메뉴 건너뛰기




Volumn 81, Issue 1, 2010, Pages 35-60

Polynomial filtration laws for low Reynolds number flows through porous media

Author keywords

Cubic law; Forchheimer; Homogenization; Inertial effects

Indexed keywords

GROUNDWATER FLOW; HOMOGENIZATION METHOD; LAMINAR FLOW; POLYNOMIALS; POROUS MATERIALS; PROBLEM SOLVING; REYNOLDS NUMBER; SEEPAGE; VELOCITY; VISCOUS FLOW;

EID: 76149128385     PISSN: 01693913     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11242-009-9388-z     Document Type: Article
Times cited : (56)

References (45)
  • 2
    • 84974746759 scopus 로고
    • Homogenization of the Stokes flow in connected porous medium
    • Allaire G.: Homogenization of the Stokes flow in connected porous medium. Asymptotic Anal. 3, 203-222 (1989).
    • (1989) Asymptotic Anal. , vol.3 , pp. 203-222
    • Allaire, G.1
  • 5
    • 33751009190 scopus 로고    scopus 로고
    • Reply to discussion of 'Beyond beta factors: A complete model for Darcy, Forchheimer, and Trans-Forchheimer flow in porous media'
    • Barree, R. D., Conway, M. W.: Reply to discussion of 'Beyond beta factors: a complete model for Darcy, Forchheimer, and Trans-Forchheimer flow in porous media'. J. Pet. Tech. 73-74 (2005).
    • (2005) J. Pet. Tech. , pp. 73-74
    • Barree, R.D.1    Conway, M.W.2
  • 8
    • 0000182202 scopus 로고
    • The resistance of packing to fluid flow
    • Blake F. C.: The resistance of packing to fluid flow. Trans. Am. Inst. Chem. Engrs. 14, 415-421 (1922).
    • (1922) Trans. Am. Inst. Chem. Engrs. , vol.14 , pp. 415-421
    • Blake, F.C.1
  • 9
    • 3242823329 scopus 로고    scopus 로고
    • Nonlinear effects for flow in periodically constricted channel caused by high injection rate
    • Bourgeat A., Marušić-Paloka E.: Nonlinear effects for flow in periodically constricted channel caused by high injection rate. Math. Models Methods Appl. Sci. 8(3), 379-405 (1998).
    • (1998) Math. Models Methods Appl. Sci. , vol.8 , Issue.3 , pp. 379-405
    • Bourgeat, A.1    Marušić-Paloka, E.2
  • 12
    • 0035425104 scopus 로고    scopus 로고
    • Derivation of the Forchheimer law via homogenization
    • Chen Z., Lyons S. L., Qin G.: Derivation of the Forchheimer law via homogenization. Transp. Porous Med. 44, 325-335 (2001).
    • (2001) Transp. Porous Med. , vol.44 , pp. 325-335
    • Chen, Z.1    Lyons, S.L.2    Qin, G.3
  • 13
    • 0001064029 scopus 로고
    • Numerical modelling of nonlinear effects in laminar flow through a porous medium
    • Couland O., Morel P., Caltagirone J. P.: Numerical modelling of nonlinear effects in laminar flow through a porous medium. J. Fluid Mech. 190, 393-407 (1988).
    • (1988) J. Fluid Mech. , vol.190 , pp. 393-407
    • Couland, O.1    Morel, P.2    Caltagirone, J.P.3
  • 14
    • 0022988319 scopus 로고
    • A continuum approach to high velocity flow in porous media
    • Cvetkovic V. D.: A continuum approach to high velocity flow in porous media. Transp. Porous Med. 1, 63-97 (1986).
    • (1986) Transp. Porous Med. , vol.1 , pp. 63-97
    • Cvetkovic, V.D.1
  • 15
    • 0018492591 scopus 로고
    • Flow through tubes with sinusoidal axial variations in diameter
    • Deiber J. A., Schowalter W. R.: Flow through tubes with sinusoidal axial variations in diameter. AICHE J. 25, 638-645 (1979).
    • (1979) AICHE J. , vol.25 , pp. 638-645
    • Deiber, J.A.1    Schowalter, W.R.2
  • 16
    • 0027067491 scopus 로고
    • Flow of Newtonian fluids through sinusoidally constricted tubes; numerical and experimental results
    • Deiber J. A., Peirotti M., Bortolozzi R. A., Durelli R. J.: Flow of Newtonian fluids through sinusoidally constricted tubes; numerical and experimental results. Chem. Eng. Commun. 117, 241-262 (1992).
    • (1992) Chem. Eng. Commun. , vol.117 , pp. 241-262
    • Deiber, J.A.1    Peirotti, M.2    Bortolozzi, R.A.3    Durelli, R.J.4
  • 17
    • 22044456743 scopus 로고
    • The influence of Reynolds number upon the apparent permeability of spatially periodic arrays of cylinders
    • Edwards, D. A., Shapiro, M., Bar-Yoseph, P., Shapira, M.: The influence of Reynolds number upon the apparent permeability of spatially periodic arrays of cylinders. Phys. Fluids A. 2 (1990).
