Modeling Geothermal Heat Extraction-Induced Potential Fault Activation by Developing an FDEM-Based THM Coupling Scheme

Abstract

One controversial issue associated with enhanced geothermal systems is induced seismicity, which limits their broader application. As induced seismicity has a strong correlation with the activation of pre-existing faults, understanding processes controlling the potential fault activation during geothermal heat extraction is of critical importance. In this study, a coupled thermal–hydraulic–mechanical (THM) scheme is formulated based on the combined finite–discrete-element method to investigate the triggering mechanisms of potential fault activation during geothermal heat extraction. The developed thermal and hydraulic solving frameworks account for the heat transfer of various kinds and fracture fluid migration in the rock mass, respectively. The fully coupled THM scheme is established by pairwise coupling between thermal, hydraulic, and mechanical solving frameworks, and is then progressively verified against analytical solutions by five validation examples. Finally, cold-fluid injection-induced potential activation of a fault during geothermal heat extraction is investigated. The results demonstrate that the gradual aseismic opening and slip of the fault at low injection pressure are caused by the thermal contraction-induced reduction of the imposed normal stress on the fault surface due to convective cooling. The thermally induced aseismic slip weakens the fault and contributes to triggering sudden (unstable) fault slips. The convective thermal transfer coefficient is found to greatly affect the onset time of the fault aseismic slip. The effects of the injection pressure and temperature as well as the in-situ stress field are also discussed. The findings justify thermal effects in controlling the potential fault slip behavior and illuminate the triggering mechanism of unexpected seismic activities during geothermal heat extraction even at injection pressure below the safety threshold value.

Highlights

• A fully coupled thermal–hydraulic–mechanical (THM) scheme is formulated based on the combined finite–discrete-element method (FDEM) to investigate the potential fault activation during geothermal heat extraction.

• Fault aseismic slip caused by thermal contraction due to convective cooling at low injection pressure contributes to triggering unstable fault slip.

• The convective thermal transfer coefficient greatly affects the onset time of the fault aseismic slip.

• The injection pressure affects the time at which the fault aseismic slip becomes stable and the in-situ stress heavily affects the aseismic slip amount.

• Thermal effects are justified in triggering seismic activities during geothermal heat extraction at injection pressure below the safety threshold.

Appendix: Basic principles of FDEM

In FDEM, the problem domain is discretized with a mesh of three-node linear elastic triangular finite elements, and four-node joint elements are inserted in between adjacent triangular element pairs. An explicit time integration method is applied to solve the equation of motion of the discretized system. The governing equation (Munjiza 2004) is expressed as

$${\mathbf{M\ddot{x}}} + {\mathbf{C\dot{x}}} + {\mathbf{F}}_{{\text{int}}} ({\mathbf{x}}) - {\mathbf{F}}_{{{\text{ext}}}} ({\mathbf{x}}) - {\mathbf{F}}_{{\text{c}}} ({\mathbf{x}}) = 0,$$

(28)

where x is the nodal displacement vector; M and C are the lumped system mass and damping diagonal matrices, respectively; F_int, F_ext, and F_c represent the vectors of the internal resisting forces, the applied external forces, and the contact forces, respectively.

Dynamic relaxation is used in the FDEM for quasi-static problems to avoid the dynamic effects and achieve a state of rest in a relatively short time (Munjiza 2004). Viscous damping proportional to stiffness is applied to the triangular finite elements as an energy dissipation mechanism, and the viscous forces are calculated using the rate of deformation tensor (Mahabadi et al. 2012). Therefore, no dynamic effects are induced, and the energy dissipation due to the non-linear behaviors (e.g., strain softening, the fracturing of the material, and friction between discrete elements) leads to the state of rest reached. Numerical viscous damping is expressed as

$${\mathbf{C}} = \mu {\mathbf{I}},$$

(29)

where I is the identity matrix and $\mu \approx 2h\sqrt {E\rho }$ is the numerical viscous damping coefficient, where h is the finite-element size, E is Young’s modulus, and ρ is the density.

The internal resisting forces account for the elastic reaction forces resulting from the elastic deformation of the constant-strain triangular elements, F_e, and inter-element bonding forces due to the deformation of the joint elements, F_b, respectively. The contact forces are computed between contacting triangular element pairs. In the normal direction, the repulsive forces are calculated with the body impenetrability scheme using a penalty method (Munjiza and Andrews 2000): the contacting pairs penetrate each other and result in the distributed reaction forces depending on the size and shape of the overlapping area. In the tangential direction, the frictional forces are captured by a Coulomb-type friction law (Mahabadi et al. 2012).

1.1 Material Deformation and Fracturing

The progressive deformation and fracturing process of the rock material is modeled by an intrinsic cohesive zone model (Munjiza et al. 1999). With this approach, the material strain is assumed to localize in the narrow cohesive zone (fracture process zone, FPZ) upon exceeding the material strength in tension, shear, or combination thereof. Therefore, the response of the triangular elements is assumed to be linearly elastic and the strain-softening behavior developing in the FPZ, which ultimately leads to the material fracturing, is simulated by joint elements.

The constitutive behavior of a joint element is defined as the variation of the bonding stresses, σ and τ, between the edges of the triangular finite-element pair in response to the relative opening, o, and slip, s, of the edges of the element pair, in the normal and tangential directions, respectively (Fig. 1a). In tension (mode I loading), the response of the joint element is governed by the tensile strength, f_t, and Mode I fracture energy, G_IC, while in shear (Mode II loading), the joint behavior depends on the peak shear strength, f_s, and Mode II fracture energy, G_IIC. The peak shear strength of the joint element is obtained by the Mohr–Coulomb criterion (Mahabadi et al. 2012) in the form of

$$f_{{\text{s}}} = c + \sigma_{{\text{n}}} \tan \phi_{i} ,$$

(30)

where c denotes the cohesion, σ_n is the normal stress acting on the joint element, and $\phi_{i}$ is the internal friction angle. The elliptical coupling relationship, as shown in Fig. 1b, between the joint opening and slip is used to account for the mixed Mode I–II loading condition. Upon breaking, the frictional resistance, f_r, is activated to act on the new discontinuity as

$$f_{{\text{r}}} = \sigma_{{\text{n}}} \tan \phi_{{\text{f}}} ,$$

(31)

where $\phi_{{\text{f}}}$ is the fracture friction angle (Fig. 20).

Fig. 20

Constitutive behavior of the joint elements: a normal (shear) bonding stress-joint opening under pure tensile/compressive loading (slip under pure shear loading) relationship; b elliptical coupling relationship between joint opening and slip for mixed-mode loading