Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Rotation of Maximum Principal Stress Zoback Day Lewis Formula

\gamma=\frac{1}{2}\tan^{-1}\left(\frac{Aq\sin 2\Delta}{1+Aq\cos 2\Delta}\right)

Rotation of Maximum Principal Stress Zoback Day Lewis calculates stress rotation 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, q, Delta_deg) 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_rad equals 0.190126 rad.

Adimensionless

0.8

qdimensionless

0.75

Delta_degdeg

Inputs

A

dimensionless

Stress Rotation Constant

q

dimensionless

Ratio of Pore Pressure Change to Differential Stress

Delta_deg

deg

Fault Orientation

Outputs

gamma_rad

rad

Stress Rotation

gamma_deg

deg

Stress Rotation

Source and review

reviewed

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

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

Source