A super-convergent staggered algorithm for the simulation of hydraulic fracturing treatments

In this paper, a super-convergent algorithm is presented for the simulation of hydraulic fracturing process in impervious domains using the extended finite element framework. The hydro-fracture inflow is modeled based on the Darcy law, in which the fracture permeability is incorporated by taking advantages from the well-known cubic law. The hydro-mechanical coupling between the fracturing fluid flow and the surrounding bulk is carried out by employing a sequential iterative procedure known as the staggered Newton algorithm. The convergence rate of the existing staggered solutions in the literature is examined, and an alternative super-convergent approach is proposed. Finally, through several numerical simulations the sanity of the developed framework is demonstrated.