Formulation of a phase field model of multiphase flow in deformable porous media

Department of Chemical Engineering Materials & Environment, University of Rome La Sapienza, via Eudossiana 18 I-00184, Rome Italy

^a Corresponding author: giulio.sciarra@uniroma1.it

Abstract

In this contribution a new model for partially saturated porous media is presented, within the framework of gradient poromechanics, based on a phase field approach. While the standard retention curve is expected still to provide the intrinsic retention properties of the porous skeleton, depending on the porous texture, an enhanced description of the surface tension between the wetting and the non-wetting fluid, occupying the pore space, is stated considering a regularized phase field model based on an additional contribution to the overall free energy depending on the saturation gradient. This approach provides similar results as those of the model based on the concept of specific interfacial area. The dependence of the free energy on the gradient of the saturation also implies that Darcy law must be extended to become a fourth order partial differential equation.