CO₂ Injection Effect on Geomechanical and Flow Properties of Calcite-Rich Reservoirs

Abstract

Geologic carbon storage is considered as a requisite to effectively mitigate climate change, so large amounts of carbon dioxide (CO₂) are expected to be injected in sedimentary saline formations. CO₂ injection leads to the creation of acidic solution when it dissolves into the resident brine, which can react with reservoir rock, especially carbonates. We numerically investigated the behavior of reservoir-caprock system where CO₂ injection-induced changes in the hydraulic and geomechanical properties of Apulian limestone were measured in the laboratory. We found that porosity of the limestone slightly decreases after CO₂ treatment, which lead to a permeability reduction by a factor of two. In the treated specimens, calcite dissolution was observed at the inlet, but carbonate precipitation occurred at the outlet, which was closed during the reaction time of three days. Additionally, the relative permeability curves were modified after CO₂–rock interaction, especially the one for water, which evolved from a quadratic to a quasi-linear function of the water saturation degree. Geomechanically, the limestone became softer and it was weakened after being altered by CO₂. Simulation results showed that the property changes occurring within the CO₂ plume caused a stress redistribution because CO₂ treated limestone became softer and tended to deform more in response to pressure buildup than the pristine rock. The reduction in strength induced by geochemical reactions may eventually cause shear failure within the CO₂ plume affected rock. This combination of laboratory experiments with numerical simulations leads to a better understanding of the implications of coupled chemo-mechanical interactions in geologic carbon storage.

1. Introduction

Geologic carbon storage is deemed as a necessary action to reach the Paris Agreement goal of limiting temperature increase to 1.5 °C [1]. To this end, widespread deployment of carbon dioxide (CO₂) capture and storage (CCS) projects will have to take place in the next decade. CCS projects can keep down the overall cost of mitigation options to achieve large reductions in CO₂ emissions [2]. The Intergovernmental Panel on Climate Change (IPCC) report [3] states that CO₂ storage in deep geological formations is one of the most promising techniques because gigatons of CO₂ can be potentially injected and trapped underground. The most suitable storage reservoirs are permeable sedimentary formations, which can be either siliciclastic or carbonate and saturated with saline water [2]. While siliciclastic formations are seen to be quite stable to CO₂ injection [4], carbonate formations could be highly reactive [5].

Recent laboratory studies show that the greatest changes in the mechanical response of reservoir formations are expected for carbonate-rich rock or rock with carbonate cement [6]. High-pressure CO₂ injection induces CO₂-brine-rock interactions in which geochemical reactions potentially lead to changes in hydraulic properties, i.e., porosity and permeability, and geomechanical properties, i.e., stiffness and strength of rock [7]. Bemer and Lombard [8] reported 1–2% increase in porosity for carbonate-rich wackestone from Lavoux formation altered in the presence of CO₂. This resulted in a decrease in strength and elastic moduli of up to 20–30%. Similarly, Alam et al. [9] observed 2–3% increase in porosity in North Sea chalk treated with supercritical CO₂ (scCO₂), leading to a 2% increase in Biot coefficient, and hence a decrease in elastic rock stiffness. Vialle and Vanorio [10] measured the changes in elastic properties of both saturated and dry limestones and observed a gradual loss of strength upon injection, as testified by the continuous decrease in the dry P- and S-wave velocity (20–25%). The decrease was also accompanied by a relative increase in permeability (up to 500%) and porosity (up to 19%), while the change in microstructure was monitored over time via scanning electron microscopy. Grombacher et al. [11] explained the ultrasonic velocities reduction in different carbonate rocks subjected to CO₂-rich water injection by the decrease in stiffness at grain contacts caused by dissolution that was observed through microimaging. However, the reduction rates of the bulk and shear moduli with injected pore volume decrease with increasing effective mean stress, which reduces the porosity and the reactive surfaces through compaction, so the effect of dissolution becomes less important [12].

Some other studies do not support the observations of significant decrease in strength and elastic properties of carbonates caused by CO₂ injection. Sterpenich et al. [13] showed that for brine-saturated Lavoux limestone, scCO₂ injection at 80 °C had a minor effect on microstructure (less than 1% calcite dissolution) and ultrasonic velocities. Liteanu et al. [14] observed the effect of water-weakening on Maastrichtian chalk, but the effect of scCO₂ on rock deformation was negligible. This minor effect was also reported by Grgic [15]. Saaltink et al. [16] found through numerical simulations that calcite dissolution at the field scale within the CO₂ plume is low. This weak interaction may be explained by the carbonate buffering effect on pH: The increase of pore fluid acidity due to CO₂ dissolution into water causes dissolution of calcite, which consumes protons, leading to pH stabilization.

Relative permeability and retention curves are used to describe the multi-phase flow induced by CO₂ injection in deep saline aquifers [17]. Specifically, the dissolution or precipitation of calcite may influence the pore structure and wetting and non-wetting procedures that occur in multi-phase flow. Bennion and Bachu [18] conducted comparative tests on relative permeability in various rocks including carbonates and provided a valuable data set to assess the fluid flow and distribution in two-phase flow. Zekri et al. [19] measured the relative permeability of limestones to evaluate the change in wettability of the porous media. The results showed that the scCO₂ flooding tends to change the wettability of saturated limestones to a more water-wet condition. Additionally, relative permeability was used as a fitting parameter for the numerical model to simulate CO₂ injection into a carbonate reservoir [20]. The simulation compared CO₂ saturated water injection and pure scCO₂ injection, concluding that the CO₂ saturated water tends to affect the reservoir structure more actively than pure scCO₂.

