The naturally fractured reservoir was treated as a dual-porosity medium consisting of the primary rock matrix system and the fractured system. Assuming the matrix and fractures in the fractured medium to be 'separate and overlapping', and applying the double effective law, the dual-porosity formulations that couple matrix and fracture deformations and fluid flow in the matrix and fracture systems for the fractured porous formations were presented.

The numerical method was applied to solve the dual-porosity formulations. The finite element solution and a windows-based pseudo-three-dimensional finite element software for any directional wellbore drilled in dual-porosity media were given, in which the mud weight considerations were presented for the permeable and impermeable boundary conditions. The failure criteria, including compressive failure, tensile failures, shear failures were introduced into the numerical model and failure stresses and failure areas around boreholes were examined. Furthermore, the elastoplastic finite element method and computational procedure were presented in the dissertation.

One of the most prominent features of rock formations is the presence of joints and fractures at all scales. Many petroleum reservoirs are situated in fractured porous formations. When boreholes are drilled in such formations, wellbore stability has been a major concern.

Several application examples including inclined and horizontal wellbore in different in-situ stress regions, the best trajectory selections for horizontal borehole, rock cutting mechanism, and stress-dependent permeability around wellbores were investigated.