Page 253 - Adsorption Technology & Design, Elsevier (1998)

Selected adsorption processes 229

This equation should be compared with equation (4.46). For strong
adsorption (K >> 1) this becomes

(ee) 1
(7.22)
HETP- - ~
2DL + 2u
u 1 ~
Two important effects contributing to axial dispersion are molecular
diffusion and turbulent mixing. The axial dispersion coefficient may be
approximated (Langer et al. 1978) by

DL = 71DM + 72dpu (7.23)

When inserted into the approximate expression for HETP, the height
equivalent of a theoretical plate takes the form of the van Deemter et al.
(1956) equation

A
HETP =--+ B + Cu (7.24)
u

where A = 271DM, B - 272d p and C = 2e/(1 -e)kK. An efficient
chromatographic process would require HETP to be as small as possible.
The optimum fluid velocity giving the minimum HETP is, from the van
Deemter equation above, seen to be Uopt = (B/C) '/2. At values less than
Uopt peaks become broadened by molecular diffusion while for values greater
than Uopt broadening of peaks is mainly due to mass transfer resistances.
In plant-scale chromatography the duration of injections must be
sufficiently long (10-30 s) to ensure that a desired throughput of products is
maintained. The input pulses therefore have a rectangular profile (Figure
7.19). Le Goff and Midoux (1981) showed that the number of theoretical
plates necessary for complete resolution is given by

O'i 12
N react 1 + (7.25)
N pulse O'A~AB'/
where Np~ is the number of theoretical plates in the column if a small-
scale pulsed column were used, 4tri the duration of the rectangular injec-
tion, CrAB = (erA + trB)/2 and RAB = (tRA -- tRB)/40"AB, t~ for each of the
components A and B represents the retention time of the component
peak measured at a point on the time axis corresponding to its maximum.
Both 40"A and tRA refer to the mean retention time and approximate
width of a Gaussian elution band for component A as shown in Figure
7.20. Npul~ is calculated from the approximate relation N (= ju2/tr 2) =
16tR2/d 2.