Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Matthews-Kelly Fracture Gradient from Stress Ratio Formula

S_{hmin}=\left(\frac{\sigma_{min}}{\sigma_v}\right)(S_v-P_p)+P_p

Matthews-Kelly Fracture Gradient from Stress Ratio calculates minimum horizontal stress or fracture gradient pressure 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 (sigma_min_ref, sigma_v_ref, 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 6,777.777778 psi.

sigma_min_refpsi

5000

sigma_v_refpsi

9000

S_vpsi

9000

P_ppsi

4000

Inputs

sigma_min_ref

psi

Reference Minimum Principal Horizontal Stress

sigma_v_ref

psi

Reference Vertical Principal Stress

S_v

psi

Vertical Stress

P_p

psi

Pore Pressure

Outputs

S_hmin

psi

Minimum Horizontal Stress or Fracture Gradient Pressure

K_MK

dimensionless

Matthews-Kelly Stress Ratio

sigma_min_ref

psi

Reference Minimum Principal Horizontal Stress

S_v

psi

Vertical Stress

P_p

psi

Pore Pressure

Source and review

reviewed

Reservoir Geomechanics, Zoback, M.D. (2007)

Zoback, M.D. 2007. Reservoir Geomechanics. Cambridge University Press, Page 281.

Source