Derivation of new models for the capillary pressure and relative permeability curves of porous media

摘要

New phenomenological models of the capillary pressure and relative permeability curves are derived for the quasi-static oil/water drainage in water-wet porous media. The porous medium is represented by a network of interconnected capillary tubes and oil/water drainage is simulated by a modified invasion percolation model with trapping. With the aid of percolation theory, effective medium approximation and fractal geometry the capillary pressure as well as the relative permeability of each fluid are expressed as approximate functions of water saturation by using as input parameters the pore size distribution, pore shape factors, fractal roughness porosity, pore network topology and physicochemical properties of the fluid system. Sample calculations for several selected parameter values are performed and guidelines are given about some methods of pore structure characterization.