Finite volume approximation for an immiscible two-phase flow in porous media with discontinuous capillary pressure
Résumé
We consider an immiscible incompressible two-phase flow in a porous medium composed of two different rocks. The flows of oil and water are governed by the Darcy-Muskat law and a capillary pressure law, where the capillary pressure field may be discontinuous at the interface between the rocks. Using the concept of multi-valued phase pressures, we introduce a notion of weak solution for the flow. We discretize the problem by means of a numerical scheme which reduces to a standard finite volume scheme in each rock and prove the convergence of an approximate solutions towards a weak solution. The numerical experiments show that the scheme can reproduce the oil trapping phenomenon.
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