LAUSR

Abstract Non-planar fractures often occur in directional well fracturing and old well refracturing, which has great influence on fracture parameters and well production. To better understand the mechanism of non-planar fracture propagation, the mathematical model of non-plane fracture propagation is established based on the coupling of rock deformation and fluid flow in fracture. The coupled model is solved by a combination of the displacement discontinuity method and finite difference method, and the whole numerical calculations are carried out by MATLAB-developed program. The accuracy of the model is verified by comparing the calculated results with existing models and published experiment. The effect of perforation angles, horizontal stress differences and injection rates on fracture extension trajectory, fracture width, injection pressure and pressure distribution in fracture is investigated. The model is also employed to explore the influence of injection rate and perforation angles on fracture propagation path in the Mahu block, Xinjiang province, China. The results indicate that the coupled model has a good agreement with the published experiment data. Fracture turning distance increases with the increasing injection rate. Perforating in the direction of maximum principal stress and low injection rate is beneficial to reduce the injection pressure. Fracture width near wellbore decreases with the increasing perforation angle and differential stress, and increase with the increasing injection rate. Injection pressure increases with the increasing perforation angle, differential stress and injection rate. In the non-planar fracture propagation process, fracture width first increases and then decreases gradually. With the growing differential stress, perforation angle and injection rate has less influence on fracture turning. In the formation with high differential stress, it is difficult to achieve long fracture turning distance.