Capillary fluctuations and energy dynamics for flow in porous media.

Capillary energy barriers have important consequences for immiscible fluid flow in porous media. We derive time-and-space averaging theory to account non-equilibrium behavior and understand the role of athermal capillary fluctuations and their relationship to phenomenological equations for multiphase flow. 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) a criterion for representative elementary volume (REV) is established based on capillary fluctuations; (5) geometric constraints are derived and imposed on the averaged thermodynamics; and (6) a new constitutive model is proposed for capillary pressure dynamics that includes contributions from fluctuations. Based on the derived definitions, capillary fluctuations are assessed quantitatively based on pore-scale simulations and experimental core-flooding data.