TOUGH2Biot: A Coupled Thermal-Hydrodynamic-Mechanical Model for Geothermal Development

Transcription

1 GRC Transactions, Vol. 38, 2014 TOUGH2Biot: A Coupled Thermal-Hydrodynamic-Mechanical Model for Geothermal Development Hongwu Lei and Tianfu Xu Key Laboratory of Groundwater Resources and Environment, Ministry of Education, Jilin University, Changchun, China Keywords Geothermal development, coupled thermal-hydrodynamicmechanical processes (THM), Biot consolidation model, mechanical failure, induced fracturing, numerical simulation Abstract Geothermal development and exploitation involve coupled thermal-hydrodynamic-mechanical (THM) processes. A mechanical module based on the extended Biot consolidation model is developed and incorporated into the well-established thermal-hydrodynamic simulator TOUGH2, resulting in an integral numerical THM simulation program TOUGH2Biot. A finite element method is employed to discretize space for rock mechanical calculation and the Mohr-Coulomb failure criterion is used to determine if rock undergoes shear-slip failure. Mechanics is partly coupled with the thermal-hydrodynamic processes and gives feedback to flow through stress-dependent porosity and permeability. TOUGH2Biot is verified against an analytical solution for the 1D Terzaghi consolidation and cooling-induced subsidence. TOUGH- 2Biot has been applied to evaluate thermal, hydrodynamic and mechanical responses of geothermal exploitation at the Geysers geothermal field, California. The results demonstrate that change in effective stress due to temperature decrease is greater than that due to pressure decrease near the production. The most likely shear-slip occurs near the injection because of an increase in shear stress. The formations are compressed and the maximum vertical displacement is up to 0.6m after 40 years of production, half of which is contributed from temperature decline. At the same time, TOUGH2Biot is proved to have the capability of analyzing change in pressure and temperature, displacement, stress and potential shear-slip failure for geothermal exploitation. Nomenclature M mass or energy accumulation [kg/m 3 or J/m 3 ] F flux of mass or energy of component [kg/(m 2 s)] ϕ porosity [-] S β saturation of phase β [-] ρ R density of rock grain [kg/m 3 ] X β mass fraction of componentk in phase β [-] C R specific heat of rock grain [J/(kg C)] T temperature [ C] u β internal energy of phase β [J/kg] K bulk modulus [Pa] ν Poisson ratio [-] β Τ Thermal expansion [1/K] w displacement, l l= xyz,, [m] σ l effective stress l= xyz,, [Pa] τ l shear stress l = xy, yz, zx [Pa] ε l normal strain l= xyz,, [-] γ l shear strain l = xy, yz, zx [-] γ sat Rock weight with saturated fluid [kg/(m 2 s2 )] c cohesion [Pa] k permeability [m 2 ] k rβ relative permeability of phase β [-] μ β viscosity of phase β [Pa s] P pressure [Pa] J β mass diffusion of component in phase β [kg/(m 2 s)] λ average thermal conductivity of grid [W/(K m)] h β specific enthalpy of phase β [J/kg] β phase components, = w,i,g are water, salt and gas, respectively q sink/source G shear modulus [Pa] φ internal friction angle [ ] ϕ 0 porosity at zero stress [-] ϕ r residual porosity at infinite stress [-] k0 permeability at zero stress [m 2 ] a,b experimental coefficient for change of ϕ and k R Residual [kg/m 3 or J/m 3 ] A area [m 2 ] V Volume [m 3 ] t time [s] KB y stiffness matrix, i=1,2,3, j=1,2,3,4,5 305

2 1. Introduction With the rapid development of the economy, the demand of energy is drastically increasing. Nowadays, the fossil fuels such as coal, oil and natural gas are the dominant energy resources. However, they are non-renewable and a potential threat for global climate. Therefore, low-carbon, renewable and economical alternative energies are required, the geothermal resource is one of them. Hydraulic fracturing for enhanced geothermal system (EGS) and long-term geothermal exploitation may result in seismicity or microseismicity and/or land subsidence (Evans et al., 2005; Majer et al., 2007; Deichmann et al., 2009; Hole et al., 2007; Vasco et al., 2013). All of those involve coupled thermal-hydrodynamicmechanical