Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Minimum Axial Stress at a Vertical Wellbore Formula

\sigma_{minaxial}=3S_{hmin}-S_{hmax}-2P_o-P-\sigma_t

Minimum Axial Stress at a Vertical Wellbore calculates minimum axial stress for in-situ stress and rock mechanics workflows in geomechanics and fracturing.

Calculate

How engineers use this formula

Use this formula when the listed inputs (S_hmin, S_hmax, P_o, P_drawdown, sigma_t) 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_minaxial equals 2,200 psi.

S_hminpsi

6000

S_hmaxpsi

8000

P_opsi

3500

P_drawdownpsi

500

sigma_tpsi

300

Inputs

S_hmin

psi

Minimum Horizontal Stress

S_hmax

psi

Maximum Horizontal Stress

P_o

psi

Pore Pressure

P_drawdown

psi

Pressure Drawdown

sigma_t

psi

Thermal Stress

Outputs

sigma_minaxial

psi

Minimum Axial Stress

S_hmin

psi

Minimum Horizontal Stress

S_hmax

psi

Maximum Horizontal Stress

P_drawdown

psi

Pressure Drawdown

Source and review

reviewed

Zoback, M.D. 2007. Reservoir Geomechanics, Cambridge University Press, Page 174.

Source