Percolation Theory of Steam/Water Relative Permeability

Abstract

ABSTRACT Thermal recovery and geothermal processes typically involve regimes where the simultaneous flow of water liquid and vapor takes place. Vapor condensation and liquid evaporation are phenomena commonly accompanying such flows. Traditionally, the flow description relies on relative permeability and capillary pressure functions. In contrast to immiscible fluids, however, relative permeability and capillary pressure characteristics of condensing phases are not well understood at present. Instead, the vapor is commonly treated as a non-condensible phase and assigned corresponding flow properties. In this work, a systematic investigation is undertaken to derive relative permeability and capillary pressure functions for condensible phases, specifically pertaining to a steam-water system. The metnod used is an extension of the approach proposed by Heiba et al1 for immiscible fluids. The novel element is the use concepts from percolation theory for the description of capillary condensation and evaporation processes in porous media obtained elsewhere2. Based on derived analytical expressions saturations and capillary pressure curves are evaluated. Relative permeabilities are next calculated from approximate expressions for Bethe lattices3. The results obtained are compared against those presently used. Implications and extensions to related processes are also discussed.