Pressure- and temperature-dependent klinkenberg slippage effect in porous media to non-ideal gases

Abstract

The present paper evaluates the effect of non-ideal gas behavior on the Klinkenberg gas slippage effect for measuring the permeability of porous media. The generic cubic equation of state, particularly van der Waals (vdW-), Soave-Redlich-Kwong (SRK-), and Peng-Robinson (PR-) equation of state, are used to consider the non-ideal behavior of the gases, including nonhydrocarbons and hydrocarbons. The above cubic equation of state is expressed in terms of the gas compressibility factor involving the temperature-dependent second and third virial coefficients. A comprehensive mathematical model leading to a generalized analytical solution for the pressure- and temperature-dependent apparent permeability of porous media to non-ideal gas is proposed after combining the first-order Klinkenberg slippage effect and virial equation of state. Experimental data of Klinkenberg (1941) and Calhoun (1976) [Klinkenberg, L. J., The permeability of porous media to liquids and gases. Drill Prod Prac. API, 200–213, 1941; Calhoun, J. C., 1976. Fundamentals of Reservoir Engineering, University of Oklahoma Press, Oklahoma] are used to validate the proposed apparent permeability models. The proposed methodology accurately predicts the liquid permeability using the 18-test core samples and 7-test gases, accounting for the non-ideal behavior. The temperature-dependency of the apparent permeability of porous media to non-ideal gases with varying mean pressure is also established.