The effects of some parameters on perforation tip initiation pressures in hydraulic fracturing

Perforations play an important role in hydraulic fracturing as channels of fracturing fluid penetrating into reservoirs. The perforation geometry and the geo-stresses of reservoirs could affect the initiation pressures (i.e. the critical hydraulic pressure as perforation tips start to initiate), and the fracture initiation direction which could affect the fracturing fluid flowing into reservoirs. In this paper, two collinear perforations emanating from a wellbore were considered, and by using conformal mapping techniques, the stress intensity factors (SIFs) of mode I and mode II at the perforation tips were obtained. According to the maximum tangential stress criterion, i.e. MTS criterion, the analytical solutions of the initiation pressures and the initiation angles at perforation tips were obtained. The theoretical results were compared with the previous test results by using cubic concrete models and the previous in-situ measuring results. The prediction results of initiation pressures generally agreed with the test results and the in-situ results. Finally, the effects of perforation lengths, perforation angles with the major principal stress and the principal stress difference on hydraulic fracturing were analyzed. The results showed that the optimal perforation angles should lie in the range from 0 degrees to 30 degrees, and the optimal perforation length should 2 or 3 times the wellbore diameter.