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Volumn 22, Issue 1, 1996, Pages 1-51

On the spatial-temporal averaging method for modeling transport in porous media

Author keywords

Averaging theorem; Heterogeneity; Macroscopic equation; Microscopic equation; Probabilistic average; REV; Spatial average; Spatial temporal average; Temporal average; Transport equation; Volume average

Indexed keywords

MODELLING-MATHEMATICAL; POROUS MEDIA-FLOW THROUGH; TRANSPORT PHENOMENA;

EID: 0029657382     PISSN: 01693913     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF00974310     Document Type: Article
Times cited : (8)

References (66)
  • 3
    • 0001397434 scopus 로고
    • Spatial macroscopization of processes in heterogeneous systems
    • Bachmat, Y.: 1972, Spatial macroscopization of processes in heterogeneous systems, Israel J. Technol. 10, 391.
    • (1972) Israel J. Technol. , vol.10 , pp. 391
    • Bachmat, Y.1
  • 4
    • 0022823733 scopus 로고
    • Macroscopic modeling of transport phenomena in porous media. 1: The continuum approach
    • Bachmat, Y. and Bear, J.: 1986, Macroscopic modeling of transport phenomena in porous media. 1: The continuum approach, Transport in Porous Media 1, 213.
    • (1986) Transport in Porous Media , vol.1 , pp. 213
    • Bachmat, Y.1    Bear, J.2
  • 6
    • 0021639953 scopus 로고
    • The operational significance of the continuum hypothesis in the theory of water movement through soils and aquifers
    • Baveye, P. and Sposito, G.: 1984, The operational significance of the continuum hypothesis in the theory of water movement through soils and aquifers, Water Resour. Res. 20, 521.
    • (1984) Water Resour. Res. , vol.20 , pp. 521
    • Baveye, P.1    Sposito, G.2
  • 7
    • 0000627183 scopus 로고
    • On the tensor form of dispersion in porous media
    • Bear, J.: 1961, On the tensor form of dispersion in porous media, J. Geophys. Res. 66(4), 1185.
    • (1961) J. Geophys. Res. , vol.66 , Issue.4 , pp. 1185
    • Bear, J.1
  • 11
    • 0022835945 scopus 로고
    • Macroscopic modeling of transport phenomena in porous media. 2: Applications to mass, momentum and energy transport
    • Bear, J. and Bachmat, Y.: 1986, Macroscopic modeling of transport phenomena in porous media. 2: Applications to mass, momentum and energy transport, Transport in Porous Media 1, 241.
    • (1986) Transport in Porous Media , vol.1 , pp. 241
    • Bear, J.1    Bachmat, Y.2
  • 13
    • 13844320326 scopus 로고
    • The lattice Boltzmann equation: Theory and applications
    • Benzi, R., Succi, S. and Vergassola, M.: 1992, The lattice Boltzmann equation: theory and applications, Phys. Rep. 222, 145.
    • (1992) Phys. Rep. , vol.222 , pp. 145
    • Benzi, R.1    Succi, S.2    Vergassola, M.3
  • 15
    • 0003308613 scopus 로고
    • General equations and two-phase flow modeling
    • G. Hetsroni (ed), Hemisphere Publishing Corp.
    • Bouré, J. A. and Delhaye, J. M.: 1982, General equations and two-phase flow modeling, in G. Hetsroni (ed), Handbook of Multiphase Systems, Hemisphere Publishing Corp.
    • (1982) Handbook of Multiphase Systems
    • Bouré, J.A.1    Delhaye, J.M.2
  • 18
    • 11944274749 scopus 로고
    • Proofs of the volume averaging theorems for multiphase flow
    • Cushman, J. H.: 1982, Proofs of the volume averaging theorems for multiphase flow, Adv. Water Resour. 5, 248.
    • (1982) Adv. Water Resour. , vol.5 , pp. 248
    • Cushman, J.H.1
  • 19
    • 0020689543 scopus 로고
    • Multiphase transport equations: I - General equation for Macroscopic statistical, local, space-time homogeneity
    • Cushman, J. H.: 1983a, Multiphase transport equations: I - General equation for Macroscopic statistical, local, space-time homogeneity, Transport Theory Statis. Phys. 12, 35.
