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Gas slip flow in a fracture: local Reynolds equation and upscaled macroscopic model

hal.structure.identifierLaboratoire d'Etanchéité [LE]
hal.structure.identifierInstitut de mécanique des fluides de Toulouse [IMFT]
dc.contributor.authorZAOUTER, Tony
hal.structure.identifierInstitut de Mécanique et d'Ingénierie de Bordeaux [I2M]
dc.contributor.authorLASSEUX, Didier
IDREF: 131294474
hal.structure.identifierInstitut de mécanique des fluides de Toulouse [IMFT]
dc.contributor.authorPRAT, Marc
dc.date.accessioned2021-05-14T09:40:47Z
dc.date.available2021-05-14T09:40:47Z
dc.date.issued2018-02-25
dc.identifier.issn0022-1120
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/76601
dc.description.abstractEnThe slightly compressible flow of a gas in the slip regime within a rough fracture featuring a heterogeneous aperture field is analyzed in depth in this work. Starting from the governing Navier-Stokes, continuity and gas state-law equations together with a first order slip boundary condition at the impermeable walls of the fracture, the two-dimensional slip-corrected Reynolds model is first derived that is shown to be second order accurate in the local slope of the roughness asperities while being first order accurate in the Knudsen number. Focusing the interest on the flow-rate to pressure-gradient relationship over a representative element of the fracture, an upscaling procedure is applied to the local Reynolds equation using the method of volume averaging, providing a macroscopic model for which the momentum conservation equation has a Reynolds-like form. The effective macroscopic transmissivity tensor, that is characteristic of the representative element, is shown to be given by a closure problem that is non-intrinsic to the geometrical structure of the fracture only due to the slip effect. An expansion to the first order in the Knudsen number is carried out on the closure, yielding a decomposition of the effective transmissivity tensor into its purely viscous part and its slip-correction, both being given by the solution of intrinsic closure sub-problems. Numerical validations of the solution to the closure problem are performed with analytical predictions for simple fracture geometries. Comparison between the macroscopic transmissivity tensor, obtained from the solution of the closure problem, and its first order approximation is illustrated on a randomly rough correlated Gaussian fracture.
dc.language.isoen
dc.publisherCambridge University Press (CUP)
dc.subject.enporous media
dc.subject.enrarefied gas flow
dc.subject.enlubrication theory
dc.title.enGas slip flow in a fracture: local Reynolds equation and upscaled macroscopic model
dc.typeArticle de revue
dc.identifier.doi10.1017/jfm.2017.868
dc.subject.halPhysique [physics]/Mécanique [physics]/Mécanique des fluides [physics.class-ph]
bordeaux.journalJournal of Fluid Mechanics
bordeaux.page413-442
bordeaux.volume837
bordeaux.hal.laboratoriesInstitut de Mécanique et d’Ingénierie de Bordeaux (I2M) - UMR 5295*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.institutionINRAE
bordeaux.institutionArts et Métiers
bordeaux.peerReviewedoui
hal.identifierhal-02366909
hal.version2
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-02366909v2
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