Extraction of Stress Intensity Factors for the Simulation of 3-D Crack Growth with the Generalized Finite Element Method

Num Anal Meth Geomechanics

2014

153

131

SUMMARYHydraulic fracturing is the method of choice to enhance reservoir permeability and well efficiency for extraction of shale gas. Multi‐stranded non‐planar hydraulic fractures are often observed in stimulation sites. Non‐planar fractures propagating from wellbores inclined from the direction of maximum horizontal stress have also been reported. The pressure required to propagate non‐planar fractures is in general higher than in the case of planar fractures. Current computational methods for the simulation of hydraulic fractures generally assume single, symmetric, and planar crack geometries. In order to better understand hydraulic fracturing in complex‐layered naturally fractured reservoirs, fully 3D models need to be developed. In this paper, we present simulations of 3D non‐planar fracture propagation using an adaptive generalized FEM. This method greatly facilitates the discretization of complex 3D fractures, as finite element faces are not required to fit the crack surfaces. A solution strategy for fully automatic propagation of arbitrary 3D cracks is presented. The fracture surface on which pressure is applied is also automatically updated at each step. An efficient technique to numerically integrate boundary conditions on crack surfaces is also proposed and implemented. Strongly graded localized refinement and analytical asymptotic expansions are used as enrichment functions in the neighborhood of fracture fronts to increase the computational accuracy and efficiency of the method. Stress intensity factors with pressure on crack faces are extracted using the contour integral method. Various non‐planar crack geometries are investigated to demonstrate the robustness and flexibility of the proposed simulation methodology. Copyright © 2014 John Wiley & Sons, Ltd.

Section: Crack Propagation Algorithmmentioning

confidence: 99%

“…In this work, the formulation and implementation of the contour integral method described in [76,77] are adopted. The SIFs are used to determine, at each crack front vertex, if the crack will propagate and the direction and magnitude of propagation.…”

Section: Crack Propagation Algorithmmentioning

confidence: 99%

Simulation of non‐planar three‐dimensional hydraulic fracture propagation

Gupta

Num Anal Meth Geomechanics

2014

153

131

“…The pressure field close to the front of a hydraulic fracture exhibits a logarithmic singularity, as illustrated in Figure 16. Accounting for the fluid pressure applied on fracture faces in energy-based extraction methods like the J-integral, 55 the interaction integral, 56 the contour integral method, 57 or the cut-off function method 58,59 is error prone. In this work, we use a DCM 60,61 to extract SIFs at the fracture front.…”

Section: Appendix A: Displacement Correlation Methods For Sif Extractionmentioning

confidence: 99%

Coupled hydromechanical‐fracture simulations of nonplanar three‐dimensional hydraulic fracture propagation

Gupta

Num Anal Meth Geomechanics

2017

SummaryThis paper presents an algorithm and a fully coupled hydromechanical-fracture formulation for the simulation of three-dimensional nonplanar hydraulic fracture propagation. The propagation algorithm automatically estimates the magnitude of time steps such that a regularized form of Irwin's criterion is satisfied along the predicted 3-D fracture front at every fracture propagation step.A generalized finite element method is used for the discretization of elasticity equations governing the deformation of the rock, and a finite element method is adopted for the solution of the fluid flow equation on the basis of Poiseuille's cubic law. Adaptive mesh refinement is used for discretization error control, leading to significantly fewer degrees of freedom than available nonadaptive methods. An efficient computational scheme to handle nonlinear time-dependent problems with adaptive mesh refinement is presented. Explicit fracture surface representations are used to avoid mapping of 3-D solutions between generalized finite element method meshes. Examples demonstrating the accuracy, robustness, and computational efficiency of the proposed formulation, regularized Irwin's criterion, and propagation algorithm are presented.

“…A characteristic variation of equivalent SIF Δ K eq is then computed using Equation . As a note, the extraction of SIFs is performed using the cutoff function method (CFM) or the contour integral method (CIM) for all three fracture modes. The CFM is more accurate than the CIM because its functional involves only displacement values, whereas the CIM uses derivatives of the GFEM solution.…”

Section: Problem Description and Governing Equationsmentioning

confidence: 99%

“…The CFM is more accurate than the CIM because its functional involves only displacement values, whereas the CIM uses derivatives of the GFEM solution. Further details can be found in . Our implementation of the CFM is limited to planar crack surfaces within the extraction domains.…”

Section: Problem Description and Governing Equationsmentioning

confidence: 99%

Improvements of explicit crack surface representation and update within the generalized finite element method with application to three‐dimensional crack coalescence

Garzon

O׳Hara

Numerical Meth Engineering

et al. 2013

Self Cite

SUMMARYThis paper presents improvements to three-dimensional crack propagation simulation capabilities of the generalized finite element method. In particular, it presents new update algorithms suitable for explicit crack surface representations and simulations in which the initial crack surfaces grow significantly in size (one order of magnitude or more). These simulations pose problems in regard to robust crack surface/front representation throughout the propagation analysis. The proposed techniques are appropriate for propagation of highly non-convex crack fronts and simulations involving significantly different crack front speeds. Furthermore, the algorithms are able to handle computational difficulties arising from the coalescence of non-planar crack surfaces and their interactions with domain boundaries. An approach based on moving least squares approximations is developed to handle highly non-convex crack fronts after crack surface coalescence. Several numerical examples are provided, which illustrate the robustness and capabilities of the proposed approaches and some of its potential engineering applications.