Ensemble Distribution for Immiscible Two-Phase Flow in Porous Media

TL;DR

This paper develops an ensemble distribution approach to model steady immiscible two-phase flow in porous media, enabling the calculation of macroscopic flow parameters and revealing the system's ergodic nature.

Contribution

It introduces a novel ensemble distribution framework for two-phase flow in porous media, linking microscopic states to macroscopic flow properties and entropy production.

Findings

Derived an expression for overall mobility from the ensemble distribution.

Confirmed ergodicity of the two-phase flow system.

Numerical tests support the theoretical results.

Abstract

We construct an ensemble distribution to describe steady immiscible two-phase flow of two incompressible fluids in a porous medium. The system is found to be ergodic. The distribution is used to compute macroscopic flow parameters. In particular, we find an expression for the overall mobility of the system from the ensemble distribution. The entropy production at the scale of the porous medium is shown to give the expected product of the average flow and its driving force, obtained from a black-box description. We test numerically some of the central theoretical results.