Macroscopic modeling of slightly compressible gas slip flow in homogeneous porous media

Abstract eng:
A macroscopic model for slightly compressible gas slip flow in homogeneous porous media is derived by upscaling the micro- scopfimndary-value problem. A Darcy-like macroscopic momentum equation is obtained first, where the apparent permeability tensor, K8, is non intrinsic and features a non linear behavior with respect to the Knudsen number, E. A further development is carried out using an expansion in gKn, g being related to the tangential momentum accommodation coefficient. All the macroscopic coefficients in this model are obtained from intrinsic and coupled closure problems. The upscaled model, up to the first order in Kn, coincides with the classical Darcy-Klinkenberg law for an ideal gas. As illustrated from numerical solutions on model porous structures, validated from analytic solutions, higher-order terms of the expansion are required in order to recover the non-linear behavior of KS versus Kn.

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