Relative Permeability Calculations From Pore Size Distribution Data

Abstract Formulas for calculating relative permeability from pore size distribution data are derived from basic laws of fluid flow in porous media. The tortuosity factors that appear in the equations are described in terms of the physical properties of the medium and the saturations of the contained fluids. Procedures for calculating and methods for measuring the tortuosity factors are discussed. Values of relative permeability calculated by the formulas are compared with results obtained by experimental measurements. Introduction Recently, several investigators have derived relative permeability equations from Darcy's and Poiseuille's Laws in which some physical factor or factors describing the porous system appear. The factor that has caused the greatest amount of comment, and which is probably least understood, is the tortuosity of the fluid path in the porous sample. Values of the tortuosity factors appearing in the equations range from a constant for all conditions of the fluid flow system to an inverse function of the pore radii. It is the purpose of this paper to compare some experimentally determined relative permeability curves with those calculated by a method which utilized capillary pressure information. The capillary pressure data were obtained preferably from pore size distribution information as determined by mercury injection but, in some cases, in the absence of suitable mercury injection information, data were taken from measurements made by the porous semi-permeable diaphragm method. The physical significance of certain tortuosity concepts is inferred and the determinations of the tortuosity factors from pore size distribution data and by electrical measurements are discussed.