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Volumn 75, Issue 3, 2008, Pages 371-400

Two-Phase inertial flow in homogeneous porous media: A theoretical derivation of a macroscopic model

Author keywords

Homogeneous porous media; Inertial or non Darcian flow; Two phase flow; Up scaling; Volume averaging

Indexed keywords

CAPILLARITY; FLUID DYNAMICS; LIQUIDS; MULTIPHASE FLOW; POROUS MATERIALS; PRESSURE GRADIENT; REYNOLDS NUMBER; TENSORS; TWO PHASE FLOW; WATER DISTRIBUTION SYSTEMS;

EID: 55149097012     PISSN: 01693913     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11242-008-9231-y     Document Type: Article
Times cited : (31)

References (65)
  • 1
    • 0000744087 scopus 로고
    • Nonlinear flow in porous media
    • Ahmed N. and Sunada D.K. (1969). Nonlinear flow in porous media. J. Hydr. Div. ASCE 95(HY6): 1847-1857
    • (1969) J. Hydr. Div. ASCE , vol.95 , Issue.HY6 , pp. 1847-1857
    • Ahmed, N.1    Sunada, D.K.2
  • 2
    • 0031464175 scopus 로고    scopus 로고
    • Dispersion in two-dimensional periodic porous media, Part I: Hydrodynamics
    • Amaral Souto H. and Moyne C. (1997). Dispersion in two-dimensional periodic porous media, Part I: Hydrodynamics. Phys. Fluids 9(8): 2243-2252
    • (1997) Phys. Fluids , vol.9 , Issue.8 , pp. 2243-2252
    • Amaral Souto, H.1    Moyne, C.2
  • 3
    • 0023286477 scopus 로고
    • Nonsaturated deformable porous media: Quasistatics
    • Auriault J.L. (1987). Nonsaturated deformable porous media: quasistatics. Transp. Porous Media 2(1): 45-64
    • (1987) Transp. Porous Media , vol.2 , Issue.1 , pp. 45-64
    • Auriault, J.L.1
  • 6
    • 0031104607 scopus 로고    scopus 로고
    • Generalized Forchheimer equation for two-phase flow based on hybrid mixture theory
    • Bennethum L. and Giorgi T. (1997). Generalized Forchheimer equation for two-phase flow based on hybrid mixture theory. Transp. Porous Media 26(3): 261-275
    • (1997) Transp. Porous Media , vol.26 , Issue.3 , pp. 261-275
    • Bennethum, L.1    Giorgi, T.2
  • 7
    • 0002826073 scopus 로고
    • Capillary orifice model for high speed flow through porous media. I and EC
    • Blick E.F. (1966). Capillary orifice model for high speed flow through porous media. I and EC. Process Design Dev. 5: 90-94
    • (1966) Process Design Dev. , vol.5 , pp. 90-94
    • Blick, E.F.1
  • 8
    • 0000036908 scopus 로고    scopus 로고
    • Phase change phenomena at liquid saturated self heated particulate beds
    • Von Karman Institute for Fluid Dynamics Rhode-Sainte-Genèse, Belgium (1987)
    • Buchlin, J., Stubos, A.: Phase change phenomena at liquid saturated self heated particulate beds. Application of Transport in Porous media, Von Karman Institute for Fluid Dynamics, vol. 4, pp. 221-276. Rhode-Sainte-Genèse, Belgium (1987)
    • Application of Transport in Porous Media , vol.4 , pp. 221-276
    • Buchlin, J.1    Stubos, A.2
  • 9
    • 0021661101 scopus 로고
    • Heat and mass transfer in porous media
    • In: Bear, J. and Corapcigolu, M.Y. (eds) Martinus Nijhoff Publishers, Dordrecht
    • Carbonell R.G. and Whitaker S. (1984). Heat and mass transfer in porous media. In: Bear, J. and Corapcigolu, M.Y. (eds) Fundamentals of Transport Phenomena in Porous Media, pp 121-198. Martinus Nijhoff Publishers, Dordrecht
