One of the Absolute permeability models based on the pipe conduit or multigrain pack:
| (1) | k = \frac{d^2}{72 \cdot \tau^2} \cdot \frac{(\phi_f -\phi_{f0})^3}{( 1 - \phi_f+\phi_{f0})^2} |
where
k | absolute permeability |
\phi_e | effective formation porosity |
\phi_0 | porosity cut-off |
d | grain size |
\tau | pore channel tortuosity |
| (2) | k = 1014.24 \cdot FZI^2 \cdot \frac{\phi^3}{( 1 - \phi )^2} |
where
The Flow Zone Indicator is considered to be constant within a given lithofacies.
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 FZI as a function of grains size distribution, grain shape and packing.
The most popular correlation with a mean grain size D_g is given as:
| (3) | FZI = a \cdot D_g |
where coefficient a is a function of grain shape, packing, inter-grain clay and, as a consequence, of inter-grain effective porosity \phi.
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.