Relations between Seepage Velocities in Immiscible, Incompressible Two-Phase Flow in Porous Media

TL;DR

This paper develops a thermodynamically consistent framework relating seepage velocities in two-phase flow through porous media, introducing a new co-moving velocity function and validating it with analytical and numerical models.

Contribution

It introduces a novel velocity function, the co-moving velocity, and formulates a closed set of equations for two-phase flow in porous media based on thermodynamics.

Findings

Analytical solutions for four capillary tube models.

Numerical validation on a network model.

Establishment of a new theoretical framework for seepage velocities.

Abstract

Based on thermodynamic considerations we derive a set of equations relating the seepage velocities of the fluid components in immiscible and incompressible two-phase flow in porous media. They necessitate the introduction of a new velocity function, the co-moving velocity. This velocity function is a characteristic of the porous medium. Together with a constitutive relation between the velocities and the driving forces, such as the pressure gradient, these equations form a closed set. We solve four versions of the capillary tube model analytically using this theory. We test the theory numerically on a network model.