A Theoretical Model for Hydraulic Fracturing through Two Symmetric Radial Perforations Emanating from A Borehole

Abstract

The production enhancement of oil, gas, or geothermal reservoirs through hydraulic fracturing requires an in-depth study on the fracture initiation and propagation from the borehole. According to the linear elastic fracture mechanics, a theoretical model is developed to calculate the stress intensity factors of two symmetric radial cracks emanating from a pressurized borehole. The maximum tangential stress criterion under the mix-mode condition is developed to investigate the hydraulic fracture initiation. The critical water pressure and critical initiation angle predicted by the theoretical model match closely the experimental results reported in the literature. The influence of the stress anisotropy coefficient, the perforation angle and length, the borehole radius, the ratio between the water pressures in the fracture and the borehole, and Biot’s coefficient are investigated. Moreover, the effects of the injected high water pressure (i.e., larger than the critical water pressure) on the fracture initiation angle are studied to further understand the characteristics of hydraulic fracture initiation. The results indicate that the perforation angle and length, the borehole radius, and the stress anisotropy coefficient have a relatively strong influence on the critical water pressure and critical initiation angle. During high-pressure water injection, the fracture initiation angle decreases as the ratio between the water pressure in the fracture and the borehole and Biot’s ratio increase. The theoretical model provides a comprehensive understanding of the fracture twist, the mixed-mode fracture propagation feature, and the hydraulic fracturing optimization.