van Genuchten water retention model

\[p_c=p_b (S_e^{-1/m}-1)^{1-m}\]

with

\[S_e=\frac{S-S_r}{S_{\mbox{max}}-S_r}\]

where

\begin{eqnarray*} &p_b& \mbox{ entry pressure,}\\ &S_r& \mbox{ residual saturation,}\\ &S_{\mbox{max}}& \mbox{ maximum saturation,}\\ &m(<=1) & \mbox{ exponent.}\\ \end{eqnarray*}

Note:

\[n=1/(1-m)\]

.

If \(\alpha\) instead of \(p_b\) is available, \(p_b\) can be calculated as

\[p_b=\rho g/\alpha\]

The regularized van Genuchten model, please ref to Marchand E, Mueller T, Knabner P. Fully coupled generalized hybrid-mixed finite element approximation of two-phase two-component flow in porous media. Part I: formulation and properties of the mathematical model. Comput Geosci 2013;17(2):431-442.

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