Von Mises stress and stability analysis of wellbore wall under non-uniform in-situ stress

In order to analyze the influence of Von Mises stress on the borehole wall under non-uniform insitu stress and its effect on the stability of the borehole wall, a mechanical analysis model of the rock near the wellbore wall under non-uniform in-situ stress was established. According to the relationship between stress and stress function in elastic mechanics, based on the superposition principles, the formulas of radial stress,circumferential stress and shear stress are derived, the influence of non-uniform in-situ stress on wellbore wall stability is analyzed, the quadratic fitting formula of the Von Mises stress on the wellbore wall with the density of drilling fluid as the independent variable is determined. The error of Von Mises stress calculated by the fitting formula is less than 2.5%, and this formula can be used to determine the density of drilling fluid in the wellbore wall rock without fractures.