1. Introduction
The North German Basin (NGB) and the Upper Rhine Graben (URG) are two of the main regions in Germany for geothermal exploration, exhibiting promising hydrothermal resources [
1]. The success of a geothermal project greatly depends on the target reservoir’ transmissivity and temperature [
2]. The high fluid mineralisation in Mesozoic sandstones [
3,
4,
5,
6,
7,
8], however, gives rise to challenges for their long-term utilisation [
9,
10]. One of which the present study focused on is barite scale formation (
), originating from lowering the fluid’s state temperature and pressure during the production–injection cycle. Barite is a low-soluble scaling mineral, typically found at geothermal installations located in the NGB and the URG area that handle fluids produced from reservoirs of depths greater
[
9,
11,
12]. Scalings are undesirable because they lower tubing diameters or reduce efficiency of heat exchangers, which leads to restoration costs [
3,
9,
12,
13]. Scale formation in the host rock at the injection site (
Figure 1a), however, may constitute a more serious threat, as the related pore clogging affects the reservoir’s hydraulic properties. In case of barite scaling, this leads to irreversible injectivity loss and thus reduced overall efficiency [
13,
14].
Due to the prograde solubility dependency of barite, reduction of temperature along the flow path results in supersaturated conditions [
16,
17]. Hence, the initial reservoir fluid’s state and chemistry as well as the surface system state need to be known in advance for evaluating the scaling potential of barite for a specific geothermal site. This can be done using geochemical modelling software that applies the law of mass action together with an appropriate thermodynamic database [
18]. The resulting equilibrium models yield a specific potential scaling mass based on the temperature and pressure change as well as according change in solubility. While they are easy to implement, this potential scale formation amount, however, only indicates whether precipitation can be expected and if there is a respective risk. These commonly applied equilibrium models (e.g., [
19,
20,
21]) are insufficient in predicting the related temporal impact on injectivity because they provide no data on the distribution near the injection well. This can be achieved by using a reactive transport simulator that implements respective solute transport and a kinetic rate law. The advantage is that further site specific parameters are accounted for, such as the injection flow velocity and the precipitation rate.
Barite growth is promoted when barite-supersaturated fluids come into contact with barite in the formation rock [
22]. Whether scalings grow dispersed or at specific locations has a significant impact on effective macro-scale permeability and injectivity [
23,
24]. It is crucial to take precipitation kinetics and flow into account to make assumptions on the expected scaling distribution in the subsurface for assessing this issue in terms of long-term utilisation of geothermal systems. Precipitation kinetics of barite have been the focus of numerous experimental studies [
25,
26,
27,
28,
29,
30,
31,
32,
33], demonstrating complex dependencies on nucleation, temperature, pH, ionic strength and ion ratios. Associated pore clogging and permeability loss effects have been also studied by means of core experiments [
34,
35] and with regards to specific pilot sites (e.g., [
13,
19,
36,
37,
38]), which highlights that barite scale formation is in fact a potential risk for geothermal systems in need of quantification and prevention measures.
Three representative cases for each geothermal region are considered in the present study. For the NGB, the geothermal plant Neustadt-Glewe (NG) was chosen, which actively produces brine from a Rhaetian sandstone aquifer [
6]. Barite scalings have been observed in the filters and in the heat exchanger within the surface installations. A gradual injectivity decline over the course of many years has been attributed to this issue [
13]. The geothermal site Landau (LND) was taken as a representative example for the URG. In the URG, a multi-horizon approach has been shown to be feasible, lowering exploration risk due to matrix permeability [
39,
40]. The well section is stretched over stratigraphical units of the Bunter sandstone, the Muschelkalk and the Permian granitic basement and also exploits a hydraulically active fault zone [
39]. Furthermore, two additional cases for each region were chosen based on averaged properties, representing hypothetical sites at various depths [
8]. Hereafter, they are called NGBa/NGBb and URGa/URGb, respectively. The corresponding depths and temperatures are shown in
Figure 1b, where it can be seen that all sites have anomalously high temperature gradients compared to the German average [
15].
This paper provides a new approach for calculating potential barite scaling amounts near the injection well and assessing the resulting impact on injectivity loss for geothermal systems in the NGB and the URG. By applying equilibrium models, the total precipitation amounts are calculated for the various sites based on the initial chemical composition of the formation fluid as well as temperature and pressure change along the flow path. One-dimensional reactive transport simulations are conducted considering radially-diverging Darcy flow and precipitation kinetics to model the constant injection of supersaturated fluids into a porous aquifer. The altered reservoir’s effective permeability and thus injectivity are assessed based on the scale formation distribution. The relevant operational parameters temperature, flow velocity and reaction rate are subjected to a sensitivity analysis in order to further provide implications for a geothermal project. Finally, a score is proposed, which aims at approximating the injectivity loss using quickly accessible parameters, applicable also to planned geothermal projects.
