Accurate prediction of fracture initiation pressure and orientation is paramount to the design of a hydraulic fracture stimulation treatment and is a major factor in the treatment’s eventual success. In this study, closed-form analytical approximations of the fracturing stresses are used to develop orientation criteria for fracture initiation from perforated wells relative-to-the-wellbore (longitudinal or transverse). These criteria were numerically assessed and found to overvalue transverse fracture initiation, which takes place under a narrow range of conditions when the rock formation’s tensile strength is lower than a critical value and the breakdown pressure falls within a "window."

A robust three-dimensional numerical model is used to evaluate solutions for the longitudinal and transverse fracturing stresses for a variable wellbore pressure, hence numerically-deriving correction factors for the closed-form approximations. Geomechanical inputs from the Barnett Shale in Texas are considered for a horizontal well aligned parallel to the direction of the least compressive horizontal principal stress. The numerically-corrected expressions can predict fracture initiation pressures for a specific orientation of fracture initiation (longitudinal or transverse). Similarly, at known breakdown pressures, the corrected expressions are used to predict the orientation of fracture initiation. Besides wellbore trajectory, the results depend on the perforation direction. For the Barnett Shale case study (normal faulting regime), perforations on the side of the borehole yield both a wider breakdown pressure window and a higher critical tensile strength by 32.5%, compared to perforations on top of the borehole. Leakage of fracturing fluid around the wellbore reduces the breakdown pressure window by 11% and the critical tensile strength by 65%.

Dimensionless plots are employed to present the range of in-situ stress states where longitudinal or transverse hydraulic fracture initiation is promoted. This is useful for completion engineers; when targeting low permeability formations such as shale reservoirs, multiple transverse fractures must be induced from the horizontal wells, as opposed to longitudinal fracture initiation, which is desired in higher permeability reservoirs or Frac-&-Pack operations.

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