This paper presents an analytical model to calculate the hydraulic fracture initiation pressure from an arbitrarily oriented wellbore in an elastic medium with and without perforations and investigates the competition between axial and transverse fractures. The model predicts the location of fractures and their initiation pressures, in relation to the in-situ stress condition and wellbore azimuth and inclination. Not only has the model been applied to different states of in-situ stress and wellbore orientations, but also the results have been presented in terms of non-dimensional parameters to improve the applicability of the study.

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