processes. Rutqvist and Oldenburg (2008) used TOUGH2-FLAC to analyze relative contributions to the cause and mechanism of injection-induced micro-earthquakes (MEQs) at the Geysers geothermal field. Their results show that cooling and associated thermal-elastic shrinkage of the rock around the injected well is the most important cause for injection-induced MEQs. Koh et al. (2011) presented a geothermal reservoir model coupled with fracture geomechanical module to investigate the long term thermo-poroelastic effects of cold water injection into naturally fractured geothermal reservoirs, indicating that tensile thermal stress normal to the fracture surfaces are induced as heat is extracted from hot reservoir rock by pervading cold fluid. Simone et al. (2013) carried out numerical simulation using THM simulator CODE_BRIGHT to study mechanical stability of geothermal reservoirs during cold water injection, showing that thermal effects induce a significant perturbation on the stress in the intact rock affected by the temperature drop and is likely to trigger induced seismicity near the injection well. Based on average Navier equation, a novel mechanical model is incorporated into TOUGH2 and a THM simulator TOUGH2-EGS is developed and applied to geothermal exploitation (Hu et al., 2013). This paper will first present a general coupled THM model, and then link the developed mechanical module with the existing TH simulator TOUGH2. Two sample problems are employed to verify the reliability of our THM simulator. Finally, this simulator is applied to analyze the THM response during the long term geothermal exploitation. 2. Mathematical and Numerical Models 2.1. Mathematical Model for Coupled Thermal and Hydrodynamic Processes Coupled thermal and hydrodynamic processes are of importance for geothermal development. The solution of coupled thermal-hydrodynamic processes in our simulator is obtained using TOUGH2 simulator, which solves the partial difference equations of pressures, temperature, saturation, and mass fraction of each component based on mass and energy conservation. The modular design is implemented in TOUGH2 and an EOS3 module is chosen in our research due 306 to their wide application to geothermal exploitation (Pruess et al., 1999; Croucher and O Sullivan, 2008; Gunnarsson et al., 2011; Pearson et al., 2014). The equation of state (EOS) describes the property of water, rock and gas (i.e., viscosity, density, enthalpy, relative permeability and so on) at different temperatures and pressures for the special flow systems. The general formulation for multiphase flow and heat convection and conduction processes is summarized in Table 1 (See Nomenclature for definition of all symbols used) Mathematical Model for Mechanical Process Model for Displacement and Stress and Strain The mechanics assumes that the rock can move as an elastic material and obey the generalized version of Hooke s law (Jaeger et al., 2007). Based on the stress equilibrium equations, compatibility equations, and the stress-strain relations, combining the effective stress law, we can obtain the commonly used Biot consolidation model (Biot, 1941) with displacements as the primary unknown variables. Considering temperature effect, a extended Biot mechanical model is expressed as in Table 2. Table 1. General mathematical model of coupled TH processes in TOUGH2. Description Multiphase Flow Process (H) Heat Convection and Conduction Process (T) Governing Equation d M dt dv = F ndγ + q dv V n Γ n Left term: M = β= A,G V n ϕs β ρ β X β, = w,i,g Right term: F β = k k ρ rβ A X µ β ( P β ρ β g) + J β, = w,i,g β d M +1 dt dv = F +1 ndγ + q +1 dv V n Γ n Left term: M +1 = (1 ϕ)ρ R C R T + Right term: F β +1 = λ T + Table 2. Three Dimensions extended Biot mechanical model. Description Displacement Stress and Strain β h β F β V n β= A,G ϕs β ρ β u β Governing Equation (Compressive stress and contractive strain are positive) G 2 w x G 1 2υ x ( w x x + w y y + w z z ) + P x + 3β K T T x = 0 G 2 w y G 1 2υ y ( w x x + w y y + w z z ) + P y + 3β K T T y = 0 G 2 w z G 1 2υ z ( w x x + w y y + w z z ) + P z + 3β K T T z = γ sat υ σ x = σ x P = 2G( 1 2υ ε + ε ) + 3β KT v x T υ σ y = σ y P = 2G( 1 2υ ε + ε ) + 3β KT v y T υ σ z = σ z P = 2G( 1 2υ ε + ε ) + 3β KT v z T τ yz = Gγ yz,τ zx = Gγ zx,τ xy = Gγ xy ε x = w x x,γ = ( w y yz z + w z y ) ε y = w y y,γ = ( w z zx x + w x z ) ε z = w z z,γ = ( w x xy y + w y x )

