Cylindrical coordinate system

The cylindrical symmetry of a wellbore prompts the utilization of a cylindrical coordinate system rather than a rectangular cartesian coordinate system. The volume element of stresses in cylindrical coordinates is shown in Fig. 6.3. The distance $r$ is measured from the axis of the wellbore. The angle $\theta$ is measured with respect to a predefined plane.

Figure 6.3: Infinitesimal volume element in cylindrical coordinates and associated stresses.

The normal stresses are: radial stress $\sigma _{rr}$, tangential or hoop stress $\sigma _{\theta \theta }$, axial stress $\sigma_{zz}$, and shear stresses $\sigma _{r\theta }$, $\sigma_{r z}$, and $\sigma_{\theta z}$.