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.