Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Stress Components in Original Coordinate System in Depletion Drive Formula

S_x=S_{hmax}-AP_p-\frac{A\Delta P_p}{2}(1-\cos 2\Delta)

Stress Components in Original Coordinate System in Depletion Drive calculates stress in x direction 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_p, DeltaP_p, A, Delta_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, S_x equals 5,050 psi.

S_hmaxpsi

7000

S_hminpsi

5000

P_ppsi

3000

DeltaP_ppsi

1000

Adimensionless

0.6

Delta_degdeg

Inputs

S_hmax

psi

Maximum Horizontal Stress

S_hmin

psi

Minimum Horizontal Stress

P_p

psi

Pore Pressure

DeltaP_p

psi

Change in Pore Pressure Due to Depletion

A

dimensionless

Stress Path Coefficient

Delta_deg

deg

Fault Orientation

Outputs

S_x

psi

Stress in X Direction

S_y

psi

Stress in Y Direction

tau_xy

psi

Shear Stress Around Wellbore

Source and review

reviewed

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

Zoback, M.D. 2007. Reservoir Geomechanics. Cambridge University Press, Page 393.

Source