Porous media equilibrium thermodynamics

Gas filtration through a porous medium is often described mathematically in the form of the Darcy equation u = KI, where is a filtration rate, / is a head gradient, and permeability coefficient K is the main characteristics of the medium. To model gas reservoirs, it is necessary to know permeability coefficients for both gas and liquid phases and to have a model to calculate reservoir liquid saturation [1,2]. The equilibrium liquid saturation depends only on the thermodynamic functions of the fluids and reservoir walls. 

It is assumed that the flow is steady, laminar, incompressible, and two-dimensional. The porous medium is considered to be homogeneous, isotropic, and in thermodynamic equilibrium with the saturated fluid the gas phase radiation is neglected. 

Two major groups of performance models have been proposed. The first group considers the membrane as a homogeneous mixture of ionomer and water. The second group involves approaches that consider the membrane as a porous medium. Water vapor equilibrates with this medium by means of capillary forces, osmotic forces resulting from solvated protons and fixed ions, hydration forces, and elastic forces. In this scenario, the thermodynamic state of water in the membrane should be specified by (at least) two independent thermodynamic variables, namely, chemical potential and pressure, subdued to independent conditions of chemical and mechanical equilibrium, respectively. The homogeneous mixture model is the basis of the so-called... 

The problem of capillary equilibrium in porous media is complicated from both experimental and theoretical points of view. The mechanisms of saturation and depletion of the porous medium are essentially nonequilibriiun. Further equilibration is due to slow processes like diffusion. The process of equilibration may be unfinished, since no significant changes of fluid distribution may occur during the time of an experiment. This especially relates to the so-called discontinuous condensate existing in the form of separate drops. As a result, thermodynamic states, which are not fully equilibrated, are interpreted from the practical point of view as equilibrium [28]. To the best of our knowledge, a consistent theory of such quasiequihbrium states has not yet been developed. In the following, we discuss the possible states of the two-phase mixtures in a porous medium, assuming complete thermodynamic equihbrium. This serves as a first approximation to a more complicated picture of the realistic fluid distribution in porous media. 

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