A pseudo-transient-based staggered algorithm for hydraulic fracturing simulations in the absence of a fluid lag

Abstract

In the present work we propose a novel approach to the simulation of fluid-driven fracture propagation in the absence of a fluid lag. The presented algorithm relies on a staggered treatment of the coupling between the fluid and solid equations describing the viscous fluid flow driving the solid deformation and fracture propagation, allowing the use of optimal solution techniques for each individual problem. Standard finite elements are employed for the discretization of the fluid equation while a hybrid Discontinuous Galerkin/cohesive zone model formulation is chosen for modeling the solid response. Under zero fluid lag conditions, coalescence of the fluid and fracture fronts results in a Neumann elliptic boundary value problem for the fluid, exhibiting non-uniqueness as well as potentially being ill-posed. We show how a false-transient treatment of the fluid equation enables the prescription of full Neumann boundary conditions without the need to resort to intermediate pressure boundary conditions, owing to the coupling with the solid problem. Stability and convergence conditions are derived under simplifying hypotheses. The performance of the algorithm is verified against known analytical solutions, with very good results.