Minimum Wellbore Hoop Stress Calculator
Enter both horizontal stresses, pore pressure, wellbore pressure minus pore pressure, and the thermal stress term in psi to calculate minimum hoop stress.
Enter both horizontal stresses, pore pressure, wellbore pressure minus pore pressure, and the thermal stress term in psi to calculate minimum hoop stress.
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Calculation context and source notes
Calculate minimum tangential stress at the wellbore wall from the two horizontal stresses, pore pressure, wellbore overbalance and thermal stress. The implemented expression is 3 Shmin - SHmax - 2 Po - dP - Sdt, with all inputs in psi.
Use this calculation to examine the minimum wall-stress term before interpreting a wellbore stability case. With the supplied inputs, 3 x 6,000 - 8,000 - 2 x 3,500 - 500 - 300 gives 2,200 psi; this is a synthetic arithmetic check, not a safe operating limit.
University of Texas: diagnostic testing and minimum hoop stressSolves for
sigma_theta_min (psi)
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Formula, variables, and sourceLearn, compare and practice
Worked explanations, controlled studies and printable exercises connected to this calculation.
Formula, 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.
6000
8000
3500
500
300
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 calculation to examine the minimum wall-stress term before interpreting a wellbore stability case. With the supplied inputs, 3 x 6,000 - 8,000 - 2 x 3,500 - 500 - 300 gives 2,200 psi; this is a synthetic arithmetic check, not a safe operating limit.
Assumptions
- The relationship represents the minimum wall-stress term for the vertical-well formulation, not an arbitrary inclined-well stress transformation.
- Horizontal stresses, pore pressure and the signed thermal term use the same pressure units and the source's stress convention.
Limitations
- This output alone does not establish tensile failure: the rock tensile strength and the applicable stress convention must also be considered.
- The calculator accepts thermal stress as an input; it does not derive it from temperatures or elastic properties, or evaluate the complete wellbore stability envelope.
Common mistakes
- Entering absolute wellbore pressure for dP instead of wellbore pressure minus pore pressure.
- Subtracting pore pressure from the horizontal stress inputs and then subtracting it again through the explicit pore-pressure term.
- Reading the 2,200 psi example as an allowable mud-pressure limit.
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. This output alone does not establish tensile failure: the rock tensile strength and the applicable stress convention must also be considered. Entering absolute wellbore pressure for dP instead of wellbore pressure minus pore pressure.
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