One of the SHF models: where model parameters
\{ a, \ b, \ c, \ d \} are calibrated on water saturation from OH logs for each lithofacies or petrotype individually. The coefficient
c 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
\phi and/or permeability
k_a:
(1)
s_{wi}(h) = 1 - a \exp \left( -\left(\frac{b}{h-h_{FWL}+c}\right)^d \right)
(2)
a = a(\phi, k_a), \; b = b(\phi, k_a), \; c = c(\phi, k_a)
See also
Physics / Fluid Dynamics / Percolation
Petroleum Industry / Upstream / Subsurface E&P Disciplines / Field Study & Modelling
[ Petrophysics ] [ Basic reservoir properties ] [ Saturation Height Function (SHF) ] [ SHF mathematical models ]
References
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