Phase-Field Modeling of Two Phase Fluid Filled Fractures in a Poroelastic Medium

We propose an immiscible two phase flow fracture model, based on a phase-field for treating crack propagation in porous media. This multifluid model is an extension of classical flow models and we take into account nonzero capillary pressure. Using lubrication theory, we provide details of the determination of effective parameters: absolute and relative permeabilities. The phase-field formulation is a generalization of previous works by the authors and extends the single phase model to the two phase case. Here the resulting flow system has four unknowns: resident and injected pressures and saturations, respectively. The solid contribution consists of displacements and a phase-field variable. Both systems are coupled employing a fixed-stress splitting. Therein, the flow problem is treated with an iterative scheme and the solid problem fully implicitly. Modeling and algorithms are substantiated with several numerical tests.