Modeling Gravity-Driven Segregation in Porous Media by a Phase Field Approach to Unsaturated Poromechanics

Abstract

The phase field model of unsaturated poromechanics recently introduced by one of the authors is numerically implemented within CODE-BRIGHT, focusing attention, at the moment, only on the behavior of the air-water mixture saturating the pore space. The model is formulated within the framework of gradient poromechanics, which implies the Darcy law, to be generalised into a fourth order partial differential equation with respect to saturation degree. From the numerical point of view this enriched structure of the differential problem is faced adopting a mixed finite element approach which means that not only the pore water pressure but also the saturation degree must be regarded as nodal unknowns. Within this framework a problem related to gravity driven segregation, say the counter-current flow, is addressed reproducing in a natural way the formation and the propagation of a bulge in the vertical saturation.