A geometric state function for two-fluid flow in porous media

TL;DR

This paper introduces a geometric state function based on algebraic topology to describe two-fluid flow in porous media, aiming to resolve non-uniqueness and hysteresis issues in traditional models.

Contribution

It proposes a novel geometric state function that relates fluid configurations to measurable properties, improving the modeling of two-fluid flow in porous media.

Findings

The geometric state function characterizes microscopic fluid configurations.

It can serve as a closure relationship to eliminate hysteresis.

Validated across six different porous media.

Abstract

Models that describe two-fluid flow in porous media suffer from a widely-recognized problem that the constitutive relationships used to predict capillary pressure as a function of the fluid saturation are non-unique, thus requiring a hysteretic description. As an alternative to the traditional perspec- tive, we consider a geometrical description of the capillary pressure, which relates the average mean curvature, the fluid saturation, the interfacial area between fluids, and the Euler characteristic. The state equation is formulated using notions from algebraic topology and cast in terms of measures of the macroscale state. Synchrotron-based X-ray micro-computed tomography ({\mu}CT) and high- resolution pore-scale simulation is applied to examine the uniqueness of the proposed relationship for six different porous media. We show that the geometric state function is able to characterize the microscopic fluid configurations that result from a wide range of simulated flow conditions in an averaged sense. The geometric state function can serve as a closure relationship within macroscale models to effectively remove hysteretic behavior attributed to the arrangement of fluids within a porous medium. This provides a critical missing component needed to enable a new generation of higher fidelity models to describe two-fluid flow in porous media.