8 Febbraio, 2013 09:30 in punto

Discretizations of two-phase Darcy flows in heterogeneous porous media with discontinuous capillary pressures

Konstantin Brenner and Roland Masson, University of Nice Sophia Antipolis and INRIA

SALA CONSIGLIO VII PIANO Dipartimento di Matematica Politecnico di Milano

The talk deals with two finite volume discretizations of two-phase Darcy flows in heterogeneous porous media. More precisely we assume that the flow takes place in a domain made of two different rocks so that the capillary pressure is discontinuous across the interface between the rocks. As a consequence the solution itself is discontinuous across the interface with nonlinear transmission conditions. The discretization of such problems is an important issue to modelize capillary barriers arising for example in CO2 storage or basin modelling.

The model is first discretized by means of a numerical scheme which reduces to a standard two point flux finite volume scheme on each sub-domain assuming the orthogonality of the mesh. This first approach is shown to lead to a convergent scheme towards a weak solution of the continuous problem.

contatto:luca.formaggia@polimi.it

In order to deal with anisotropic media or more general meshes, the previous approach is then extended using the vertex approximate gradient scheme (VAG). The proposed extension of the VAG scheme is based on a specific choice of the
primary unknowns at the vertices that allows for discontinuous saturations at the interface between different rock types and respect the continuity of the phase pressures. Numerical
tests exhibit the efficiency of both schemes on various 2D and 3D problems.

contatto:
luca.formaggia@polimi.it, edie. miglio@polimi.it