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Article Dans Une Revue Physics of Fluids Année : 2014

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

Résumé

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 theKnudsen 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.
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.
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Dates et versions

hal-01003016 , version 1 (09-06-2014)

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Didier Lasseux, Francisco J. Valdès-Parada, Jesus Alberto Ochoa-Tapia, Benoit Goyeau. A macroscopic model for slightly compressible gas slip-flow in homogeneous porous media. Physics of Fluids, 2014, 26, pp.053102. ⟨10.1063/1.4875812⟩. ⟨hal-01003016⟩
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