Immiscible two-phase flow in porous media: a statistical mechanics approach

TL;DR

This paper introduces a statistical mechanics-based thermodynamics-like framework for modeling immiscible two-phase flow in porous media at continuum scales, connecting pore-scale physics with macroscopic descriptions.

Contribution

It applies Jaynes' information-theoretic entropy approach to develop a manageable, thermodynamics-like formalism for two-phase flow, incorporating new emergent variables like co-moving velocity.

Findings

The formalism relates pore-scale physics to continuum-scale flow.

Emergent variables such as co-moving velocity are identified.

The approach offers a thermodynamics analogy for multiphase flow.

Abstract

The central problem in the physics of immiscible two-phase flow in porous media is to find a proper description of the flow at scales large enough so that the medium may be regarded as a continuum: the scale-up problem. So far, the only workable approach to the multiphase flow scale-up problem has been a set of phenomenological equations that have obvious weaknesses. Attempts at going beyond this relative permeability theory have so far not led to practical applications due to exploding complexity. Edwin T. Jaynes proposed in the fifties a generalization of statistical mechanics to non-thermal systems based on the information theoretical entropy of Shannon. This approach is used to construct a description of immiscible two-phase flow in porous media at the continuum scales, which is directly related to the physics at the pore scale, and at a level of complexity that is manageable. The approach leads to a thermodynamics-like formalism at the continuum scale with all the relations between variables that "normal" thermodynamics has to offer. New emergent variables appear. Among these, the co-moving velocity stands out as a key variable with implications for ordinary thermodynamics. We present here a short review of this approach.