This paper aims to investigate how CO₂ injection affects the properties of porous carbonate reservoirs. We first present the geometry of the considered problem and explain the numerical model that includes the changes in hydro-mechanical properties of a limestone when it is altered with CO₂. Then, we describe the experimental techniques applied to saturate water-filled limestone with liquid CO₂ and measure its hydraulic and mechanical response. Subsequently, we present the results of laboratory tests performed on a number of pristine and CO₂ treated limestone specimens. Additionally, the numerical model that utilizes the laboratory data is used to evaluate the stability of carbonate reservoir and predict its long-term behavior. Finally, we discuss the findings and implications of this study and draw the conclusions.

2. Numerical Model

We modeled CO₂ injection into a carbonate reservoir and investigated the effect of the changes in rock properties induced by geochemical reactions on the geomechanical response of the system. To this end, we considered the coupled hydro-mechanical problem, which implied solving simultaneously mass conservation of each phase and momentum balance. Mass conservation of each phase, neglecting the diffusive component, is expressed as [21]:

$$\frac{\partial \left(\phi S_{\alpha }{\rho }_{\alpha }\right)}{\partial t}+\nabla \cdot \left({\rho }_{\alpha }{q}_{\alpha }\right)=r_{\alpha },\alpha =c,w$$

(1)

where φ is porosity, S_α is saturation of the α -phase, ρ_α is the density of the α -phase, t is time, q_α is the volumetric flux, r_α is the phase change term, and α is either CO₂ rich phase, c, or aqueous phase, w. Here, evaporation of water into CO₂ is neglected, i.e., r_w = 0. Fluid properties, i.e., density and viscosity, are functions of both pressure and temperature.

The volumetric flux is given by Darcy’s law.

$$q_{\alpha }=-\frac{k{k}_{r\alpha }}{{\mu }_{\alpha }}\left(\nabla p_{\alpha }+{\rho }_{\alpha }g\nabla z\right),\alpha =c,w$$

(2)

where k is intrinsic permeability, k_rα is the α -phase relative permeability, μ_α is its viscosity, p_α is its pressure, g is gravity, and z is the vertical coordinate, which is positive upwards.

The saturation degree is a function of the capillary pressure. We adopt the van Genuchten model [22], which reads:

$$S_e={\left(1+{\left(\frac{p_c}{p_0}\right)}^{1/(1-m)}\right)}^{-m}$$

(3)

where p_c is capillary pressure, p₀ is entry pressure, and m is the shape parameter and

$$S_e=\frac{S_l-S_{rl}}{S_{\max }-S_{rl}}$$

(4)

where S_l is liquid saturation, S_rl is residual liquid saturation, and S_max is the maximum liquid saturation.

For the mechanical problem, assuming that inertial terms are negligible, the momentum balance of the porous media reduces to the equilibrium of stresses.

$$\nabla \cdot \mathsf{\sigma }+b=0$$

(5)

where σ is the total stress tensor and b is the body forces vector. A complete description of the hydro-mechanical formulation is provided in Appendix A in Reference [23].

We assume that the medium behaves in a brittle manner and assess its stability by adopting the Mohr-Coulomb failure criterion

$$\tau =c^{\prime }+{{\sigma }^{\prime }}_n\tan {\varphi }^{\prime }$$

(6)

where τ is the shear stress, σ_n′ is the normal effective stress, c′ is cohesion, and ϕ′ is the friction angle.

We considered a 100 m-thick carbonate reservoir that is overlaid and underlain by a 50 m-thick low-permeable formation (Figure 1). The top of the reservoir is placed at 1500 m. CO₂ is injected through a vertical well, and, thus, the model is axisymmetric. The injection rate is of 0.25 Mt/year and injection is performed during 3 years. The model extends radially for 5 km. A constant pressure equal to hydrostatic is imposed in the outer boundary. No displacement perpendicular to the boundary is imposed on the lateral and lower boundaries, and a constant overburden equal to 36.25 MPa is imposed on the top boundary. We considered a normal faulting stress regime, with the vertical stress following a lithostatic stress of 25 MPa/km and the horizontal total stresses equal to 0.65 times the vertical total stress. The model is assumed isothermal, with a temperature of 60 °C, which corresponds to a surface temperature of 10.5 °C and a geothermal gradient of 33 °C/km.

The material properties were measured in the laboratory (see Section 3). While the properties of the reservoir (Apulian limestone) are measured in this study (see Section 4 for results), the properties of the caprock (Opalinus clay—Jurassic shale from Switzerland) have been measured in previous studies and are reported in

Table 1. Properties of the caprock representative–Opalinus clay (shale) [24,25].

