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.