The stress state around an elliptical borehole in anisotropy medium

Abstract

Under the assumption of generalized plane strain condition, this paper presents an analytical solution for stresses near an inclined elliptical wellbore drilled in anisotropic formation based on the linear theory of anisotropic elasticity and complex variable method. The solution is suitable for calculating the stresses around an elliptical borehole drilled with any inclination and orientation angles in a linear elastic, continuous, homogeneous and general anisotropic medium. The solution for the stresses can also show the effects of the liquid pressure exerted by drilling mud, the ratio and the direction of the in-situ stresses. For engineering utilization the transformation of compliance matrix for the transversely isotropic medium is formulated. An example is calculated and shown by contours of stress components around an inclined elliptical wellbore in a transversely isotropic formation. The stress contours can be utilized to some extent to predict the location, the range, the depth and even the outlines of fractured or collapsed well wall. Then a range of parametric analysis is carried out on the impacts of borehole inclination, orientation and ellipticity on the first principal stress and maximum shearing stress. The results indicate that for various boreholes with different degree of formation anisotropy the algebraic values of the first principal stress and maximum shearing stress go down gradually with the increase of borehole inclination, and these two stresses vary in the pattern of half a sinusoidal wave with the variation of orientation angles. Furthermore, the stresses go up with the increase of ellipticity. The solution presented in this paper might supply a more realistic technique for assessing the stability of borehole and optimizing the well path in anisotropic medium.