    • (1990) Phys. Fluids A. 2
    • Edwards, D.A.1    Shapiro, M.2    Bar-Yoseph, P.3    Shapira, M.4
  • 18
    • 84925484326 scopus 로고
    • Flow of simple fluids through porous materials
    • Fancher G. H., Lewis J. A.: Flow of simple fluids through porous materials. Ind. Eng. Chem. 25, 1139-1147 (1933).
    • (1933) Ind. Eng. Chem. , vol.25 , pp. 1139-1147
    • Fancher, G.H.1    Lewis, J.A.2
  • 19
    • 0031177676 scopus 로고    scopus 로고
    • Nonlinear corrections to Darcy's law at low Reynolds numbers
    • Firdaouss M., Guermond J. L., Le Quéré P.: Nonlinear corrections to Darcy's law at low Reynolds numbers. J. Fluid Mech. 343, 331-350 (1997).
    • (1997) J. Fluid Mech. , vol.343 , pp. 331-350
    • Firdaouss, M.1    Guermond, J.L.2    Le Quéré, P.3
  • 20
    • 0000279859 scopus 로고
    • Wasserbewegung durch Boden
    • Forchheimer P.: Wasserbewegung durch Boden. Zeits V. Deutsch Ing. 45, 1782-1788 (1901).
    • (1901) Zeits V. Deutsch Ing. , vol.45 , pp. 1782-1788
    • Forchheimer, P.1
  • 21
    • 0004237494 scopus 로고
    • 3rd edn, Leipzig: Teubner
    • Forchheimer P.: Hydraulik, 3rd edn. Teubner, Leipzig (1930).
    • (1930) Hydraulik
    • Forchheimer, P.1
  • 25
    • 0035842090 scopus 로고    scopus 로고
    • The first effects on fluid inertia on flows in ordered and random arrays of spheres
    • Koch D. L., Ladd A. J. C.: The first effects on fluid inertia on flows in ordered and random arrays of spheres. J. Fluid Mech. 448, 213-241 (2001).
    • (2001) J. Fluid Mech. , vol.448 , pp. 213-241
    • Koch, D.L.1    Ladd, A.J.C.2
  • 28
    • 76149089348 scopus 로고    scopus 로고
    • Lectures at the IV Latin-American School of Mathematics, Lima, 1978, in Lions, Jacques-Louis (Euvres choisies de Jacques-Louis Lions. Vol. II. (French)) [Selected works of Jacques-Louis Lions. Vol. II] Contrôle. Homogénéisation [Control. Homogenization]. Edited by Alain Bensoussan, Philippe G. Ciarlet, Roland Glowinski, Roger Temam, François Murat and Jean-Pierre Puel, and with a preface by Bensoussan. EDP Sciences, Les Ulis; Société de Mathématiques Appliquées et Industrielles, Paris
    • Lions, J. L.: Some problems connected with Navier-Stokes equations. Lectures at the IV Latin-American School of Mathematics, Lima, 1978, in Lions, Jacques-Louis (Euvres choisies de Jacques-Louis Lions. Vol. II. (French)) [Selected works of Jacques-Louis Lions. Vol. II] Contrôle. Homogénéisation [Control. Homogenization]. Edited by Alain Bensoussan, Philippe G. Ciarlet, Roland Glowinski, Roger Temam, François Murat and Jean-Pierre Puel, and with a preface by Bensoussan. EDP Sciences, Les Ulis; Société de Mathématiques Appliquées et Industrielles, pp. xvi+864. Paris, (2003).
    • (2003) Some Problems Connected with Navier-Stokes Equations
    • Lions, J.L.1
  • 29
    • 0034274964 scopus 로고    scopus 로고
    • The derivation of a non-linear filtration law including the inertia effects via homogenization
    • Marušić-Paloka E., Mikelić A.: The derivation of a non-linear filtration law including the inertia effects via homogenization. Nonlinear Anal. Theory Methods Appl. 42, 97-137 (2000).
    • (2000) Nonlinear Anal. Theory Methods Appl. , vol.42 , pp. 97-137
    • Marušić-paloka, E.1    Mikelić, A.2
  • 30
    • 0026359762 scopus 로고
    • The effect of weak inertia on flow through a porous medium
    • Mei C. C., Auriault J.-L.: The effect of weak inertia on flow through a porous medium. J. Fluid Mech. 222, 647-663 (1991).
    • (1991) J. Fluid Mech. , vol.222 , pp. 647-663
    • Mei, C.C.1    Auriault, J.-L.2
  • 31
    • 0000729803 scopus 로고    scopus 로고
    • Homogenization theory and applications to filtration through porous media
    • Lecture Notes Centro Internazionale Matematico Estivo (C. I. M. E.) Series, Lecture Notes in Mathematics, Springer
    • Mikelić, A.: Homogenization theory and applications to filtration through porous media. In: Filtration in Porous Media and Industrial Applications, Lecture Notes Centro Internazionale Matematico Estivo (C. I. M. E.) Series, Lecture Notes in Mathematics, vol. 1734, pp. 127-214. Springer (2000).
