Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Tangential Stress Extremes at a Deviated Wellbore Formula

\sigma_{tmax}=\frac{1}{2}\left(\sigma_{zz}+\sigma_{aa}+\sqrt{(\sigma_{zz}-\sigma_{aa})^2+4\tau^2}\right)

Tangential Stress Extremes at a Deviated Wellbore calculates maximum tangential 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 (sigma_zz, sigma_aa, tau) 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, sigma_tmax equals 7,118.033989 psi.

sigma_zzpsi

7000

sigma_aapsi

5000

taupsi

500

Inputs

sigma_zz

psi

Stress in Radial Direction

sigma_aa

psi

Stress in Axial Direction

tau

psi

Shear Stress

Outputs

sigma_tmax

psi

Maximum Tangential Stress

sigma_tmin

psi

Minimum Tangential Stress

Source and review

reviewed

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

Zoback, M.D. 2007. Reservoir Geomechanics. Cambridge University Press, Page 239.

Source