    • (1983) Transport Theory Statis. Phys. , vol.12 , pp. 35
    • Cushman, J.H.1
  • 20
    • 1542630309 scopus 로고
    • Volume averaging, probabilistic averaging, and ergodicity
    • Cushman, J. H.: 1983b, Volume averaging, probabilistic averaging, and ergodicity,Adv. Water Resour. 6, 182.
    • (1983) Adv. Water Resour. , vol.6 , pp. 182
    • Cushman, J.H.1
  • 21
    • 0021489414 scopus 로고
    • Fourier interpretation of multiphase averaging theory
    • Cushman, J. H.: 1984a, Fourier interpretation of multiphase averaging theory, Adv. Water Resour. 7, 126.
    • (1984) Adv. Water Resour. , vol.7 , pp. 126
    • Cushman, J.H.1
  • 22
    • 0021641594 scopus 로고
    • On unifying the concepts of scale, instrumentation, and stochastics in development of multiphase transport theory
    • Cushman, J. H.: 1984b, On unifying the concepts of scale, instrumentation, and stochastics in development of multiphase transport theory, Water Resour. Res. 11, 1668.
    • (1984) Water Resour. Res. , vol.11 , pp. 1668
    • Cushman, J.H.1
  • 23
    • 0001996419 scopus 로고
    • On the averaging operators introduced in two-phase flow modeling
    • Toronto, August
    • Delhaye, J. M. and Achard, J. L.: 1976, On the averaging operators introduced in two-phase flow modeling, Proceedings of CSNI Specialists Meeting, Toronto, August, 1 5.
    • (1976) Proceedings of CSNI Specialists Meeting , vol.1 , pp. 5
    • Delhaye, J.M.1    Achard, J.L.2
  • 25
    • 0015077923 scopus 로고
    • Averaged field equations for two-phase media
    • Drew, D. A.: 1971, Averaged field equations for two-phase media, Studies Appl. Math. 50, 133.
    • (1971) Studies Appl. Math. , vol.50 , pp. 133
    • Drew, D.A.1
  • 27
    • 0016470063 scopus 로고
    • A derivation of the equations for multi-phase transport
    • Gray, W. G.: 1975, A derivation of the equations for multi-phase transport, Chem. Eng. Sci. 30, 229.
    • (1975) Chem. Eng. Sci. , vol.30 , pp. 229
    • Gray, W.G.1
  • 28
    • 0020892865 scopus 로고
    • Local volume averaging of multiphase using a non-constant averaging volume
    • Gray, W. G.: 1983, Local volume averaging of multiphase using a non-constant averaging volume, Internat. J. Multiphase Flow 9, 755.
    • (1983) Internat. J. Multiphase Flow , vol.9 , pp. 755
    • Gray, W.G.1
  • 29
    • 0017505662 scopus 로고
    • On the theorems for local volume averaging of multiphase systems
    • Gray, W. G. and Lee, P. C. Y.: 1977, On the theorems for local volume averaging of multiphase systems, Internat. J. Multiphase Flow 3, 333.
    • (1977) Internat. J. Multiphase Flow , vol.3 , pp. 333
    • Gray, W.G.1    Lee, P.C.Y.2
  • 31
    • 37249006592 scopus 로고
    • General conservation equations for multi-phase systems: 1. Averaging procedure
    • Hassanizadeh, M. and Gray, W. G.: 1979a, General conservation equations for multi-phase systems: 1. Averaging procedure, Adv. Water Resour. 2, 131.
    • (1979) Adv. Water Resour. , vol.2 , pp. 131
    • Hassanizadeh, M.1    Gray, W.G.2
  • 32
    • 0013726079 scopus 로고
    • General conservation equations for multi-phase systems: 2. Mass, momenta, energy, and entropy equations
    • Hassanizadeh, M. and Gray, W. G.: 1979b, General conservation equations for multi-phase systems: 2. Mass, momenta, energy, and entropy equations, Adv. Water Resour. 2, 191.
    • (1979) Adv. Water Resour. , vol.2 , pp. 191
    • Hassanizadeh, M.1    Gray, W.G.2
  • 33
  • 35
    • 0021938510 scopus 로고
    • The spatial averaging theorem revisited
    • Howes, F. A. and Whitaker, S.: 1985, The spatial averaging theorem revisited, Chem. Eng. Sci. 40, 1387.
    • (1985) Chem. Eng. Sci. , vol.40 , pp. 1387
    • Howes, F.A.1    Whitaker, S.2
  • 36
    • 0001594016 scopus 로고
    • Darcy's law and the field equations of the flow of underground fluid
