Minimum Hoop Stress at the Wellbore Wall Calculator
Enter the required inputs, confirm the units, and run the calculator to solve sigma_theta_min. Review the formula source and assumptions before using the result in engineering work.
Calculation context and source notes
Minimum Hoop Stress at the Wellbore Wall calculates minimum 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_hmin, S_hmax, P_o, dP, S_dt) 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_min (psi)
Best next page
Formula, variables, and sourceFormula, variables, and default calculation
Reproducible default result
With the default values shown below, the calculation returns sigma_theta_min = 2,200 psi. Defaults demonstrate the implementation; they are not recommended field values.
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Input definitions
S_hmin
psiMinimum Principal Stress in Reservoir
S_hmax
psiMaximum Principal Stress in Reservoir
P_o
psiPore Pressure
dP
psiDifference Between Wellbore Pressure and Pore Pressure
S_dt
psiThermally Induced Stress
Output definitions
sigma_theta_min
Minimum Hoop Stress at the Wellbore Wall
S_hmin
Minimum Principal Stress in Reservoir
S_hmax
Maximum Principal Stress in Reservoir
P_o
Pore Pressure
dP
Difference Between Wellbore Pressure and Pore Pressure
S_dt
Thermally Induced Stress
Engineering use, assumptions, and limits
Use this formula when the listed inputs (S_hmin, S_hmax, P_o, dP, S_dt) 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 Minimum Hoop Stress at the Wellbore Wall calculator need?
The calculation uses Minimum Principal Stress in Reservoir (S_hmin), Maximum Principal Stress in Reservoir (S_hmax), Pore Pressure (P_o), Difference Between Wellbore Pressure and Pore Pressure (dP), Thermally Induced Stress (S_dt). Enter values on the units shown beside each field.
What result does this calculator return?
The primary result is minimum 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.
Zoback, M.D. 2007. Reservoir Geomechanics, Cambridge University Press, Page 238.
Open source reference