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3.4 Discussion of results
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Figure 3.7: The relation between upscaled distribution coefficient
(K D = katt/k ∗ det) ∗ as a function of the pore-scale dimensionless distribution
coefficient, κ for the Single-Tube Model.
pore-scale distribution coefficient, κ, also shows the validity of our upscaling
process. Both K D and κ are a measure of the capacity of the porous medium
to absorb mass and thus they should be linearly related.
3.4 Discussion of results
Equations (3.40a) and (3.40b) can be converted to dimensional forms using
Equations (3.31) and (3.37). This gives
and
k att = 4.0(1 − k D
e−3 R0
) v 0.05 D0
0.95
R0
1.95
k det
= 9.0 v0.05 D0
0.95
(0.5 + 4.5 k D
R0
)R0
1.95
(3.42a)
(3.42b)
We observe that k att and k det are only weak functions of velocity but they
depend strongly on the geometry of the pore space and the diffusion coefficient
as well as the pore-scale distribution coefficient. We could compare Equations
(3.42) with corresponding equations derived using the averaging method in
Section 3.2.2. For the case of the Single Tube, it is plausible to assume that
c i∣ ∣
pore
, at a position somewhere between the pore center and pore wall (denoted
by w R0 , where 1.0 > w > 0) will be equal to the average fluid concentration,
c i . This means that in Equation (3.19) we may set
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