A macroscopic model for slightly compressible gas slip-flow in homogeneous porous media

The study of gas slip-flow in porous media is relevant in many applications ranging from nanotechnology to enhanced oil recovery and in any situation involving low-pressure gas-transport through structures having sufficiently small pores. In this paper, we use the method of volume averaging for deriving effective-medium equations in the framework of a slightly compressible gas flow. The result of the upscaling process is an effective-medium model subjected to time- and length-scale constraints, which are clearly identified in our derivation. At the first order in the Knudsen number, the macroscopic momentum transport equation corresponds to a Darcy-like model involving the classical intrinsic permeability tensor and a slip-flow correction tensor that is also intrinsic. It generalizes the Darcy-Klinkenberg equation for ideal gas flow, and exhibits a more complex form for dense gas. The component values of the two intrinsic tensors were computed by solving the associated closure problems on two-and three-dimensional periodic unit cells. Furthermore, the dependence of the slip-flow correction with the porosity was also verified to agree with approximate analytical results. Our predictions show a power-law relationship between the permeability and the slip-flow correction that is consistent with other works. Nevertheless, the generalization of such a relationship to any configuration requires more analysis. (C) 2014 AIP Publishing LLC.