One of the Absolute permeability models based on simulating the flow through the multi-pipe conduits or multi-grain pack:
|
|
where
{\rm FZI} | Flow Zone Indicator | S_{gV} = \Sigma_e/V_\phi | \Sigma_e | pore surface area | |
|---|---|---|---|---|---|
\phi | effective porosity | F_S | pore shape factor | V_\phi | pore volume |
\phi_0 | \tau | pore channel tortuosity |
The alternative form is derived from the correlation which is valid in some practical cases:
| (3) | \frac{1}{\sqrt{F_S} \, S_{gV}} \approx 0.0037 \cdot d |
where
d | average grain size |
so that Absolute permeability is going to be:
| (4) | k = \frac{d^2}{72 \cdot \tau^2} \cdot \frac{(\phi -\phi_0)^3}{( 1 - \phi+\phi_0)^2} |
where
k | absolute permeability |
\phi | effective formation porosity |
\phi_0 | porosity cut-off |
d | grain size |
\tau | pore channel tortuosity |
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:
| (5) | 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.