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Formation permeability to a given fluid $\begin{array}{l}\alpha\end{array}$ -phase normalised to the reference value, usually to air permeability $\begin{array}{l}k_{air}\end{array}$ :

(1)	$\begin{array}{l}\displaystyle k_{r\alpha} = \frac{k_\alpha}{k_{air}}\end{array}$

Units = dimensionless

The concept of relative permeability implies that different phases sweep through the same rock and under the same pressure gradient at different pace even if their viscosities are the same.

It is closely related to Wettability.

The relative permeability depends on the current rock saturation:

(2)	$\begin{array}{l}\displaystyle k_{r\alpha} = k_{r\alpha}(s = \{s_\alpha\})\end{array}$

For 3-phase Oil + Gas + Water fluid model this is going to be:

(3)	$\begin{array}{l}\displaystyle k_{rw} = k_{rw}(s_w, s_g)\end{array}$

(4)	$\begin{array}{l}\displaystyle k_{ro} = k_{ro}(s_w, s_g)\end{array}$

(5)	$\begin{array}{l}\displaystyle k_{rg} = k_{rg}(s_w, s_g)\end{array}$

Mathematical models of relative permeability are called RPM.

The usual practice is to build 2-phase RPM based on SCAL data and then use 3-phase correlations (see table below).

In case the 2-phase SCAL data is insufficient or highly scattered one can use 2-phase ROM correlations (see table below), calibrated to whatever SCAL and production data available.

2-phase RPM correlations	3-phase RPM correlations
Corey Oil+Water RPM Corey Oil+Gas RPM	Baker Stone I Stone II Ternary Phase Diagram

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Reference

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Relative Permeability (RelPerm)

See also

Reference