Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Normal Radial Stress Near a Wellbore Formula

\sigma_{rr}=\frac{1}{2}(S_{hmax}+S_{hmin}-2P_o)\left(1-\frac{R^2}{r^2}\right)+\frac{1}{2}(S_{hmax}-S_{hmin})\left(1-4\frac{R^2}{r^2}+3\frac{R^4}{r^4}\right)\cos(2\theta)+P_o\frac{R^2}{r^2}

Normal Radial Stress Near a Wellbore calculates normal radial stress near wellbore 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_hmax, S_hmin, P_o, R, r, theta_deg) 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, sig_rr equals 3,799.988815 psi.

S_hmaxpsi

8000

S_hminpsi

6000

P_opsi

3500

Rft

0.33

rft

theta_degdeg

Inputs

S_hmax

psi

Maximum Principal Stress in Reservoir

S_hmin

psi

Minimum Principal Stress in Reservoir

P_o

psi

Pore Pressure

R

Wellbore Radius

r

Distance from Wellbore Center

theta_deg

deg

Azimuth from Maximum Horizontal Stress Direction

Outputs

sig_rr

psi

Normal Radial Stress Near Wellbore

Source and review

reviewed

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

Zoback, M.D. 2007. Reservoir Geomechanics. Cambridge University Press, Page 100.

Source