메뉴 건너뛰기




Volumn 200, Issue 13-16, 2011, Pages 1591-1606

Stability and convergence of sequential methods for coupled flow and geomechanics: Fixed-stress and fixed-strain splits

Author keywords

B stability; Convergence; Geomechanics; Operator splitting; Poromechanics; Von Neumann method

Indexed keywords

B-STABILITY; CONVERGENCE; GEOMECHANICS; OPERATOR-SPLITTING; PORO-MECHANICS; VON NEUMANN METHOD;

EID: 79954439397     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2010.12.022     Document Type: Article
Times cited : (402)

References (57)
  • 1
    • 0026916661 scopus 로고
    • A new unconditionally stable fractional step method for coupled thermomechanical problems
    • Armero F., Simo J.C. A new unconditionally stable fractional step method for coupled thermomechanical problems. Int. J. Numer. Methods Engrg. 1992, 35:737-766.
    • (1992) Int. J. Numer. Methods Engrg. , vol.35 , pp. 737-766
    • Armero, F.1    Simo, J.C.2
  • 2
    • 0027187966 scopus 로고
    • A prior stability estimates and unconditionally stable product formula algorithms for nonlinear coupled thermoplasticity
    • Armero F., Simo J.C. A prior stability estimates and unconditionally stable product formula algorithms for nonlinear coupled thermoplasticity. Int. J. Plasticity 1993, 9:749-782.
    • (1993) Int. J. Plasticity , vol.9 , pp. 749-782
    • Armero, F.1    Simo, J.C.2
  • 3
    • 0033115656 scopus 로고    scopus 로고
    • Formulation and finite element implementation of a multiplicative model of coupled poro-plasticity at finite strains under fully saturated conditions
    • Armero F. Formulation and finite element implementation of a multiplicative model of coupled poro-plasticity at finite strains under fully saturated conditions. Comput. Methods Appl. Mech. Engrg. 1999, 171:205-241.
    • (1999) Comput. Methods Appl. Mech. Engrg. , vol.171 , pp. 205-241
    • Armero, F.1
  • 4
    • 0020849840 scopus 로고
    • Stabilization of partitioned solution procedure for pore fluid-soil interaction analysis
    • Park K.C. Stabilization of partitioned solution procedure for pore fluid-soil interaction analysis. Int. J. Numer. Methods Engrg. 1983, 19(11):1669-1673.
    • (1983) Int. J. Numer. Methods Engrg. , vol.19 , Issue.11 , pp. 1669-1673
    • Park, K.C.1
  • 5
    • 0024012209 scopus 로고
    • Unconditionally stable staggered solution procedure for soil-pore fluid interaction problems
    • Zienkiewicz O.C., Paul D.K., Chan A.H.C. Unconditionally stable staggered solution procedure for soil-pore fluid interaction problems. Int. J. Numer. Methods Engrg. 1988, 26(5):1039-1055.
    • (1988) Int. J. Numer. Methods Engrg. , vol.26 , Issue.5 , pp. 1039-1055
    • Zienkiewicz, O.C.1    Paul, D.K.2    Chan, A.H.C.3
  • 7
    • 2342449953 scopus 로고    scopus 로고
    • Multiphase flow in deforming porous material
    • Schrefler B.A. Multiphase flow in deforming porous material. Int. J. Numer. Methods Engrg. 2004, 60:27-50.
    • (2004) Int. J. Numer. Methods Engrg. , vol.60 , pp. 27-50
    • Schrefler, B.A.1
  • 8
    • 52749095566 scopus 로고    scopus 로고
    • Stabilized low-order finite elements for coupled solid-deformation/fluid-diffusion and their application to fault zone transients
    • White J.A., Borja R.I. Stabilized low-order finite elements for coupled solid-deformation/fluid-diffusion and their application to fault zone transients. Comput. Methods Appl. Mech. Engrg. 2008, 197:4353-4366.
    • (2008) Comput. Methods Appl. Mech. Engrg. , vol.197 , pp. 4353-4366
    • White, J.A.1    Borja, R.I.2
  • 9
    • 0032207827 scopus 로고    scopus 로고
    • Von Neumann stability analysis of Biot's general two dimensional theory of consolidation
    • Miga M.I., Paulsen K.D., Kennedy F.E. Von Neumann stability analysis of Biot's general two dimensional theory of consolidation. Int. J. Numer. Methods Engrg. 1998, 43:955-974.