    • (1984) Fundamentals of Transport Phenomena in Porous Media , pp. 121-198
    • Carbonell, R.G.1    Whitaker, S.2
  • 10
    • 0035425104 scopus 로고    scopus 로고
    • Derivation of the Forchheimer law via homogenization
    • Chen Z., Lyons S.L. and Qin G. (2001). Derivation of the Forchheimer law via homogenization. Transp. Porous Media 44(2): 325-335
    • (2001) Transp. Porous Media , vol.44 , Issue.2 , pp. 325-335
    • Chen, Z.1    Lyons, S.L.2    Qin, G.3
  • 11
    • 0001064029 scopus 로고
    • Numerical modeling of non-linear effects in laminar flow through a porous medium
    • Coulaud O., Morel P. and Caltagirone J.P. (1988). Numerical modeling of non-linear effects in laminar flow through a porous medium. J. Fluid Mech. 190: 393-407
    • (1988) J. Fluid Mech. , vol.190 , pp. 393-407
    • Coulaud, O.1    Morel, P.2    Caltagirone, J.P.3
  • 12
    • 0022988319 scopus 로고
    • A continuum approach to high velocity flow in a porous medium
    • Cvetkovic V.D. (1986). A continuum approach to high velocity flow in a porous medium. Transp. Porous Media 1(1): 63-97
    • (1986) Transp. Porous Media , vol.1 , Issue.1 , pp. 63-97
    • Cvetkovic, V.D.1
  • 13
    • 0003464575 scopus 로고
    • Librairie des corps impériaux des ponts et chaussées et des mines, Paris
    • Darcy H. (1856). Les fontaines publiques de la ville de Dijon. Librairie des corps impériaux des ponts et chaussées et des mines, Paris
    • (1856) Les Fontaines Publiques De La Ville De Dijon
    • Darcy, H.1
  • 14
    • 84985597814 scopus 로고
    • Flow rate-pressure gradient measurement in periodically nonuniform capillary tube
    • Dullien A.L. and Azzam M.I.S. (1973). Flow rate-pressure gradient measurement in periodically nonuniform capillary tube. AIChE J. 19: 222-229
    • (1973) AIChE J. , vol.19 , pp. 222-229
    • Dullien, A.L.1    Azzam, M.I.S.2
  • 15
    • 0002127397 scopus 로고
    • Fluid flow through packed columns
    • Ergun S. (1952). Fluid flow through packed columns. Chem. Eng. Prog. 48: 89-94
    • (1952) Chem. Eng. Prog. , vol.48 , pp. 89-94
    • Ergun, S.1
  • 16
    • 0023717891 scopus 로고
    • Influence of an immobile or mobile saturation on non-Darcy compressible flow of real gases in propped fractures
    • Evans E.V. and Evans R.D. (1988). Influence of an immobile or mobile saturation on non-Darcy compressible flow of real gases in propped fractures. J. Petrol. Technol. 40(10): 1343-1351
    • (1988) J. Petrol. Technol. , vol.40 , Issue.10 , pp. 1343-1351
    • Evans, E.V.1    Evans, R.D.2
  • 17
    • 0023453827 scopus 로고
    • The effect of an immobile liquid saturation on the non-Darcy flow coefficient in porous media
    • Evans R.D., Hudson C.S. and Greenlee J.E. (1987). The effect of an immobile liquid saturation on the non-Darcy flow coefficient in porous media. J. SPE Prod. Eng. Trans. AIME 283: 331-338
    • (1987) J. SPE Prod. Eng. Trans. AIME , vol.283 , pp. 331-338
    • Evans, R.D.1    Hudson, C.S.2    Greenlee, J.E.3
  • 18
    • 0000953750 scopus 로고
    • Sur l'homogénéisation des équations de Navier-Stokes à faible nombre de Reynolds
    • Firdaouss M. and Guermond J.L. (1995). Sur l'homogénéisation des équations de Navier-Stokes à faible nombre de Reynolds. C. R. Acad. Sci. Paris, Série I 320: 245-251
