Calculations of Unsteady-State Gas Flow Through Porous Media, Corrected for Klinkenberg Effect

Abstract

Abstract Mathematical equations have been derived to show the effect of the slippagephenomenon (Klinkenberg effect) on unsteady-state gas flow through porousmedia. It is pointed out that most of the existing data on unsteady gas flow may becorrected for slippage by a simple change in definition of the dimensionlessgroups. Introduction Several solutions to the various problems associated with the unsteady-stateflow of gas through porous media have been recently presented in theliterature. The cited publications have presented solutions for flow underideal conditions. The principal assumptions involved include:the densityof the gas obeys the perfect gas law;the viscosity of the gas is constant; andthe gas permeability is constant. Few, if any, actual gases under reservoir conditions are believed to conformwith the above, but the ideal solutions do provide the basis for makingimproved estimates on the performance of gas reservoirs. The purpose of thispaper is to show the performance characteristics when assumption (c) iscorrected for the slippage phenomenon or the Klinkenberg effect. This isbelieved to be a step nearer to reality. Mathematical Development Case 1. Gas Flow - Ideal Conditions The equations describing the flow of gas under ideal conditions have beenclearly presented in the cited literature; however, for completeness of thiswork they are repeated here. The basic differential equation describing the flow of gas is Equation (6). T.N. 191