A statistical mechanics for immiscible and incompressible two-phase flow in porous media

TL;DR

This paper develops a novel statistical mechanics framework for immiscible, incompressible two-phase flow in porous media, introducing new variables and relations that improve understanding and modeling of such flows beyond traditional theories.

Contribution

It introduces a maximum entropy-based formalism with new variables, agiture and flow derivative, providing a thermodynamics-like approach to two-phase flow in porous media.

Findings

Reveals new relations between flow variables and fluctuations.

Provides a thermodynamics-like formalism for flow characterization.

Offers a practical alternative to relative permeability theory.

Abstract

We construct a statistical mechanics for immiscible and incompressible two-phase flow in porous media under local steady-state conditions based on the Jaynes maximum entropy principle. A cluster entropy is assigned to our lack of knowledge of, and control over, the fluid and flow configurations in the pore space. As a consequence, two new variables describing the flow emerge: The agiture, that describes the level of agitation of the two fluids, and the flow derivative which is conjugate to the saturation. Agiture and flow derivative are the analogs of temperature and chemical potential in standard (thermal) statistical mechanics. The associated thermodynamics-like formalism reveals a number of hitherto unknown relations between the variables that describe the flow, including fluctuations. The formalism opens for new approaches to characterize porous media with respect to multi-phase flow for practical applications, replacing the simplistic relative permeability theory while still keeping the number of variables tractable.