From Interface Dynamics to Darcy Scale Description of Multiphase Flow in Porous Media

Abstract: An outstanding characteristic of porous media, desired in many applications, is the large surface area, which facilitates solid-fluid interactions, making porous media an extreme case in colloid and interface science. In two-fluid systems, wetting and the balance of capillary and viscous forces control fluid displacement processes, leading to a wide range of complex flow regimes with rich spatio-temporal dynamics. Macroscopic two-phase flow is historically described through the phenomenological extensions of Darcy's law. Besides many other shortcomings and inconsistencies, it covers only connected pathway flow in the capillary-dominated flow regime in a rigorous manner while other flow regimes with moving interfaces and associated topological changes are entirely implicit. Given the lack of adequate descriptions, upscaling multiphase flow from pore to Darcy scale represents a long-standing challenge paving into the fields of thermodynamics, statistical mechanics and integral geometry. In this review, we compare novel concepts which have been largely motivated by experimental insights, enabled by significant advances in pore-scale imaging and modeling over the last decade.