Potentials and Their Role in Transport in Porous Media

Abstract

The concept of “capillary,” or “matric,” potentials is commonly used in soil physics to describe water movement in unsaturated soils. The rigorous definition of these and other potentials is presented from fundamental thermodynamic principles at the microscopic level and extended to the macroscopic level by averaging over a representative elementary volume. Of special interest is the treatment of adsorptive surface forces and their associated potentials. Porous medium potentials are extended to a domain containing multiple fluid phases and multiple components. A macroscopic motion equation for a fluid phase (Darcy's law) is derived, incorporating the effect of potentials and surface forces. It relates advective fluxes to gradients of macroscopic chemical potentials and temperature. It reduces to the usual form of Darcy's law only when the aqueous phase is sufficiently dilute and temperatures are uniform. Kelvin's law, which relates relative humidity to matric potential, is extended to the case of multiple multicomponent fluid phases in a porous medium domain. The concept of “irreducible” (or “residual”) wetting fluid saturation and its relationship to capillary pressure, surface forces, and the Gibbs chemical potential, are discussed. Common methods for determining the matric potential are reexamined in light of this work.