Thermo-hydro-mechanical modeling of carbon dioxide injection for enhanced gas-recovery (CO₂-EGR): a benchmarking study for code comparison

The THM-coupled simulation is performed with two different numerical simulators, the integrated code TOUGH2/EOS7C-FLAC3D, which is based on the TOUGH-FLAC simulator (Rutqvist et al. 2002), and OpenGeoSys (OGS) (Wang et al. 2011; Watanabe et al. 2012; Kolditz et al. 2012a, b).

In TOUGH-FLAC, the gas mixing process is simulated using the TOUGH2 EOS-module EOS7C (Fig. 1). EOS7C is an EOS-module which considers five mass components, namely water, brine, CO₂, tracer, and NCG (non-condensable gas, in this case CH₄). Cubic equations of state according to Peng–Robinson are adopted to calculate the density, enthalpy, and viscosity of the real gas mixture of the system H₂O–CO₂–CH₄. The partition of CO₂ and CH₄ between aqueous and gas phases is calculated using a very accurate chemical equilibrium approach. Darcy’s law for multiphase flow is used to model the flow and transport of gas and aqueous phase mixtures taking into consideration of the Fick’s diffusion law (Oldenburg et al. 2004).

The coupling concept in Rutqvist et al. (2002) is adopted to consider the geomechanical effects of the CO₂-EGR and CO₂-storage processes (Fig. 2). In every time step, TOUGH2 variables, including pressure and saturation are transferred to FLAC3D to calculate the deformation and stress redistribution in the rock formations. The new stresses and deformations of each element are then transferred back to TOUGH2 to calculate the corresponding changes of hydraulic properties. The concrete mathematical description of the used coupling concept is found in Rutqvist et al. (2002).

The general equation for balance of fluid or transported species mass isfor the porosity ϕ, bulk fluid density ρ, fluid velocity vector u, the solid mass fraction of the desired species X _α, a mass source term Q, and the diffusive/dispersive flux i _α. Utilizing Darcy’s law, and taking into account that in deformation problems the fluid velocity must be considered relative to the solid, we writefor the intrinsic permeability tensor k, the dynamic viscosity μ, and for velocity relative to the solid u _r, and the solid velocity u _s.

Both simulators are fit with the same constitutive laws regarding porosity and permeability change for these simulations. Hydraulic properties are correlated with the effective mean stress using Eqs. 11 and 12 and parameters from Rutqvist and Tsang (2002): where

In order to consider the influence of plastic dilatancy \( \varepsilon_{\text{vol}}^{\text{p}} \) on the permeability, an extra term is multiplied by the original function (Gou 2011)

A generic 3D simulation model (20,000 × 3,000 × 100 m) was generated. For TOUGH-FLAC, this was discretized into 3,344 structured cells (Fig. 3). For the OGS finite element solution, an unstructured mesh was generated that attempted to utilize nearly the same number of cells as the finite difference solution, while maintaining reasonable element aspect ratios and sufficient element quality. The result is a mesh with 8,078 elements in precisely the same geometric layout as the TOUGH-FLAC solution (Fig. 4). The whole model includes four horizontal rock layers from top to bottom, namely overburden (1,200 m Buntsandstein), caprock (100 m claystone), gas reservoir (200 m sandstone), and base rock (1,500 m vulcanite). Two wellbores for production and injection are 1,200 m apart in the horizontal direction and are drilled to a depth of 1,300 m, the upper surface of the reservoir layer.

All rock layers are assumed as elasto-plastic materials in the TOUGH-FLAC simulations (using Mohr–Coulomb model) and as elastic materials in the OGS simulations. The parameters are listed in Table 1. The initial porosity and permeability under the effective primary stresses are calculated after Eqs. 1 and 2 using the effective primary mean stress, the zero stress porosity, and permeability. Since the effective primary mean stress in each rock layer is not constant and is a function of depth, the porosity and permeability of the reservoir formation vary in the range of 0.0928–0.0935 and 1.2–1.4 D, respectively.

