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 deri...

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Bibliographic Details
Published in:Physics of fluids (1994) 2014-05, Vol.26 (5)
Main Authors: Lasseux, D., Parada, F. J. Valdes, Tapia, J. A. Ochoa, Goyeau, B.
Format: Article
Language:English
Subjects:
Compressibility
Constraint modelling
Dependence
Engineering Sciences
Enhanced oil recovery
Fluid dynamics
Gas flow
Gas transport
Ideal gas
Low pressure gases
Macroscopic models
Mathematical analysis
Nanotechnology
Permeability
Physics
Porosity
Porous media
Slip
Tensors
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Summary: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.
ISSN:1070-6631
1089-7666
DOI:10.1063/1.4875812