Page 252 - Adsorption Technology & Design, Elsevier (1998)

228 Selected adsorption processes

difficulties of packing adsorbent solids homogeneously, large-scale
chromatographic processes would be a most helpful method of separating
components from gases or liquids when the relative volatilities of the
constituents of the mixture are too low for distillation, or the separation
factors of components are too small for either pressure or thermal swing
adsorption. One large-scale liquid phase chromatographic separation of
xylene from ethylbenzene has been designed by the Asahi Company (Seko
et al. 1979 and 1982).
The concept of the height equivalent of a theoretical plate (HETP),
which is common terminology in the subject of chromatography, is useful
when referring to column separation efficiencies. Any chromatographic
column is considered to consist of a finite number of hypothetical or
theoretical plates on each of which equilibrium is established between the
fluid and solid phases. The larger the number of theoretical plates in a
column of length L the better the separation of the components of a
mixture, which depends on the relative strength of adsorption of each
component and the rate of mass transfer between the fluid and solid.
Mathematical models of the chromatographic column consist of both dis-
cretized representations (in which the column is represented as a finite
number of mixing cells where mass transfer and equilibrium occur) and
continuous flow models with axial dispersion of the fluid and linear mass
transfer kinetics as given by Glueckauf and Coates (1947) and alluded to
in Section 4.4. Villermaux (1981) has discussed the equivalence between
these two alternative model descriptions. The height equivalent of a
theoretical plate, HETP, may be measured in terms of the output response
signal obtained when an input concentration of a component is injected as
a pulse into the column. The output response can be characterized by the
first moment, /~, about the origin of the output signal and the second
central moment or variance o -2 . The first moment gives the location of the
centre of gravity or mean of the peak and the second moment measures
the dispersion of the data from the mean. The number of theoretical
plates required in a column to obtain resolution between component
chromatographic peaks is expressed by N (= /~2/cr2) and the height
equivalent of a theoretical peak is given by HETP (= Ltr2/112). Considering
a continuous model of a chromatographic column with bed voidage e, axial
dispersion (dispersion coefficient DL), a rate proportional to the driving
force between fluid and solid (rate coefficient k) and a linear adsorption
isotherm relating the concentrations in the fluid and adsorbed phases,
Villermaux (1981 ) showed that
Lcr 2 2DL e 1 e
= + 2u 1 + (7.21)
HETP = p2 u ~-e k-K ~-e