The whole simulation consisted of 30-year production, 5-year CO₂-EGR, and 1-year CO₂-storage. In TOUGH-FLAC, the model was first initialized with a hydrostatic pore pressure distribution while the reservoir, consisting only of single phase gas, was given an initial pore pressure of 13 MPa and temperature of 53 °C. In OGS, where simulations do not consider the presence of a water phase, the hydrostatic gradient was allowed to evolve naturally, by running the first several time steps without fluid or solid storage, from an initial uniform pressure of 13 MPa, which allows a nearly instantaneous development of pressure distribution. The overburden was considered to be fully water saturated and the remainder of the domain fully gas saturated. This allows pressure to evolve to the same hydrostatic value at the top of the caprock layer as for TOUGH-FLAC.

Then gas production of CH₄ was performed from both wells with a fixed bottomhole pressure of 5 MPa for 30 years. After the 30-year production, CO₂ was injected into the left well at a rate of 31,500 tons/year, while the well on the right was constantly kept in production of the gas at the same bottomhole pressure (this occurs from year 30 to 35). A CO₂-storage phase was then initiated at the 35-year mark in which the right well was sealed and CO₂ further injected into the left well at a rate of 315,000 tons/year (occurring from year 35 to 40).

There are several fundamental differences between the TOUGH-FLAC and OGS simulators, some of which will have a small impact on the results presented below. First, OGS is a fully finite element (FEM) simulator, while TOUGH2 is an integral finite difference scheme. This will lead to slight differences in the numerical dispersion of the simulators. TOUGH2 is fully upwinded with respect to mass transport, while for these simulations OGS utilizes a standard Galerkin FEM procedure (Park et al. 2011), with dispersion introduced via coefficients of dispersion designed to maintain the Peclet number near 2.0, and thus produce dispersive characteristics similar to an upwinded scheme. Both codes include molecular diffusion of gasses (utilizing a binary gas molecular diffusion calculation). Coupling between the fluid and solid equations occurs at the gauss point level within the Gaussian integration scheme of OGS, while in TOUGH-FLAC, element center properties of TOUGH2 are interpolated to nodal values for the stress calculation in FLAC.

Second, OGS here utilizes single-phase fractional mass transport of gaseous species (see the above equation system) in a monolithic coupling with the fluid transport equation and TOUGH2 uses two-phase fractional transport in a staggered Newton–Raphson scheme with the flow equation. To maintain a similar pressure evolution, the overburden fluid is assumed to be water (as for TOUGH-FLAC). Because some CO₂ is expected to penetrate the base rock, it is not possible to assume water saturation here, and instead all areas below the overburden are initially gas saturated. This will lead to some differences in the way that pressure from the base rock serves as replenishment to the under pressured reservoir.

After 30-year gas production, the reservoir pressure was reduced from 13 to 5 MPa in both simulators. The total produced gas was roughly 2,260,000 tons (3,183 MMSCM) in the production element of TOUGH-FLAC and lower value of 1,440,000 tons at the production node of OGS. This discrepancy may be due to the presence of a water phase in the base rock of the TOUGH-FLAC solution, which would serve as a replenishment of pressure that behaves differently in the OGS solution, but this will require further investigation. These values are comparable with the analytically estimated gas production according to the thermodynamic condition and stress state. The total gas recovery rate after 30-year production was estimated at 63.5 %.

Figure 5 shows the time-dependent gas production rate and CO₂ mass fraction in the produced gas during the CO₂ injection phase for the TOUGH-FLAC solution and Fig. 6 for the OGS solution. Stationary production was reached after 1 year and the first CO₂ breakthrough occurred 1.5 years after the start of CO₂-injection in both simulators. After 5 years of injection, CO₂ mass fraction in the produced gas rose to 8 % and CO₂-EGR was stopped. The OGS solution ceased EGR at the same time despite having much larger CO₂ mass fractions in the produced fluid. The injected CO₂ was 158,000 tons (81 MMSCM) identically in both simulators (both utilized the same injection rate) while total produced gas during the 5-year CO₂-EGR was 49,200 tons (69 MMSCM) in TOUGH-FLAC and nearly double this value (102,000 tons) in OGS (see also Figs. 5, 6). This value is much larger than 158 tons (0.2 MMSCM), which was simulated with neither changes of bottom hole pressure nor CO₂-injection. For TOUGH-FLAC the volume ratio CO₂/CH₄ (SCM/SCM) was about 1.16 and the gas recovery rate increased by 1.4 %. But these results were based on the fact that the injector and producer are 1,200 m apart. A larger distance between them will delay the CO₂ breakthrough, which makes the EGR effect better. With a well distance of 5 km the recovery rate increase is estimated at 5.83 %.

