A peridynamic model for sleeved hydraulic fracture

[摘要] ENGLISH ABSTRACT: Current numerical methods in theeld of hydraulic fracturing are based mainly oncontinuum methods, such as the Finite Element Method (FEM) and the Boundary ElementMethod (BEM). These methods are governed by Linear Elastic Fracture Mechanics(LEFM) criteria, which su er from the inherent aw of a non-physical stress representationat the fracture tip. In response to this, a non-local method is proposed, namelythe peridynamic theory, to model sleeved hydraulic fracture. A 2D implicit quasi-staticordinary state based peridynamic formulation is implemented on various benchmarkproblems, to verify the ability to capture constitutive behaviour in a linear elastic solid,as well as, the quanti cation of adverse e ects on the accuracy of the displacement solution,due to the nature of the non-local theory. Benchmark tests consist of a plate intension, where convergence to the classical displacement solution, non-uniform re nementand varying cell sizes are tested, as well as, a thick walled cylinder with internalpressure, where three di erent loading techniques are tested. The most accurate loadingtechnique is applied to the sleeved fracture model, in order to simulate fracture initiationand propagation. This model is then veri ed and validated by using the Rummel &Winter hydraulic fracturing model and experimental results, respectively. Displacementerror minimisation methods are implemented and as a result, the displacement solutionsfor a plate in tension converges to the analytical solution, while the thick walled cylindersolutions su er from inaccuracies due to an applied load on an irregularly discretizedregion. The fracture initiation test captures the fracture tip behaviour of the Rummel& Winter model and the fracture propagation test show good correlation with experimentalresults. This research shows that the peridynamic approach to sleeved hydraulicfracture can yield a realistic representation of fracture initiation and propagation, however,further research is needed in the area of a pressure load application on a solid usingthe peridynamic approach.

[发布机构] Stellenbosch University