Capillary fluctuations and energy dynamics for flow in porous media

TL;DR

This paper develops a comprehensive averaging theory to model non-equilibrium capillary effects and fluctuations in porous media flow, integrating pore-scale phenomena into larger-scale thermodynamic and flow models.

Contribution

It introduces a novel multi-scale framework that incorporates capillary fluctuations and film dynamics into averaged thermodynamics and constitutive models for porous media flow.

Findings

Quantitative assessment of capillary fluctuations from simulations and experiments.

A new constitutive model for capillary pressure including film effects.

Criteria for defining representative elementary volume based on fluctuations.

Abstract

Capillary energy barriers have important consequences for immiscible fluid flow in porous media. We derive time-and-space averaging theory to account for non-equilibrium behavior and understand the role of athermal capillary fluctuations in the context of their relationship to larger scale phenomenological equations. The formulation resolves several key challenges associated with two-fluid flow in porous media: (1) geometric and thermodynamic quantities are constructed as smooth functions of time based on time-and space averages; (2) averaged thermodynamics are developed for films; (3) multi-scale fluctuation terms are identified, which account for transient behaviours of interfaces and films that occur due to pore-scale events; (4) geometric constraints are derived and imposed on the averaged thermodynamics; (5) a new constitutive model is proposed for capillary pressure dynamics that includes contributions from films; and (6) a time-and-space criterion for representative elementary volume (REV) is established based on capillary fluctuations. Capillary fluctuations are assessed quantitatively based on pore-scale simulations and experimental core-flooding data.