4. Discussion
Total barite scaling potential is determined by fluid composition, temperature reduction, pressure reduction and ion ratio of and . For the presented geothermal cases in the NGB and the URG, formation fluid temperature and salinity increase with greater reservoir depth. The deeper cases also showed ion ratios closer to unity. These factors all increase the precipitation potential and thus increase the scaling risk for deeper reservoirs. Furthermore, for cases at similar depths, fluid salinity is higher in the NGB and temperature is higher in the URG, but total scaling potential is in the same order of magnitude. As the corresponding saturation ratios were significantly higher for the URG cases, this illustrates that these values are not linearly correlated. Saturation ratios can only be taken as an indication of whether precipitation can be expected or not. Scaling amounts need to be investigated in detail for a specific location, taking the mentioned factors into consideration.
An irreversible injectivity decline of about
after 16 years of injection has been reported at the geothermal site Neustadt-Glewe [
13]. The authors attributed this mainly to formation of sparingly soluble scales in the reservoir, such as barite, celestite and various sulfides [
9,
13]. This order of magnitude is in fact in accordance with calculated injectivity losses, even though only barite scaling was taken into consideration in the present study. In this regard, some conservative assumptions were made, to the effect that the upper range of risk associated to barite scaling was assessed. For instance, it was assumed that barite growth does not happen until the re-injected fluid comes into contact with active growth sites (solid barite) in the formation rock. Precipitation rate and injectivity loss are further increased. Formation of additional active growth sites can occur through nucleation, increasing the precipitation and injectivity loss rate further. Whether this effect is significant depends on site characteristics such as mineralogy of the in-situ rock. This process was disregarded in the models, hence the real precipitation rate will be underestimated to some degree. For the considered cases, nucleation was not considered to be a growth determining step, as the highest saturation ratios were presumed to be too low for this [
59,
60]. Nuclei formation can be promoted, however, by longer shut-in periods [
10,
11,
36]. As a consequence, scale formation sets in prior to the fluid reaching the formation rock, thus not affecting the injectivity as strongly, but perhaps with other unwanted impediments [
10]. Furthermore, re-injected fluids heat-up again gradually in the reservoir, depending on flow rate and heat transfer, which has not been taken into consideration. This increases barite solubility again and thus reduces scaling risk, more so if flow rate is reduced. In light of the simulated scaling reach of below
, however, this effect appears to be negligible. On the other hand, injection pressure must be increased to maintain injection rates if permeability decreases. This could pose problems, as this increases the chance for loose particles to redistribute and clog pores. This process, however, is hard to quantify and also was not considered.
Supersaturation and kinetic rate both depend on the fluid’s salinity and temperature. An increase in salinity therefore increases the precipitation rate two-fold. The relationship with regards to temperature is different: supersaturation increases further with temperature reduction (increased
), whereas the rate constant is proportional to the absolute temperature. For quartz scaling in high-enthalpy systems, something similar was shown by Pandey et al. [
61]. Reducing temperature results in a counter effect of higher supersaturation, but lower kinetic rate constant. Temperature variations as part of the sensitivity analysis had no significant impact on calculated injectivity loss, at least in the considered
range. This explains why the NGB cases are generally affected more strongly.
Scaling potential needs to be put into perspective with regards to distribution along the flow path in order to assess implications for system longevity. Due to the radial diverging flow, large spatial distribution of scale formation means less effective permeability loss. This is promoted by slower reaction rates and higher flow velocities. The URG cases generally showed widespread distribution along the flow path, i.e., flatter precipitation curves, attributable to lower reaction rates. An important point is that equal hydraulic properties were assumed for all cases, in order to be able to compare them with regards to fluid chemistry and precipitation kinetics. While the model assumptions of radial diverging and planar flow are reasonable for homogeneous and isotropic porous aquifers with fully penetrating injection wells, they are simplifying for partially penetrating wells and especially fractured aquifers. The former have spherical flow components, thus this model treatment overestimates flow velocities and underestimates the permeability loss in the near-vicinity of the injection well for these cases. Projects in the URG rely on multi-horizontal approaches in order to minimise exploration risk [
39]. Therefore, there are sections with slow flow through the porous matrix, but also sections with increased permeability due to fractures. Fracture permeability is characterised by preferential flow with increased flow velocities and also decreased water–rock contact, i.e., less effective reactive surface area. Both factors hypothetically increase the scaling distribution in the formation rock, reducing the scaling risk for the URG even further compared to the NGB.
