Average Permeabilities of Heterogeneous Oil Sands

Abstract This paper discusses the practical problem of estimating a single equivalentpermeability for an oil reservoir, or a portion thereof, whose actualpermeability varies in an irregular manner. Limiting averages for general typesof permeability. variation are developed, and illustrated by examples involvingimportant, specific types of variation. Introduction The theory of the flow of fluids through porous media is becoming increasinglyimportant in predictions of oil-reservoir behavior. In practical applications, however, reservoirs are seldom found.to which simple theory strictly applies.Actual reservoirs have complicated shapes and non-uniform permeabilities andporosities. This paper discusses the problem of estimating a single equivalent permeabilityfor an oil reservoir, or a segment of an oil reservoir, whose actualpermeability varies in an irregular manner. The equivalent permeability of areservoir segment is defined as the permeability of a homogeneous segment ofthe same dimensions that would pass the same flux under the same pressure drop.It is the permeability value that can be used in simple theoretical formulas tocalculate the reservoir behavior. To the authors' knowledge, previous theoretical calculations on systems ofnon-uniform permeability have been carried out only by Muskat and he has notdealt with irregular variations, except in writing down the generaldifferential equation for the pressure in variably permeable systems. a In practical work, many calculations necessarily have been made to estimateequivalent permeabilities from the permeability profiles obtained by coreanalyses. Regarding such calculations, Johnston and Sherborne say: Simple arithmetic and weighted averages have been tried on many wells and ithas been found that, where frequent sampling has occurred, the arithmeticaverage is as satisfactory as a weighted average. It is possible that theapplication of statistical methods to the analysis of permeability data asrecently presented by Laws may prove fruitful. Law has made a valuable contribution in showing how statistical analyses mayaid in picturing the characteristics of a reservoir from those of a necessarilylimited number of core samples. It is believed however that the particularproblem of the estimation of equivalent permeabilities can be most directlyapproached from a fluid dynamical viewpoint as given in the present paper. Anexample is presented of the use of the conclusions herein in conjunction withLaw's method. T.P. 1852