Theoretical Generalizations Leading to the Evaluation of Relative Permeability

Abstract

Abstract Theoretical expressions are presented to describe wetting and non-wettingphase relative permeability relations. These expressions have then beencompared with existing published data, the conformance noted being sufficientlygood to satisfy the requirements of some engineering use. As a consequence, itmay be supposed that relative permeability characteristics of porous media nowcan be inferred from basic core analysis data, in a manner more convenient(although less direct) than presently available methods of experimentalevaluation. Introduction This paper presents a new approach to the problem of relative permeabilityevaluation. A classification of published discussions of relative permeabilityconcepts which have appeared in the petroleum literature will show thatpreviously emphasis has been placed on methods of experimental measurement, onthe interpretation of the data so obtained with respect to the variableproperties of the system, and on theoretical and practical considerations whichrelate relative permeability to gross fluid behavior in petroleum reservoirs.Essentially, no detailed examination has appeared which treats the fundamentalfactors controlling the quantitative features of the relative permeabilityrelation, although certain references can be cited where a qualitativeawareness of their existence and nature is indicated. This condition isexplainable in terms of the recognized complexity of the problem, and in orderto provide some basis for theoretical development, the general emphasis hasbeen placed in the past on experimental procedures of evaluation, the validityof which, in principle, could be confirmed by the analysis of well andreservoir performance. However, because of the experimental difficulties whichhave been encountered (notably, difficulties due to the so-called "endeffects"), and because of the general unreliability of field performancetests required to study the applicability of the data, relative permeabilityphenomena continue to be incompletely understood and described. In this paper is examined the possibility of predicting relative permeabilitiesentirely from fundamental considerations. In addition, attention is called tocertain important factors, previously unemphasized in the published literature, which now can serve as a basis for the eventual experimental confirmation ofthis and similar theoretical approaches, as well as the experimental solutionof the problem in general. Therefore, the analysis presented herein has thedual purpose both of orienting future experimental activity and also ofproviding an immediate solution for the relative permeability problem, sufficiently adequate for some engineering use. It will be seen that theconclusions reached are supported by theoretical and intuitive considerations, and they are not contradicted insofar as gross features are concerned byexisting concepts and interpretations of published experimental data, except asspecifically noted. T.P. 2563