3 Rock Shear Failure Criterion Change in fluid pressure and temperature will result in rock local effective stress alteration, which probably induces shear slip along the existing fault plane. The most fundamental criterion for shear slip is derived from the effective stress law and the Mohr- Coulomb failure criterion, written as, τ = c +σ n tanϕ (1) The shear and normal stress acting on a given plane can be calculated from the normal and shear stresses as (Fig. 1a), τ = 1 2 (σ σ z x )sin(2θ) + τ xz cos(2θ) (2-1) σ n = σ x cos 2 (θ) +σ z sin 2 (θ) + 2τ xz sin(2θ) (2-2) Equations (2) can be also represented by Mohr s stress circle as been seen in Fig. 1b. This form is very convenient for shear-slip analysis. The figure indicates that decrease in effective stress (e.g. fluid injection) would shift the Mohr s stress circle to the left, which possibly induces slip failure. Under the conservative assumption that fracture of any orientation could exist anywhere in fractured media or homogeneous porous media, there are the two most possible planes of shear failure. Each of these two planes orients an angle of 45 φ /2 to the maximum principal stress. It also appears that the orientation of the maximum principal stress varies with time due to change in fluid pressure and temperature stress. To determine the most possible direction of shear slip, we should find the orientation and magnitude of the principal stress based on the calculated stress result of extended Biot mechanical model. The ratio of shear stress to effective normal stress (τ / σ n ) is commonly used to evaluate the potential shear-slip at the exiting plane. For porous media, the most possible failure direction depends on the local state of stress. We employ the intercept of tangent line of the Morh s stress circle with the same slope as the Mohr-Coulomb failure criterion line, due to its more consideration of the most possible shear-slip failure direction, given by, F c = σ σ 1 3 2cos(ϕ) σ > c failure +σ 1 3 tan(ϕ) = c equilibrium (3) 2 < c no failure Equation (3) indicates that a lager value of F c means more possibility of shear-slip. Specially, shear-slip will happen when (a) Local stress transform σ 1 > 3σ 3 with the cohesion c of zero and internal friction angle φ of 30, similar to that adopted by Rutqvist et al. (2002) Method for Coupling Mechanics with Thermal and Hydrodynamic Processes In general, approaches for coupled THM processes can be classified into two types: fully coupled and partly coupled. The approach using fully coupled iteration can obtain accurate solution, but the algorithm is time consuming and may not be robust. On the other hand, the approach of partly coupled iteration is robust at the expense of accuracy. TOUGH2Biot uses fully coupled iteration for thermal and hydrodynamic processes, which is inherited from TOUGH2. Stress and strain can be obtained by solving the extended Biot mechanical equations. Similar to the study of Rutqvist (Rutqvist et al., 2002; Rutqvist and Tsang, 2002), mechanical process gives the feedback to flow through the stress-depended porosity and permeability, which are described as, Coupled 1: P = S l P l + S g P g (4-1) Coupled 2:ϕ = ϕ r + (ϕ 0 ϕ r )exp(a σ M ) k = k 0 exp[b (φ / φ 0 1)] (4-2) where the average effective stress is σ M = (σ x +σ y +σ z ) / 3. As in Rutqvist et al. (2002), the experimental parameters a and c are /Pa and 22.2, respectively. Although there are five unknowns in the extended Biot mechanical model, only three need to be solved by mechanical governing equations, due to solving temperature and pressure by TOUGH2 before the mechanical calculation. (b) Mohr-Coulomb failure criterion Figure 2. Methodology of coupling thermalhydrodynamic-mechanical processes. Figure 1. Sketch map for effective stress state and shear-slip analysis Numerical Model for Coupled THM Processes The discrete equations of coupled THM processes consist of thermal, hydrodynamic, and mechanical discretization. The first two are fully coupled and are integrated into one coefficient matrix to solve by a linear solver. The integral finite-difference method and fully implicit finite-difference scheme, are used to discretize the continuous space and time, respectively (Pruess 307

