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.