In stimulating tight carbonate formations, the propagation of multiple transverse fractures is highly desirable to contact as much matrix as possible. The application of this method to openhole well environments is challenged by the dominating impact of hoop stresses in the near-wellbore vicinity rather than far-field stress in the producing layer. As a result, even if the open hole is drilled in the direction of minimal horizontal far-field stress, there is a high probability that hydraulic fractures initiate longitudinally and then turn to the preferred fracture plane, creating undesired tortuosity.

One of the approaches towards controlling both the position and direction of fracture initiation is to cut notches in the wellbore wall at specified positions. As pressure increases during fracturing, those notches can locally eliminate the influence of the wellbore hoop stress and develop high tensile stress concentrations initiating transverse hydraulic fractures at lower pressures.

A theoretical model is proposed herein that aims to predict the position, orientation, and pressure at which a fracture initiates. In the model, the 3D stress state around wellbore and notch(es) is analyzed using the brittle fracture criteria. In the numerical implementation, the stresses are efficiently resolved using the boundary element method. The model is used to interpret published laboratory data on fracture initiation including those from hydraulic fracturing block tests. It is shown that the conventional maximum tensile stress (MTS) criterion fails to reproduce the observed trends in initiation pressure and fracture orientation. The nonlocal modification of the MTS criterion based on the stress averaging technique (SAMTS), reveals a good match with initiation pressures in simplified tests. When applied to hydraulic fracturing block test data, SAMTS captures the observed fracture orientations while overestimating the absolute pressure values. The discussion of possible reasons for that overestimate and the way forward concludes the paper.

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