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General slip regime permeability model for gas flow through porous media
A theoretical effective gas permeability model was developed for rarefied gas flow in porous media, which holds over the entire slip regime with the permeability derived as a function of the Knudsen number. This general slip regime model (GSR model) is derived from the pore-scale Navier-Stokes equat...
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Published in: | Physics of fluids (1994) 2016-07, Vol.28 (7) |
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Main Authors: | , , , |
Format: | Article |
Language: | English |
Subjects: | |
Citations: | Items that this one cites Items that cite this one |
Online Access: | Get full text |
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Summary: | A theoretical effective gas permeability model was developed for rarefied gas flow in porous media, which holds over the entire slip regime with the permeability derived as a function of the Knudsen number. This general slip regime model (GSR model) is derived from the pore-scale Navier-Stokes equations subject to the first-order wall slip boundary condition using the volume-averaging method. The local closure problem for the volume-averaged equations is studied analytically and numerically using a periodic sphere array geometry. The GSR model includes a rational fraction function of the Knudsen number which leads to a limit effective permeability as the Knudsen number increases. The mechanism for this behavior is the viscous fluid inner friction caused by converging-diverging flow channels in porous media. A linearization of the GSR model leads to the Klinkenberg equation for slightly rarefied gas flows. Finite element simulations show that the Klinkenberg model overestimates the effective permeability by as much as 33% when a flow approaches the transition regime. The GSR model reduces to the unified permeability model [F. Civan, “Effective correlation of apparent gas permeability in tight porous media,” Transp. Porous Media 82, 375 (2010)] for the flow in the slip regime and clarifies the physical significance of the empirical parameter b in the unified model. |
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ISSN: | 1070-6631 1089-7666 |
DOI: | 10.1063/1.4954503 |