    • (1998) Int. J. Numer. Methods Engrg. , vol.43 , pp. 955-974
    • Miga, M.I.1    Paulsen, K.D.2    Kennedy, F.E.3
  • 10
    • 0032167142 scopus 로고    scopus 로고
    • A coupled reservoir and geomechanical simulation system
    • Settari A., Mourits F.M. A coupled reservoir and geomechanical simulation system. Soc. Pet. Engrg. J. 1998, 3(3):219-226.
    • (1998) Soc. Pet. Engrg. J. , vol.3 , Issue.3 , pp. 219-226
    • Settari, A.1    Mourits, F.M.2
  • 12
    • 33645838823 scopus 로고    scopus 로고
    • A comparison of techniques for coupling porous flow and geomechanics
    • Dean R.H., Gai X., Stone C.M., Minkoff S.E. A comparison of techniques for coupling porous flow and geomechanics. Soc. Pet. Engrg. J. 2006, 11(1):132-140.
    • (2006) Soc. Pet. Engrg. J. , vol.11 , Issue.1 , pp. 132-140
    • Dean, R.H.1    Gai, X.2    Stone, C.M.3    Minkoff, S.E.4
  • 13
    • 0016994107 scopus 로고
    • The Bachaquero study - a composite analysis of the behavior of a compaction drive/solution gas drive reservoir
    • Merle H.A., Kentie C.J.P., van Opstal G.H.C., Schneider G.M.G. The Bachaquero study - a composite analysis of the behavior of a compaction drive/solution gas drive reservoir. J. Pet. Technol. 1976, 1107-1114.
    • (1976) J. Pet. Technol. , pp. 1107-1114
    • Merle, H.A.1    Kentie, C.J.P.2    van Opstal, G.H.C.3    Schneider, G.M.G.4
  • 14
    • 0342717196 scopus 로고
    • Finite element simulation of Wilmington oil field subsidence: I. Linear modelling
    • Kosloff D., Scott R.F., Scranton J. Finite element simulation of Wilmington oil field subsidence: I. Linear modelling. Tectonophysics 1980, 65:339-368.
    • (1980) Tectonophysics , vol.65 , pp. 339-368
    • Kosloff, D.1    Scott, R.F.2    Scranton, J.3
  • 15
    • 0033760611 scopus 로고    scopus 로고
    • Geomechanical modeling of reservoir compaction, surface subsidence, and casing damage at the Belridge diatomite field
    • Fredrich J.T., Arguello J.G., Deitrick G.L., de Rouffignac E.P. Geomechanical modeling of reservoir compaction, surface subsidence, and casing damage at the Belridge diatomite field. SPE Reserv. Eval. Engrg. 2000, 3(4):348-359.
    • (2000) SPE Reserv. Eval. Engrg. , vol.3 , Issue.4 , pp. 348-359
    • Fredrich, J.T.1    Arguello, J.G.2    Deitrick, G.L.3    de Rouffignac, E.P.4
  • 17
    • 0027788469 scopus 로고
    • Finite-element modeling of 3-phase flow in deforming saturated oil-reservoirs
    • Lewis R.W., Sukirman Y. Finite-element modeling of 3-phase flow in deforming saturated oil-reservoirs. Int. J. Numer. Anal. Methods Geomech. 1993, 17(8):577-598.
    • (1993) Int. J. Numer. Anal. Methods Geomech. , vol.17 , Issue.8 , pp. 577-598
    • Lewis, R.W.1    Sukirman, Y.2
  • 18
    • 0028669820 scopus 로고
    • Finite element modelling for simulating the surface subsidence above a compacting hydrocarbon reservoir
    • Lewis R.W., Sukirman Y. Finite element modelling for simulating the surface subsidence above a compacting hydrocarbon reservoir. Int. J. Numer. Anal. Methods Geomech. 1993, 18:619-639.
    • (1993) Int. J. Numer. Anal. Methods Geomech. , vol.18 , pp. 619-639
    • Lewis, R.W.1    Sukirman, Y.2
  • 19
    • 0036641823 scopus 로고    scopus 로고
    • Coupling of fluid and deformation in underground formations
    • Gutierrez M.S., Lewis R.W. Coupling of fluid and deformation in underground formations. Engrg. Mech. - ASCE 2002, 128(7):779-787.
    • (2002) Engrg. Mech. - ASCE , vol.128 , Issue.7 , pp. 779-787
    • Gutierrez, M.S.1    Lewis, R.W.2
  • 20
    • 0035473726 scopus 로고    scopus 로고
    • A fully coupled hydro-thermo-poro-mechanical model for black oil reservoir simulation
    • Pao W.K.S., Lewis R.W., Masters I. A fully coupled hydro-thermo-poro-mechanical model for black oil reservoir simulation. Int. J. Numer. Anal. Methods Geomech. 2001, 25(12):1229-1256.
