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Volumn 230, Issue 24, 2011, Pages 8729-8743

A hierarchical fracture model for the iterative multiscale finite volume method

Author keywords

Fractured porous media; Hierarchical fractured modeling; Iterative multiscale finite volume; Iterative multiscale methods; Multiscale finite volume; Multiscale fracture modeling; Multiscale methods

Indexed keywords

ALGEBRA; COMPUTATIONAL EFFICIENCY; DEGREES OF FREEDOM (MECHANICS); FINITE VOLUME METHOD; ITERATIVE METHODS; MULTIPHASE FLOW; POROUS MATERIALS;

EID: 80053622415     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2011.08.021     Document Type: Article
Times cited : (350)

References (48)
  • 1
    • 0000233812 scopus 로고
    • Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks
    • Barenblatt G.I., Zheltov Iu.P., Kochina I.M. Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks. PMM 1960, 24(5):852-864.
    • (1960) PMM , vol.24 , Issue.5 , pp. 852-864
    • Barenblatt, G.I.1    Zheltov, I.2    Kochina, I.M.3
  • 2
    • 0000749480 scopus 로고
    • The behavior of naturally fractured reservoirs
    • Warren J., Root P. The behavior of naturally fractured reservoirs. SPE J. 1963, 245-255.
    • (1963) SPE J. , pp. 245-255
    • Warren, J.1    Root, P.2
  • 3
    • 0014618506 scopus 로고
    • Pressure transient analysis of naturally fractured reservoirs with uniform fracture distribution
    • Kazemi H., Gilman J. Pressure transient analysis of naturally fractured reservoirs with uniform fracture distribution. SPE J. 1969, 451-462.
    • (1969) SPE J. , pp. 451-462
    • Kazemi, H.1    Gilman, J.2
  • 4
    • 0017275045 scopus 로고
    • Numerical simulation of water-oil flow in naturally fractured reservoirs
    • Kazemi H., Merill L.S., Porterfield K.L., Zeman P.R. Numerical simulation of water-oil flow in naturally fractured reservoirs. SPE J. 1976, 16(6):317-326.
    • (1976) SPE J. , vol.16 , Issue.6 , pp. 317-326
    • Kazemi, H.1    Merill, L.S.2    Porterfield, K.L.3    Zeman, P.R.4
  • 5
    • 0020332120 scopus 로고
    • An upstream finite element method for solution of transient transport equation in fractured porous media
    • Noorishad J., Mehran M. An upstream finite element method for solution of transient transport equation in fractured porous media. Water Resour. Res. 1982, 3(18):588-596.
    • (1982) Water Resour. Res. , vol.3 , Issue.18 , pp. 588-596
    • Noorishad, J.1    Mehran, M.2
  • 6
    • 36248938881 scopus 로고
    • Basic concepts in the theory of seepage of homogeneous fluids in fissurized rocks
    • Barenblatt G., Zheltov Y., Kochina I. Basic concepts in the theory of seepage of homogeneous fluids in fissurized rocks. J. Appl. Math. Mech. 1983, 5(24):1286-1303.
    • (1983) J. Appl. Math. Mech. , vol.5 , Issue.24 , pp. 1286-1303
    • Barenblatt, G.1    Zheltov, Y.2    Kochina, I.3
  • 7
    • 0020635993 scopus 로고
    • Fractured reservoir simulation
    • Thomas L.K., Dixon T.N., Pierson R.G. Fractured reservoir simulation. SPE J. 1983, 23(1):42-54.
    • (1983) SPE J. , vol.23 , Issue.1 , pp. 42-54
    • Thomas, L.K.1    Dixon, T.N.2    Pierson, R.G.3
  • 8
    • 0021639798 scopus 로고
    • Modeling fluid flow in fractured porous rock masses by finite element techniques
    • Baca R., Arnett R., Langford D. Modeling fluid flow in fractured porous rock masses by finite element techniques. Int. J. Numer. Methods Fluids 1984, 4:337-348.
    • (1984) Int. J. Numer. Methods Fluids , vol.4 , pp. 337-348
    • Baca, R.1    Arnett, R.2    Langford, D.3
  • 9
    • 85189841421 scopus 로고
    • Analysis of reinfiltration in fractured porous media. SPE 24900, in: The 67th SPE Annual Technical Conference and Exhibition, Washington D.C., Oct.
