The Thermodynamics of Evaporation and Condensation in Porous Media

Abstract

ABSTRACT The thermodynamics of a single component, vapor-liquid system subjected to capillary pressures characteristic of porous rock have been examined. Van der Waal's equation was coupled with the Gibbs-Duhem differential expression for the chemical potential and integrated. The resulting expression for chemical potential as a function of pressure, temperature and specific volume provided the key to the understanding of the thermodynamic equilibrium between the wetting liquid and its vapor across the capillary pressure discontinuity. Through this analysis it was found that when capillary pressures are present, thermodynamic equilibrium can only exist if both liquid and vapor phases are in a superheated state. This result is consistant with Kelvin's equation for vapor lowering. Furthermore, the superheated liquid phase, which is in a metastable state if no vapor or capillary pressures are present, is in an unconditionally stable state if capillary pressures are imposed. The degree of liquid superheat was found to be a function of contact angle, interfacial tension, effective pore radius and heat of vaporization. Using water as an example, quantitative values of liquid and vapor pressure lowering are presented for various pressures and pore radii. It was found that for porous media of pore size distribution similar to that of reservoir rock, the vapor thermodynamic equilibrium pressures and temperatures do not differ significantly from the steam table values. Significant liquid pressure lowering does result. Also the transition from capillary condensation to thin film adsorption may be identified from the liquid pressure lowering curves. Applications to other systems in thermodynamic equilibrium with a porous media are discussed.