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.