Thermodynamically constrained averaging theory approach for modeling flow and transport phenomena in porous medium systems: 9. Transition region models

This work is the ninth in a series of papers on the thermodynamically constrained averaging theory (TCAT) approach for modeling flow and transport phenomena in multiscale porous medium systems. A fundamental approach is developed to model the transition region between a two-fluid-phase porous medium system and a single-fluid-phase system, including species transport. A general model formulation is developed along with an entropy inequality to guide the specification of closure relations. The general model formulation and entropy inequality are then used to specify a closed system. The transition region model developed in this work is a generalization and extension of coupling conditions commonly used in sharp interface models. The theoretical framework has multiple areas of potential applicability including terrestrial-atmospheric contact zones, surface water-sediment interface zones, and industrial drying processes.

► Transition regions between two domains with a different entities are considered. ► TCAT is used to derive an exact constrained entropy inequality. ► Restrictions and approximations are introduced and used to produce a simplified entropy inequality suitable to guide model closure. ► An example closed model is formulated from the hierarchy of potential models.