Fracture pressure model for inclined wells in layered formations with anisotropic rock strengths

Fracture pressure is one of the most important foundations of drilling engineering, and the anisotropy of tensile strength is also a distinct feature of layered formations, but the anisotropy of tensile strength has seldom received attention in the analysis of fracture pressure. In the present paper, a novel fracture pressure model was proposed for inclined wells in layered formations with anisotropic rock strengths. Firstly, the characteristics of anisotropic tensile strength were investigated. Secondly, four typical anisotropic tensile criteria were collected and assessed using the maximum absolute relative error (MARE), the average absolute relative error (AARE), and the standard error (SE). Thirdly, the fracture pressure model was proposed based on the stress distribution model and anisotropic tensile criterion. Finally, the influences of anisotropy ratio, bedding planes' occurrence, well path, in-situ stress and pore pressure on fracture pressure were investigated. The results indicated that the layered rocks display the distinct anisotropy in tensile strength, and the strength increases with the loading angle. The MARE, AARE and SE of the Nova-Zaninetti criterion is the lowest for all six kinds of typical layered rocks, followed by the Lee-Pietruszczak, Hobbs-Barron, and Single Plane of Weakness criteria, and therefore the Nova-Zaninetti criterion is recommended. The higher the anisotropy ratio in tensile strength, the higher the influence on fracture pressure involved. The influence of bedding planes' occurrence mainly depends on the initiation position of the fractures, the influence increases with increasing the horizontal stress ratio and pore pressure. Thus, the influence of anisotropy cannot be ignored in the prediction of fracture pressure.