A new set of equations describing immiscible two-phase flow in isotropic porous media

TL;DR

This paper derives a new set of thermodynamics-based equations that simplify the modeling of immiscible two-phase flow in porous media by relating flow rates and reducing the problem to a single-phase flow framework.

Contribution

It introduces a novel thermodynamics-derived set of equations for two-phase flow, connecting flow rates and relative permeability in porous media.

Findings

Equations successfully tested on model systems

Reduced two-phase flow to a single-phase problem

Provides a new theoretical framework for flow modeling

Abstract

Based on non-equilibrium thermodynamics we derive a set of general equations relating the partial volumetric flow rates to each other and to the total volumetric flow rate in immiscible two-phase flow in porous media. These equations together with the conservation of saturation reduces the immiscible two-phase flow problem to a single-phase flow problem of a complex fluid. We discuss the new equation in terms of the relative permeability equations. We test the equations on model systems, both analytically and numerically.