# 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.

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