THREE-DIMENSIONAL THERMO-PORO-MECHANICAL MODELING OF RESERVOIR STIMULATION AND INDUCED MICROSEISMICITY IN GEOTHERMAL RESERVOIR

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1 PROCEEDINGS, Thirty-Sixth Workshop on Geothermal Reservoir Engineering Stanor University, Stanor, Caliornia, January 31 - February 3, 2011 SGP-TR-191 THREE-DIMENSIONAL THERMO-PORO-MECHANICAL MODELING OF RESERVOIR STIMULATION AND INDUCED MICROSEISMICITY IN GEOTHERMAL RESERVOIR Sang Hoon Lee an Ahma Ghassemi Department o Petroleum Engineering, Texas A&M University 3116 TAMU 507 Richarson Builing College Station, TX, 77845, USA ahma.ghassemi@pe.tamu.eu ABSTRACT Analysis o stress change an permeability variations cause by rock ailure is much interest in geothermal reservoir. Col water injection into the reservoir can cause signiicant change o pore pressure, temperature, an the stress state in the hot reservoir which in turn impact rock permeability. Analysis o this process is useul in esigning geothermal reservoirs. In view o the complexity o the process, numerical moeling is generally necessary. In this paper, we present a three-imensional ully-couple thermo-poro-mechanical inite element moel with amage mechanics to simulate reservoir stimulation by hyraulic racturing. The moel consiers stressepenent permeability, an convective heat transport in the thermo-poroelastic ormulation. Rock amage is relecte in the alteration o elastic moulus an permeability. A series o numerical experiments have been carrie out to stuy the impact o col water injection on the reservoir. Results show ierent patterns o amage localization aroun the wellbore an its propagation into the reservoir uner ierent stress regime. In aition to the geometry o the stimulate zone, locations o potential inuce-seismicity cause by injection are calculate, an show qualitative agreement observations in the iel. The moel provies a useul tool or the analysis o stress inuce micro-seismicity an racture propagations in geothermal an petroleum reservoirs. INTRODUCTION Water injection in geothermal reservoir involves couple rock eormation an lui low as escribe in Biot s poroelastic theory [1]. Thermal an chemical eects can also be signiicant in this context [2]. The inluence o lui low an temperature change aroun the wellbore on the stress variations in the reservoir can be escribe using thermo-poroelasticity. This inluence is oten compute base on a linear rock behavior without rock ailure. The assumptions o linear elastic rock skeleton an constant permeability have limitations or use in preicting the real behavior o the reservoir rock. Generally, the strain-stress behavior o rocks in triaxial tests shows harening an post-peak sotening. This behavior epens on the rock type, pore pressure, stress conitions, an temperature. The continuum amage mechanics approach is one o the methos that can capture the harening an sotening behavior o the rock. The continuum amage mechanics was irst introuce by Kachanov an since has been evelope by many researchers [3-8] who have investigate inelastic behavior cause by crack initiation, micro-voi growth, an racture propagation. Also, the evolution o rock amage in the presence o poroelastic an thermo-poroelastic eects has been consiere. Selvaurai [8] stuie inluence o amage an permeability in porous rock. His results showe a signiicant permeability alteration cause by amage evolution in consoliation problems. Tang et al. propose a amage an permeability moel base on experimental strain-stress observations an permeability measurements [6-7]. The permeability variations inuce by altere stress an rock ailure has been stuie by many researchers [e.g., 9-12], an relations have been suggeste between permeability change an micro-crack an voi evolution [12] showing that or granite permeability can increase by a actor o our. Other stuies present ierent magnitues or the increase in the level o permeability epening on rock type an experimental conitions. In this work, we present the evelopment o a inite element moel to stuy the inluence o thermo-poromechanical coupling on rock amage evolution an permeability variation. The amage moel use correspons to the brittle rock ailure behavior with crack initiation, micro-voi growth an permanent eormation prior to racture. In orer to capture the ull eects o rock cooling by injection in the presence o higher lui luxes cause by rock egraation an permeability enhancement, the moel consiers both the conuctive an convective heat transer in porous meium. Numerical

