Page 157 - Adsorption Technology & Design, Elsevier (1998)

Design procedures 145

In order to optimize a design it is desirable to carry out predictive
mathematical modelling of the heat, mass and momentum transfer pro-
cesses occurring in both the adsorption and the desorption stages in a
process. This helps to avoid the need to carry out expensive and time-
consuming experiments. Research on fixed bed adsorption is very active
and so a large number of models exist, each of which can be complex,
require extensive computation and need verification. The accuracy of the
predictions will be related to the accuracy and availability of fundamental
data as well as to the number and importance of the assumptions and
approximations which need to be made in order to obtain the solution. For
the simplest cases, or for those cases in which many simplifying assumptions
and approximations are made, the solutions can be analytical. For most
practical situations it is likely that the solutions will need to be obtained by
numerical analysis.
The concentration profile of a single adsorbate as it breaks through
from a fixed bed of length L is shown schematically in Figure 5.6 (a). For
a single component such a breakthrough curve can be obtained relatively
easily from laboratory-scale, pilot-scale or industrial-scale experiments by
placing an analytical sensor at the bed exit. For example, a katharometer
would suffice for a hydrocarbon. For multicomponent adsorption it would
be necessary to take samples from the bed effluent at different times for
subsequent analysis of composition. Breakthrough is deemed to have
occurred at some time tb when the concentration of the adsorbate leaving
the bed increases to an arbitrarily defined value, c~, which is often the
minimum detectable or maximum allowable concentration of the com-
ponent to be removed in the bed effluent. Figure 5.6 (b) shows the
concentration profile of the adsorbate in the fluid phase inside the bed at
time tb. At the point of initial breakthrough, the mass transfer zone
(MTZ) will have passed through the bed from its entrance to its exit at
L~. The fluid within the bed from the entrance up to L~ will be at the
same concentration as that of the feed, namely co. The adsorbent loading
in this region of the bed will be in equilibrium with the feed concentra-
tion. The MTZ will exist from L~ to the end of the bed L.
It is clearly possible to design a fixed adsorption bed by adding together
the lengths which correspond first to the equilibrium portion (0 to L~) and
second to the MTZ (L~ to L). The former length can be obtained from
a simple mass balance and requires that the equilibrium isotherm rela-
tionship is known (see Chapter 3). In contrast, rigorous and/or short-cut
techniques must be used to obtain the MTZ length and to determine its
rate of progress through the packed bed.