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Tangential Stress Extremes at a Deviated Wellbore Calculator

σtmax=12(σzz+σaa+(σzz−σaa)2+4τ2)\sigma_{tmax}=\frac{1}{2}\left(\sigma_{zz}+\sigma_{aa}+\sqrt{(\sigma_{zz}-\sigma_{aa})^2+4\tau^2}\right)

Enter the required inputs, confirm the units, and run the calculator to solve sigma_tmax. Review the formula source and assumptions before using the result in engineering work.

Tabular solver

Inputs

Defaults provide a quick field-unit example for the equation.

3 variables

Your input values and calculation stay in this browser.

Engineering reference summary

Calculation context and source notes

Tangential Stress Extremes at a Deviated Wellbore calculates maximum tangential stress for in-situ stress and rock mechanics workflows in geomechanics and fracturing. The page keeps the declared variables, units, source relationship, and output definition visible for technical review.

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.

Solves for

sigma_tmax (psi)

Best next page

Formula, variables, and source
Formula reference

Formula, variables, and default calculation

σtmax=12(σzz+σaa+(σzz−σaa)2+4τ2)\sigma_{tmax}=\frac{1}{2}\left(\sigma_{zz}+\sigma_{aa}+\sqrt{(\sigma_{zz}-\sigma_{aa})^2+4\tau^2}\right)

Reproducible default result

With the default values shown below, the calculation returns sigma_tmax = 7,118.033989 psi. Defaults demonstrate the implementation; they are not recommended field values.

sigma_zzpsi

7000

sigma_aapsi

5000

taupsi

500

Input definitions

sigma_zz

psi

Stress in Radial Direction

sigma_aa

psi

Stress in Axial Direction

tau

psi

Shear Stress

Output definitions

sigma_tmax

psi

Maximum Tangential Stress

sigma_tmin

psi

Minimum Tangential Stress

Engineering use, assumptions, and limits

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.

Frequently asked questions

What inputs does the Tangential Stress Extremes at a Deviated Wellbore calculator need?

The calculation uses Stress in Radial Direction (sigma_zz), Stress in Axial Direction (sigma_aa), Shear Stress (tau). Enter values on the units shown beside each field.

What result does this calculator return?

The primary result is maximum tangential stress in psi. The formula section shows the declared relationship, variables, and a reproducible default calculation.

What should I check before using the result?

Confirm the unit basis, source applicability, and input quality. The calculation does not replace a full engineering model or operating procedure. Mixing unit systems without converting the inputs.

Source and record status

Source metadata identifies the relationship implemented by the calculator. Check the cited edition, unit basis, and scope against the engineering case before operational use.

reviewedguidance published

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

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

Open source reference

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