Property	Pristine Rock
Permeability, k [m2]	4 × 10−21
Porosity, φ [−]	0.12
Relative water permeability, krw [−]	Sw6
Relative CO2 permeability, krc [−]	Sc6
Gas entry pressure, p0 [MPa]	6.0
van Genuchten shape parameter m [−]	0.3
Undrained Young’s modulus, E [GPa]	2.8
Undrained Poisson’s ratio, νu [−]	0.40
Cohesion, c′ [MPa]	5.0
Friction angle, ϕ [°]	24

. Due to nanoDarcy scale permeability, the response of the caprock is assumed to be undrained during the time of injection [24,25]. Given the relatively low permeability of the reservoir (~10⁻¹⁵ m², see Section 4), viscous forces dominate during the injection phase, which leads to a plug-like advance of the CO₂ plume [26,27]. After a 3-year injection period, the CO₂ plume reached a radius of 150 m. To assess the effect of the property changes on the geomechanical response of the rock, we ran two models, one in which the whole reservoir had the properties of the pristine material and another one in which the cylinder of 150 m in radius around the injection well had the properties of the altered material as a result of its interaction with CO₂. We simulated this hydro-mechanical problem using the fully coupled finite element numerical code CODE_BRIGHT [28], which was extended to be applied to CO₂ injection [29].

3. Experimental Methods

3.1. Material

Apulian limestone (or Calcarenite) was selected for the laboratory study of CO₂ injection in carbonate reservoirs because of the reported effect of aqueous fluids on its mechanical behavior [30] and weak stress-dependence of its properties [31]. It is a glauconitic fossiliferous limestone, showing a pale orange to grayish color, composed of mostly calcite (95–98%), with quartz, plagioclase, glauconite, and iron oxide. The rock matrix is supported with allochems, which chiefly comprises fragmental calcitic foraminifera that range from approximately 0.05 mm to 1 mm (rare) in maximum dimension and are cemented with calcitic mud (micrite). The P-wave velocity varies just by 2% in different directions (from 2.52 km/s to 2.57 km/s), meaning that the limestone is almost isotropic [31].

Rock interconnected porosity was measured by vacuum saturation technique and was found to be 0.35. This measurement was confirmed by mercury intrusion porosimetry test that provided not only the volume of the accessible pores but also the retention (or capillary pressure) curve shown in Figure 2. Suction was the difference between non-wetting and wetting fluid pressures. Supercritical CO₂ retention curve for water-saturated Apulian limestone was calculated from its pore size distribution by taking CO₂–water contact angle in calcite to be 40° and interfacial tension of 0.032 N/m [32]. This allowed for the evaluation of CO₂ entry pressure (0.02 MPa) and van Genuchten [22] parameter m = 0.42. We assumed that this parameter did not change after CO₂ treatment.

3.2. Hydraulic Properties

The permeability was measured on limestone cores (50 mm in diameter and 100 mm long) installed inside a core flooding device that was connected to three syringe pumps: one syringe pump (70 MPa, SANCHEZ, Frépillon, France) for confining pressure applied with hydraulic oil and two other syringe pumps (25 MPa, Teledyne ISCO, Lincoln, NE, USA) for upstream and downstream pore water pressure control (Figure 3a). The confining pressure pump could be operated in three different regimes: pressure control (50 kPa accuracy), volume control (0.2 mL accuracy), and flow control (0.1% of setpoint). The pore water pressure pumps could be controlled in two regimes: pressure control (25 kPa accuracy) and flow control (0.5% of setpoint). The lateral stress (confining pressure) was the major principal stress in this setup, while the axial stress was provided through a passive restraint (fixed platens) and calculated from generalized Hooke’s law, σ_ax = 2ν σ_lat with ν = Poisson’s ratio of rock. A steady-state flow was implemented by assigning different pressures for upstream and downstream syringe pumps. Pure deionized water with viscosity of 0.001 Pa∙s was used in these experiments. Assuming that the viscosity of pore fluid was constant (all tests were performed at T ≈ 22 °C), and measuring the inflow and outflow fluid pressure difference Δp, inflow and outflow fluid volumes (ΔV in steady-state flow) during time step Δt, the intrinsic permeability (k) was calculated as:

$$k=\frac{\mu \cdot L\cdot \Delta V}{A\cdot \Delta t\cdot \Delta p}$$

(7)

where L and A are the length and cross-section area of the specimen, respectively. The flow occurs in the horizontal direction, so the effect of gravity is disregarded.