    • (1995) C. R. Acad. Sci. Paris, Série I , vol.320 , pp. 245-251
    • Firdaouss, M.1    Guermond, J.L.2
  • 19
    • 0031177676 scopus 로고    scopus 로고
    • Nonlinear corrections to Darcy's law at low Reynolds numbers
    • Firdaouss M., Guermond J.L. and Le Quéré P. (1997). Nonlinear corrections to Darcy's law at low Reynolds numbers. J. Fluid Mech. 343: 331-350
    • (1997) J. Fluid Mech. , vol.343 , pp. 331-350
    • Firdaouss, M.1    Guermond, J.L.2    Le Quéré, P.3
  • 20
    • 0018435271 scopus 로고
    • An analysis of high-velocity gas flow through porous media
    • Firoozabadi A. and Katz D.L. (1979). An analysis of high-velocity gas flow through porous media. J. Petrol. Technol. February 1979: 211-216
    • (1979) J. Petrol. Technol. February , vol.1979 , pp. 211-216
    • Firoozabadi, A.1    Katz, D.L.2
  • 22
    • 0000279859 scopus 로고
    • Wasserbewgung durch boden
    • Forchheimer P. (1901). Wasserbewgung durch boden. Z. Ver. Deutsch. Ing. 45: 1782-1788
    • (1901) Z. Ver. Deutsch. Ing. , vol.45 , pp. 1782-1788
    • Forchheimer, P.1
  • 23
    • 0033686455 scopus 로고    scopus 로고
    • Inertial effects in two-phase flow through fractures
    • Fourar M. and Lenormand R. (2000). Inertial effects in two-phase flow through fractures. Oil Gas Sci. Technol. - Rev. IFP 55(3): 259-268
    • (2000) Oil Gas Sci. Technol. - Rev. IFP , vol.55 , Issue.3 , pp. 259-268
    • Fourar, M.1    Lenormand, R.2
  • 24
    • 0016114558 scopus 로고
    • Estimating the coefficient of inertial resistance in fluid flow through porous media
    • Geertsma J. (1974). Estimating the coefficient of inertial resistance in fluid flow through porous media. Soc. Petrol. Eng. J. 14: 445-450
    • (1974) Soc. Petrol. Eng. J. , vol.14 , pp. 445-450
    • Geertsma, J.1
  • 25
    • 0031277535 scopus 로고    scopus 로고
    • Derivation of the Forchheimer law via matched asymptotic expansions
    • Giorgi T. (1997). Derivation of the Forchheimer law via matched asymptotic expansions. Transp. Porous Media 29(2): 191-206
    • (1997) Transp. Porous Media , vol.29 , Issue.2 , pp. 191-206
    • Giorgi, T.1
  • 26
    • 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: 229-233
    • (1975) Chem. Eng. Sci. , vol.30 , pp. 229-233
    • Gray, W.G.1
  • 28
    • 0021938510 scopus 로고
    • The spatial averaging theorem revisited
    • Howes F. and Whitaker S. (1985). The spatial averaging theorem revisited. Chem. Eng. Sci. 40: 1387-1392
    • (1985) Chem. Eng. Sci. , vol.40 , pp. 1387-1392
    • Howes, F.1    Whitaker, S.2
  • 29
    • 0142158092 scopus 로고
    • On the theoretical derivation of Darcy and Forchheimer formulas
    • Irmay S. (1958). On the theoretical derivation of Darcy and Forchheimer formulas. J. Geophys. Res. 39: 702-707
    • (1958) J. Geophys. Res. , vol.39 , pp. 702-707
    • Irmay, S.1
  • 30
    • 0025444746 scopus 로고
    • Origin and quantification of coupling between relative permeabilities for two-phase flows in porous media
    • Kalaydjian F. (1990). Origin and quantification of coupling between relative permeabilities for two-phase flows in porous media. Transp. Porous Media 5(3): 215-229
    • (1990) Transp. Porous Media , vol.5 , Issue.3 , pp. 215-229
    • Kalaydjian, F.1
  • 31
    • 0031250079 scopus 로고    scopus 로고
