Sequential Methods for Coupled Geomechanics and Multiphase Flow

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

66 CHAPTER 3. STABILITY OF THE DRAINED AND UNDRAINED SPLITS Dimensionless pressure (P/P i ) Dimensionless pressure (P/P i ) 0.8 0.75 0.7 0.65 Case 3.2, τ=0.95 Drained ∆ t d =4.4 × 10 −5 Drained ∆ t d =4.4 × 10 −2 0.6 0 0.2 0.4 0.6 0.8 1 Dimensionless time (pore volume produced) 0.8 0.75 0.7 0.65 Case 3.2, τ=1.05 Drained ∆ t d =4.4 × 10 −5 Drained ∆ t d =4.4 × 10 −2 0.6 0 0.2 0.4 0.6 0.8 1 Dimensionless time (pore volume produced) Figure 3.11: Case 3.2 (1D injection–production problem). Results are shown for the drained split with two different coupling strengths: τ = 0.95 (top), and τ = 1.05 (bottom) and two very different time step sizes. The stability of the drained split is independent of the time step size. The drained split is stable if τ < 1 and unstable if τ > 1, regardless of the time step size.
3.7. NUMERICAL EXAMPLES 67 Dimensionless pressure(P/P i ) Dimensionless pressure(P/P i ) 1 0.95 0.9 0.85 0.8 0.75 0.7 0.65 Case 3.1. α=0.5 and τ=0.083 Drained Undrained Fully Coupled 0.6 0 0.05 0.1 0.15 0.2 Dimensionless time (pore volume produced) 1 0.95 0.9 0.85 0.8 0.75 0.7 0.65 Case 3.1. α=1.0 and τ=0.083 Drained Undrained Fully Coupled 0.6 0 0.05 0.1 0.15 0.2 Dimensionless time (pore volume produced) Figure 3.12: 1D problem with injection and production (Case 3.2). τ = 0.083 is considered. Top: α = 0.5 for both flow and mechanics. Bottom: α = 1.0 for both flow and mechanics.
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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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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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116 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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