Page 177 - Adsorption Technology & Design, Elsevier (1998)

Design procedures 165

6.7.1 Length of unused bed (LUB)
The LUB design method requires that constant pattern behaviour occurs.
It-provides the basis for a very simple design method which allows the
design and scale-up from small-scale laboratory experiments particularly
for dilute single-component systems in which there is a favourable
isotherm. A dilute system implies that the process will be isothermal. Care
must be taken if the process is not isothermal because it is possible for the
temperature effects to cause a favourable isotherm to take on effectively an
unfavourable shape.
Reference is made to Figures 5.6 (a) and 5.6 (b) in the following analysis
of the LUB concept. The length of the MTZ increases as the mass transfer
resistance increases in adsorption. However, for situations in which mass
transfer rates are very high, the process approaches equilibrium control and
the mass transfer front esb tends to become a straight line, or shock, dsc, and
is known as the stoichiometric front. The used adsorbent capacity is
represented by the area fesbaf (Figure 5.6(b)) while the unused adsorbent
capacity is represented by the area ehbse. The area fesbaf is equal to the area
fdcaf since the latter area up to the stoichiometric front also represents used
capacity.
Up to the stoichiometric point, s, the length (or weight) of equivalent
equilibrium section, LES (or WES) is represented by the area fesbaf. The
rest of the bed from the stoichiometric point, s, to the breakthrough point, b,
is equivalent to the length (or weight) of unused bed, LUB (or WUB),
because it is equivalent to a bed at the residual loading in the stoichiometric
interpretation. Thus the design of an adsorption bed can be obtained by
adding LES and LUB together. LUB is defined as follows:

LUB = ( 1 - ~] (6.53)

A single dynamic adsorption experiment which generates the entire
breakthrough curve shown in Figure 5.6(a) is sufficient to enable the
breakthrough time, tb, and the stoichiometric time, t~ to be determined. The
LUB depends only on the adsorbate-adsorbent combination, the temper-
ature and the fluid velocity. With constant pattern behaviour it is indepen-
dent of column length. The LUB can therefore be measured at the design
velocity in a small-scale laboratory column packed with the selected
adsorbent. The design of the full-scale adsorption column can be obtained
by simply adding the LUB to the length of bed needed to achieve the
required stoichiometric capacity (LES).
The LUB (WUB) method should not be used for adsorbate-adsorbent