OGS
[case] SaturationVanGenuchten

The van Genuchten capillary pressure model.

The van Genuchten capillary pressure model ([40]) is:

\[p_c(S)=p_b (S_\text{eff}^{-1/m}-1)^{1-m}\]

with effective saturation defined as

\[S_\text{eff}=\frac{S-S_r}{S_{\text{max}}-S_r}.\]

Above, \(S_r\) and \(S_{\text{max}}\) are the residual and the maximum saturations. The exponent \(m \in (0,1)\) and the pressure scaling parameter \(p_b\) (it is equal to \(\rho g/\alpha\) in original publication) are given by the user. The scaling parameter \(p_b\) is given in same units as pressure.

In the original work another exponent \(n\) is used, but usually set to \(n = 1 / (1 - m)\), and also in this implementation.

The saturation is computed from the capillary pressure as follows:

\[S(p_c)= \begin{cases} S_{\text{max}} & \text{for $p_c \leq 0$, and}\\ \left( \left(\frac{p_c}{p_b}\right)^{\frac{1}{1-m}} +1\right)^{-m} (S_{\text{max}}-S_r) +S_r& \text{for $p_c > 0$.} \end{cases} \]

The result is then clamped between the residual and maximum liquid saturations.

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Used in the following test data files

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