# 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.

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