1 KOZENY-CARMAN EQUATION REVISITED Jack Dvorkin -- 2009 ...

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Also, if
a → b, the infinity in the denominator of the third term in the square
brackets in Equation (5.2) has the same order as that in the numerator, and
In Figure 5.2 we display the ratio ξ of the flux computed according to Equation
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(5.2) to that according to Equation (5.3):
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ξ = (1− €
a2 a2 a2 1
)[1+ + (1− ) ], 2 2 2
b b b ln(a /b)
(5.4)
which behaves predictably.
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q → 0.
Figure 5.2. Ratio of annular flux to that through a round pipe versus the normalized radius of a
kernel.
The total flux through
Q = Nq = −N
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π ΔP
8µ
N pipes with a kernel is
Lτ b4 (1− a2 a2
)[1+ 2
b b
Hence the absolute permeability is
kabsolute = N πb
Aτ
4
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(1− a2
b
2 )[1+ a2
The porosity of this block is now
φ = Nπ(b2 − a 2 )l
AL
The specific surface area is
a2
+ (1− 2
b b
a2
+ (1− 2
b
2 )
2 )
1
]. (5.5)
ln(a/b)
1
]. (5.6)
ln(a/b)
= Nπ(b2 − a 2 )τ
. (5.7)
A