Summary 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.
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 where the local maximum tensile stress exceeds the rock tensile strength. The 3D boundary element method is used for stress analysis. The model is aiming at predicting the location of initial fractures and the difference in FIP between different perforation intervals in arbitrarily oriented non-cemented wellbores. There are many practical applications where this knowledge is required, 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. 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 (e.g. length, diameter and shape) on FIP is substantially less. Addtionally 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 horizontal wellbore and properly aligned perforations. Based on the model developed, an approximate approach to the evaluation of the impact of wellbore cementation on fracture initiation was suggested. It was discovered that taking into account the state of stress within the cement prior to well pressurization can result in both an increase and reduction of FIP depending on the parameters of perforating as well as wellbore orientation. The presented model is the necessary step toward predictable and controllable fracture initiation, which is vital for multistage fracturing treatment diversion.
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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