Flows of two slightly miscible fluids in porous media: two scale numerical modelling
Résumé
We address the two-scale homogenization of the Navier-Stokes and Cahn-Hilliard equations in the case of a weak miscibility of a two-component fluid. To this end a notion of the miscibility strength is formulated on the basis of a corre- lation between the upscaling parameter and the surface tension. As a result, a two-scale model is derived. Macro-equations turn out to be a generalization of the Darcy law enjoying cross-coupling permeability tensors. It implies that the Darcy velocity of each phase depends on pressure gradients of both the phases. Micro-equations serve for determination both of the permeability tensors and the capillary pressure. An example is constructed by analytical tools to describe cap- illary displacement of oil by mixture of water with Carbon dioxide in a system of hydrophobic parallel channels.
Origine : Fichiers produits par l'(les) auteur(s)
Licence : CC BY - Paternité
Licence : CC BY - Paternité