A Multiscale Diffuse-Interface Model for Two-Phase Flow in Porous Media

TL;DR

This paper introduces a multiscale phase-field model for two-phase flow in porous media that simplifies complex Navier-Stokes-Cahn-Hilliard equations while accurately capturing macroscopic behavior, validated through numerical tests.

Contribution

The paper develops a reduced multiscale model for capillarity-driven flows in porous media, maintaining key dynamics and equilibrium properties with lower computational complexity.

Findings

Model accurately predicts capillary rise in simplified geometries.

Numerical results agree with analytical solutions.

Effective in representing flow in complex porous structures.

Abstract

In this paper we consider a multiscale phase-field model for capillarity-driven flows in porous media. The presented model constitutes a reduction of the conventional Navier-Stokes-Cahn-Hilliard phase-field model, valid in situations where interest is restricted to dynamical and equilibrium behavior in an aggregated sense, rather than a precise description of microscale flow phenomena. The model is based on averaging of the equation of motion, thereby yielding a significant reduction in the complexity of the underlying Navier-Stokes-Cahn-Hilliard equations, while retaining its macroscopic dynamical and equilibrium properties. Numerical results are presented for the representative 2-dimensional capillary-rise problem pertaining to two closely spaced vertical plates with both identical and disparate wetting properties. Comparison with analytical solutions for these test cases corroborates the accuracy of the presented multiscale model. In addition, we present results for a capillary-rise problem with a non-trivial geometry corresponding to a porous medium.