Phase-field simulation of hydraulic fracturing with a revised fluid model and hybrid solver

With an intrinsic advantage in describing complex fracture networks, the phase field method has demonstrated promising potential for the simulation of hydraulic fracturing processes in recent literatures. We critically examine the existing phase-field hydraulic fracturing models, and propose a hybrid solution scheme with a revised fluid model. Specifically, the formation deformation and phase field are solved using the finite element method (FEM), while the fluid flows are solved using the finite volume method (FVM). The proposed hybrid scheme is validated with the analytical solution for the toughness-dominated fracture propagation and is tested on the complex hydraulic fracturing process in a naturally fractured formation. Demonstrated by numerical examples, the proposed hybrid phase-field framework has several advantages: (1) it captures the effect of fluid pressure inside the fracture and reservoir more accurately than existing models; (2) it provides a sharper capture of formation fractures; (3) it avoids the nonphysical oscillation of fluid pressure when using a pure FEM solver; and (4) it has a superior performance in mesh and time step convergence