c</sup> = 50 MPa and *σ* = 30 MPa in response to a temperature increase from 25 to 90 ◦C (Figure 7). This observation suggests that thermal dilation is more effective at high effective normal stress since the mean fracture aperture is lower than at low pc, *σ* conditions (e.g., [52,56]). However, performing experiments over a longer time range may be necessary to reliably record chemical processes such as diffusion and mineral precipitation as reported by [22]. These authors performed similar flow-through experiments on samples prepared from the same slate material emphasizing the effect of fluid-rock interactions on the time-dependent transmissivity of fractures.

Concerning the influence of pressure and stress on transmissivity, we observed that the transmissivity is slightly (about two times) higher at enhanced p<sup>c</sup> compared to a similar enhancement of *σ* alone, although the effective stress acting normal to the interface is the same (e.g., Figure 7). The difference may be explained by the increasing strength of the matrix adjacent to the fracture and the suppression of tensile fracturing with increasing pressure, whereas with increasing stress but constant (low) confining pressure the strength of the aggregate is lower than at high pc. In both cases, the observed reduction in fracture transmissivity with increasing p<sup>c</sup> or *σ* (Figures 5 and 6) is likely induced by indentation and damage of fracture surface asperities (Figures 9 and 10), resulting in a change of contact area and therefore mean aperture. A similar trend of decreasing fracture transmissivity induced by mechanical and/or pressure solution processes is reported for other rocks, e.g., shales, (tight) sandstones, granites, and granodiorite [1,16,19,50,52,53,57–59].

Interestingly, the transmissivity of WBS at low applied stress was distinctly lower for the sample tested with Argon at p<sup>c</sup> = 14 MPa, p<sup>p</sup> = 10 MPa than for the sample flushed with water at p<sup>c</sup> = 5 MPa, p<sup>p</sup> = 1 MPa, i.e., at the same effective pressure (Figure 6a). The difference may be attributed to the experimental protocol, where in the case of Argon the initial 14 MPa confining pressure was applied before applying the fluid pressure. This may induce more initial damage of the surface compared to the test with water at only 5 MPa confining pressure (cf., Figure 5a). In addition, it is not well established that Terzaghi's principle of effective stresses, i.e., pc\_eff = p<sup>c</sup> − δ p<sup>p</sup> with δ =1, is valid here because at the microscale asperities are in contact, which reduces the Biot coefficient δ to a value < 1. This effect may result in a higher effective pressure in the experiment conducted with Argon gas compared to that with water, which would reduce the transmissivity difference at low stress. On the long term, chemical effects may also contribute to the transmissivity evolution due to different chemical fluid-rock interaction rates for different types of fluids. *Geosciences* **2022**, *12*, x FOR PEER REVIEW 25 of 34

In Figure 11, a comparison of our data with that measured by [19] on Westerly granite, Pennant sandstone and Bowland shale is presented, revealing that the influence of effective pressure on transmissivity disappears at high pc\_eff. The transmissivity of WBS appears to be comparable to that of Pennant sandstone, whereas the transmissivity of our granite appears to be considerably lower than that of Westerly granite. Bowland shale exhibits the lowest transmissivity values, which are even lower than our clay-rich samples. The difference may be attributed to the initial roughness of the samples used by [19], which was unfortunately not provided by the authors. of our granite appears to be considerably lower than that of Westerly granite. Bowland shale exhibits the lowest transmissivity values, which are even lower than our clay-rich samples. The difference may be attributed to the initial roughness of the samples used by [19], which was unfortunately not provided by the authors.

**Figure 11.** Effect of effective confining pressure, pc\_eff = pc-pp, on fracture transmissivity, k\*t, in Wissenbach slate (WBS) in comparison with other formations as reported by [19]. Data of the other formations investigated here (at = 0 MPa, c.f., Figure 6) are shown in addition. **Figure 11.** Effect of effective confining pressure, pc\_eff = p<sup>c</sup> − pp, on fracture transmissivity, k∗t, in Wissenbach slate (WBS) in comparison with other formations as reported by [19]. Data of the other formations investigated here (at *σ* = 0 MPa, c.f., Figure 6) are shown in addition.

The non-linear transmissivity reduction with increasing pressure and/or stress (Figures 5, 6 and 8) may be explained by the initial elastic deformation of the asperities that is gradually replaced by irreversible damage due to high stress concentrations. Since the effective contact area also increases with load (e.g., [60]), deformation or the breaking of further asperities or grains in the vicinity of the fracture surface become increasingly hampered and additional deformation is increasingly promoted by matrix deformation. As a consequence, the fluid flow pattern likely changes towards a higher tor-The non-linear transmissivity reduction with increasing pressure and/or stress (Figures 5, 6 and 8) may be explained by the initial elastic deformation of the asperities that is gradually replaced by irreversible damage due to high stress concentrations. Since the effective contact area also increases with load (e.g., [60]), deformation or the breaking of further asperities or grains in the vicinity of the fracture surface become increasingly hampered and additional deformation is increasingly promoted by matrix deformation. As a consequence, the fluid flow pattern likely changes towards a higher tortuosity of the flow path and probably towards more localized flow through channels at high pressures, as also

tuosity of the flow path and probably towards more localized flow through channels at high pressures, as also observed for other rocks (e.g., [50]). A number of theoretical at-

normal stress (e.g., [61–66]). From that and from empirical correlations based on experiments, the change in fracture permeability with stress was described by a hyperbolic relationship [67], power law [68], or an exponential law [17,61]. Here, we used an expo-

∗ = ∗

where c is a constant and x is the slope in a plot of ln(k\*t) vs. n\_eff, with x = for the loading path and x = for the unloading path (c.f., Figure 8). For WBS, is about 3 times smaller than (Table 9), showing that irreversible damage changes the stress-sensitivity

**Sample Bcompo** WBS −0.061 ± 0.002 −0.018 ± 0.002 0.32 WBSAr −0.044 ± 0.001 −0.025 ± 0.002 0.32 GRW −0.061 ± 0.003 −0.019 ± 0.003 0.41

∗\_ (2)

**Table 9.** Influence of host rock composition on fracture transmissivity.

nential law of the following form:

of transmissivity considerably.

observed for other rocks (e.g., [50]). A number of theoretical attempts were made to relate fracture transmissivity to surface roughness and the applied normal stress (e.g., [61–66]). From that and from empirical correlations based on experiments, the change in fracture permeability with stress was described by a hyperbolic relationship [67], power law [68], or an exponential law [17,61]. Here, we used an exponential law of the following form:

$$k\*t = c\*e^{\chi\*\sigma\_{n\multimap}}\tag{2}$$

where c is a constant and x is the slope in a plot of ln(k∗t) vs. *σ*n\_eff, with x = *α* for the loading path and x = *β* for the unloading path (c.f., Figure 8). For WBS, *β* is about 3 times smaller than *α* (Table 9), showing that irreversible damage changes the stress-sensitivity of transmissivity considerably.

**Table 9.** Influence of host rock composition on fracture transmissivity.


*α* = slope of loading branch, *β* = slope of the unloading branch, Bcompo = brittleness index based on sample composition. WBS = Wissenbach slate, WBSAr = Wissenbach slate tested with Argon, GRW = Graywacke, QTZ\_HV = Quartzite Havelange, GRA\_DV = Granite Death Valley, GOU\_DV = Gouge Death Valley, OPA\_SD = Opalinus clay sandy facies, OPA\_SH = Opalinus clay shaly facies.

#### *4.2. Sample Composition and Mechanical Properties*

To better quantify the influence of composition and mechanical properties on fracture transmissivity, we applied the exponential law on the transmissivity–stress data of all other rocks, yielding values in the range of −0.03 and −0.32 for *α*, and −0.008 and −0.064 for *β* (Table 9).

Lowest (absolute) *α*-values were fitted for granite and quartzite samples, whereas absolute *α*-values of the graywacke and slate are about twice as high and comparable to the sandy facies of OPA. Lowest (absolute) *β*-values were found in the granite and graywacke. In order to relate these values to composition, we superimposed them in ternary diagrams (Figure 12).

Low (absolute) *α*-values, indicative of a weak reduction in transmissivity at elevated stress appear to be correlated with a high fraction of strong components (QFSO) and a low amount of weak constituents (Phyl), whereas carbonates appear to have no influence (Figure 12a). For the unloading sensitivity *β*, which is high for strong fracture transmissivity recovery, we observed a trend of enhanced unloading recovery with an increasing quantity of weak minerals and decreasing amount of QFSO (Figure 12b). Note that other parameters, which likely influence *α* and *β*, for example, porosity and cementation, are not captured in the diagrams.

In addition, we compared the *σ*-sensitivity of transmissivity for the different rock types with their brittleness defined by composition. Here, we used the empirical brittleness definition suggested by [69]:

$$B\_{\rm compo} = \frac{w\_{\rm QFSO} \* f\_{\rm QFSO}}{w\_{\rm QFSO} \* f\_{\rm QFSO} + w\_{\rm Cb} \* f\_{\rm Cb} + w\_{\rm Phy1} \* f\_{\rm Phy1}} \tag{3}$$

where *f* xx is the fraction of minerals xx given in wt% and *w*QFSO, *w*Cb, and *w*Phyl are the weighting factors ranging from 0 to 1. We set *w*QFSO = *w*Phyl = 1 and *w*Cb = 0.5 as suggested by [69]. Calculated brittleness values are given in Table 9, ranging from 0.16 to 0.90. Based on the simplified assumption that in the absence of strong (QFSO) minerals the mechanical behavior is dominantly ductile, B values can vary between 0 and 1, indicating ductile and brittle deformation behavior, respectively. For rocks with high brittleness, the effect of increasing pressure or axial stress on fracture transmissivity is expected to be lower than for those with low B values. With the exception of the gouge, absolute values of *α* decrease with increasing Bcompo (Figure 13a) in line with the common assumption that the deformation of brittle rocks is less stress-sensitive than that of ductile rocks. The low *α* value of the gauge-like material recovered from the Death Valley is most likely due induced by the high initial roughness and a high porosity of about 13 vol% (Table 1). Similarly, the (absolute) unloading sensitivity *β* seems to slightly decrease with increasing brittleness (Figure 13b), which may be explained by the crushing of strong and brittle minerals at the fracture surface at elevated stresses, where the produced fines prevent the recovery of fracture transmissivity during unloading. sample composition. WBS = Wissenbach slate, WBSAr = Wissenbach slate tested with Argon, GRW = Graywacke, QTZ\_HV = Quartzite Havelange, GRA\_DV = Granite Death Valley, GOU\_DV = Gouge Death Valley, OPA\_SD = Opalinus clay sandy facies, OPA\_SH = Opalinus clay shaly facies. *4.2. Sample Composition and Mechanical Properties* To better quantify the influence of composition and mechanical properties on fracture transmissivity, we applied the exponential law on the transmissivity–stress data of all other rocks, yielding values in the range of −0.03 and −0.32 for , and −0.008 and −0.064 for (Table 9). Lowest (absolute) -values were fitted for granite and quartzite samples, whereas absolute -values of the graywacke and slate are about twice as high and comparable to the sandy facies of OPA. Lowest (absolute) β-values were found in the granite and graywacke. In order to relate these values to composition, we superimposed them in

QTZ\_HV −0.030 ± 0.001 −0.022 ± 0.003 0.71 GRA\_DV −0.032 ± 0.001 −0.008 ± 0.002 0.90 GOU\_DV −0.319 ± 0.023 −0.026 ± 0.003 0.61 OPA\_SD −0.065 ± 0.001 −0.030 ± 0.005 0.61 OPA\_SH −0.110 ± 0.014 −0.064 ± 0.008 0.16 = slope of loading branch, = slope of the unloading branch, Bcompo = brittleness index based on

*Geosciences* **2022**, *12*, x FOR PEER REVIEW 26 of 34

ness definition suggested by [69]: compo = QFSO ∗ QFSO QFSO ∗ QFSO + Cb ∗ Cb + Phyl ∗ Phyl (3) **Figure 12.** Influence of sample composition on the (effective) stress-sensitivity of fracture transmissivity indicated by superimposed *α*-values for the loading path (**a**) and by *β*-values for the unloading path (**b**). The (absolute) sensitivity generally decreases for a high fraction of strong (QFSO) minerals and low amount of weak (Phyl) constituents.

where *f*xx is the fraction of minerals xx given in wt% and *w*QFSO, *w*Cb, and *w*Phyl are the weighting factors ranging from 0 to 1. We set *w*QFSO = *w*Phyl = 1 and *w*Cb = 0.5 as suggested by [69]. Calculated brittleness values are given in Table 9, ranging from 0.16 to 0.90. Based on the simplified assumption that in the absence of strong (QFSO) minerals the mechanical behavior is dominantly ductile, B values can vary between 0 and 1, indicating ductile and brittle deformation behavior, respectively. For rocks with high brittleness, the effect of increasing pressure or axial stress on fracture transmissivity is expected to be lower than for those with low B values. With the exception of the gouge, absolute values of decrease with increasing Bcompo (Figure 13a) in line with the common Another parameter that likely explains the stress-sensitivity of the fracture transmissivity of the different investigated rocks are their mechanical properties. The measured unconfined uniaxial strength, *σ*UCS, and the static Young's moduli, E, vary over wide range and appear to be linearly correlated (Table 1, Figure A3), as has been observed frequently (e.g., [48,70]). Compared to composition-based brittleness, both (absolute) *α* and *β* values decrease with increasing *σ*UCS and E (c.f., Figure 13c–f, respectively), revealing that rocks with a high strength and/or elastic stiffness are less sensitivity to stress-induced damage of the fracture surface and associated transmissivity reduction.

assumption that the deformation of brittle rocks is less stress-sensitive than that of ductile rocks. The low value of the gauge-like material recovered from the Death Valley is most likely due induced by the high initial roughness and a high porosity of about 13

vol% (Table 1). Similarly, the (absolute) unloading sensitivity seems to slightly decrease with increasing brittleness (Figure 13b), which may be explained by the crushing of strong and brittle minerals at the fracture surface at elevated stresses, where the pro-

duced fines prevent the recovery of fracture transmissivity during unloading.

**Figure 13.** Influence of brittleness based on composition, Bcompo,, uniaxial compressive strength, UCS, and static Young's modulus, E, on the (effective) stress-sensitivity of fracture transmissivity, , for the loading path (**a**,**c**,**e**) and for the unloading path (**b**,**d**,**f**), respectively. The (absolute) sensitivity decreases with increasing brittleness, strength, and elastic stiffness. **Figure 13.** Influence of brittleness based on composition, Bcompo, uniaxial compressive strength, *σ*UCS, and static Young's modulus, E, on the (effective) stress-sensitivity of fracture transmissivity, *α*, for the loading path (**a**,**c**,**e**) and for the unloading path *β* (**b**,**d**,**f**), respectively. The (absolute) sensitivity decreases with increasing brittleness, strength, and elastic stiffness.

#### Another parameter that likely explains the stress-sensitivity of the fracture trans-*4.3. Implications for EGS in Different Host Rocks*

missivity of the different investigated rocks are their mechanical properties. The measured unconfined uniaxial strength, UCS, and the static Young's moduli, E, vary over wide range and appear to be linearly correlated (Table 1, Figure A3), as has been observed frequently (e.g., [48,70]). Compared to composition-based brittleness, both (absolute) and values decrease with increasing UCS and E (c.f., Figure 13c–f, respectively), revealing that rocks with a high strength and/or elastic stiffness are less sensitivity to stress-induced damage of the fracture surface and associated transmissivity reduction. *4.3. Implications for EGS in Different Host Rocks* An assessment of the performance and sustainability of fractured rock systems for An assessment of the performance and sustainability of fractured rock systems for EGS requires knowledge of the response of fractures to the acting effective stress, temperature, and fluid flow. The effective normal stress on fractures changes during and after hydraulic stimulation of reservoirs. As may be expected, our results of flow through experiments on various rock types (i.e., slate, quartzite, graywacke, granite, claystone, and gouge material) demonstrate that the key parameters that determine the stress resistance of fracture transmissivity are fracture surface roughness and the mechanical properties of the respective rock material. Fractures with similar surface roughness display the highest transmissivity in slate, quartzite, graywacke, and fresh granite, all of which contain a high amount of strong minerals and display high brittleness, high strength, and high elastic stiffness. On the other hand, in weak and porous rocks such as claystone and gouge material, transmissivity is reduced by several orders of magnitude by deformation of

EGS requires knowledge of the response of fractures to the acting effective stress, tem-

the soft matrix and limited crushing of contact asperities. Therefore, highly altered, claybearing formations are not favorable candidates for EGS. For hard rocks, grain size may also play a role if fracture propagation is predominantly intergranular. For example, the grain size of slate and graywacke is much smaller than that of quartzite and granite (Figure 2), so that at the microscale the real contact area of fine-grained rocks is higher, which reduces the stress acting on contact asperities, thereby maintaining a higher transmissivity.

Our results also imply that beside fracture surface roughness and composition, the degree of consolidation and metamorphic grade affects the potential of reservoir rocks for EGS. For example, the shaly facies of Opalinus Clay, graywacke and slate are relatively rich in phyllosilicates (Figure 1), but the latter two experienced a higher degree of metamorphosis with a strong cementation of grains, resulting in a much higher strength and elastic stiffness (Figure A3). Accordingly, fractures in slates are much more resistant against stress-induced fracture closure than in OPA (Figure 8).

We also noticed that (for slate samples) an increase in the fracture surface roughness (Sq) by about three times yields a fracture transmissivity of almost one order of magnitude higher at a low effective pressure (<5 MPa), which vanishes at high pressure (up to 25 MPa in our experiments), possibly due to the fact that the mechanical strength of slate at the microscale is not sufficient to resist high effective stresses. During hydraulic stimulation in EGS, tensile fractures are created that may connect to a preexisting fracture network. The surface roughness of these fractures is likely higher than the roughness of the artificially prepared surfaces in our study. For example, we measured a significantly larger (up to 20×) and more heterogeneously distributed roughness of tensile fractures created in WBS by Brazilian Disk (BD) experiments in divider, short-transverse, and arrester configuration following the ISRM suggested method [71]. However, even fractures with high initial roughness, e.g., created during hydraulic fracturing, may show a strong transmissivity decline at high stress conditions as long as they are not self-propped by shearing or artificially kept open by the addition of proppants (e.g., [72]). For the latter, high stress may crush the proppants and embed them into the matrix, which leads again to a transmissivity reduction (e.g., [73]).

Other parameters, which were not investigated in this study, may also affect the efficiency and sustainability of an EGS in different formations, for example self-propping due to a shear deformation event or fine production and clogging of flow path by ongoing deformation. Additionally, chemical effects due to long-term fluid–rock interactions or scaling may change the fracture transmissivity, depending on fluid and rock composition and thermodynamic boundary conditions.

#### **5. Conclusions**

Fracture transmissivity decreases asymptotically with increasing confining pressure and stress due to the damage caused to surface asperities and the matrix deformation of weak rocks, which is largely irreversible. A lower initial roughness also reduces transmissivity, while a temperature increase only significantly reduces the transmissivity by thermal dilation if the fracture aperture is already low. As may be expected, the fracture transmissivity of hard brittle rocks with a high fraction of strong minerals is less sensitive to stress-induced fracture closure and exhibits less irreversible damage. However, since the transmissivity of slates is much higher than of claystone, as well as the transmissivity of granite compared to a highly altered and sheared granitic gouge, the grade of consolidation, metamorphosis, and alteration of rocks is also important for fluid flow within discrete fractures under in situ conditions. Our results suggest that Variscan metamorphic rocks such as slate, graywacke and quartzite can be considered as host rocks for unconventional Enhanced Geothermal systems, with resistance to fracture transmissivity against thermodynamic boundary conditions that is as good as that of granite or quartzite for similar initial fracture roughness.

**Author Contributions:** Conceptualization, J.H.; methodology, J.H. and V.S.; software, J.H., V.S. and E.R.; validation, J.H., V.S., C.C., H.M. and E.R.; formal analysis, J.H.; investigation, J.H. and V.S.; resources, J.H., V.S. and C.C.; data curation, J.H. and V.S.; writing—original draft preparation, J.H.; writing—review and editing, J.H., V.S., C.C., H.M. and E.R.; visualization, J.H., V.S., C.C. and E.R. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the "Multidisciplinary and multi-context demonstration of Enhanced Geothermal Systems Exploration and Exploitation Techniques and potentials (MEET)" research project funded by the European Union's Horizon 2020 research and innovation programme under Grant Agreement No. 792037.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** We thank Michael Naumann for the construction of the modified MuSPIS apparatus and for their assistance with the uniaxial and triaxial deformation as well as fracture transmissivity experiments, Stefan Gehrmann for sample and thin section preparation, Anja Schreiber for carbon coating of SEM samples, Bianca Wagner and Bernd Leiss from the University of Göttingen for XRD results and providing Wissenbach slate and graywacke samples, Yves Vanbrabant from Institut Royal des Sciences Naturelles de Belgique for providing Havelange quartzite samples, Ghislain Trullenque and Johanne Klee from Institut Polytechnique LaSalle Beauvais for providing granite and gouge samples, and Kristian Bär and Aysegül Turan from the Technical University of Darmstadt for providing some mechanical and petrophysical data. *Geosciences* **2022**, *12*, x FOR PEER REVIEW 30 of 34

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Appendix A Appendix A**

**Figure A1.** Fracture surface height distribution before and after experiments for Wissenbach slate tested at different temperatures (**a**), confining pressures (**b**,**c**), and a combination of different pressures, stresses and temperatures (**d**). Initial sample roughness was Sq = 0.019 mm in (**a**,**b**,**d**) and Sq = 0.006 mm in (**c**). **Figure A1.** Fracture surface height distribution before and after experiments for Wissenbach slate tested at different temperatures (**a**), confining pressures (**b**,**c**), and a combination of different pressures, stresses and temperatures (**d**). Initial sample roughness was S<sup>q</sup> = 0.019 mm in (**a**,**b**,**d**) and Sq = 0.006 mm in (**c**).

**Figure A2.** Fracture surface height distribution before and after testing at elevated stresses for graywacke (**a**), quartzite (**b**), fresh granite (**c**), altered granitic gouge (**d**), Opalinus clay—sandy fa**Appendix A**

= 0.006 mm in (**c**).

**Figure A1.** Fracture surface height distribution before and after experiments for Wissenbach slate tested at different temperatures (**a**), confining pressures (**b**,**c**), and a combination of different pressures, stresses and temperatures (**d**). Initial sample roughness was Sq = 0.019 mm in (**a**,**b**,**d**) and Sq

**Figure A2.** Fracture surface height distribution before and after testing at elevated stresses for graywacke (**a**), quartzite (**b**), fresh granite (**c**), altered granitic gouge (**d**), Opalinus clay—sandy fa-**Figure A2.** Fracture surface height distribution before and after testing at elevated stresses for graywacke (**a**), quartzite (**b**), fresh granite (**c**), altered granitic gouge (**d**), Opalinus clay—sandy facies (**e**), and Opalinus clay—shaly facies (**f**). Wissenbach slate tested at different temperatures (**a**), confining pressures (**b**,**c**), and a combination of different pressures, stresses and temperatures (**d**). cies (**e**), and Opalinus clay—shaly facies (**f**). Wissenbach slate tested at different temperatures (**a**), confining pressures (**b**,**c**), and a combination of different pressures, stresses and temperatures (**d**).

**Figure A3.** Static Young's modulus E vs. uniaxial compressive strength UCS of all tested rock **Figure A3.** Static Young's modulus E vs. uniaxial compressive strength *σ*UCS of all tested rock types.

<sup>g</sup> Grain density g/cm<sup>3</sup> He Sample Porosity (using Helium pycnometry) vol% kmatrix Matrix permeability m<sup>2</sup> UCS Uniaxial compressive strength MPa TCS Triaxial compressive strength MPa E Static Young's modulus GPa p<sup>c</sup> Confining pressure MPa p<sup>p</sup> Fluid pressure Pa T Temperature °C Axial deviatoric stress MPa S<sup>q</sup> Fracture surface roughness (root mean square) mm k Fracture permeability m<sup>2</sup> t Fracture thickness/ hydraulic aperture mm Q Volumetric flow rate ml/min Dynamic viscosity Pa\*s 2a Distance between up- and downstream borehole mm r<sup>0</sup> Radius of up- and downstream borehole mm ∆p<sup>p</sup> Differential pore pressure within the fracture Pa ∆x Distance within the fracture over which is ∆p<sup>p</sup> measured mm B Geometry factor / Bcompo Brittleness based on composition / wxx Mineral weighting factor / fxx Mineral fraction wt%

1. Vogler, D.; Amann, F.; Bayer, P.; Elsworth, D. Permeability evolution in natural fractures subject to cyclic loading and gouge

formation. *Rock Mech. Rock Eng.* **2016**, *49*, 3463–3479. https://doi.org/10.1007/s00603-016-1022-0.

types.

**References**

**Table A1.** List of symbols.


**Table A1.** List of symbols.

#### **References**


## *Article* **Impact of Well Placement in the Fractured Geothermal Reservoirs Based on Available Discrete Fractured System**

**Saeed Mahmoodpour 1,\*, Mrityunjay Singh 1,\* , Kristian Bär <sup>1</sup> and Ingo Sass 1,2**


**Abstract:** Well placement in a given geological setting for a fractured geothermal reservoir is necessary for enhanced geothermal operations. High computational cost associated with the framework of fully coupled thermo-hydraulic-mechanical (THM) processes in a fractured reservoir simulation makes the well positioning a missing point in developing a field-scale investigation. To enhance the knowledge of well placement for different working fluids, we present the importance of this topic by examining different injection-production well (doublet) positions in a given fracture network using coupled THM numerical simulations. Results of this study are examined through the thermal breakthrough time, mass flux, and the energy extraction potential to assess the impact of well position in a twodimensional reservoir framework. Almost ten times the difference between the final amount of heat extraction is observed for different well positions but with the same well spacing and geological characteristics. Furthermore, the stress field is a strong function of well position that is important concerning the possibility of high-stress development. The objective of this work is to exemplify the importance of fracture connectivity and density near the wellbores, and from the simulated cases, it is sufficient to understand this for both the working fluids. Based on the result, the production well position search in the future will be reduced to the high-density fracture area, and it will make the optimization process according to the THM mechanism computationally efficient and economical.

