Comptes Rendus
Homogenization of two-phase flow: high contrast of phase permeability
Comptes Rendus. Mécanique, Volume 331 (2003) no. 1, pp. 9-15.

The steady-state two-phase flow non-linear equation is considered in the case when one of phases has low effective permeability in some periodic set, while on the complementary set it is high; the second phase has no contrast of permeabilities in different zones. A homogenization procedure gives the homogenized model with macroscopic effective permeability of the second phase depending on the gradient and on the second order derivatives of the macroscopic pressure of the first phase. This effect cannot be obtained by classical (one small parameter) homogenization.

On considére l'équation d'écoulement diphasique stationnaire non-linéaire dans le cas où une phase est peu perméable dans une zone alors que la perméabilité efficace est haute dans l'ensemble complémentaire ; la seconde phase n'a pas de contraste de perméabilité dans les différentes zones. L'homogénéisation de ce problème conduit à un modèle homogénéisé où la perméabilité macroscopique efficace de la seconde phase dépend du gradient et des dérivées secondes de la pression macroscopique de la prémiere phase. Cet effet ne peut pas être obtenu par l'homogénéisation classique (i.e. avec un seul petit paramétre).

Received:
Revised:
Published online:
DOI: 10.1016/S1631-0721(02)00008-6
Keywords: Computational fluid mechanics, Homogenization, Steady-state two-phase flow, Contrasting effective phase permeability
Mot clés : Mécanique des fluides numérique, Homogénéisation, Écoulement diphasique stationnaire, Contraste de perméabilité d'une phase

Gregory P. Panasenko 1, 2; George Virnovsky 3

1 Équipe d'analyse numérique, UPRES EA 3058, Université de Saint-Etienne, 23, rue Paul Michelon, 42023 Saint-Etienne, France
2 Laboratoire de modélisation en mécanique – CNRS UMR 7607, Université Pierre et Marie Curie – Paris 6, 8, rue du Capitaine Scott, 75015 Paris, France
3 RF – Rogaland Research Postboks 8046, Ullandhaug, 4068 Stavanger, Norway
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Gregory P. Panasenko; George Virnovsky. Homogenization of two-phase flow: high contrast of phase permeability. Comptes Rendus. Mécanique, Volume 331 (2003) no. 1, pp. 9-15. doi : 10.1016/S1631-0721(02)00008-6. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/S1631-0721(02)00008-6/

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