    • Hubbert, M. K.: 1956, Darcy's law and the field equations of the flow of underground fluid, AIME Petrol 207, 222.
    • (1956) AIME Petrol , vol.207 , pp. 222
    • Hubbert, M.K.1
  • 39
    • 0018955148 scopus 로고
    • A note on volume-averaging
    • Narasimhan, T. N.: 1980, A note on volume-averaging, Adv. Water Resour. 3, 135.
    • (1980) Adv. Water Resour. , vol.3 , pp. 135
    • Narasimhan, T.N.1
  • 41
    • 0000936583 scopus 로고
    • Eulerian kinematics of flow through spatially periodic models of porous media
    • Nitsche, L. C. and Brenner, H.: 1989, Eulerian kinematics of flow through spatially periodic models of porous media, Arch. Rational Mech. Anal. 107, 225.
    • (1989) Arch. Rational Mech. Anal. , vol.107 , pp. 225
    • Nitsche, L.C.1    Brenner, H.2
  • 42
    • 84945071836 scopus 로고
    • Dispersion in heterogeneous porous media. 1. Local volume averaging and large-scale averaging
    • Plumb, O. A. and Whitaker, S.: 1988a, Dispersion in heterogeneous porous media. 1. Local volume averaging and large-scale averaging, Water Resour. Res. 24, 913.
    • (1988) Water Resour. Res. , vol.24 , pp. 913
    • Plumb, O.A.1    Whitaker, S.2
  • 43
    • 84945091439 scopus 로고
    • Dispersion in heterogeneous porous media. 2. Predictions for stratified and two-dimensional spatially periodic systems
    • Plumb, O. A. and Whitaker, S.: 1988b, Dispersion in heterogeneous porous media. 2. Predictions for stratified and two-dimensional spatially periodic systems, Water Resour. Res. 24, 927.
    • (1988) Water Resour. Res. , vol.24 , pp. 927
    • Plumb, O.A.1    Whitaker, S.2
  • 44
    • 0028372271 scopus 로고
    • Transport in ordered and disordered porous media, I: The cellular average and the use of weighting functions
    • Quintard, M. and Whitaker, S.: 1994a, Transport in ordered and disordered porous media, I: The cellular average and the use of weighting functions, Transport in Porous Media 14, 163.
    • (1994) Transport in Porous Media , vol.14 , pp. 163
    • Quintard, M.1    Whitaker, S.2
  • 45
    • 0028372270 scopus 로고
    • Transport in ordered and disordered porous media, II: Generalized volume averaging
    • Quintard, M. and Whitaker, S.: 1994a, Transport in ordered and disordered porous media, II: Generalized volume averaging, Transport in Porous Media 14, 179.
    • (1994) Transport in Porous Media , vol.14 , pp. 179
    • Quintard, M.1    Whitaker, S.2
  • 46
    • 12044257626 scopus 로고
    • Lattice-gas models of phase separation: Interfaces, phase transitions, and multiphase flow
    • Rothman, D. H. and Zaleski, S.: 1994, Lattice-gas models of phase separation: interfaces, phase transitions, and multiphase flow, Rev. Modern Phys. 66, 1417.
    • (1994) Rev. Modern Phys. , vol.66 , pp. 1417
    • Rothman, D.H.1    Zaleski, S.2
  • 47
    • 25444528412 scopus 로고
    • The G-asymptotic form of operators and averaging in the mechanics of multiphase media
    • Salamatin, A. N.: 1985, The G-asymptotic form of operators and averaging in the mechanics of multiphase media, Soviet Math. 29, 85.
    • (1985) Soviet Math. , vol.29 , pp. 85
    • Salamatin, A.N.1
  • 50
    • 0000660083 scopus 로고
    • Flow of viscoelastic fluids through porous media
    • Slattery, J. C.: 1967, Flow of viscoelastic fluids through porous media, A.I.Ch.E. J. 13, 1066.
    • (1967) A.I.Ch.E. J. , vol.13 , pp. 1066
    • Slattery, J.C.1
  • 52
    • 0018322795 scopus 로고
    • Foundations theories of solute transport in porous media: A critical review
    • Sposito, G., Gupta, V. K. and Bhattacharya, R. N.: 1979, Foundations theories of solute transport in porous media: a critical review, Adv. Water Resour. 2, 59.
    • (1979) Adv. Water Resour. , vol.2 , pp. 59
    • Sposito, G.1    Gupta, V.K.2    Bhattacharya, R.N.3
