In recent years, horizontal completions have become "fashionable" with the consequence that induced fractures are usually not planar due to the inclination angle between the borehole and the prevailing reservoir in-situ principal stresses. Hence, such stimulations imply mixed-mode (opening and sliding modes) fracture propagation. Opening mode contributes to fracture opening, and sliding mode contributes to fracture twisting.

A hydraulic fracturing model is developed to study how and why a fracture gets twisted near the wellbore under biaxial loading. Three different fracture criteria (maximum tangential stress criterion, maximum energy release rate, and minimum strain energy density) have been applied to study fracture initiation mechanisms in mixed modes. Semi-analytical solutions of fracture initiation angles at different consecutive inclination angles based on the three criteria are obtained with analytical and modified bisection methods. It is found that the three criteria yield results with similar trends but with different magnitudes. The fracture initiation angle does not increase with the increasing inclination angle monotonically. The plot of fracture initiation angle with respect to inclination angle (0 to 90°) is a bell-shaped curve. The influence of pore pressure, fracturing pressure, stress anisotropy, Biot’s coefficient, and Poisson’s ratio on initiation angle is studied thoroughly, which shows that the initiation angle will decrease with increasing pore pressure, fracturing pressure, and Biot’s coefficient, but will increase with increasing stress anisotropy; however, the inclination angle is not sensitive to Poisson’s ratio. The analysis of the influence of fracturing pressure and pore pressure helps engineers understand why fracture tortuosities are different for various stages.

The conclusions and analysis in this paper can be applied to study both the fracture geometry near-wellbore and the optimization of hydraulic fracturing design for vertical, deviated, and horizontal wells. Recommendations on controlling wellbore azimuth and adjusting perforation phasing are given for wells in formation with high stress anisotropy.

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