Analytical Analysis of Wellbore Stresses under Fluid Pressure and In-Situ Stress in Three-Dimensional Wellbores

During fluid injection operations such as fracturing and well killing, the casing, cement sheath, and borehole wall rock are subjected to three-dimensional in-situ stresses and internal pressure. If the equivalent stress exceeds the material’s yield strength, component failure may occur, leading to wellbore failure or even blowout accidents. In order to investigate the stress distribution in wellbores under specific working conditions, a three-dimensional mechanical model of curved wellbores was established. By adopting the superposition principle and stress function method, the influence of horizontal in-situ stress non-uniformity on the fourth equivalent stress of various components was analyzed. The study demonstrates that under three-dimensional in-situ stress, the fourth equivalent stress of each component increases with the rise of horizontal in-situ stress load non-uniformity and azimuth angle. Meanwhile, borehole azimuth angle and in-situ stress load non-uniformity exert a greater influence on the fourth equivalent stress of the casing, while internal pressure has a lesser impact on it. The effects of azimuth angle, horizontal in-situ stress load non-uniformity, and internal pressure on the fourth equivalent stress of the casing are more significant than those on the cement sheath and borehole wall rock. The research results can provide theoretical and technical references for wellbore design and safety improvement, as well as for the structural safety assessment of components such as automotive chassis and body frames under complex dynamic loads.