A Semianalytical Modeling Approach for Hydraulic Fracture Initiation and Orientation from Perforated Wells

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 relative-to-the-wellbore (longitudinal or transverse) fracture initiation from perforated wells. These criteria were assessed numerically and found to overestimate the occurrence of transverse fracture initiation, which only takes place under a narrow range of conditions in which the tensile strength of the rock formation is lower than a critical value, and the breakdown pressure falls within a “window.” For a case study performed on the Barnett Shale, transverse fracture initiation is shown to take place for breakdown pressures below 4,762 psi, provided that the formation's tensile strength is below 2,482 psi. A robust 3D finite volume numerical model is used to evaluate solutions for the longitudinal and transverse fracturing stresses for a variable wellbore pressure, hence developing correction factors for the existing closed-form approximations. Geomechanical inputs from the Barnett Shale are considered for a horizontal well aligned parallel to the direction of the least compressive horizontal principal stress. The corrected numerically derived expressions can predict initiation pressures for a specific orientation of fracture initiation. 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, which is under a normal faulting stress regime, the perforations on the side of the borehole yield a wider breakdown pressure window by 71% and higher critical tensile strength by 32.5%, compared to perforations on top of the borehole, implying better promotion of transverse fracture initiation. Leakage of fracturing fluid around the wellbore, between the cemented casing and the surrounding rock, 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 in which 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-and-pack” operations.