Stress component near normal faulting in reservoir
Input(s)
\(\alpha\): Biot (dimensionless)
\(v\): Poisson (dimensionless)
\(\mathrm{Sh}_{\text {max }}\): Maximum Principal Stress (psi)
\(\mathrm{Sh}_{\text {min }}\): Minimum Principal Stress (psi)
\(\mathrm{dP}\): Change in Pore Pressure (psi)
\(\theta\): Fault Orientation (degrees)
Output(s)
A: Constant a Value (dimensionless)
\(\mathrm{S}_{\mathrm{x}}\): Stress in \(\mathrm{X}\) Direction (psi)
\(\mathrm{S}_{\mathrm{y}}\): Stress in \(\mathrm{Y}\) Direction (psi)
\(\mathrm{T}_{\mathrm{xy}}\): Normal Stress in Y Direction (psi)
Formula(s)
\[
\begin{gathered}
\mathrm{A}=\alpha * \frac{1-2 * v}{1-\mathrm{v}} \\
\mathrm{Sx}=\mathrm{Sh}_{\text {max }}-\mathrm{A} * \mathrm{dP}-\mathrm{A} * \frac{\mathrm{dP}}{2} *\left(1-\cos \left(2 * \theta * \frac{\pi}{180}\right)\right) \\
\mathrm{Sy}=\mathrm{Sh}_{\text {min }}-\mathrm{A} * \mathrm{dP}-\mathrm{A} * \frac{\mathrm{dP}}{2} *\left(1+\cos \left(2 * \theta * \frac{\pi}{180}\right)\right) \\
\text { Txy }=\mathrm{A} * \frac{\mathrm{dP}}{2} * \sin \left(2 * \theta * \frac{\pi}{180}\right)
\end{gathered}
\]
Reference(s)
Mark D. Zoback, Reservoir Geomechanics, Cambridge University Press, UK, Page: 381.