An Analytical Model for Fracture Initiation of Radial Drilling-Fracturing in Shale Formations

Radial drilling-fracturing, the combination of radial drilling and hydraulic fracturing, can guide fractures toward the target area and effectively enhance the recovery of the low permeable reservoir. In this paper, based on the stress superposition principle, we establish an analytical model to predict fracture initiation pressure (FIP) and the shale failure mode for radial drilling-fracturing applied in shale formations. In contrast with the former studies, this model can additionally consider the failure from shale beddings and is more applicable in the shale reservoir. The model classifies the shale failure into three modes and, respectively, gives the criterion for each failure mode. Then, a series of sensitivity analyses is conducted by examining effects of various parameters. By analyzing the variation characteristic of the initiation pressures required for three failure modes, the main conclusions are as follows. Firstly, matrix failure and shear failure along bedding tend to take place when the azimuth of radial borehole is moderate. Small and large azimuths are favorable for the occurrence of tensile failure along bedding. Secondly, a high ratio of horizontal in situ stress predisposes shale to generate matrix failure, and bedding tensile failure and bedding shear failure are apt to occur when the ratio of horizontal in situ stress is low. Thirdly, with the increasing intersection angle of the radial borehole wall and bedding plane, the failure mode apt to occur changes from bedding tensile failure to bedding shear failure and then to matrix failure. Fourthly, shale prefers to yield bedding shear failure under a small Biot coefficient and generate the other two failure modes when Biot coefficient is large. Fifthly, permeability coefficient virtually has no influence on the failure mode of shale. The research clarifies the fracture initiation characteristics of radial drilling-fracturing in shale formations and provides a reference for the field application of radial drilling-fracturing.