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.