4 et al., 1999). The discretization of mass and energy conservation equations can be written in residual form as follows, R,t+1 n = M,t+1 n M,t n Δt ( A V nm F,t+1 nm +V n q,t+1 n ) = 0 (5) n m = 1,!, NK The discretization of mechanics is carried out by the finite element method because of the difficulty of dealing with the cross term (i.e. x y, y z and ) in this model with x z finite-difference method. Based on the Galerkin finite element, the discretization of extended Biot model can be described as, KB i1 w x + KB i2 w y + KB i3 w z + KB i4 P + KB i5 T = F i i=1,2,3 (6) The variables of temperature T and pressure P are known from TOUGH2. Each node has three equations for solving the displacements in x, y and z directions. The boundary types include specified stress boundary and fixed displacement boundary. Specified stress boundary at the element face is assigned to all nodes which are on the face. Fixed displacement boundary can be dealt with by giving a large value to the diagonal element of corresponding node and the fixed displacement multiplied by this large value to the right term. To take into account the consistence of finite-difference and finite element methods, cuboids are chosen to discretize the continuous space. Fig. 3 demonstrates the calculated location for TOUGH2 and Biot. Pressure and temperature at the nodes Figure 3. Sketch map for finite element and finite difference mixed grid generation. and displacement at the cells are calculated by interpolation method Architecture of TOUG2Biot Program The Biot mechanical module is incorporated into TOUGH2 as an integral code. The flowchart is illustrated in Fig. 4. The initialization of mechanics includes reading grid geometry information (i.e. elements topology and node coordinates), reading mechanical property such as shear modulus, poisson ratio, and thermal expansion and so on, setting the boundary conditions, and calculating the initial state of stress and displacement for reference. In the internal time loop, fully coupled processes between heat and hydrodynamics and mechanics calculations are sequentially executed. Pressure and temperature are given to mechanical module for displacement calculation. At each time step of mechanical evaluation, stiffness matrix needs to update for consideration of Figure 4. Flowchart of TOUGH2Biot (dashed line denotes modification). the variable shear modulus at high stress. After stress calculation, stress-depended permeability and porosity are updated by Eq. (3-2). Failure analysis consists of two steps: finding the maximum and minimum principal stresses and then evaluating the value of F for determining the potential of the rock based on Eq. (3). c 3. Verification of TOUGH2Biot To verify the validity of the TOUGH2Biot code, two simple problems which have analytical solutions are employed D Consolidation in a Porous Permeable Column The first problem is the classical Terzaghi consolidation problem, which describes that excess pore pressure, induced by surface load, dissipates and results in consolidation settlement (Fig.5). The analytical solutions for excess pore pressure, surface displacement and total stress change can be found (Jaeger et al., 2007) as, u(z,t) = 4P π m= m=1 s(t) = PH (1 8 m= 1 E s π 2 1 sin( mπ z m 2 π 2 ( m 2H )e 4 )T V (7-1) m 2 m=1 e m 2 π 2 ( 4 )T V ) (7-2) 1 2ν Δσ x = Δσ y = 1 v ΔP Δσ = 0 z (7-3) where T V = ke s t / (µh 2 ) is time factor, and E s = K(1+ν) / [3(1 ν)] is compressibility modulus. Fig.6 and Fig.7 show that although there is a little difference at the bottom resulting from sequential calculation for coupled processes and effect of grid size, the numerical results are very close to the analytical solutions, which lead creditability to our simulator. 308

