The Flow of Real Gases in Porous Media

Abstract

American Institute of Mining, Metallurgical and Petroleum Engineers Inc. Abstract The pressure dependence of the viscosity and deviation factor of real gases means that the flow equations for gases in porous media are highly non-linear. The linearisation of these equations leads to diffusion-type equations similar to those governing the flow of slightly compressible liquids in porous media. Such approximations are only porous media. Such approximations are only valid for small changes in pressure; for large pressure changes the non-linear terms must be retained. The use of a "pseudo-pressure" variable for transforming the gas flow equation has recently been studied by a number of authors, and numerical solutions of the equations obtained. In this paper the radial flow of gas to a well is considered, and it is shown that a simple approximation technique leads to analytical solutions involving only elementary functions. These solutions agree well with the numerical results and provide a sound theoretical basis for empirical equations derived by other authors. The possibility of extending these methods to two-phase flow systems is briefly reviewed. Introduction During the past twenty years an increasing amount of effort has been devoted to the study of gas flow in porous media. In spite of this activity the development of solutions for the equations governing the flow of real gases in porous media has not progressed as far as one would have hoped. progressed as far as one would have hoped. The reason for this is not difficult to discover. The equations are highly non-linear and present great problems when analytical solutions are sought. An excellent survey of the literature on the flow of gases through porous media is given in Al-Hussainy et al. porous media is given in Al-Hussainy et al. The basic equation for the flow of real gases in porous media, taking account of the variation of viscosity and deviation factor with pressure, may be written as ..........................................(1)