2 simulations are presente to veriy the moel an to illustrate the role o various mechanisms in rock racture an istribute amage evolution uring stimulation. THERMO-POROELASTIC MODEL The theory o thermo-poroelasticity (or porothermoelasticity) is evelope by combining the inluence o thermal stress an ierential soli/lui expansion to rock stresses an lui iusion. Governing Equations The governing equations inclue the constitutive an transport laws. The constitutive equations o thermoporoelasticity have been evelope by McTigue [13] an Palciauskas an Domenico [14]. Using the geomechanics sign convention o compression positive, the constitutive equations are: 2G σij 2Gε & = & ij + K & εkkδij + α p& δij + γ1t& δij (1) 3 & ζ = αε& ii + β p& γ 2T & (2) where σ ij an ε ij are the total stress an strain tensors, p an T are the pore pressure an temperature respectively. α is the Biot coeicient, ζ is the variation o lui contents, K is bulk moulus, an G is the shear moulus; γ 1, γ 2 an β are given by: α ϕ ϕ β = + (3) K K s γ = Kα m γ = α α + ( α α )φ 1 (4) 2 m m (5) where φ is the porosity, α an α m the thermal expansion coeicients o soli an lui, respectively. Flui low in porous rock is governe by Darcy s law, an heat conuction obeys Fourier s law, so that: k J = ρ p (6) η J T where T = k T (7) ρ is lui mass ensity, k an η the permeability an viscosity, respectively, thermal conuctivity. T k the The balance o orce an continuity or the lui mass are given by: σ = (8) ij, j 0 ζ 1 = J t ρ (9) By substituting the constitutive equations into the balance equations given by Eqn. (8), (9), we obtain the iel equations or the rock eormation an lui low, namely Eqn. (10) an Eqn. (11). The conservation o energy with Fourier s law yiels the iel equation or the temperature istribution: G 2 K + ( u) + G u + m( α p + γ 1 T ) = 0 (10) 3 k 2 α ( u &) + β p& p γ 2T & = 0 η (11) 2 T& T + v( T ) c T = 0 (12) where u is the isplacement an m = [ 1,1,1,0,0,0] T or three-imensional cases. In Eqn. (12), we consier convective heat transer because o cooling eects which are rom increase low velocity in amage phase. This lui velocity is couple with pore pressure variations in Darcy s law, k v = p. η DAMAGE AND PERMEABILITY MODEL We use a moel o rock amage an permeability as propose by Tang et al. base on experiments [6, 7]. The moel is moiie herein to consier continuous stress relaxation rom the peak stress to the resiual strength (sotening regime). Accoring to this moel, the strain-stress behavior o rock can be ivie into an elastic phase an a amage phase. In the elastic phase there is no amage in the rock, whereas the rock begins to ail by crack initiation, crack-growth an voi-growth when the stress conitions reach the ailure level i.e., they satisy the ailure criterion. An elastic-amage mechanics represents the rock egraation by expressing the amage in terms o a reuction on the elastic moulus as the amage procees: E = ( 1 ) E0 (13) where represents the internal amage variable escribing the amount o egraation (crack initiation, micro-voi growth an crack propagation) an E0 is the initial rock moulus. I amage occurs by compressive stress, the amage variable is eine in terms o strain, peak stress, an resiual compressive strength o the rock as: 1 cr c = ( ε ε ) ε ε ε E c + c (14) 0 cr c ε < ε < ε ) ( c cr

3 cr = 1 ( ε > ε cr ) (15) E0ε where cr an ε cr are the resiual compressive strength an strain, an c an ε r are the peak stress an strain in compressive iel. ε is the equivalent strain. I amage evolves in a tensile stress iel, the amage variable is eine using the resiual tensile strength o the rock as: tr = 1 ( ε > εtr ) (16) E0ε where tr an ε tr are the resiual tensile strength an strain, respectively. To trace the progress o amage uner shear or tensile stress, a Mohr-Coulomb ailure criterion is use: σ + σ 3 σ1 σ 3 F = 1 sinφ c cosφ 2 2 (17) where σ 1 an σ 3 are the maximum an minimum principal stresses, respectively; φ an c represent the riction angle an cohesion, respectively. The rock permeability moel use also consiers altere permeability in the elastic an amage phase [6, 7]: β σ ii / 3 α p (18) k = k ( ) ( 0) β ( σ ii / 3 α p) ( 0 < 1) 0 e = k0e k = ζ (19) where k 0 is the initial permeability, ζ an β are material constants