**Keywords:** well placement; CO<sup>2</sup> -EGS; water-EGS; discrete fracture networks; THM modeling

#### **1. Introduction**

Geothermal field development and management is a complex process. Engineering a geothermal system requires appropriate well placement and fracture connectivity to ensure well connectivity and least fluid loss [1,2]. Placement of injection and production wells or a doublet system in a given geological framework to achieve maximum geothermal energy extraction is one of the most complicated and expensive procedures. The location of the injection well concerning production well decides the production mass flux [3,4]. Practically, there is an infinite number of sites where an injection well can be placed in designing an enhanced geothermal system (EGS). Well placement in association with fracture network requires two critical aspects to ensure high heat extraction potential. First, the fractures must be connected sufficiently, and they must provide a high fluid flow rate at a lowpressure difference, and secondly, fluid residence time in the fractures should be increased to allow sufficient heat exchange. Longer residence time enhances the heat extraction capacity and reduces the chances of short-circuiting [5,6]. Figure 1 shows a subsurface fracture network where red is the high-temperature region. Hot water is produced through the red color well from the reservoir, and after passing it through the heat exchanger, it is reinjected to the reservoir with the blue color well. Fractures are the main paths for fluid flow that allow for heat extraction from the various MEET geothermal sites,

**Citation:** Mahmoodpour, S.; Singh, M.; Bär, K.; Sass, I. Impact of Well Placement in the Fractured Geothermal Reservoirs Based on Available Discrete Fractured System. *Geosciences* **2022**, *12*, 19. https:// doi.org/10.3390/geosciences12010019

Academic Editors: Ronan L. Hébert, Ghislain Trullenque, Albert Genter, Eléonore Dalmais, Jean Hérisson and Jesus Martinez-Frias

Received: 23 September 2021 Accepted: 30 December 2021 Published: 4 January 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

including Soultz sous Forêts, United Down, Göttingen, and Havelange. Discrete Fracture Network (DFN) characterization is an essential step toward the simulation of reservoir performance. However, the total number of fractures resulting from DFN characterization is a high number (in the order of millions of fractures) which is not feasible for performing numerical simulation (due to computational costs) while considering all of them discretely through the thermal-hydraulic (TH) or thermal-hydraulic-mechanical (THM) simulator. Recently, Lepillier et al. [7] combined TH behavior with the steady-state solid mechanics process to examine the well positioning impact with four doublet scenarios. However, transient temperature and pressure changes will affect the stress field, and four scenarios are not sufficient to accurately demonstrate the impact of well position. crete Fracture Network (DFN) characterization is an essential step toward the simulation of reservoir performance. However, the total number of fractures resulting from DFN characterization is a high number (in the order of millions of fractures) which is not feasible for performing numerical simulation (due to computational costs) while considering all of them discretely through the thermal-hydraulic (TH) or thermal-hydraulic-mechanical (THM) simulator. Recently, Lepillier et al. [7] combined TH behavior with the steadystate solid mechanics process to examine the well positioning impact with four doublet scenarios. However, transient temperature and pressure changes will affect the stress field, and four scenarios are not sufficient to accurately demonstrate the impact of well position.

the main paths for fluid flow that allow for heat extraction from the various MEET geothermal sites, including Soultz sous Forêts, United Down, Göttingen, and Havelange. Dis-

*Geosciences* **2021**, *11*, x FOR PEER REVIEW 2 of 19

**Figure 1.** An enhanced geothermal system. The subsurface plan shows an intricate network of fractures. For optimized power generation, appropriate placement of the injection and production wells is necessary. **Figure 1.** An enhanced geothermal system. The subsurface plan shows an intricate network of fractures. For optimized power generation, appropriate placement of the injection and production wells is necessary.

At the same time, the fracture network alignment also contributes to the thermal drawdown, mass flux, and extracted energy. Therefore, it is essential to estimate the well locations a priori for better connectivity and maximum energy extraction. For example, a second well was designed at Rittershoffen (Upper Rhine Graben, France) in the damage zone of the Rittershoffen fault after the drilling of the first one and an additional geophysical survey [8]. At the same time, the fracture network alignment also contributes to the thermal drawdown, mass flux, and extracted energy. Therefore, it is essential to estimate the well locations a priori for better connectivity and maximum energy extraction. For example, a second well was designed at Rittershoffen (Upper Rhine Graben, France) in the damage zone of the Rittershoffen fault after the drilling of the first one and an additional geophysical survey [8].

This paper considers a two-dimensional fractured reservoir for a potential enhanced geothermal system. Fully coupled thermo-hydro-mechanical (THM) processes are simulated on the fractured reservoir to estimate maximum geothermal energy extraction po-This paper considers a two-dimensional fractured reservoir for a potential enhanced geothermal system. Fully coupled thermo-hydro-mechanical (THM) processes are simulated on the fractured reservoir to estimate maximum geothermal energy extraction potential.

tential. Several optimization techniques are available for determining well placement in a reservoir [9]. Some of these methods are gradient-free methods, including genetic algorithms [10], particle swarm optimization algorithm [11], fast marching method [12], and simultaneous perturbation stochastic approximation [13,14], and gradient-based optimization methods, including adjoint methods [15–17]. These models lack geological uncertainty, e.g., fracture network connectivity, while considering well placement optimization [18]. Few thermo-hydraulic compositional reservoir simulation-based models on well spacing optimization [19–26]. Based on a coupled thermo-hydraulic model, Akin et al. [27] developed artificial neural networks (ANN) and a search algorithm to optimize an injection well for a geothermal reservoir whereas, Samin et al. [28] developed a hybrid approach integrating a multi-objective genetic algorithm with finite element modeling of Several optimization techniques are available for determining well placement in a reservoir [9]. Some of these methods are gradient-free methods, including genetic algorithms [10], particle swarm optimization algorithm [11], fast marching method [12], and simultaneous perturbation stochastic approximation [13,14], and gradient-based optimization methods, including adjoint methods [15–17]. These models lack geological uncertainty, e.g., fracture network connectivity, while considering well placement optimization [18]. Few thermo-hydraulic compositional reservoir simulation-based models on well spacing optimization [19–26]. Based on a coupled thermo-hydraulic model, Akin et al. [27] developed artificial neural networks (ANN) and a search algorithm to optimize an injection well for a geothermal reservoir whereas, Samin et al. [28] developed a hybrid approach integrating a multi-objective genetic algorithm with finite element modeling of thermo-hydraulic processes. EGS involves complex THM processes. Gudmundsdottir and Horne [29] developed an ANN model to characterize fractured geothermal reservoirs for a coupled TH model. Training data necessary for creating a robust ANN model based on a coupled thermo-hydro-mechanical process requires many numerical reservoir simulations. A recent

study using an ANN model for a coupled thermo-hydraulic approach supports this idea for a fracture in a hot geothermal reservoir [30] and supercritical geothermal reservoirs [31].

While performing a parametric investigation for a multi-well reservoir, Chen and Jiang [19] found that production well configuration concerning injection well affects the heat mining potential. Chen et al. [32] used a multivariate adaptive regression spline technique coupled with hydrothermal numerical simulation to optimize the well placement under the given fault size and permeability for a prospective geothermal site near Superstition Mountain in Southern California USA. They found that for the maximum net profit over fifty years, the optimal well spacing is 473 m at 30.7 kg/s. For 45◦ angle between fracture orientation and inlet-outlet connection in a given fracture network, Zhang et al. [33] observed optimized geothermal energy extraction performance. They obtained a stable heat mining rate at reduced efficiency for higher orientation angles. Zhang et al. [2] found that the presence of many fractures in the vicinity of the production well increases the working fluid residence time, and heat recovery efficiency significantly improves. They suggested that thermally-induced fractures near the production well assist in greater power generation than when the fracture density is high in the vicinity of the injection well. They also observed that placing the production well in the high permeability region increases heat production. Gao et al. [34] used a coupled thermo-hydraulic model for a discrete fracture network in a fractured geothermal reservoir to investigate heat extraction performance. They used multilateral well orientations with a varying number of branch wells and well orientation. They found that production temperature decreases with an increase in the well and fracture intersections, whereas injection pressure increases. Aliyu et al. [35] and Aliyu and Chen [36] used COMSOL Multiphysics to develop a model depicting THM and TH processes in a geothermal reservoir for two fractures and single fractures, respectively. They estimated the impact of well spacing on thermal energy extraction performance.

The MEET project framework considers water as the working fluid or heat-carrying fluid from a geothermal system. However, this study finds CO<sup>2</sup> as an alternative to water because the loss of CO<sup>2</sup> as the heat-carrying fluid is environment friendly [37,38]. Furthermore, the use of supercritical CO<sup>2</sup> may assist in the formation of an interconnected fracture network of multiple channels at a lower pressure than water due to smaller fluid density and viscosity [38]. Due to the lower reactivity of CO<sup>2</sup> in comparison to water, the possible silica dissolution and precipitation at high temperatures and pressure decreases [37–39]. Additionally, Bongole et al. [40] observed that the reservoir deformation is more minor when CO<sup>2</sup> is the working fluid compared to water due to the lower heat capacity of CO2. The lower freezing point of CO<sup>2</sup> than water helps heat rejection at a much lower temperature. Therefore, its geothermal systems may work even for cold climatic conditions where water is unusable [41]. The above literature shows no available THM model for determining the well placement in a geothermal reservoir concerning a given fracture map to maximize mass flux, energy extraction, and the thermal drawdown duration. In this work, a fully coupled THM model is developed and used to demonstrate the importance of well position by characterizing the fracture network connectivity and density. This study will build a basis for future well placement optimization considering THM processes for a given fracture network. The present study is organized in the following manner. First, a mathematical and numerical model is presented for a coupled THM process followed by results and discussion on optimizing well positions in a two-dimensional fracture network based on thermal drawdown, mass flux, and energy extraction potential followed by conclusions.

#### **2. Methodology**

This study uses a fracture network based on outcrop fractures mapped from Otsego County in New York state [42] for THM modeling. The total number of fractures in this outcrop map is 440. As depicted in Figure 1, this study considers a two-dimensional geometry at subsurface conditions. The reservoir geometry is a two-dimensional planar model (1000 m × 600 m), and the injection-production wells are placed 500 m apart. An

initial case is considered where the injection well is present at point 0 and the production well at point 180, as shown in Figure 2. Considering this axis as diameter, a circular zone is assumed, and the perimeter is divided into 36 equal intervals. These 36 intervals are considered for placing the injection and production wells, and they are arranged at α angle from the base case. All fractures are assumed as interior boundaries, and the displacement is constrained in all normal directions. The side boundaries are assumed as no flow for both heat and mass exchange. initial case is considered where the injection well is present at point 0 and the production well at point 180, as shown in Figure 2. Considering this axis as diameter, a circular zone is assumed, and the perimeter is divided into 36 equal intervals. These 36 intervals are considered for placing the injection and production wells, and they are arranged at α angle from the base case. All fractures are assumed as interior boundaries, and the displacement is constrained in all normal directions. The side boundaries are assumed as no flow for both heat and mass exchange.

This study uses a fracture network based on outcrop fractures mapped from Otsego County in New York state [42] for THM modeling. The total number of fractures in this outcrop map is 440. As depicted in Figure 1, this study considers a two-dimensional geometry at subsurface conditions. The reservoir geometry is a two-dimensional planar model (1000 m × 600 m), and the injection-production wells are placed 500 m apart. An

*Geosciences* **2021**, *11*, x FOR PEER REVIEW 4 of 19

**2. Methodology**

**Figure 2.** The geometry of the reservoir. Injection and production wells are placed 500 m apart. Total 36 cases or 36 values of α are considered for simulations. Here, when the injection well is present at 0 and production well is present at 180 and they are 500 m placed apart, the value of α is 0. When the injection well is present at 340 and the production well is present at 160, the value of α is 340. **Figure 2.** The geometry of the reservoir. Injection and production wells are placed 500 m apart. Total 36 cases or 36 values of α are considered for simulations. Here, when the injection well is present at 0 and production well is present at 180 and they are 500 m placed apart, the value of α is 0. When the injection well is present at 340 and the production well is present at 160, the value of α is 340.

Conservation equation of mass when coupled with pore volume and fluid temperature alteration for a porous medium is [43]: Conservation equation of mass when coupled with pore volume and fluid temperature alteration for a porous medium is [43]:

$$\rho\_1(\phi\_m S\_1 + (1 - \phi\_m) S\_m) \frac{\partial p}{\partial t} - \rho\_1(a\_m(\phi\_m \beta\_1 + (1 - \phi\_m)\beta\_m)) \frac{\partial T}{\partial t} + \rho\_1 a\_m \frac{\partial \varepsilon\_V}{\partial t} = \nabla \cdot \left(\frac{\rho\_1 k\_m}{\mu} \nabla p\right) \tag{1}$$

All the parameters are listed in Appendix A. Water and supercritical CO<sup>2</sup> are considered heat-transmitting fluids in this study. The equation that governs fluid flow along the internal fractures is: All the parameters are listed in Appendix A. Water and supercritical CO<sup>2</sup> are considered heat-transmitting fluids in this study. The equation that governs fluid flow along the internal fractures is:

$$\rho\_1 \left(\boldsymbol{\phi}\_f \mathbf{S}\_1 + \left(1 - \boldsymbol{\phi}\_f\right) \mathbf{S}\_{\text{mf}}\right) \mathbf{e}\_h \frac{\partial p}{\partial t} - \rho\_1 \left(\boldsymbol{a}\_f \left(\boldsymbol{\phi}\_f \mathbf{\hat{e}}\_1 + \left(1 - \boldsymbol{\phi}\_f\right) \boldsymbol{\theta}\_f\right)\right) \mathbf{e}\_h \frac{\partial T}{\partial t} + \rho\_1 \mathbf{a}\_f \boldsymbol{e}\_h \frac{\partial \varepsilon\_V}{\partial t} = \boldsymbol{\nabla}\_T \cdot \left(\frac{\boldsymbol{e}\_h \boldsymbol{\rho}\_1 \mathbf{k}\_f}{\mu} \boldsymbol{\nabla}\_T p\right) + \boldsymbol{n} \cdot \mathbf{Q}\_{\text{mf}} \quad \text{(2)}$$

ture is much smaller than the fracture length. Fractures and the rock matrix are assumed at thermodynamic inequilibrium. In other words, the local thermal non-equilibrium model is implemented in this investigation. In Equation (2), fluid flow along the fracture width is ignored because fracture aperture is much smaller than the fracture length. Fractures and the rock matrix are assumed at thermodynamic inequilibrium. In other words, the local thermal non-equilibrium model is implemented in this investigation.

$$(1 - \phi\_m)\rho\_m \mathcal{C}\_{p,m} \frac{\partial T\_m}{\partial t} = \nabla \cdot ((1 - \phi\_m)\lambda\_m \nabla T\_m) + q\_{ml}(T\_l - T\_m) \tag{3}$$

$$\frac{1}{2}\left(1-\phi\_f\right)e\_\hbar\rho\_f\mathcal{C}\_{p,f}\frac{\partial T\_\mathrm{m}}{\partial t} = \nabla\_T\cdot\left(\left(1-\phi\_f\right)e\_\hbar\lambda\_f\nabla\_T T\_\mathrm{m}\right) + e\_\hbar q\_f(T\_l - T\_\mathrm{m}) + n \cdot \left(-\left(1-\phi\_\mathrm{m}\right)\lambda\_\mathrm{m}\nabla T\_\mathrm{m}\right) \tag{4}$$

The energy balance equation for the rock matrix and fractures are shown by Equations (3) and (4), respectively. The energy balance equation for either water or CO<sup>2</sup> is:

$$
\rho\_m \rho\_l \mathcal{C}\_{p,l} \frac{\partial T\_l}{\partial t} + \phi\_m \rho\_l \mathcal{C}\_{p,l} \left(-\frac{k\_m \nabla p}{\mu}\right) \cdot \nabla T\_l = \nabla. (\phi\_m \lambda\_l \nabla T\_l) + q\_{ml} (T\_m - T\_l) \tag{5}
$$

The following equation can write heat exchange between a rock and the fracture matrix:

$$
\Phi\_f \mathbf{e}\_h \rho\_l \mathbf{C}\_{pJ} \frac{\partial T\_l}{\partial t} + \Phi\_f \mathbf{e}\_h \rho\_l \mathbf{C}\_{pJ} \left( -\frac{k\_f \nabla\_T p}{\mu} \right) \cdot \nabla\_T T\_l = \nabla\_T \cdot \left( \Phi\_f \mathbf{e}\_h \lambda\_l \nabla\_T T\_l \right) + e\_h q\_{fl} (T\_{\text{fl}} - T\_l) + n \cdot \left( -\phi\_l \lambda\_l \nabla T\_l \right) \tag{6}
$$

In Equation (6), the Darcy flux in the fractures is *u<sup>f</sup>* = − *k <sup>f</sup>* ∇*<sup>T</sup> p µ* and heat flux is *n*.*q<sup>l</sup>* = *n*·(−*φlλl*∇*Tl*).

A fully coupled thermo-hydro-mechanical model is developed in this study. If effective stress is *σ ij e f f* = *σij* + *α<sup>p</sup> pδij* and the volumetric expansion coefficient of porous media is *β<sup>T</sup>* = *φlβ<sup>l</sup>* + (1 − *φm*)*βm*, then the stress-strain relationship considering fully coupled thermoelastic and poroelastic stress can be written as:

$$
\sigma\_{\rm ij} = 2G\varepsilon\_{\rm ij} + \lambda t \tau \varepsilon \delta\_{\rm ij} - \alpha\_p p \delta\_{\rm ij} - K' \beta\_T T \delta\_{\rm ij} \tag{7}
$$

The reservoir deformation equation can be written as:

$$\mathbf{G}u\_{i,\vec{j}\vec{j}} + (\mathbf{G} + \lambda)u\_{\vec{j},\vec{j}\vec{i}} - \mathfrak{a}\_p p\_{,\vec{i}} - \mathbf{K}^l \mathfrak{b}\_T T\_{,\vec{i}} + f\_{\vec{i}} = \mathbf{0} \tag{8}$$

The opening and closure of the thermo-poroelastic stress-dependent fracture aperture are modeled using the Barton and Bandis model [44,45] as follow:

$$
\Delta e\_{\text{ll}} = \frac{e\_0}{1 + 9\frac{\sigma\_{eff}^n}{\sigma\_{\text{mref}}}} \tag{9}
$$

In Equation (9), ∆*e<sup>n</sup>* is the fracture aperture change under in-situ stress conditions.

Thermodynamic properties of water and CO<sup>2</sup> are represented by dynamic viscosity (Equations (10) and (11)), specific heat capacity (Equations (12) and (13)), density (Equations (14) and (15)), and thermal conductivity (Equations (16) and (17)) [42], and they are implemented in Equations (1)–(6).

$$\begin{array}{c} \mu\_{w} = 1.38 - 2.12 \times 10^{-2} \times T^{1} + 1.36 \times 10^{-4} \times T^{2} - 4.65 \times 10^{-7} \times T^{3} + 8.90 \times 10^{-10} \times T^{4} \\ \quad - 9.08 \times 10^{-13} \times T^{5} + 3.85 \times 10^{-16} \times T^{6} \quad (273.15 - 413.15 \text{ K}) \end{array} \tag{10}$$

$$\mu\_{\rm CO\_2} = -1.49 \times 10^{-6} - 6.47 \times 10^{-8} \times T^1 - 3.66 \times 10^{-11} \times T^2 + 1.25 \times 10^{-14} \times T^3 \tag{220 - 600 K} \tag{11}$$

$$\mathcal{C}\_{p, \mu} = 1.20 \times 10^4 - 8.04 \times 10^1 \times T^1 + 3.10 \times 10^{-1} \times T^2 - 5.38 \times 10^{-4} \times T^3 + 3.63 \times 10^{-7} \times T^4 \tag{12}$$

$$\mathcal{C}\_{p,\mathcal{CO}\_2} = 459.91 + 1.86 \times T^1 - 2.13 \times 10^{-3} \times T^2 + 1.22 \times 10^{-6} \times T^3 \ (220 - 600 \,\text{K}) \tag{13}$$

$$
\rho\_w = 1.03 \times 10^{-5} \times T^3 - 1.34 \times 10^{-2} \times T^2 + 4.97 \times T + 4.32 \times 10^2 \tag{14}
$$

$$
\rho\_{CO\_2} = pA \times 0.04401/RT \tag{15}
$$

$$\kappa\_{\overline{w}} = -8.69 \times 10^{-1} + 8.95 \times 10^{-3} \times T^1 - 1.58 \times 10^{-5} \times T^2 + 7.98 \times 10^{-9} \times T^3 \tag{16}$$

$$\kappa\_{\rm CO\_2} = -1.32 \times 10^{-3} + 4.14 \times 10^{-5} \times T^1 + 6.71 \times 10^{-8} \times T^2 - 2.11 \times 10^{-11} \times T^3 \tag{17}$$

In Equation (15), *pA* is the absolute pressure, and *R* is the molar gas constant. Coefficients in Equations (10)–(17) are constants and obtained from various correlations [42].

COMSOL Multiphysics version 5.5 [43] is used to perform numerical modeling of THM processes. It uses a finite element method to solve general purpose partial differential equations. The full mesh contains 112,818 domain elements and 13,071 boundary elements. This free triangular mesh is generated by using the maximum element size of 37 m, and

minimum element size of 0.125 m, maximum element growth of 1.25 with the curvature factor 0.25, and the resolution of the narrow regions is 1. For the numerical modeling purpose, we have used a scaled absolute tolerance of magnitude 10−<sup>8</sup> and automatic time step constraint. We assumed Backward Differentiation Formula (BDF) for timestepping with maximum BDF order as two and minimum BDF order as 1. Further, we have validated our model with a soil thermal consolidation model as Bai [46] demonstrated in Mahmoodpour et al. [47].

#### **3. Results and Discussions**

Numerical simulation results from coupled THM mechanisms associated with a geothermal energy extraction process from a fractured reservoir are presented in this section. First, we performed a sensitivity analysis for three different mesh elements. For the following stage, the adopted sequence of presentation is:


The results are presented for two working fluids: water and CO2. Reservoir permeability of 2 mD and 5 mD are considered. These values are chosen in a way that sweep efficiency with the different working fluids to be similar at the same time.

Furthermore, permeability values are kept constant to understand the working fluid effect by running another case 180. Other parameters are listed in Table 1 that are not site specific and selected to represent a generic geothermal system, and the fracture map is the same for all scenarios. Constant injection and production pressures are considered at both the wellbores. A two-dimensional horizontal cross-sectional reservoir is considered for all the simulations.

We performed a mesh sensitivity analysis with case 180 for CO<sup>2</sup> (it has the highest velocity variation, and the simulations convergence is the most complex among all the cases). Here, the mesh sensitivity analysis is attached for the simulations with (a) 92,655 domain elements and 12,103 boundary elements, (b) 112,818 domain elements and 13,071 boundary elements and (c) 181,410 domain elements and 15,687 boundary elements. Convergence was not achieved with the mesh size of the 71,089 domain elements and 10,357 boundary elements. The maximum element size for the standard case is (a) 67 m, (b) 37 m, and (c) 18 m, whereas the minimum element size is (a) 0.3 m, (b) 0.125 m, and (c) 0.075 m. The maximum element growth rate is (a) 1.3, (b) 1.25, and (c) 1.2, the curvature factor is (a) 0.3, (b) 0.25, and (c) 0.25, and the resolution of the narrow regions is 1 for all three cases. Free triangular meshes are used for discretizing this domain.

Based on this description, our results are insensitive to the mesh refinements (see Figure 3).

Figure 4 shows the time evolution of reservoir temperature distribution during the heat extraction operation using water and CO<sup>2</sup> for case 180. Here, the injection well is present at 180, and the production well is present at 0 as shown in Figure 2. The reservoir permeability for the left (Figure 4(a1–d1)) and right (Figure 4(a3–d3)) columns is 5 mD whereas the middle column has 2 mD permeability (Figure 4(a2–d2)). Higher reservoir permeability in the case of the left column causes faster cold fluid propagation through the fracture network. Additionally, water propagation through the fractures becomes less dominant, and it starts flowing through the rock matrix at higher permeability as shown in Figure 4(c1,d1). We adopted smaller reservoir permeability for well placement when water is the working fluid to account for both these factors. The cold-water propagation is aligned along the dominant fracture rather than the horizontal axis between the doublet. The reason behind selecting different permeability values for water and CO<sup>2</sup> is to reach a similar sweep efficiency with different fluids; however, we provided the quantitative comparison between simulation of water at 5 mD, 2 mD and CO<sup>2</sup> at 5 mD for case 180 as shown in Figure 5. Figure 5a–c shows that CO<sup>2</sup> is a better-working fluid concerning

the breakthrough time, mass flux, and cumulatively extracted energy, respectively over 30 years. Fracture zone thermal conductivity 2.5 W m × K

W m × K

3

2.5

800

W m × K

> W m × K

J kg × K


**Table 1.** Numerical simulation parameters (see the range of database in [48]). Rock specific heat capacity 800 J

Rock thermal conductivity 3

*Geosciences* **2021**, *11*, x FOR PEER REVIEW 7 of 19

**Figure 3.** Mesh sensitivity results for three different number of mesh elements.

**Figure 3.** Mesh sensitivity results for three different number of mesh elements.

present at 180, and the production well is present at 0 as shown in Figure 2. The reservoir permeability for the left (Figure 4(a1–d1)) and right (Figure 4(a3–d3)) columns is 5 mD whereas the middle column has 2 mD permeability (Figure 4(a2–d2)). Higher reservoir permeability in the case of the left column causes faster cold fluid propagation through the fracture network. Additionally, water propagation through the fractures becomes less dominant, and it starts flowing through the rock matrix at higher permeability as shown in Figure 4(c1,d1). We adopted smaller reservoir permeability for well placement when water is the working fluid to account for both these factors. The cold-water propagation is aligned along the dominant fracture rather than the horizontal axis between the doublet. years.

**Figure 4.** Reservoir temperature distribution at time 1 year (**a1**–**a3**), 5 years (**b1**–**b3**), 10 years (**c1**–**c3**) and 30 years (**d1**–**d3**) when the injection well is present at 180 and the production well is placed at 0. Results from water for reservoir permeability 5 mD and 2 mD are shown by (**a1**–**d1**) and (**a2**–**d2**) respectively. CO<sup>2</sup> as working fluid results are displayed in (**a3**–**d3**). The reservoir permeability for CO<sup>2</sup> simulations is 5 mD. The injection wellbore position is shown by cross symbol whereas a circle indicates production wellbore position. **Figure 4.** Reservoir temperature distribution at time 1 year (**a1**–**a3**), 5 years (**b1**–**b3**), 10 years (**c1**–**c3**) and 30 years (**d1**–**d3**) when the injection well is present at 180 and the production well is placed at 0. Results from water for reservoir permeability 5 mD and 2 mD are shown by (**a1**–**d1**) and (**a2**–**d2**) respectively. CO<sup>2</sup> as working fluid results are displayed in (**a3**–**d3**). The reservoir permeability for CO<sup>2</sup> simulations is 5 mD. The injection wellbore position is shown by cross symbol whereas a circle indicates production wellbore position. *Geosciences* **2021**, *11*, x FOR PEER REVIEW 9 of 19

The reason behind selecting different permeability values for water and CO<sup>2</sup> is to reach a similar sweep efficiency with different fluids; however, we provided the quantitative comparison between simulation of water at 5 mD, 2 mD and CO<sup>2</sup> at 5 mD for case 180 as shown in Figure 5. Figure 5a–c shows that CO<sup>2</sup> is a better-working fluid concerning the breakthrough time, mass flux, and cumulatively extracted energy, respectively over 30

**Figure 5.** Comparison of working fluid effects, (**a**) temperature at the production well, (**b**) mass flux of different fluid, and (**c**) extracted energy. **Figure 5.** Comparison of working fluid effects, (**a**) temperature at the production well, (**b**) mass flux of different fluid, and (**c**) extracted energy.

tures only as seen in Figure 4(a2,b2). Figure 4(a3–d3) shows that the cold fluid plume spread is much diffusive compared to water, and flow is primarily occurring through the matrix. However, Figure 4(d3) shows that CO<sup>2</sup> flows through the dominant fractures near the production well. Therefore, fluid propagation through the fractures is the principal mechanism between the doublet, which is assisted by flow through permeable rock ma-

The viscosity of supercritical CO<sup>2</sup> at injection conditions is approximately half compared to water. Higher reservoir permeability and lower viscosity indicate CO<sup>2</sup> propaga-

Furthermore, convective heat transfer inside the rock matrix and the fracture is the primary heat transfer mechanism. Therefore, the fractures control the heat transfer in a fractured reservoir. To show the relative importance of convective to conductive heat transfer, we calculated Peclet number (), a nondimensional number which indicates the

> , ,

> > is the

is the fluid thermal conduc-

ratio of convective to conductive heat transfer [49] and it can be written as =

is the specific heat capacity of fluid and

where is the fluid velocity, is the characteristic length (here it is 500 m, the distance between the two wells), the subscript indicates the fluid either water or CO2,

tivity. Figure 6a shows the value after one year for the entire reservoir for case 180, where CO<sup>2</sup> is the working fluid. To elaborate on the relative impact of convective heat transfer inside the fracture, one fracture is selected as shown in Figure 6b, and the corresponding number is shown in Figure 6c. number is estimated for five different times, and for all the cases, number is significantly larger than 1, indicating more vig-

trix.

fluid density, ,

orous convection than conduction.

