A revisit to the Lekhnitskii-Amadei solution for borehole stress calculation in tilted transversely isotropic media

Calculation of the distribution of stress around a borehole subjected to far field in situ stress is essential in drilling stability analysis, borehole breakout analysis, sonic log interpretation as well as tunnel and mine excavations. Drilling a borehole in a rock significantly alters the stress distribution around the hole over a distance of several borehole diameters away from the wellbore. The magnitude and variation of borehole stresses depends on well trajectory (i.e., azimuth and deviation), in situ stresses, borehole pressure and rock properties. The classical Kirsch solution, which is derived based on the assumption of isotopic rocks, is widely used in the calculation of bore-hole stress distribution. However, the isotropic assumption is invalid for rocks such as shale and phyllite that can exhibit anisotropic elastic properties. For both conventional elastic and unconventional reservoirs, a significant portion of the overburden formations and in some circumstances even reservoir rocks can be shaly and anisotropic.