Modeling Kinetic Interphase Mass Transfer for Two-Phase Flow in Porous Media Including Fluid–Fluid Interfacial Area

TLDR: In this article, a new formulation of two-phase flow with interphase mass transfer is proposed based on thermodynamic principles, which comprises a mass balance for each component in each phase and a mass imbalance for specific interfacial area.

Abstract: Interphase mass transfer in porous media takes place across fluid–fluid interfaces. At the field scale, this is almost always a kinetic process and its rate is highly dependent on the amount of fluid–fluid interfacial area. Having no means to determine the interfacial area, modelers usually either neglect kinetics of mass transfer and assume local equilibrium between phases or they estimate interfacial area using lumped parameter approaches (in DNAPL pool dissolution) or a dual domain approach (for air sparging). However, none of these approaches include a physical determination of interfacial area or accounts for its role for interphase mass transfer. In this work, we propose a new formulation of two-phase flow with interphase mass transfer, which is based on thermodynamic principles. This approach comprises a mass balance for each component in each phase and a mass balance for specific interfacial area. The system is closed by a relationship among capillary pressure, interfacial area, and saturation. We compare our approach to an equilibrium model by showing simulation results for an air–water system. We show that the new approach is capable of modeling kinetic interphase mass exchange for a two-phase system and that mass transfer correlates with the specific interfacial area. By non-dimensionalization of the equations and variation of Peclet and Damkohler number, we make statements about when kinetic interphase mass transfer has to be taken into account by using the new physically based kinetic approach and when the equilibrium model is a reasonable simplification.