etermine empirically. Here ζ ( ζ > 1 ) inicates permeability increase by amage. The parameter β [Pa -1 ] in the exponent term is the control parameter or stress sensitivity o permeability in porous rock. 3D FINITE ELEMENT METHOD FOR THERMO-POROELASTICITY At this stage o the work, we evelop a 3D inite element program with ull poro-thermoelasticity capability [15]. The moel uses eight-noe hexaheron elements or the isplacements u, an eight-noe elements or the pore pressure p, an temperature T to improve numerical resolution o isplacements. The ollowing variables are approximate using Galerkin s metho or u, p, an T : u = Nu~ u (20) p = N ~ p p (21) ~ T = NTT (22) where the shape unctions or the isplacement, pore pressure an temperature are N u, N p, an N T, respectively, an noal variables or isplacements, pore pressure an temperature are u ~, ~ p an T ~, respectively. Weak ormulations are obtaine by substituting Eqns. (20)-(22) to the iel Eqn. (10)- (12). For iscretizing the time omain, the Crank- Nicolson type approximation is applie. Full escription o couple chemo-thermo-poroelastic inite element ormulation an veriications are publishe by Zhou an Ghassemi (2009) or the 2D case. In convective heat transer computation, we applie Streamline-Upwin/Petrov-Galerkin (SUPG) metho to avoi numerical oscillation [17]. Three-imensional poro-elastic stress analysis has been carrie out using pressurization o the misection o the well by a lui. Results show that eective raial stress istributions are similar to 2D plane-strain case but inuce eective tangential stress istributions are ierent because o the inluence o inuce vertical stress aroun injection zone an pore pressure istributions which low in x-, y-, an z-irections (Fig 1). Figure 1: Injection-inuce eective raial an tangential stress variation with respect to time. Injection pore pressure is 10 MPa. Numerical Implementation o Damage Theory Theory o amage mechanics has been implemente in the 3D inite element coe escribe above. Accoring to the experimental results rom Park et al. an Tang et al. [18, 6-7], stresses show a rapi ecrease which is relate to the sotening regime ater rock ailure.

4 Figure 2: Finite element simulations o compressive triaxial test. Blue line: strain-stress relationships. Damage variable(re line) evolves ater rock ailure. the level o sotening in the amage phase. By comparing the strain-stress behavior an permeability change with experimental ata in [18, 6-7], we selecte the optimum parameters or permeability ζ, β, an the cohesive strength in Mohr- Coulomb ailure criterion. The simulations involve axisymmetric analysis using 400 elements an 1317 noes. The aspect ratio (with to height) or the omain use in the triaxial test simulations was 1:4; the conining stresses were applie in the lateral sie at the level o experimental conitions (10 MPa). Fig 2-3 show inite element results o stain-stress behavior or shear an tensile ailure. The results show a linear strain-stress behavior in elastic phase, however, the stress rops to its resiual stress o the sotening regime in amage phase. This amage moel has avantages to control stress rop rom the peak stress to resiual stress, an the value o resiual stress with respect to strain variations. To simulate more realistic triaxial test, we consiere heterogeneity o moulus using Weibull istribution unction which is wiely use in a geomechanics simulation to epict heterogeneity o rock. The heterogeneous results are presente in Fig 4 that stress-strain curve is varie smoothly. Figure 3: Finite element simulations o tensile triaxial test or comparison o shearailure amage moel. Blue line: strainstress relationships. Re line: Damage variable Figure 4: Finite element simulations o a triaxial test. Green line: strain-stress relationships with homogeneous Young s moulus. Damage variable evolves ater rock ailure; Re line: results rom the heterogeneous Young s moulus. We irst perorme a number o simulations (o triaxial compression tests) to in the material parameters or the resiual strength which etermines NUMERICAL EXAMPLES 3D Simulation o Col-Water Injection In this section, we present numerical examples or hyraulic racturing experiments uner the inluence o ierent ar-iel stress while taking into account lui an temperature variations aroun a wellbore. Beore conucting large reservoir simulations, we teste a small simulation omain