A parallel staggered hydraulic fracture simulator incorporating fluid lag

In this work we present a computational framework for the parallel simulation of hydraulic fracturing processes. The simulation algorithm is built upon the staggered coupling of a fluid model that describes the viscous flow in the fractured domain and a model of the solid deformation and fracture response, driven by the pressure field induced by the fluid injection. The use of standard finite elements for the fluid model and a DG formulation for the solid tied together in a staggered fashion, allowing us to focus on the optimal solution strategy for each individual system, furnish the simulator with the robustness and parallel scalability properties needed to handle the strongly nonlinear processes associated with this physical phenomenon as well as the highly demanding computational requirements that come with large-scale field simulations. Importantly, the fluid is allowed to lag behind the crack front thus giving place to a lag region, which has recently been recognized as important in some hydraulic fracture applications, and further broadens the range of applicability of the simulator. We verify the proposed computational framework against known analytical results and we demonstrate its capabilities in complex scenarios such as the interaction with natural cracks and the propagation of simultaneous and sequential fractures, as well as its parallel scalability properties.