Multiphase flow through multilayers of thin porous media: General balance equations and constitutive relationships for a solid-gas-liquid three-phase system

Abstract

In this work, we propose a new approach to modeling multiphase flow and solute transport through a stack of thin porous layers. Currently, numerical simulation of thin layers involves discretization across the layer thickness. In our new approach, thin porous layers are treated as a bunch of two-dimensional (2D) interacting continua. Macroscale balance laws are formulated in terms of thickness-averaged material properties. A number of exchange terms are employed to account for exchanges of mass, momentum, energy, and entropy between two neighboring layers. The entropy inequality is then exploited for obtaining constitutive equations to close the problem under study. As an example, simplified governing equations are derived for a system of air–water flow and heat transfer through two thin porous layers. In comparison to previous macroscale models, our model possesses the following distinctive advantages: (1) it is rigorous thermodynamics-based model; (2) it is formulated in terms of layer-thickness-averaged material properties which are usually easily measurable; and (3) it reduces 3D modeling to 2D leading to a very significant reduction of computational efforts.