Axis of a deviated borehole from an arbitrary origin
Input(s)
\(P_{o}\): Pore Pressure \((\mathrm{psi})\)
\(\mathrm{R}\): Radius of Wellbore (ft)
\(\mathrm{r}\): Position in Respect to Centre of Wellbore (ft)
\(\Theta\): Azimuth of Shmax (rad)
\(\sigma^{\Delta \mathrm{t}}\): Thermal Stress (psi)
\(\mathrm{S}_{\mathrm{hmax}}\): Maximum Horizontal Stress (psi)
\(\mathrm{S}_{\mathrm{hmin}}\): Minimum Horizontal Stress (psi)
Output(s)
\[
\sigma_{\mathrm{aa}}: \quad \text { Stress }(\mathrm{psi})
\]
Formula(s)
\[
\sigma_{\mathrm{aa}}=0.5 *\left(\mathrm{~S}_{\mathrm{h} \max }+\mathrm{S}_{\mathrm{hmin}}-2 * \mathrm{P}_{\mathrm{o}}\right) *\left(1+\left(\frac{\mathrm{R}^{2}}{\mathrm{r}^{2}}\right)\right)-0.5 *\left(\mathrm{~S}_{\mathrm{h} \max }-\mathrm{S}_{\mathrm{hmin}}\right) *\left(1+\left(\frac{3 * \mathrm{R}^{4}}{\mathrm{r}^{4}}\right)\right) * \cos (2 * \Theta)-\left(\frac{\mathrm{P}_{\mathrm{o}} * \mathrm{R}^{2}}{\mathrm{r}^{2}}\right)-\sigma^{\Delta \mathrm{t}}
\]
Reference(s)
Mark D. Zoback., Reservoir Geomechanics, Cambridge University Press, UK, Page: 170.