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Macroscopic momentum and mechanical energy equations for incompressible single-phase flow in porous media

dc.contributor.authorPAÉZ-GARCÍA, Catherine
dc.contributor.authorVALDÉS-PARADA, Francisco
dc.contributor.authorLASSEUX, Didier
IDREF: 131294474
dc.date.accessioned2021-05-14T09:31:13Z
dc.date.available2021-05-14T09:31:13Z
dc.date.issued2017-02-01
dc.identifier.issn2470-0045
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/75870
dc.description.abstractEnModeling flow in porous media is usually focused on the governing equations for mass and momentum transport, which yield the velocity and pressure at the pore or Darcy scales. However, in many applications, it is important to determine the work (or power) needed to induce flow in porous media, and this can be achieved when the mechanical energy equation is taken into account. At the macroscopic scale, this equation may be postulated to be the result of the inner product of Darcy's law and the seepage velocity. However, near the porous medium boundaries, this postulate seems questionable due to the spatial variations of the effective properties (velocity, permeability, porosity, etc.). In this work we derive the macroscopic mechanical energy equation using the method of volume averaging for the simple case of incompressible single-phase flow in porous media. Our analysis shows that the result of averaging the pore-scale version of the mechanical energy equation at the Darcy scale is not, in general, the expected product of Darcy's law and the seepage velocity. As a matter of fact, this result is only applicable in the bulk region of the porous medium and, in the derivation of this result, the properties of the permeability tensor are determinant. Furthermore, near the porous medium boundaries, a more novel version of the mechanical energy equation is obtained, which incorporates additional terms that take into account the rapid variations of structural properties taking place in this particular portion of the system. This analysis can be applied to multiphase and compressible flows in porous media and in many other multiscale systems.
dc.language.isoen
dc.publisherAmerican Physical Society (APS)
dc.title.enMacroscopic momentum and mechanical energy equations for incompressible single-phase flow in porous media
dc.typeArticle de revue
dc.identifier.doi10.1103/physreve.95.023101
dc.subject.halSciences de l'ingénieur [physics]
dc.subject.halSciences de l'ingénieur [physics]/Milieux fluides et réactifs
dc.subject.halSciences de l'ingénieur [physics]/Mécanique [physics.med-ph]
dc.subject.halPhysique [physics]
dc.subject.halPlanète et Univers [physics]
dc.subject.halSciences de l'environnement
dc.subject.halSciences de l'ingénieur [physics]/Génie des procédés
bordeaux.journalPhysical Review E
bordeaux.volume95
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-03140897
hal.version1
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-03140897v1
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