Finite element modeling of hydraulic fracturing on a reservoir scale in 2D

A finite element based procedure is suggested for the modeling of hydraulic fracturing of heterogeneous rocks on a macroscopic scale. The scheme is based on the Biot-equations for the rock, and a finite element representation for the fracture pressure, where the fracture volume appears as fracture porosity. The fracture and the rock are represented unified on the same regular finite element grid. The numerical solutions of pressure and displacement are verified against exact 1D results. The 1D model also shows how the tension forces that open the fracture decreases as the gradient of the pore pressure decreases. The fracture criterion is based on the “strength” of bonds in the finite element grid. It is shown how this criterion scales with the grid size. It is assumed that fracturing happens instantaneously and that the fluid volume in the fracture is the same after a fracture event. The pressure drop that follows a fracture event is computed with a procedure that preserves the fluid volume in the fracture. The hydraulic fracturing procedure is demonstrated on a homogeneous and an inhomogeneous rock when fluid is injected at a constant rate by a well at the center of the grid. A case of a homogeneous rock shows that a symmetric fracture develops around the well, where one bond breaks in each fracture event. A heterogeneous case shows the intermittent nature of the fracture process, where several bonds break in each fracture event.