consisting o a 3D block o rock with imensions o m 3 (Fig. 5) with a 0.2 m injection interval. We use eightnoe hexaheron element or isplacements an 8- noes or pore pressure an temperature. All reservoir properties are represente in Table 2 or granite reservoir. The permeability in the maximum ar-iel stress irection (x-irection) is 5 times higher than that in the minimum ar-iel stress irection (y-irection). The vertical permeability value is assume to be 10% o the permeability in the minimum ar-iel stress irection. In this example, the maximum horizontal stress is 30 MPa (xirection), minimum horizontal stress is 20 MPa (yirection), an the vertical stress is 10 MPa (zirection). The injection pressure starts at 13 MPa an is increase at 0.5 hr intervals until it reaches 20 MPa.

5 Figure 5: Iso-surace (20%) o injection-inuce amage variable or the case when the minimum in-situ stress is S v. Table 2: Material properties use in simulations. Young s moulus, E 10 GPa ν, ν u 0.22, 0.46 Skempton's coeicient, B 0.92 Permeability, k m Porosity, φ 0.30 ρ Flui mass ensity, Flui viscosity, η Thermal expansion coeicient o soli, α an luiα m 1111 kg/m Pa s K K -1 T Thermal iusivity, c m 2 /s Friction angle, Cohesive orce, φ c MPa Material constant, ζ 100 Material constant, β The permeability an pore pressure istributions in the racture zone are represente in Fig. 6. Note that axial stress (σ zz ) istribution (Fig. 7) contributes to ailure aroun the wellbore, along with the tangential stress. It is observe in our racture simulation that amage area (micro-crack & voi growth area) becomes sharper when amage variable convergences are satisie. Also, anisotropic permeability moel uner anisotropic ar-iel stress shows more realistic results since lui injection plays an important role in this process an its simulation. Figure 6: Cross sectional view o permeability an pore pressure istributions. Results are or a time o 6 hrs. Permeability istributions: (a) an (b); pore pressure istributions: (c) an (). See Table 2 or units. Figure 7: Cross sectional view o eective axial (σ zz ) stress istributions at 6 hrs. Cross sectional view or maximum horizontal irection is plotte in (a) an minimum horizontal irections are plotte in (b). Ater carrying out small reservoir geomechanical simulations, we conucte large scale reservoir simulations using a large mesh with 83,232 8-noe hexaheron elements or a reservoir size o m 3 as shown in Fig. 8. We teste three ierent ar-iel stress regimes: strike-slip: (S H, max = 30 MPa, S h, min = 10 MPa, S v = 20 MPa), horizontal ar-iel stress as the minimum in-situ stress; thrust (S H, max = 30 MPa, S h, min = 20 MPa, S v = 10 MPa), vertical ar iel stress as the minimum stress component; an normal aulting regime (S H, max = 20 MPa, S h, min = 10 MPa, S v = 30 MPa), the vertical ar iel stress as the maximum in-situ stress component. All reservoir properties are the same as the previous simulations, an permeability anisotropy is oriente accoring to the ar-iel stress irection, or example, k h,min = m, k H, max = m, k v = m are applie or strike-slip regime, k h,min = m, k H, max = m, kv = m or thrust regime, an k h,min = m, k H, max =

6 m, k v = m are applie or normal ault regime. Table 3: Reservoir properties use in threeimensional iulations. Case 1 (Strike-slip) Case 2 (Thrust) Case 3 (Normal) S H, max 30 MPa 30 MPa 20 MPa S h, min 10 MPa 20 MPa 10 MPa S v 20 MPa 10 MPa 30 MPa k H, max m m m k h,min m m m k v m m m In these simulations, amage propagation cause by lui injection was investigate in relation to the insitu stress regime. The irst case was when the minimum in-situ stress is horizontal (Case 1). The injection interval zone is 2 m an injection pressure begins at 8 MPa an is increase at 2.5 MPa increments every 0.5 hr until it reaches 32 MPa. Flui injection causes both eective tangential an eective axial stresses to become tensile. These two stress components contribute to tensile principal stress insie the rock. Fig. 9 shows 20% amage area. Note that amage an racture propagate vertically an horizontally in this case where the minimum stress is horizontal. Height growth occurs rapily near the wellbore where the axial stress eects ominate. Away rom the wellbore, the in-situ stress controls the manner o amage zone propagation similar to hyraulic racture. The eective axial stress an pore pressure istributions are shown in Fig. 10. Figure 8: Mesh use in simulation; S H,max represents maximum horizontal stress, S h,min is the minimum horizontal stress, an S v is vertical stress. Figure 9: Damage an permeability istributions or minimum horizontal ar-iel stress at 12 hrs. 20 % amage o iso-surace is plotte in (a) an (b) is magniie image. Cross sectional view o permeability istributions are illustrate in (c) an ().

