IRP=11 Modified van Genuchten Model

IRP = 11 Modified van Genuchten Model

A modified version of the van Genuchten model (Luckner et al., 1989) has been implemented to prevent the capillary pressure from decreasing towards negative infinity as the effective saturation approaches zero. The modified van Genuchten model is invoked by setting both IRP and ICP to 11.

${k_{rl}} = S_{ekl}^\gamma \cdot {S_{ekl}}^{(1 - \gamma )\eta } \cdot {\left[ {1 - {{\left( {1 - {S_{ekl}}^{(1 - \gamma )/m}} \right)}^m}} \right]^2}$

{k_{rg}} = \left\{ {\begin{array}{*{20}{c}} {{{\left( {1 - {S_{ekg}}} \right)}^\zeta }{{\left[ {1 - {S_{ekg}}^{1/m}} \right]}^{2m}}{\rm{ if RP(3) }} = {\rm{ 0}}}\\ {1 - {k_{rl}}{\rm{ if RP(3)}}{\rm{ }} \ne {\rm{ 0}}} \end{array}} \right.

where

${S_{ekl}} = \frac{{{S_l} - {S_{lrk}}}}{{1 - {S_{lrk}}}}$, ${S_{ekg}} = \frac{{{S_l}}}{{1 - {S_{gr}}}}$

Parameters: RP(1) = ${S_{lrk}}$

if negative, ${S_{lrk}} = 0$ for calculating krg, and absolute value is used for calculating krl

RP(2) = ${S_{gr}}$if negative, ${S_{gr}} = 0$ for calculating krl, and absolute value is used for calculating krg

RP(3) = flag to indicate which equation is used for krg

RP(4) = $\eta$ (default = 1/2)

RP(5) = $\epsilon_k$

use linear function between ${k_{rl}}({S_e} = 1 - {\varepsilon _k})$ and 1.0.

RP(6) = ${a_{fm}}$ Constant fracture-matrix interaction reduction factor, in combination with Active Fracture Model (see online user manual)

RP(7) = ζ (default = 1/3)