Derivation of basic equations of mass transport in porous media, Part 1. Macroscopic balance laws

Abstract This paper is the first part of a series of two papers on the development of a general thermodynamic basis for the study of transport phenomena in a porous medium composed of a multi-component fluid flowing through a porous rock skeleton. Fluid components are miscible and homogenous thermodynamic interactions among them take place at the molecular level. Heterogeneous thermodynamic interactions occur between fluid components and the rock at solid-fluid interfaces. In the microscopic description of the medium, balance laws of continuum theories of mixtures are employed as the governing equations at points within the fluid phase. At points within the rock aggregates, classical balance equations of continuum mechanics are employed. Interfacial jump conditions are given to account for interactions between fluid species and the rock. By averaging of these three sets of equations, we arrive at macroscopic equations of balance of mass, momentum, energy and entropy for the rock and for individual fluid species, as well as restrictions on interaction terms. Also, a macroscopic formulation of the second law of thermodynamics for the medium is provided. Macroscopic balance laws will have to be supplemented by appropriate constitutive relations to obtain a complete thermodynamic theory of transport processes in porous media. This approach, both in concept and methodology, is the same as that developed by Hassanizadeh and Gray 14–16 . It makes it possible to take into account coupling of thermodynamic effects. Among the final results, we shall provide a generalization of Fick's Law and Darcy's for transport of concentrated brine in porous media.

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