7 Figure 10: Eective vertical stress an pore pressure istributions or minimum horizontal ar-iel stress at 12 hrs. Cross sectional views o eective vertical stress are in (a) an (b) an pore pressure istributions are in (c) an (), respectively. For the Case 2, vertical minimum in-situ stress regime, the injection interval zone is 0.2 m an the pressure is prescribe to begin rom 20 MPa an is increase at 2.5 MPa at 0.5 hr until it reaches 42 MPa. Fig. 11 shows lui inuce 20% amage area an the permeability istribution. Results show that injection inuce amage an racture area propagate horizontally. Pore pressure an stress istribution with amage evolution aroun a wellbore as shown in Fig. 12. Figure 12: Eective vertical stress an pore pressure istributions or the case when vertical stress is the ar-iel minimum stress, at 6 hrs. Cross sectional views o eective vertical stress are in (a) an (b) an pore pressure istributions are in (c) an (), respectively. Figure 13: Distributions o amage, permeability, pore pressure, an eective vertical stress or the case when vertical stress is the ar-iel maximum stress, at 6 hrs. 20% amage o iso-surace is plotte in (a) an cross sectional views o permeability is in (b). Pore pressure an eective vertical stress istributions are in (c) an (), respectively. Figure 11: Damage an permeability istributions or minimum vertical ariel stress at 6 hrs. 20 % amage o isosurace is plotte in (a) an (b) is magniie image. Cross sectional view o permeability istributions are illustrate in (c) an (). For the Case 3, vertical stress as the maximum ar iel stress, the same injection rate conitions o Case 1 are use or the comparison o normal ault regime with strike-slip regime (Case 1). Only ierent properties are ar-iel stress istribution an permeability anisotropy because o maximum ariel stress irections are varie rom y-irection to z-irection. Results show a stronger tenency or the

8 inuce amage an racture zone to propagate vertically; however as shown in Fig 13, the amage area is smaller (or the same injection rate o Case 1) because o the inluence o large vertical ar iel stress. The ierent geometry o the ailure plane or the case o S h,min an S v as the minimum in-situ stress component can be attribute to ierent patterns o lui an stress istribution in each case. In this simulation, it is observe that eective axial stress cause by lui injection is the main contributor to tensile ailure across the wellbore or case 1 an case 3 (S h,min. as minimum). However, in the case o S v as the minimum stress, the eective axial stress is not signiicant compare to the minimum S h,min an the wellbore hoop stress which serve to propagate the amage. We observe that a higher injection pressure is neee to generate the racture plane in the homogeneous rock case, when S v is the minimum in-situ stress rather than S h,min because o the eective stress contributions or tensile ailure. This is reasonable since there is aitional hoop tensile stress when the racture in initiate in a vertical plane (as oppose to only axial). Figure 15: Iso-surace 20% amage plot o three-imensional amage propagation with respect to time uner vertical ariel stress as the minimum: (a): 1 hr, (b): 1.2 hr, (c): 1.5 hr, (): 1.9 hr. Figure 14: Iso-surace 20% amage plot o three-imensional amage propagation with respect to time uner horizontal ariel stress as the minimum: (a): 0.5hr, (b): 1 hr, (c): 1.2 hr, (): 1.5 hr The variation o amage propagations with time or the strike-slip, thrust an normal ault regimes are illustrate in Fig or comparison. Figure 16: Iso-surace 20% amage plot o three-imensional amage propagation with respect to time uner vertical ariel stress as the maximum: (a): 1.5 hr, (b): 2 hr, (c): 4 hr, (): 8 hr. Hyraulic racturing with col water injection has been illustrate in Fig 17. Initial reservoir temperature is 200 C an col water temperature is 65 C. Injection pressure is maintaine 35 MPa or 6 hr which starts rom 8 MPa. Both lui injection an temperature ierence contribute racture propagation. In this simulation, we assume hyraulic racture (macro crack) as 90% amage. Results show that 90% amage zone length is 24 m, height is 8 m, an average thickness near the well 10 cm. Note that temperature istribution is inluence by lui low which is relate with convective heat transer but transer rate is very slow.

