Macroscopic Equations of Motion for Two Phase Flow in Porous Media

TL;DR

This paper derives a comprehensive set of macroscopic equations for two-phase flow in porous media that incorporate surface tension effects and interfacial energies, improving upon traditional models.

Contribution

The authors develop a more general system of equations based on mixture theory that includes surface tension and interfacial energy variations, capturing wetting phenomena and residual saturation dynamics.

Findings

Equations include surface tension effects instead of capillary pressure functions.

Capillary pressure function shows saturation dependence consistent with experiments.

Model describes spatiotemporal changes of residual saturations during displacement.

Abstract

The established macroscopic equations of motion for two phase immiscible displacement in porous media are known to be physically incomplete because they do not contain the surface tension and surface areas governing capillary phenomena. Therefore a more general system of macroscopic equations is derived here which incorporates the spatiotemporal variation of interfacial energies. These equations are based on the theory of mixtures in macroscopic continuum mechanics. They include wetting phenomena through surface tensions instead of the traditional use of capillary pressure functions. Relative permeabilities can be identified in this approach which exhibit a complex dependence on the state variables. A capillary pressure function can be identified in equilibrium which shows the qualitative saturation dependence known from experiment. In addition the new equations allow to describe the spatiotemporal changes of residual saturations during immiscible displacement.