Stress components in original coordinate system in depletion drive
Input(s)
\(\mathrm{S}_{\mathrm{hmax}}\): Maximum Stress in Horizontal Direction (psi)
\(\mathrm{S}_{\mathrm{hmin}}\): Minimum Stress in Horizontal Direction (psi)
\(\delta \mathrm{P}_{\mathrm{p}}\): Change in Pore Pressure due to Depletion (psi)
A: Stress Path (dimensionless)
\(\Delta\): Fault Orientation (degrees)
Output(s)
\(\mathrm{S}_{\mathrm{x}}\): Stress in \(\mathrm{X}\)-direction (psi)
\(\mathrm{S}_{\mathrm{y}}\): Stress in \(\mathrm{Y}\)-direction \((\mathrm{psi})\)
\(\tau\): Stress Around Wellbore (psi)
Formula(s)
\[
\begin{gathered}
\mathrm{S}_{\mathrm{x}}=\mathrm{S}_{\mathrm{h} \max }-\mathrm{A} * \mathrm{P}_{\mathrm{p}}-\left(\frac{\mathrm{A} * \delta \mathrm{P}_{\mathrm{p}}}{2}\right) *(1-\cos (2 * \Delta)) \\
\mathrm{S}_{\mathrm{y}}=\mathrm{S}_{\mathrm{h} \min }-\mathrm{A} * \mathrm{P}_{\mathrm{p}}-\left(\frac{\mathrm{A} * \delta \mathrm{P}_{\mathrm{p}}}{2}\right) *(1+\cos (2 * \Delta)) \\
\tau=\left(\frac{\mathrm{A} * \delta \mathrm{P}_{\mathrm{p}}}{2}\right) * \sin (2 * \Delta)
\end{gathered}
\]
Reference(s)
Mark D. Zoback, Reservoir Geomechanics, Cambridge University Press, UK, Page: 393.