    • (2001) Int. J. Numer. Anal. Methods Geomech. , vol.25 , Issue.12 , pp. 1229-1256
    • Pao, W.K.S.1    Lewis, R.W.2    Masters, I.3
  • 21
    • 0037192727 scopus 로고    scopus 로고
    • Three dimensional finite element simulation of three-phase flow in a deforming fissured reservoir
    • Pao W.K.S., Lewis R.W. Three dimensional finite element simulation of three-phase flow in a deforming fissured reservoir. Comput. Methods Appl. Mech. Engrg. 2002, 191:2631-2659.
    • (2002) Comput. Methods Appl. Mech. Engrg. , vol.191 , pp. 2631-2659
    • Pao, W.K.S.1    Lewis, R.W.2
  • 22
    • 25844496893 scopus 로고    scopus 로고
    • Mixed finite element method for couple thermo-hydro-mechanical process in poro-elastic-plastic media at large strains
    • Li X., Liu Z., Lewis R.W. Mixed finite element method for couple thermo-hydro-mechanical process in poro-elastic-plastic media at large strains. Int. J. Numer. Methods Engrg. 2005, 64(5):667-708.
    • (2005) Int. J. Numer. Methods Engrg. , vol.64 , Issue.5 , pp. 667-708
    • Li, X.1    Liu, Z.2    Lewis, R.W.3
  • 23
    • 0027789568 scopus 로고
    • A finite element solution of a fully coupled implicit formulation for reservoir simulation
    • Sukirman Y., Lewis R.W. A finite element solution of a fully coupled implicit formulation for reservoir simulation. Int. J. Numer. Anal. Methods Geomech. 1993, 17(10):677-698.
    • (1993) Int. J. Numer. Anal. Methods Geomech. , vol.17 , Issue.10 , pp. 677-698
    • Sukirman, Y.1    Lewis, R.W.2
  • 24
    • 0042366194 scopus 로고    scopus 로고
    • Fully coupled modelling of seabed subsidence and reservoir compaction of North Sea oil fields
    • Lewis R.W., Makurat A., Pao W.K.S. Fully coupled modelling of seabed subsidence and reservoir compaction of North Sea oil fields. Hydrogeol. J. 2003, 11(1):142-161.
    • (2003) Hydrogeol. J. , vol.11 , Issue.1 , pp. 142-161
    • Lewis, R.W.1    Makurat, A.2    Pao, W.K.S.3
  • 25
    • 10844280067 scopus 로고    scopus 로고
    • Fractional step methods for index-1 differential-algebraic equations
    • Vijalapura P.K., Strain J., Govindjee S. Fractional step methods for index-1 differential-algebraic equations. J. Comput. Phys. 2005, 203:305-320.
    • (2005) J. Comput. Phys. , vol.203 , pp. 305-320
    • Vijalapura, P.K.1    Strain, J.2    Govindjee, S.3
  • 26
    • 0019075858 scopus 로고
    • Staggered transient analysis procedures for coupled mechanical systems: formulation
    • Felippa C.A., Park K.C. Staggered transient analysis procedures for coupled mechanical systems: formulation. Comput. Methods Appl. Mech. Engrg. 1980, 24:61-111.
    • (1980) Comput. Methods Appl. Mech. Engrg. , vol.24 , pp. 61-111
    • Felippa, C.A.1    Park, K.C.2
  • 27
    • 0035454209 scopus 로고    scopus 로고
    • Advances in coupled geomechanical and reservoir modeling with applications to reservoir compaction
    • Settari A., Walters D.A. Advances in coupled geomechanical and reservoir modeling with applications to reservoir compaction. Soc. Pet. Engrg. J. 2001, 6(3):334-342.
    • (2001) Soc. Pet. Engrg. J. , vol.6 , Issue.3 , pp. 334-342
    • Settari, A.1    Walters, D.A.2
  • 28
    • 18744438076 scopus 로고    scopus 로고
    • Coupling fluid flow and rock mechanics: formulations of the partial coupling between reservoir and geomechanics simulators
    • Mainguy M., Longuemare P. Coupling fluid flow and rock mechanics: formulations of the partial coupling between reservoir and geomechanics simulators. Oil Gas Sci. Technol. 2002, 57:355-367.