The viscosity of supercritical CO<sup>2</sup> at injection conditions is approximately half compared to water. Higher reservoir permeability and lower viscosity indicate CO<sup>2</sup> propagation through the fractures as well as through the matrix rather than flowing through fractures only as seen in Figure 4(a2,b2). Figure 4(a3–d3) shows that the cold fluid plume spread is much diffusive compared to water, and flow is primarily occurring through the matrix. However, Figure 4(d3) shows that CO<sup>2</sup> flows through the dominant fractures near the production well. Therefore, fluid propagation through the fractures is the principal mechanism between the doublet, which is assisted by flow through permeable rock matrix.

Furthermore, convective heat transfer inside the rock matrix and the fracture is the primary heat transfer mechanism. Therefore, the fractures control the heat transfer in a fractured reservoir. To show the relative importance of convective to conductive heat transfer, we calculated Peclet number (*Pe*), a nondimensional number which indicates the ratio of convective to conductive heat transfer [49] and it can be written as *Pe* = *uLρiCp*,*<sup>i</sup> ki* , where *u* is the fluid velocity, *L* is the characteristic length (here it is 500 m, the distance between the two wells), the subscript *i* indicates the fluid either water or CO2, *ρ<sup>i</sup>* is the fluid density, *Cp*,*<sup>i</sup>* is the specific heat capacity of fluid and *k<sup>i</sup>* is the fluid thermal conductivity. Figure 6a shows the *Pe* value after one year for the entire reservoir for case 180, where CO<sup>2</sup> is the working fluid. To elaborate on the relative impact of convective heat transfer inside the fracture, one fracture is selected as shown in Figure 6b, and the corresponding *Pe* number is shown in Figure 6c. *Pe* number is estimated for five different times, and for all the cases, *Pe* number is significantly larger than 1, indicating more vigorous convection than conduction.

Results obtained from the 36 reservoir simulations on the well positioning are shown in Figure 7. For water simulations, reservoir permeability is 2 mD, whereas, for cases with CO<sup>2</sup> as working fluid, permeability is 5 mD. Water-based models demonstrate faster thermal breakthrough (Figure 7a) due to higher specific heat capacity than CO2. Therefore, water simulations are presented for 30 years whereas CO<sup>2</sup> results are plotted for 300 years. We magnified the results for the CO<sup>2</sup> over 30 years in Figure 7b,d,f to compare it with water (see Figure 7a,c,e). Figure 7a shows thermal drawdown at the production well when water is the working fluid. The fastest thermal drawdown was observed for case 220 (see Figure 8(c1)) whereas the slowest thermal drawdown occurred for case 130 (see Figure 8(a1)). From Figure 2, it is clear that case 220 has a well position along a dominant fracture supported by minor intersecting fractures, whereas case 130 wells are aligned approximately orthogonal to this prevalent fracture. Figure 8(a2,a3) show thermoelastic stress along the horizontal and vertical directions, respectively, indicating stress localization spans across the cold fluid plume region. Greater concentration of connected fractures in the area away from the doublet axis causes prolonged thermal breakthrough time. Therefore, in 30 years, the temperature drop is approximately 40 ◦C for case 130, whereas case 220 shows a 75 ◦C temperature drop at the production well.

In comparison to water, CO<sup>2</sup> has approximately seven times smaller thermal conductivity at the injection conditions. Due to this, thermal depletion time is prolonged when CO<sup>2</sup> is the working fluid compared to water as the heat-carrying fluid. Figure 7b shows the thermal drawdown at the production well when CO<sup>2</sup> is the operating fluid. It shows that the thermal drawdown curves depend significantly on the fracture network connectivity than water. The slowest thermal drawdown is demonstrated by case 40, where production well temperature drops by approximately 20 ◦C in 300 years. In contrast, the fastest thermal drawdown is displayed by case 180, where around 90 ◦C temperature drop is estimated. Figure 9(a1,a2) show reservoir temperature distribution for case 40 and case 180, respectively. In Figure 9(a1), the cold fluid spread is extremely slow since a high fracture density is present near point 40, as shown in Figure 2 that is present away from the doublet axis. This leads to a reduced amount of cold fluid injection and restricted heat exchange between the fluid–fractures and fluid–matrix in the reservoir, decreasing the horizontal and vertical thermoelastic stress as shown in Figure 9(a2,a3), respectively. A detailed sensitivity analysis of dependent parameters is performed for water [47] and

CO<sup>2</sup> [50] based geothermal systems for the same fractured reservoir as mentioned in this paper. Our numerical simulations consider poroelastic stress, but we have not shown here that they contribute little due to the fluid injection and production, as shown in our previous findings [47,50]. For case 180, Figure 9(b1) shows reservoir temperature distribution after 300 years. It indicates that the hot fluid has been completely extracted between the doublet, and the heat replenishment is too slow to recharge this depleting heat content. Figure 9(b2,b3) approves this reasoning that due to favorable fracture density along the doublet axis, higher fluid flux reinjection results in higher thermoelastic stress evolution. *Geosciences* **2021**, *11*, x FOR PEER REVIEW 10 of 19

**Figure 6.** For case 180 and CO<sup>2</sup> as the working fluid after one year, (**a**) Peclet number distribution across the reservoir, (**b**) fracture considered for estimating fracture length, and (**c**) Peclet number along with the fracture length. **Figure 6.** For case 180 and CO<sup>2</sup> as the working fluid after one year, (**a**) Peclet number distribution across the reservoir, (**b**) fracture considered for estimating fracture length, and (**c**) Peclet number along with the fracture length.

Results obtained from the 36 reservoir simulations on the well positioning are shown in Figure 7. For water simulations, reservoir permeability is 2 mD, whereas, for cases with

water simulations are presented for 30 years whereas CO<sup>2</sup> results are plotted for 300 years. We magnified the results for the CO<sup>2</sup> over 30 years in Figure 7b,d,f to compare it with

**Figure 7.** The temperature at the production well for (**a**) water and (**b**) CO2, mass flux at the production well for (**c**) water and (**d**) CO2, and cumulative energy extraction using (**e**) water and (**f**) CO<sup>2</sup> as heat-carrying fluid. Results from 36 simulation cases are plotted as shown by the legend, and case 180 is indicated by bold magenta color. Here Case 180 means injection well is present at 180, and production well is present at 0 (see Figure 2). **Figure 7.** The temperature at the production well for (**a**) water and (**b**) CO<sup>2</sup> , mass flux at the production well for (**c**) water and (**d**) CO<sup>2</sup> , and cumulative energy extraction using (**e**) water and (**f**) CO<sup>2</sup> as heat-carrying fluid. Results from 36 simulation cases are plotted as shown by the legend, and case 180 is indicated by bold magenta color. Here Case 180 means injection well is present at 180, and production well is present at 0 (see Figure 2).

**Figure 8.** Distribution of (**a1**–**e1**) reservoir temperature, (**a2**–**e2**) horizontal thermoelastic stress and (**a3**–**e3**) vertical thermoelastic stress when water is used as the working fluid. Here Case 130 is displayed by (**a1**–**a3**), Case 180 is displayed by (**b1**–**b3**), Case 220 is displayed by (**c1**–**c3**), Case 250 is displayed by (**d1**–**d3**), and Case 350 is displayed by (**e1**–**e3**). All contours are plotted at ten years. The injection wellbore position is shown by cross symbol whereas a circle indicates production wellbore position. **Figure 8.** Distribution of (**a1**–**e1**) reservoir temperature, (**a2**–**e2**) horizontal thermoelastic stress and (**a3**–**e3**) vertical thermoelastic stress when water is used as the working fluid. Here Case 130 is displayed by (**a1**–**a3**), Case 180 is displayed by (**b1**–**b3**), Case 220 is displayed by (**c1**–**c3**), Case 250 is displayed by (**d1**–**d3**), and Case 350 is displayed by (**e1**–**e3**). All contours are plotted at ten years. The injection wellbore position is shown by cross symbol whereas a circle indicates production wellbore position.

**Figure 9.** Distribution of (**a1**–**c1**) reservoir temperature, (**a2**–**c2**) horizontal thermoelastic stress and (**a3**–**c3**) vertical thermoelastic stress when CO<sup>2</sup> is used as the working fluid. Here Case 40 is displayed by (**a1**–**a3**), Case 180 is displayed by (**b1**–**b3**), and Case 350 is displayed by (**c1**–**c3**). All contours are plotted at 100 years. The injection wellbore position is shown by cross symbol whereas a circle indicates production wellbore position. **Figure 9.** Distribution of (**a1**–**c1**) reservoir temperature, (**a2**–**c2**) horizontal thermoelastic stress and (**a3**–**c3**) vertical thermoelastic stress when CO<sup>2</sup> is used as the working fluid. Here Case 40 is displayed by (**a1**–**a3**), Case 180 is displayed by (**b1**–**b3**), and Case 350 is displayed by (**c1**–**c3**). All contours are plotted at 100 years. The injection wellbore position is shown by cross symbol whereas a circle indicates production wellbore position.

Figure 7c,d show mass flux at the production well for 36 cases when the working fluid in the reservoir is water and CO2, respectively. The mass flux for CO<sup>2</sup> is approximately five times higher than water to compensate for smaller viscosity and higher permeability by maintaining the reservoir injection pressure. For both the fluids highest mass flux is observed for case 180, and the smallest mass flux is marked for case 350. Even though these two doublet arrangements have approximately the same axis (endpoints of a single line connecting injection and production wells), the fracture density near the production well plays a crucial role in mass flux; a similar observation was made by Zhang et al. [2]. For case 180, fractures are well connected near the production well, which assists in higher fluid production, whereas in the case of 350, fractures are not connected in a wide area leading to smaller fluid production. The temperature front in Figure 8(e1) shows the weak convective flow for case 350. This can be easily seen from the stress distribution plots in Figure 8(e2,e3) for case 350 when water is the working fluid and in Figure 9(c2,c3) for case 350 when CO<sup>2</sup> is the working fluid. The decrease in mass flux for all the cases with time is due to a in water viscosity with increased fluid temperature. However, we observe that the mass flux increases with time if CO<sup>2</sup> is the working fluid. This increase is approximately <30% between the period when CO<sup>2</sup> production starts till 300 years of numerical simulation. This increase is pronounced for the case 180 where we observe that the mass flux increases from 1.15 to 1.5 kg/s and the increase starts after approximately 50 years from the beginning of the operation. This discrepancy is observed due to Figure 7c,d show mass flux at the production well for 36 cases when the working fluid in the reservoir is water and CO2, respectively. The mass flux for CO<sup>2</sup> is approximately five times higher than water to compensate for smaller viscosity and higher permeability by maintaining the reservoir injection pressure. For both the fluids highest mass flux is observed for case 180, and the smallest mass flux is marked for case 350. Even though these two doublet arrangements have approximately the same axis (endpoints of a single line connecting injection and production wells), the fracture density near the production well plays a crucial role in mass flux; a similar observation was made by Zhang et al. [2]. For case 180, fractures are well connected near the production well, which assists in higher fluid production, whereas in the case of 350, fractures are not connected in a wide area leading to smaller fluid production. The temperature front in Figure 8(e1) shows the weak convective flow for case 350. This can be easily seen from the stress distribution plots in Figure 8(e2,e3) for case 350 when water is the working fluid and in Figure 9(c2,c3) for case 350 when CO<sup>2</sup> is the working fluid. The decrease in mass flux for all the cases with time is due to a in water viscosity with increased fluid temperature. However, we observe that the mass flux increases with time if CO<sup>2</sup> is the working fluid. This increase is approximately <30% between the period when CO<sup>2</sup> production starts till 300 years of numerical simulation. This increase is pronounced for the case 180 where we observe that the mass flux increases from 1.15 to 1.5 kg/s and the increase starts after approximately 50 years from the beginning of

the operation. This discrepancy is observed due to limitations in the equation of state used in modeling using COMSOL Multiphysics. Since viscosity is a function of temperature only, the mass flux increase is observed after the breakthrough time (see Equation (11)).

The energy extraction potential from the reservoir for both the fluids are approximately the same (see Figure 7e,f) since in the case of water simulations, reservoir permeability is 2.5 times more negligible compared to CO2, and the mass flux of CO<sup>2</sup> is approximately 3–5 times greater than water. In contrast, the specific heat capacity of water is around three times higher compared to CO<sup>2</sup> with three times higher viscosity. Due to higher mass flux and delayed thermal drawdown operation, total energy extraction potential is significantly higher when CO<sup>2</sup> is the working fluid. Case 180 for both the fluids shows the highest energy extraction potential due to the maximum mass flow rate in Figure 8(b1–b3). However, due to higher mass flux, thermal depletion is also fastest, and therefore, doublet placed for case 180 may not show a longer operation when water is the working fluid. Case 250 for water and case 350 for CO<sup>2</sup> show the least energy extraction potential over 30 and 300 years, respectively. Figure 8(d1) shows the reservoir temperature distribution for case 250 when water is used for heat transmission. It is visible from Figure 8d1 that a more incredible amount of cold fluid is present near the injection well, and there is only one large fracture along the doublet axis. This limits the fluid transmission at a higher rate only through a narrow region causing limited energy extraction.

Furthermore, Figure 8(d2,d3) shows the corresponding stress distribution for the horizontal and vertical directions. On the other hand, Figure 9(c1) shows reservoir temperature distribution for case 350 and CO<sup>2</sup> is used as working fluid and localization of cold fluid near the injection well in the absence of any dominating fracture system. The passage of fluid is limited through the fractures toward the production well. The stress field in Figure 8(c2,c3) shows the horizontal and vertical stress are well aligned with the temperature propagation. However, since thermal breakthrough is slower when CO<sup>2</sup> is used for heat transmission, energy extraction potential may enhance if EGS operation is performed beyond 300 years.

#### **4. Conclusions**

Geothermal energy extraction from deep fractured reservoirs can support high energy demand for a long duration. Water and CO<sup>2</sup> are two fluids that can extract energy from the subsurface. A fractured reservoir shows a complex network of fractures, and fracture conductivity controls the primary fluid passage for heat extraction longevity of the operation. Well placement for a given fracture network should consider the fracture density and orientation. Keeping all the parameters constant except the injection–production doublet axis orientation, we observe a difference of approximately ten times of energy extracted among the studied cases. High fracture density in the vicinity of the production well is the reason behind this increased energy extraction. The doublet axis orientation affects the injectivity (poroelastic stress) and temperature propagation (thermoelastic stress). It has a great impact on the stress field development during heat extraction.

Fluid type plays a significant role in determining the THM behavior of the EGS. The viscosity of fluid determines the temperature propagation through the fractures, as well as through the rock matrix. CO<sup>2</sup> with lower viscosity can penetrate easily inside the matrix zone. This effect, combined with the lower specific heat capacity of CO2, eventuates the cold front of fluid propagation through the matrix and fracture. While water with high viscosity and specific heat capacity mainly transmits heat alongside the fracture and results in early breakthrough time. Different cases with water have a small range of breakthrough time compared to CO2. While CO<sup>2</sup> shows a higher flow rate, resulting from the lower viscosity, this behavior is compensated by the higher heat capacity of water. Therefore, the overall heat extraction is comparable for both fluids.

**Author Contributions:** Conceptualization, S.M. and M.S.; methodology, S.M. and M.S.; software, S.M. and M.S.; validation, S.M. and M.S. writing—original draft preparation, S.M. and M.S.; writing review and editing, K.B.; visualization, S.M. and M.S.; supervision, K.B. and I.S.; project administration, K.B.; funding acquisition, K.B. All authors have read and agreed to the published version of the manuscript.

**Funding:** The work is conducted as part of the MEET project that has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No 792037.

**Data Availability Statement:** Data used in this paper are synthetic and can be reproduced from the Table 1.

**Acknowledgments:** Group of Geothermal Science and Technology, Institute of Applied Geosciences, Technische Universität Darmstadt has provided institutional support to authors. Authors would like to acknowledge anonymous reviewers for their valuable comments and suggestions.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Appendix A**

**Table A1.** List of parameters.



**Table A1.** *Cont.*

### **References**


## *Article* **Study of Corrosion Resistance Properties of Heat Exchanger Metals in Two Different Geothermal Environments**

**Svava Davíðsdóttir <sup>1</sup> , Baldur Geir Gunnarsson <sup>1</sup> , Kjartan Björgvin Kristjánsson <sup>1</sup> , Béatrice A. Ledésert <sup>2</sup> and Dagur Ingi Ólafsson 1,\***


**Abstract:** Geothermal fluids harnessed for electricity production are generally corrosive because of their interaction with the underground. To ensure the longevity and sustainability of geothermal Organic Rankine Cycle (ORC) powerplants, the choice of heat exchanger material is essential. The performance of heat exchangers is affected by corrosion and scaling due to the geothermal fluids, causing regular cleaning, part replacement, and in the worst cases, extensive repair work. The properties of geothermal fluids vary between geothermal settings and even within geothermal sites. Differences in exposure conditions require different material selection considerations, where factors such as cost, and material efficiency are important to consider. This work studies in-situ geothermal exposure testing of four metals at two geothermal locations, in different geological settings. Four corrosion-resistant materials were exposed for one month at Reykjanes powerplant in Iceland and four months at Chaunoy oil field in France as material candidates for heat exchangers. The tested alloys were analysed for corrosion with macro- and microscopic techniques using optical and electron microscopes, which give an indication of the different frequencies of repairs and replacement. Inconel 625 showed no effects at Reykjanes and cracks at Chaunoy. The others (316L, 254SMO, and titanium grade 2) showed either corrosion or erosion traces at both sites.

**Keywords:** geothermal; oil; heat exchanger; corrosion; scaling; geology

## **1. Introduction**

Material selection for geothermal equipment is a crucial parameter to consider when constructing an Organic Rankine Cycle (ORC) geothermal power plant. The heat exchanger transfers heat energy from the geothermal power source to the organic fluid within the closed loop of the ORC, boiling it. The organic fluid in its vapour form is then used to transfer the energy to the turbines of the ORC plant, generating electricity, before being condensed to repeat the continuous cycle. Geothermal environments differ between locations and the material selection for the heat exchanger needs to be tailored for each environment. The geothermal fluids can be challenging for heat exchanger materials due to high velocity, abrasive particles, reactive gasses such as H2S, and in some cases salinity [1,2].

The focus of the current study is to investigate heat exchange plate candidates, metals, and metal alloys which are more prone to local corrosion rather than uniform corrosion. Local corrosion is often associated with metals and metal alloys forming natural passivation layers, which protect the surface of the metal. The performance of the metals and alloys is often dependent on its natural initial passivation layer and its ability to re-passivate if it gets attacked during operation. Alloying elements such as Cr and Mo form protective oxides at the metal surface [3]. Furthermore, the amount of Cr and Mo within the alloy is often used for ranking the alloys with pitting resistance equivalent number (PRE) [4].

**Citation:** Davíðsdóttir, S.; Gunnarsson, B.G.; Kristjánsson, K.B.; Ledésert, B.A.; Ólafsson, D.I. Study of Corrosion Resistance Properties of Heat Exchanger Metals in Two Different Geothermal Environments. *Geosciences* **2021**, *11*, 498. https://

doi.org/10.3390/geosciences11120498

Academic Editors: Romain Augier, Thomas Hermans and Jesus Martinez-Frias

Received: 8 October 2021 Accepted: 2 December 2021 Published: 7 December 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

Oxygen is rarely present within the geothermal fluid of heat exchange systems and if it is, special precautions need to be taken [5]. Gasses such as CO<sup>2</sup> and H2S are common in geothermal environments [2,6].

The surface area and thermal conductivity of the heat exchanger plates are crucial for optimising the efficiency of the heat transfer. Scaling and corrosion often result in insulating layers forming on the surface of the plates, which reduce the heat transfer efficiency from the geothermal fluid. Scaling and corrosion are therefore important to avoid or minimize.

There are three main failure mechanisms of a heat exchanger: leakages, blocking due to deposits, and material thinning [7]. The main reasons for material thinning are erosion and corrosion. Erosion is caused by mechanical abrasion which results in mechanical removal of the surface material. Erosion depends on fluid velocity and the presence of abrasive particles in the fluid [7]. There is a correlation between material hardness and erosion resistance [8]. To minimize maintenance costs, production downtime, and part replacement in geothermal power plants, it is important to study the corrosion, erosion, and scaling issues affecting the various equipment in contact with the geothermal brine and to acquire a better understanding of how to ensure the sustainability of the plants. In the case of ORC power plants, the main equipment in contact with the geothermal brine are heat exchangers.

The majority of geothermal power plants, and especially those that run on the ORC principle, operate at low or medium temperatures, below 200 ◦C. This is reflected in the demonstration sites of the MEET H2020 project (Multidisciplinary and multi-context demonstration of Enhanced geothermal systems exploration and Exploitation Techniques and potentials) to which this study is dedicated, such as Soultz-sous-Forêts, Grásteinn, Cazaux, Chaunoy, and Krauma. Various corrosion and scaling studies have been conducted at Soultz-sous-Forêts where the geothermal fluid is quite saline, corrosive, and tends to form scales which accumulate naturally occurring radioactive materials [9–12]. Ledésert et al. [13] studied the scaling formation at Soultz-sous-Forêts when the reinjection temperature of the geothermal fluid was reduced from 70 ◦C to 40 ◦C. They concluded that the scaling formation observed was not influenced by the alloy of the heat exchanger material.

In recent years, several material experiments have been conducted at supercritical temperatures [14,15] where the conditions vary significantly from standard geothermal plants. For geothermal power plants operating at a low or medium temperature a few studies have been published [16–18] but no review paper is available. For a tailored material selection, a common evaluation method is to expose material candidates in the actual geothermal environment. It is recommended for material evaluation that the samples be tested for as long as possible although commonly it is based on the convenience of the plant operators [19]. Frequently, test durations range from a month and upwards. The exposure time is short compared to the lifetime of the material but gives an indication of the performance of the material in the actual environment. The most common method to evaluate exposed materials for geothermal applications is with weight loss measurements using standard ASTM G1-03, which estimates uniform corrosion. However, the materials evaluated in this study are more prone to local corrosion.

Metal and metal alloys forming natural passivation layers are more often affected by local corrosion than uniform corrosion. The passivation layer is locally broken, resulting in the direct electrical contact of the metal with the fluid. The fluid can either be in liquid or vapour form depending on the temperature and pressure. Geothermal fluids usually contain ions which increase their conductivity which can accelerate corrosion [2]. Furthermore, Cl ions in connection with oxygen and water have been reported to assist with the breakdown of the passivation layer of stainless steel resulting in corrosion [20]. For example, 316L stainless steel has been reported to have low performance in humid and oxygen rich environments; however, it has been successfully used in oxygen free CO<sup>2</sup> brines at temperatures as high as 150 ◦C [21].

The 316L and 304L are some of the most used and studied materials in the geothermal industry and are widely used in heat exchangers [5]. Nickel alloys have shown promising results in the S rich environment and Ti and its alloys in an oxygen rich environment [5,22]. However, due to the lower hardness of pure Ti, its alloys are often preferred for the geothermal environment [23,24]. Furthermore, from the oil and gas industry it is reported that the main failure mechanism of Ni-based alloy is from hydrogen embrittlement [25]. It has been reported by Karlsdóttir et al. [14] that the most corrosive resistant material tested for geothermal heat exchange application in superheated geothermal steam was Inconel 625 and Ti-alloy (Ti gr. 7). Furthermore, the group reported that 254SMO had a corrosion rate of 0.001 mm/year measured according to ASTM G1-03 [14], which is in line with results from the same group's measuring in simulated superheated geothermal conditions' corrosion rate of 0.001 mm/year [26]. Therefore, 254SMO has been recommended to be used by the Icelandic geothermal industry [10]. However, due to its cost it is not as commonly used in geothermal environments [27] as other cheaper materials such as 316L, for example.

The pH of the fluid is an important factor for determining the lifetime of components and 316L is, for example, not recommended to be used at a pH lower than 3.2 [28] where superaustenitic steels, such as 254SMO, can be a good option [29]. For geothermal applications, stainless steels and Ni-alloys are recommended to have a minimum of 3% Mo [30]. However, high levels of Mo could result in more risk for inducing segregation, the formation of hard and brittle phases within the material, which could initiate cracks and voids during exposure [31]. The grain size of steel can be crucial as smaller grain size can reduce interdenritic segregation as well as the chances of high temperature cracking [32]. Inclusions are common within stainless steels and have been reported to be found in 254SMO [31,32] and 316 [33]. The inclusions can be a preferential place for crack development at the subsurface of the material [33]. Inclusions can create geometric discontinuities where stress and strain can accumulate [34]. Moreover, for surfaces with a passive layer, an inclusion might act as an initiation site for pitting [35].

To identify suitable materials for heat exchangers in low-temperature volcanic and sedimentary ORC power plants, four metal samples were exposed in two different geothermal environments, namely at high salinity locations in Reykjanes, Iceland and Chaunoy, France. The effects on the coupons were then examined macro- and microscopically. The selected materials consisted of stainless steels 316L (EN 1.4404) and 254SMO (EN 1.4547), nickel alloy Inconel 625 (EN 2.4856), and titanium grade 2 (EN 3.7035). All these materials are reported to be used in the geothermal industry [29]. In general, failure during the plate heat exchange operation accrues in the weakest points of the material. Additionally, the materials studied here are more prone to local corrosion than uniform corrosion. Therefore, the main interest of this study is to investigate the most affected areas of the exposed materials and report on the observed local corrosion. The testing period was one and four months, respectively, for Reykjanes and Chaunoy, while the expected lifetime of a heat exchanger is around 20–30 years. All samples tested were affected by the exposure, including 254SMO and Inconel 625. Further investigation is needed to determine the development of the defects found after the exposure.