5 Parameters used in this consolidation model: Parameters Value Thickness (H) m 50 Permeability (k) m 2 1.0*10-14 Porosity (φ) 0.2 Viscosity (μ) kg m -1 s *10-3 Bulk modulus (K) Pa 8*10 7 Poisson ratio (ν) 0.20 Biot coefficient (α P ) 1.0 Surface load (P) *10 5 Pa 3.0 Figure 5. Conceptual model of 1-D settlement induced by consolidation and relative parameters. (a) Excess pore fluid pressure T(z,t) = T b + (T i T b )erf ( w( z = 0,t) = ( ) ( T T i b) ( ) α 1+ν T 1 ν (b) Vertical Displacement at the top of column z 4D T t ) (8-1) H H (1 erf 4D T t ) + exp( H 2 / ( 4D T t) ) 1 π / ( 4D T t) (8-2) 1 2ν Δσ x = Δσ y = 3β T K 1 ν ΔT Δσ = 0 (8-3) z 2 where erf = e η2 dη and D T = λ a π ρc is thermal diffusivity. Fig.9 and Fig.10 show that difference between numerical and analytical solutions is small. 4 Application to Geothermal Exploitation at the Geysers Geothermal Field Figure 6. Comparison of analytical and numerical solutions on pressure and vertical displacement. 4.1 Model Setup The Geysers is the site of the largest geothermal electricity generating operation in the world, and also one of the most seismically active regions due Figure 7..Comparison of analytical and numerical solutions on change in total horizontal stress D Heat Conduction in a Deformable Rock Column The second problem is about 1-D heat conduction in a deformable media, which is taken from Jaeger et al. (2007). It s a non-permeable column that undergoes uniaxial strain in the vertical direction only. The column is subjected to a constant temperature on the top (Fig.8). Only heat conduction takes place. Temperature profiles, vertical displacement with time and change in stress are given as, 309 Parameters used in 1-D heat conduction model Parameter Value Thickness (H) m 50 Permeability (k) m Density (ρ) kg/m Porosity (φ) 0.01 Heat conductivity (λ) W/(m*K) 2.34 Thermal expansion (αt) K *10-6 Specific heat capacity (C) J/(kg*K) 690 Bulk modulus (K) Pa 8*10 9 Poisson rate (ν) 0.20 Initial temperature (Ti) C 60 Boundary temperature (Tb) C 10 Figure 8. Conceptual model of 1D settlement induced by thermal conduction and relative parameters. to injection/projection activation in northern California (Majer and Peterson, 2007). It is a vapor dominated geothermal reservoir and sealed by a low a permeability caprock. In the mid 1990s, an injection at the location of 217 m away form production well is carried out to stabilize the reservoir steam pressure. Numerical investigations on injection-induced stress changes and their relative contributions to the causes and mechanisms of induced seismicity are performed by some researchers (Rutqvist and Oldenburg, 2008; Rutqvist, 2011). As the study of Rutqvist and Oldenburg (2008) and Hu et al. (2013), a 2D cross section model is constructed to evaluate the thermal, hydrodynamic and mechanical responses during the injection/production activity. Fig.11

6 Lei and Xu (a) Temperature (b) Vertical displacement at the top of column Figure 9. Comparison of analytical and numerical solutions on temperature and vertical displacement. Figure 10. Comparison of analytical and numerical solutions on change in horizontal stress. demonstrates the conceptual model, including permeability zone, initial and boundary conditions. The rock-mass bulk modulus and Poisson ratio is 3.0 GPa and 0.25, respectively. The linear thermal expansion coefficient is C Results According to Fig.12, we can see that the pressure declines in the whole reservoir and the maximum decrease is up to 2 MPa at the production well. Cold water injection causes formation of a wet zone extending to the production well. The temperature descent mainly occurs at the production/injection region with maximum decrease of more than 40 C near the production well resulting from a large pressure decline. Fig.13 shows comparison of the distribution and evolution of vertical displacement among InSAR and simulation results. The simulation result is consistent with observed InSAR data. The observed accumulation subsidence from InSAR is close to 0.6 m above the production well in 1999, with a half is contributed by (a) Figure 11. Half-symmetry model domain with hydraulic properties and boundary conditions (taken from Hu et al., 2013). temperature-induced shrinkage. The subsidence due to pressure decline gradually overwhelms that due to temperature decrease with the distance far away from the production/injection well region. The Figures also shows that our simulation result is similar to that by TOUGH2-FLAC (Rutqvist, 2011). (b) (c) Figure 12. Calculated profiles of (a) change of pressure, (b) liquid saturation and (c) change of temperature after 44 years of production/injection. 310