    • (2002) Oil Gas Sci. Technol. , vol.57 , pp. 355-367
    • Mainguy, M.1    Longuemare, P.2
  • 29
    • 0031141175 scopus 로고    scopus 로고
    • Standard staggered and staggered Newton schemes in thermo-hydro-mechanical problems
    • Schrefler B.A., Simoni L., Turska E. Standard staggered and staggered Newton schemes in thermo-hydro-mechanical problems. Comput. Methods Appl. Mech. Engrg. 1997, 144:93-109.
    • (1997) Comput. Methods Appl. Mech. Engrg. , vol.144 , pp. 93-109
    • Schrefler, B.A.1    Simoni, L.2    Turska, E.3
  • 30
    • 0037436440 scopus 로고    scopus 로고
    • A LATIN computational strategy for multiphysics problems: application to poroelasticity
    • Dureisseix D., Ladeveze P., Schrefler B.A. A LATIN computational strategy for multiphysics problems: application to poroelasticity. Int. J. Numer. Methods Engrg. 2003, 56:1489-1510.
    • (2003) Int. J. Numer. Methods Engrg. , vol.56 , pp. 1489-1510
    • Dureisseix, D.1    Ladeveze, P.2    Schrefler, B.A.3
  • 31
  • 32
    • 0027788628 scopus 로고
    • On convergence condition of partitioned solution procedures for consolidation problems
    • Turska E., Schrefler B.A. On convergence condition of partitioned solution procedures for consolidation problems. Comput. Methods Appl. Mech. Engrg. 1993, 106:51-63.
    • (1993) Comput. Methods Appl. Mech. Engrg. , vol.106 , pp. 51-63
    • Turska, E.1    Schrefler, B.A.2
  • 34
    • 53549121954 scopus 로고    scopus 로고
    • A time-domain FEM approach based implicit Green's functions for the dynamic analysis of the porous media
    • Soares D.J. A time-domain FEM approach based implicit Green's functions for the dynamic analysis of the porous media. Comput. Methods Appl. Mech. Engrg. 2008, 197:4645-4652.
    • (2008) Comput. Methods Appl. Mech. Engrg. , vol.197 , pp. 4645-4652
    • Soares, D.J.1
  • 35
    • 35348863234 scopus 로고    scopus 로고
    • A locally conservative finite element framework for modeling coupled fluid flow and reservoir geomechanics
    • Jha B., Juanes R. A locally conservative finite element framework for modeling coupled fluid flow and reservoir geomechanics. Acta Geotech. 2007, 2(3):139-153.
    • (2007) Acta Geotech. , vol.2 , Issue.3 , pp. 139-153
    • Jha, B.1    Juanes, R.2
  • 36
    • 79954441329 scopus 로고    scopus 로고
    • Stability and convergence of sequential methods for coupled flow and geomechanics: Mechanics followed by flow, Comput. Methods Appl. Mech. Engrg., accepted for publlication.
    • J. Kim, H.A. Tchelepi, R. Juanes, Stability and convergence of sequential methods for coupled flow and geomechanics: Mechanics followed by flow, Comput. Methods Appl. Mech. Engrg., accepted for publlication.
    • Kim, J.1    Tchelepi, H.A.2    Juanes, R.3
  • 37
    • 0000975035 scopus 로고
    • Coupling of geomechanics and reservoir simulation models, in: Siriwardane, Zeman (Eds.), Geomech., Balkema, Rotterdam
    • A. Settari, F.M. Mourits, Coupling of geomechanics and reservoir simulation models, in: Siriwardane, Zeman (Eds.), Geomech., Balkema, Rotterdam, 1994, pp. 2151-2158.
    • (1994) , pp. 2151-2158
    • Settari, A.1    Mourits, F.M.2
  • 38
    • 79954447083 scopus 로고    scopus 로고
    • Stability and convergence analysis of partially coupled schemes for geomechanics reservoir simulations, in: European Conference on the Mathematics of Oil Recovery, Baveno, Italy
    • D. Bevillon, R. Masson, Stability and convergence analysis of partially coupled schemes for geomechanics reservoir simulations, in: European Conference on the Mathematics of Oil Recovery, Baveno, Italy, 2000.
    • (2000)
    • Bevillon, D.1    Masson, R.2
  • 42
    • 0345643551 scopus 로고
    • General theory of three-dimensional consolidation
    • Biot M.A. General theory of three-dimensional consolidation. J. Appl. Phys. 1941, 12:155-164.
    • (1941) J. Appl. Phys. , vol.12 , pp. 155-164
    • Biot, M.A.1
  • 43
    • 0000388128 scopus 로고
    • The effect of fluid pressure decline on volumetric change of porous rocks
    • Geertsma J. The effect of fluid pressure decline on volumetric change of porous rocks. Trans. AIME 1957, 210:331-340.
