Modeling initiation and propagation of a hydraulic fracture under subcritical conditions

A numerical model has been developed for simulating the initiation and propagation of a plane strain or axisymmetric hydraulic fracture from an openhole wellbore in an impermeable homogeneous rock formation. The main novelty is inclusion of a subcritical growth law, thereby allowing consideration of hydraulic fracture growth when the wellbore pressure is otherwise considered insufficient to initiate fracturing. To enable tracking the moving crack front in the simulations, we develop a new tip asymptotics based on a subcritical crack growth law. The results are first validated against available analytical solutions for plane strain and axisymmetric hydraulic fractures. A comparison is presented between the solutions of the subcritical growth model and a conventional hydraulic fracture model in which fracture growth is not allowed until the stress intensity factor equals the fracture toughness of the rock. This comparison, as well as a study of the influence of the relevant parameters appearing in the subcritical growth law, indicates significant influence of subcritical growth on the evolution of the crack length and the wellbore pressure. Notably, this model provides the capability to simulate delayed growth of hydraulic fractures under pressures that are insufficient to generate instantaneous growth, which is a behavior observed in experiments but not considered by conventional hydraulic fracturing models.