# Porosity irreversible plastic deformation occurs

## Input(s)

$$\mu$$: Viscosity $$(\mathrm{cP})$$

$$S_{v}$$: Vertical Stress (psi)

$$S_{H}$$: Maximum Horizontal Stress (psi)

$$S_{h}$$: Minimum Horizontal Stress (psi)

$$P_{p}$$: Change in Pore Pressure $$(\mathrm{psi})$$

## Output(s)

M: Mobility (dimensionless)

p: Porosity (dimensionless)

## Formula(s)

$\begin{gathered} \mathrm{M}=\frac{6 * \mu}{3 *\left(\left(\left(\mu^{2}\right)+1\right)^{0.5}\right)-\mu} \\ \mathrm{p}=\left(\frac{1}{3 *\left(\mathrm{~S}_{\mathrm{v}} * \mathrm{~S}_{\mathrm{H}}+\mathrm{S}_{\mathrm{h}}\right)-9 * \mathrm{P}_{\mathrm{p}}}\right) *\left(9 * \mathrm{P}_{\mathrm{p}}^{2}+\left(1+\frac{9}{\mathrm{M}^{2}}\right) *\left(\mathrm{~S}_{\mathrm{v}}^{2}+\mathrm{S}_{\mathrm{H}}^{2}+\mathrm{S}_{\mathrm{h}}^{2}\right)+\left(2-\frac{9}{\mathrm{M}^{2}}\right) *\left(\mathrm{~S}_{\mathrm{v}} * \mathrm{~S}_{\mathrm{H}}+\mathrm{S}_{\mathrm{v}} * \mathrm{~S}_{\mathrm{h}}+\mathrm{S}_{\mathrm{H}} * \mathrm{~S}_{\mathrm{h}}\right)-6 * \mathrm{P}_{\mathrm{p}} *\left(\mathrm{~S}_{\mathrm{v}}+\mathrm{S}_{\mathrm{H}}+\mathrm{S}_{\mathrm{h}}\right)\right) \end{gathered}$

## Reference(s)

Mark D. Zoback, Reservoir Geomechanics, Cambridge University Press, UK, Page: 400.

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