    • (1957) Trans. AIME , vol.210 , pp. 331-340
    • Geertsma, J.1
  • 44
    • 31444439189 scopus 로고    scopus 로고
    • On the mechanical energy and effective stress in saturated and unsaturated porous continua
    • Borja R.I. On the mechanical energy and effective stress in saturated and unsaturated porous continua. Int. J. Solids Struct. 2006, 43(6):1764-1786.
    • (2006) Int. J. Solids Struct. , vol.43 , Issue.6 , pp. 1764-1786
    • Borja, R.I.1
  • 46
    • 34250159113 scopus 로고    scopus 로고
    • A coupling of mixed and continuous Galerkin finite element methods for poroelasticity. I: The continuous in time case
    • Phillips P.J., Wheeler M.F. A coupling of mixed and continuous Galerkin finite element methods for poroelasticity. I: The continuous in time case. Comput. Geosci. 2007, 11:131-144.
    • (2007) Comput. Geosci. , vol.11 , pp. 131-144
    • Phillips, P.J.1    Wheeler, M.F.2
  • 47
    • 34250218216 scopus 로고    scopus 로고
    • A coupling of mixed and continuous Galerkin finite element methods for poroelasticity. II: The discrete-in-time case
    • Phillips P.J., Wheeler M.F. A coupling of mixed and continuous Galerkin finite element methods for poroelasticity. II: The discrete-in-time case. Comput. Geosci. 2007, 11:145-158.
    • (2007) Comput. Geosci. , vol.11 , pp. 145-158
    • Phillips, P.J.1    Wheeler, M.F.2
  • 48
    • 79954450414 scopus 로고    scopus 로고
    • Stability, accuracy and efficiency of sequential methods for coupled flow and geomechanics, Soc. Pet. Engrg. J., in press.
    • J. Kim, H.A. Tchelepi, R. Juanes, Stability, accuracy and efficiency of sequential methods for coupled flow and geomechanics, Soc. Pet. Engrg. J., in press.
    • Kim, J.1    Tchelepi, H.A.2    Juanes, R.3
  • 50
    • 0026170491 scopus 로고
    • Nonlinear stability of the time-discrete variational problem of evolution in nonlinear heat conduction, plasticity and viscoplasticity
    • Simo J.C. Nonlinear stability of the time-discrete variational problem of evolution in nonlinear heat conduction, plasticity and viscoplasticity. Comput. Methods Appl. Mech. Engrg. 1991, 88:111-131.
    • (1991) Comput. Methods Appl. Mech. Engrg. , vol.88 , pp. 111-131
    • Simo, J.C.1
  • 51
    • 0025838442 scopus 로고
    • Nonlinear B-stability and symmetry preserving return mapping algorithms for plasticity and viscoplasticity
    • Simo J.C., Govindjee S. Nonlinear B-stability and symmetry preserving return mapping algorithms for plasticity and viscoplasticity. Int. J. Numer. Methods Engrg. 1991, 31:151-176.
    • (1991) Int. J. Numer. Methods Engrg. , vol.31 , pp. 151-176
    • Simo, J.C.1    Govindjee, S.2
  • 53
    • 33846997747 scopus 로고
    • Generalization of the Trotter-Lie formula
    • Lapidus M.L. Generalization of the Trotter-Lie formula. Integr. Eq. Oper. Theory 1981, 4/3:366-413.
    • (1981) Integr. Eq. Oper. Theory , pp. 366-413
    • Lapidus, M.L.1
  • 56
    • 0025262941 scopus 로고
    • Cam-clay plasticity. Part I: Implicit integration of elasto-plastic constitutive relations
    • Borja R.I., Lee S.R. Cam-clay plasticity. Part I: Implicit integration of elasto-plastic constitutive relations. Comput. Methods Appl. Mech. Engrg. 1990, 78:49-72.
    • (1990) Comput. Methods Appl. Mech. Engrg. , vol.78 , pp. 49-72
    • Borja, R.I.1    Lee, S.R.2
  • 57
    • 0026190905 scopus 로고
    • Cam-Clay plasticity. Part II: Implicit integration of constitutive equation based on a nonlinear elastic stress predictor
    • Borja R.I. Cam-Clay plasticity. Part II: Implicit integration of constitutive equation based on a nonlinear elastic stress predictor. Comput. Methods Appl. Mech. Engrg. 1991, 88:225-240.
    • (1991) Comput. Methods Appl. Mech. Engrg. , vol.88 , pp. 225-240
    • Borja, R.I.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.