    • Moderate Reynolds number flows through periodic and random arrays of aligned cylinders
    • Koch J.B. and Ladd A.J.C. (1997). Moderate Reynolds number flows through periodic and random arrays of aligned cylinders. J. Fluid Mech. 349: 31-66
    • (1997) J. Fluid Mech. , vol.349 , pp. 31-66
    • Koch, J.B.1    Ladd, A.J.C.2
  • 32
    • 0030207842 scopus 로고    scopus 로고
    • Determination of permeability tensors for two-phase flow in homogeneous porous media: Theory
    • Lasseux D., Whitaker S. and Quintard M. (1996). Determination of permeability tensors for two-phase flow in homogeneous porous media: theory. Transp. Porous Media 24(1): 107-137
    • (1996) Transp. Porous Media , vol.24 , Issue.1 , pp. 107-137
    • Lasseux, D.1    Whitaker, S.2    Quintard, M.3
  • 33
    • 0009996121 scopus 로고
    • A particle bed dryout model with upwind and downward boiling
    • Lipinski R.J. (1980). A particle bed dryout model with upwind and downward boiling. Trans. Am. Nucl. Soc. 35: 350-358
    • (1980) Trans. Am. Nucl. Soc. , vol.35 , pp. 350-358
    • Lipinski, R.J.1
  • 35
    • 0029522050 scopus 로고
    • Correlations of the non-Darcy flow coefficient
    • Liu X., Civan F. and Evans R.D. (1995). Correlations of the non-Darcy flow coefficient. J. Can. Petrol. Technol. 34(10): 50-54
    • (1995) J. Can. Petrol. Technol. , vol.34 , Issue.10 , pp. 50-54
    • Liu, X.1    Civan, F.2    Evans, R.D.3
  • 36
    • 0001975490 scopus 로고
    • Proposed correlation of data for isorthermal two-phase two-component flow in pipes
    • Lockhart R. and Martinelli R. (1949). Proposed correlation of data for isorthermal two-phase two-component flow in pipes. Chem. Eng. Prog. 45: 39
    • (1949) Chem. Eng. Prog. , vol.45 , pp. 39
    • Lockhart, R.1    Martinelli, R.2
  • 37
    • 0027693114 scopus 로고
    • The microscopic analysis of high Forchheimer number flow in porous media
    • Ma H. and Ruth D.W. (1993). The microscopic analysis of high Forchheimer number flow in porous media. Transp. Porous Media 13(2): 139-160
    • (1993) Transp. Porous Media , vol.13 , Issue.2 , pp. 139-160
    • Ma, H.1    Ruth, D.W.2
  • 39
    • 0001032632 scopus 로고
    • Ecoulements monophasiques en milieu poreux
    • Marle C.M. (1967). Ecoulements monophasiques en milieu poreux. Rev. Inst. Frantais du Ptrole 22: 1471-1509
    • (1967) Rev. Inst. Frantais Du Ptrole , vol.22 , pp. 1471-1509
    • Marle, C.M.1
  • 40
    • 0026359762 scopus 로고
    • The effect of weak inertia on flow through a porous medium
    • Mei C.C. and Auriault J.L. (1991). The effect of weak inertia on flow through a porous medium. J. Fluid Mech. 222: 647-663
    • (1991) J. Fluid Mech. , vol.222 , pp. 647-663
    • Mei, C.C.1    Auriault, J.L.2
  • 41
    • 0004152907 scopus 로고
    • International Human Resources Development Corporation (reprint from McGraw-Hill, 1982), Boston
    • Muskat, M.: The flow of homogeneous fluids through porous media. International Human Resources Development Corporation (reprint from McGraw-Hill, 1982), Boston (1937)
    • (1937) The Flow of Homogeneous Fluids Through Porous Media
    • Muskat, M.1
  • 42
    • 0035477922 scopus 로고    scopus 로고
    • A computational evaluation of the Ergun and Forchheimer equations for fibrous porous media
