Lak wettability index

In petroleum engineering, Lak wettability index is a quantitative indicator to measure wettability of rocks from relative permeability data. This index is based on a combination of Craig's first rule.^[1][2] and modified Craig's second rule ^[3][4]

${\displaystyle I_{\mathit {L}}={\frac {A(0.3-k_{\mathit {rw,Sor}})}{\ 0.3}}+{\frac {B(0.5-k_{\mathit {rw,Sor}})}{\ 0.5}}+{\frac {CS-RCS}{\ 1-Sor-Swc}}}$

where

${\displaystyle I_{\mathit {L}}}$ : Lak wettability index (index values near -1 and 1 represent strongly oil-wet and strongly water-wet rocks, respectively)

${\displaystyle k_{\mathit {rw,Sor}}}$ : Water relative permeability measured at residual oil saturation

${\displaystyle CS}$ : Water saturation at the intersection point of water and oil relative permeability curves (fraction)

${\displaystyle Sor}$ : Residual oil saturation (in fraction)

${\displaystyle Swc}$ : Irreducible water saturation (in fraction)

${\displaystyle RCS}$ : Reference crossover saturation (in fraction) defined as:

${\displaystyle RCS=0.5+{\frac {Swc-Sor}{\ 2}}}$

and ${\displaystyle A}$ and ${\displaystyle B}$ are two constant coefficients defined as:

${\displaystyle A=0.5}$ and ${\displaystyle B=0}$ if ${\displaystyle k_{\mathit {rw,Sor}}<0.3}$

${\displaystyle A=0}$ and ${\displaystyle B=0}$ if ${\displaystyle 0.3<=k_{\mathit {rw,Sor}}<=0.5}$

${\displaystyle A=0}$ and ${\displaystyle B=0.5}$ if ${\displaystyle k_{\mathit {rw,Sor}}>0.5}$

To use the above formula, relative permeability is defined as the effective permeability divided by the oil permeability measured at irreducible water saturation.^[1]