Finite-Element Modeling of the Growth and Interaction of Hydraulic Fractures in Poroelastic Rock Formations

This chapter presents a finite element-based method for simulating the hydraulic fracturing process in porous rocks. The finite-element method is used to compute the mechanical deformation of the rock, and it accounts for the effects of poroelasticity, thermoelasticity, and fluid flow in both the fractures and the rock matrix, in a fully coupled manner. The fractures are represented in the mesh as fully three-dimensional objects, with evolving local apertures that are computed as part of the solution. Fracture growth is modeled using stress intensity factors, and the direction and rate of growth is evaluated individually at each fracture tip node. Specifically, the direction of fracture growth at each tip node is governed by the maximum circumferential stress criterion, and the extent of fracture growth is approximated using a Paris-type growth law. Contact between opposing fracture surfaces is handled using a gap-based augmented Lagrangian approach. Fracture growth is computed independently of the underlying mesh, and the fracture path is not constrained to follow the mesh. Instead, a new mesh is constructed after each time step, if the fracture has grown in that time step. This numerical framework is then applied to the growth of multiple hydraulic fractures in impermeable and permeable formations to investigate the effects of matrix permeability, matrix poroelasticity, and temperature contrast (between the rock and the injected fluid) on the growth and interaction of hydraulic fractures.