Applied Scientific Research

, Volume 55, Issue 2, pp 155–169 | Cite as

Viscous coupling in a model porous medium geometry: Effect of fluid contact area

  • N. Rakotomalala
  • D. Salin
  • Y. C. Yortsos


We study the effect of fluid contact area on viscous coupling in the parallel flow of immiscible fluids in a porous media geometry. We consider flow on opposite sides of a planar interface, consisting of alternating solid and open (slit) segments. We use the analytical solution of Tio and Sadhal [15] to derive explicit expressions for viscous coupling in terms of the fractional area of contact between the fluids and the viscosity ratio,M. ForM=1, the coefficient matrix obtained is symmetric showing that Onsager's relations are satisfied. In this case, the resulting viscous coupling is typically very small, in agreement with recent experimental results. Lattice gas simulations forM=1 using theBGK model support the theoretical results and show that viscous coupling further diminishes as the wall thickness increases. Assuming the same configuration, analytical results are next derived forM≠1. The results confirm an existing reciprocity relation between the off-diagonal terms. Viscous coupling remains small.

Key words

porous medium cross-permeability lattice gas 


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  1. 1.
    De Gennes, P.-G., Theory of slow biphasic flows in porous media.Physicochemical Hydrodynamics 4 (1983) 175.Google Scholar
  2. 2.
    Whitaker, S., Flow in porous media II: The governing equations for immiscible two-phase flow.Transport in Porous Media 1 (1986) 105.Google Scholar
  3. 3.
    Kalaydjian, F., A macroscopic description of multiphase flow in porous media involving spacetime evolution of fluid/fluid interface.Transport in Porous Media 2 (1987) 537.Google Scholar
  4. 4.
    Kalaydjian, F., Origin and quantification of coupling between relative permeabilities for two-phase flows in porous media.Transport in Porous Media 5 (1990) 215.Google Scholar
  5. 5.
    Yuster, S.T., Theoretical consideration of multiphase flow in idealized capillary systems. In:Proceedings of the Third World Petroleum Congress, Section II, The Hague (1951) p 437.Google Scholar
  6. 6.
    Bacri, J.-C., Chaouche, M. and Salin, D., Modèle simple de perméabilités relatives croisées.Comptes Rendus de l'Académie des Sciences, Paris 309, série 2 (1990) 591.Google Scholar
  7. 7.
    Kalaydjian, F. and Legait, B., Ecoulement lent à contre-courant en imbibition spontanée de deux fluides non miscibles dans un capillaire présentant un rétrécissement.Comptes Rendus de l'Académie des Sciences, Paris 304, série 2 (1987) 869.Google Scholar
  8. 8.
    Kalaydjian, F. and Legait, B., Perméabilités relatives couplées dans des écoulements en capillaire et en milieu poreux.Comptes Rendus de l'Académie des Sciences, Paris 304, série 2 (1987) 1035.Google Scholar
  9. 9.
    Rose, W., Coupling coefficients for two-phase flow in pore space of simple geometry.Transport in Porous Media 5 (1990) 97.Google Scholar
  10. 10.
    Ehrlich, R., Viscous coupling in two-phase flow in porous media and its effects on relative permeabilities.Transport in Porous Media 11 (1993) 201.Google Scholar
  11. 11.
    Gustensen, A.K. and Rothman, D.H., Lattice-Boltzmann studies of immiscible two-phase flow through porous media.Journal of Geophysical Research 98 (1993) 6431.Google Scholar
  12. 12.
    Goode, P.A. and Ramakrishna, T.S., Moment transfer across fluid-fluid interfaces in porous media: A network model.AICHE Journal 39 (1993) 1124.Google Scholar
  13. 13.
    Avraam, D.G. and Payatakes, A.C., Flow regimes and relative permeabilities during steady-state two-phase flow in porous media. Preprint (1994).Google Scholar
  14. 14.
    Zarcone, C. and Lenormand, R., Détermination expérimentale du couplage visqueux dans les écoulements diphasiques en milieu poreux.Comptes Rendus de l'Académie des Sciences, Paris 318, série 2 (1994) 1429.Google Scholar
  15. 15.
    Tio, K.K. and Sadhal, S.S., Boundary conditions for Stokes flows near a porous membrane.Applied Scientific Research 52 (1994) 1.Google Scholar
  16. 16.
    Bhatnagar, P., Gross, E.P. and Krook, M.K., A model for collision processes in gases: I. Small amplitude processes in charged and neutral one-component systems.Physical Review 94 (1954) 511.Google Scholar
  17. 17.
    Qian, Y.H., d'Humieres, D. and Lallemand, P., Lattice BGK models for Navier-Stokes equation.Europhysics Letters 17(6) (1992) 479.Google Scholar
  18. 18.
    McNamara, G.R. and Zanetti, G., Use of the Boltzmann equation to simulate lattice gas automata.Physical Review Letters 61 (1988) 2332.Google Scholar
  19. 19.
    Higuera, F.J. and Succi, S., Simulating the flow around a circular cylinder with a lattice Boltzmann equation.Europhysics Letters 8(6) (1989) 517.Google Scholar
  20. 20.
    Higuera, F.J., Succi, S. and Benzi, R., Lattice gas dynamics with enhanced collisions.Europhysics Letters 9(4) (1989) 345.Google Scholar
  21. 21.
    Higuera, F.J. and Jimenez, J., Boltzmann approach to lattice gas simulation.Europhysics Letters 9(7) (1989) 663.Google Scholar
  22. 22.
    Frisch, U., Hasslacher, B. and Pomeau, Y., Lattice gas automata for the Navier-Stokes equation.Physical Review Letters 56 (1986) 1505.Google Scholar
  23. 23.
    Auriault, J.-L., Nonsaturated deformable porous media: Quasistatics.Transport in Porous Media 2 (1987) 45.Google Scholar
  24. 24.
    Lasseux, D., Quintard, M. and Whitaker, S., Determination of permeability tensors for two-phase flow in homogeneous porous media: Theory. Preprint (1995).Google Scholar

Copyright information

© Kluwer Academic Publishers 1995

Authors and Affiliations

  • N. Rakotomalala
    • 1
  • D. Salin
    • 1
  • Y. C. Yortsos
    • 2
  1. 1.Laboratoire Fluides Automatiques et Systèmes Thermiques, Bâtiment 502Campus UniversitaireOrsay CédexFrance
  2. 2.Department of Chemical EngineeringUniversity of South CaliforniaLos AngelesUSA

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