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.