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Geomechanics and FracturingIn-Situ Stress and Rock MechanicsIn-depth reference

Normal Hoop Stress at the Wellbore Wall Calculator

σθ=Shmax+Shmin2(ShmaxShmin)cos(2θ)2PoΔPSdt\sigma_\theta=S_{hmax}+S_{hmin}-2(S_{hmax}-S_{hmin})\cos(2\theta)-2P_o-\Delta P-S_{dt}

Enter the required inputs, confirm the units, and run the calculator to solve sigma_theta. 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.

6 variables

Your input values and calculation stay in this browser.

Engineering reference summary

Calculation context and source notes

Normal Hoop Stress at the Wellbore Wall calculates hoop stress at the wellbore wall 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 (S_hmax, S_hmin, P_o, dP, S_dt, theta_deg) are known and the assumptions behind the cited in-situ stress and rock mechanics relationship match the engineering case being checked.

Solves for

sigma_theta (psi)

Formula reference

Formula, variables, and default calculation

σθ=Shmax+Shmin2(ShmaxShmin)cos(2θ)2PoΔPSdt\sigma_\theta=S_{hmax}+S_{hmin}-2(S_{hmax}-S_{hmin})\cos(2\theta)-2P_o-\Delta P-S_{dt}

Reproducible default result

With the default values shown below, the calculation returns sigma_theta = 6,200 psi. Defaults demonstrate the implementation; they are not recommended field values.

S_hmaxpsi

8000

S_hminpsi

6000

P_opsi

3500

dPpsi

500

S_dtpsi

300

theta_degdeg

45

Input definitions

S_hmax

psi

Maximum Principal Stress in Reservoir

S_hmin

psi

Minimum Principal Stress in Reservoir

P_o

psi

Pore Pressure

dP

psi

Wellbore Pressure Difference

S_dt

psi

Thermally Induced Stress

theta_deg

deg

Azimuth from Maximum Horizontal Stress Direction

Output definitions

sigma_theta

psi

Hoop Stress at the Wellbore Wall

dP

psi

Wellbore Pressure Difference

S_dt

psi

Thermally Induced Stress

Engineering use, assumptions, and limits

Use this formula when the listed inputs (S_hmax, S_hmin, P_o, dP, S_dt, theta_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.

Frequently asked questions

What inputs does the Normal Hoop Stress at the Wellbore Wall calculator need?

The calculation uses Maximum Principal Stress in Reservoir (S_hmax), Minimum Principal Stress in Reservoir (S_hmin), Pore Pressure (P_o), Wellbore Pressure Difference (dP), Thermally Induced Stress (S_dt), Azimuth from Maximum Horizontal Stress Direction (theta_deg). Enter values on the units shown beside each field.

What result does this calculator return?

The primary result is hoop stress at the wellbore wall 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

Zoback, M.D. 2007. Reservoir Geomechanics, Cambridge University Press, Page 102.

Open source reference

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