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 (pressure) 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.

Another (saturaton) exponent $n$ is usually set to $n = 1 / (1 - m)$.

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.

Either the exponent (which is the pressure exponent $m$ in the equations) must be set and then the saturation exponent is $n = 1 / (1 - m)$. Or both values the pressure_exponent and the saturation_exponent must be set independently.

Child parameters, attributes and cases

Additional info

Used in the following test data files