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)
Output(s)
\(S g_{t h}\): Normal Stress in Tangential Direction Near Wellbore (Hoop Stress) (psi)
Formula(s)
\[
\begin{aligned}
\mathrm{Sg}_{\mathrm{th}}= & 0.5 *(\operatorname{Shmax}+\operatorname{Shmin}-2 * \operatorname{Po}) *\left(1+\frac{\mathrm{R}^{2}}{\mathrm{r}^{2}}\right)-0.5 *(\operatorname{Shmax}-\operatorname{Shmin}) *\left(1+3 * \frac{\mathrm{R}^{4}}{\mathrm{r}^{4}}\right) * \cos \left(2 * \theta * \frac{3.142}{180}\right)-\operatorname{Po} * \frac{\mathrm{R}^{2}}{\mathrm{r}^{2}} \\
& - \text { Sdt }
\end{aligned}
\]
Reference(s)
Mark D. Zoback, Reservoir Geomechanics, Cambridge University Press, UK, Page: 104.