Wellbore instability in petroleum operations remains a major concern among operators, due to its significant safety-related issues and economic consequences. This thesis investigates issues related to the mechanical stability of drilling through the types of anisotropic rocks that are commonly encountered in petroleum operations. The contribution of this thesis is two-fold: (1) to present a unified approach through which the influence of the elastic and strength anisotropy on wellbore stability can be thoroughly examined, and (2) to propose a new unified semi-analytical solution based on graphical conformal mapping and complex potential methods to compute the in-plane stress around an arbitrarily-shaped hole in isotropic or anisotropic materials.

A unified approach to investigate the influence of the elastic and strength anisotropy on wellbore stability has been developed, that utilises the Lekhnitskii-Amadei anisotropic elasticity formalism to compute the stresses around an arbitrarily-oriented circular borehole. Failure is modelled by coupling the Jaeger plane of weakness model to the fully-triaxial Mogi-Coulomb failure criterion. The model is used to study the safe drilling mud pressure window, and considerable differences are found between the predictions of the new model, and predictions that ignore elastic anisotropy when calculating the stresses. The results underscore the importance of fully accounting for rock anisotropy and fully-triaxial failure criteria when doing wellbore stability analysis.

A new semi-analytical approach has been proposed to study the stresses around non-circular holes in isotropic or anisotropic materials. The method requires only the outline coordinates of the hole, the elastic moduli of the material, and the magnitudes and directions of the far-field stresses. The proposed method has been applied for two purposes. Firstly, to model episodic borehole breakout development to track the stress evolution around the breakout, and to investigate the possibility of estimating the in situ stress state based on observations of breakout geometry. The method has also been used to compute the near-wellbore stress around a damaged wellbore whose geometry is obtained from ultrasonic data.