Sequential Methods for Coupled Geomechanics and Multiphase Flow

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$Drilling-induced tensile wall-fractures - Stanford University$

58 CHAPTER 3. STABILITY OF THE DRAINED AND UNDRAINED SPLITS 3.7 Numerical Examples We use five test cases to compare the various coupling strategies. Case 3.1 The Terzaghi problem in a 1D linear poroelastic medium (the left picture in Figure 3.7). The driving mechanical force is provided by the overburden. Case 3.2 Injection and production in a 1D poroelastic medium. The driving force is due to injection and production (the right picture in Figure 3.7). Case 3.3 The Mandel problem in a 2D elastic medium. The driving force is provided by the side burden (the left picture in Figure 3.8). Case 3.4 Injection and production in a 1D poro-elasto-plastic medium with isotropic hard- ening. The driving force is due to injection and production (the right picture in Figure 3.7). Case 3.5 Fluid production in 2D with elasto-plastic behavior described by the modified Cam-clay model. The compaction of the reservoir occurs due to production (the right picture in Figure 3.8). The numerical results are based on one iteration per time step (i.e., staggered method) unless noted explicitly otherwise. 3.7.1 Numerical results for elasticity Case 3.1—The Terzaghi problem We have drainage boundaries for flow at the top and bottom, where the boundary fluid pressure is Pbc = 2.125 MPa. The overburden is ¯σ = 2 × 2.125 MPa at the top, and a no- displacement boundary condition is applied to the bottom. The domain has 20 grid blocks. The length of the domain is Lz = 40 m with grid spacing ∆z = 2 m. The bulk density of the porous medium is ρb = 2400 kg m −1 . Initial fluid pressure is Pi = 2.125 MPa. Fluid density and viscosity are ρf,0 = 1000 kg m −1 and µ = 1.0 cp, respectively. Permeability is
3.7. NUMERICAL EXAMPLES 59 Figure 3.7: Left: the Terzaghi problem in 1D (Case 3.1). Right: 1D problem with injection and production wells (Case 3.2 and 3.4). Table 3.1: Input data for Case 3.1 Property Value Permeability (kp) 50 md Porosity (φ0) 0.3 Biot coefficient (b) 1.0 Drained (constrained) modulus (Kdr) 100 MPa Bulk density (ρb) 2400 kg m −3 Fluid density (ρf,0) 1000 kg m −3 Fluid viscosity (µ) 1.0 cp Initial pressure (Pi) 2.125 MPa Boundary pressure (Pbc) 2.125 MPa Overburden (¯σ) 2×2.125 MPa Grid spacing (∆z) 2 m
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SEQUENTIAL METHODS FOR COUPLED GEOM
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splits, are, at best, conditionally
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deeply. There was deep discussion o
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3 Stability of the Drained and Undr
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3.7 Left: the Terzaghi problem in 1
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2 CHAPTER 1. INTRODUCTION Reservoir
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4 CHAPTER 1. INTRODUCTION problem (
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6 CHAPTER 1. INTRODUCTION undrained
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108 CHAPTER 4. CONVERGENCE OF THE D
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118 CHAPTER 5. FIXED-STRAIN AND FIX
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164 CHAPTER 6. COUPLED MULTIPHASE F
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208 CHAPTER 7. CONCLUSIONS 7.2 Coup
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210 CHAPTER 7. CONCLUSIONS 7.2.3 Ac
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212 CHAPTER 7. CONCLUSIONS
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214 APPENDIX A. STABILITY IN SPACE
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226 APPENDIX B. MISCELLANEOUS DERIV
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236 APPENDIX C. CONSTITUTIVE RELATI
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244 BIBLIOGRAPHY Mech Eng 122: 145-
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246 BIBLIOGRAPHY Aug. Murad M.A. an
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248 BIBLIOGRAPHY ˇZeniˇsek A. 198
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Sequential Methods for Coupled Geomechanics and Multiphase Flow

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