Sequential Methods for Coupled Geomechanics and Multiphase Flow

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

240 APPENDIX C. CONSTITUTIVE RELATIONS IN RESERVOIR SIMULATION For the gas phase, introducing the solution gas ratio, δ( Sg ) = Sgδ( Bg 1 ) + Bg 1 δSg Bg 1 = Sg cgδpg + 1 δSg = Sg = Sg Bg 1 Bg 1 Bg δ( RsoSo ) = RsoSoδ( Bo 1 Bo Bg cgδ(po + pcg) + 1 cgδpo + (Sg ) + So Bo 1 Bg Bg δSg dpcg cg + dSg 1 )δSg, (C.18) Bg δRso + Rso δSo Bo 1 = RsoSo coδpo + Bo So dRso δpo + Bo dpo Rso (−δSw − δSg) Bo 1 = RsoSo co + Bo So dRso δpo − Bo dpo Rso δSw − Bo Rso δSg. (C.19) Bo Then, from Equations 2.38, C.7, C.18, <strong>and</strong> C.19, we have δmg ρg,0 = φ + +( Sg Bg 1 Sg Bg cgδpo + (Sg 1 1 Bg RsoSo co + Bo So dRso Bo + RsoSo ) Bo dpcg cg dSg + 1 )δSg Bg δpo − dpo Rso δSw − Bo Rso δSg Bo b − φ dpco dpcg δpo − Sw δSw + Sg δSg Ks dSw dSg Rearranging Equations C.15, C.17, <strong>and</strong> C.20, we have δmo ρo,0 = + bδεv .(C.20) 1 φSo co + Bo So b − φ δpo + −φ Bo Ks 1 − Bo So b − φ dpco Sw δSw Bo Ks dSw + −φ 1 + Bo So b − φ dpcg Sg δSg + Bo Ks dSg So bδεv, (C.21) Bo
C.2. PO, SW, SG FORMULATION 241 δmw ρw,0 δmg ρg,0 = = 1 φSw Bw + φ(−Sw cw + Sw Bw 1 Bw b − φ δpo Ks dpco cw + dSw 1 ) − Bw Sw Bw b − φ Ks dpco Sw dSw + Sw b − φ dpcg Sg Bw Ks dSg 1 1 φSg cg + φRsoSo co + φ Bg Bo So dRso + ( Bo dpo Sg Bg + −φ Rso − ( Bo Sg + Bg RsoSo ) Bo b − φ dpco Sw δSw Ks dSw 1 dpcg + φSg cg + φ Bg dSg 1 − φ Bg Rso + ( Bo Sg + Bg RsoSo ) Bo b − φ +( Sg Bg δSw δSg + Sw bδεv, (C.22) Bw + RsoSo ) Bo b − φ Ks dpcg Sg Ks dSg + RsoSo )bδεv. (C.23) Bo δpo δSg
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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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xiv
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xvi
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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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118 CHAPTER 5. FIXED-STRAIN AND FIX
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164 CHAPTER 6. COUPLED MULTIPHASE F
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Page 216 and 217: 190 CHAPTER 6. COUPLED MULTIPHASE F
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Page 274: 248 BIBLIOGRAPHY ˇZeniˇsek A. 198
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Sequential Methods for Coupled Geomechanics and Multiphase Flow

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