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

Shibin Tang,Zhuo Dong,Dong Duan,Yingchun Li

doi:10.1155/2019/6094305

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.

Highlights

Hydraulic fracturing has been widely used in the petroleum industry since the 1930s for enhancing production from oil and gas wells [1]
The stress anisotropy coefficient is defined as the ratio of the maximum to minimum horizontal stresses and denoted by the parameter k which is illustrated in Figure 1(a). e minimum horizontal stress is kept constant, and the different values k of the stress anisotropy coefficient are obtained by changing the maximum horizontal stress. e obtained results are depicted in Figure 8, in which 8(a)–8(c) illustrate the effect of stress anisotropy coefficient on the critical water pressure under different perforation lengths, i.e., a 10 mm, 100 mm, respectively, while 8(b)–8(d) show the corresponding critical initiation angle
An analytical model is proposed for investigating the hydraulic fracture initiation through a borehole with two symmetric radial perforations. e proposed model is implemented to predict the critical water pressure and fracture initiation angle for the hydraulic fracturing by considering the effect of the stress anisotropy coefficient, the borehole radius, the perforation angle and length, the injected water pressure, and the pore pressure in reservoir formation

Summary

Introduction

Hydraulic fracturing has been widely used in the petroleum industry since the 1930s for enhancing production from oil and gas wells [1]. When a borehole with symmetric cracks is subjected to both external compressive load and inner water pressure, the stress intensity factors at the crack tips include those in both opening mode (KI) and sliding mode (KII). Since it is critical to predict the accurate path of new fractures in the hydraulic fracturing operations and well production, the geometry and direction of the hydraulic fracture under the condition shown in Figure 1(a) are theoretically studied by an analytical method in this work

Theoretical Model

Validations

Theoretical Results of the Hydraulic Fracture Initiation

Effect of High-Pressure Water Injection

Conclusions