@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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1014.24 \cdot {\rm FZI}^2 \cdot \frac{(\phi -\phi_0)^3}{( 1 - \phi+\phi_0)^2} |
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| {\rm FZI} = \frac{1}{\sqrt{F_S} \, S_{gV} \, \ |
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where
LaTeX Math Inline |
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body | --uriencoded--%7B\rm FZI%7D |
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| Flow Zone Indicator | LaTeX Math Inline |
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body | --uriencoded--S_%7BgV%7D = \ |
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phieffective porosity | ...
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RQI = FZI \phi_r |
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The alternative form is derived from the correlation which is valid in some practical cases
D_g | :
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anchor | FZI_dgd |
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alignment | left |
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FZI\frac{1}{\sqrt{F_S} \sim, D_gS_{gV}} \approx 0.0037 \cdot d |
where
so that Absolute permeability is going to be и предполагается постоянным для каждой литофации
Явное выражение проницаемости в модели Кармана-Козени дается следующей формулой:
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k = 1014.24\frac{d^2}{72 \,cdot FZI^2\tau^2} \,cdot \frac{\phi^3(\phi -\phi_0)^3}{( 1 - \phi )^2}+\phi_0)^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: LaTeX Math Block |
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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
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Petroleum Industry / Upstream / Subsurface E&P Disciplines / Petrophysics / Absolute permeability / Absolute permeability @model
References
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J. Kozeny, "Ueber kapillare Leitung des Wassers im Boden." Sitzungsber Akad. Wiss., Wien, 136(2a): 271-306, 1927.