@wikipedia
One of the Absolute permeability models based on simulating the flow through the multi-pipe conduits or multi-grain pack:
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| k = 1014.24 \cdot {\rm FZI}^2 \cdot \frac{(\phi_f -\phi_{f0})^3}{( 1 - \phi_f+\phi_{f0})^2} |
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| {\rm FZI} = \frac{1}{\sqrt{F_S} \, S_{gV} \, \tau } |
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where
The alternative form is derived from the correlation which is valid in some practical cases:
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\frac{1}{\sqrt{F_S} \, S_{gV}} \approx 0.0037 \cdot d |
where
so that Absolute permeability is going to be:
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k = \frac{d^2}{72 \cdot \tau^2} \cdot \frac{(\phi_f -\phi_{f0})^3}{( 1 - \phi_f+\phi_{f0})^2} |
where
This correlation was historical the first physical permeability model, based on the fluid flow in porous media with simplified structure consisted of a bunch of independent capillaries with various diameters.
Later on it's been upgraded to percolation through inter-grain porous space which specifies the Flow Zone Indicator
as a function of grains size distribution, grain shape and packing.
The most popular correlation with a mean grain size
is given as:
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FZI = a \cdot D_g |
where coefficient
is a function of grain shape, packing, inter-grain clay and, as a consequence, of inter-grain
effective porosity .
See also
Petroleum Industry / Upstream / Subsurface E&P Disciplines / Petrophysics / Absolute permeability / Absolute permeability @model
References
J. Kozeny, "Ueber kapillare Leitung des Wassers im Boden." Sitzungsber Akad. Wiss., Wien, 136(2a): 271-306, 1927.
