Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Least Principal Stress - Matthews and Kelly Formula

S_{hmin}=K_i(S_v-P_p)+P_p

Least Principal Stress - Matthews and Kelly calculates minimum principal stress in reservoir 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 (K_i, S_v, 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, S_hmin equals 7,250 psi.

K_idimensionless

0.65

S_vpsi

9000

P_ppsi

4000

Inputs

K_i

dimensionless

Depth-Dependent Stress Coefficient

S_v

psi

Vertical Overburden Stress

P_p

psi

Pore Pressure in Reservoir

Outputs

S_hmin

psi

Minimum Principal Stress in Reservoir

K_i

dimensionless

Depth-Dependent Stress Coefficient

S_v

psi

Vertical Overburden Stress

P_p

psi

Pore Pressure in Reservoir

Source and review

reviewed

Zoback, M.D. 2007. Reservoir Geomechanics, Cambridge University Press, Page 280.

Source