A stabilized extended finite element framework for hydraulic fracturing simulations

We present a stabilized extended finite element formulation to simulate the hydraulic fracturing process in an elasto-plastic medium. The fracture propagation process is governed by a cohesive fracture model, where a trilinear traction-separation law is used to describe normal contact, cohesion and strength softening on the fracture face. Fluid flow inside the fracture channel is governed by the lubrication equation, and the flow rate is related to the fluid pressure gradient by the 'cubic' law. Fluid leak off happens only in the normal direction and is assumed to be governed by the Carter's leak-off model. We propose a 'local' U-P (displacement-pressure) formulation to discretize the fluid-solid coupled system, where volume shape functions are used to interpolate the fluid pressure field on the fracture face. The 'local' U-P approach is compatible with the extended finite element framework, and a separate mesh is not required to describe the fluid flow. The coupled system of equations is solved iteratively by the standard Newton-Raphson method. We identify instability issues associated with the fluid flow inside the fracture channel, and use the polynomial pressure projectionmethod to reduce the pressure oscillations resulting from the instability. Numerical examples demonstrate that the proposed framework is effective in modeling 3D hydraulic fracture propagation. (C) 2016 John Wiley & Sons, Ltd.