# Normal stress in radial direction near wellbore

## Input(s)

$$\mathrm{S}_{\mathrm{hmax}}$$: Maximum Principal Stress in reservoir (psi)

$$\mathrm{S}_{\mathrm{hmin}}$$: Minimum Principal Stress in reservoir (psi)

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

Po: Pore Pressure (psi)

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

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

## Output(s)

$$s i g_{r r}$$: Normal Stress in Radial Direction Near Wellbore (psi)

## Formula(s)

$$\operatorname{sig}_{\mathrm{rr}}=0.5 *(\operatorname{Shmax}+\operatorname{Shmin}-2 * \mathrm{Po}) *\left(1-\frac{\mathrm{R}^{2}}{\mathrm{r}^{2}}\right)+0.5 *(\operatorname{Shmax}-\operatorname{Shmin}) *\left(1-4 * \frac{\mathrm{R}^{2}}{\mathrm{r}^{2}}+3 * \frac{\mathrm{R}^{4}}{\mathrm{r}^{4}}\right) * \cos \left(2 * \theta * \frac{3.142}{180}\right)+\mathrm{Po} * \frac{\mathrm{R}^{2}}{\mathrm{r}^{2}}$$

## Reference(s)

Mark D. Zoback, Reservoir Geomechanics, Cambridge University Press, UK, Page: 100.

## Related

### Normal stress in tangential direction near wellbore (hoop stress)

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