Gas flow in porous media with Klinkenberg effects

Abstract

Gas flow in porous media differs from liquid flow because of the large gas compressibility and pressure-dependent effective permeability. The latter effect, named after Klinkenberg, may have significant impact on gas flow behavior, especially in low permeability media, but it has been ignored in most of the previous studies because of the mathematical difficulty in handling the additional nonlinear term in the gas flow governing equation. This paper presents a set of new analytical solutions developed for analyzing steady-state and transient gas flow through porous media including Klinkenberg effects. The analytical solutions are obtained using a new form of gas flow governing equation that incorporates the Klinkenberg effect. Additional analytical solutions for one-, two- and three-dimensional gas flow in porous media could be readily derived by the following solution procedures in this paper. Furthermore, the validity of the conventional assumption used for linearizing the gas flow equation has been examined. A generally applicable procedure has been developed for accurate evaluation of the analytical solutions which use a linearized diffusivity for transient gas flow. As application examples, the new analytical solutions have been used to verify numerical solutions, and to design new laboratory and field testing techniques to determine the Klinkenberg parameters. The proposed laboratory analysis method is also used to analyze data from steady-state flow tests of three core plugs from The Geysers geothermal field. We show that this new approach and the traditional method of Klinkenberg yield similar results of Klinkenberg constants for the laboratory tests; however, the new method allows one to analyze data from both transient and steady-state tests in various flow geometries.