Stress components in original coordinate system in depletion drive

Input(s)

Shmax\mathrm{S}_{\mathrm{hmax}}: Maximum Stress in Horizontal Direction (psi)

Shmin\mathrm{S}_{\mathrm{hmin}}: Minimum Stress in Horizontal Direction (psi)

δPp\delta \mathrm{P}_{\mathrm{p}}: Change in Pore Pressure due to Depletion (psi)

A: Stress Path (dimensionless)

Δ\Delta: Fault Orientation (degrees)

Output(s)

Sx\mathrm{S}_{\mathrm{x}}: Stress in X\mathrm{X}-direction (psi)

Sy\mathrm{S}_{\mathrm{y}}: Stress in Y\mathrm{Y}-direction (psi)(\mathrm{psi})

τ\tau: Stress Around Wellbore (psi)

Formula(s)

Sx=ShmaxAPp(AδPp2)(1cos(2Δ))Sy=ShminAPp(AδPp2)(1+cos(2Δ))τ=(AδPp2)sin(2Δ)\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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