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

k_{rw} = k_{rw}(s_w, s_g)

k_{ro} = k_{ro}(s_w, s_g)

k_{rg} = k_{rg}(s_w, s_g)

Mathematical models of relative permeability are called often abbreviated 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.

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See also

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Physics /  Fluid Dynamics / Percolation

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Petroleum Industry / Upstream / Subsurface E&P Disciplines / PetrophysicsField Study & Modelling 

[ PermeabilityPetrophysics ] [ Absolute permeabilityBasic reservoir properties ] [ Wettability ] [ Permeability ] [ Absolute permeability ]  [Relative permeability] 

Reference

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[1] Fekete – Relative Permeability Correlations