# 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.