Modeling competing hydraulic fracture propagation with the extended finite element method

We present an extended finite element framework to numerically study competing hydraulic fracture propagation. The framework is capable of modeling fully coupled hydraulic fracturing processes including fracture propagation, elastoplastic bulk deformation and fluid flow inside both fractures and the wellbore. In particular, the framework incorporates the classical orifice equation to capture fluid pressure loss across perforation clusters linking the wellbore with fractures. Dynamic fluid partitioning among fractures during propagation is solved together with other coupled factors, such as wellbore pressure loss (\(\Delta p_w\)), perforation pressure loss (\(\Delta p\)), interaction stress (\(\sigma _\mathrm{int}\)) and fracture propagation. By numerical examples, we study the effects of perforation pressure loss and wellbore pressure loss on competing fracture propagation under plane-strain conditions. Two dimensionless parameters \(\Gamma = \sigma _\mathrm{int}/\Delta p\) and \(\Lambda = \Delta p_w/\Delta p\) are used to describe the transition from uniform fracture propagation to preferential fracture propagation. The numerical examples demonstrate the dimensionless parameter \(\Gamma \) also works in the elastoplastic media.