1 KOZENY-CARMAN EQUATION REVISITED Jack Dvorkin -- 2009 ...
1 KOZENY-CARMAN EQUATION REVISITED Jack Dvorkin -- 2009 ...
1 KOZENY-CARMAN EQUATION REVISITED Jack Dvorkin -- 2009 ...
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€<br />
€<br />
€<br />
€<br />
€<br />
space is<br />
4Mπr 2 . Therefore, for this specific case,<br />
s = 3(1− φ 0 ) /r = 6(1− φ 0 ) /d, (8.2)<br />
€<br />
where d = 2 r.<br />
Note that this equation is only valid for a sphere pack with porosity<br />
we assume that the same equation applies to the entire porosity range, which is clearly<br />
€<br />
invalid since s should be generally decreasing with decreasing porosity, we obtain form<br />
€<br />
Equations (8.1) and (8.2)<br />
2<br />
€ r φ<br />
k = absolute<br />
18<br />
3<br />
(1− φ) 2 2<br />
d φ<br />
= 2<br />
τ 72<br />
3<br />
(1− φ) 2 , (8.3)<br />
2<br />
τ<br />
where<br />
d = 2 r.<br />
(Mavko and Nur, 1997) as<br />
€<br />
14<br />
φ 0 ≈ 0.36. If<br />
We can also modify this last equation by introducing a percolation porosity<br />
k absolute =<br />
2<br />
d (φ − φ p)<br />
€<br />
72<br />
3<br />
(1− φ + φ ) p 2 , (8.4)<br />
2<br />
τ<br />
The corresponding curve for<br />
€<br />
φ p = 0.025,<br />
tortuosity τ = 0.25 is plotted in Figure 8.1.<br />
€<br />
€<br />
φ p<br />
d = 0.25 mm = 0.00025 m, and constant<br />
Figure 8.1. Black curve: permeability versus porosity for shrinking pipes with the tortuosity given<br />
by Equation (7.6). Red curve: permeability versus porosity according to Equation (8.4) with<br />
parameters described in the text.
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