Non-equilibrium interphase heat and mass transfer during two-phase flow in porous media—Theoretical considerations and modeling

Mass and heat transfer occurring across phase-interfaces in multi-phase flow in porous media are mostly approximated using equilibrium relationships or empirical kinetic models. However, when the characteristic time of flow is smaller than that of mass or heat transfer, non-equilibrium situations may arise. Commonly, empirical approaches are used in such cases. There are only few works in the literature that use physically-based models for these transfer terms. In fact, one would expect physical approaches to modeling kinetic interphase mass and heat transfer to contain the interfacial area between the phases as a variable. Recently, a two-phase flow and solute transport model was developed that included interfacial area as a state variable [36]. In that model, interphase mass transfer was modeled as a kinetic process.In this work, we extend that model to account for kinetic heat transfer between two fluid phases as well as the solid phase. Therefore, we have introduced energy balances for both fluid phases and the solid phase and exchange terms that are proportional to specific interfacial areas.We briefly discuss how these macro-scale energy balances are developed. The resulting macro-scale equation system for two-phase flow, including kinetic heat and mass transfer, is discussed and non-dimensionalized. Based on the dimensionless equation system, possible simplifications are discussed. A numerical example illustrates a case where both kinetic interphase mass and heat transfer are relevant, and results are compared to those from a classical approach with equilibrium mass and heat transfer.