    • T. Barkve, A. Firoozabadi, Analysis of reinfiltration in fractured porous media. SPE 24900, in: The 67th SPE Annual Technical Conference and Exhibition, Washington D.C., Oct. 4-7, 1992.
    • (1992) , Issue.4-7
    • Barkve, T.1    Firoozabadi, A.2
  • 10
    • 0034994182 scopus 로고    scopus 로고
    • Hierarchical modeling of flow in naturally fractured formations with multiple length scales
    • Lee S.H., Lough M.F., Jensen C.L. Hierarchical modeling of flow in naturally fractured formations with multiple length scales. Water Resour. Res. 2001, 37(3):443-455.
    • (2001) Water Resour. Res. , vol.37 , Issue.3 , pp. 443-455
    • Lee, S.H.1    Lough, M.F.2    Jensen, C.L.3
  • 11
    • 0034261209 scopus 로고    scopus 로고
    • Efficient finite-difference model for flow in a reservoir with multiple length-scale fractures
    • Lee S.H., Jensen C.L., Lough M.F. Efficient finite-difference model for flow in a reservoir with multiple length-scale fractures. SPE J. 2000, 3(5):268-275.
    • (2000) SPE J. , vol.3 , Issue.5 , pp. 268-275
    • Lee, S.H.1    Jensen, C.L.2    Lough, M.F.3
  • 12
    • 52949106034 scopus 로고    scopus 로고
    • Efficient field-scale simulation of black oil in naturally fractured reservoir through discrete fracture networks and homogenized media
    • Li L., Lee S.H. Efficient field-scale simulation of black oil in naturally fractured reservoir through discrete fracture networks and homogenized media. SPE Reserv. Evaluat. Eng. 2008, 750-758.
    • (2008) SPE Reserv. Evaluat. Eng. , pp. 750-758
    • Li, L.1    Lee, S.H.2
  • 13
    • 43649090781 scopus 로고    scopus 로고
    • Numerical simulation of water injection in 2d fractured media using discrete-fracture model
    • Karimi-Fard M., Firoozabadi A. Numerical simulation of water injection in 2d fractured media using discrete-fracture model. SPE REE J. 2003, 4:117-126.
    • (2003) SPE REE J. , vol.4 , pp. 117-126
    • Karimi-Fard, M.1    Firoozabadi, A.2
  • 14
    • 85189837485 scopus 로고    scopus 로고
    • Control-volume finite-element two phase flow experiments with fractured rock represented by unstructured 3d hybrid meshes. SPE 93341-MS, 31 Jan.-2 Feb., The Woodlands, Texas
    • S. Matthai, A. Mezentsev, M. Belayneh, Control-volume finite-element two phase flow experiments with fractured rock represented by unstructured 3d hybrid meshes. SPE 93341-MS, 31 Jan.-2 Feb., The Woodlands, Texas, 2005.
    • (2005)
    • Matthai, S.1    Mezentsev, A.2    Belayneh, M.3
  • 15
    • 85189839016 scopus 로고    scopus 로고
    • Multiscale mimetic solvers for efficient streamline simulation of fractured reservoirs. SPE 119132-MS, 2-4 Feb., The Woodlands, Texas
    • J.R. Natvig, B. Skaflestad, F. Bratvedt, K. Bratvedt, K.-A. Lie, V. Laptev, S.K. Khataniar, Multiscale mimetic solvers for efficient streamline simulation of fractured reservoirs. SPE 119132-MS, 2-4 Feb., The Woodlands, Texas, 2009.
    • (2009)
    • Natvig, J.R.1    Skaflestad, B.2    Bratvedt, F.3    Bratvedt, K.4    Lie, K.-A.5    Laptev, V.6    Khataniar, S.K.7
  • 16
    • 77954849072 scopus 로고    scopus 로고
    • A multiscale mixed finite element method for vuggy and naturally fractured reservoirs
    • Gulbransen A.F., Hauge V.L., Lie K.-A. A multiscale mixed finite element method for vuggy and naturally fractured reservoirs. SPE J. 2010, 15(2):395-403.
    • (2010) SPE J. , vol.15 , Issue.2 , pp. 395-403
    • Gulbransen, A.F.1    Hauge, V.L.2    Lie, K.-A.3
  • 17
    • 0031161210 scopus 로고    scopus 로고
    • A multiscale finite element method for elliptic problems in composite materials and porous media
    • Hou T.Y., Wu X.-H. A multiscale finite element method for elliptic problems in composite materials and porous media. J. Comput. Phys. 1997, 134:169-189.
