# 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.

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