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An improved macroscale model for gas slip flow in porous media

Published online by Cambridge University Press:  16 September 2016

Didier Lasseux ,
Francisco J. Valdés Parada  and
Mark L. Porter
Didier Lasseux*
Affiliation:
CNRS, (Univ. Bordeaux, IPB, ENSAM) - I2M, UMR5295, Esplanade des Arts et Métiers, 33405 Talence, CEDEX, France
Francisco J. Valdés Parada
Affiliation:
Universidad Autónoma Metropolitana-Iztapalapa, Departamento de Ingeniería de Procesos e Hidráulica, Av. San Rafael Atlixco 186, 09340 Mexico D.F., Mexico
Mark L. Porter
Affiliation:
Earth Systems Observations, MS D462, Los Alamos National Laboratory, Los Alamos, NM 85745, USA
*
†Email address for correspondence: didier.lasseux@ensam.eu
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Abstract

We report on a refined macroscopic model for slightly compressible gas slip flow in porous media developed by upscaling the pore-scale boundary value problem. The macroscopic model is validated by comparisons with an analytic solution on a two-dimensional (2-D) ordered model structure and with direct numerical simulations on random microscale structures. The symmetry properties of the apparent slip-corrected permeability tensor in the macroscale momentum equation are analysed. Slip correction at the macroscopic scale is more accurately described if an expansion in the Knudsen number, beyond the first order considered so far, is employed at the closure level. Corrective terms beyond the first order are a signature of the curvature of solid–fluid interfaces at the pore scale that is incompletely captured by the classical first-order correction at the macroscale. With this expansion, the apparent slip-corrected permeability is shown to be the sum of the classical intrinsic permeability tensor and tensorial slip corrections at the successive orders of the Knudsen number. All the tensorial effective coefficients can be determined from intrinsic and coupled but easy-to-solve closure problems. It is further shown that the complete form of the slip boundary condition at the microscale must be considered and an important general feature of this slip condition at the different orders in the Knudsen number is highlighted. It justifies the importance of slip-flow correction terms beyond the first order in the Knudsen number in the macroscopic model and sheds more light on the physics of slip flow in the general case, especially for large porosity values. Nevertheless, this new nonlinear dependence of the apparent permeability with the Knudsen number should be further verified experimentally.

JFM classification

Low-Reynolds-number flows: Low-Reynolds-number flows Low-Reynolds-number flows: Porous media Rarefied Gas Flow: Rarefied Gas Flow
Type
Papers
Information
Journal of Fluid Mechanics , Volume 805 , 25 October 2016 , pp. 118 - 146
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Copyright
© 2016 Cambridge University Press 

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