Multiscale Modeling of Multiphase Flow in Porous Media Using the Thermodynamically Constrained Averaging Theory Approach

Traditional approaches to multiscale modeling of multiphase flow and transport are riddled with deficiencies and inconsistencies across scales. The thermodynamically constrained averaging theory (TCAT) approach for modeling flow and transport phenomena in multiscale porous medium systems addresses many of the shortcomings of traditional models. The TCAT approach is used here, in conjunction with primary restrictions to the system of interest, to formulate two distinct hierarchies of models: macroscale two-fluidphase flow of continuous fluids and two-fluid-phase flow and transport in a transition region between a multiphase porous medium system and a free flow system. Application of the TCAT approach produces a constrained entropy inequality for each system and secondary restrictions and approximations allow for simplified entropy inequalities to be determined in each case. The simplified entropy inequality is formulated relying upon approximations of terms involving geometric variables and recently derived evolution equations for specific entity measures that include interfacial areas and common curve lengths. The general model formulation and entropy inequality are then used to close a series of successively less complex models. The formulated models are compared to existing models when available. The advantages of the models produced using the TCAT approach are highlighted and the remaining open issues are discussed.