Two-phase flows involving capillary barriers in heterogeneous porous media

TL;DR

This paper develops a new framework for modeling two-phase flows with capillary barriers in heterogeneous porous media, introducing a generalized solution concept and proving existence and uniqueness results.

Contribution

It introduces a novel method to connect capillary pressures at interfaces, broadening the class of problems that can be analyzed in two-phase flow models.

Findings

New solution concept for capillary barrier problems

Existence of solutions in general cases

Uniqueness and regularity in one-dimensional cases

Abstract

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.