Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Horizontal Effective Stress - Lorenz and Teufel Formula

S_{hor}=\frac{\nu}{1-\nu}S_v+\alpha P\left(1-\frac{\nu}{1-\nu}\right)

Horizontal Effective Stress - Lorenz and Teufel calculates horizontal effective 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 (nu, S_v, alpha, P) 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, S_hor equals 4,533.333333 psi.

nudimensionless

0.25

S_vpsi

8000

alphadimensionless

0.8

Ppsi

3500

Inputs

nu

dimensionless

Poisson Ratio

S_v

psi

Vertical Overburden Stress

alpha

dimensionless

Biot Coefficient

P

psi

Pore Pressure

Outputs

S_hor

psi

Horizontal Effective Stress

S_v

psi

Vertical Overburden Stress

P

psi

Pore Pressure

alpha

dimensionless

Biot Coefficient

Source and review

reviewed

Zoback, M.D. Reservoir Geomechanics. Cambridge University Press, Page 381.

Source