Two-dimensional modeling of the near-wellbore fracture tortuosity effect

A two-dimensional (2D) model is proposed for the hydraulic fracture propagating along some given curvilinear trajectory. The turning of the trajectory is conditioned by the difference between the perforation angle of a wellbore and the direction of the maximum principal in-situ stress. Two kinds of equations are coupled and solved numerically in the model: one-dimensional (1D) equations of a power-law fluid flow along the fracture trajectory and 2D equations of the linear elasticity for the rock mass. Based on numerous computations, it is ascertained that the pinching of the fracture occurs only if the trajectory is curvilinear and the in-situ stress in the formation is nonuniform (anisotropic compression). The influence of the fluid rheology and the perforation misalignment angle on the fracture width is investigated as well.