The Efficacy of Thermodynamics in Development of Governing Equations and Constitutive Relations for Saline Solutions in Variably Saturated Porous Media

Relations are presented that describe the behavior of water with high salt concentrations in variably saturated porous media for isothermal systems. Equations were derived using classic equilibrium thermodynamics of closed systems. Resulting corrections for vapor pressure, liquid pressure, and Darcy coefficients are presented, and an extension of the relations to non-isothermal systems is proposed. Next, the governing equations obtained using general process thermodynamics for continuous systems are presented. A discussion of the usual use of these equations follows, along with some general observations. Historically, the principles of Onsager have been employed to develop a linearly coupled set of forces and fluxes. Except for the reciprocity relations, which allow the determination of fewer coefficients, little is gained by this standard approach. A similar set of governing equations results from simply assuming every flux may be driven by a gradient in any of the potentials, but this requires estimation of every coefficient separately. On the other hand, the use of Onsager relations requires a unique separation of the reversible and irreversible terms in the energy equation, which is not always a trivial derivation. Either method guarantees a sufficient number of coefficients requiring determination that within the experimental uncertainty, it may be difficult to tell if the physics is really captured, or if there just exists sufficient freedom of the parameters to fit the data. Results of recent research indicates that for the case of water movement in the vicinity of highly concentrated salts, the dilute approximations extended by use of a more general chemical activity term is sufficient for modeling the constitutive relations, except in very dry, fine textured sediments.