Numerical simulation of hydraulic fracturing in orthotropic formation based on the extended finite element method

Shale shows remarkable anisotropy in terms of mechanical properties, and it can often be regarded as an orthogonal anisotropic linear elastic body. In this paper, we present a two-dimensional fluid-solid coupled numerical model based on the extended finite element method (XFEM) to simulate the propagation of hydraulic fracture in orthotropic formations. The interaction between rock deformation and fluid flow within fracture is taken into account. Special crack tip enrichment functions of XFEM are used to model fractures in orthotropic formations, and the maximum circumferential tensile stress criterion is modified to determine the fracture propagation direction. The simulation results show that the hydraulic fracture will deviate from its straight-ahead path if there is an angle (defined as the material angle) between the initial fracture direction and the material axes of orthotropy. The initial deviation angle of fracture changes with the variation of the material angle, and the extent of fracture deviation increases with the Young's Modulus ratio. The fracture deviation can be avoided only when the initial fracture is parallel to one of the material axes of orthotropy. In the case where the maximum and minimum horizontal stresses are not equal, the direction of fracture propagation is determined by the combined effects of in-situ stress and orthotropy of the material. These findings offer new insights into the hydraulic fracturing design in orthotropic formations, helping to improve the production rates in shale gas reservoirs.