Thermodynamics-Like Formalism for Immiscible and Incompressible Two-Phase Flow in Porous Media

TL;DR

This paper explores a thermodynamics-inspired mathematical framework for immiscible, incompressible two-phase flow in porous media, linking variables like flow pressure and saturation to entropy and configurational states.

Contribution

It reviews and extends a thermodynamics-like formalism for two-phase flow, introducing new variables and conjectures about their physical interpretations and relationships.

Findings

Flow pressure is related to a temperature-like variable.

Configurational entropy correlates with fluid distribution and velocity.

A formalism using fractional flow as a control variable is developed.

Abstract

It is possible to formulate immiscible and incompressible two-phase flow in porous media in a mathematical framework resembling thermodynamics based on the Jaynes generalization of statistical mechanics. We review this approach and discuss the meaning of the emergent variables that appear, agiture, flow derivative and flow pressure, which are conjugate to the configurational entropy, the saturation and the porosity respectively. We conjecture that the agiture, the temperature-like variable, is directly related to the pressure gradient. This has as a consequence that the configurational entropy, a measure of how the fluids are distributed within the porous media and the accompanying velocity field, and the differential mobility of the fluids are related. We also develop elements of another version of the thermodynamics-like formalism where fractional flow rather than saturation is the control variable, since this is typically the natural control variable in experiments.