One of the SHF models:

(1)	$\begin{array}{l}\displaystyle s_w(h) = \frac{b}{\phi} \; (h-h_{FWL}-c)^{\ a}\end{array}$

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

The coefficient $\begin{array}{l}c\end{array}$ 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 and/or permeability:

(2)	$\begin{array}{l}\displaystyle a = a(\phi), \; b = b(\phi), \; c = c(\phi)\end{array}$

References

1	Cuddy, S., Allinson, G. and Steele, R.: “A simple, convincing model for calculating water saturations in Southern North Sea gas fields”, Paper H, SPWLA 34th Annual Logging Symposium, June 13th – 16th (1993).
2	SPE 71326, B. Harrison (Enterprise Oil), X.D. Jing (Imperial College, London), Saturation Height Methods and Their Impact on Volumetric Hydrocarbon in Place Estimates, 2001

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References