    • (1997) J. Comput. Phys. , vol.134 , pp. 169-189
    • Hou, T.Y.1    Wu, X.-H.2
  • 19
    • 0039982148 scopus 로고    scopus 로고
    • Convergence of a multiscale finite element method for elliptic problems with rapidly oscillating coefficients
    • Hou T.Y., Wu X.-H., Cai Z. Convergence of a multiscale finite element method for elliptic problems with rapidly oscillating coefficients. Math. Comput. 1999, 68(227):913-943.
    • (1999) Math. Comput. , vol.68 , Issue.227 , pp. 913-943
    • Hou, T.Y.1    Wu, X.-H.2    Cai, Z.3
  • 20
    • 0000713961 scopus 로고    scopus 로고
    • Convergence of a nonconforming multiscale finite element method
    • Efendiev Y., Ginting V., Hou T., Ewing R. Convergence of a nonconforming multiscale finite element method. SIAM J. Numer. Anal. 2000, 37(3):888-910.
    • (2000) SIAM J. Numer. Anal. , vol.37 , Issue.3 , pp. 888-910
    • Efendiev, Y.1    Ginting, V.2    Hou, T.3    Ewing, R.4
  • 21
    • 0002596717 scopus 로고    scopus 로고
    • Numerical subgrid upscaling of two-phase flow in porous media, in: Numerical Treatment of Multiphase Flows in Porous Media. Lecture Notes in Physics
    • T. Arbogast, Numerical subgrid upscaling of two-phase flow in porous media, in: Numerical Treatment of Multiphase Flows in Porous Media. Lecture Notes in Physics, vol. 552, issue 3-4, 2000, pp. 35-49.
    • (2000) , vol.552 , Issue.3-4 , pp. 35-49
    • Arbogast, T.1
  • 22
    • 0036927305 scopus 로고    scopus 로고
    • Implementation of a locally conservative numerical subgrid upscaling scheme for two-phase darcy flow
    • Arbogast T. Implementation of a locally conservative numerical subgrid upscaling scheme for two-phase darcy flow. Comput. Geosci. 2002, 6(3-4):453-481.
    • (2002) Comput. Geosci. , vol.6 , Issue.3-4 , pp. 453-481
    • Arbogast, T.1
  • 23
    • 0037376524 scopus 로고    scopus 로고
    • A mixed multiscale finite element method for elliptic problems with oscillating coefficients
    • Chen Z., Hou T.Y. A mixed multiscale finite element method for elliptic problems with oscillating coefficients. Math. Comput. 2002, 72(242):541-576.
    • (2002) Math. Comput. , vol.72 , Issue.242 , pp. 541-576
    • Chen, Z.1    Hou, T.Y.2
  • 24
    • 0037408094 scopus 로고    scopus 로고
    • Multi-scale finite-volume method for elliptic problems in subsurface flow simulation
    • Jenny P., Lee S.H., Tchelepi H.A. Multi-scale finite-volume method for elliptic problems in subsurface flow simulation. J. Comput. Phys. 2003, 187:47-67.
    • (2003) J. Comput. Phys. , vol.187 , pp. 47-67
    • Jenny, P.1    Lee, S.H.2    Tchelepi, H.A.3
  • 25
    • 15744392935 scopus 로고    scopus 로고
    • Adaptive multiscale finite volume method for multi-phase flow and transport
    • Jenny P., Lee S.H., Tchelepi H.A. Adaptive multiscale finite volume method for multi-phase flow and transport. SIAM Multiscale Model. Simul. 2004, 3(1):50-64.
    • (2004) SIAM Multiscale Model. Simul. , vol.3 , Issue.1 , pp. 50-64
    • Jenny, P.1    Lee, S.H.2    Tchelepi, H.A.3
  • 26
    • 85128810254 scopus 로고    scopus 로고
    • Multiscale finite element methods for nonlinear problems and their applications
    • Efendiev Y., Hou T., Ginting V. Multiscale finite element methods for nonlinear problems and their applications. Commun. Math. Sci. 2004, 2(4):553-589.