To induce a two-phase flow in the specimen, another syringe pump (50 MPa, Teledyne ISCO, USA) was connected in parallel with the upstream pore pressure pump. CO₂ was injected in liquid state (7 MPa, 22 °C, 7.7 × 10⁻⁵ Pa∙s viscosity), just 1 MPa above the transition pressure between liquid and gaseous phases. Liquid CO₂ injection conditions are favorable to minimize the injection cost and are usually encountered in CO₂ injection wells within the first 1–2 km depth [29]. The mean stress was preserved at 12 MPa, and the pore pressure was 6.7 MPa (effective mean stress P’ = 5.3 MPa). The injected CO₂ initially dissolved in water, and additional CO₂ was subsequently injected. This procedure was repeated until saturation of water with CO₂ was reached and the latter one started flowing as a separate fluid. The CO₂ pump and the upstream water pump were operated by flow control, and the fraction of the two fluids in the two-phase flow could be represented by the ratio of the two flow rates of the two pumps. The flow rates of the two pumps (upstream water–CO₂) were controlled as 5–0 mL/min, 4–1 mL/min, 2.5–2.5 mL/min, 1–4 mL/min, and 0–5 mL/min, where the sum of the two flow rates were always constant and equal to 5 mL/min. Each pair of the flow rates represented the ratio of the volume of two fluids in the two-phase flow (water: CO₂), such as 100:0%, 80:20%, 50:50%, 20:80%, and 0:100%. The flow rates 5–0 mL/min and 0–5 mL/min were related to one-phase flow and measurements of permeability (k) for water (α = w) and CO₂ (α = c), respectively.

$$k_{r\alpha }=\frac{{\mu }_{\alpha }\cdot L\cdot \Delta V_{\alpha }}{k\cdot A\cdot \Delta t\cdot \Delta p_{\alpha }}$$

(8)

Here ΔV_α is the change of the volume of α-phase in the syringe pump, and Δp_α is the pressure difference between the α-phase and the downstream pressure. Δp_α is changing at the beginning of injection and then reaches a constant value, so the relative permeability is reported for steady flow. For this study, the intrinsic permeability and relative permeability curves of water and CO₂ were measured for pristine and CO₂ treated specimens. For the pristine specimens, the conducted tests should be short term (a couple of hours), such that the influence of the acidic CO₂–water mixture on limestone does not affect the results of relative and absolute permeability tests.

3.3. CO₂ Saturation and Treatment

Proper assessment of relative permeability required evaluation of the degree of saturation of two fluids, water and CO₂, during the relative permeability tests. Recent studies on relative CO₂ permeability are based on the calculation of water and CO₂ saturation using X-ray computed tomography (CT) scanning [18,33,34,35]. Here, we propose a method to calculate the saturation of water and CO₂ from the changes in (undrained) mechanical response of the rock during the injection of the second fluid.

During the relative permeability tests, two fluids were continuously injected at a constant flow rate until their pressures reached equilibrium. After measuring relative permeability, the valves on the upstream and downstream channels were closed simultaneously, setting the specimen in an undrained (no flow) condition. For the core flooding device, the increment in confining pressure was not equal to the mean stress like it would be in a conventional triaxial apparatus. Specimen deformation was limited in the axial direction (ε_ax = 0), and from generalized Hooke’s law, the change in the mean stress could be expressed as ΔP = (2 + 2ν_u)Δσ_lat/3, where ν_u is the undrained Poisson’s ratio of rock, since the specimen was deforming under the undrained condition. The Skempton’s B coefficient [36] was then measured by recording the change in pore pressure (Δp) caused by the increase in the mean stress (ΔP).

$$B=\frac{1}{\frac{\Delta P}{\Delta p}-C_{cor}}=\frac{\left(1-\frac{K}{K_s{}^{\prime }}\right)}{\left(1-\frac{K}{K_s{}^{\prime }}\right)+\phi K\left(\frac{1}{K_f}-\frac{1}{K_s{}^{″}}\right)}$$

(9)

The effect of pore water lines that connect pressure transducers to the specimen (Figure 3a) was taken into account through the correction factor C_cor [37], which appeared to be very small for core flooding device (0.5 × 10⁻²), so the applied correction was within the accuracy of our B measurements (±0.005). As shown in Equation (9), Skempton’s B coefficient can also be expressed through poroelastic parameters [38], where K is the drained bulk modulus, K_s′ is the unjacketed bulk modulus, K_s′′ is the unjacketed pore modulus, and K_f is the bulk modulus of the saturating fluid (K_w ≈ 2.3 GPa for water). Since the fluid in the pores consists of water and CO₂, its bulk modulus K_f depends on the degree of saturation. For each test stage that involved differential flows of water and CO₂, a sufficient amount of fluid (a few pore volumes) needed to be flushed through the specimen to guarantee that the outflow fluid had the same ratio of fluid phases. Subsequently, the residual degree of saturation of water and CO₂ could be measured. If all poromechanical parameters and correction factors are known, K_f can be calculated for the mixture of two fluids (K_mix). The bulk modulus of liquid CO₂, K_c is calculated from the knowledge of its density and P-wave velocity (ρ_c = 769.3 kg/m³, V_pc = 302.1 m/s) at testing conditions, T = 22 °C and p = 7 MPa [39].

$$K_c={\rho }_c{V}_{pc}{}^2=0.070\mathrm{GPa}$$

(10)

At each stage of relative permeability test, the bulk modulus of the mixed fluid K_mix (=K_f) can be calculated from Equation (9). Then, knowing the bulk modulus of water and CO₂, the corresponding degree of water saturation S_w can be obtained from Wood’s formula [40].

$$\frac{1}{K_{mix}}=\frac{S_w}{K_w}+\frac{1-S_w}{K_c}$$

(11)

