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4.5 Discussion
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Figure 4.10: Calculated values of the core-scale detachment coefficient,
kdet, c as a function of the local-scale distribution coefficient, k d ,
and mean pore-water velocity. The circles are data points and the
surface represents results of Equation (4.16) fitted to kdet c − k d − v data
points.
k c att = Kc D kc det = S k d
This equation may be approximated by
D 0.95
mol v0.05
(0.02 + 0.5k d )R 0.95 (4.18)
k c att = S D 0
0.5 R
(4.19)
which is the same as the equation derived through the averaging method by
Raoof and Hassanizadeh [2010a].
As mentioned above, Equations (4.16) and (4.18) were obtained based on results
from a specific pore network. We have verified these equations by applying
them to another pore network with the same pore-body size distribution as in
Figure (4.2) but with a different mean pore-throat size, as well as a network
with different pore-body size distribution and a mean pore-body diameter of
0.36 × 10 −3 m. Figures (4.11) and (4.12) show the results of the verification;
plotted lines are obtained from Equation (4.16) for these networks while the
circles indicate pore-network computations. It is evident that the agreement is
excellent.
Equations (4.16) and (4.18) show the upscaling relations for the core scale
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