Derivation of the Coordinate and the Stress Components Transformation Equation in Wellbore Stability Mechanics Analysis

Based on CauChy formula and the basic principles of space coordinate transformation, investigated arbitrary inclined borehole, derived borehole coordinate components transformation and stress components transformation between borehole coordinate system and in-situ stress coordinate system, and the main conclusions are as follows: (1) Got any inclination of the wellbore coordinate transformation coefficient matrix [L]; (2) Got the transformation equation between the stress components and in-situ stress components; (3) Through research and analysis the coordinate components transformation and the stress components transformation applicated in the engineering fields, aware of their applicated in engineering fields mainly to solve the basic problems of the mechanics and the kinematics. Keywordswellbore stability; coordinate transformation; stress components transformation; directional wells; in-situ stress