#### *1.1. Geological Context*

#### 1.1.1. Reykjanes

Iceland began to form in Tertiary (16 Ma) [36] and is considered to be the product of anomalously high volcanism related to the interaction of the divergent plate boundaries on the Mid-Atlantic Ridge (MAR) and the Iceland mantle plume [37]. The MAR cuts across Iceland in a roughly SW-NE trending direction and at the crest of it is where the most vigorous magmatic activity occurs. Thus, numerous active volcanic systems can be found along the ridge axis [38]. The Reykjanes Peninsula, in SW Iceland, is a continuation of the median fault zone of the MAR and continues as Reykjanes Ridge offshore SW of Iceland. The Peninsula is formed of hyaloclastite ridges and basaltic lavas [39]. The oldest lavas on the surface are from the Late Pleistocene age while the youngest are from the Holocene [40]. Furthermore, the area is intensely fractured with normal faults and extension fractures,

within a narrow belt, along with eruptive fissures lying perpendicular to those extensional rifts [39,41]. There are four distinct volcanic systems on the Reykjanes Peninsula, from west to east: Reykjanes, Krísuvík, Brennisteinsfjöll, and Hengill fissure swarms [42,43], see Figure 1.

**Figure 1.** Geological map showing the location of the Reykjanes Peninsula and the fissure swarms in the area (image courtesy of Iceland GeoSurvey (ÍSOR)).

The Reykjanes fissure swarm, which the Reykjanes geothermal field is a part of, is at least 45 km in length, where 30 km are on land [44]. The Reykjanes geothermal field is at the SW tip of the Peninsula and is one of the smallest geothermal areas in Iceland. It is about 1–1.5 km<sup>2</sup> , based on the geothermal features displayed on the surface [39]. The heat source of the Reykjanes geothermal field is thought to be dykes, thin sills, and/or a sheeted dyke complex. At a 5.5–6 km depth, a brittle-ductile transition marks the bottom of potential permeability, hence, the base of the hydrothermal system [45]. The chemical composition of the high-temperature hydrothermal fluid derives from the interaction of seawater with basaltic rocks made up mostly by hyaloclastite, volcanic breccias, and tuffaceous units to a depth of 1000 m [46]. Observations from the 2054 m deep well, RN-10, shows that at increased depths the stratigraphy consists predominantly of pillow basalts and formations exhibit relatively high porosity and low permeability with aquifers that are related to fractures along sub-vertical dyke intrusions [47]. The chemical composition of the liquid phase of the geothermal brine in well RN-29 at Reykjanes geothermal powerplant was measured by Iceland GeoSurvey (ÍSOR) in 2014 [48] and is shown in Table 1.

#### 1.1.2. Chaunoy

The Keuper Triassic sediments were deposited during an extensional phase that induced the subsidence of the Paris basin [49]. The sediments were deposited in a continental environment, ranging from alluvial (west of the basin) to evaporitic (east of the basin) [50]. The maximum subsidence occurred east of Chaunoy while, to the west, the basin overlapped gently with the armorican variscan massif [51]. The Chaunoy reservoir is part of the Chaunoy sandstone, a Carnian-Norian lithostratigraphic formation due to a second-order Scythian-Carnian cycle of tectonic origin [52,53]. It lies conformably on reddish dolomitic shales deposited in a coastal plain [51]. The Chaunoy oil field (Figure 2A), located 50 km

south-east of Paris, is the largest oil field of the Paris basin [54]. It is a broad north-south anticline structure 15 km long and 5 km wide, with a faulted eastern flank [51,55]. The average thickness of the reservoir is approximately 66 m [51,55]. It developed in the distal part of alluvial deposits. Small ribbon channel deposits are interbedded with a flood plain and lacustrine deposits. The channel amalgamation occurred during periods of low accommodation, producing highly heterogeneous sand sheets [51]. During higher accommodation periods, channels became progressively isolated within flood plain mudstones. Finally, lacustrine mudstones were deposited, creating a vertical permeability barrier. Then, the decrease in accommodation induced a strong pedogenetic alteration responsible for dolocrete and groundwater dolomite. The amalgamation rate varied with cyclic lake-level variations, which directly controlled the reservoir geometry [51]. Due to this history, the reservoir is strongly heterogeneous. An upper siliciclastic/dolomitic member can be divided into two units with porous conglomeratic channels interfingered with cemented lagoonal dolomites. A lower siliciclastic member shows four heterogeneous sand sheets (7 m thick), which have been correlated across the field. Each of them is made up of stacked single channel sequences. The sand sheets are separated by extensive lacustrine and flood plain mudstone layers acting as permeability barriers. Bourquin et al. [56] presented a high-resolution sequence stratigraphy of the Chaunoy reservoir. The maximum net oil pay is 25 m with a 11 m average [51], in which the thickness of each reservoir unit ranges from 1 m to 5 m. In this field, the well spacing, 600 m in average, is larger than the channel width [51,54] which does not allow for a complete understanding either of the structure or of fluid flows as well-to-well correlations are hypothetical. The Liassic shales located directly above the Triassic reservoir constitute the oil source rock [51].


**Table 1.** Chemical composition of the liquid phase of well RN-29 at Reykjanes geothermal powerplant.

The timing of the in-situ material exposure performed at Chaunoy oil field coincided with an ORC powerplant demonstration performed within the framework of the MEET project. Exhaust water coming out of the CNY40 oil well (Figure 2B) was connected to the inlet of an ORC powerplant. The samples tested in this work at Chaunoy were placed within the exhaust water flowline (Figure 2C) connected to the inlet of the small-scale ORC unit (Figure 2D). The cooled water coming out of the ORC was reinjected with the whole exhaust flow. The oil field showed a high water cut with approximately 96 L of water for every 1 L of oil produced (Vermilion, personal communication).

**Figure 2.** The small-scale mobile Organic Rankine Cycle (ORC) unit installed at Chaunoy oil field. (**A**): one of the oil wellheads, (**B**): head of the CNY40 well from which the oil and hot water are extracted, (**C**): the connection of the hot water pipe to the ORC unit, (**D**): the mobile ORC unit connected to the water pipe. The samples tested at Chaunoy in this work were placed within the inlet of the ORC unit during a 4-month demonstration.

#### **2. Materials and Methods**

The corrosion experiments were based on the Standard Guide for Conducting Corrosion Tests in Field Applications, ASTM-G4-1 [4]. The corrosion experiments were conducted by exposing the four potential heat exchanger materials in the form of metal coupons at the two locations: Reykjanes and Chaunoy. The coupons were placed on a sample holder, with ceramic isolation rings to avoid the electrical contact between the holder and the coupon samples. The sample holder was placed in a pressure vessel for Reykjanes and in a flow-line pipe for Chaunoy. The 254SMO was bought from Outokumpu, Inconel 625 was bought from ThyssenKrupp, 316L was bought from Outokumpu and Stálnaust, and Ti gr. 2 was acquired from The Welding Institute (TWI). The dimensions of the coupons were in all cases 50 × 25 × 3 mm except for Ti gr. 2 which was 4 mm in thickness. The elemental compositions of the materials tested are shown in Table 2.

#### *2.1. Reykjanes*

The coupon samples were exposed inside a pressure vessel at Reykjanes, seen in Figure 3, for 30 days. The temperature and pressure were 200 ◦C and 18 bar, respectively. The fluid in the pressure vessel was saturated with geothermal steam which had already passed through a separator. The gas concentrations of the steam present in the pressure vessel, which is the same steam as is fed to the turbines of the Reykjanes power plant, can be seen in Table 3.


**Table 2.** Elemental composition of the materials tested in this work.

**Figure 3.** The coupons being removed from the pressure vessel at Reykjanes power plant where they were exposed.



#### *2.2. Chaunoy*

The Chaunoy oil field is in the Paris basin, in northern France, where the salinity is around 6.5 wt.%. The fluid from the tested oil well is mostly hot geothermal water, with a

small amount of oil. The test was conducted by placing the coupons on a sample holder rack, which was placed inside a flowline at the inlet of an ORC power production unit. The sample rack before and after testing can be seen in Figure 4.

**Figure 4.** (**A**): The samples on a rack which was inserted into an oil flowline at Chaunoy. (**B**): The rack and samples after testing had been conducted. It is interesting to note that two carbon steel coupons, which are not investigated in this work, had corroded severely, and fallen off of the threaded rod during exposure as marked with red arrows.

> The Chaunoy exposure was conducted in well CNY40 for four months. The temperature at the wellhead was measured at 94 ◦C, the oil ratio of the fluid was 1.85%, and the flow rate was 6.25 l/s. The pressure was on average 9.5 bar. A chemical analysis of the fluid can be seen in Table 4.


**Table 4.** Chemical analysis of the fluid in well CNY40.

#### *2.3. Material Assessment*

The samples were analysed both topographically and cross-sectionally using an optical microscope, AXIO from Zeiss, and a Scanning Electron Microscope (SEM), Supra 25. A chemical analysis was conducted using an Energy-Dispersive X-ray spectroscopy (EDX) detector, Oxford Instrument X-max. For simplicity, the analysis was only given for elements over 0.5 wt.%.

The samples were dismounted from the racks and photocopied with Canon MG5450 before assessment. The Backscatter Electron (BSE) detector of the SEM was used for the topography imaging and a secondary detector was used for cross-section imaging. The cross-sections were prepared by cutting the samples with a diamond cutter and baking in conductive phenolic epoxy for 3.5 min at 150 ◦C. The samples were polished in steps until reaching 1 µm roughness. The macro and micro-structure images were taken at the most affected areas with a good distance from the edges to avoid artifacts from surface preparation. For the EDX analysis, the cross-section might contain C and O contamination from sample preparation and handling as well as from the vacuum chamber of the SEM.

#### **3. Results and Discussion**

#### *3.1. Material Evaluation*

Visual appearance is the first indicator of material performance after exposure and the photocopied samples can be seen in Figure 5. Where the coupons were fastened to the rack, marked with a red circle, there was an area which was masked, sometimes partially, from the geothermal environment. Utilising masked areas as a reference in corrosion exposure has been reported [58]. The difference in surface appearance between the exposed areas compared to the masked areas was evident for 316L, 254SMO, and Ti gr. 2 tested at Reykjanes. It is important to note, due to the testing set-up, that only the area, marked with a blue box, of Ti gr. 2 was exposed. Inconel 625 did not show visible discoloration after being exposed at Reykjanes. The discoloration formed at the surface of the 316L, 254SMO, and Ti samples tested at Reykjanes was well adhering. The samples exposed at Chaunoy had an indication of fluid deposits where layers had loosely formed on the surfaces of the samples with low adherence.

**Figure 5.** Coupons after exposure, the sample size is 25 mm in the vertical direction. The red circles indicate the covered areas, unexposed, due to ceramic shielding of the fastener. The blue square on the Ti gr. 2 sample exposed in Reykjanes marks the main affected area of the sample. The samples exposed in Reykjanes showed discoloration on all samples except the Inconel 625. The samples exposed in Chaunoy showed an indication of deposits from the fluid for all samples.

The macroscopic topography evaluation of the tested samples gave an indication of the general surface texture of the samples which can be seen in Figure 6, where high roughness is evident for 254SMO and Inconel 625. There was a surface texture difference within 316L exposed at different locations which might partly be due to a different provider.

**Figure 6.** Optical topography images where the above line has the samples tested in Reykjanes and below are the samples tested in Chaunoy.

Topography images taken with the BSE detector are shown in Figure 7, where the 316L had microscopic defects at the surface both when tested in Reykjanes and Chaunoy. Inconel 625 and 254SMO had high surface roughness. Furthermore, there was a pit present at the surface of 254SMO exposed at Reykjanes. The topography microstructure indicated erosion in the Ti gr. 2 both tested at Reykjanes and Chaunoy where valleys are present. Furthermore, there were Fe-S rich deposits at the surface. Similar deposits have been reported for Ti in supercritical geothermal environments [59]. The microstructure analyses of the surfaces demonstrated point defects on 316L, micro-roughness on Inconel 625, defect on 254SMO, and Ti gr. 2 showed an indication of erosion.

**Figure 7.** Topography images taken with Backscatter Electron (BSE) detector of the surfaces of the exposed coupons.

Similar to the topography images, seen in Figure 7, the microscopic cross-sectional images, seen in Figure 8, contained micro roughness for 254SMO and Inconel 625. The 316L tested at Chaunoy had a smooth surface with a defect of around 5 µm into the subsurface containing corrosion deposits. The Reykjanes-exposed 316L sample had unhomogenized corrosion layers covering the surface. The 254SMO had subsurface cracks after exposure in Reykjanes and Chaunoy while Inconel 625 had subsurface cracks only for samples tested in Chaunoy. Both 254SMO and Inconel 625 contained high amounts of Ni and Mo. Furthermore, there was the presence of inclusions within both materials contributing to weak areas.

**Figure 8.** Scanning Electron Microscope (SEM) cross-section images taken of the most affected areas detected after exposure in both locations. The arrows indicate areas of interest: corrosion layer for 316L (Reykjanes), subsurface cracks for Inconel 625 (Chaunoy) and 254SMO (Chaunoy and Reykjanes), and abrasion of Ti gr. 2 surfaces (Chaunoy and Reykjanes).

## *3.2. Material Characterisation*

The results from the microstructural analysis are detailed in the section below. The chemical composition of the bulk material for reference is included in the material characterisation.

#### 3.2.1. Austenitic Stainless Steel—316L

The 316L is one of the most commonly used materials in the geothermal environment [29]. Figure 9 shows the cross-section of 316L where two corrosion layers are present along the profile. The estimated pH level of the environment was 5 at Reykjanes, which is an unstable state for Cr. The inner corrosion layer marked 1, 2, and 5 in Figure 9 consisted of high Cr/Fe and Mo/Fe ratios of 0.51–0.76 and 0.05–0.07 respectively. The measured reference ratio of Cr/Fe and Mo/Fe for bulk material was 0.26 and 0.03, respectively. The outer corrosion layer marked 3, and 4 consisted mostly of Fe and O products. The elemental analysis of the locations in the figure is detailed in Table 5. This finding is in line with 316L tested in an H2S environment where the inner layer is Cr and Mo rich and the outer layer has Fe segregation measured at pH 4 [60].

Unlike after exposure in Reykjanes, the 316L after exposure in Chaunoy, which had a pH level of 7, did not show the same corrosion layer formation. However, there were local defects scattered over the surface as seen in the topography image in Figure 10A. Furthermore, defects were seen in the cross-section images, Figure 10B. The elemental analysis of locations shown in Figure 10A is detailed in Table 6. There were traces of S and Si from the exposure found within corrosion deposits at the defects. The deposits

mainly consisted of Fe, O, and Cr. Traces of Al were found, which can be a typical inclusion material in stainless steels [61].

**Figure 9.** Elemental analysis and mapping of 316L after being exposed in the pressure vessel at Reykjanes at 200 ◦C, showing locations where Energy-Dispersive X-ray spectroscopy (EDX) elemental analysis was performed. There are two semi-homogenous layers over all the cross-sections analysed. The layer in locations 1, 2 and 5 is an inner corrosion layer while the top layer, locations 3 and 4, is an outer corrosion layer mostly composed of Fe and O. The colour map shows the relative composition of Cr, S, Fe, O and C in the material.



**Figure 10.** EDX elemental analysis of 316L after exposure in Chaunoy. (**A**): Cross-sectional elemental mapping of a surface defect, where locations marked for EDX elemental analysis are shown. Location 3 is inside the small surface defect, while locations 1, 2 and 4 are corrosion deposits around the defect. The colour map shows the relative elemental composition of Ni, Cr, Fe, O and C in the image. (**B**): Topography image of the surface defect by SEM.


**Table 6.** EDX elemental analysis of locations shown in Figure 10A.

#### 3.2.2. Nickel Alloy—Inconel 625

Inconel 625 is a Ni-alloy used within the geothermal sector and is recommended for sulphur rich environments [62]. Figure 11 shows locations of the chemical and microstructural analysis of Inconel 625 after exposure in Reykjanes. Table 7 details the chemical analysis of the locations analysed in the figure. A horizontal crack was detected within the material after exposure. The crack contained O and a high ratio of Cr/Ni was measured at 1.4–1.8 while the base material had a ratio of 0.3. Furthermore, the Mo/Ni ratio was slightly higher in the crack. The results indicate that when the crack is formed, Cr and Mo will diffuse into the crack and together with oxygen seal it. A trace of S was also found within the crack. The surface seemed to be unaffected by the exposure which is reflected in Figure 5 where the exposed sample contains a similar appearance to the masked area.

**Figure 11.** Elemental mapping and EDX analysis of Inconel 625 exposed in Reykjanes, which showed crack propagation that might have initiated from inclusions as a high amount of Nb is present in location 1. Nb carbides are commonly found inclusions within Inconel 625 [63]. The measured area within the crack shows traces of S in locations 1 and 2. The colour map shows the relative composition of Mo, Cr, Ni, S and C in the material.

> The Inconel 625 exposed in Chaunoy contained subsurface cracks parallel to the surface which crossed the inclusions as seen in Figure 12. Due to geometric discontinuity, the inclusions often act as weak points in materials [34] and can be prone to cracking and crack propagation.


**Table 7.** EDX elemental analysis of locations shown in Figure 11. For comparison, an analysis of the bulk material after exposure at Reykjanes is included.

**Figure 12.** SEM cross-sectional image of the Inconel 625 after exposure in Chaunoy where inclusions are seen within crack propagation, marked with arrows.

Microstructural analysis of another crack propagation within the Chaunoy-exposed Inconel 625 can be seen in Figure 13. The Cr/Ni and Mo/Ni ratios were 0.26–0.3 and 0.1–0.12, respectively, in bulk material and within cracks where the inclusions were present as seen in Table 8. Similar ratio was found within the bulk material of the Reykjanesexposed samples. The pH level of the environment was 7 which indicates a passive state of Cr and Mo, resulting in poor mobility for the elements to diffuse into the crack and seal it.

**Figure 13.** Microstructural analysis of Chaunoy-exposed Inconel 625 taken with SEM, where inclusions are seen within crack propagation in location 1. The colour map shows the relative composition of Mo, Fe, Cr, Ni and C in the material.


**Table 8.** EDX elemental analysis of locations shown in Figure 13. For comparison, an analysis of the bulk material after exposure at Chaunoy is included.

The crack propagation from the weak inclusion areas could be due to the brittleness of the alloy when exposed to rapid temperature changes. From Figure 5, and the microscopic analysis, there is little to no evidence of corrosion taking place at the surface.

#### 3.2.3. Super Austenitic Stainless Steel 254SMO

The 254SMO is a super austenitic stainless steel, which contains high amounts of alloying elements Cr, Ni, and Mo. Furthermore, 254SMO has shown good performance in acidic [33] and sea water environments [21]. The cross-section of 254SMO and topography after exposure in Reykjanes can be seen in Figure 14. The topography image shows the typical surface texture found over the surface of the sample after being exposed at Reykjanes. Furthermore, contamination was present at the surface. The cross-section shows voids at the subsurface in close proximity to grooves at the external surface. These voids contained O and S as can be seen from Table 9.

**Figure 14.** The 254SMO after exposure in Reykjanes taken with BSE detector (**A**): Cross-sectional SEM of the surface of the sample showing locations elementally analysed. (**B**): Topography SEM image of the 254SMO after exposure at Reykjanes.

A pit was found on the surface of the material after testing in Reykjanes as seen in Figure 15A. Due to the naturally formed passivation layer on the 254SMO surface, pits grow under the surface layer [64]. The cross-section, in Figure 15B, shows a crack propagation at the subsurface which led to the breaking of the material causing direct exposure of the metal which could result in pit formation as seen in Figure 15A.


**Table 9.** EDX elemental analysis of locations shown in Figure 14. For comparison, an analysis of the bulk material after exposure at Reykjanes is included.

**Figure 15.** 254SMO microstructural analysis using secondary detector (SEM) from Reykjanes exposed sample (**A**): Pit found at the surfaces of the 254SMO. (**B**): Cross-section where a sub-crack is present. The area marked in blue is further analysed in Figure 16.

**Figure 16.** Elemental mapping of within the subsurface crack propagation of 254SMO after Reykjanes exposure, showing the locations of EDX elemental analysis inside the crack. The colour map details the relative elemental composition of S, Ni, Cr, Fe and C in the material.

Higher magnification of the crack in the area marked with blue in Figure 15B, is shown in Figure 16 and an elemental analysis of locations in the crack is presented in Table 10. Within the crack was a high ratio of Cr/Fe, or 0.6–0.8, compared with the bulk material and voids at the subsurface with around 0.4 Cr/Fe ratio. Like Inconel 625, the Cr could have diffused from the bulk material forming the thin layer where the pH level was 5. There was a high wt.% ratio of O/Fe within the crack of 0.4–0.6. The Cr rich layer in the crack

seemed to be brittle, and part of the material was breaking off at places. The 254SMO might contain weak areas due to inclusion and increased brittle areas due to high wt.% of Mo [31]. The practical environment could promote crack propagation from weak areas resulting in material thinning.


**Table 10.** EDX elemental analysis of locations shown in Figure 16. For comparison, an analysis of the bulk material after exposure at Reykjanes is included.

The sample exposed in Chaunoy, seen in Figure 17, had a crack forming parallel to the surface of 254SMO. Between the detachment layer and the 254SMO there were both inclusion elements such as Al and Si as well as elements from the fluid such as Cl, Ca, Na, and S as seen in Table 11.

**Figure 17.** Element mapping and analysis of 254SMO after being exposed in Chaunoy. Within the crack there is visible inclusion of Al and Si, number 5. Furthermore, there is corrosion deposit in locations number 1, 2, and 3, containing S and elements from the base material, Cr, Fe, and Ni. The colour map shows the relative chemical composition of Cr, Ca, Fe, Si and C in the material.

#### 3.2.4. Titanium Grade 2

Ti gr. 2 is commercially pure, and is often preferred where high specific strength is needed [65]. The Ti gr. 2 naturally forms a TiO<sup>2</sup> passivation layer of a few nm which protects the bulk material. However, due to the low thickness of the TiO<sup>2</sup> passivation layer it can easily erode during exposure from the high velocity fluid which can contain abrasive particles. Figure 18 shows the sample after exposure where the affected area is evident. There were parallel subsurface cracks where the metal was adhering in a few contact points. The EDX revealed Cu deposits, which can be found at Reykjanes [66]. The cross-section clearly supports the observation of the topography, from Figure 7, where erosion has taken place at the surface as can be seen in Figure 18. The EDX analysis performed in between the loosely adhering Ti contained high wt.% of O and C, presented in Table 12. Due to the position of the point evaluation, it cannot be excluded that phenolic epoxy, the sample mounting material, contributed to the signal from C and O. The Ti gr. 2 has been reported to be successfully used in an oxygen rich environment [67–69]. However, in geothermal environments, where free O is limited, a Ti alloy might be better suitable.

**Table 11.** EDX elemental analysis of locations shown in Figure 17. For comparison, an analysis of the bulk material after exposure at Chaunoy is included.


**Figure 18.** Ti gr. 2 after exposure in Reykjanes where around 10 µm of material is loosely attached to the base material. Four locations analysed with EDX are shown. Locations 1,3 and 4 show high amounts of Cu deposits while location 2 is nearly pure Ti. The profile shows an indication of erosion. The colour map shows the relative composition of Cu, Ti, Si, O and C in the material.

> The Ti gr. 2 tested in Chaunoy, seen in Figure 6, showed an indication of erosion at the surface which is further supported with topography images. Figure 19 shows the affected area where Ti was eroding and a 10 µm metal part was loosely adhering to the surface along with S-Fe rich corrosion products. Table 13 details the elemental analysis of locations shown in the figure.


**Table 12.** EDX elemental analysis of locations shown in Figure 18. For comparison, an analysis of the bulk material after exposure at Reykjanes is included.

**Figure 19.** Ti gr. 2 after exposure at Chaunoy where there is visible detachment of Ti subsurface. The detached material is seen in location number 1. Furthermore, locations 2 and 4 contain Ti with high amounts of Fe and S. The colour map shows the relative composition of Fe, Ti, Ca, S and C in the material.

**Table 13.** EDX elemental analysis of locations shown in Figure 19. For comparison, an analysis of the bulk material after exposure at Chaunoy is included.


## **4. Conclusions**

The most accurate method for evaluating the material performance for a geothermal application is with direct exposure of the material in the geothermal environment. Such

experiments give an important indication of the viability of engineering materials in the particular geothermal setting in order to ensure the sustainability of geothermal projects. The material exposure is dependent on fluid parameters such as the ratio between steam and liquid form, corrosive ions and gases, temperature, and pressure. Furthermore, the abrasiveness of particles found within the fluid coming from the underground or high fluid velocity can also affect the material.

While the two geothermal locations differ widely in geological setting, they have some similarities when it comes to geochemistry. Both geothermal fluids, at the wellhead, have high salinity and calcium content. However, the fluid in Reykjanes is quite a bit more acidic when compared to the Chaunoy fluid, and while Reykjanes holds a high amount of SiO2, the fluid at Chaunoy is a mixture of geothermal brine and oil. The experiment at Reykjanes, a volcanic geothermal area, exposed the samples to a separated vapour state 200 ◦C and 18 bar geothermal fluid, resulting in a visually homogeneous appearance after exposure. The Chaunoy experiment, performed in a sedimentary basin, on the other hand, exposed the materials to a 94 ◦C and 9.5 bar liquid state geothermal fluid.

The duration of the exposure was 1 and 4 months for Reykjanes and Chaunoy, respectively. The Reykjanes geothermal exposure conditions are substantially more severe, resulting in similar or more affected samples compared to Chaunoy.

The microstructure analysis of 316L at Reykjanes showed the formation of two inhomogeneous layers where the inner layer is Cr and Mo rich, and the outer layer contains Fe segregation. The 316L tested in Chaunoy showed local corrosion of around 4 µm in diameter and 2.5 µm in depth. The 254SMO tested in both locations showed subsurface elongated cracks of approximately 100 µm and longer.

The cracks in the 254SMO tested at Reykjanes showed a Cr rich layer forming within them as well as areas where material is breaking off. Corrosion was not observed on the surface of the Inconel 625 after Reykjanes testing. After both exposures, the material showed subsurface cracking. The Ti gr. 2 samples tested both in Reykjanes and Chaunoy showed an indication of erosion. The results are both supported by topography and cross-section images.

Even though all tested materials showed defects after exposures at both locations, no defect was observed to reach deeper than 50 µm into the coupon samples. Further testing is required to accurately predict the long-term sustainability of the tested materials for usage in heat exchanger plates at the tested locations and to investigate how the different defects evolve over time.

**Author Contributions:** Conceptualisation, S.D., B.G.G., K.B.K., B.A.L. and D.I.Ó.; Formal analysis, S.D.; Investigation, S.D.; Methodology, S.D. and D.I.Ó.; Project administration, D.I.Ó.; Supervision, D.I.Ó.; Writing—original draft, S.D.; Writing—geological context, K.B.K., B.G.G., D.I.Ó. and B.A.L.; Writing—review and editing, S.D., B.G.G., K.B.K., B.A.L. and D.I.Ó. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the European Union's Horizon 2020 research and innovation program and was part of the H2020 project MEET: Multidisciplinary and Multi-context Demonstration of EGS Exploration and Exploitation Techniques and Potentials. Call H2020-LCE-2017-RES-IA, grant number 792037.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** We would like to thank Geir Þórólfsson in assisting with testing at Reykjanes as well as André-Charles Mintsa do Ango at Enogia and Eric Leoutre at Vermilion in assisting with testing at Chaunoy. We would also like to thank Helen Ósk Haraldsdóttir and Kolbrún Ragna Ragnarsdóttir for their contribution to the MEET project.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

<sup>1.</sup> Sundén, B.; Manglik, R.M. *Plate Heat Exchangers: Design, Applications and Performance*, 11th ed.; Wit Press: Southampton, UK, 2007.


