Subsidence due to uniform pore pressure reduction in free surfaces
Input(s)
\(\mathrm{c}_{\mathrm{m}}\): Formation Compaction per Unit Change in Pore Pressure Reduction \(\left(\mathrm{ft}^{3} / \mathrm{psi}\right)\)
\(v\): Poisson's (dimensionless)
r: Radius of Area Involved (ft)
D: Depth of Formation in Consideration ( \(\mathrm{ft}\) )
\(\Delta \mathrm{P}_{\mathrm{p}}\): Pore Pressure Change \((\mathrm{psi})\)
\(\mathrm{V}\): Volume of Reservoir \(\left(\mathrm{ft}^{3}\right)\)
Output(s)
\(\mathrm{u}_{\mathrm{z}}\): Subsidence in \(\mathrm{Z}\) Direction \((\mathrm{ft})\)
\(\mathrm{u}_{\mathrm{r}}\): Subsidence Along \(\mathrm{R}(\mathrm{ft})\)
Formula(s)
\[
\begin{gathered}
\mathrm{u}_{\mathrm{z}}=(-1) *\left(\frac{\mathrm{c}_{\mathrm{m}} *(1-\mathrm{v}) * \mathrm{D} * \Delta \mathrm{P}_{\mathrm{p}} * \mathrm{~V}}{\pi *\left(\left(\mathrm{r}^{2}\right)+\left(\mathrm{D}^{2}\right)\right)^{1.5}}\right) \\
\mathrm{u}_{\mathrm{r}}=\left(\frac{\mathrm{c}_{\mathrm{m}} *(1-\mathrm{v}) * \mathrm{r} * \Delta \mathrm{P}_{\mathrm{p}} * \mathrm{~V}}{\pi *\left(\left(\mathrm{r}^{2}\right)+\left(\mathrm{D}^{2}\right)\right)^{1.5}}\right)
\end{gathered}
\]
Reference(s)
Mark D. Zoback, Reservoir Geomechanics, Cambridge University Press, UK, Page: 412.