Maximum plane tangential stress acting on deviated wellbore (1)

Input(s)

σzz\sigma_{z z}: Stress in Radial Direction (psi)

σaa\sigma_{a a}: Stress in Axial Direction (psi)

τ\tau: Shear Stress (psi)

Output(s)

σtmax \sigma_{\text {tmax }}: Maximum Tangential Stress (psi)

Formula(s)

σtmax=12(σzz+σaa+(σzzσaa)2+4τ2)σtmax=12(σzz+σaa(σzzσaa)2+4τ2)\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.


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