download pdf version of PhD book - Universiteit Utrecht

4.4 Macro-scale adsorption coefficients
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
the dependency decrease at higher velocities. This behavior is to be expected
considering the power, 0.05, of the velocity term in Equation (4.9). This means
that dependence on velocity is significant only for small velocities.
Figure 4.8: Detachment rate coefficient as a function of average pore
water velocity.
4.4.3 Core-scale distribution coefficient (K c D )
We define the core-scale distribution coefficient, K c D , as
K c D
= kc att
k c det
(4.15)
Since we obtained core-scale coefficients, katt c and kdet c , we can calculate upscaled
distribution coefficient. The result is shown in Figure (4.9). It is evident
that K c is a linear function of the pore-scale distribution coefficient, k D
d. This
linear relationship is a verification of our upscaling process. Since both K c D
and k d are a measure of the capacity of the porous medium to adsorb mass,
and given the fact that k d is kept constant for all pores, they should be linearly
related. We have found that the proportionality constant in this linear relation
is equal to the solid specific surface area, S (the solid surface area divided by
the total sample volume) i.e. K c = Sk D d. Since in our pore-network model, adsorption
is taking place only in the pore throats (pore bodies are considered to
be non adsorptive), we use only the surface of pore throats to calculate specific
surface. Figure (4.9) is based on results from a network with the value of S
equal to 5.28 × 10 3 m −1 , which is exactly the slope of the line fitting the data
points.
81