Carbonate reservoirs are reported to react with the injected CO₂ when it mixes with the aqueous pore fluid. In this study, after measuring the properties of pristine specimen, such as porosity, intrinsic permeability, relative permeability, and Skempton’s B coefficient, we injected CO₂ in the specimen and treated it for three days (72 h). High porous, weakly-bonded Apulian limestone seemed to be quickly affected by acidic water-CO₂ mixture when left under the condition of no outward flow. It was observed that the pressure of the mixture of CO₂ and water had a tendency to decrease towards the boundary of the liquid state with gas state (~6 MPa at 22 °C). Therefore, the upstream CO₂ pressure was controlled by the CO₂ pump to preserve it at 7 MPa. After CO₂ treatment, we flushed the specimen with water and periodically emptied the downstream pump until no CO₂ was left in the downstream fluid. Additionally, we released the pore pressure in the specimen to get rid of the trapped CO₂ and then fully saturated the specimen with only water. After that, we repeated the relative permeability tests for the CO₂ treated specimen for comparison.

3.4. Geomechanical Properties

The elastic and strength properties of Apulian limestone were measured within 3.5 MPa Global Digital Systems (GDS) triaxial cell that allowed testing of 50 mm in diameter and 90–110 mm long soil and rock cores. Three 3.5 MPa pressure pumps provided the control of the confining pressure and input and output pore pressures. The pumps could work in either pressure (1 kPa accuracy) or volume control (1 mm³ accuracy) regimes. The triaxial cell was fixed on the bottom piston inside the 50 kN load frame and axial load was applied by the passive restraint on the top of the frame through the movement of the piston (Figure 3b). Two additional pore pressure transducers were installed at the input and output pore pressure lines to provide measurements of the upstream and downstream pore pressure in flow and undrained mechanical tests. Measurements of axial and lateral specimen deformation were conducted by attaching the set of three Linear Variable Differential Transformers (LVDTs), two axial and one lateral, to the rubber membrane (1 mm thick) around the specimen (Figure 3b).

Constant Terzaghi effective mean stress, P’ = P − p = 1 MPa, was applied by preserving the same difference between the mean stress (=confining pressure) and pore pressure. For all geomechanical experiments, the specimens were fully saturated with water. Water saturation was achieved by a back pressure saturation technique. Initially, water was flushed through the specimen until the outlet fluid volume equalized with the injected (inlet) volume. The outlet valve was then closed and pore (back) pressure was gradually increased while preserving the effective mean stress constant. At each stage of injection, Skempton’s B coefficient was measured. The back pressure saturation procedure was stopped when the measured B-value became constant [41]. After that, the permeability of the specimen was measured from Equation (7) when the steady-state flow through the specimen was established.

The drained condition was developed by imposing a constant pressure on the pressure controllers connected to the specimen. The elastic parameters, such as Young’s modulus (E) and Poisson’s ratio (ν), were measured during the application of axial load with the axial strain rate equal to 10⁻⁵/s. The LVDTs attached to the specimen provide the calculation of axial and lateral strains. The slope of the linear (elastic) part of axial stress—axial strain curve provided the value of Young’s modulus (E). The relationship between the axial and (negative) lateral strains allowed for the calculation of Poisson’s ratio (ν). If the axial loading was continued until reaching the peak load, the strength characteristics of the rock were evaluated. Performing strength tests at different effective lateral stresses and obtaining a few data points for axial stress at failure, provided the evaluation of the strength characteristics of rock, e.g., cohesion c′ and friction angle φ′ if Mohr-Coulomb failure criterion is adopted (Equation (6)) with τ = (σ_ax − σ_lat)/2 and σ_n′ = (σ_ax + σ_lat)/2. After the strength test, every specimen was trimmed to a cylindrical shape with a known volume and vacuum saturation method was applied to measure the porosity of treated rock.

4. Results

We measured the intrinsic and relative permeability, poroelastic properties, and strength properties of Apulian limestone on six pristine and four CO₂ treated specimens. The elastic properties and permeability of the pristine specimens were consistent between all the specimens and have little stress dependence, so we reported them only for one test (Calc-0). CO₂ treated specimens (Calc-1 to Calc-4) have some variation in their properties (

Table 2. Properties of pristine and carbon dioxide (CO₂) treated Apulian limestone.

	Pristine	CO2-Treated
	Calc-0	Calc-1	Calc-2	Calc-3	Calc-4
Min. principal stress, σlat [MPa]	2.0	3.5	3.5	3.5	3.5
Pore pressure p, [MPa]	1.8	3.4	2.0	0.5	1.0
Permeability, k [m2] (at P’ = 1 MPa)	9 × 10−15	3.5 × 10−15	5.1 × 10−15	5.6 × 10−15	5.8 × 10−15
Porosity, φ [−]	0.35	0.34	0.34	0.32	0.34
Young’s modulus, E [GPa]	7.1	3.4	4.4	4.7	4.5
Poisson’s ratio, ν [−]	0.25	-	-	0.25	0.25
Max. principal stress at failure, σax [MPa]	15.6	7.7	10.7	12.5	12.6

).