7 (a) (b) Figure 13. Comparison of simulated and InSAR evaluated vertical displacements from year 32 to 40 ( ) at The Geysers: (a) transient evolution above the production well and (b) total subsidence for the cross section. Fig.14a and b illustrates change in effective stress after 44 years of production/injection. The change in effective stress is caused by pressure depletion and cooling effect. It is obvious that vertical effective stress reduction due to temperature decrease is larger than that increase due to pressure depletion in the vicinity of the production well. Therefore, there is vertical effective stress change of up to 8MPa near the production well. However, change in vertical effective stress is positive due to dominant pressure depletion near the injection well. The horizontal effective stress increases above and below the production well, also due to pressure depletion. Fig.14c shows the potential shear-slip based on the method proposed by Rutqvist et al. (2002). Increase in vertical effective stress and decrease in horizontal stress near the injection well will enlarge stress Mohr s circle and increase shear stress, which induce the potential of shear-slip. Stress calculation from TOUGH2Biot is also close to that of TOUGH2-FLAC, which increases reliability of our simulator. Compared with TOUGH2-FLAC, mechanical calculation in TOUGH2Biot is embedded into each time step and external data exchange is not necessary. TOUGH2Biot is computationally more efficient. At the same time, TOUGH2Biot can be easily extended for considering complex coupled process problems in fractured media. For a large scale THM problem, because TOUGH2Biot is a integrated code, it can also be easily updated to parallel version on different platform taking advantage of high-performance computing. 5. Conclusions Based on extended Biot consolidation model and finite element method, we have developed a mechanical simulation module and incorporated it into the well-established thermalhydrodynamic simulator TOUGH2, resulting in an integral thermal-hydrodynamic-mechanical simulator TOUGH2Biot. Mechanical process is partly coupled with thermal-hydrodynamic processes, which means that mechanical calculation is performed after pressure and temperature calculation and then gives feedback to flow through stress-dependent porosity and permeability at one time step. (a) (b) (c) Figure 14. Calculated stress responses after 44 years of production/injection. Change in (a) horizontal effective stress (b) vertical effective stress and (c) potential for failure, Δσ m = Δσ 1 3Δσ

8 Two simple problems having analytical solution are employed to verify the THM simulator. One dimension Terzaghi consolidation problem shows that our simulator can analyze the coupled hydrodynamic-mechanical processes. The second problem - one dimension cooling induced displacement shows the capability of the simulator to solve the coupled thermal-mechanical processes. A long time of geothermal exploitation at the Geysers geothermal field results in decrease in pressure and temperature. Change in effective stress due to temperature decrease is greater than that due to pressure decrease near the production. The most likely shear-slip occurs near the injection because of an increase in shear stress. The formations are compressed and the maximum vertical displacement is up to 0.6 m after 40 years of production, half of which is contributed from temperature decline. Although our simulator TOUGH2Biot is an integral THM program for analyzing coupled thermal-hydrodynamic-mechanic processes in geothermal development and can be easily