Figure 6 shows time-dependent production for the OGS solution. Like TOUGH-FLAC, steady production occurs after approximately 1 year at a similar magnitude, but higher value of 0.0056 kg/s/m. Carbon dioxide breakthrough occurs at nearly the same time of 1.5 years, but the arrival front is much steeper and obtains a higher fraction of CO₂ in the produced fluid.

Figure 7a–d show the CO₂ mass fraction in the gas mixture within the 5-year CO₂-EGR (Fig. 7a–c) and at the end of CO₂-storage (Fig. 7d) for TOUGH-FLAC. Figure 8 is an identical display for OGS. It is clearly seen how CO₂ moves down from the injection point due to its large density in comparison with CH₄ at the same thermodynamic conditions.

In the TOUGH-FLAC solution during the whole CO₂-EGR process the reservoir pressure remained unchanged (5 MPa). Under this reservoir pressure, there is still no obvious CO₂–CH₄ interface in the gas mixture. At the end of 5-year CO₂-EGR the maximal CO₂ mass fraction in the gas mixture reaches roughly 80 % (only near the injection well). With further CO₂-injection during CO₂-storage the reservoir pressure increased from 5 to 8 MPa. Most of the reservoir is occupied by CO₂ (CO₂ maximal fraction reached 99 %). Most of CH₄ is located directly under the caprock due to buoyancy effect and CO₂ at the bottom.

For the OGS solution, behavior is quite similar during the EGR and storage phases. During EGR, the reservoir pressure remains essentially unchanged at 5 MPa and CO₂ mass fractions of roughly 80 % are achieved near injection. During CO₂ storage the reservoir pressure increases from 5 to 7.9 MPa, or nearly the same as for TOUGH-FLAC. Much of the reservoir is completely saturated with CO₂ at the end of the storage phase.

We now proceed to examine in more detail the mechanical consequences of injection. Figure 9 (TOUGH_FLAC) and Fig. 10 (OGS) show stress changes along the vertical line from the injection point at end of the CO₂-storage process, resulting from the reservoir pressure increase from 5 to 8 MPa. The total vertical stress slightly increased (<0.1 MPa), while the effective vertical stress decreased by 2 MPa due to the reservoir pressure increase of 3 MPa. However, the horizontal stress had the opposite tendency. The horizontal effective stress slightly changed due to a Biot’s coefficient (α = 0.645), while the total stress increased by 1.7 MPa. There are only small differences here between the two simulators. In the TOUGH-FLAC simulation a Mohr–Coulomb model was adopted for elasto-plasticity, but during the whole process no plastic deformation was observed, i.e., the reservoir and caprock behaved elastically. The OGS solution was conducted under fully elastic conditions. There is an analytical solution for the stress change under this condition according to Hou et al. (2009): where

The calculated horizontal stress change in the reservoir (ca. 1.65 MPa after Eq. 14) agrees well with the numerically simulated result (ca. 1.7 MPa). The maximal change (~0.3 MPa) of the horizontal stresses in caprock is very small in comparison with that in the reservoir. That means the caprock integrity is not influenced at all. Furthermore, neither pore pressure nor stress in overburden changes during the 15-year CO₂-injection.

Figure 11 shows the stress paths at the injection point for three different primary stress regimes.

