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Excerpt
LaTeX Math Block
anchorISW80
alignmentleft
s_{wi}(h) = 1 - a \exp \left( -\left(\frac{b}{h-h_{FWL}+cd}\right)^d^c \right)

where model parameters 

LaTeX Math Inline
body\{ a, \ b, \ c, \ d \}
  are calibrated on water saturation from OH logs for each lithofacies or petrotype individually.

The coefficient 

LaTeX Math Inline
bodyc
 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 

LaTeX Math Inline
body\phi
and/or permeability
LaTeX Math Inline
bodyk_a
:

LaTeX Math Block
anchorY202C
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a = a(\phi, k_a), \; b = b(\phi, k_a), \; c = c(\phi, k_a)

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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

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SPE 71326, B. Harrison (Enterprise Oil), X.D. Jing (Imperial College, London), Saturation Height Methods and Their Impact on Volumetric Hydrocarbon in Place

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