Phase-field modelling of fluid driven fracture propagation in poroelastic materials considering the impact of inertial flow within the fractures

This paper presents a computational framework for modelling of fluid pressurised fracture propagation in saturated porous media. The framework rests on the principle of the variational phase-field theory to predict the fracture propagation pathway. The paper sets out the variational formulations and associated weak forms of the partial differential equations describing the pressure-deformation interplays of the fracturing domain, which are solved in the context of the Updated Lagrangian Finite Element method. The proposed formulation reflects the impact of the temporal evolution of the porous media attributes such as porosity, compressibility, permeability, and mechanical stiffness, on the nonlinear hydro-mechanical behaviour of the porous media during the fracture propagation. The inertial effect of the nonlinear flow inside the fracture is resolved using Forchheimer equation. Robustness of the modelling framework is examined by simulating benchmark examples. The effects of poroelastic characteristics of porous media such as the compressibility of solid skeleton and drained bulk modulus on the hydro-mechanical and cracking behaviour of porous rocks and on the total energy of the system are addressed. The nonlinearity of the fluid flow is found to be influential on the length of the leak-off and flow-back regions across the fractured zones, and on the amount of the fluid to be exchanged between the fractures and the porous zone, which is important in the prediction of the productivity of the fracking process in engineering applications.