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Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Thermal Hoop Stress from Wellbore Temperature Change Formula

σΔT=αTE1νΔT\sigma^{\Delta T}=\frac{\alpha_T E}{1-\nu}\Delta T

Thermal Hoop Stress from Wellbore Temperature Change calculates thermally induced hoop stress for in-situ stress and rock mechanics workflows in geomechanics and fracturing.

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How engineers use this formula

Use this formula when the listed inputs (alpha_T, E, nu, DeltaT) 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_DT equals -666.666667 psi.

alpha_T1/degF

0.000005

Epsi

5000000

nudimensionless

0.25

DeltaTdegF

-20

Inputs

alpha_T

1/degF

Linear Thermal Expansion Coefficient

E

psi

Young's Modulus

nu

dimensionless

Poisson Ratio

DeltaT

degF

Wellbore Temperature Change

Outputs

sigma_DT

psi

Thermally Induced Hoop Stress

DeltaT

degF

Wellbore Temperature Change

Source and review

reviewed

Introduction to Energy Geomechanics, Espinoza, D.N.

Espinoza, D.N. Introduction to Energy Geomechanics, Chapter 6.4, thermal stress term following Eq. 6.18.

Source

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