ON EQUILIBRIUM AND PRIMARY VARIABLES IN TRANSPORT IN POROUS-MEDIA

Thermodynamic equilibrium, which involves mechanical, thermal, and chemical equilibria, in a multiphase porous medium, is defined and discussed, both at the microscopic level, and at the macroscopic one. Conditions are given for equilibrium in the presence of forces between the surface of the solid matrix and the fluid phases. The concept of approximate thermodynamic equilibrium is introduced and discussed, employing the definition of a thermodynamic potential. This discussion serves as the basis for the methodology of determining the number of degrees of freedom in models of phenomena of transport (of mass, energy, and momentum) in porous media. Equilibrium and nonequilibrium cases are considered. The proposed expressions for the number of degrees of freedom in macroscopic transport models, represent the equivalent of Gibbs phase rule in thermodynamics. Based on balance considerations and thermodynamic relationships, it is shown that the number of degrees of freedom, NF, in a problem of transport in a deformable porous medium, involving NP fluid phases and NC components, under nonisothermal conditions, with equilibrium among all phases and components, is NF = NC + NP + 4. Under nonequilibrium conditions among the phases, the rule takes the form NF = NC x NP + 2NP + NC + 4. In both cases, when fluid phase velocities are determined by Darcy's law, NF is reduced by NP. When the solid matrix is nondeformable, NF is reduced by 3. The number of degrees of freedom is also determined for conditions of approximate chemical and thermal equilibria, and for conditions of equilibrium that prevail only among some of the phases present in the system. Examples of particular cases are presented to illustrate the proposed methodology.