9 Table 4: Reservoir properties use in threeimensional heterogeneous simulations. Case 1 Case 2 Case 3 Case 4 Case 5 Case 6 Stress regime Strike-slip Thrust Normal E 10 GPa (n=1.5) 10 GPa (n=1.5) 10 GPa (n=1.5) K, m (n=1.5) -2 k max= k min = k v = k max = k min = k v = k max = k min = k v = C MPa (n=2) 100 MPa (n=2) 100 MPa (n=2) T 0 5 MPa (n=2) 5 MPa (n=2) 5 MPa (n=2) Figure 17: Plot or hyraulic racturing zone (90% amage area) in horizontal stress as the minimum (a), an pore pressure istribution (b). Dierent planes view o temperature istributions in (c) an (). All results have the same time step at 6 hr. Three-Dimensional Simulation o Injection- Inuce Micro-Seismicity In this section, we consier inuce micro-seismicity simulations with amage evolution. It is assume that seismic events are generate when the eective rock stress reaches the level prescribe by the ailure criterion (Mohr-Coulomb) as lui iniltrates the rock an stresses change. The simulation mesh is the same in the previous homogeneous three-imensional simulations. However, heterogeneities o moulus an permeability are consiere using Weibull istribution unctions. The initial moulus an permeability istributions are illustrate in Fig. 18. As beore, three ierent ar-iel stress regimes are teste one with horizontal stress as the minimum, another with vertical stress as the minimum an the other with vertical stress as the maximum. To investigate the permeability an ar-ile stress relationship, we also consiere two ierent permeability moels namely (1) reservoir permeability properties are highly relate to the ariel stress (anisotropic permeability) an permeability are inepenent o the ar-iel stress (isotropic permeability). Details o reservoir properties are escribe in Table 4. In the case o anisotropic permeability, we simply assume a permeability that is 10 times higher in the maximum in-situ stress irection an 10 times lower in minimum in-situ stress irection. Figure 18: Initial heterogeneous moulus is plotte in (a), (b) an permeability istribution is presente in (c), (). The resulting seismic events an permeability istributions are plotte in Fig. 19 or ierent reservoir permeability. Fig. 19 (a) shows the seismic events in time or the conitions o isotropic permeability with minimum horizontal ar-iel stress. Fig. 19 (b) shows a plot or the same ar-iel stress conitions an injection rate but with anisotropic permeability. It is observe the seismic events are scatte broaly when permeability is isotropic since there are no signiicant ierences in lui sweep velocities in the x-, y-, an z-irections. However, in the case o anisotropic permeability, seismic events are highly localize because lui invasion is ocuse in the maximum ar-iel stress irection an this leas to localize seismic events. Same conitions are simulate or the minimum vertical ar-iel stress case (Fig. 20). It is similarly observe that broa istribute seismic events occur uner isotropic permeability conitions, an scattere

10 localize events are observe in the anisotropic permeability case. Vertical stress as the maximum has been plotte in Fig. 21. Note that same injection conitions are use or both stress regime simulations. Results show that or the normal aulting case, the inuce-seismicity oes not propagate an stabilizes earlier because vertical stress is higher compare to the thrust regime where a higher injection rate is neee to generate tensile ailure or racture propagation in the vertical irection. It is worth pointing out that the smaller grey points show the istribution o micro-seismic events as a result o the ar-ile stresses an might be interprete as backgroun values. Figure 20: Micro-seismic events ater 6 hrs o pumping or the case that the vertical stress is the minimum ar-iel. (a) the case o isotropic permeability an (b) anisotropic permeability. Figure 19: Preicte micro-seismic events ater 10 hrs o pumping or the case o horizontal stress being the minimum ariel stress: (a) the case o isotropic permeability an (b) anisotropic permeability.

