title: Averaged model for momentum and dispersion in hierarchical porous media.
abstract: Hierarchical porous media are multiscale systems, where different characteristic pore sizes and structures are encountered at each scale. Focusing the analysis to three pore scales, an upscaling procedure based on the volume-averaging method is applied twice, in order to obtain a macroscopic model for momentum and diffusion-dispersion. The effective transport properties at the macroscopic scale (permeability and dispersion tensors) are found to be explicitly dependent on the mesoscopic ones. Closure problems associated to these averaged properties are numerically solved at the different scales for two types of bidisperse porous media. Results show a strong influence of the lower-scale porous structures and flow intensity on the macroscopic effective transport properties.
authors.affiliation: Mechanical and Aerospace Engineering, University of California San Diego, La Jolla, California 92093, USA.|MSSMat, UMR-CNRS 8579, Ecole Centrale Paris, Grande Voie des Vignes, 92295 Châtenay-Malabry, France.|EM2C, UPR-CNRS 288, Ecole Centrale Paris, Grande Voie des Vignes, 92295 Châtenay-Malabry, France.
authors.forename: Morgan
authors.initials: M
authors.lastname: Chabanon
authors.affiliation: MSSMat, UMR-CNRS 8579, Ecole Centrale Paris, Grande Voie des Vignes, 92295 Châtenay-Malabry, France.
authors.forename: Bertrand
authors.initials: B
authors.lastname: David
authors.affiliation: EM2C, UPR-CNRS 288, Ecole Centrale Paris, Grande Voie des Vignes, 92295 Châtenay-Malabry, France.
authors.forename: Benoît
authors.initials: B
authors.lastname: Goyeau