Hydraulic fracturing technology has been wildly used in shale oil exploitation. The unconventional characteristics of shale reservoir, including the development of natural fractures and rigid interlayers, make it difficult to form effective fracture networks. It is of great importance for the hydraulic fracture to communicate the natural fractures to create the complex hydraulic fracture network. There are few fracturing parameters that engineers can control in the field, but we can control pump rates and fluid viscosity. It is important to know how to control the pumping rate and fluid viscosity to make the hydraulic fracture penetrate and activate natural fractures, thus creating a better fracture network for production. In this paper, based on cohesive element method, a two-dimensional model simulating the penetration of the hydraulic fracture through single natural fracture is established. The influences of different factors are investigated numerically, including the cross angle between the hydraulic fracture and natural fracture, natural fracture tensile strength, Young's modulus of rock and fracturing fluid viscosity. It is found that there is a critical pumping rate that only when the pumping rate is larger than the critical pumping rate, the hydraulic fracture will penetrate and activate the natural fracture. Some conclusions can be drawn from the simulation results: 1) The larger the crossing Angle is, the easier it is to pass through the natural fracture, and the smaller the crossing angle is, the larger the critical pumping rate is required. 2) The influence of natural fracture tensile strength and fracturing fluid viscosity on critical pumping rate is not obvious. 3) With the increase of Young's modulus of rock, the critical pumping rate decreases gradually. In order to better apply the research results to the field fracturing construction, we also draw the critical pressure chart under different influencing factors.

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