4.1. Permeability and Porosity

Permeability and porosity were measured for pristine and CO₂ treated Apulian limestone. While pristine specimens had an intrinsic permeability of 9 × 10⁻¹⁵ m² at P’ = 1 MPa, the CO₂ treated rock showed a decrease in permeability to 5–6 × 10⁻¹⁵ m². This decrease in permeability may be related to the observed porosity variation, which was reduced from 0.35 to 0.34 when specimens were treated with CO₂. Additionally, porosity measurements on 10 mm thick discs cuts from the upstream and downstream ends of the specimen were performed for specimens Calc-3 and Calc-4. The results showed that the porosity for the upstream part was 0.37–0.38, whereas the downstream part porosity was 0.28–0.30.

4.2. Relative Permeability and Saturation

Results of the relative permeability tests were plotted as a function of the degree of saturation evaluated from compressibility of pore fluid K_f (Equation (11)). K_f is calculated from the measurements of Skempton’s B coefficient and knowledge of poroelastic properties from Equation (9) (see Section 4.3). For 100% water saturation, Skempton’s B coefficient is equal to 0.55. As the portion of CO₂ in the two-phase flow increased, the B coefficient decreased significantly, giving values of 0.18 (water: CO₂ = 80:20), 0.13 (water: CO₂ = 50:50), 0.10 (water: CO₂ = 20:80), and decreasing down to 0.06 (water: CO₂ = 0:100) for pure CO₂ flow. These tests were performed under Terzaghi effective mean stress equal to P’ = 5 MPa. For pristine Apulian limestone, the relative permeability of water decreased from 1 to 0 for a reduction in the water saturation from 1.0 to 0.39 (Figure 4a). The relative permeability of CO₂ increased with the decrease in water saturation, but the increase rate of the relative permeability to CO₂ was much smaller, reaching only a value of approximately 0.1. For CO₂ treated limestone, the change in relative CO₂ permeability was insignificant (Figure 4b). However, the relative water permeability turned from a quadratic to a quasi-linear function of water saturation degree. Additionally, the maximum degree of CO₂ saturation increased from 0.61 to 0.66 in CO₂-treated limestone. We acknowledge that an even higher degree of CO₂ saturation could be achieved if the controllers with higher maximum flow rates are used.

The obtained relative permeability curves are fitted as power-law functions of the degree of saturation, similarly to the Brooks–Corey model [42].

$$k_{rw}={(S_e)}^{N_w}\mathrm{and}{k}_{rc}={(1-S_e)}^{N_c}$$

(12)

where, S_e is the saturation parameter from Equation (4), and N_w and N_c are the exponent coefficients for water and CO₂, respectively. Note that N_w value for Apulian limestone changes from 2.1 to 1.2 after CO₂ treatment (Figure 4).

4.3. Geomechanical Properties

Conventional triaxial tests were conducted on both pristine and CO₂ treated Apulian limestone and the results of the experiments conducted at σ_lat′ = 2.5 MPa are shown in Figure 5. Young’s modulus E decreased from 7.1 GPa to 4.5 GPa and also the deviatoric stress (=axial stress–lateral stress) at failure decreased from 17.1 MPa to 9.2 MPa after CO₂ treatment. Measurements of Poisson’s ratio with lateral LVDT displacement were not successful on treated specimens, so it was evaluated for specimens Calc-3 and Calc-4 from the ultrasonic wave velocity (“dynamic”) measurements. P- and S-wave velocities (c_p, c_s) measured before (2.55 km/s, 1.46 km/s) and after (2.38 km/s, 1.40 km/s) treatment show that Young’s modulus decreased by 20%, but Poisson’s ratio presents little changes due to CO₂ injection, so the constant value, ν = 0.25, was used in the numerical model (

Table 3. Properties of pristine and CO₂ treated Apulian limestone.

Property	Pristine Rock	CO2-Treated Rock
Permeability, k [m2]	9 × 10−15	5–6 × 10−15
Porosity, φ [−]	0.35	0.34
Relative water permeability, krw [−]	Sw2.1	Sw1.2
Relative CO2 permeability, krc [−]	Sc6	Sc5.5
Gas entry pressure, p0 [MPa]	0.02	0.02
van Genuchten shape parameter m [−]	0.42	0.42
Young’s modulus, E [GPa]	7.1	4.4
Poisson ratio, ν [−]	0.25	0.25
Cohesion, c′ [MPa]	5.6	3.0
Friction angle, ϕ′ [°]	21	14

). Obviously, the inhomogeneity of pore space distribution caused by injection may produce local changes in Poisson’s ratio that need to be assessed from local strain measurements. Undrained Poisson’s ratio ν_u was calculated from poroelastic relationship [38] to be 0.36. The bulk modulus K = 4.7 GPa for pristine rock and 3.0 GPa for treated limestone. K_s′ of pristine rock was measured to be 42.9 GPa [31]. Here, we assumed that the solid bulk properties of the rock did not change after treatment, so K_s′ remains the same. Additionally, since Apulian limestone is a monomineralic rock, it is assumed that K_s′ = K_s′′. The strength tests provided the cohesion of pristine rock as c′ = 5.6 MPa and the friction angle as φ′ = 21°. After CO₂ treatment, both the cohesion and friction angle decreased to c′ = 3.0 MPa and φ′ = 14°, respectively (Figure 6).

