Complex fracture network makes it possible for commercial exploition of shale gas by means of hydraulic fracturing. It was believed that the interaction between hydraulic fracture (HF) and natural fracture (NF) had a significant impact on HF complexity. In this paper, a new numerical model has been developed to investigate HF/NF intersection under different geological and engineering parameters. Displacement discontinuity method (DDM) and finite volume method (FVM) are used to numerically model and solve the problem of coupled rock deformation, fluid flow, interface slipping, and opening associated with HF propagation and its interaction with NF. In addition, the model also considers the effects of fracture fluid leak-off. Based on the model, sensitivity analyses of key influence parameters are implemented. The numerical model results provide detailed quantitative information on fracture-geometry evolution, interfacial stress distribution and injection-pressure history. The simulation results show that the HF tends to cross the NF under the conditions of high principal stress difference, high intersection angle, high interfacial friction, high injection rate, high fracturing fluid viscosity and low initial conductivity of the NF. Moreover, the morphology of HF is significantly affected by two engineering parameters, the injection rate and the viscosity of the fracturing fluid. The effect of these two engineering parameters on the morphology of HF can be expressed as the product of them. The same value of the product results in the same HF morphology at the times of same injected-fluid volumes. In addition, the injection pressure curves can also help determine whether a crossing HF is developed when a HF interacts with a NF. The numerical model provides an effective approach for quantitatively analyzing the development of various types of HF/NF interaction behavior. It allows us to gain a better insight to the performance of hydraulic fracturing treatments in naturally fractured reservoirs.
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