VALDÉS-PARADA, Francisco J.; LASSEUX, Didier

doi:10.3389/frwa.2021.666279

Institut de Mécanique et d'Ingénierie [I2M]

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Frontiers in Water. 2021-07-30, vol. 3, p. 666279

Résumé en anglais

In this work, a macroscopic model for incompressible and Newtonian gas flow coupled to Fickian and advective transport of a passive solute in rigid and homogeneous porous media is derived. At the pore-scale, both momentum and mass transport phenomena are coupled, not only by the convective mechanism in the mass transport equation, but also in the solid-fluid interfacial boundary condition. This boundary condition is a generalization of the Kramers-Kistemaker slip condition that includes the Knudsen effects. The resulting upscaled model, applicable in the bulk of the porous medium, corresponds to: 1) A Darcy-type model that involves an apparent permeability tensor, complemented by a dispersive term and 2) A macroscopic convection-dispersion equation for the solute, in which both the macroscopic velocity and the total dispersion tensor are influenced by the slip effects taking place at the pore-scale. The use of the model is restricted by the starting assumptions imposed in the governing equations at the pore scale and by the (spatial and temporal) constraints involved in the upscaling process. The different regimes of application of the model, in terms of the Péclet number values, are discussed as well as its extents and limitations. This new model generalizes previous attempts that only include either Knudsen or diffusive slip effects in porous media.< Réduire

Mots clés en anglais

Darcy's law

diffusive slip

dispersion in porous media

Knudsen slip

volume averaging

URI

https://oskar-bordeaux.fr/handle/20.500.12278/124283

DOI

http://dx.doi.org/10.3389/frwa.2021.666279

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Institut de Mécanique et d’Ingénierie de Bordeaux (I2M) - UMR 5295

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Macroscopic Model for Passive Mass Dispersion in Porous Media Including Knudsen and Diffusive Slip Effects

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Résumé en anglais

Mots clés en anglais

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