    • (2004) Commun. Math. Sci. , vol.2 , Issue.4 , pp. 553-589
    • Efendiev, Y.1    Hou, T.2    Ginting, V.3
  • 27
    • 81255135476 scopus 로고    scopus 로고
    • On the use of a mixed multiscale finite element method for greater flexibility and increased speed or improved accuracy in reservoir simulation
    • Aarnes J.E. On the use of a mixed multiscale finite element method for greater flexibility and increased speed or improved accuracy in reservoir simulation. Multiscale Model. Simul. 2004, 2(3):421-439.
    • (2004) Multiscale Model. Simul. , vol.2 , Issue.3 , pp. 421-439
    • Aarnes, J.E.1
  • 28
    • 2942655408 scopus 로고    scopus 로고
    • Analysis of two-scale finite volume element method for elliptic problem
    • Ginting V. Analysis of two-scale finite volume element method for elliptic problem. J. Numer. Math. 2004, 12:119-141.
    • (2004) J. Numer. Math. , vol.12 , pp. 119-141
    • Ginting, V.1
  • 29
    • 13844298952 scopus 로고    scopus 로고
    • Mixed multiscale finite elements and streamline methods for reservoir simulation of large geomodels
    • Aarnes J.E., Kippe V., Lie K.-A. Mixed multiscale finite elements and streamline methods for reservoir simulation of large geomodels. Adv. Water Resour. 2005, 28(3):257-271.
    • (2005) Adv. Water Resour. , vol.28 , Issue.3 , pp. 257-271
    • Aarnes, J.E.1    Kippe, V.2    Lie, K.-A.3
  • 30
    • 33748582917 scopus 로고    scopus 로고
    • Adaptive fully implicit multi-scale finite-volume method for multi-phase flow and transport in heterogeneous porous media
    • Jenny P., Lee S.H., Tchelepi H.A. Adaptive fully implicit multi-scale finite-volume method for multi-phase flow and transport in heterogeneous porous media. J. Comput. Phys. 2006, 217:627-641.
    • (2006) J. Comput. Phys. , vol.217 , pp. 627-641
    • Jenny, P.1    Lee, S.H.2    Tchelepi, H.A.3
  • 31
    • 51549121853 scopus 로고    scopus 로고
    • A locally conservative variational multiscale method for the simulation of porous media flow with multiscale source terms
    • Juanes R., Dub F.X. A locally conservative variational multiscale method for the simulation of porous media flow with multiscale source terms. Comput. Geosci. 2008, 12:273-295.
    • (2008) Comput. Geosci. , vol.12 , pp. 273-295
    • Juanes, R.1    Dub, F.X.2
  • 32
    • 85189837088 scopus 로고    scopus 로고
    • Error estimate and control in the msfv method for multiphase flow in porous media, in: Proceedings of XVIII International Conference on Computational Methods in Water Resources (CMWR XVIII), Barcelona, Spain
    • H. Hajibeygi, I. Lunati, S.H. Lee, Error estimate and control in the msfv method for multiphase flow in porous media, in: Proceedings of XVIII International Conference on Computational Methods in Water Resources (CMWR XVIII), Barcelona, Spain, 2010.
    • (2010)
    • Hajibeygi, H.1    Lunati, I.2    Lee, S.H.3
  • 33
    • 85189837125 scopus 로고    scopus 로고
    • Accurate and efficient simulation of multiphase flow in a heterogeneous reservoir by using error estimate and control in the multiscale finite-volume framework. SPE 141954, 21-23 Feb., The Woodlands, Texas
    • H. Hajibeygi, I. Lunati, S.H. Lee, Accurate and efficient simulation of multiphase flow in a heterogeneous reservoir by using error estimate and control in the multiscale finite-volume framework. SPE 141954-PP, 21-23 Feb., The Woodlands, Texas, 2011.
    • (2011)
    • Hajibeygi, H.1    Lunati, I.2    Lee, S.H.3
  • 35
    • 67349215455 scopus 로고    scopus 로고
    • Multiscale finite-volume method for parabolic problems arising from compressible multiphase flow in porous media
    • Hajibeygi H., Jenny P. Multiscale finite-volume method for parabolic problems arising from compressible multiphase flow in porous media. J. Comput. Phys. 2009, 228:5129-5147.
