Sequential Methods for Coupled Geomechanics and Multiphase Flow

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238 APPENDIX C. CONSTITUTIVE RELATIONS IN RESERVOIR SIMULATION Then Equations 2.38, C.7, C.8, and C.9 yield δmg ρg,0 = φ +φ + Rso Bo +( Sg Bg 1 Sg Bg cgδpg + 1 1 RsoSo Bo − dSw dpco + RsoSo ) Bo dSg Bg dpcg Ks (δpg − δpo) dRso Rearranging Equations C.3, C.6, and C.10, we have δmo ρo,0 δmw ρw,0 δmg ρg,0 coδpo + So δpo Bo dpo + dSg δpo + dpcg dSw δpw − dpco dSg δpg dpcg b − φ [Soδpo + Swδpw + Sgδpg] + bδεv . (C.10) 1 = φSo co + φ Bo 1 − Bo dSw + dpco dSg + dpcg So b − φ So δpo Bo Ks + φ 1 dSw + Bo dpco So b − φ Sw δpw Bo Ks + φ 1 − Bo dSg + dpcg So b − φ Sg δpg + Bo Ks So bδεv, (C.11) Bo = φ 1 dSw + Bw dpco Sw b − φ 1 So δpo + φSw cw − φ Bw Ks Bw 1 dSw + Bw dpco Sw b − φ Sw δpw Bw Ks + Sw b − φ Sgδpg + Bw Ks Sw bδεv, (C.12) Bw = −φ 1 dSg + φ Bg dpcg RsoSo co + φ Bo So dRso Bo dpo +φ Rso − Bo dSw + dpco dSg Sg + + dpcg Bg RsoSo b − φ So δpo Bo Ks + φ Rso dSw Sg + + Bo dpco Bg RsoSo b − φ Sw δpw Bo Ks 1 + φSg cgdpg + φ Bg 1 dSg − φ Bg dpcg Rso dSg Sg + + Bo dpcg Bg RsoSo b − φ Sg δpg Bo Ks + Sg Bg + RsoSo Bo bδεv. (C.13)
C.2. PO, SW, SG FORMULATION 239 C.2 po, sw, sg formulation Similarly to the po, pw, pg formulation, δ(So/Bo) for oil phase is written as δ( So ) = Soδ( Bo 1 ) + Bo 1 δSo Bo 1 = So coδpo + 1 δSo = So Bo 1 Bo Bo coδpo + 1 Then, from Equations 2.38, C.1, and C.14, we obtain δmo ρo,0 = φ + So Bo So Bo For water phase, δ(Sw/Bw) is expanded as Bo (−δSw − δSg) (−δSw − δSg). (C.14) 1 coδpo + 1 Bo b − φ dpco dpcg δpo − Sw δSw + Sg δSg + bδεv . (C.15) Ks dSw dSg δ( Sw ) = Swδ( Bw 1 ) + Bw 1 δSw Bw 1 = Sw cwδpw + 1 δSw = Sw = Sw Bw 1 Bw 1 Bw Bw cwδ(po − pco) + 1 cwδpo + (−Sw Then, from Equations 2.38, C.4, and C.16, we obtain δmw ρw,0 = φ + Sw Bw Sw Bw 1 Bw Bw δSw dpco cw + dSw 1 )δSw. (C.16) Bw 1 1 dpco cwδpo + (−Sw cw + Bw dSw 1 )δSw Bw b − φ dpco dpcg δpo − Sw δSw + Sg δSg + bδεv . (C.17) Ks dSw dSg
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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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164 CHAPTER 6. COUPLED MULTIPHASE F
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Page 240 and 241: 214 APPENDIX A. STABILITY IN SPACE
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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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