    • Papathanasiou T.D., Markicevic B. and Dendy E.D. (2001). A computational evaluation of the Ergun and Forchheimer equations for fibrous porous media. Phys. Fluids 13(10): 2795-2804
    • (2001) Phys. Fluids , vol.13 , Issue.10 , pp. 2795-2804
    • Papathanasiou, T.D.1    Markicevic, B.2    Dendy, E.D.3
  • 43
    • 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. Transp. Porous Media 14(2): 163-177
    • (1994) Transp. Porous Media , vol.14 , Issue.2 , pp. 163-177
    • Quintard, M.1    Whitaker, S.2
  • 44
    • 0028372270 scopus 로고
    • Transport in ordered and disordered porous media II: Generalized volume averaging. Transp
    • Quintard M. and Whitaker S. (1994b). Transport in ordered and disordered porous media II: Generalized volume averaging. Transp. Porous Media 14(2): 179-206
    • (1994) Porous Media , vol.14 , Issue.2 , pp. 179-206
    • Quintard, M.1    Whitaker, S.2
  • 45
    • 0028431289 scopus 로고
    • Transport in ordered and disordered porous media V: Geometrical results for two-dimensional systems
    • Quintard M. and Whitaker S. (1994c). Transport in ordered and disordered porous media V: Geometrical results for two-dimensional systems. Transp. Porous Media 15(2): 183-196
    • (1994) Transp. Porous Media , vol.15 , Issue.2 , pp. 183-196
    • Quintard, M.1    Whitaker, S.2
  • 46
    • 0000470345 scopus 로고
    • Transport in soils: The balance of momentum
    • Raats D.A.C. and Klute A. (1968). Transport in soils: The balance of momentum. Soil Sci. Soc. Am. Proc. 32: 161-166
    • (1968) Soil Sci. Soc. Am. Proc. , vol.32 , pp. 161-166
    • Raats, D.A.C.1    Klute, A.2
  • 47
    • 0001139009 scopus 로고
    • Nonlinear seepage flow through a rigid porous medium
    • Rasoloarijaona M. and Auriault J.L. (1994). Nonlinear seepage flow through a rigid porous medium. Eur. J. Mech. B/Fluids 13(2): 177-195
    • (1994) Eur. J. Mech. B/Fluids , vol.13 , Issue.2 , pp. 177-195
    • Rasoloarijaona, M.1    Auriault, J.L.2
  • 48
    • 0000299373 scopus 로고    scopus 로고
    • Nonlinear flow in porous media
    • Rojas S. and Koplik J. (1998). Nonlinear flow in porous media. Phys. Rev. E 58(4): 4476-4782
    • (1998) Phys. Rev. E , vol.58 , Issue.4 , pp. 4476-4782
    • Rojas, S.1    Koplik, J.2
  • 49
    • 0007568848 scopus 로고
    • Data interpretation problems to be expected in the study of coupled fluid flow in porous media
    • Rose W. (1989). Data interpretation problems to be expected in the study of coupled fluid flow in porous media. Transp. Porous Media 4(2): 185-189
    • (1989) Transp. Porous Media , vol.4 , Issue.2 , pp. 185-189
    • Rose, W.1
  • 50
    • 0027693115 scopus 로고
    • Numerical analysis of the viscous incompressible flow in a diverging-converging RUC
    • Ruth D. and Ma H. (1993). Numerical analysis of the viscous incompressible flow in a diverging-converging RUC. Transp. Porous Media 13(2): 161-177
    • (1993) Transp. Porous Media , vol.13 , Issue.2 , pp. 161-177
    • Ruth, D.1    Ma, H.2
  • 52
    • 0033372356 scopus 로고    scopus 로고
    • High-velocity laminar and turbulent flow in porous media
    • Skjetne E. and Auriault J.L. (1999). High-velocity laminar and turbulent flow in porous media. Transp. Porous Media 36: 131-147
    • (1999) Transp. Porous Media , vol.36 , pp. 131-147
