Macroscopic permeability of doubly porous solids with spheroidal macropores: close form approximate solutions of the longitudinal permeability - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Proceedings of the Royal Society of London. Series A, Mathematical and physical sciences Année : 2020

Macroscopic permeability of doubly porous solids with spheroidal macropores: close form approximate solutions of the longitudinal permeability

Résumé

The presence of macropores and fractures significantly affects the effective transport properties of porous solids such as concrete or rocks. The dimensions of the fractures are generally large behind that of the initial porosity, so that the problem contains two porosities. The influence of the macroporosity is studied in the homogenization framework by solving at the intermediate scale, that of the macropores, a coupled Darcy/Stokes problem with the Beavers-Joseph-Saffman (BJS) interface condition. We derive analytic expressions of the macroscopic permeability in the case of an isotropic permeable matrix containing spheroidal shaped macropores. To this aim, we consider a Representative Volume Element (RVE) on which uniform boundary conditions are considered for the velocity and pressure fields. The local problem is written as minimum principles; kinematic and static approaches are developed in order to derive rigorous bounds for the macroscopic permeability. Close form expressions of the longitudinal permeability (along the revolution axe of the spheroid) are determined by considering a simplified RVE constituted of two confocal spheroids. They depend on the volume fraction and the eccentricity of the spheroidal macropores, the scale factor between the two porosities and the slip coefficient of the BJS model. Illustrations show the influence of these parameters.
Fichier principal
Vignette du fichier
Monchiet-biporous - R3.pdf (290.1 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03183588 , version 1 (28-03-2021)

Identifiants

Citer

Vincent Monchiet. Macroscopic permeability of doubly porous solids with spheroidal macropores: close form approximate solutions of the longitudinal permeability. Proceedings of the Royal Society of London. Series A, Mathematical and physical sciences, 2020, ⟨10.1098/rspa.2020.0224⟩. ⟨hal-03183588⟩
13 Consultations
58 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More