    • (2009) J. Comput. Phys. , vol.228 , pp. 5129-5147
    • Hajibeygi, H.1    Jenny, P.2
  • 36
    • 67349120337 scopus 로고    scopus 로고
    • An efficient multi-scale poisson solver for the incompressible Navier-Stokes equations with immersed boundaries
    • Bonfigli G., Jenny P. An efficient multi-scale poisson solver for the incompressible Navier-Stokes equations with immersed boundaries. J. Comput. Phys. 2009, 228:4568-4587.
    • (2009) J. Comput. Phys. , vol.228 , pp. 4568-4587
    • Bonfigli, G.1    Jenny, P.2
  • 37
    • 78651443043 scopus 로고    scopus 로고
    • An iterative multiscale finite volume algorithm converging to exact solution
    • available online doi:10.1016/j.jcp.2010.11.036
    • Lunati I., Tyagi M., Lee S.H. An iterative multiscale finite volume algorithm converging to exact solution. J. Comput. Phys. 2010, available online doi:10.1016/j.jcp.2010.11.036.
    • (2010) J. Comput. Phys.
    • Lunati, I.1    Tyagi, M.2    Lee, S.H.3
  • 38
    • 85189840257 scopus 로고    scopus 로고
    • Recent developments in the multi-scale-finite-volume procedure. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 5910 LNCS:124-131
    • G. Bonfigli, P. Jenny, Recent developments in the multi-scale-finite-volume procedure. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 5910 LNCS:124-131, 2010.
    • (2010)
    • Bonfigli, G.1    Jenny, P.2
  • 39
    • 85189838131 scopus 로고    scopus 로고
    • Two-stage algebraic multiscale linear solver for highly heterogeneous reservoir models. SPE 141473-PP, 21-23 Feb., The Woodlands, Texas
    • H. Zhou, H.A. Tchelepi, Two-stage algebraic multiscale linear solver for highly heterogeneous reservoir models. SPE 141473-PP, 21-23 Feb., The Woodlands, Texas, 2011.
    • (2011)
    • Zhou, H.1    Tchelepi, H.A.2
  • 40
    • 79957905939 scopus 로고    scopus 로고
    • Adaptive iterative multiscale finite volume method
    • Hajibeygi H., Jenny P. Adaptive iterative multiscale finite volume method. J. Comput. Phys. 2011, 230(3):628-643.
    • (2011) J. Comput. Phys. , vol.230 , Issue.3 , pp. 628-643
    • Hajibeygi, H.1    Jenny, P.2
  • 43
    • 85189842665 scopus 로고
    • Interpretation of well-block pressure in numerical reservoir simulation. Society of Petroleum Engineers of AIME (SPE 6893), presented at the PSE-AIME 52nd Annual Fall Technical Conference and Exhibition, Denver
    • D.W. Peaceman, Interpretation of well-block pressure in numerical reservoir simulation. Society of Petroleum Engineers of AIME (SPE 6893), presented at the PSE-AIME 52nd Annual Fall Technical Conference and Exhibition, Denver, 1978, pp. 183-194.
    • (1978) , pp. 183-194
    • Peaceman, D.W.1
  • 45
    • 57649096964 scopus 로고    scopus 로고
    • Modeling complex wells with the multi-scale finite volume method
    • Jenny P., Lunati I. Modeling complex wells with the multi-scale finite volume method. J. Comput. Phys. 2009, 228:687-702.
    • (2009) J. Comput. Phys. , vol.228 , pp. 687-702
    • Jenny, P.1    Lunati, I.2
  • 46
    • 85189841859 scopus 로고    scopus 로고
    • ML 5.0 smoothed aggregation user's guide. Technical Report SAND2006-2649, Sandia National Laboratories
    • M.W. Gee, C.M. Siefert, J.J. Hu, R.S. Tuminaro, M.G. Sala, ML 5.0 smoothed aggregation user's guide. Technical Report SAND2006-2649, Sandia National Laboratories, 2006.
    • (2006)
    • Gee, M.W.1    Siefert, C.M.2    Hu, J.J.3    Tuminaro, R.S.4    Sala, M.G.5
  • 48
    • 51549103361 scopus 로고    scopus 로고
    • On the relationship between the multiscale finite volume method and domain decomposition preconditioners
    • Nordbotten J.M., Bjøstad P.E. On the relationship between the multiscale finite volume method and domain decomposition preconditioners. Comput. Geosci. 2008, 13(3):367-376.
    • (2008) Comput. Geosci. , vol.13 , Issue.3 , pp. 367-376
    • Nordbotten, J.M.1    Bjøstad, P.E.2


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