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3. Upscaling of Adsorbing Solutes; Pore Scale
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The CXTFIT curve-fitting program [Toride et al., 1995] was used for the purpose
of solving Equations (3.35) and (3.36) and fitting to the breakthrough
curves. Figure (3.4) shows an example fit to a breakthrough curves and the
corresponding parameters. Through the fitting process, we have been checking
the covariance matrix to make sure that parameters are not correlated.
This procedure was repeated for a range of pore-scale parameters (1 < P e p <
Figure 3.4: The resulting breakthrough curves for pore-scale (circles)
and 1D upscale (solid line) models. In this illustration, at the porescale
parameters are: P e p = 35 and κ = 5.0. And the corresponding
upscaled parameters by fitting found to be: katt ∗ = 0.14 and kdet ∗ = 0.05.
Using Equation (3.38), P e will be 1.3.
300, and 0.1 < κ < 20), and finding the corresponding upscaled k ∗ att and k ∗ det
we could determine relations between these set of parameters. Figures (3.5)
and (3.6) show the resulting plot of k ∗ att and k ∗ det as functions of P e p and κ.
From the relations shown in Figures (3.5) and (3.6), we found the best fit
formulas (through minimizing the least squares) for k ∗ att and k ∗ det
k ∗ att = 4.0(1 − e−3κ )
P e p
0.95
(3.40a)
k ∗ det =
9.0
(0.5 + 4.5κ)P e p
0.95
(3.40b)
We define the upscaled distribution coefficient (K D ) by:
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