4.4. Numerical Results

The changes in Apulian limestone properties as a result of interaction with CO₂ affect the hydro-mechanical response of the reservoir-caprock system. Even though laboratory measurements were not performed at representative conditions, they still can be used for the demonstration of CO₂ injection effect on carbonate reservoirs, especially considering weak stress-dependence of Apulian limestone properties [31].

On the one hand, the CO₂ plume dynamics and pore pressure evolution were slightly affected by the skin effect that results from the local reduction in permeability occuring within the CO₂ plume. This permeability reduction around the injection well caused a higher pressure buildup that lead to a slightly steeper CO₂-brine interface at early times of injection (during the first few months). Nevertheless, since the permeability reduction was local, the effective permeability of the reservoir became equal to that of the intact rock in the long term [43]. Thus, pressure buildup eventually became the same as if there were no local permeability reduction around the injection well [44,45], leading to a practically identical CO₂ plume shape after 3 years of injection (Figure 7). The long-term pressure buildup at the injection well was 4.3 MPa. On the other hand, contrary to the transient effect of the change in the hydraulic properties of the reservoir within the CO₂ plume, the effect of the changes in the geomechanical properties is permanent.

Figure 8 shows the changes in reservoir and caprock stability, in terms of mobilized friction angle, with distance to the injection well. The mobilized friction angle is the angle of the tangent to the Mohr’s circle, considering that there is no cohesion. Rock stability was clearly affected by the changes in Apulian limestone stiffness within the CO₂ plume, which extended laterally for 150 m after 3 years of injection. These changes were caused by the limestone becoming softer while interacting with CO₂. As a result, the rock within the CO₂ plume expanded more in response to pressure buildup, than the rock outside the plume. However, the expansion of the rock within the CO₂ plume was highly constrained laterally by the stiffer rock around it. This constraint on deformation lead to a higher increase in the horizontal total stresses than in the case where the reservoir was homogeneous. Additionally, to satisfy equilibrium of stresses, an increase in the vertical stress occurred within the zone affected by CO₂ plume, especially at the CO₂-brine interface, where shear stresses concentrate as a result of the stiffness contrast between the altered and intact rock. These stress changes caused a slight rotation of the stress tensor in the vicinity of the CO₂-brine interface. As for the effect on the stability within the reservoir, the stress changes that occurred within the altered rock inside the CO₂ plume caused a lower decrease in stability than when no changes in the geomechanical properties were accounted for.

The situation in the caprock was reversed, leading to a higher decrease in stability above the CO₂ plume when the changes in the geomechanical properties were accounted for. This is a consequence of the stress redistribution that occurred as a result of the increase in the vertical stress within the CO₂ plume to satisfy stress equilibrium. Since the overburden is constant, the increase in the vertical stress inside the CO₂ plume caused a decrease in the horizontal stresses outside it. This geomechanical response is analogous to the one that takes place when cooling occurs around the injection well, but with the opposite sign [29].

The described stress changes can be represented by Mohr’s circles (Figure 9). In the reservoir (Figure 9a), the initial stress state is far from failure conditions. This state of stress is displaced towards the left during injection as a result of pressure buildup. However, the Mohr’s circle also experiences a decrease in its size because of the poromechanical response of the rock (pore pressure increase), which induces an increase in the horizontal total stress. If the changes in Apulian limestone properties due interaction with CO₂ are also accounted for, the horizontal total stresses undergo a higher increase and the vertical total stress also increases. These changes slightly shift the Mohr’s circle to the right and reduce its size, leading to a lower decrease in stability. However, interaction with CO₂ also decreases the strength of the limestone. As a result, the failure envelope of the altered limestone approaches the Mohr’s circle, which may lead to failure conditions depending on the initial stress state and induced pressure buildup.

Considering the caprock (Figure 9b), the pore pressure slightly dropped as a result of the caprock deformation induced by the expansion of the reservoir, displacing the Mohr’s circle to the right. The expansion of the reservoir caused an increase in the volumetric strain of the caprock, and since the caprock permeability was extremely low and fluid flow was negligible, the fluid within the pores of the caprock was accommodated in a larger volume, which resulted in a slight pressure drop [46]. This phenomenon is known as the reverse-water level fluctuation [47]. Additionally, the horizontal total stresses decreased in the caprock, leading to an increase in the size of the Mohr’s circle. As a result, caprock stability slightly decreased but not dramatically, since the strength of the caprock is not affected due to the inability of CO₂ to penetrate into it at considered overpressures [25].

5. Discussion

In this study, comprehensive experimental testing was conducted to assess hydraulic, poroelastic, and failure properties of Apulian limestone (calcarenite). In particular, relative permeability considering two-phase flow of water and CO₂ was measured. For all these measurements, the experimental procedures were performed for both pristine and CO₂ treated limestone to evaluate the influence of CO₂ injection on mechanical and hydraulic properties. Given the low strength of the material, it is less likely to be chosen as the host formation for deep geological storage. This study can be seen, though, as a demonstration of a strong effect of CO₂ injection on carbonate-rich rock. Low shear strength, almost pure calcite framework, and large specific surface area of the pores allow for quick (within a few days) observations of the deterioration in rock properties. The choice of boundary conditions for the tests was dictated by linearity of material response within the elastic range, so high pressures were avoided.

