Two-phase flows involving capillary barriers in heterogeneous porous media

Details Two-phase flows involving capillary barriers in heterogeneous porous media Two-phase flows involving capillary barriers in heterogeneous porous media

2010-05-31

arxiv.org/abs/1005.5634v1

Interfaces and free boundaries 11, 2 (2009) pp. 239-258

Mathematics

Analysis of PDEs

Scientific paper

10.4171/IFB/210

We consider a simplified model of a two-phase flow through a heterogeneous porous medium, in which the convection is neglected. This leads to a nonlinear degenerate parabolic problem in a domain shared in an arbitrary finite number of homogeneous porous media. We introduce a new way to connect capillary pressures on the interfaces between the homogeneous domains, which leads to a general notion of solution. We then compare this notion of solution with an existing one, showing that it allows to deal with a larger class of problems. We prove the existence of such a solution in a general case, then we prove the existence and the uniqueness of a regular solution in the one-dimensional case for regular enough initial data.

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