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