## *Article* **Analysis of Enhanced Geothermal System Development Scenarios for District Heating and Cooling of the Göttingen University Campus**

**Dmitry Romanov 1,2,3,\* and Bernd Leiss 1,2**


**Abstract:** The huge energy potential of Enhanced Geothermal Systems (EGS) makes them perspective sources of non-intermittent renewable energy for the future. This paper focuses on potential scenarios of EGS development in a locally and in regard to geothermal exploration, poorly known geological setting—the Variscan fold-and-thrust belt —for district heating and cooling of the Göttingen University campus. On average, the considered single EGS doublet might cover about 20% of the heat demand and 6% of the cooling demand of the campus. The levelized cost of heat (LCOH), net present value (NPV) and CO<sup>2</sup> abatement cost were evaluated with the help of a spreadsheet-based model. As a result, the majority of scenarios of the reference case are currently not profitable. Based on the analysis, EGS heat output should be at least 11 MWth (with the brine flow rate being 40 l/s and wellhead temperature being 140 ◦C) for a potentially profitable project. These parameters can be a target for subsurface investigation, reservoir modeling and hydraulic stimulation at a later stage. However, sensitivity analysis presented some conditions that yield better results. Among the most influential parameters on the outcome are subsidies for research wells, proximity to the campus, temperature drawdown and drilling costs. If realized, the EGS project in Göttingen might save up to 18,100 t CO<sup>2</sup> (34%) annually.

**Keywords:** deep geothermal energy; EGS; Variscan fold-and-thrust belt; district heating and cooling; economic indicators; CO<sup>2</sup> abatement cost; sensitivity analysis

#### **1. Introduction**

According to the report by the German Federal Ministry for Economic Affairs and Energy (BMWi) [1], the share of geothermal energy in renewable-based electricity generation in Germany in 2019 was just 0.1%. The analogous value for heat generation is 8.9%. While 8.2% are related to shallow geothermal energy, which is usually used for local, decentralized low temperature applications in urban areas [2], deep geothermal energy accounts for only 0.7%. At the same time, deep geothermal energy is potentially an enormous source of renewable energy of a non-intermittent nature that has low land and water requirements and significant CO<sup>2</sup> sequestration potential [3,4]. Other positive and negative sustainability issues of geothermal energy are reviewed in Ref. [5].

An Enhanced (or engineered) Geothermal System (EGS), which is also referred to as Hot Dry Rock (HDR) in some works, is a technology implying artificial enhancements of rock permeabilities, e.g., by the creation of new fractures in rocks or by opening and/or widening preexisting ones to extract geothermal energy from depths of 3–5 km where sufficient natural permeability is low or absent [6]. In paper [7], the authors developed a subsurface model for evaluating maximum electric output from an EGS in dependence on

**Citation:** Romanov, D.; Leiss, B. Analysis of Enhanced Geothermal System Development Scenarios for District Heating and Cooling of the Göttingen University Campus. *Geosciences* **2021**, *11*, 349. https:// doi.org/10.3390/geosciences11080349

Academic Editors: Béatrice A. Ledésert, Ronan L. Hébert, Ghislain Trullenque, Albert Genter, Eléonore Dalmais, Jean Hérisson and Jesús Martínez-Frías

Received: 7 June 2021 Accepted: 16 August 2021 Published: 19 August 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

brine flow rate and the distance between the wells. The authors estimated that 13,450 EGS plants can be built in crystalline areas in Germany providing 474 GWel (4155 TWhel). At the same time, the technical potential of EGS in Europe was assessed at 6560 GWel [8], which is a significant amount of renewable energy. However, the risks and uncertainties of developing EGS are still high. This is why various research groups currently focus on the development and exploitation of EGS and overcoming related geological, technical, economic, ecological and social issues and risks [9–14].

As of now, the technology is not mature enough, and there are just a few successful R&D or commercial EGS projects, e.g., [15,16]. Most of them have been realized in igneous and sedimentary rocks and have reservoir temperatures less than 165 ◦C and flow rates less than 40 l/s [17]. However, there are some exceptions, e.g., the geothermal heat plant in Rittershoffen producing more than 70 l/s of brine with temperature of 170 ◦C [18].

Many research works related to EGS focus on electricity generation or combined generation of heat and power via Organic Rankine Cycle (ORC) or Kalina cycle [19–21]. In [22], multiple-criteria decision making (MCDM) for EGS and a decision-making tool were presented, and the authors used the tool to calculate the levelized cost of electricity (LCOE) and perform a sensitivity analysis. Levelized costs of electricity generated from EGS were acquired and analyzed in other works as well [23–26]. The values of LCOE for solargeothermal plants in Northern Chile were estimated in Ref. [27]. In the work [28], Monte Carlo simulations were used to assess the LCOE of a double-flash geothermal plant, and the values were compared with gas prices. The investments in the plant are more attractive if natural gas prices are higher. Two software packages, EURONAT and GEOPHIRES, were used in Ref. [29] for economic studies, and the authors concluded that EGS facilities are not likely to be competitive with either renewable on non-renewable energy sources by 2030. Nevertheless, the latest studies and reports by different organizations [30–33] have shown that the LCOE of renewables, including geothermal energy, is already competitive or even lower than the LCOE of fossil fuel-based alternatives. The findings of work [34] show that 4600 GWel of EGS with an LCOE less than 50 €/MWhel can be installed worldwide by 2050.

While renewable energy sources met 42.1% of Germany's gross electricity consumption in 2019, the share of renewables in the final energy consumption in the heating/cooling sector was just 14.7%. In addition, final energy consumption was 576 TWhel and 1218 TWhth, respectively [1]. It can be observed that Germany's energy transition (Energiewende) focuses much more on the electricity sector than on the heating and cooling one. Additionally, electricity (e.g., from distant wind farms) can be transmitted on long distances easier than heat. This is why this work considers EGS as a locally available energy source to cover the base load for heat and cold supply rather than for electricity supply. The latter can be met by various other renewable energy sources like solar, wind energy or biomass.

In work [35], the authors also used the tool GEOPHIRES to estimate LCOE and levelized cost of heat (LCOH) for different technology readiness levels of EGS. The estimated value of LCOH for today's technology is about 42 €/MWhth. In the study [36], LCOH for a doublet in the West Netherlands Basin with a production rate of 200 m3/h was estimated at around 30 €/MWhth. The cost of geothermal heat for oil sands extraction in Northern Alberta (Canada) was estimated at up to 38 €/MWhth [37]. An economic analysis made for a university in the USA showed that a low-potential geothermal reservoir at a 3-km depth assisted by a heat pump can supply the university's district heating system, the LCOH being about 20 €/MWhth [38]. The perspective development of CO<sup>2</sup> storage technologies is CO2-EGS, which utilizes CO<sup>2</sup> as the circulating heat exchange fluid or the working fluid. For potential cogeneration of CO2-EGS in Central Poland, the calculations showed that LCOH varies from 25 to 45 €/MWhth [39].

The existing literature gives quite a good overview of economic indicators of electricity and heat generation from geothermal systems. Meanwhile, the majority of LCOH values found in different works show a quite promising and optimistic economic picture when considering that the current average costs of heat from oil and gas boilers in German households are 65–75 €/MWhth [40] and from natural gas CHP—74 €/MWhth [41]. This

means that energy transition from fossil fuels to geothermal energy in Germany might be quite attractive. However, this work focuses on the EGS exploration of metasedimentary sequences of the Variscan fold-and-thrust belt in the Göttingen region, which has been poorly investigated as of yet, especially with regard to geothermal exploration and exploitation. This is why one of the goals of this work is to perform an economic and ecological analysis of different potential scenarios on the preliminary stage of EGS development for district heating and cooling of the Göttingen University campus. Such analysis is necessary because of many geological uncertainties of EGS exploration in a Variscan geotectonic setting, and it is supposed to show the minimum required brine parameters of a successful EGS project, which will be a target for subsurface investigation, reservoir modeling and hydraulic stimulation at a later stage. Another goal is to show potential investors and stakeholders the range of possible outcomes of EGS development and define which factors are the most important for the outcome and need of increased attention when developing EGS systems.

### **2. Background**

The campus of the Georg August University (UGOE) and University Medical Centre (UMG) (both UGOE and UMG referred to as "the university" further on) takes up a large area in the center and in the north of the city of Göttingen. Being a demo site of the EU Horizon 2020 project MEET (Multidisciplinary and multi-context demonstration of EGS exploration and Exploitation Techniques and potentials [42,43]), the university has a good chance to commit itself to renewable energy utilization, and particularly to geothermal energy by developing an EGS concept in deformed metasedimentary rocks. In the best-case scenario, the Göttingen demo site can become a real laboratory for exploring and expanding the knowledge about EGS in Variscan fold-and-thrust belt and serving as a representative case study for other places with similar geotectonic settings in Europe.

#### *2.1. Geological Setting*

The geological setting in Göttingen and its vicinity is quite poorly investigated since there are only a few exploration wells with a maximum depth of 1500 m in the surrounding area. This indicates that the exploration of geothermal energy potential in Göttingen is currently at a very early stage. However, some progress was made in 2015 when a seismic campaign with two profiles crossing the campus area at an exploration depth of 1500 m validated that the upper several thousand meters of the subsurface of Göttingen are built up of three main units [44]:


The whole sequence is overprinted tectonically by the north−south striking Leinetal Graben structure which developed during Mesozoic to Cenozoic times. It is still not clear whether the faults continue into the Variscan rock sequences or if they are decoupled mechanically by the Zechstein successions and possibly located elsewhere. Within the Leinetal Graben structure, Quaternary alluvial and wind-carried sediments form an additional unit of minor thickness but of importance regarding the utilization of shallow geothermal systems.

Considering the very low natural permeability of the basement, either EGS or a deep closed loop system with horizontal multilateral wellbores can be applied [45,46]. In this study, only EGS is considered, which means that permeability is to be increased by hydraulic stimulation. However, for the Variscan geotectonic setting underneath Göttingen, the fluid flow rate after the stimulation is not expected to be higher than 50 l/s.

### *2.2. Current Energy System of the Campus*

The campus' main energy supplier is a combined heat and power (CHP) plant which includes a gas turbine and several steam and hot water boilers. The existing hightemperature district heating (HTDH) network (13 km of pipelines) delivers heat from the plant to the consumers of the campus. Apart from electricity and heat for district heating, the UMG also needs steam and cold. The latter is produced by both absorption cooling (base load) and vapor compression machines (peak load). In 2018, total natural gas consumption of the CHP plant and boilers for producing electricity (partly for cold), hot water (district heating) and steam (partly for cold) for the campus was about 358 GWh/a [47], and corresponding CO<sup>2</sup> emissions were about 72,000 t/a. Additional indirect emissions resulted from an external power grid and external district heating for the campus (about 22,000 and 5000 t/a, respectively).

The complete renewal of most of the UMG buildings within the next 15–20 years and the soon-expected end of the gas turbine lifetime (produced in 1997) put a question to the UGOE and the UMG on what their energy supply system should consist of in the future. The plans of the university involve the construction of not only new buildings but also a low-temperature district heating (LTDH) network. Although it is not exactly clear at the moment at which level of temperatures the planned LTDH network will operate, design supply and return temperatures in the network for this work were assumed to be 70 ◦C and 40 ◦C, respectively. This level of temperatures correlates with Refs. [48,49]. Additionally, steam absorption cooling machines are planned to be replaced with low-temperature ones supplied by hot water with the minimum temperature of 70 ◦C. Although these measures are good prerequisites for utilization of geothermal energy at different depths and for energy transition at the campus, other additional measures can be also considered [50], including an integrated energy concept, energy efficient construction of new buildings and refurbishment of old buildings of the campus. The latter aspect is one of the key elements of a successful energy transition and CO<sup>2</sup> neutrality until 2050 [51].

#### *2.3. Initial Data and Scenarios*

Since there are no geological and geophysical well data and no reliable numerical reservoir models yet, several probable scenarios for brine flow rate and wellhead temperature were considered. The values varied from 10 to 50 l/s with a step of 10 l/s and from 90 to 140 ◦C with a step of 10 ◦C, respectively. Higher flow rates and temperatures can hardly be expected in this Variscan geological setting. The density and specific heat capacity of the brine were derived from dependencies provided in Ref. [52]. Average geothermal gradient was considered to be a standard value for Europe, which is 30 ◦C/km [53]. There are no accessible or reliable data on the geothermal gradient for a better specification for the Variscan basement. Several other uncertain parameters were composed in the reference case and two cases for sensitivity analysis: unfavorable and favorable deviations, which are presented in Table 1. The values of CO<sup>2</sup> tax equal to 55–65 €/t correspond to the ones set by the German Government and coming into effect from 2026 [54]. Since CO<sup>2</sup> taxes in Sweden and Switzerland are already much higher [55], 100 €/t was also considered as additional favorable scenario in this work. Parameter "Subsidy for production well" included 50% or 80% (both favorable deviations) subsidy for drilling and stimulation of the research well (to be transformed in the production well later on).


**Table 1.** Parameters for the reference case and two cases with parameters for sensitivity analysis.

*L*—distance to the campus; *Cdrill*—cost of drilling; *OPEX*—operational expenditures; *dn*—nominal discount rate; *Sgov*—subsidy for research (production) well; *Ccarb*—CO<sup>2</sup> tax; *β*—brine salinity; *τ*—construction time; *Tdraw*—temperature drawdown; *Tinj*—injection temperature.

> The EGS system in Göttingen is supposed to represent a doublet (one production and one injection well). The research (production) well depth was assumed to be 5000 m since it is not known at what depth the most suitable conditions can be found. Only after a first research well is drilled, it will be clear at what depth an EGS could be developed with the highest efficiency. Thus, the depth of the second well (injection) is a variable, and it is defined by the considered temperature scenarios and the geothermal gradient.

> For different values of the parameter "Distance to the campus", heat losses in the pipelines and specific electricity consumption for pumping the heat carrier from the site to the campus were assumed based on Ref. [56] and are shown in Table 2.

**Table 2.** Heat losses and specific electricity consumption for different distances to the campus [56].


*L*—distance to the campus; *qhl*—heat losses in the pipelines; *espec*—specific electricity consumption for pumping.

Usually, it takes from 5 to 7 years to develop a deep geothermal project from the early stages of exploration to operating facilities [57,58]. In order to make planning of the geothermal system construction clear and coherent with the planning of the reconstruction of the campus' buildings, the Gantt chart for potential EGS development in Göttingen is proposed in Table 3. There are also the reference case, unfavorable deviation and favorable deviation in the chart. Parameter "Construction time" from Table 1 correlates with the parameter "Start of operation" from Table 3.

For investors, important milestones in the chart are marked with darker shades, which means moments when investments for the project are needed. The investments can be split up into three parts: the research well (on average 45%), the second well (on average 37%), and surface infrastructure (on average 18%). The decisive part of the whole project is the first one, when the research well drilling is financed, the research work is done and it will be clear what outcome can be achieved. In case of geologically unsuitable and unpromising conditions leading to a failure of the project, the first part of the investments is lost and the other two parts make no further sense for investors. This shows that EGS projects can be quite risky and not very attractive for investors. However, there are initiatives and projects aiming at establishing financial instruments for insurance of deep geothermal projects [59] which might be able to attract investors.

**Table 3.** Gantt chart for potential development of EGS for Göttingen demo site. Squares with green color—favorable deviation; squares with yellow color—reference case; squares with red color—unfavorable deviation; darker shades moments for investments.

#### **3. Materials and Methods**

Based on the test reference year data from the German weather service [60] and internal documents from the university, an expected heat load profile of the campus after its reconstruction, which includes the heat demand for the new (to-be-built) buildings, for the existing buildings (a part of the existing buildings is planned to be deconstructed, and only remaining buildings are meant here) and for the absorption cooling machines was compiled. The assumption was made that a potential EGS supplies the new buildings as the first priority, then the remaining existing buildings, and, in the last turn, the absorption chillers. The calculations of the total EGS heat generation were performed considering the limitation that the injection temperature is at least 5 ◦C higher than the return temperature from a consumer and not lower than noted in Table 1.

The main focus of the methodology is the calculation of LCOH, net present value (NPV), and CO<sup>2</sup> abatement cost for the campus for different scenarios described in Section 2.3. These parameters are one of the main indicators for potential investors and stakeholders to make a decision with regard to an EGS project. A spreadsheet-based (Microsoft Excel 2019) model, which is explained below, was developed for evaluating those parameters.

Capital expenditures (CAPEX) include the following components:

$$\text{CAPEX} = \mathbb{C}\_{drill} + \mathbb{C}\_{\text{stimul}} + \mathbb{C}\_{pips} + \mathbb{C}\_{land} + \mathbb{C}\_{mange} + \mathbb{C}\_{equip} \tag{1}$$

where:

*Cdrill*—cost of drilling. Dependencies of drilling costs from depth were acquired from several sources [61–65], and the average values are plotted in Figure 1 and were taken for the calculations.

*Cstimul*—cost of hydraulic stimulation; assumed to be 2 M€/well.

*Cpipes*—cost of the main pipelines from the site to the campus (distribution pipelines are already a part of the existing HTDH network and not included here, and the cost of the planned distribution LTDH network is also not included); derived from work [66].

*Cland*—cost of land; specific value was assumed to be 37.5 €/m<sup>2</sup> [64]. Land requirement is 5000 m2/MW [67]. For the scenario "0.5 km from the campus", this cost is zero since the university already owns the land.

*Cmanage*—cost of project management, cost of campaigning for public acceptance and other costs [64,68].

*Cequip*—cost of equipment (pumps, heat exchangers, piping valves, auxiliaries), which can be calculated as follows:

$$\mathcal{C}\_{equip} = \mathcal{C}\_{sub\\_pumps} + \mathcal{C}\_{pumps} + \mathcal{C}\_{HEX} + \mathcal{C}\_{valves} \tag{2}$$

*Csub*\_*pumps*—cost of submersible pumps; derived from Ref. [69] using Producer Price Index (PPI) equal to 1.6 [70] (exchange rate in November 2020: 1 USD = 0.85 EUR). The pumps are to be replaced every 5 years.

*Cpumps*—cost of circulation pumps for district heating network. The values were obtained from price lists of manufacturers.

*CHEX*—cost of surface heat exchangers; average specific cost is 0.009 M€/MWth [61].

*Cvalves*—cost of piping valves and auxiliaries; assumed to be 25% of the equipment cost.

Operational expenditures (OPEX) include the following components:

$$\text{OPEX} = \text{C}\_{el\\_pump} + \text{C}\_{labor} + \text{C}\_{mainten} + \text{C}\_{insur} \tag{3}$$

where:

*Cel*\_*pump*—annual cost of electricity for pumping. Submersible pumps' electricity consumption was assumed to be 10% of the total heat production from EGS [67,71]. For the circulation pumps in the district heating network, specific values from Table 2 were used. The electricity price for non-households in Germany in 2020 was 178 €/MWhel [72]. *Clabor*—annual cost of labor [64].

*Cmainten*—annual cost of maintenance and repair [64].

*Cinsur*—annual cost of insurance and legal assistance [64].

LCOH was calculated according to Ref. [73]:

$$\text{LCOOH} = \frac{\sum\_{j=0}^{L} \left( \text{CAPEX}\_{j} + \text{OPEX}\_{j} \right) \cdot (1 + d\_{n})^{-j}}{\sum\_{j=S}^{L} \text{Q}\_{\text{cS}j} \cdot (1 + d\_{n})^{-j}} \tag{4}$$

where *CAPEXj*—capital expenditures from year 0 to *S*; *OPEXj*—annual operational expenditures from year *S* to *L*; *S*—year of the operation start; *L*—total project lifetime; *Qegsj*—annual amount of heat delivered from the EGS to the campus (from year *S* to *L*) considering heat losses derived from Table 2; *dn*—nominal discount rate [74], which can be calculated by Equation (5):

$$d\_n = (1 + d\_r) \cdot (1 + e) - 1 \tag{5}$$

where *dr*—real discount rate; *e* = 0.015—annual average inflation rate [72].

Operational lifetime was defined by temperature drawdown: the operation ends when the wellhead temperature reaches the value of 10 ◦C higher than the injection temperature. Otherwise, operational lifetime was considered to be 30 years.

NPV was calculated according to Equation (6):

$$\text{NPV} = \sum\_{j=0}^{L} \frac{-\text{CAPE}\_j - \text{OPEX}\_j + \text{Q}\_{\text{egsj}} \cdot \text{C}\_{\text{heat}}}{(1 + d\_n)^j} \tag{6}$$

where *Cheat* = 89 €/MWhth—prognosed heat tariff (price) for the university from fossil-fuel based system taking into account the CO<sup>2</sup> tax in Germany equal to 55 €/t from the year of 2026 [54]. For the favorable deviations of CO<sup>2</sup> tax in Table 1, the heat tariff is 91 and 100 €/MWhth, respectively.

The CO<sup>2</sup> abatement cost was calculated according to Equation (7):

$$A\mathcal{C} = \frac{-\text{NPV}}{\sum\_{j=S}^{L} \text{CO} \mathbf{2}\_{j}^{sav}}\tag{7}$$

where *CO*2 *sav <sup>j</sup>* —annual CO<sup>2</sup> savings during operation from year *S* to *L* considering electricity mix and natural gas emission factors equal to 397 t CO2/GWhel and 202 t CO2/GWh, respectively [75,76]. Positive values of *AC* show how much money is required to avoid one ton of CO<sup>2</sup> emission, while negative values show that the process is economically profitable.

#### **4. Results**

#### *4.1. Heat Demand of the Campus and Potential Heat Supply from EGS*

Figure 2 illustrates the expected heat load of the campus when its reconstruction is finished. The design heat load of the to-be-built buildings and the remaining existing buildings is estimated at 32.6 and 23.2 MWth, respectively, while the heat load of absorption chillers can reach up to 10.7 MWth in summer. Thus, the influence of the to-be-built buildings on the future heat and cold supply of the campus might be quite high. The heat demand of the campus in summer is, in many scenarios, lower than potential heat production. That is why practically achievable EGS heat generation is lower than the potential one. The red dashed line in Figure 2 displays the estimated maximum geothermal output, and in this case, the load factor is 88%, while other values of the output lead to higher load factors. The average distribution of geothermal energy between the heat demand of the to-be-built buildings, remaining existing buildings, and absorption cooling machines is 91%, 7% and 2%, respectively.

**Figure 2.** Expected heat load duration curve after reconstruction of the campus (including to-be-built buildings, remaining existing buildings, and heat for absorption cooling) in comparison with the estimated maximum geothermal output. Note: absorption cooling is assumed to be constant throughout the year, except for summer peak.

In Figure 3, lifetime-average EGS heat generation (without heat losses in the network) and design EGS heat output for the reference case are presented depending on brine flow rate and wellhead temperature. The heat generation can vary from 7.6 to 86.0 GWhth/a, while the heat output—from 1.1 to 14.5 MWth. Table 4 displays how much the heat demand of different consumers of the campus can be potentially covered by an EGS. On average, the values amount to 30.8%, 5.0% and 6.1% of the heat demand of new buildings, remaining existing buildings and absorption chillers, respectively. Existing heat and cold supply sources of the campus, which are supposed to cover the remaining demand, and back-up options were not considered in this study. Additionally, CO<sup>2</sup> emissions from the fossilfuel based heating and cooling system of the campus (the specific CO<sup>2</sup> emissions are 252.7 g/kWhth) are shown in Table 4. Thus, from 3.6 to 41.1% of CO<sup>2</sup> emissions could be theoretically saved if the EGS caused no greenhouse gas emissions during operation.


**Table 4.** Lifetime-average potential heat supply from EGS as a share of heat demand of different consumers and CO<sup>2</sup> emissions of a future fossil-fuel based heating and cooling system.

**Figure 3.** Lifetime-average EGS heat generation (columns) and design EGS heat output (symbols) for the reference case.

#### *4.2. Economic and Ecological Results*

Capital expenditures for the reference case conditions along with 0.5 km, 5 km and 10 km scenarios are shown in Figure 4. Costs of drilling and stimulation of two wells represent from 56 to 86% of CAPEX, and the next costly items are the costs of pipelines and the cost of project management. It is worth noting that components "Land", "Pipes\_5 km" and "Pipes\_10 km" are applicable only for 5 km and 10 km scenarios. Since drilling-related costs form the biggest part of the CAPEX, the components of CAPEX are presented in the chart only in dependence to the wellhead temperature, which is directly related to the drilling depth, and the influence of fluid flow rate on the total CAPEX is relatively small. In the same chart, specific CAPEX for different flow rates in the reference case are shown. The smallest values correspond to the highest considered flow rate (50 l/s); they vary from 5.8 to 2.9 k€/kWth for the temperatures from 90 to 140 ◦C. At the same time, the values for 10 l/s vary from 26.1 to 12.3 k€/kWth.

In Figure 5, temperature- and flow rate-average structure of operational costs and average annualized capital costs for the reference case are compared with each other. Annualized capital costs were obtained with the help of an annuity factor [77], but such an approach was used only in this part of the work to allow for the comparison in Figure 5. It can be noted that electricity costs for pumping represent the biggest part of the OPEX.

The results of LCOH and NPV calculations for the reference case are demonstrated in Figure 6. For illustrative comparison, the prognosed heat tariff for the campus (89 €/MWhth) from a fossil-fuel based system under CO<sup>2</sup> tax equal to 55 €/t and a hypothetic heat tariff (100 €/MWhth if CO<sup>2</sup> tax is 100 €/t) are also plotted in the chart. LCOH varies from 80 to 525 €/MWhth for the highest and lowest parameters of brine, respectively. It is clear that the majority of the scenarios of the reference case have worse LCOH than the prognosed fossil fuel-based heat tariff. The exceptions are the few scenarios with brine temperatures of 120 ◦C or higher and brine flow rates equal to 50 l/s, as well as the scenario with parameters 140 ◦C and 40 l/s. Although the scenarios with high temperatures and flow rates are considered in this work, their practical accomplishment in a Variscan geological setting is doubtful, especially regarding quite high flow rates such as 40–50 l/s. A slightly more realistic flow rate is 30 l/s, for which high temperature scenarios result in an LCOH of about 111 and 104 €/MWhth, i.e., relatively close to the prognosed heat tariff and might

be even profitable under some favorable conditions. Scenarios with flow rates less than 30 l/s are far from being economically feasible.

**Figure 4.** Components of CAPEX for different wellhead temperatures and different distances to the campus under the reference case conditions (columns) and specific CAPEX for different flow rates under the reference case conditions (symbols). Note: the value of specific CAPEX for 10 l/s under 90 ◦C is 26.1 k€/kWth.

**Figure 5.** Average structure of operational costs and average annualized capital costs for the reference case.

**Figure 6.** LCOH (columns), prognosed heat tariff for the campus (dashed line), hypothetic heat tariff for the campus if CO<sup>2</sup> tax is 100 €/t (dotted line), and NPV (symbols) for the reference case. Note: the values of LCOH for 90 ◦C, 100 ◦C and 110 ◦C under 10 l/s are 525, 406 and 342 €/MWhth, respectively.

