Axis of a deviated borehole from an arbitrary origin

Input(s)

PoP_{o}: Pore Pressure (psi)(\mathrm{psi})

R\mathrm{R}: Radius of Wellbore (ft)

r\mathrm{r}: Position in Respect to Centre of Wellbore (ft)

Θ\Theta: Azimuth of Shmax (rad)

σΔt\sigma^{\Delta \mathrm{t}}: Thermal Stress (psi)

Shmax\mathrm{S}_{\mathrm{hmax}}: Maximum Horizontal Stress (psi)

Shmin\mathrm{S}_{\mathrm{hmin}}: Minimum Horizontal Stress (psi)

Output(s)

σaa: Stress (psi)\sigma_{\mathrm{aa}}: \quad \text { Stress }(\mathrm{psi})

Formula(s)

σaa=0.5( Shmax+Shmin2Po)(1+(R2r2))0.5( ShmaxShmin)(1+(3R4r4))cos(2Θ)(PoR2r2)σΔt\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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