    • (2000) Filtration in Porous Media and Industrial Applications , vol.1734 , pp. 127-214
    • Mikelić, A.1
  • 32
    • 34547290484 scopus 로고    scopus 로고
    • On the justification of the Reynolds equation, describing isentropic compressible flows through a tiny pore
    • Mikelić A.: On the justification of the Reynolds equation, describing isentropic compressible flows through a tiny pore. Ann. Univ. Ferrara 53, 95-106 (2007).
    • (2007) Ann. Univ. Ferrara , vol.53 , pp. 95-106
    • Mikelić, A.1
  • 34
    • 0001139009 scopus 로고
    • Non-linear seepage flow through a rigid porous medium
    • Rasoloarijaona M., Auriault J.-L.: Non-linear seepage flow through a rigid porous medium. Eur. J. Mech. B Fluids 13(2), 177-195 (1994).
    • (1994) Eur. J. Mech. B Fluids , vol.13 , Issue.2 , pp. 177-195
    • Rasoloarijaona, M.1    Auriault, J.-L.2
  • 35
    • 0000299373 scopus 로고
    • Nonlinear flow in porous media
    • Rojas S., Koplik J.: Nonlinear flow in porous media. Phys. Rev. E. 58(4), 4776-4782 (1988).
    • (1988) Phys. Rev. E. , vol.58 , Issue.4 , pp. 4776-4782
    • Rojas, S.1    Koplik, J.2
  • 36
    • 0026836320 scopus 로고
    • On the derivation of the Forchheimer equation by means of the averaging theorem
    • Ruth D. W., Ma H.: On the derivation of the Forchheimer equation by means of the averaging theorem. Transp. Porous Med. 7, 255-264 (1992).
    • (1992) Transp. Porous Med. , vol.7 , pp. 255-264
    • Ruth, D.W.1    Ma, H.2
  • 37
    • 0027693114 scopus 로고
    • The microscopic analysis of high Forchheimer number flow in porous media
    • Ruth D. W., Ma H.: The microscopic analysis of high Forchheimer number flow in porous media. Transp. Porous Med. 13, 139-160 (1993).
    • (1993) Transp. Porous Med. , vol.13 , pp. 139-160
    • Ruth, D.W.1    Ma, H.2
  • 39
    • 0007041839 scopus 로고
    • Hydrodynamics in Porous Media
    • In: Flügge, S., Fluid Dynamics II, Springer-Verlag, Berlin
    • Scheidegger, A. E.: Hydrodynamics in Porous Media. In: Flügge, S. Encyclopedia of Physics, vol. VIII/2 (Fluid Dynamics II), pp. 625-663. Springer-Verlag, Berlin (1963).
    • (1963) Encyclopedia of Physics , vol.VIII-2 , pp. 625-663
    • Scheidegger, A.E.1
  • 40
    • 0032647659 scopus 로고    scopus 로고
    • New insights on steady, non-linear flow in porous media
    • Skjetne E., Auriault J. L.: New insights on steady, non-linear flow in porous media. Eur. J. Mech. B Fluids 18(1), 131-145 (1999).
    • (1999) Eur. J. Mech. B Fluids , vol.18 , Issue.1 , pp. 131-145
    • Skjetne, E.1    Auriault, J.L.2
  • 41
    • 0035368403 scopus 로고    scopus 로고
    • Physics of the cigarette filter: Fluid flow through structures of randomly-packed obstacles
    • Stanley H. E., Andrade J. S.: Physics of the cigarette filter: fluid flow through structures of randomly-packed obstacles. Physica A 295, 17-30 (2001).
    • (2001) Physica A , vol.295 , pp. 17-30
    • Stanley, H.E.1    Andrade, J.S.2
  • 43
    • 23644448280 scopus 로고    scopus 로고
    • Discussion of SPE 89325, 'Beyond beta factors: A complete model for Darcy, Forchheimer, and Trans-Forchheimer flow in porous media'
    • van Batenburg, D., Milton-Taylor, D.: Discussion of SPE 89325, 'Beyond beta factors: a complete model for Darcy, Forchheimer, and Trans-Forchheimer flow in porous media'. J. Pet. Tech. 72-73 (2005).
    • (2005) J. Pet. Tech. , pp. 72-73
    • van Batenburg, D.1    Milton-Taylor, D.2
  • 44
    • 0030267168 scopus 로고    scopus 로고
    • The Forchheimer equation: A theoretical development
    • Whitaker S.: The Forchheimer equation: a theoretical development. Transp. Porous Med. 25, 27-61 (1996).
    • (1996) Transp. Porous Med. , vol.25 , pp. 27-61
    • Whitaker, S.1
  • 45
    • 0026070616 scopus 로고
    • Correction non linéaire de la loi de Darcy
    • Série II, Springer-Verlag, Berlin
    • Wodié, J.-C., Levy, T.: Correction non linéaire de la loi de Darcy. C. R. Acad. Sci. Paris t. 312, Série II, 157-161 (1991).
    • (1991) C. R. Acad. Sci. Paris t. 312 , pp. 157-161
    • Wodié, J.-C.1    Levy, T.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.