Macroscopic Model for Passive Mass Dispersion in Porous Media Including Knudsen and Diffusive Slip Effects
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...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Frontiers Media S.A.
2021-07-01
|
| Series: | Frontiers in Water |
| Subjects: | |
| Online Access: | https://www.frontiersin.org/articles/10.3389/frwa.2021.666279/full |
| _version_ | 1818922120801943552 |
|---|---|
| author | Francisco J. Valdés-Parada Didier Lasseux |
| author_facet | Francisco J. Valdés-Parada Didier Lasseux |
| author_sort | Francisco J. Valdés-Parada |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-20T01:48:30Z |
| format | Article |
| id | doaj.art-ff384c71b0d1478a88da89b379cd85d2 |
| institution | Directory Open Access Journal |
| issn | 2624-9375 |
| language | English |
| last_indexed | 2024-12-20T01:48:30Z |
| publishDate | 2021-07-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Water |
| spelling | doaj.art-ff384c71b0d1478a88da89b379cd85d22022-12-21T19:57:41ZengFrontiers Media S.A.Frontiers in Water2624-93752021-07-01310.3389/frwa.2021.666279666279Macroscopic Model for Passive Mass Dispersion in Porous Media Including Knudsen and Diffusive Slip EffectsFrancisco J. Valdés-Parada0Didier Lasseux1Departamento de Ingeniería de Procesos e Hidráulica, Universidad Autónoma Metropolitana Iztapalapa, Ciudad de México, MexicoI2M, UMR 5295, CNRS, Univ. Bordeaux, Cours de la Libération, Talence, FranceIn 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.https://www.frontiersin.org/articles/10.3389/frwa.2021.666279/fulldispersion in porous mediaKnudsen slipdiffusive slipvolume averagingDarcy's law |
| spellingShingle | Francisco J. Valdés-Parada Didier Lasseux Macroscopic Model for Passive Mass Dispersion in Porous Media Including Knudsen and Diffusive Slip Effects Frontiers in Water dispersion in porous media Knudsen slip diffusive slip volume averaging Darcy's law |
| title | Macroscopic Model for Passive Mass Dispersion in Porous Media Including Knudsen and Diffusive Slip Effects |
| title_full | Macroscopic Model for Passive Mass Dispersion in Porous Media Including Knudsen and Diffusive Slip Effects |
| title_fullStr | Macroscopic Model for Passive Mass Dispersion in Porous Media Including Knudsen and Diffusive Slip Effects |
| title_full_unstemmed | Macroscopic Model for Passive Mass Dispersion in Porous Media Including Knudsen and Diffusive Slip Effects |
| title_short | Macroscopic Model for Passive Mass Dispersion in Porous Media Including Knudsen and Diffusive Slip Effects |
| title_sort | macroscopic model for passive mass dispersion in porous media including knudsen and diffusive slip effects |
| topic | dispersion in porous media Knudsen slip diffusive slip volume averaging Darcy's law |
| url | https://www.frontiersin.org/articles/10.3389/frwa.2021.666279/full |
| work_keys_str_mv | AT franciscojvaldesparada macroscopicmodelforpassivemassdispersioninporousmediaincludingknudsenanddiffusiveslipeffects AT didierlasseux macroscopicmodelforpassivemassdispersioninporousmediaincludingknudsenanddiffusiveslipeffects |