An enriched FEM technique for modeling hydraulically driven cohesive fracture propagation in impermeable media with frictional natural faults: Numerical and experimental investigations

Abstract

SUMMARYIn this paper, an enriched finite element technique is presented to simulate the mechanism of interaction between the hydraulic fracturing and frictional natural fault in impermeable media. The technique allows modeling the discontinuities independent of the finite element mesh by introducing additional DOFs. The coupled equilibrium and flow continuity equations are solved using a staggered Newton solution strategy, and an algorithm is proposed on the basis of fixed-point iteration concept to impose the flow condition at the hydro-fracture mouth. The cohesive crack model is employed to introduce the nonlinear fracturing process occurring ahead of the hydro-fracture tip. Frictional contact is modeled along the natural fault using the penalty method within the framework of plasticity theory of friction. Moreover, an experimental investigation is carried out to perform the hydraulic fracturing experimental test in fractured media under plane strain condition. The results of several numerical and experimental simulations are presented to verify the accuracy and robustness of the proposed computational algorithm as well as to investigate the mechanisms of interaction between the hydraulically driven fracture and frictional natural fault. Copyright

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

“…See also Mohammadnejad and Khoei (2013a,b); Salimzadeh and Khalili (2015) for the fully or partially saturated case but with fewer benchmarks, and Mohammadnejad and Andrade (2016) for the case of fracture closure and re-opening. Extensions to account for frictional joints/fractures have also been proposed by Khoei et al (2015). When using XFEM for fluid infiltrated medium, a proper enrichment needs to be implemented to reproduce the pore-pressure variation in the solid matrix associated with the fracture (discontinuity in the pressure gradient normal to the fracture).…”

On the undrained and drained hydraulic fracture splits

“…Many of the published articles on the simulation of HF in impermeable media use a simple sequential iterative coupling scheme, which has been labeled the P → W scheme by Gordeliy and Peirce, and will be referred to here as the drained HF split. In the sequential solution scheme that uses the drained HF split, the equilibrium equation is solved first for the displacement and crack opening, assuming that the pressure is fixed, and then fluid equation is solved for the fluid pressure, assuming that the fracture aperture is fixed . Alternatively, coupling can be imposed through an approach labeled W → P by Gordeliy and Peirce .…”

“…2 The first trend focuses on improving the computational aspects of the models by employing state-of-the-art numerical techniques to develop models that overcome the limitations of their existing counterparts. Examples are studies that employed different variations of the boundary integrals method, [3][4][5][6][7][8][9][10][11] finite element method, [12][13][14][15][16] extended/generalized finite elements, [17][18][19][20][21][22][23][24][25][26][27][28][29][30] phase field methods, [31][32][33][34][35][36] and hybrid finite element/eXtended finite element-distinct element techniques (FEM-DEM or XFEM-DEM) [37][38][39][40] to develop 2D and 3D HF models. Additionally, some recent studies have coupled boundary integral or extended finite element methods with fracture tip asymptotes and presented efficient multiscale models of HFs under different propagation regimes.…”

“…In the sequential solution scheme that uses the drained HF split, the equilibrium equation is solved first for the displacement and crack opening, assuming that the pressure is fixed, and then fluid equation is solved for the fluid pressure, assuming that the fracture aperture is fixed. 17,21,48,[57][58][59][60] Alternatively, coupling can be imposed through an approach labeled W → P by Gordeliy and Peirce. 17 This sequential approach solves the fluid equation under the assumption of a fixed fracture aperture.…”

Coupled Finite Volume Methods and Extended Finite Element Methods for the Dynamic Crack Propagation Modelling with the Pressurized Crack Surfaces

“…It is necessary to use an algorithm that can solve iteratively the fluid pressure and crack width. The staggered Newton algorithm [40] is used here. The iteration processes for solving fluid pressure at time are stated as follows:…”