Axial stress around vertical wellbore

Input(s)

R: Radius of Wellbore (ft)

$\mathrm{r}$: Position in Respect to Centre of Wellbore (ft)

$\Theta$: Azimuth of $\mathrm{S}_{\mathrm{hmax}}(\mathrm{rad})$

$\mathrm{S}_{\mathrm{hmax}}$: Maximum Horizontal Stress (psi)

$\mathrm{S}_{\mathrm{hmin}}$: Minimum Horizontal Stress (psi)

Output(s)

$\tau$: Twisting Stress (psi)

Formula(s)

$$ \tau=0.5 *\left(\mathrm{~S}_{\mathrm{h} \max }-\mathrm{S}_{\mathrm{h} \min }\right) *\left(1+\left(\frac{2 * \mathrm{R}^{2}}{\mathrm{r}^{2}}\right)-\left(\frac{3 * \mathrm{R}^{4}}{\mathrm{r}^{4}}\right)\right) * \sin (2 * \Theta) $$

Reference(s)

Mark D. Zoback, Reservoir Geomechanics, Cambridge University Press, UK, Page: 170.