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.