IRP=32 Modified Stone's first 3-phase method

IRP = 32 Modified version of Stone’s first three-phase method (Stone, 1970).

${k_{rg\,}}\quad = \quad {\left[ {\frac{{{S_{g\,}}\; - \;\,{S_{gr}}}}{{1\; - \;{S_{ar}}}}} \right]^n}$

${k_{rl}}\quad = \quad {\left[ {\frac{{{S_l}\; - \;{S_{lr}}}}{{1\; - \;{S_{lr}}}}} \right]^n}$

${k_{rn}}\quad = \quad \left[ {\frac{{1\; - \;{S_g}\; - \;{S_l}\; - \;{S_{nr}}}}{{1\; - \;{S_g}\; - \;{S_{lr}}\; - \;{S_{nr}}}}} \right]\;\left[ {\frac{{1\; - \;{S_{lr}}\; - \;{S_{nr}}}}{{1\; - \;{S_l}\; - \;{S_{nr}}}}} \right]\;{\left[ {\frac{{\left( {1\; - \;{S_g}\; - \;{S_{lr}}\; - \;{S_{nr}}} \right)\;\left( {1\; - \;{S_l}} \right)}}{{\left( {1\; - \;{S_{nr}}} \right)}}} \right]^n}$

When $S_n$ = 1 - $S_l$ - $S_g$ - $S_s$ is near irreducible liquid saturation,

$S_{nr}$ ≤ $S_n$ ≤$S_{nr}$ + .005, liquid relative permeability is taken to be

${k'_{rn}}\quad = \quad {k_{rn}}\; \cdot \;\frac{{{S_n}\; - \;{S_{nr}}}}{{.005}}$

Parameters are $S_{lr}$ = RP(1), $S_{nr}$ = RP(2), $S_{gr}$ = RP(3), n = RP(4).