As for the NPV values, they vary from −27.1 to 6.6 M€ for the lowest and highest parameters of brine, respectively. Most of the calculated values are below zero, except for the same high temperature and high flow rate scenarios as in the LCOH part. In general, the values of NPV show similar trends to LCOH. When looking at NPV values, the scenarios with the flow rate of 30 l/s and high temperatures seem to be not so optimistic since the highest achievable NPV for such scenarios is −7.5 M€; however, these can be improved under favorable conditions.

Even though many scenarios are not economically beneficial, their ecological effect is an important factor to consider. CO<sup>2</sup> abatement cost and lifetime-average operational CO<sup>2</sup> savings for the reference case are presented in Figure 7. The CO<sup>2</sup> savings vary from 1.6 to 18.1 kt/a (3–34% of the emissions from the fossil-fuel based heat supply system of the remaining existing buildings, new buildings and absorption chillers) and the CO<sup>2</sup> abatement costs—from −12 to 655 €/t. The highest parameters of the brine yield the best results, as it was demonstrated for LCOH and NPV. The high-temperature scenarios with brine flow rates of 30 l/s present quite acceptable CO<sup>2</sup> abatement costs, which range from 21 to 31 €/t.

The average specific value of CO<sup>2</sup> emissions resulting from the operation of a potential geothermal plant in Göttingen is 42.4 g/kWhth. In work [16], life cycle assessment for currently operating direct-use geothermal plant Rittershoffen in France was performed, which indicated that specific CO<sup>2</sup> emissions are 7.0–9.2 g/kWhth. However, it should be noted that the nuclear power-dominated French electricity mix is nine times less carbon-intensive than the German one (44 g/kWhth vs. 397 g/kWhth) [75], which explains the difference.

**Figure 7.** CO<sup>2</sup> abatement cost (columns) and lifetime-average CO<sup>2</sup> operational savings (symbols) for the reference case. Note: the values of CO<sup>2</sup> abatement cost for 90, 100 and 110 ◦C under 10 l/s are 655, 445 and 355 €/t, respectively.

#### *4.3. Sensitivity Analysis*

In order to cope with the uncertainty of the parameters and to get a better understanding of potential deviations from the obtained results of the reference case, a sensitivity analysis was carried out. The temperature-averaged results of LCOH sensitivity analysis for the parameters from Table 1 (unfavorable and favorable deviations) are displayed in Figure 8.

Increasing temperature drawdown from 1%/year to 2%/year leads to the biggest increase of LCOH (24–18% for the flow rates from 10 to 50 l/s, respectively). The other significant factor leading to increase of LCOH by 16–20% is a 30% increase of the nominal discount rate. Additional parameters worth noting are a 10 ◦C increase of injection temperature, 10 km-distance from the field to the campus and a 30% increase of drilling costs contributing 13–21%, 17–18% and 13–18% to the increase of LCOH, respectively. Less important parameters are OPEX, construction time (or the year of operation start) and brine salinity.

The most important parameter leading to decrease of LCOH is the research well subsidy of 50 or 80%, which allows to achieve 13–18% or 21–29% of LCOH reduction, respectively. Decreasing the distance from 5 km to 0.5 km has also a large effect (15–18%) on LCOH decrease. The remaining considered parameters are of less importance and contribute not more than 10% to LCOH decrease each.

It can be noted that, in general, factors influencing LCOH have less effect on higher flow rate scenarios which can be explained by larger amount of produced heat by EGS, thus smoothing the fluctuations. The exceptions are "Distance" and "OPEX" parameters showing the opposite trend since they are both proportionally and strongly related to the amount of produced heat.

The temperature-averaged results of NPV sensitivity analysis for the parameters from Table 1 (unfavorable and favorable deviations) are presented in Figure 9.

**Figure 8.** LCOH sensitivity analysis for the parameters from Table 1.

**Figure 9.** NPV sensitivity analysis for the parameters from Table 1.

Parameters "Distance" and "Drilling cost" are very influential on unfavorable deviations of NPV. If the distance from the field to the campus is increased from 5 to 10 km, NPV decreases by 4.3–8.7 M€ for the scenarios with flow rates from 10 to 50 l/s. Increas-

ing drilling cost by 30% leads to NPV decrease by 6.7 M€. Temperature drawdown is also a parameter worth noting, especially for high flow rates, since it can worsen NPV value by up to 7.6 M€. Other parameters—OPEX, nominal discount rate and injection temperature—have some impact on NPV, and the remaining parameters have a relatively minor one.

As for favorable deviation of the parameters, 50 and 80% subsidy will lead to NPV increase by 6.7 and 10.8 M€, respectively. The possibility to build the geothermal plant just 0.5 km from the campus will result in 4.3–9.6 M€ increase of NPV for the scenarios with flow rates from 10 to 50 l/s. Reducing drilling cost by 15% can improve NPV by 3.4 M€. A potential increase of CO<sup>2</sup> tax up to 100 €/t can lead to 1.3–6.4 M€ increase of NPV. While the influence of temperature drawdown, nominal discount rate and OPEX becomes significant under high flow rates, the other remaining parameters have much less effect.

As seen in Figure 9, the influence of most of the parameters intensifies for higher flow rates. And for low flow rates, e.g., 10 l/s, some parameters barely lead to any change in NPV. Parameters "Construction time" and "Nominal discount rate" show shifting behavior when the flow rate increases. For small flow rates, they lead to NPV increase, while NPV decreases for large flow rates. It can be explained by the fact that longer construction time leads to a shift in the schedule for investments (Table 3) which is "beneficial" for low flow rate scenarios because of later discounting of those CAPEX. It simply means that the scenarios are not profitable anyway, but the losses are a bit reduced because the investments were made later. For high flow rates, the situation is the opposite since longer construction time delays obtaining relatively high revenues from the plant operation. Being discounted in later years, those revenues obtain less value and influence on the overall result leading to decrease of NPV with regard to the reference case. Moreover, a similar behavior is true for the nominal discount rate.

#### **5. Discussion**

Although the results were acquired for the Göttingen demo site, the considered parameters for the calculations and analysis were quite typical. This is why the results can be also applied to an early-stage development analysis of other EGS projects in poorly known geological settings for district heating and cooling. However, it should be noted that electricity prices in Germany are among the highest in Europe [72], and the district heating prices are above the average level [78]. Therefore, the results will be economically better for the countries with lower electricity prices and higher heat prices.

Interconnection and interdependence between different parameters were not considered during the sensitivity analysis. For example, large extraction of heat from the geothermal reservoir (high brine flow rate and low injection temperature) might lead to a bigger and faster temperature drawdown, and consequently, to a much smaller operation lifetime of the project, which puts forward a question of sustainable energy generation from EGS. Additionally, brine salinity and injection temperature are also correlated parameters since injection temperature might be limited by scaling and corrosion issues in the case of a high-salinity brine. Thus, some parameters from the sensitivity analysis can depend on each other and/or aggregate, leading to more complex effects on the final result.

The development of the EGS system in the Variscan basement in Göttingen is associated with many uncertainties and risks. Although the risks are not explicitly considered in this study, they are addressed in a follow-up work [79]. One of the biggest uncertainties and risks for any EGS is induced seismicity risk since it affects public acceptance of EGS projects [80] and can completely freeze any further works and lead to the cancellation of a project [81]. Cost-benefit analysis was applied to quantify the trade-off between seismicity risks and proximity to district heating and heat consumers in Ref. [82]. The authors concluded that remote EGS is less favorable even if the seismicity risk is considerably decreased or close to zero. The results of the sensitivity analysis of this work have also demonstrated that proximity of the geothermal plant to the campus significantly improves the economic indicators of the project. Nevertheless, it might be quite challenging to drill

the wells, conduct hydraulic stimulation tests and build the plant close to the campus without public acceptance. That is why public acceptance is one of the prerequisites of future successful realization of the EGS project in Göttingen.

One of the obstacles of the project is to correlate and synchronize the university's plans of the campus reconstruction and the development of the EGS plant, which was partially addressed in this study by proposing the Gantt diagram of the EGS development. Nevertheless, effective communication and cooperation between different stakeholders within the university and outside of it is also one of the key prerequisites to launch the project.

The performed analysis has demonstrated that the reference case might not currently be competitive with the existing fossil fuel alternatives. Moreover, such long-term projects are usually not very attractive for private investors. Therefore, the government's support is another necessary prerequisite for the project.

Even if the economic part of the project might happen to be not very promising after the research drilling and hydraulic stimulation tests are carried out, the importance of its ecological effect is undoubtful. Economic and political measures for CO<sup>2</sup> emission reduction are likely to become stricter in the future which will pave the way for initially commercially unfeasible projects to be supported and implemented. The hypothetic value of the heat tariff depicted in Figure 6 and the values in Figure 9 show that CO<sup>2</sup> tax can be a powerful tool of the government to impact the profitability of EGS projects. On the other hand, other renewable options, which also benefit from high CO<sup>2</sup> tax and can yield better results than EGS due to more mature technological level and undercut the heat tariff, were not considered in this work.

The next important and essential step of the project development is to get research well funding. An additional opportunity of EGS projects in sites with poorly known geological settings, which can be provided by a deep research well, is investigation of shallow and medium layers and their further exploitation, e.g., for underground seasonal thermal energy storages. Such an integrated approach helps not only to increase the overall contribution of geothermal energy, i.e., renewable energy, but also to maximize the public subsidies for a research well, since the research focus is on both deep and medium deep target zones. In Germany, this is crucial when applying for public subsidies because financial support for drilling is preferentially given to the drilling sections defined as not yet investigated target rock units.

#### **6. Conclusions**

The geological setting in Göttingen—Variscan fold-and-thrust belt—is relatively poorly investigated for Enhanced Geothermal Systems exploitation. Nevertheless, there are expectations that geothermal energy will be able to partially meet the heat and cold demands of the Göttingen University campus (a demo site of the MEET project). This is why various scenarios of potential development of EGS for the campus were considered and analyzed in order to deal with different geological, technical and economic uncertainties of the project. On average, the considered single EGS doublet might cover about 20% of the expected heat demand and 6% of the cooling demand of the campus after its reconstruction. For different wellhead temperatures (90–140 ◦C) and flow rates (10–50 l/s) of brine, the obtained values of LCOH, NPV and CO<sup>2</sup> abatement cost vary from 80 to 525 €/MWhth, from −27.1 to 6.6 M€ and from −12 to 655 €/t, respectively.

The most influential parameters on LCOH and NPV, which were identified during the sensitivity analysis, are subsidies for research wells, distance from the field to the campus, temperature drawdown and drilling costs. These parameters should be primarily dealt with when considering EGS development. CO<sup>2</sup> tax, operational expenditures, injection temperature and nominal discount rate can be also quite influential, especially under high brine flow rates. Other analyzed parameters, namely construction time and brine salinity, have significantly less effect on the economic indicators.

For the considered initial conditions in the reference case, it can be concluded that EGS heat output should be at least 11.0 MWth (corresponds to brine flow rate and wellhead temperature of 40 l/s and 140 ◦C, respectively) in order to have a more or less economically justified EGS project. If the distance between the field and the campus is 0.5 km, minimum EGS heat output can be 7.2 MWth (30 l/s and 125 ◦C). In case of 50 and 80% subsidy, the minimum heat output is 8.1 MWth (30 l/s and 135 ◦C) and 7.2 MWth, respectively. The abovementioned parameters of brine can serve as a benchmark for geologists, engineers, managers, investors and other involved stakeholders to evaluate the success rate of the project, especially with regard to subsurface investigation, reservoir modeling and hydraulic stimulation.

The support of the government, public acceptance and effective cooperation between all stakeholders are the key prerequisites for launching the EGS project in Göttingen, which might save 1600–18,100 t CO<sup>2</sup> annually (3–34% of the emissions from the fossil fuel-based heat supply system of the remaining existing buildings, new buildings and absorption chillers).

**Author Contributions:** Conceptualization, D.R. and B.L.; methodology, D.R.; investigation, D.R.; writing—original draft preparation, D.R.; writing—review and editing, D.R. and B.L.; supervision, B.L.; funding acquisition, B.L. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work has received funding from the European Union's Horizon 2020 research and innovation program (grant agreement № 792037—MEET Project).

**Acknowledgments:** The authors are grateful to Bianca Wagner for having contributed to the funding strategy for this study as well as for her discussions. Inga Moeck's helpful comments and remarks on the manuscript are appreciated. We thank Real Estate and Facilities Management (Gebäudemanagement) departments of UGOE and UMG for providing data and discussions.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


**Josipa Hrani´c 1,\*, Sara Raos <sup>1</sup> , Eric Leoutre <sup>2</sup> and Ivan Rajšl <sup>1</sup>**


**Abstract:** There are numerous oil fields that are approaching the end of their lifetime and that have great geothermal potential considering temperature and water cut. On the other hand, the oil industry is facing challenges due to increasingly stringent environmental regulations. An example of this is the case of France where oil extraction will be forbidden starting from the year 2035. Therefore, some oil companies are considering switching from the oil business to investing in geothermal projects conducted on existing oil wells. The proposed methodology and developed conversions present the evaluation of existing geothermal potentials for each oil field in terms of water temperature and flow rate. An additional important aspect is also the spatial distribution of existing oil wells related to the specific oil field. This paper proposes a two-stage clustering approach for grouping similar wells in terms of their temperature properties. Once grouped on a temperature basis, these clusters should be clustered once more with respect to their spatial arrangement in order to optimize the location of production facilities. The outputs regarding production quantities and economic and environmental aspects will provide insight into the optimal scenario for oil-to-water conversion. The scenarios differ in terms of produced energy and technology used. A case study has been developed where the comparison of overall fields and clustered fields is shown, together with the formed scenarios that can further determine the possible conversion of petroleum assets to a geothermal assets.

**Keywords:** geothermal; conversion; clustering; upscaling; heat; electricity; scenarios; LCOE; LCOH; NPV; CO<sup>2</sup> emissions

#### **1. Introduction**

Geothermal heat has been traditionally extracted at locations characterized by hydrogeological anomalies, but recent advances in engineering have enabled the development of alternative approaches such as enhanced geothermal systems (EGS) and borehole heat exchangers (BHE) [1–3]. Both technologies can enable harvesting Earth's heat without any (or little) location constraints. EGS systems are used to produce energy by enhancing in situ permeability and harvesting heat from hot rock reservoirs [4]. The connection between production and injection wells in EGS is engineered by various stimulation techniques. The viability of an EGS project is mostly influenced by brine flow rate and production temperature, where higher flow rates and temperatures support electricity generation and lower values support direct usage of hot water, i.e., heating power production. Regarding fluid flow rates, the increase in low rates could be achieved by applying reservoir stimulation, whereas temperatures can be increased only by drilling deeper wells [5]. BHEs harvest geothermal energy without direct interaction of flowing fluid with the soil or rock. Different from the EGS, the efficiency of deep BHEs strongly depends on heat exchanger configurations and the host rock thermal properties [6]. The economic viability of both technologies, especially considering high depths (>3 km), depends on emerging technologies, drilling technologies, reservoir technologies, etc.

**Citation:** Hrani´c, J.; Raos, S.; Leoutre, E.; Rajšl, I. Two-Stage Geothermal Well Clustering for Oil-to-Water Conversion on Mature Oil Fields. *Geosciences* **2021**, *11*, 470. https:// doi.org/10.3390/geosciences11110470

Academic Editors: Suzanne Golding and Jesús Martínez-Frías

Received: 26 October 2021 Accepted: 12 November 2021 Published: 16 November 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

In order to bypass exploration and drilling risks, mature and abandoned oil wells could be used. There are thousands of onshore wells in Europe, and most of them are mature oil provinces where it is expected that the existing wells are now producing much more water than oil, with an average water to oil ratio higher than 90%; thus, the cost of wastewater disposal increases. The oil reservoir's depth ranges between few hundreds to few thousand meters; therefore, fluid temperature at the surface can reach up to 90 ◦C and more, thus enabling the production of electricity, heat, or both. In most cases, hot water is reinjected into the reservoir to increase production through pressure support and sweep; hence, the calorific energy of water is wasted. This is the coupling point between oil industry and geothermal energy production. Namely, the possibility of using these high temperature fluids to produce geothermal energy during the final stage of the life of an oil field and converting the field into a geothermal one is an emerging and interesting option for energy strategy. Numerous studies have been conducted on mature oil fields where geothermal potential has been proven with simulations or with actual exploitation [7–16]. In reference [17], the authors revised mature oil and gas fields across the world where waste heat from geothermal water has already been recovered or its potential has been determined. In order to ensure profitable waste heat recovery, a list of criterions formed on reservoir, geological, production, and economic characteristics was suggested. The criteria were used as a guideline in the assessment of geothermal energy utilization and were tested on the Villafortuna-Trecate field in Italy. The results showed that roughly 25 GWh of electricity could be produced with installed capacity of 500 kW from a single well in the period of 10 years. Another case of retrofitting the hydrocarbon wells into a geothermal ones was introduced in [18], where the method used for exploiting geothermal energy took into account economic and environmentally friendly solutions for the efficient production of electricity by considering mathematical and 3D numerical models of heat extraction. The model resulted in viable and efficient electricity and heat generation over the lifetime of the reservoir. The conducted sensitivity analysis of main parameters controlling the outlet fluid temperature implied that abandoned gas wells are applicable sources of geothermal energy. In reference [19], the authors evaluated the abandoned petroleum wells in Hungary, which are suitable for potential applications of enhanced geothermal systems. The database of 168 wells defined with moderate to high heat flow (75–100 mW/m<sup>2</sup> ) proved the feasibility of using abandoned wells for direct uses, all using either hydrothermal or EGS with identified influencing factors such as well geometries, geothermal gradient, pipe diameter, etc. The authors in [20] investigated the possible production of geothermal energy from inactive wells in the Arun Field, and their study confirmed the feasibility of extracting geothermal energy for electricity and heat generation and stated that, with 2.56 kg/s of mass flow and 170 ◦C, it is possible to produce 2900 kW of electricity and satisfy the heating and cooling demands of various industry objects. Such positive retrofitting project outcomes have significant contributions to meeting rising global energy demands with renewable energy use without necessitating additional land usage and costs such as exploration, drilling, casing, surface pipeline, and decommissioning costs.

However, it is important to determine the optimal applicable exploitation technology with respect to the site and potentially close end users for the heating power production case. Given its promising future, plenty of studies on geothermal energy extractions from abandoned oil wells have been carried out and appraised [21–25]. The focus of the mentioned studies was on retrofitting an abandoned oil well for feasible technical and economic exploitation of geothermal energy, performance during the operational phase, decision on open-loop or closed-loop geothermal extraction choice between borehole heat exchanger (double pipe or U-tube), and heat transfer improvements. The fundamental parameters such as the working fluid characteristics, well geometry, and operational parameters that concern working fluid flow rate, inlet temperature, operating pressure, etc., were likewise examined [26–28].

Moreover, the majority of work that has been performed on retrofitting abandoned petroleum wells as a source for geothermal energy has been focused on open loop systems that repurpose the petroleum reservoir as a geothermal reservoir [29]. There are multiple countries that have sponsored research and/or investigations specific to adapting an open loop design for abandoned wells, including the following: Albania, China, Croatia, Hungary, Israel, New Zealand, Poland, and the US. Additionally, Vermilion Energy is recovering heat from two producing oil fields in sedimentary basins in France. On the Parentis oil field in SW France, 60 wells producing a total of 400 m3/h water at 60 ◦C water have been used to heat up 8 ha of tomato greenhouses since 2008, creating more than 100 jobs. In La Teste in SW France, two producing wells yielded 40 m3/h at 70 ◦C, which is enough to cover 80% of the heat needed for 450 new flats. These two projects demonstrate that recovering heat from produced water creates value and jobs at any scale (small or large oil fields). Based on these successfully conducted projects, the idea of shifting the paradigm from investing in geothermal projects from the beginning, starting with exploration and drilling activities, to start where geology is already known through existing wells in the oil industry emerged. Therefore, the end-of-life oil well conversion methodology is part of the Horizon 2020 project: Multidisciplinary and multi-context demonstration of EGS exploration and Exploitation Techniques and potentials (MEET, GA No 792037).

End-of-life oil well conversion methodology towards the geothermal wells defines the roadmap for further conversion of oil wells into geothermal production wells, thereby enabling a certain niche for geothermal energy penetration into the market. Namely, notable potentials for conversion to geothermal wells include abandoned, mature, or high watercut wells since they are almost instantly available, i.e., there is no need for drilling, and available and thorough logging of production data facilitate well performance assessment which results in diminishing risks and enhancing cost estimation [7,29]. Furthermore, petroleum infrastructure and facilities available on the field can be converted to enable geothermal exploitation; in doing so, major costs related to drilling a new geothermal well and power plant are economized [29,30]. Retrofitting petroleum wells into geothermal wells also prospers from reducing or even excluding the cost of decommissioning of the oil well, thus maintaining the economic viability of the well.

The methodology conducted in this study and corresponding support tool for an economic evaluation of end-of-life conversion will enable pre-technical economic feasibility studies for converting an oil field to a geothermal field at the end of its economic "petroleum" life, including geological, technological, financial, and environmental aspects of an oil field and the technology used. The clustering feature, where wells can be clustered based on production temperature and spatial distribution, enables including wells at a specific oil field in the calculations that are best suited for a certain option—only heating power production, electricity generation, or both (combined heat and electricity production, CHP). This two-level clustering method facilitates the decision process regarding the possible usage of produced heat. The first step starts with temperature clustering, which is based on sorting the oil wells into different groups based on the temperature ranges from modified Lindal diagram [31]. Additionally, spatial clustering, which is based on the grouping a certain number of wells into one group according to their mutual distances, enables the best allocation of power plant installation and piping connection system between the selected wells. The output results of the methodology are based on economic metrics (net present value (NPV), levelized cost of electricity (LCOE), and levelized cost of heat (LCOH)) and production metrics (yearly/monthly production values, avoided CO<sup>2</sup> emissions) that are used in the decision-making process with respect investing in a specific project or not.

#### **2. Background**

The mentioned conversion is based on input data from the oil field, default values about the heating demand, energy prices, emission factors that can be changed by the user, proxy values of pump power consumption, thermal efficiency of Organic Rankine Cycle power plant, etc. Based on the mentioned data, five scenarios of geothermal energy produc-

tion with different production technologies are developed with the main goal of comparing different options for heat and/or electricity production and to choose the optimal one. One of the main features of the conversion is temperature and spatial clustering, which clusters the wells according to the geothermal fluid temperature into a different end-use group and, once again, clusters the wells into spatial groups according to the distance between each well. Spatial clustering enables the user to include all wells on the field with high water cut in the conversion in order to upscale production quantities and to decrease piping connection cost. Additionally, three submodules are developed to calculate the power consumption of the production pump, injection pump, and deep borehole heat exchanger pump. After entering the input data for each scenario, the conversion tool will calculate four main outputs: produced energy quantities, LCOE or LCOH, NPV, and avoided CO<sup>2</sup> emissions. Based on these results, the user can decide which conversion option is optimum for a given petroleum asset.

### *2.1. Developed Scenarios*

The methodology for an economic evaluation of end-of-field life conversion is a decision-making framework that uses different input data in which the main goal is to compare different options for heat and/or electricity production and to choose the most suitable option. The main purpose of the methodology is to offer the optimal scenario for converting the petroleum asset to a geothermal one. Based on the input data of mature or abandoned petroleum fields, economic or environmental parameters, and technological features, five scenarios are modelled, and the result is output data. The output data, based on the extensive and thorough calculations, provide insight into the economic and environmental aspects of the geothermal project for each scenario.

One of the key benefits of the proposed work is the avoidance of decommissioning the cost of wells and surface facilities and generating income through electricity and heat production by repurposing the mature oil field into a geothermal asset. One of the main contributions of the methodology is two-stage clustering that enables the temperature and spatial arrangement of the wells and, among the oil wells, also includes the wells from the field that were previously flooded and were not producing oil or newly drilled wells in terms of upscaling geothermal energy production. Two-stage clustering is an optimization process because it clusters the wells according to the temperature of the end-use and according to the spatial distribution so that the position of the geothermal plant can be determined along with the inclusion of the wells in the gathering system corresponding to the shortest distance from the geothermal plant.

The developed methodology should serve as a pre-feasibility study of converting a petroleum field to a geothermal one. The methodology provides guidelines in terms of retrofitting mature or abandoned petroleum fields to geothermal energy exploitation and user-friendly environment for which its outputs could encourage possible users to invest in geothermal projects. In the following bulleted list, the developed scenarios are described.

• Scenario 1—"Do nothing"

This scenario refers to plugging and dismantling all the wells and surface facilities and can represent hundreds of thousands of Euros of abandonment cost per well required by mining law. The operating life of an oil field has a certain limitation, and when reaching the end of its viable life, the next step is strategy planning for plugging and abandonment operations.

This is dependent on factors such as well location and depth, type of the surface and subsurface facility, number and weight of structures needed to be removed, removal method, transportation, and disposal options, etc [32].

• Scenario 2—"Heat doublets"

The developed scenario concerns heat production from production wells and the injection of geothermal fluid into the reservoir by using the injection wells. The main challenge that concerns the geothermal industry is associated with capital-intensive costs of drilling

geothermal wells; hence, the utilization of abandoned petroleum wells is encouraged. The aforementioned wells can potentially be harnessed for geothermal energy for direct usage depending on the temperature of geothermal water [3,22,33]. This scenario consists of two sub-scenarios: *Temperature range* sub-scenario and *Heat needs* sub-scenario. The *Temperature range* sub-scenario is the scenario where heat production is based on utilizing the temperature range of geothermal fluid (production temperature and fixed injection temperature). The latter scenario, *Heat needs* sub-scenario, is based on satisfying the heat demand of the end-user. The heat demand is set as the user's input, or it is calculated based on the heat demand of three different type of buildings.

• Scenario 3—"Heat via BHE"

The modelled scenario regards heat production using one well, i.e., the borehole heat exchanger. Borehole heat exchangers are used to extract heat without producing geothermal fluid from wells, i.e., with running circulation fluid through the wellbore. The usage of abandoned wells in such a manner can decrease gas emissions with respect to the atmosphere and the energy needed for reinjection. The circulating fluid is injected through annular space and produced at the wellhead through production tubing or vice versa [1,23,34]. This scenario consists of two sub-scenarios, *Temperature range* sub-scenario and *Heat needs* sub-scenario, which is the same as described in Scenario 2.

• Scenario 4—"ORC power production"

This scenario represents electric power generation using the Organic Rankine Cycle (ORC). Electricity can be produced by using production and injection wells or using a deep borehole heat exchanger. The power capacity is determined primarily by the production rate, temperature of produced water, ambient temperature, water salinity, conversion efficiency of the geothermal power plant, heat transfer efficiency between the reservoir rocks and circulating fluid, etc. [3,8,17,21,35,36].

• Scenario 5—"Combined power and heat"

The developed scenario refers to combined heat and power production (CHP) with parallel configuration modes [37]. The total geothermal fluid flow is divided into two branches as follows: Primarily, heat demand is satisfied, and electric power is then produced with the residual flow. Two sub-scenarios are developed: the first one with the production and injection wells and second one with BHE. The well for BHE is the well with the highest temperature according to the wells clustered by the "electricity" end-use [3,8,21–23,34].

