Simulation of non‐planar three‐dimensional hydraulic fracture propagation

Abstract

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.

Simulating fully 3D non-planar evolution of hydraulic fractures

“…Essentially, two main methods for the solution of elasticity sub-problem are used in the papers that concern 3D initiation and evolution of hydraulic fractures: the finite element method (FEM) (Gupta and Duarte 2014) and the boundary element method (BEM). The prototype of the latter is the so-called "direct method" of linear elasticity based on Somigliana's solution (Rizzo 1967).…”

“…The classical formulation of the strain energy release rate criterion for the spatial mixed mode loading fractures (Nuismer 1975;Germanovich and Cherepanov 1995;Weber and Kuhn 2008;Gupta and Duarte 2014) consists in the following. The fracture propagates when the energy release rate in the direction of crack propagation θ * reaches the critical energy release rate of the material (G-criterion)…”

Numerical methods for hydraulic fracture propagation: A review of recent trends

“…In the limit of toughness dominated propagation (which implies a uniform distribution of fluid pressure), Gupta and Duarte (2014) have developed a formulation to model 3D mixed mode hydraulic fracture propagation, although conserving the continuity of the fracture front and therefore not fully reproducing the fracture front segmentation observed experimentally under mixed mode I+III. The formulation has been extended to account for the coupling with lubrication flow (Gupta and Duarte, 2015) and results for the case of a static fracture (no propagation) presented.…”

Modeling Simultaneous Multiple Fracturing Using the Combined Finite-Discrete Element Method

“…FEM with advanced remeshing technologies is still difficult to implement for field-scale reservoirs because of the meshing burden. The extended finite element method (XFEM) [18][19][20] and the generalized finite element method (GFEM) [21,22] have been proposed to overcome the meshing burden associated with FEM and applied to model hydraulic fracturing. However, XFEM and GFEM still have difficulties in representing multiple complex fracture networks.…”