Capillary fluctuations and energy dynamics for flow in porous media
James E. McClure, Steffen Berg, Ryan T. Armstrong
Abstract
Capillary energy barriers have important consequences for immiscible fluid flow in porous media. We derive a time-and-space averaging theory to account for the 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 behaviors 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 is established based on capillary fluctuations. Capillary fluctuations are assessed quantitatively based on pore-scale simulations and experimental core-flooding data.