#### *2.2. Input Data*

The main input data used in the methodology for calculations and clustering process are shown in Table 1.

Even at very high water cut, an oil field often displays mixed flow, meaning that a given geological layer produces both oil and water. It is, therefore, expected to produce both water and oil after conversion. Since the oil cut is very low, it is expected that gravity separation in water tanks will take place. Yearly water-cut increment is a linear percentage value of the annual average water-cut increase, based on historical data. Yearly thermal dropdown is defined as the annual average temperature decline rate for petrothermal reservoirs, as the reservoir is expected to be cooled down by colder fluid injection. Additionally, at the beginning of calculations, it should be determined if the production pump is already installed and running or not. If the pump is already installed, additional input regarding the pump power is required, which is used afterwards to calculate pump consumption power, i.e., parasitic load. In both cases, if the pump is already installed or not yet installed, the user should proceed with the calculation related to the electric submersible pump (ESP) design in order to either design the required new pump that should be installed or to estimate pump consumption for the already installed pump. Temperature loss along the wellbore is also stated as the user's input, and it is automatically subtracted from the reservoir temperature to calculate the wellhead's temperature, i.e., production temperature.

The rest of the input data follows the developed scenario's data and will be set as the default or calculated with the possibility of user's input.

**Table 1.** Input data required for conducting clustering methods and further calculations.


#### **3. Materials and Methods**

At the end of its economic life, a certain spatial footprint of oil field exists. Based on the development history of the oil fields, well pads are made of several wells drilled from the same surface location and are connected to the main facilities by flowlines [38]. Each of the wells on the oil field has different surface flow rates and temperatures. When converting the oil field to geothermal usage, the wells on the field are optimized and the wells that deliver the most suitable flow rate and temperature are kept. The example of temperature and spatial clustering was shown in [39], where the author used the Cluster and Outlier Analysis tool for spatial and temperature well clustering for deep borehole heat exchanger (DBHE) geothermal systems, which solves for the Anselin Local Moran's "I" statistic of spatial association. The statistic was used to identify the aggregation of wells with high bottomhole temperatures. Temperature data of 42,601 wells were collected, and areas with significant densities of oil and gas wells with the accompanying high temperatures were outlined. The described approach could result in an increase in system efficiency and economic viability of the geothermal projects, which are based on the already built subsurface infrastructure of oil and gas fields. The main advantage of clustering methods is the possibility of selecting clusters and/or wells that are already connected to built surface piping infrastructure or are near existing power distribution infrastructure. Moreover, the ability to connect new wells that so far have not produced any oil and gas and have high water cut to a gathering system would result in upscaling the overall capacity of geothermal energy production.

The basis of the developed methodology and the supporting tool is the clustering of the wells, both in terms of temperature and spatial clustering. For both clustering layers, the Python programming language is used with integrated pre-made libraries.

In the first layer of clustering, i.e., temperature clustering, the production wells are sorted into the temperature groups according to their well temperature, and each well is sorted into groups for one or more end-uses. The well that has more than one end-use is used in calculations for more than one scenario.

The second layer of clustering is spatial clustering where the used method of clustering sorts the wells in certain number of clusters based on their distances between each other. Spatial clustering enables the inclusion of unused wells on the field in further calculations that have a high water cut that is suitable for geothermal energy production; the wells that were not previously included in oil production; and newly drilled wells that have a high water cut and are drilled for geothermal purposes on the mature or abandoned oil field. Spatial clustering also defines the data point (centroid, most commonly an imaginary point), which is in the middle of the cluster and the well (existing data point that is nearest to the centroid) upon which the new thermal or power plant should be built with minimum cost of a new pipeline system.

#### *3.1. Temperature Clustering*

The temperature clustering layer is based on Lindal's diagram [31] with minor modifications. Minor modifications of Lindal's diagram and the possible applications of geothermal energy made for the purpose of the methodology concern the expansion of temperature ranges for end-uses. The main modification is the expansion of temperature range for electricity production using Organic Rankine Cycle (ORC) smart mobile units, which is one on the main goals of the MEET project, i.e., enhancing heat-to-power conversion at low temperature (60 ◦C–90 ◦C). The temperature ranges for different end-uses are shown in Figure 1. The temperature spans from 0 ◦C to 200 ◦C with the heat pump, heat generation, and electricity generation as the end-uses. Electricity generation end-use covers electricity production by using smart mobile ORC units and electricity production in binary systems (ORC). The temperature range for heat pump is stated here as the informational data, and it does not proceed to further calculations for the purposes of methodology and tools. *Geosciences* **2021**, *11*, x FOR PEER REVIEW 8 of 30

**Figure 1.** Modified Lindal's diagram with different end‐uses. there are no other data points around any data point within the epsilon radius, then it is **Figure 1.** Modified Lindal's diagram with different end-uses.

*3.2. Spatial clustering*

any shape [40].

array.

as in the neighbourhood;

termined:

The method used in the developed methodology and case study is the Density‐Based

For the mentioned clustering method, a few important parameters need to be prede‐

chine learning algorithm. Unsupervised machine learning algorithms are used to allocate unlabelled data. DBSCAN method examines the clusters as high‐density regions sepa‐ rated by low‐density regions; therefore, the clusters found by DBSCAN method can be of

Epsilon, as the maximum distance between two data points for one to be considered

 Minimum samples, as the number of data points (ortotal weight) in a neighbourhood for a point to be recognized as a core point and includes the point itself; Metric, as the metric used when calculating the distance between instances in the

DBSCAN creates a circle of *Epsilon* radius around every data point and classifies them into core point, border point, and noise point. A data point is a core point if the circle around it contains at least a number of *Minimum Samples* points. If the number of points is less than the *Minimum Samples* number, then it is classified as a border point, and if

#### *3.2. Spatial Clustering*

The method used in the developed methodology and case study is the Density-Based Spatial Clustering of Applications with Noise or DBSCAN, which is an unsupervised machine learning algorithm. Unsupervised machine learning algorithms are used to allocate unlabelled data. DBSCAN method examines the clusters as high-density regions separated by low-density regions; therefore, the clusters found by DBSCAN method can be of any shape [40].

For the mentioned clustering method, a few important parameters need to be predetermined:


DBSCAN creates a circle of *Epsilon* radius around every data point and classifies them into core point, border point, and noise point. A data point is a core point if the circle around it contains at least a number of *Minimum Samples* points. If the number of points is less than the *Minimum Samples* number, then it is classified as a border point, and if there are no other data points around any data point within the epsilon radius, then it is treated as a noise point [41]. The *Epsilon* value can be calculated as the average distance between each point in the data set and its *Minimum samples* number of nearest neighbours. The average distance is then plotted by ascending value where the sorted values produce an elbow plot that indicates the maximum curvature on the point, which is the *Epsilon* value.

The main advantage of the considered method is the determination of outlier points and the selection of clusters according to the different shapes of the data set. The main weakness of the method is that it does not work well with the data set that has different densities (different distances between the points), and due to the fact that *Epsilon* is a fixed value, it will characterize the points with different densities as outlier points.

#### *3.3. Outputs*

When two-layer clustering is conducted, the number of clusters in the specific field is obtained, and the filtering option is enabled. Namely, various filtering options are possible: filtering of the individual wells, filtering the number of end-uses for each well, filtering desired end-uses to be included in further calculations, filtering regarding the wellhead temperature, and filtering according to the number of the cluster in which the well is located. This type of listing and filtering later enables the calculation of results for each scenario, including both heat and electricity generation, and provides the user with an option to include or exclude a particular well or cluster from further calculations and scenario development.

#### 3.3.1. Energy Production Quantities

Regarding energy production, the quantities of produced electricity and/or heat are calculated for each modelled scenario. For both electricity and heat generation scenarios, when using the production–injection wells, the temperature of the mixed fluids, density of the mixed fluids, and specific heat capacity of the mixed fluids are all computed from all wells from the field, which are filtered after the clustering process. The temperature of filtered wells is calculated by using Richmann's rule of mixing [42], shown in Equation (1):

$$\mathbf{T} = \frac{\sum\_{\mathbf{i}=1}^{\mathbf{n}} \dot{\mathbf{m}}\_{\mathbf{i}} \cdot \mathbf{c}\_{\mathbf{i}} \cdot \mathbf{T}\_{\mathbf{i}}}{\sum\_{\mathbf{i}=1}^{\mathbf{n}} \dot{\mathbf{m}}\_{\mathbf{i}} \cdot \mathbf{c}\_{\mathbf{i}}} \,\tag{1}$$

where the <sup>T</sup> represents the fluid's temperature (◦C), . m is the mass flow (kg/s), c is the specific heat capacity (J/kg◦C) of the geothermal fluid from each well, and n is the number

of wells. Moreover, the density of the mixed fluid [43] from the geothermal water from all wells used in the methodology is calculated by using Equation (2):

$$\rho\_{\mathbf{f}} = \frac{\sum\_{\mathbf{i}=1}^{\mathbf{n}} \rho\_{\mathbf{i}} \cdot \dot{\mathbf{m}}\_{\mathbf{i}}}{\sum\_{\mathbf{i}=1}^{\mathbf{n}} \dot{\mathbf{m}}\_{\mathbf{i}}},\tag{2}$$

where ρ<sup>f</sup> represents the density of the geothermal water (kg/m<sup>3</sup> ) from a specific well, and . m is the mass flow (kg/s) from the well. The specific heat capacity of the mixed fluid is determined by using Equation (3) [44]:

$$\mathbf{c}\_{\mathbf{p}} = \frac{\sum\_{i=1}^{n} \dot{\mathbf{m}}\_{i} \cdot \mathbf{c}\_{i}}{\sum\_{i=1}^{n} \dot{\mathbf{m}}\_{i}},\tag{3}$$

where the <sup>c</sup><sup>p</sup> refers to the specific heat capacity of geothermal fluid (J/kg◦C), and . m is the mass flow (kg/s).

For the scenarios with heat production, thermal energy production concerns the exploitation of a fixed temperature range between geothermal fluid production temperature and fixed outlet temperature from the plant where heat can be delivered to multiple endusers during the entire year or serves as the base load thermal power plant. The installed capacity (Qth) is a direct function of specific heat capacity of geothermal fluid, density of geothermal fluid, fluid flow, and the temperature difference between the temperature inlet and outlet in the thermal power plant, as shown in Equation (4):

$$\mathbf{Q\_{th}} = \mathbf{c\_p} \cdot \rho\_\mathbf{f} \cdot \mathbf{q} \cdot (\mathbf{T\_i} - \mathbf{T\_o}) \,\tag{4}$$

where c<sup>p</sup> is the specific heat capacity of the geothermal fluid (J/kg◦C), ρ<sup>f</sup> represents the density of the geothermal water (kg/m<sup>3</sup> ), q is the fluid flow (m3/s), T<sup>i</sup> is the wellhead temperature (◦C), i.e., the temperature at the inlet of the thermal power plant, and T<sup>o</sup> is the temperature (◦C) at the outlet of the thermal power plant. The produced heat is calculated by using Equation (5):

$$\mathbf{E\_{th}} = \mathbf{c\_{p}} \cdot \mathbf{\rho\_{f}} \cdot \mathbf{q} \cdot (\mathbf{T\_{i}} - \mathbf{T\_{o}}) \cdot \mathbf{t} \cdot \boldsymbol{\eta}\_{\rm HE} \tag{5}$$

where the t is time (hours) in which the thermal power plant is operating, and ηHE is the efficiency (%) of the heat exchanger between the geothermal (circulating) fluid and the working fluid in the secondary loop (end user side).

For Scenario 3, i.e., heat production using the borehole heat exchanger, heat transfer between the reservoir rocks and the circulating fluid is quantified by using the temperature ratio (XTR). Temperature ratio is the number that represents heat transfer correlation between the reservoir rock and circulating fluid, including the heat transfer through cement, casing, tubing, and tubing isolation, i.e., the ratio of the temperature outlet from the deep borehole heat exchanger and bottomhole temperature. It is assumed that the reservoir temperature is the same as the temperature of the reservoir (geothermal) fluid and that the changes in reservoir porosity and thermal conductivity do not change significantly in the reservoir. The theoretical lower limit of XTR is zero, which means that there is no heat transfer between the fluid and the rock, and the theoretical upper limit is one, which means that heat transfer from the reservoir rock to circulating fluid happened completely. The temperature ratio is derived from the database of several real and simulated cases of deep borehole heat exchanger performances provided in Appendix A. The temperature ratio should imply how much heat is lost in the transfer process by using circulating fluid rather than geothermal fluid. The maximum ratio is 0.864, which means that more than 86% of heat from geothermal reservoir is transferred on the circulating fluid. The minimum ratio is 0.240, which means that only 24% of heat from reservoir rock is transferred to the circulating fluid. The generated temperature ratio enables the simplified estimation of heat transfer without the need for simulation or measurements on the field. General knowledge about favorable technical and geological parameters and configuration is of key importance. The explained factor, XTR, is included in Equations (6) and (7) for the

calculation of the installed capacity and heat production as the factors, which are multiplied with reservoir temperature:

$$\mathbf{Q\_{th}} = \mathbf{c\_p} \cdot \rho\_{\mathbf{f}} \cdot \mathbf{q} \cdot (\mathbf{X\_{TR}} \cdot \mathbf{T\_r} - \mathbf{T\_o}) \tag{6}$$

$$\mathbf{E\_{th}} = \mathbf{c\_p} \cdot \mathbf{\rho\_f} \cdot \mathbf{q} \cdot (\mathbf{\mathcal{X}\_{TR}} \cdot \mathbf{T\_r} - \mathbf{T\_o}) \cdot \mathbf{t} \cdot \eta\_{\rm{HE}} \tag{7}$$

where XTR is the temperature ratio used to describe the heat transfer between the reservoir and the circulating fluid (-), T<sup>r</sup> is the reservoir temperature, and T<sup>o</sup> is the injection temperature (◦C) which is the temperature at the outlet of the thermal power plant.

For the scenarios with electricity production using Organic Rankine Cycle (ORC) technology to assess heat exchange performances of the used binary power plant, thermal efficiency is analysed and calculated by using the following equations. For the wellhead temperatures higher than 120 ◦C, the method proposed by the Massachusetts Institute of Technology [3] is used. Namely, regression Equation (8), based on the data from fourteen ORC power plant, is used to calculate thermal efficiency (%):

$$
\eta\_{\rm{ORC}} = 0.0005 \cdot \text{T}\_{\text{Inlet}}^2 - 0.0577 \cdot \text{T}\_{\text{Inlet}} + 8.2897 \,, \tag{8}
$$

where Tinlet ( ◦C) represents the production temperature in the scenario with the production and injection wells, and in the BHE scenarios, it represents the product of temperature ratio and the reservoir temperature at a certain depth.

The installed power is calculated by using Equation (9) [3].

$$\mathbf{Q}\_{\rm el} = \mathbf{c}\_{\rm p} \cdot \mathbf{p}\_{\rm f} \cdot \mathbf{q} \cdot (\mathbf{T}\_{\rm Inlet} - \mathbf{T}\_{\rm o}) \,, \tag{9}$$

The produced energy is a direct function of installed power, thermal efficiency, and operating time, as shown in Equation (10).

$$\mathbf{E}\_{\rm el} = \mathbf{c}\_{\rm P} \cdot \rho\_{\rm f} \cdot \mathbf{q} \cdot (\mathbf{T}\_{\rm inlet} - \mathbf{T}\_{\rm o}) \cdot \mathbf{t} \cdot \eta\_{\rm ORC} \tag{10}$$

Additionally, for wellhead temperatures lower than 120 ◦C, the approach from the Deliverable D7.1, based on the data provided from ENOGIA for the purposes of the EU Horizon 2020 project MEET [45], was applied in order to evaluate the ORC power plant production. The following parameters should be considered:


As observed, both ηORC are a function of two variables. In addition, there was a limited number of ORC operating points available from ENOGIA. For that reason, the "MATLAB Curve Fitting Tool" was used to approximate these three-dimensional relationships. Polynomial approximation including third degree was performed.

Equation (11) represents the functional relationship between net ORC power plant efficiency (z), geothermal water extraction temperature, or circulating fluid temperature in case of BHE (y) and DT (x).

$$\begin{array}{l} \mathbf{z}(\mathbf{x}, \mathbf{y}) = & -0.06849 - 0.001452 \ast \mathbf{x} + 0.002209 \ast \mathbf{y} - 1.017 \mathbf{e}^{-5} \ast \mathbf{x}^{2} \\ & + 1.639 \mathbf{e}^{-5} \ast \mathbf{x} \ast \mathbf{y} - 1.096 \mathbf{e}^{-5} \ast \mathbf{y}^{2} + 3.241 \mathbf{e}^{-8} \ast \mathbf{x}^{2} \ast \mathbf{y} \\ & - 4.203 \mathbf{e}^{-8} \ast \mathbf{x} \ast \mathbf{y}^{2} + 1.866 \mathbf{e}^{-8} \ast \mathbf{y}^{3} \end{array} \tag{11}$$

It should be noted that relationship from Equation (11) between these variables is best suited for brine extraction temperature values in the range from 80 ◦C to 120 ◦C and for DT values in the range from 0 ◦C to 40 ◦C. In cases when Equation (11) is used for values outside of the suggested ranges, slightly less accurate results can be expected.

Finally, installed power and produced electricity are calculated according to Equations (9) and (10) with corresponding power plant efficiencies.

#### 3.3.2. Levelized Cost of Energy

The levelized cost of electricity or heat (LCOE or LCOH) is defined as the total discounted lifetime costs of an energy project divided by the total discounted amount of energy it either produces or saves in its lifetime [46].

The approach used in this methodology is based on a discounted cash flow (DCF) analysis. Additionally, it must be emphasized that the LCOE/LCOH metric should be considered rather as an informing measure for investment decisions than an absolute decision metric. Actual system and project planning should also consider reliability issues and other factors. Namely, the availability factor of the power plant, i.e., the time that the plant is available for running influences the produced amount of electricity in a specific period.

The LCOE/LCOH is calculated according to Equations (12) and (13).

$$\text{LCOE} = \frac{\sum\_{\text{t=1}}^{\text{TPL}} \frac{\mathbf{I}\_{\text{t}} - \mathbf{S}\_{\text{t}}}{(1+\mathbf{r})^{\text{t}}} + \sum\_{\text{t=1}}^{\text{TPL}} \frac{\text{OM}\_{\text{t}} \cdot (1-\text{TR})}{(1+\mathbf{r})^{\text{t}}}}{\sum\_{\text{t=1}}^{\text{TPL}} \frac{\text{EE}\_{\text{t}}}{(1+\mathbf{r})^{\text{t}}}} \tag{12}$$

$$\text{LCOH} = \frac{\sum\_{t=1}^{\text{TPL}} \frac{\text{I}\_t - \text{S}\_t}{(1+\text{r})^t} + \sum\_{t=1}^{\text{TPL}} \frac{\text{OM} \cdot (1-\text{TR})}{(1+\text{r})^t}}{\sum\_{t=1}^{\text{TPL}} \frac{\text{EH}\_t}{(1+\text{r})^t}} \tag{13}$$

In Equations (12) and (13), TPL represents the total lifetime of the project [years], r represents the nominal discount rate (%/100), I<sup>t</sup> represents investment costs in year t, S<sup>t</sup> represents incentives or subsidies in year t, OM<sup>t</sup> represents operation and maintenance costs in year t, TR represents effective tax rate, EE<sup>t</sup> represents generated electricity in year t, and EH<sup>t</sup> represents produced heating energy in year t. Total investment costs I<sup>t</sup> for specific year t in Equations (12) and (13) are calculated as shown in Equation (14):

$$\mathbf{I}\_{\mathbf{t}} = \mathbf{I}\_{\mathbf{t}}^{\text{exp,est}} + \mathbf{I}\_{\mathbf{t}}^{\text{prod,inje}} + \mathbf{I}\_{\mathbf{t}}^{\text{ppinst}} + \mathbf{I}\_{\mathbf{t}}^{\text{admi,man}} + \mathbf{I}\_{\mathbf{t}}^{\text{other}},\tag{14}$$

where I exp,est t represents yearly exploration and establishment costs (summarizes the cost of concession or lease acquisition of oil field, permissions, environmental studies, civil work, support facilities, surface exploring, shallow drilling, make-up well deepening, and pre-feasibility and feasibility studies), I prod,inje t represents yearly production and injection wells and system costs (includes mobilization, drilling, logging, testing, production piping, separators, water tanks, injection piping, production and injection pumps, and corrosion inhibitor systems), I ppinst t represents yearly power plant installation costs (it includes power plant design and engineering, procurement procedures and complete phase of construction, testing and controlling, grid connection, and transmission), I admi,man t represents yearly administration and management costs (it includes project management, project and company administration, insurance costs, and different financing fees), and Iother,t represents yearly other investment costs not included in any of the aforementioned categories. Additionally, operation and maintenance costs OM<sup>t</sup> in year t are calculated according to Equation (15):

$$\text{OM}\_{\text{l}} = \text{FO\&M}\_{\text{l}} + \text{O\&M}\_{\text{l}}^{\text{production pump}} + \text{O\&M}\_{\text{l}}^{\text{injection pump}} + \text{O\&M}\_{\text{l}}^{\text{other}},\tag{15}$$

where FO&M<sup>t</sup> represents yearly fixed O&M (including labor costs, maintenance of field and/or wells and/or power plant) in Euros, O&M production pump t (€) represents yearly production pump variable costs that depend on the installed power of the pump, working hours and electricity price, O&M injection pump t (€) represents yearly injection pump variable costs that depend on the installed power of the pump, working hours, and electricity price, and O&Mother t (€) represents yearly variable costs that were not covered by other defined categories.

The nominal discount rate, r, is calculated from the real discount rate, rr, and inflation rate, i, according to Equation (16).

$$\mathbf{r} = (\mathbf{1} + \mathbf{r}\_{\mathbf{r}}) \cdot (\mathbf{1} + \mathbf{i}) - \mathbf{1} \tag{16}$$

For combined heat and power (CHP) applications, more complex equations are used, dependent on what the main product is. Namely, the LCOE is used if the decision maker chooses the main product of interest as electricity; consequently, when calculating the LCOE for CHP plant, revenues from heat sales must be deduced, and if the main product is heat, when calculating the LCOH for CHP plant, revenues from electricity sales must be deduced (Equations (17) and (18)):

$$\text{LCOE}(\text{chp}) = \frac{\sum\_{t=1}^{\text{TPL}} \frac{\mathbf{l}\_t - \mathbf{S}\_t}{(1+\mathbf{r})^t} + \sum\_{t=1}^{\text{TPL}} \frac{\text{OM}\_{t'}(\mathbf{l} - \mathbf{T}\mathbf{R})}{(1+\mathbf{r})^t} - \sum\_{t=1}^{\text{TS}} \frac{\text{RHS}\_{t'}(\mathbf{l} - \mathbf{T}\mathbf{R})}{(1+\mathbf{r})^t} - \sum\_{t=\text{TS}+1}^{\text{TPL}} \frac{\text{RHS}\_{t'}(\mathbf{l} - \mathbf{T}\mathbf{R})}{(1+\mathbf{r})^t}}{\sum\_{t=1}^{\text{TPL}} \frac{\text{E}\mathbf{R}\_{t}}{(1+\mathbf{r})^t}}\,\tag{17}$$

$$\text{LCOH}(\text{chp}) = \frac{\sum\_{t=1}^{\text{TPL}} \frac{\text{h}\_t - \text{S}\_t}{(1+\text{r})^t} + \sum\_{t=1}^{\text{TPL}} \frac{\text{OM} \cdot (1-\text{TR})}{(1+\text{r})^t} - \sum\_{t=1}^{\text{TS}} \frac{\text{RES} \cdot (1-\text{TR})}{(1+\text{r})^t} - \sum\_{t=\text{TS}+1}^{\text{TPL}} \frac{\text{REM} \cdot (1-\text{TR})}{(1+\text{r})^t}}{\sum\_{t=1}^{\text{TPL}} \frac{\text{EEt}\_t}{(1+\text{r})^t}}},\tag{18}$$

where RHS<sup>t</sup> represents revenues from subsidized heating power sales in year t, RHM<sup>t</sup> represents revenues from the market heating power sales in year t, RES<sup>t</sup> represents revenues from subsidized electricity sales in year t, REM<sup>t</sup> represents revenues from the market electricity sales in year t, and TS represents the duration of subsidized price of electricity or heating power.

#### 3.3.3. Net Present Value

The NPV metric is in this methodology is calculated as shown in Equation (19):

$$\text{NPV} = \sum\_{\mathbf{t}=0}^{\text{TPL}} \mathbf{a}\_{\mathbf{t}} \cdot \mathbf{S}\_{\mathbf{t}} = \frac{\mathbf{S}\_0}{\left(1+\mathbf{r}\right)^0} + \frac{\mathbf{S}\_1}{\left(1+\mathbf{r}\right)^1} + \dots + \frac{\mathbf{S}\_{\mathbf{T}}}{\left(1+\mathbf{r}\right)^{\text{T}}} \tag{19}$$

where S<sup>t</sup> is the balance of cash flow (inflows minus outflows) at time t, a<sup>t</sup> is the financial discount factor chosen for discount at time t, and r is the nominal discount factor. The nominal discount factor is calculated according to Equation (16). Inflows include revenues obtained from electricity and/or heat sells. Outflows include investment costs, which are calculated according to Equation (14) and operating costs, which are further calculated according to Equation (15) but also include yearly tax payments.

## 3.3.4. Avoided CO<sup>2</sup> Emissions

In order to assess the environmental impact of such conversion projects and, consequently, to approximate the money savings based on this indicator, calculation of avoided CO<sup>2</sup> emissions during operational phase of the plant is proposed and calculated in this methodology. The avoided emissions during operational phase are calculated based on the comparison with the production of the same services with the reference electricity mix and reference heat mix, respectively. The reference mixes are country specific and represent business-as-usual developments until 2019 for each country.

For scenarios with only electricity generation, the amount of avoided CO<sup>2</sup> emissions (tons) is calculated as stated in Equation (20):

$$\mathbf{E}\_{\rm CO\_2} = \sum\_{\mathbf{p}=1}^{\mathbf{t}\_{\rm op}} \left( \dot{\mathbf{E}}\_{\rm P} \cdot \mathbf{e}\_{\rm CO\_2, \rm elemix} \right)\_{\prime} \tag{20}$$

where top represents the duration of the operational phase of the plant, . E<sup>p</sup> is the net electricity production by system at the operating conditions of period p (MWhe), and eCO2,elemix

is the specific CO<sup>2</sup> emissions of electricity production from the reference electricity mix (kgCO2/MWhe).

For scenarios with only heating power production, the amount of avoided CO<sup>2</sup> emissions (tons) is calculated as stated in Equation (21):

$$\mathbf{E}\_{\rm CO\_2} = \sum\_{\mathbf{p}=1}^{\mathbf{t}\_{\rm op}} \left( \dot{\mathbf{Q}}\_{\mathbf{p}} \cdot \mathbf{e}\_{\rm CO\_2, heatmix} \right) \tag{21}$$

where top represents the duration of the operational phase of the plant, . Q<sup>p</sup> is the produced heat energy to cover heating requirement during period p (MWhth), and eCO2,heatmix is the specific CO<sup>2</sup> emissions of heating production from a heat mix (kgCO2/MWhth).

