Sequential Methods for Coupled Geomechanics and Multiphase Flow

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

204 CHAPTER 6. COUPLED MULTIPHASE FLOW AND GEOMECHANICS ||P d || ||S w || 12 11 10 9 8 7 Variation of P d during iterations Drained Fixed−strain Undrained Fully coupled Fixed−stress 6 0 2 4 6 8 10 Number of iterations 0.102 0.1 0.098 0.096 0.094 0.092 Variation of S w during iterations Drained Fixed−strain Undrained Fully coupled Fixed−stress 0.09 0 2 4 6 8 10 Number of iterations Figure 6.7: Convergence behaviors during iterations at the first time step. Top: pressure. Bottom: water saturation.
6.6. NUMERICAL EXAMPLES WITH THE STAGGERED METHOD 205 difference decreases significantly because the fixed-stress split uses updated information from the mechanical problem, capturing the effect of the instantaneous loading. After the second iteration, the fixed-stress shows the same convergence behavior as the fully coupled method. 6.6 Numerical Examples with the staggered method We perform numerical simulation with the staggered method, reusing Case 6.2. The top of Figure 6.8 shows the results from the drained and fixed-strain splits. At early time, the two splits are stable because the coupling strength is below unity even though they have severe oscillation. However, the coupling strength increases during simulation because of injection of the less compressible fluid, namely, water. Then the solutions of the drained and fixed strain splits become unstable because the coupling strength exceeds unity eventually. On the other hand, the undrained and fixed-stress splits are stable for all time. The bottom of Figure 6.8 illustrates that the solutions of the undrained and fixed-stress splits are stable with good accuracy with one or two iterations.
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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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Page 240 and 241: 214 APPENDIX A. STABILITY IN SPACE
Page 252 and 253: 226 APPENDIX B. MISCELLANEOUS DERIV
Page 262 and 263: 236 APPENDIX C. CONSTITUTIVE RELATI
Page 270 and 271: 244 BIBLIOGRAPHY Mech Eng 122: 145-
Page 272 and 273: 246 BIBLIOGRAPHY Aug. Murad M.A. an
Page 274: 248 BIBLIOGRAPHY ˇZeniˇsek A. 198
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Sequential Methods for Coupled Geomechanics and Multiphase Flow

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