The van Genuchten capillary pressure model.

The van Genuchten capillary pressure model ([39]) 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.

Child parameters, attributes and cases

Additional info

No additional info.

Used in the following test data files

Used in no end-to-end test cases.