    • Skjetne, E.1    Auriault, J.L.2
  • 55
    • 0032051399 scopus 로고    scopus 로고
    • Network modeling of non-Darcy flow through porous media
    • Thauvin F. and Mohanty K.K. (1998). Network modeling of non-Darcy flow through porous media. Transp. Porous Media 31(1): 19-37
    • (1998) Transp. Porous Media , vol.31 , Issue.1 , pp. 19-37
    • Thauvin, F.1    Mohanty, K.K.2
  • 56
    • 0023397372 scopus 로고
    • Closure of the governing equations for immiscible two-phase flow: A research comment
    • Torres F.E. (1987). Closure of the governing equations for immiscible two-phase flow: A research comment. Transp. Porous Media 2(4): 383-393
    • (1987) Transp. Porous Media , vol.2 , Issue.4 , pp. 383-393
    • Torres, F.E.1
  • 58
    • 0002611980 scopus 로고
    • Turbulent flow in porous media
    • Ward J.C. (1964). Turbulent flow in porous media. J. Hydr. Div., ASCE 90(HY5): 1-12
    • (1964) J. Hydr. Div., ASCE , vol.90 , Issue.HY5 , pp. 1-12
    • Ward, J.C.1
  • 59
    • 0023033970 scopus 로고
    • Flow in porous media I: A theoretical derivation of Darcy's law
    • Whitaker S. (1986a). Flow in porous media I: A theoretical derivation of Darcy's law. Transp. Porous Media 1(1): 3-25
    • (1986) Transp. Porous Media , vol.1 , Issue.1 , pp. 3-25
    • Whitaker, S.1
  • 60
    • 0022964273 scopus 로고
    • Flow in porous media II: The governing equation for immiscible two-phase flow
    • Whitaker S. (1986b). Flow in porous media II: The governing equation for immiscible two-phase flow. Transp. Porous Media 1(1): 105-125
    • (1986) Transp. Porous Media , vol.1 , Issue.1 , pp. 105-125
    • Whitaker, S.1
  • 61
    • 0028388980 scopus 로고
    • The closure problem for two-phase flow in homogeneous porous media
    • Whitaker S. (1994). The closure problem for two-phase flow in homogeneous porous media. Chem. Eng. Sci. 49: 765-780
    • (1994) Chem. Eng. Sci. , vol.49 , pp. 765-780
    • Whitaker, S.1
  • 62
    • 0030267168 scopus 로고    scopus 로고
    • The Forchheimer equation: A theoretical development
    • Whitaker S. (1996). The Forchheimer equation: A theoretical development. Transp. Porous Media 25(1): 27-61
    • (1996) Transp. Porous Media , vol.25 , Issue.1 , pp. 27-61
    • Whitaker, S.1
  • 63
    • 0003776105 scopus 로고    scopus 로고
    • Theory and Applications of Transport in Porous Media. Kluwer Academic, Dordrecht, The Netherlands
    • Whitaker S. (1999). The Method of Volume Averaging. Theory and Applications of Transport in Porous Media. Kluwer Academic, Dordrecht, The Netherlands
    • (1999) The Method of Volume Averaging
    • Whitaker, S.1
  • 64
    • 0026070616 scopus 로고
    • Correction non linéaire de la loi de Darcy
    • Wodie, J.C., Levy, T.: Correction non linéaire de la loi de Darcy. C. R. Acad. Sci. Paris II 157-161 (1991)
    • (1991) C. R. Acad. Sci. Paris , vol.2 , pp. 157-161
    • Wodie, J.C.1    Levy, T.2
  • 65
    • 0010493712 scopus 로고
    • Etude du couplage visqueux en milieu poreux: Mesure des perméabilités relatives croisées
    • Ph.D. Thesis, INP Toulouse
    • Zarcone, C.: Etude du couplage visqueux en milieu poreux: Mesure des perméabilités relatives croisées. Ph.D. Thesis, INP Toulouse (1994)
    • (1994)
    • Zarcone, C.1


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