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Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Fracture Gradient - Zoback and Healy Formula

Shmin=(1+μf2+μf)2(SvPp)+PpS_{hmin} = (\sqrt{1 + \mu_f^2} + \mu_f)^{-2}(S_v - P_p) + P_p

Fracture gradient estimates the pressure gradient required to initiate or propagate a fracture under a stated stress model.

Calculate

How engineers use this formula

Use it for geomechanics screening, mud-window checks, and fracture-pressure comparisons before detailed wellbore stability work.

Assumptions

  • The selected stress model is appropriate for the local geologic setting.
  • Input stress and pore-pressure values are representative at depth.
  • Units are consistent across pressure and gradient terms.

Limitations

  • Does not replace leak-off tests, mini-frac interpretation, or calibrated geomechanical models.
  • Local depletion, anisotropy, natural fractures, and tectonic effects may change fracture pressure.

Common mistakes

  • Using a generic stress model without local calibration.
  • Mixing gradient and pressure units.
  • Treating screening results as operational limits without review.

Default example

Using the default inputs, S_hmin equals 5,602.857726 psi.

mu_fdimensionless

0.6

S_vpsi

9000

P_ppsi

4000

Inputs

mu_f

dimensionless

Friction Coefficient

S_v

psi

Vertical Stress

P_p

psi

Pore Pressure

Outputs

S_hmin

psi

Minimum Horizontal Stress

Source and review

reviewed

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

Source

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