An efficient computational framework for height-contained growing and intersecting hydraulic fracturing simulation via SGBEM–FEM

Abstract

An efficient computational framework to model the growth of intersecting height-contained hydraulic fractures is proposed. The fracture in solids is modeled by the classical theory of linear elastic fracture mechanics, whereas the injection flow in hydraulic fractures is treated as channel flow. The governing equations of fracture mechanics are formulated in terms of weakly-singular weak-form boundary integral equations, with the knowledge of the fracture surface geometry exploited to reduce the integral dimension. The fluid flow within the fracture is treated using finite element method as one dimensional flow in an arbitrarily curved channel. The symmetric Galerkin boundary element method and finite element method are coupled with the traction continuity condition. The model is then formulated in a variational form and augmented with Lagrange multipliers to prescribe displacement constraints on intersections of hydraulic fractures, while fluid constraints are enforced by a consolidation of associated pressure degrees of freedom. Pertinent numerical implementation techniques, including spatial and temporal discretizations, special crack tip element, crack propagation criteria and remeshing strategy, are presented. The proposed framework is verified by comparing to the numerical results from a three dimensional hydraulic fracturing simulator and then verified by comparing the stress intensity factors to the XFEM and Murakami’s results for both star shaped cracks and symmetric branched cracks. The verification shows the utility properly enforces the physical constraints on the intersections of fractures. Three numerical examples are shown to demonstrate the capability of the proposed computational framework modeling the intersecting hydraulic fracturing process in a single or separated height-contained pay zones.