11 racture plane in a thrust aulting regime compare to the vertical racture plane in strike-slip stress regime. This is because o the eective stress contributions to tensile ailure. Realistic patterns o micro-seismicity have been generate or these stimulation experiments. Results show the signiicant roles o stress state an initial rock permeability in the resulting pattern. The results o this stuy inicate that the inite element metho with amage can be use to moel reservoir stimulation an inuce seismicity. Eort is ongoing to simulate amage propagation an inuce seismicity uner ierent injection rates, various permeability structures involving aults, an ierent in-situ stress regimes or small an large size reservoirs an to compare results with available lab an iel experiments. ACKNOWLEDGEMENT This project was supporte by the U.S. Department o Energy Oice o Energy Eiciency an Renewable Energy uner Cooperative Agreement DE-PS36-08GO This support oes not constitute an enorsement by the U.S. Department o Energy o the views expresse in this publication. Support o Texas A&M University in publishing this work is also acknowlege. Figure 21: Micro-seismic events ater 6 hrs o pumping or the case that the vertical stress is the maximum ar-iel. (a) the case o isotropic permeability an (c) anisotropic permeability. CONCLUSIONS A three-imensional ully couple inite element metho has been evelope or moeling amageinuce stress variations an permeability change along with inuce seismicity. The moel was use to simulate a number o synthetic hyraulic racturing experiments or ierent stress regimes. Vertical amage propagation observe when the horizontal ar-iel stress is the minimum in-situ stress component, whereas horizontal amage propagation is observe when the vertical ar iel stress as the minimum. Comparison between the results or the strike-slip an normal aulting regimes using the same injection rate show that amage area is smaller or the latter case. Also, it is observe that higher injection pressure is neee to generate a horizontal REFERENCES 1. Biot M. A. (1941), General theory o threeimensional consoliation, J. Appl. Phys, 12, Ghassemi A. an A. Diek. (2002), Porothermoelasticity or swelling shales, J. Pet. Sci. Eng., 34, Kachanov L. M. (1958), Time o the rupture process uner creep conitions, Isv. Aka. Nauk SSR. Ot Tekh. Nauk., 8, Mazars J. (1986), A escription o micro- an macroscale amage o concrete structures, Eng. Fracture. Mech., 25, Simakin A. an Ghassemi A. (2005), Moelling eormation o partially melte rock using a poroviscoelastic rheology with ynamic power law viscosity, Tectonophysics, 397, Tang C.A., Tham L.G., Lee P.K.K., Yang T.H. an Li L.C. (2002), Couple analysis o low, stress an amage (FSD) in rock ailure, Int. J. Rock Mech. & Min. Sci., 39, Li L.C, Tang C.A., Tham L.G., Yang T.H. an Wang S.H. (2005), Simulation o multiple hyraulic racturing in non-uniorm pore pressure iel, Av. Mater. Res., 9,

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