Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Initial Effective Horizontal Stress Formula

\sigma_h=\frac{\nu}{1-\nu}\left(\frac{\rho_bH}{144}-\alpha P_p\right)

Initial Effective Horizontal Stress calculates initial effective horizontal 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 (nu, rho_b, H, alpha, P_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, sigma_h equals 2,405.555556 psi.

nudimensionless

0.25

rho_blb/ft^3

150

Hft

10000

alphadimensionless

0.8

P_ppsi

4000

Inputs

nu

dimensionless

Poisson Ratio

rho_b

lb/ft^3

Overburden Density

H

Formation Depth

alpha

dimensionless

Biot Constant

P_p

psi

Reservoir Pressure

Outputs

sigma_h

psi

Initial Effective Horizontal Stress

nu

dimensionless

Poisson Ratio

rho_b

lb/ft^3

Overburden Density

H

Formation Depth

alpha

dimensionless

Biot Constant

P_p

psi

Reservoir Pressure

Source and review

reviewed

Guo, B., Lyons, W.C., and Ghalambor, A. 2007. Petroleum Production Engineering: A Computer-Assisted Approach, Page 259.

Source