Publication Cover
Applicable Analysis
An International Journal
Volume 60, 1996 - Issue 1-2
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Original Articles

Existence of solutions to various rock types odel model of two-phase flow in porous media

, &
Pages 121-132 | Received 01 Sep 1992, Published online: 02 May 2007
 

Abstract

We study the flow of two immiscible and incompressible fluids through a porous media c,onsisting of different rock types: capillary pressure and relative permeablities curves are different in each type of porous media. This process can be formulated as a coupled system of partial differential equations which includes an elliptic pressurevelocity equation and a nonlinear degenerated parabolic saturation equation. Moreover the transmission conditions are nonlinear and the saturation is discontinuous at interfaces separating different media. A change of unknown leads to a new formulation of this problem. We derive a weak form for this new problem, which is a combination of a mixed formulation for the elliptic pressure-velocity equation and a standard variational formulation for the new parabolic equation. Under some realistic assumptions, we prove the existence of weak solutions to the implicit system given by time discretization.

*Laboratoire de Mathdmatiques Appliqudes, URA-CNRS 1204, Universitd de Pau et des Pays de l'Adour, Av. de l'université, 64000 Pau, France

**Equipe d'Analyse Numdrique, URA-CNRS 740, UFR Sciences, Université J. Monnet,23 Rue du Dr. Paul Michelon, 42023 Saint-Etienne, France

**Equipe d'Analyse Numdrique, URA-CNRS 740, UFR Sciences, Université J. Monnet,23 Rue du Dr. Paul Michelon, 42023 Saint-Etienne, France

*Laboratoire de Mathdmatiques Appliqudes, URA-CNRS 1204, Universitd de Pau et des Pays de l'Adour, Av. de l'université, 64000 Pau, France

**Equipe d'Analyse Numdrique, URA-CNRS 740, UFR Sciences, Université J. Monnet,23 Rue du Dr. Paul Michelon, 42023 Saint-Etienne, France

**Equipe d'Analyse Numdrique, URA-CNRS 740, UFR Sciences, Université J. Monnet,23 Rue du Dr. Paul Michelon, 42023 Saint-Etienne, France

Notes

*Laboratoire de Mathdmatiques Appliqudes, URA-CNRS 1204, Universitd de Pau et des Pays de l'Adour, Av. de l'université, 64000 Pau, France

**Equipe d'Analyse Numdrique, URA-CNRS 740, UFR Sciences, Université J. Monnet,23 Rue du Dr. Paul Michelon, 42023 Saint-Etienne, France

**Equipe d'Analyse Numdrique, URA-CNRS 740, UFR Sciences, Université J. Monnet,23 Rue du Dr. Paul Michelon, 42023 Saint-Etienne, France

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