# Radial stress around vertical wellbore

## Input(s)

$$S_{\text {hmax }}$$: Maximum Horizontal Stress (psi)

$$S_{\text {hmin }}$$: Minimum Horizontal Stress (psi)

$$P_{o}$$: Pore Pressure $$(\mathrm{psi})$$

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

r: Relative Position to Centre (ft)

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

## Output(s)

$$\sigma_{r r}$$: Stress (psi)

## Formula(s)

$$\sigma_{\mathrm{rr}}=0.5 *\left(\mathrm{~S}_{\mathrm{hmax}}+\mathrm{S}_{\mathrm{h} \text { min }}-2 * \mathrm{P}_{\mathrm{o}}\right) *\left(1-\left(\frac{\mathrm{R}^{2}}{\mathrm{r}^{2}}\right)\right)+0.5 *\left(\mathrm{~S}_{\mathrm{h} \max }-\mathrm{S}_{\mathrm{h} \min }\right) *\left(1+\left(\frac{3 * \mathrm{R}^{4}}{\mathrm{r}^{4}}\right)-\left(\frac{4 * \mathrm{R}^{2}}{\mathrm{r}^{2}}\right)\right) * \cos (2 * \theta)+\left(\frac{\mathrm{P}_{\mathrm{o}} * \mathrm{R}^{2}}{\mathrm{r}^{2}}\right)$$

## Reference(s)

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

## Related

### Axial stress around vertical wellbore

An unhandled error has occurred. Reload 🗙