The impact of the near-tip logic on the accuracy and convergence rate of hydraulic fracture simulators compared to reference solutions

We benchmark a series of simulators against available reference solutions for propagating plane-strain and radial hydraulic fractures. In particular, we focus on the accuracy and convergence of the numerical solutions in the important practical case of viscosity dominated propagation. The simulators are based on different propagation criteria: linear elastic fracture mechanics (LEFM), cohesive zone models/tensile strength criteria, and algorithms accounting for the multi-scale nature of hydraulic fracture propagation in the near-tip region. All the simulators tested here are able to capture the analytical solutions of the different configurations tested, but at vastly different computational costs. Algorithms based on the classical LEFM propagation condition require a fine mesh in order to capture viscosity dominated hydraulic fracture evolution. Cohesive zone models, which model the fracture process zone, require even finer meshes to obtain the same accuracy. By contrast, when the algorithms use the appropriate multi-scale hydraulic fracture asymptote in the near-tip region, the exact solution can be matched accurately with a very coarse mesh. The different analytical reference solutions used in this paper provide a crucial series of benchmark tests that any successful hydraulic fracturing simulator should pass.