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

We propose an immiscible two phase flow fracture model, based on phase-field for treating crack propagation in porous media. This multifluid model is an extension of classical flow models and we take into account non-zero 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. 1. Introduction. Coupled multiphase fluid flow and deformation in fractured porous rock are important in energy and environmental applications. Hydraulic fracturing and horizontal drilling are considered to be the major reasons U.S. has been having an energy revolution , one that has changed the energy picture from scarcity to abundance. Fracking, the forcing opening of fissures in subsurface rocks by introducing liquid at high pressure, is letting the U.S. tap vast oil and natural gas reserves that previously were locked away in shale and other tight-rock formations. Up to 95 percent of natural gas wells drilled in the next decade will utilize hydraulic fracturing [33] and by 2040, over 80 percent of US natural gas production is projected to come from formations that need to be hydraulically fractured to be accessible [1]. Additional important examples involving subsurface fluid structure interactions include geothermal energy production, deep underground injection of hazardous wastes, and storage of carbon sequestration into saline aquifers and depleted oil and gas reservoirs. The latter has been considered to be a major technology for reducing the emission of greenhouse gases to the atmosphere.