Asymptotic behavior of two-phase flows in heterogeneous porous media for capillarity depending only on space. II. Non-classical shocks to model oil-trapping

TL;DR

This paper analyzes the asymptotic behavior of two-phase flows in heterogeneous porous media with space-dependent capillarity, revealing the emergence of non-classical shocks that model oil-trapping phenomena.

Contribution

It demonstrates that, under certain conditions, the limit solution involves non-classical shocks at interfaces, extending previous models to include oil-trapping effects.

Findings

Non-classical shocks can occur at interfaces due to capillarity discontinuities.

The limit solution differs from the classical entropy solution in certain configurations.

Oil-trapping is effectively modeled by these non-classical shock phenomena.

Abstract

We consider a one-dimensional problem modeling two-phase flow in heterogeneous porous media made of two homogeneous subdomains, with discontinuous capillarity at the interface between them. We suppose that the capillary forces vanish inside the domains, but not on the interface. Under the assumption that the gravity forces and the capillary forces are oriented in opposite directions, we show that the limit, for vanishing diffusion, is not in general the optimal entropy solution of the hyperbolic scalar conservation law as in the first paper of the series \cite{NPCX}. A non-classical shock can occur at the interface, modeling oil-trapping.