Modeling nonplanar hydraulic fracture propagation using the XFEM: An implicit level-set algorithm and fracture tip asymptotics

摘要

We describe the development of a fluid-coupled 2D extended finite element method (XFEM) algorithm to model the propagation of nonplanar radially-symmetric hydraulic fractures. The model determines the fracture propagation trajectory according to the maximum tangential stress criterion of Erdogan and Sih (1963). An implicit level-set algorithm (ILSA) is employed for locating the moving fracture front. The aim of the paper is to validate the radially-symmetric XFEM-ILSA model for nonplanar fracture propagation for mixed modes I and II. First, the results of the model are compared to the analytical solution for viscosity-dominated propagation of a penny-shaped crack. Next, we compare the results of the XFEM-ILSA scheme to the results of laboratory experiments and the results of an axisymmetric displacement discontinuity model for the near-surface propagation of hydraulic fractures with fluid lag (Bunger et al., 2013). For this comparison, a mixed-mode toughness tip asymptote is employed within ILSA to locate the fracture front. An improved algorithm is used for locating the fluid front within the fracture. (C) 2018 Elsevier Ltd. All rights reserved.