Role of Fractal Effect in Predicting Crack Initiation Angle and Its Application in Hydraulic Fracturing

In hydraulic fracturing, a prominent issue is to predict the crack initiation angle, especially for the directional fracturing process. However, the influence of the geometric irregularity of the hydraulic fracture on its initiation angle is unclear. In this study, the geometric irregularity of fractures is represented by fractal dimension, three fractal fracture criteria are derived to judge the crack initiation angle, and then their predicted values are compared to the reported experimental results. The result shows that the energy-based fractal criterion prediction is the most accurate. Furthermore, the energy-based fractal criterion is applied to evaluate the crack initiation angle in hydraulic fracturing. The predicted initiation angle of hydraulic fractures considered the crack fractal effect is more consistent with the experimental data. When the crack roughness is ignored, the predicted crack initiation angles are smaller than the experimental values, with 36–50% deviations. According to the parametric sensitivity analysis results, the initiation angle of hydraulic fractures increases with the crack fractal dimension. Moreover, the effect of the crack fractal dimension on the initiation angle of hydraulic fractures can be amplified with the increase of in situ stress difference or decrease of the Biot coefficient.