ICP=31 Parker et al 3-phase function

ICP=31 Three-phase capillary functions from Parker et al. (1987).

m = 1 -1/n

${\bar S_l} = ({S_l} - {S_m})/(1 - {S_m})$

${\bar S_n} = ({S_l} + {S_n} - {S_m})/(1 - {S_m})$

${P_{cgn}}\quad = \quad - \;\frac{{{\rho _l}g}}{{{\alpha _{gn}}}}\;{[{({\bar S_n})^{ - 1/m}} - 1]^{1/n}}$

${P_{cgl}} = - \frac{{{\rho _l}g}}{{{\alpha _{nl}}}}{\left[ {{{\left( {{{\bar S}_l}} \right)}^{ - 1/m}} - 1} \right]^{1/n}} - \frac{{{\rho _l}g}}{{{\alpha _{gn}}}}{\left[ {{{\left( {{{\bar S}_n}} \right)}^{ - 1/m}} - 1} \right]^{1/n}}$

where $S_m$ = CP(1); n = CP(2); $\alpha _{gn}$ = CP(3); $\alpha _{nl}$ = CP(4).

These functions have been modified so that the capillary pressures remain finite at low aqueous saturations. This is done by calculating the slope of the capillary pressure functions at ${\bar S_l}$ and ${\bar S_n}$ = 0.1. If t ${\bar S_l}$ or t ${\bar S_n}$ is less than 0.1, the capillary pressures are calculated as linear functions in this region with slopes equal to those calculated at scaled saturations of 0.1.