After 45 years, none of the stress paths had reached the strength of the reservoir rock, which has an internal friction angle of 29° and cohesion of 11.9 MPa. It is clearly seen that the stress states for the whole process, namely 30 years’ production, 5 years’ CO₂-EGR and 10 years’ CO₂-storage, in all three different primary stress regimes are far away from the reservoir rock strength, although the used strength of the reservoir rock is much lower than the strength of the Northern German sandstone, e.g., in Hou et al. (2009). Since the reservoir formation is still in the range of elastic condition, the further stress path till the plastic state could be quantitatively predicted according to Eqs. 14 and 15. The predicted stress paths are presented in Fig. 11. The maximal and minimal effective stress at the end of production phase (t = 30 year) for both extensional and isotropic primary stress regimes are in the vertical and horizontal direction, respectively, and the in situ effective stress factor \( \left[ {\Updelta \sigma_{ \min }^{\prime } /\Updelta \sigma_{ \max }^{\prime } = \nu /\left( { 1- \nu } \right)} \right] \) is smaller than one \( \left( {\sigma_{ \max }^{\prime } = \sigma_{\text{z}}^{\prime } ,\sigma_{ \min }^{\prime } = \sigma_{\text{h}}^{\prime } } \right) \). So \( \sigma_{ \max }^{\prime } \) decreases faster than \( \sigma_{ \max }^{\prime } \), which cause the stress paths move directly toward the isotropic effective stress line with further pressure rise (but never exceed it because \( \sigma_{ \max }^{\prime } \ge \sigma_{ \min }^{\prime } \)). When it reaches this isotropic line, the directions of the maximal and minimal effective stress will switch \( \sigma_{ \max }^{\prime } = \sigma_{\text{H/h}}^{\prime } ,\sigma_{ \min }^{\prime } = \sigma_{\text{z}}^{\prime } \). The corresponding pore pressure increases are listed in Table 2. After that both extensional and isotropic primary stress regimes switch to the compressional regime and the corresponding stress paths will move away from that isotropic line and toward the \( \sigma_{ 1}^{\prime } \) axes. With further injection the stress paths would cross the \( \sigma_{1}^{\prime } \) axes at first but not the rock strength line. According to this analysis tension failure in the reservoir would occur (if we assume the rock tension strength is zero), but shear failure will never happen even with further CO₂-injection.

As scenario study a worse case is analyzed, namely the reservoir is assumed as naturally fractured (although such sandstone formation does not really exist in Germany). As a conservative assumption, the strength of such fractured reservoir formations has just a small internal friction angle of 20° and zero cohesion (Fig. 10). It reveals that potential fracture slip in such reservoirs could occur for all of the three primary stress regimes. The sequence of three stress paths reaching the strength of the fractured reservoir formation is compressional, isotropic, extensional, and the corresponding pore pressure rises are 13.26, 28.34, and 33.18 MPa (Table 3). But the maximal storage pressure is also restricted by the barrier integrity criteria. Here the allowed storage pressure is calculated with simultaneous consideration of both tensile fracture and penetration criteria according to Hou et al. (2009), namely where

As shown in Table 3 the possible reservoir pressure based on the penetration criterion is 17 MPa for all three primary stress regimes. The minimal horizontal stresses in caprock bottom are 43, 28, and 22 MPa, respectively. So the maximal allowed storage pressure for CO₂-storage is determined by the penetration criterion with consideration of a safety factor, e.g., 1.25, namely 13.6 MPa. With Consideration of the 3 MPa pressure rise due to 3.15 million ton CO₂-injection, another 5.88 million ton CO₂ could be injected.

Figure 12 (TOUGH-FLAC) and Fig. 13 (OGS) show the vertical displacements of selected points under and above the injection point. P1 locates at the ground surface and P2, P3, and P4 at the interface between overburden, caprock, reservoir, and base rock. The ground surface and caprock top (P1 and P2) have similar displacement (5 cm downward in TOUGH-FLAC and 6.5 cm in OGS) resulting from the gas production and recover upward (nearly 2 cm recovery in both simulators) due to CO₂-injection. The reservoir top (P3) has the similar displacement tendency, while the reservoir bottom (P4) moves downward during the CO₂-EGR and CO₂-injection phases and reaches 0.2 cm at the end of 45 years in TOUGH-FLAC as water is depleted in the base rock towards the under pressured reservoir. In OGS, this value is much larger (1.3 cm), which is as expected for a gas saturated base rock that is more compressive than one that is water saturated, and requires a greater volume of gas depletion to recover reservoir pressure than is the case for water.

The compaction of the rock formation could be calculated from the displacement difference between P1–P2, P2–P3, and P3–P4, e.g., the reservoir has a compaction Δε _z (P3–P4) of 0.023 % in TOUGH-FLAC and 0.0236 % in OGS at the end of the production and after 10 years’ CO₂-injection 0.0143 % in TOUGH-FLAC and 0.015 % in OGS. This value could be analytically calculated according to Hou et al. (2009):

The calculated reservoir compactions after Eq. 17 are correspondingly about 0.023 and 0.0146 % which are comparable with the numerically simulated values.