Non-equilibrium imbibition of a porous block

Abstract

We consider a phenomenological model proposed by Barenblatt [1] for non-equilibrium two-phase flow in porous media. In the case of zero total flow it reduces to a pair of equations:where Φ(σ) is a non-decreasing (not necessarily increasing) smooth function defined in the interval 0 ≤ σ ≤ 1. We consider initial-boundary problems for this system in which the initial data are given only for s, and the boundary data only for ς (which corresponds to the physical sense of the model). The degenerate character of the system allows us to apply simple topological methods. We show that the boundary problem is well-posed, in the sense that there exits a unique (weak) solution which satisfies the maximum principle and depends continuously on the initial data. The solution is no less smooth than the initial and boundary data.