A 3D numerical model of fracture initiation from a perforated wellbore in linear elastic rock is developed, which allows one to determine the fracture-initiation pressure (FIP) and the location and direction of an initial rupture. The model assumes that the fracture initiates at the point at which the local maximal tensile stress exceeds the rock tensile strength. The 3D boundary-element method (BEM) is used for stress analysis.

The model aims to predict the location of initial fractures and the difference in FIP between different perforation intervals in arbitrarily oriented noncemented wellbores. There are many practical applications for this knowledge, but of particular interest for this research is the employment of differently oriented perforations for creating heterogeneity of FIP between wellbore intervals in multistage fracturing treatment. This can enable stimulation of these intervals in a sequential mode and significantly simplify current treatment diversion and completion practices.

Comprehensive analysis revealed that the main parameter that can be used for controlling FIP during multistage fracturing treatment is the angle between the direction of the perforation channel and the preferred fracture plane (PFP). The model allows obtaining the range of the angles that is the most suitable for designing and implementation of diversion between the perforated wellbore intervals. The influence of geometrical parameters of perforation (such as length, diameter, and shape) on FIP is substantially less. In addition, we found that against all expectations, increase of perforation diameter can result in higher FIP. It was also discovered that the influence of the intermediate in-situ stress on FIP is comparable with the effect of perforation misalignment, especially in the situation of a horizontal wellbore and properly aligned perforations. On the basis of the model developed, an approximate approach to the evaluation of the effect of wellbore cementation on fracture initiation was suggested. It was discovered that taking into account the state of stress within the cement before well pressurization can result in both an increase and a reduction of FIP, depending on the parameters of perforating and the wellbore orientation.

The presented model is a necessary step toward predictable and controllable fracture initiation, which is vital for multistage-fracturing-treatment diversion.

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