  • 53
    • 0020330874 scopus 로고
    • Numerical simulation of flow and contaminant migration at an extensive monitored landfill
    • Sykes, J. F., Pahwa, S. B., Lantz, R. B. and Ward, D. S.: 1982, Numerical simulation of flow and contaminant migration at an extensive monitored landfill, Water Resour. Res. 18(6), 1687.
    • (1982) Water Resour. Res. , vol.18 , Issue.6 , pp. 1687
    • Sykes, J.F.1    Pahwa, S.B.2    Lantz, R.B.3    Ward, D.S.4
  • 54
    • 0022715173 scopus 로고
    • A second-order approach for the modeling of dispersive transport in porous media. 1. Theoretical development
    • Tompson, A. F. B. and Gray, W. G.: 1986a, A second-order approach for the modeling of dispersive transport in porous media. 1. Theoretical development, Water Resour. Res. 22(5), 591.
    • (1986) Water Resour. Res. , vol.22 , Issue.5 , pp. 591
    • Tompson, A.F.B.1    Gray, W.G.2
  • 55
    • 0022709419 scopus 로고
    • A second-order approach for the modeling of dispersive transport in porous media. 2. Application to solute motion in pipes and capillary tubes
    • Tompson, A. F. B. and Gray, W. G.: 1986b, A second-order approach for the modeling of dispersive transport in porous media. 2. Application to solute motion in pipes and capillary tubes, Water Resour. Res. 22(5), 601.
    • (1986) Water Resour. Res. , vol.22 , Issue.5 , pp. 601
    • Tompson, A.F.B.1    Gray, W.G.2
  • 56
    • 0022873529 scopus 로고
    • A second-order approach for the modeling of dispersive transport in porous media. 3. Application to two porous media problems
    • Tompson, A. F. B. and Gray, W. G.: 1986c, A second-order approach for the modeling of dispersive transport in porous media. 3. Application to two porous media problems, Water Resour. Res. 22(13), 1959.
    • (1986) Water Resour. Res. , vol.22 , Issue.13 , pp. 1959
    • Tompson, A.F.B.1    Gray, W.G.2
  • 57
    • 0019396650 scopus 로고
    • Theorem for the local volume average of a gradient revised
    • Veverka, V.: 1981, Theorem for the local volume average of a gradient revised, Chem. Eng. Sci. 28, 833.
    • (1981) Chem. Eng. Sci. , vol.28 , pp. 833
    • Veverka, V.1
  • 58
    • 0001318470 scopus 로고
    • The equations of motion in porous media
    • Whitaker, S. 1966, The equations of motion in porous media, Chem. Eng. Sci. 21, 291.
    • (1966) Chem. Eng. Sci. , vol.21 , pp. 291
    • Whitaker, S.1
  • 59
    • 84984083570 scopus 로고
    • Diffusion and dispersion in porous media
    • Whitaker, S. 1967, Diffusion and dispersion in porous media, A.I.Ch.E. J. 13, 420.
    • (1967) A.I.Ch.E. J. , vol.13 , pp. 420
    • Whitaker, S.1
  • 60
    • 85023669587 scopus 로고
    • Advances in theory of fluid Motion in porous media
    • Whitaker, S. 1969, Advances in theory of fluid Motion in porous media, Industr. Eng. Chem. 61, 14.
    • (1969) Industr. Eng. Chem. , vol.61 , pp. 14
    • Whitaker, S.1
  • 61
    • 0015564308 scopus 로고
    • The transport equations for multi-phase systems
    • Whitaker, S. 1973, The transport equations for multi-phase systems, Chem. Eng. Sci. 28, 139.
    • (1973) Chem. Eng. Sci. , vol.28 , pp. 139
    • Whitaker, S.1
  • 62
    • 0022260146 scopus 로고
    • A simple geometrical derivation of the spatial averaging theorem
    • Whitaker, S.: 1985, A simple geometrical derivation of the spatial averaging theorem, Chemical Engineering Education 19, 18.
    • (1985) Chemical Engineering Education , vol.19 , pp. 18
    • Whitaker, S.1
  • 66
    • 0001468597 scopus 로고
    • On the dispersed flow in the laminar flow regime
    • Zuber, N.: 1964, On the dispersed flow in the laminar flow regime, Chem. Eng. Sci. 19, 897.
    • (1964) Chem. Eng. Sci. , vol.19 , pp. 897
    • Zuber, N.1


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