  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.
