Porosity irreversible plastic deformation occurs

Input(s)

μ\mu: Viscosity (cP)(\mathrm{cP})

SvS_{v}: Vertical Stress (psi)

SHS_{H}: Maximum Horizontal Stress (psi)

ShS_{h}: Minimum Horizontal Stress (psi)

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

Output(s)

M: Mobility (dimensionless)

p: Porosity (dimensionless)

Formula(s)

M=6μ3(((μ2)+1)0.5)μp=(13( Sv SH+Sh)9Pp)(9Pp2+(1+9M2)( Sv2+SH2+Sh2)+(29M2)( Sv SH+Sv Sh+SH Sh)6Pp( Sv+SH+Sh))\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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