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.

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