extended for different coupled problems, future improvements and development are needed, such as the plastic deformation and consideration of the complexity in fractured media (e.g. hydraulic fracturing in EGS systems). Acknowledgments This work is jointly supported by the National High Technology Research and Development Program of China (Grant 2012AA052801), China Geological Survey project (Grant ), doctoral interdisciplinary scientific research project of Jilin University (No. 2012JC014), and graduate innovation fund of Jilin University (No ). References Biot M.A., General theory of three-dimension consolidation. J. Appl. Phys., v. 12, p Croucher A.E. and M.J. O Sullivan, Application of the computer code TOUGH2 to the simulation of supercritical conditions in geothermal systems. Geothermics, v. 37(6), p Deichmann N. and D. Giardini, Earthquakes induced by the stimulation of an enhanced geothermal system below Basel (Switzerland). Seismological Research Letters, v. 80(5), p Evans K.F., H. Moriya, H. Niitsuma, R.H. Jones, W.S. Phillips, A. Genter, J. Sausse, R. Jung, and R. Baria, Microseismicity and permeability enhancement of hydrogeologic structures during massive fluid injectors into granite at 3 km depth at the Soultz HDR site. Geophysical Journal International, v. 160(1), p Gunnarsson G., A. Arnaldsson, and A.L. Oddsdottir, Model Simulations of the Hengill Area, Southwestern Iceland. Transp. Porous Med., v. 90, p Hole J.K., C.J. Bromley, N.F. Stevens, and G. Wadge, Subsidence in the geothermal fields of the Taupo Volcanic Zone, New Zealand from 1996 to 2005 measured by InSAR. Journal of Volcanology and Geothermal Research, v. 166(3-4), p Hu L.T., P.H. Winterfeld, P. Fakcharoenphol, and Y.S. Wu, A novel fully-coupled flow and geomechanics model in enhanced geothermal reservoirs. Journal of Petroleum Science and Engineering, v. 107, p Jaeger J.C., N.G.W. Cook, and R.W. Zimmerman, Fundamentals of rock mechanics. Blackwell, Forth edition. Koh J., H. Roshan, and S.S. Rahman, A numerical study on the long term thermo-poroelastic effects of cold water injection into naturally fractured geothermal reservoirs. Computers and Geotechnics, v. 38, p Majer E.L. and J.E. Peterson, The impact of injection on seismicity at The Geysers, California Geothermal Field. International Journal of Rock Mechanics and Mining Sciences, v. 44(8), p Majer E.L., R. Baria, and M. Stark, Induced seismicity associated with enhanced geothermal systems. Geothermics, v. 36(3), p Pearson S.C.P., S.A. Alcaraz and J. Barber, Numerical simulations to assess thermal potential at Tauranga low-temperature geothermal system, New Zealand. Hydrogeology Journal, v. 22(1), p Pruess K., O. Curt, and M. George, TOUGH2 USER S GUIDE, VERSION 2.0. Earth Science Division, Lawrence Berkeley National Laboratory, University of California, Berkeley. Rutqvist J., Y.S. Wu, C.F. Tsang, and G. Bodvarsson, A modeling approach for analysis of coupled multiphase fluid flow, heat transfer, and deformation in fractured porous rock. International Journal of Rock Mechanics & Mining Sciences, v. 39, p Rutqvist J. and C.F. Tsang, A study of caprock hydromechanical changes associated with CO 2 -injection into a brine formation. Environmental Geology, v. 42, p Rutqvist J. and C.M. Oldenburg, Analysis of injection-induced microearthquakes in a geothermal steam reservoir, Geysers Geothermal Field, California. The 42nd U.S. Rock Mechanics/Geomechanics Symposium, San Francisco, California, USA. Rutqvist J., Status of the TOUGH-FLAC simulator and recent applications related to coupled fluid flow and crustal deformations. Computers & Geosciences, v. 37, p Simone S.D., V. Vilarrasa, J. Carrera, A. Alcolea, and P. Meier, Thermal coupling may control mechanical stability of geothermal reservoirs during cold water injection. Physics and Chemistry of the Earth, v. 64, p Vasco D.W., J. Rutqvist, A. Ferreti, A. Rucci, F. Bellotti, P. Dobson, C. Oldenburg, J. Garcia, M. Walters, and C. Hartline, Monitoring deformation at the Geysers Geothermal Field, California using C-band and X-band interferometric synthetic aperture radar. Geophysical Research Letters, v. 40, p