Sequential Methods for Coupled Geomechanics and Multiphase Flow

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

152 CHAPTER 5. FIXED-STRAIN AND FIXED-STRESS SPLITS Dimensionless horizontal displacement u x /L x Dimensionless horizontal displacement u x /L x −1 −1.1 −1.2 −1.3 −1.4 x 10 −3 Case 5.3. The Mandel Problem, τ=0.90 −1.5 0 0.5 1 1.5 −1 −1.1 −1.2 −1.3 −1.4 Dimensionless time(c v t/(Lx) 2 ) Analytic sol Fully coupled Fixed stress Fixed strain x 10 −3 Case 5.3. The Mandel Problem, τ=1.10 −1.5 0 0.5 1 1.5 Dimensionless time(c v t/(Lx) 2 ) Fixed strain Fixed stress Fully coupled Analytic Sol Figure 5.10: Case 5.3 (the Mandel problem). Evolution of the dimensionless horizontal displacement on the right side as a function of dimensionless time. Shown are the results for the fully coupled, fixed-strain, and fixed-stress split methods. Top: τ = 0.90. Bottom: τ = 1.10.
5.6. NUMERICAL EXAMPLES 153 Dimensionless pressure(P/P i ) τ 1 0.9 0.8 0.7 0.6 0.5 (plasticity with hardening) FSN FSS (1 iter) FSS (2 iter) FC 0.4 0 0.01 0.02 0.03 0.04 Dimensionless time (pore volume produced) 8 7 6 5 4 3 2 1 Variation of coupling strength 0 0 0.01 0.02 0.03 0.04 Dimensionless time (pore volume produced) Figure 5.11: 2D problem with a production well (Case 5.4). Top: the history of pressure. Bottom: the history of the coupling strength. FSN and FSS indicate the fixed-strain and fixed-stress splits, respectively. The model enters the plastic regime at td ≈ 0.018. Beyond this point, the fixed-strain split becomes unstable.
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SEQUENTIAL METHODS FOR COUPLED GEOM
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I certify that I have read this dis
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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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6.2.3 Undrained split . . . . . . .
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3.7 Left: the Terzaghi problem in 1
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4.1 The distribution of the error a
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5.3 Case 5.2 (1D injection-producti
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5.18 Pressure history at the observ
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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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8 CHAPTER 1. INTRODUCTION where A c
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10 CHAPTER 1. INTRODUCTION Even whe
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12 CHAPTER 1. INTRODUCTION
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14 CHAPTER 2. FORMULATION full form
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16 CHAPTER 2. FORMULATION dE dt =
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18 CHAPTER 2. FORMULATION where the
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20 CHAPTER 2. FORMULATION coupling
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22 CHAPTER 2. FORMULATION where Div
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24 CHAPTER 2. FORMULATION between g
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26 CHAPTER 2. FORMULATION
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28 CHAPTER 3. STABILITY OF THE DRAI
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82 CHAPTER 4. CONVERGENCE OF THE DR
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100 CHAPTER 4. CONVERGENCE OF THE D
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202 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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