In case of CHP scenario, Equations (20) and (21) are combined into Equation (22).

$$\mathbf{E}\_{\rm CO\_2} = \sum\_{\mathbf{p}=1}^{\rm t\_{\rm op}} \left( \dot{\mathbf{E}}\_{\rm P} \cdot \mathbf{e}\_{\rm CO\_2, \rm elemix} + \dot{\mathbf{Q}}\_{\rm P} \cdot \mathbf{e}\_{\rm CO\_2, \rm heatmix} \right)\_{\rm \prime} \tag{22}$$

#### **4. Case Study**

A case study was formed, i.e., mature oil field with high water-cut production served as the basis for forming the case and conduction of two-layer clustering. The oil field formed for the case study was slightly altered from the existing oil field for the purposes of retaining realistic parameters needed for the conduction of further calculations. The remaining required input data were modelled in such manner as to replicate geothermal systems that could be found in reality regarding technology, modelling of the developed scenarios, environmental and economic data such as the market price of electricity, emission factors, share of fossil fuels in total energy mix for each country, weather data for each country, etc. The rest of the input data for the purposes of the heat demand calculation and variable operational cost of production pumps, injection pumps, and BHE pumps are based on proxy values and can be replaced with the user's input.

In order for the outputs of methodology to be comparable with the outputs from other scenarios, it is desirable for the input data to be similar, referring to data such as heat needs, temperature difference, downtime, etc.

Regarding the heat production, the heat produced by exploiting the default temperature range will be shown. The calculation of heat demand is based on the building's heating system, i.e., heating curve [47]. The operational cost of production pumps is based on [48], where inserting data is required with respect to the well's geometrics for each well, well fluids parameters, productivity, and the associated pressures such as dynamic pressure, differential pressure, hydrostatic pressure, pump intake pressure, etc. For the wells that are newly included in the production of geothermal water, at the start of the calculation there is a short check up to verify if there is a need for production pump installation; if the outcome is positive, the well with its parameters enters the above-mentioned calculation. For the selection of the production pump, an optimization process of selection based on the Schlumberger catalogue [49] is developed where the pump with highest efficiency at the corresponding flow is chosen while satisfying the minimum velocity check-up and operating range check-up. The operational cost of injection pump is based on the performance curves of injection pumps installed at the facilities for geothermal exploitation. The operational cost of BHE pump is estimated by calculating the pump's head loss and Darcy–Weisbach friction factor by using Colebrook's equation [50]. For operational costs, it is assumed that the electricity from the grid is used at the market price and electricity generated from the power plant is sold at the subsidized price.

For the purposes of the case study, the oil asset will be called "Reservoir 1," and it is determined to be in France in the Aquitaine basin. The temperatures in the basin are mainly between 65 ◦C and 90 ◦C. The reservoir is characterized with tidal and fluvial sandstones interbedded with clays with thermal conductivity of 3 W/m/K. Reservoir 1 for

the conversion to geothermal field consists of 26 production wells and 10 injection wells. The choice for performing deep borehole technology can be any well from the field with suitable production temperature of circulating fluid. The well chosen for Scenario 3 will be the well with the maximum temperature of the geothermal fluid at the wellhead. All injection wells are considered to be of suitable properties for the injection of overall fluid flow. In Figure 2, the spatial distribution of production wells is shown. *Geosciences* **2021**, *11*, x FOR PEER REVIEW 15 of 30

**Figure 2.** Spatial distribution of production and injection wells at Reservoir 1. **Figure 2.** Spatial distribution of production and injection wells at Reservoir 1.

The main input parameters with respect to Reservoir 1 are shown in the Table 2. Most of the data are shown as the average of all wells taken into calculation. The wells on the field were all oil production wells with no newly added wells, and the data used for fur‐ ther clustering and calculations are more detailed and well specific. Depending on well depth, wells on the field range from 22 °C to 97 °C with respect to the temperature of geothermal water at the wellhead. Depending on the distance from the gathering station, pipe material, and insulation, temperature loss from gathering lines from the wellhead also varies from 0.2 °C to 2 °C overall. The yearly thermal dropdown explains the annual decline rate of reservoir temperature, and the yearly water‐cut increment represents an‐ nual linear water‐cut increase. For the simplification of the calculations, two mentioned values are taken as constant during the duration of project. The main input parameters with respect to Reservoir 1 are shown in the Table 2. Most of the data are shown as the average of all wells taken into calculation. The wells on the field were all oil production wells with no newly added wells, and the data used for further clustering and calculations are more detailed and well specific. Depending on well depth, wells on the field range from 22 ◦C to 97 ◦C with respect to the temperature of geothermal water at the wellhead. Depending on the distance from the gathering station, pipe material, and insulation, temperature loss from gathering lines from the wellhead also varies from 0.2 ◦C to 2 ◦C overall. The yearly thermal dropdown explains the annual decline rate of reservoir temperature, and the yearly water-cut increment represents annual linear water-cut increase. For the simplification of the calculations, two mentioned values are taken as constant during the duration of project.

**Input Data Value Unit Table 2.** General data about the Reservoir-1.

**Table 2.** General data about the Reservoir‐1.


following one. The downtime presents the yearly percentage of time when the well, plant,

#### *4.1. Modelling of the Heat Production Scenarios*

The input data for modelling heat production scenarios for all wells on the field are presented in Table 3. Scenario 1, which is about decommissioning oil assets, has no input parameters regarding the production, and it will not be shown in this subchapter or the following one. The downtime presents the yearly percentage of time when the well, plant, and other surface facilities were not operating. It could be due to disruption in production, maintenance, or similar reasons. The outlet temperature is the temperature of the fluid at the outlet of the plant. In Scenario 5, a parallel configuration model was applied where heat demand is calculated based on input data stated in Table 3 needed for heating curve performance computation and, consequently, the building's heat demand. The pipeline temperature coefficient corresponds to temperature loss caused by transmission pipelines from the plant to the end-user. It ranges from 0 to 1, where 1 means all the heat is transferred through the pipeline, and 0 corresponds to total temperature loss. The presented value is dependent on the pipeline material and geometry.

**Table 3.** Input data for the heat production scenarios.


#### *4.2. Modelling of the Electricity Production Scenarios*

The input data for modelling electricity production scenarios for all wells on the field are presented in Table 4. The outlet temperature is the temperature of the fluid at the outlet of the ORC power plant.

#### **Table 4.** Input data for the electricity production scenarios.


#### *4.3. Environmental and Economic Input Parameters*

For further calculations of the outputs, it is important to define environmental and economic parameters that will be used for calculating avoided CO<sup>2</sup> emissions, levelized cost of electricity or heat, and net present value. The stated outputs are dependent on production quantities and will have the same input parameters except the specific costs that are related to the installed power.

Economic input parameters used in calculations are shown in Table 5. For the market price of electricity, the ARIMA model developed in MATLAB was used to predict the market price of electricity for the time of the project duration based on the historical values [51].


**Table 5.** Economic parameters used in calculations.

The input values regarding the environmental aspects are stated in the Table 6. The share of each fossil fuel in total fossil fuel electricity or heat generation is taken here as the default value and is based on the data from [52] for a chosen country. The emission factors of each fossil fuel for each energy type, i.e., electricity or heat, are obtained from [53] and will not be publicly shown due to legal reasons.

**Table 6.** Environmental parameters used in calculation.


#### **5. Results**

After conducting two-stage clustering, the results of temperature and spatial clustering are shown in the Table 7. The column "Number of end-uses" represents how many enduses are possible for the conversion of each well based on the wellhead temperature, respectively. The first eight wells have low temperature for district heating and electricity generation but are adequate for the installation of heat pump systems; as such, they are automatically excluded from further calculations. The remaining wells from the field, i.e., eighteen wells in total, were chosen for further calculations of methodology outputs. The first subcase "Whole field" includes all eighteen wells. Furthermore, after applying the DBSCAN method for spatial clustering, the wells were sorted into two clusters, "Cluster 1" and "Cluster 2," without outlier wells. Namely, eighteen wells in total were chosen for further calculations of methodology outputs for sub-cases as follows:


**Table 7.** Results of temperature and spatial clustering.


The input data for the subcases Whole field and Cluster 1 remain the same, as described in Sections 4.1 and 4.2. For Cluster 2, the data are changed in order to have realistic scenarios and meaningful production and are shown in Table 8. The spatial representation of conducted clustering of production wells is shown in Figure 3.

**Table 8.** The changed input values for the sub-case "Cluster 2".


Reservoir 1—Two‐stage clustering output

Outlet temperature from the plant in Scenario 2 50 °C Outlet temperature from the plant in Scenario 4 47 °C Outlet temperature from the plant in Scenario 5 47 °C

**Input Data Value Unit**

**Figure 3.** Graphical results of the two‐stage clustering. **Figure 3.** Graphical results of the two-stage clustering.

**Table 8.** The changed input values for the sub‐case "Cluster 2."

#### *5.1. Calculated input values. 5.1. Calculated Input Values*

After the two‐stage clustering, the values described in Section 3.3.1. are calculated and shown for each scenario, i.e., subcase in Tables 9–12: calculated input values for Sce‐ nario 5. The calculated values, together with the required input data, are substituted into further calculation of methodology outputs. After the two-stage clustering, the values described in Section 3.3.1. are calculated and shown for each scenario, i.e., subcase in Tables 9–12: calculated input values for Scenario 5. The calculated values, together with the required input data, are substituted into further calculation of methodology outputs.

#### **Calculated Value Unit Whole Field Cluster 1 Cluster 2 Table 9.** Calculated input values for Scenario 2.

**Table 9.** Calculated input values for Scenario 2.


**Calculated Value Unit Whole field Cluster 1 Cluster 2**

Specific heat capacity of geothermal water J/kg °C 3900.69 3902.03 3890.20

Wellhead temperature °C 78.93 78.93 82.44 **Table 10.** Calculated input values for Scenario 3.


Density of geothermal water kg/m<sup>ଷ</sup> 1012.30 1011.22 1020.79 **Table 11.** Calculated input values for Scenario 4.


**Table 12.** Calculated input values for Scenario 5.


Contrary to greenfield geothermal projects, end-of-life oil wells conversion into geothermal ones enables omitting more than a half of the costs related to drilling and stimulation. The values for CAPEX and OPEX are for the purpose of this study estimated based on real data collected by the authors. CAPEX is represented with specific investment costs in Euro per kilowatt and consists of costs included in Equation (14), which depend on the analysed scenario. For each scenario, OPEX is calculated according to Equation (15). Additionally, tax rates are country specific, the discount rate was calculated according to Equation (16) where annual inflation rate for France at the moment of the analysis was 2.3% [54], and the discount rate was considered to be 6.5% [55,56].

CAPEX and OPEX for each scenario and "Whole field" case and additional subcases "Cluster 1" and "Cluster 2" are shown in Table 13.


**Table 13.** Calculated CAPEX and OPEX for each case and each scenario.

### *5.2. Methodology Outputs*

The graphical results for each subcase and its outputs for each scenario are shown for the first year of operation. The production quantities of heat and electricity scenarios are shown in Figures 4 and 5. *Geosciences* **2021**, *11*, x FOR PEER REVIEW 21 of 30

**Figure 4.** Heat production quantities for each of three sub‐cases. **Figure 4.** Heat production quantities for each of three sub-cases.

**Figure 5.** Electricity production quantities for each of three subcases.

0

100

Electricity

production

quantities

[MWh]

200

300

400

500

600

700

The differences between the production quantities are due to number of wells in‐ cluded in each subcase; thus, fluid flow and the temperature varies. In Scenario 3, the production quantities between each subcase are directly dependent of the fluid's temper‐ ature, since the remaining input data are the same; hence, heat production is the greatest for Cluster 2. In Scenario 5, the heat production quantities are similar for all three sub‐ cases since it is required in order to satisfy the heat demand first. The electricity produc‐ tion temperatures are directly dependent on fluid flow and thermal efficiency of the ORC turbine, which is conditioned by the geothermal fluid temperature at the inlet of the

Whole field Cluster 1 Cluster 2

Scenario 4 Scenario 5

Scenario 2 Scenario 3 Scenario 5

Whole field Cluster 1 Cluster 2

**Figure 5.** Electricity production quantities for each of three subcases. **Figure 5.** Electricity production quantities for each of three subcases.

**Figure 4.** Heat production quantities for each of three sub‐cases.

0

2000

4000

Heat

production

quantities

[MWh]

6000

8000

10000

12000

14000

The differences between the production quantities are due to number of wells in‐ cluded in each subcase; thus, fluid flow and the temperature varies. In Scenario 3, the production quantities between each subcase are directly dependent of the fluid's temper‐ ature, since the remaining input data are the same; hence, heat production is the greatest for Cluster 2. In Scenario 5, the heat production quantities are similar for all three sub‐ cases since it is required in order to satisfy the heat demand first. The electricity produc‐ tion temperatures are directly dependent on fluid flow and thermal efficiency of the ORC turbine, which is conditioned by the geothermal fluid temperature at the inlet of the The differences between the production quantities are due to number of wells included in each subcase; thus, fluid flow and the temperature varies. In Scenario 3, the production quantities between each subcase are directly dependent of the fluid's temperature, since the remaining input data are the same; hence, heat production is the greatest for Cluster 2. In Scenario 5, the heat production quantities are similar for all three sub-cases since it is required in order to satisfy the heat demand first. The electricity production temperatures are directly dependent on fluid flow and thermal efficiency of the ORC turbine, which is conditioned by the geothermal fluid temperature at the inlet of the power plant and the temperature difference between the mentioned temperature and the outlet temperature from the power plant. The levelized costs of heat and levelized costs of electricity are shown in Figures 6 and 7. *Geosciences* **2021**, *11*, x FOR PEER REVIEW 22 of 30 power plant and the temperature difference between the mentioned temperature and the outlet temperature from the power plant. The levelized costs of heat and levelized costs of electricity are shown in Figures 6 and 7.

**Figure 6.** Levelized cost of heat for each of three subcases. **Figure 6.** Levelized cost of heat for each of three subcases.

**Figure 7.** Levelized cost of electricity for each of three subcases.

nario of three subcases is shown in Figure 8.

0

200

400

600

800

LCOE

[€/MWh]

1000

1200

1400

1600

1800

The levelized cost of heat is greater that the levelized cost of electricity since the pro‐ duction of electricity is significantly lower than the production of heat, according to the set case study. The net present value is generally negative since it is required in investing in the conversion to geothermal assets, and due to the great investments in the first year of the operation period, the expenses exceed revenues. The net present value for each sce‐

Whole field Cluster 1 Cluster 2

Scenario 4 Scenario 5

Scenario 2 Scenario 3 Scenario 5

power plant and the temperature difference between the mentioned temperature and the outlet temperature from the power plant. The levelized costs of heat and levelized costs

> Whole field Cluster 1 Cluster 2

of electricity are shown in Figures 6 and 7.

**Figure 7.** Levelized cost of electricity for each of three subcases. **Figure 7.** Levelized cost of electricity for each of three subcases.

**Figure 6.** Levelized cost of heat for each of three subcases.

0 50

LCOH

[€/MWh]

The levelized cost of heat is greater that the levelized cost of electricity since the pro‐ duction of electricity is significantly lower than the production of heat, according to the set case study. The net present value is generally negative since it is required in investing in the conversion to geothermal assets, and due to the great investments in the first year of the operation period, the expenses exceed revenues. The net present value for each sce‐ The levelized cost of heat is greater that the levelized cost of electricity since the production of electricity is significantly lower than the production of heat, according to the set case study. The net present value is generally negative since it is required in investing in the conversion to geothermal assets, and due to the great investments in the first year of the operation period, the expenses exceed revenues. The net present value for each scenario of three subcases is shown in Figure 8. *Geosciences* **2021**, *11*, x FOR PEER REVIEW 23 of 30

**Figure 8.** Net present value for each scenario of three subcases. **Figure 8.** Net present value for each scenario of three subcases.

9.

**6. Discussion**

0.00

0.50

Avoided CO2

emissions

 (tonnes

CO2eq)

1.00

1.50

2.00

2.50

3.00

Thousands

The COଶ emissions that are avoided in the production of geothermal energy are di‐ rectly dependent of the energy production quantities, since the emission factors and the share of each fossil fuel in the fossil fuel mix are the same and are, as said, country specific. The avoided COଶ emissions for each scenario of the three sub‐cases are shown in Figure The CO<sup>2</sup> emissions that are avoided in the production of geothermal energy are directly dependent of the energy production quantities, since the emission factors and the share of each fossil fuel in the fossil fuel mix are the same and are, as said, country specific. The avoided CO<sup>2</sup> emissions for each scenario of the three sub-cases are shown in Figure 9.

**Figure 9.** Avoided CO2 emissions for each scenario of three subcases.

When comparing the production of energy in each scenario and for each subcase, the production directly depends on fluid flow and the inlet temperature of the geothermal

Scenario 2 Scenario 3 Scenario 4 Scenario 5

Whole field Cluster 1 Cluster 2

9.

‐7500

‐6500

‐5500

Net

present value (€)

‐4500

‐3500

‐2500

‐1500

‐500

Thousands

The COଶ emissions that are avoided in the production of geothermal energy are di‐ rectly dependent of the energy production quantities, since the emission factors and the share of each fossil fuel in the fossil fuel mix are the same and are, as said, country specific.

Whole field Cluster 1 Cluster 2

Scenario 2 Scenario 3 Scenario 4 Scenario 5

**Figure 8.** Net present value for each scenario of three subcases.

**Figure 9.** Avoided CO2 emissions for each scenario of three subcases. **Figure 9.** Avoided CO<sup>2</sup> emissions for each scenario of three subcases.

#### **6. Discussion**

**6. Discussion**

When comparing the production of energy in each scenario and for each subcase, the production directly depends on fluid flow and the inlet temperature of the geothermal When comparing the production of energy in each scenario and for each subcase, the production directly depends on fluid flow and the inlet temperature of the geothermal fluid or circulating fluid. When producing heat, in Scenario 2, for the Whole field and Cluster 1 subcases, the quantities are nearly the same; the greater inlet temperature in Cluster 1 compensates for the part of the lower flow that is caused by the lower number of production wells compared to Whole field. In Scenario 3, heat production using the borehole heat exchanger produces the most heat in Cluster 2 since the wellhead temperature is higher by more than 3 ◦C compared to rest of the subcases. In Scenario 5, subcases Whole field and Cluster 1 with similar inlet temperatures and flow of geothermal fluid managed to satisfy the heat needs where the remaining available flow was directed to the electricity production facility. Regarding Cluster 2, the changed input parameter of the outlet temperature, i.e., the greater exploitable temperature range, delivered enough heat to satisfy head demand, and more than 60% of the available flow was directed to the electricity production facility. Regarding electricity production, subcase Whole field produced more electricity than Cluster 1, where greater fluid flow in Whole field compensated for greater wellhead temperature and thermal efficiency of ORC turbine in Cluster 1. Cluster 2, with its two production wells, the wellhead temperature of 72.93 ◦C, and a low thermal efficiency of the ORC turbine (2.35%), produced about 90% less electricity than Whole field and Cluster 1, even with decreased outlet temperature from the ORC power plant. As stated before, in line with the objectives of MEET 2020 for enhancing heat-to-power conversion, the modelled case study uses low temperature (60 ◦C—90 ◦C) at the inlet of the power plant where smart mobile Organic Rankine Cycle units can be used for electricity production. Using mobile ORC greatly enlarges the potential sites that could be exploited together with the use of abandoned oil wells. Such usage of low temperature sources can result in uneconomic scenarios with respect to lower energy production quantities, but existing oil wells can minimize capital investments and increase cost competitiveness.

#### *6.1. Economic Results*

The levelized cost of electricity or heat and net present values are the main indicators for investment. For the modelled case study and associated subcases, the mentioned outputs quite differ depending on each subcase and scenario.

For the Whole field subcase, LCOH varies from 59.41 €/MWh in Scenario 3 to 301.36 €/MWh in Scenario 5 for heat generation, and the LCOE varies from 1365.82 €/MWh in Scenario 4 up to 1532.94 €/MWh in Scenario 5 for electricity production. Such variations can be explained by the different costs of capital investment, operational costs, and produced energy. It can be observed in the scenarios of electricity generation that lower thermal efficiency greatly affects production where revenue from selling electricity cannot exceed the cost of capital investment and high operational cost of running the production pumps. The operational cost of running the production pumps corresponds to the changes in electricity market price since the electricity from the grid is used to power pumps.

For the Cluster 1 subcase, LCOH varies from 59.41 €/MWh in Scenario 3 up to 465.76 €/MWh in Scenario 5, and as for LCOE, it varies from a minimum of 1052.14 €/MWh in Scenario 5 up to 1143.25 €/MWh in Scenario 4. Different values between two mentioned subcases can be explained with the difference in the number of production wells where there are 18 production wells in Whole field and 16 production wells in Cluster 1. For Scenario 3, a similar value of LCOH results from the fact that the same well was chosen to be converted into the borehole heat exchanger.

For subcase Cluster 2, there are two production wells, and LCOH ranges from 42.76 €/MWh in Scenario 3 to 100.21 €/MWh in Scenario 5, and LCOE ranges from 1307.08 €/MWh in Scenario 4 to 1664.96 €/MWh in Scenario 5. The lower values of LCOH in this subcase can be explained by lower pump operation costs and higher inlet temperatures in Scenario 3 for the borehole heat exchanger.

As for the entire case study, Cluster 2 has the lowest values of LCOH. In Scenario 3, Whole field and Cluster 1 have the same LCOH, but they slightly differ in Scenario 2. The largest difference is in Scenario 5 where the LCOH of Cluster 1 exceeds the LCOH of Whole field since the calculation of LCOH counts for the overall investment cost of combined heat and power, and the revenue from the electricity generation is subtracted. The LCOE values are the lowest for Cluster 1 in both scenarios and for Scenario 4; for the subcases Whole field and Cluster 2, the LCOE is slightly lower in the latter subcase due to lower thermal efficiency. In Scenario 5, Cluster 2 has the highest LCOE due to lower electricity production quantities and the result of subtracting revenues from selling heat.

As for the net present value of the case study, the values range from −7.616 M€ for Scenario 5 up to −0.116 M€ for Scenario 3 in the Whole field subcase, from −6.351 M€ for Scenario 5 up to −0.116 M€ in Scenario 3 in the Cluster 1 subcase, and from −1.263 M€ in Scenario 4 to 0.063 M€ in Scenario 3 in sub-case Cluster 2. The negative values of the net present value are the result of the investment cost of the plant at the beginning of the project and the replacement cost of the production pumps in year 15 of the project duration. Another reason for the negative NPV values is the high operating costs of production pumps and injection pumps that depend upon the electricity market price and the running time of the facility. In general, the lowest net present value for all scenarios is the Whole field followed by Cluster 1 where the differences are manifested from the production pump investment and operational cost of the pumps, among other associated costs. Cluster 2 has higher net present values since it consists of only two production wells and one injection well. Scenario 3 for all subcases has the highest net present value since the investment consists of plant and well configuration costs. For subcase Cluster 2, Scenario 3 has a positive net present value since the revenue from the heat produced exceeds the investment costs.

In general, the heat production scenarios are more economically feasible than the electricity generation scenarios due to low production quantities of electricity. The greater heat production quantities cover the initial investment cost of the oil-to-water conversion, but pump replacement lowers the cumulative cash flow of each scenario, along with the operational cost of each pump.

#### *6.2. Environmental Results*

Although almost all the scenarios of subcases are not economically feasible, it is important to elaborate about their environmental footprint regarding the potentially produced CO<sup>2</sup> emissions. The CO<sup>2</sup> savings during the operational period are shown as the avoided CO<sup>2</sup> emission, which is substituted with the geothermal exploitation. The quantity of the avoided emissions is directly correlated with energy production, emission factors of each fossil fuel, and the share of fossil fuel type in the total share of fossil fuels. The latter two are the same for all scenarios performed; thus, the only influencing value is the energy produced. The avoided CO<sup>2</sup> emissions range from 49.94 to 2837.73 t of CO<sup>2</sup> eq/year for Whole field, from 49.64 to 2783.77 t of CO<sup>2</sup> eq/year for Cluster 1, and it ranges from 29.54 to 637.01 t of CO<sup>2</sup> eq/year for Cluster 2. It can be concluded that the highest production generates the greatest CO<sup>2</sup> savings, and it cannot stand alone as the output based on which decisions will be made.

#### **7. Conclusions**

The presented methodology and the demonstrated case study offer solutions for the conversion of mature or abandoned oil fields to a geothermal asset and, for this reason, extend the production life of the reservoir. The comprehensive methodology takes into account production technology, economic and environmental parameters, and, together with the presented two-stage clustering, provides various options for further converting petroleum to a geothermal facility while regulatory and policy aspects of such action are left with the knowledge of the user or potential investor, since this is highly country and project specific.

One of the main features of the conversion is bi-level clustering, which facilitates firstly clustering of the wells according to geothermal fluid temperature into a different end-use group, and secondly, clustering of the wells into spatial groups according to the distance between each well. This approach allows optimal conversion and usage of the cumulative production flow from the production wells, simultaneously minimizing the costs for piping infrastructure and power plant spatial positioning and avoiding the decommissioning and abandonment costs of an oil field. An extensive review of input parameters and calculated values such as wellhead temperature, geothermal water flow, specific heat capacity, and density of geothermal fluid produced a thorough background for creating the different scenarios for conversion.

The methodology was applied to the modelled Reservoir 1, which replicates the petroleum reservoir that could be found in reality, in order to evaluate the best conversion scenario for the Whole field or the given clusters for the modelled case study. The outputs indicate that the best scenarios for the oil-to-water conversion were heat production scenarios due to highest production and avoided CO<sup>2</sup> emission quantities, which are directly related. The calculated economic parameters, LCOE, LCOH, and NPV, indicate that the optimal scenario for conversion was Scenario 3 for performing the deep borehole heat exchanger in all three subcases due to its lowest investment and operating costs, followed by Scenario 2 where production and injection wells are used to generate heat. Temperature clustering enabled considering a greater number of wells in heat production calculation rather than in electricity generation scenarios that had influence on the cumulative flow and the temperature of the geothermal fluid. The clustered wells showed different outputs in each cluster, which considered pipeline costs due to spatial clustering, and since there were no newly added wells, the pipeline cost was reduced to a minimum.

The mentioned scenarios resulted in the different main outputs such as production quantities, levelized cost of electricity, levelized cost of heat, and net present value which served as the peculiar roadmap towards the optimal oil-to-water conversion.

**Author Contributions:** Conceptualization, J.H. and S.R.; methodology, J.H.; validation, J.H., S.R. and E.L.; formal analysis, J.H. and S.R.; data curation, J.H., S.R. and I.R.; writing—original draft preparation, J.H. and S.R.; writing—review and editing, J.H., S.R. and I.R.; visualization, J.H. and S.R. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work has received funding from the European Union's Horizon 2020 research and innovation program (Grant agreement № 792037—MEET Project).

**Data Availability Statement:** All data related to this study can be obtained from the corresponding author upon request.

**Acknowledgments:** The authors are grateful to Guillaume Ravier for contributing to cost estimation for corresponding outputs and for his helpful comments.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Appendix A**


## **References**


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