Modeling of the propagation of hydraulic fracture using cohesive zone models

Hydraulic fracturing (HF) is widely used in the oil and gas industry to enhance production from tight reservoirs. The process involves the injection of fluid at a given flow rate into a wellbore in order to propagate a fracture in rocks and thus increase their permeability. Linear hydraulic fracture mechanics (LHFM) theories have been developped to predict the fracture propagation, assuming a linear elastic solid and the lubrication fluid flow in the fracture. However, some studies (Chudnovsky et al. 2008; Papanastasiou 1999) have shown deviations from LHFM predictions which indicates an existence of solid non-linearity and a deviation of the Poiseille law. We revisit the problem of a plane-strain hydraulic fracture driven by the injection of a Newtonian fluid in a tight rock. By modelling the quasi-brittle nature of the rock with different cohesive zone models, we study the effect of solid non-linearity on toughness and viscosity-dominated HF regimes. A fixed regular grid is used and an implicit scheme is adopted to solve the increments of the pressure and dislocation for this fully-coupled problem. The elasticity is solved using displacement discontinuity method using piece-wise linear element while the equation of mass conservation is solved by a finite volume method. The numerical algorithm reproduces the same results as LHFM solutions at large time when the cohesive zone is small compared to the fracture length. The shape of the material softening law or cohesive zone model does not influence the results. The accuracy of this method shows a dependence on the mesh refinement in the cohesive zone, which can be costly using a fixed uniform mesh.