Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Pressure to Grow Fractures - Abe, Mura et al. Formula

P_{grow}=S_c\frac{1-(P_p/S_c)\sqrt{1-(c_f/c_i)^2}}{1-\sqrt{1-(c_f/c_i)^2}}

Pressure to Grow Fractures - Abe, Mura et al. calculates fracture growth 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 (S_c, P_p, c_f, c_i) 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, P_grow equals 8,000 psi.

S_cpsi

5000

P_ppsi

3000

c_fin

c_iin

Inputs

S_c

psi

Minimum Principal Stress

P_p

psi

Pore Pressure

c_f

Radius of Fracture

c_i

Radius of Invaded Zone

Outputs

P_grow

psi

Fracture Growth Pressure

Source and review

reviewed

Zoback, M.D. 2007. Reservoir Geomechanics, Cambridge University Press, Page 326.

Source