Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Subsidence Due to Uniform Pore Pressure Reduction in Free Surfaces Formula

u_z=-\frac{c_m(1-\nu)D\Delta P_pV}{\pi(r^2+D^2)^{1.5}}

Subsidence Due to Uniform Pore Pressure Reduction in Free Surfaces calculates subsidence in z 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 (c_m, nu, r, D, DeltaP_p, V) 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, u_z equals -0.047451 ft.

c_m1/psi

0.00001

nudimensionless

0.25

rft

3000

Dft

6000

DeltaP_ppsi

1000

Vft^3

1000000000

Inputs

c_m

1/psi

Formation Compaction per Unit Pore-Pressure Reduction

nu

dimensionless

Poisson Ratio

r

Radius of Area Involved

D

Depth of Formation

DeltaP_p

psi

Pore Pressure Change

V

ft^3

Reservoir Volume

Outputs

u_z

Subsidence in Z Direction

u_r

Radial Subsidence

Source and review

reviewed

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

Zoback, M.D. 2007. Reservoir Geomechanics. Cambridge University Press, Page 412.

Source