Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Rotation of Maximum Principal Stress Near Wellbore Formula

\gamma=\frac{1}{2}\tan^{-1}\left(\frac{A\Delta P_p\sin 2\theta}{S_{hmax}-S_{hmin}+A\Delta P_p\cos 2\theta}\right)

Rotation of Maximum Principal Stress Near Wellbore calculates rotation of maximum principal stress for in-situ stress and rock mechanics workflows in geomechanics and fracturing.

Calculate

How engineers use this formula

Use this formula when the listed inputs (A, DeltaP_p, theta_deg, S_hmax, S_hmin) are known and the assumptions behind the cited in-situ stress and rock mechanics relationship match the engineering case being checked.

Assumptions

Input values are representative for the well, reservoir, fluid, or equipment case being evaluated.
The declared units match the field-unit constants used in the formula.
The cited formula applies to the selected petroleum engineering workflow.

Limitations

The calculation does not replace a full engineering model or operating procedure.
Accuracy depends on the source correlation, assumptions, input quality, and unit consistency.

Common mistakes

Mixing unit systems without converting the inputs.
Using default example values as field recommendations.
Applying the formula outside the source assumptions.

Default example

Using the default inputs, gamma_deg equals 10.893395 deg.

Adimensionless

0.8

DeltaP_ppsi

1500

theta_degdeg

S_hmaxpsi

7000

S_hminpsi

5000

Inputs

A

dimensionless

Stress Field Direction Coefficient

DeltaP_p

psi

Change in Pore Pressure

theta_deg

deg

Fault Orientation

S_hmax

psi

Maximum Principal Stress

S_hmin

psi

Minimum Principal Stress

Outputs

gamma_deg

deg

Rotation of Maximum Principal Stress

gamma_rad

rad

Rotation of Maximum Principal Stress

Source and review

reviewed

Reservoir Geomechanics, Zoback, M.D. (2007)

Zoback, M.D. 2007. Reservoir Geomechanics. Cambridge University Press, Page 393.

Source