Numerical simulation of hydraulic fracture initialization and deflection in anisotropic unconventional gas reservoirs using XFEM

Unconventional gas reservoirs, e.g., coal, shale, or tight sand, are generally anisotropic. However, the propagation mechanism of hydraulic fractures in an anisotropic reservoir has not been well studied. By means of XFEM, the influence of the anisotropic characteristics of reservoirs, including the perforation direction on the propagation of hydraulic fractures is studied in this paper. The initialization and deflection angle of a hydraulic fracture are governed by the modified maximum circumferential tensile stress criterion. The crack tip stress field is calculated by the theoretical solutions of stress complex variable functions, which are suitable for anisotropic materials. It is shown that the deflection angle increases with the increasing of reservoir anisotropic degree when the perforation fracture is in the principle direction that the rock is hardest to be cracked. However, the fracture does not deflect when the fracture toughness ratio and the elasticity modulus ratio in different directions are small. The critical fracture toughness ratio when a hydraulic fracture begins to deflect decreases exponentially with the increasing of elasticity modulus ratio. In addition, deflection angle of a hydraulic fracture in an anisotropic reservoir dependents a lot on the perforation direction.