Non-equilibrium thermodynamics of groundwater flow systems: Symmetry properties of phenomenological coefficients and considerations of hydrodynamic dispersion

Abstract

The theory of non-equilibrium thermodynamics is applied to transport processes in groundwater flow systems. The theory is postulated to be applicable to a continuum model of porous medium in which fluxes and forces at points in the fluid phase are averaged over a representative elementary volume. Group-theoretic principles are applied to the phenomenological coefficients, and it is shown that these considerations can simplify the phenomenological equations both by removing unallowed coupled effects and by reducing the apparent number of independent, numerical components contained in a given phenomenological coefficient. It is found, for example, that in porous media having certain symmetry properties, chemical reaction rates cannot be coupled to vector flows of heat and matter. Examination of the current theory of hydrodynamic dispersion in the light of non-equilibrium thermodynamics leads to a proposed modification of the former. It is proposed that phenomenological coefficients for coupled and direct dispersive processes be formed of the product of a fourth-rank tensor, dispersivity of the medium, with the dyadic product of solute velocities, rather than with fluid flow velocities. Group theory is applied to the resulting coefficients, and new results are obtained for the forms assumed by the coefficients in certain anisotropic media.