Normal stress in tangential direction near wellbore (hoop stress)

Input(s)

Shmax: Maximum Principal Stress in reservoir (psi)

Shmin: Minimum Principal Stress in reservoir (psi)

Po: Pore Pressure (psi)

$S d t$ : Stress induced due to temperature (psi)

$d P$ : Difference between Wellbore Pressure and Mud Weight (psi)

$\theta$ : Angle from $S_{\text {hmax }}$ at which stress is measured (degrees)

$\mathrm{r}$ : Distance from wellbore $(\mathrm{ft})$

$\mathrm{R}$ : Radius of wellbore (ft)

$S g_{t h}$ : Normal Stress in Tangential Direction Near Wellbore (Hoop Stress) (psi)

\begin{aligned} \mathrm{Sg}_{\mathrm{th}}= & 0.5 *(\operatorname{Shmax}+\operatorname{Shmin}-2 * \operatorname{Po}) *\left(1+\frac{\mathrm{R}^{2}}{\mathrm{r}^{2}}\right)-0.5 *(\operatorname{Shmax}-\operatorname{Shmin}) *\left(1+3 * \frac{\mathrm{R}^{4}}{\mathrm{r}^{4}}\right) * \cos \left(2 * \theta * \frac{3.142}{180}\right)-\operatorname{Po} * \frac{\mathrm{R}^{2}}{\mathrm{r}^{2}} \\ & - \text { Sdt } \end{aligned}

Mark D. Zoback, Reservoir Geomechanics, Cambridge University Press, UK, Page: 104.