Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Effect of Pore Pressure on Stress Formula

S = \lambda \xi_o \delta + 2G\xi - \alpha\delta P

Effect of Pore Pressure on Stress calculates stress including pore pressure effect 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 (lambda_lame, delta, xi_o, xi, G, 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_stress equals 4,100 psi.

lambda_lamepsi

2000000

deltadimensionless

xi_odimensionless

0.001

xidimensionless

0.0015

Gpsi

1500000

alphadimensionless

0.8

Ppsi

3000

Inputs

lambda_lame

psi

Lame First Constant

delta

dimensionless

Kronecker Delta

xi_o

dimensionless

Initial Strain

xi

dimensionless

Final Strain

G

psi

Modulus of Shear

alpha

dimensionless

Biot Coefficient

P

psi

Applied Pore Pressure

Outputs

S_stress

psi

Stress Including Pore Pressure Effect

Source and review

reviewed

Zoback, M.D. 2007. Reservoir Geomechanics, Cambridge University Press, Page 68.

Source