Maximum plane tangential stress acting on deviated wellbore (1)
Input(s)
\(\sigma_{z z}\): Stress in Radial Direction (psi)
\(\sigma_{a a}\): Stress in Axial Direction (psi)
\(\tau\): Shear Stress (psi)
Output(s)
\(\sigma_{\text {tmax }}\): Maximum Tangential Stress (psi)
Formula(s)
\[
\begin{aligned}
& \sigma_{\mathrm{tmax}}=\frac{1}{2} *\left(\sigma_{\mathrm{zz}}+\sigma_{\mathrm{aa}}+\sqrt{\left(\sigma_{\mathrm{zz}}-\sigma_{\mathrm{aa}}\right)^{2}+4 * \tau^{2}}\right) \\
& \sigma_{\mathrm{tmax}}=\frac{1}{2} *\left(\sigma_{\mathrm{zz}}+\sigma_{\mathrm{aa}}-\sqrt{\left(\sigma_{\mathrm{zz}}-\sigma_{\mathrm{aa}}\right)^{2}+4 * \tau^{2}}\right)
\end{aligned}
\]
Reference(s)
Mark D. Zoback, Reservoir Geomechanics, Cambridge University Press, UK, Page: 239.