One of the SHF models:

where model parameters  $//<![CDATA[ \begin{array}{l}\{ a, \ b, \ c, \ d \}\end{array} //]]>$  are calibrated on water saturation from OH logs for each lithofacies or petrotype individually.

The coefficient  $//<![CDATA[ \begin{array}{l}c\end{array} //]]>$ is related to FWL correction but usually set the same for all lithofacies / petrotypes of a given reservoir unit.

If core data is abundant then one can build a reasonable correlation of model parameters on porosity  $//<![CDATA[ \begin{array}{l}\phi\end{array} //]]>$ and/or permeability $//<![CDATA[ \begin{array}{l}k_a\end{array} //]]>$:

See also

Physics /  Fluid Dynamics / Percolation

Petroleum Industry / Upstream / Subsurface E&P Disciplines / Field Study & Modelling / Petrophysics / Saturation Height Function (SHF) / SHF mathematical models

[ Basic reservoir properties ]

References

Harrison, B., and X.D. Jing. "Saturation Height Methods and Their Impact on Volumetric Hydrocarbon in Place Estimates." Paper presented at the SPE Annual Technical Conference and Exhibition, New Orleans, Louisiana, September 2001. doi: https://doi.org/10.2118/71326-MS