Investigation of the notch angle in hydraulic fracturing using XFEM

Abstract

This paper analyzes the initiation and propagation of hydraulic fracturing by nonlinear numerical modeling. A notch located at the wellbore stimulates hydraulic fracturing. The notch has a pivotal role in hydraulic fracturing. There is evidence that the notch can affect the required fluid pressure and the fracture propagation and velocity. Therefore, it has been associated with the effectiveness of hydraulic fracturing in tight gas reservoirs. The objective of this study is to explore the effect of the notch angle on hydraulic fracturing. Models in two-and three dimensions are presented and analyzed. These models are used to find the breakdown pressure and stress intensity factors, respectively. The numerical approximation of hydraulically driven fracture propagation is based on the extended finite element method (XFEM). XFEM enriches finite elements and nodes at elements intersected by the crack during the crack propagation. XFEM reproduces the discontinuity in the displacement domain without the discretization of this property directly in the mesh. Therefore, the generated mesh is independent of the crack propagation. The accuracy of the numerical approach is validated by reproducing laboratory-scale hydraulic fracturing tests and comparing results.

Research on the impact of pre‐existing geological fractures on hydraulic fracturing in high in situ stress environments

“…There are four types of numerical simulation methods in hydraulic fracturing: extended finite element (XFEM), boundary element (BEM), discrete element (DEM), and finite element discrete element method (FDEM). XFEM characterizes discontinuity by adding a local enrichment function to the element containing the fracture, allowing the fracture to penetrate the mesh without the need for mesh reconstruction, so it can be widely used in hydraulic fracturing simulation tests, but it is not dominant in dealing with complex fracture networks 15,16 . The BEM discretizes the domain's BEMs and approximates the boundary conditions using a function that fulfills the governing equation.…”

“…XFEM characterizes discontinuity by adding a local enrichment function to the element containing the fracture, allowing the fracture to penetrate the mesh without the need for mesh reconstruction, so it can be widely used in hydraulic fracturing simulation tests, but it is not dominant in dealing with complex fracture networks. 15,16 The BEM discretizes the domain's BEMs and approximates the boundary conditions using a function that fulfills the governing equation. However, the BEM shows a large discreteity in describing the propagation path of hydraulic fracture.…”

Numerical Investigation on Mesoscale Evolution of Hydraulic Fractures in Hydrate-Bearing Sediments

“…Extended finite-element method (XFEM): XFEM is a variation of FEM in which discontinuous enrichment functions are introduced to describe the discontinuity of fractures, thereby solving the calculation burden caused by mesh reconstruction [37]. Although the method is effective, the XFEM introduces additional difficulties such as the need for special integration techniques to resolve the stiffness matrix, blending of enriched and non-enriched elements, and ill-conditioned stiffness matrices [38].…”