Pure deionized water was used to saturate the specimens and, in general, its use can trigger chemical reactions and affect measurements of permeability and drained properties [48]. Here, the saturation of specimens with water was performed for at least 2–3 days and this period of time has been observed to be enough to establish chemical equilibrium between the pore fluid and carbonate rock [48]. This observation is confirmed by the constant values of rock permeability obtained during the repetitive measurements. Saline water that would represent the in-situ fluid for deep carbonate aquifers was not used because possible effects of salt precipitation and evaporation are involved and could not be captured by the model, even though we recognize that these effects may influence the evolution of rock’s petrophysical properties.

CO₂ injection produced change in mean porosity within 1%, indicating that the mass balance was fairly followed in the experiment. Some dissolved calcite may remain in an aqueous state [49], and may have induced 1% error to the total porosity. Therefore, mean porosity of the specimens can be considered to be practically constant after CO₂ treatment, but permeability decreased by a factor of two as a result of CO₂–rock interaction. Luquot and Gouze [5] observed that CO₂-rich brine reacts with calcite, dissolving it and leading to an increase in permeability, especially near an injection well, while the macroscopic porosity was just moderately affected. It should be noted that in this study, the CO₂ treatment procedure was conducted by establishing an undrained condition, whereas Luquot and Gouze [5] continuously injected brine with dissolved CO₂. This means that here, CO₂ was injected through the upstream, but during the CO₂ treatment process, it did not flow throughout to the downstream pump basically being trapped in the specimen. Porosity measurements for the upstream and downstream part of the specimen differed, showing a porosity increase upstream and decrease downstream. This difference suggests that calcite dissolution occurred upstream, and precipitation of carbonates took place downstream, where it was undrained. In addition to this qualitative analysis, a further detailed study will be conducted in the future to identify the dissolution/precipitation patterns.

CO₂ treatment of Apulian limestone causes changes in the relative permeability. The main change is that the exponent of the relative permeability to water varies from quadratic to quasi-linear after CO₂ treatment. This implies that for a given saturation degree, the relative permeability to water becomes higher after CO₂ treatment. This effect is considered to have implications for long-term CO₂ injection [48] and highlights that predictive simulations of industrial-scale CO₂ storage should incorporate the change in relative permeability.

Drained conventional triaxial compression tests showed that CO₂ treatment tends to decrease the strength of Apulian limestone. The strength parameters decrease significantly (cohesion by a factor of 2, friction angle by a factor of 1.5), highlighting the importance of considering these chemo-mechanical changes when evaluating the stability of the reservoir. In addition, changes in the stress–strain curve indicate that the CO₂ treatment makes carbonate rock a more ductile material compared to pristine limestone. Therefore, for low-stress conditions, more deformation may be expected for post-treated rock.

These changes in hydro-mechanical properties induced by geochemical reactions affect the response of the reservoir-caprock system to CO₂ injection. Simulation results show that the portion of the reservoir that has been affected by CO₂–rock interactions alter both the two-phase flow dynamics and the geomechanical response of the rock. While the changes in the hydraulic properties are transient, the geomechanical response is permanent. The stiffness contrast between the pristine and CO₂ treated portion of the reservoir causes differential deformation that results in stress redistribution that improves stability in the reservoir, but worsens it in the caprock, in comparison with the case in which no changes in the geomechanical properties are considered. Nevertheless, the changes in stability are minor and limited to a few degrees in the mobilized friction coefficient. What may really compromise reservoir stability is the reduction in the limestone strength after being exposed to CO₂. Geochemical reactions bring the failure envelope close to the effective stress state, which could induce shear failure depending on the initial stress state and injection conditions, i.e., injection pressure and temperature. If shear failure occurs, shear slip of fractures or creation of new fractures may occur, inducing microseismic events. If failure is local, around the injection well, sheared fractures will enhance injectivity. Such enhancement would be beneficial for storage operations, especially if caprock stability is not compromised, as it is the case of the modeled scenario. These simulation results show the importance of accounting for chemo-mechanical couplings to assess caprock integrity and the geomechanical response of carbonate storage formations to CO₂ injection.

6. Conclusions

We have measured in the laboratory the effect of geochemical reactions induced by CO₂ injection on hydraulic and geomechanical properties of water-saturated Apulian limestone (calcarenite) and evaluated the implications of these property changes at the field scale through numerical simulations. CO₂–rock interactions cause calcite dissolution where CO₂ injection occurs, i.e., upstream of the specimens, but leads to carbonate precipitation downstream, which has been set as undrained. This dissolution/precipitation pattern resulted in a slight porosity decrease, but a permeability reduction by a factor of two. The relative permeability curves were also affected, especially the one of water, which changed from being quadratic to being quasi-linear with the water saturation degree. CO₂ treatment induced a reduction in the stiffness and strength of the limestone. Accounting for these property changes in numerical simulations at the industrial scale leads to stress redistribution within the CO₂ plume altered rock. This stress redistribution reduces caprock stability comparing with the case in which rock properties are considered to remain unaltered by CO₂–rock interaction.