Scaling distribution patterns in the subsurface can be described by fluid flux, total scaling potential and Damköhler number. The latter relates the respective magnitudes of advection and precipitation kinetics. Assuming that rock reactivity is homogeneous on a large scale, the Damköhler number increases linearly along the
r-axis due to the radially diverging flow. The steeper is the slope (
), the closer isthe scaling distribution to the injection well. Further, the volumetric scaling potential (
) as well as fluid flux (
Q) are also necessary to determine scaling in the subsurface with regards to injectivity decline, as these quantify the total amount that can precipitate from solution. In essence, these three factors provide insights into distribution and intensity of scaling in the subsurface. If they are simply lumped together, the following scaling score is derived:
The resulting scores for the respective cases and scenarios are provided in
Table 4. They qualitatively suggest which cases’ injectivity will be affected more than others and therefore generate a ranking fit. Although this score only yields an approximation, it can nevertheless be used as a quick comparative value, without having to run elaborate reactive transport simulations. Furthermore, this scaling score is correlated with the previously calculated injectivity losses. For instance, the NGBb case has the largest values, while URGa has the lowest, which corresponds closely to the simulation results. If plotted against each other, a clear linear correlation can be seen (
Figure 9). This is a valuable insight, since the calculated injectivity losses result from multiple non-linear considerations: (I) steady-state reactive transport simulations; (II) porosity–permeability relationship; and (III) effective permeability approximation. By calibrating the score with the reactive transport simulation results, the obtained linear correlation represents a lightweight score for approximating the temporal injectivity loss associated to barite scaling:
It is easily applicable to new geothermal installations and may be calibrated further if additional data becomes available in this regard. The overall presented approach specifically treats barite as the sole scale formation agent. It can be adapted to make respective predictions for similar formation reactions of minerals exhibiting prograde solubility, for example silica or other sulfates. Though it is explicitly pointed out that the respective reaction mechanism needs detailed consideration.
5. Conclusions
Two model concepts were presented to approximate barite scaling formation in geothermal systems of the North German Basin and Upper Rhine Regions regions: an equilibrium model approach and a transport model coupled with precipitation kinetics. It was shown that temperature and pressure reduction during the production–injection cycle results in supersaturated conditions for barite in all cases, which is accountable for scaling. Equilibrium models were used to calculate the total potential scaling amount, which gives a first indication on the related risk for a long-term operation. This scaling potential increases proportionally to the imposed degree of temperature and pressure reduction dependent on the respective geothermal system management, as well as to formation fluid salinity. These parameters are generally correlated with reservoir depth. Fluids encountered at similar depths are hotter in the URG, while they are more saline in the NGB. The scaling potential is similarly high for both regions, while deeper reservoirs tend to be affected more strongly.
A comprehensive assessment of scaling risk needs to include the respective scaling location and distribution along the flow path in order to quantify the accompanied injectivity decline. From reactive transport simulations, information on both the scaling distribution in the subsurface and the related injectivity loss was obtained. Precipitation kinetics are taken into account, which also depend on temperature and salinity, similarly to the total scaling potential. Injection temperatures are usually in the same order for different geothermal installations, thus the corresponding temperature reduction () varies. The barite precipitation rate is higher for the NGB cases due to their higher fluid salinities. Thus, scaling will preferentially happen closer to the injection well and damage reservoir permeability more severely. Therefore, the NGB cases are generally at higher risk with regards to injectivity losses, while the shallow URG case showed almost no losses. A sensitivity analysis showed that varying temperature within a margin, as well as significantly reducing the flow rate had negligible effects on injectivity loss. The kinetic rate, on the other hand, exhibited a strong sensitivity.
A scaling score was developed, which takes the total scaling potential, the Damköhler number and the flow rate into account. It correlates strongly with the results of the reactive transport simulations and may be calibrated with further data. It is easily applicable in order to get an indication on the accompanied scaling risk for a specific geothermal location, without having to run elaborate reactive transport simulations. The presented approach can be adapted to make scale formation and injectivity loss predictions for mineral formation reactions similar to that of barite.