Page 203 - Separation process principles 2

168 Chapter 5 Cascades and Hybrid Systems

where stage. Equation (5-46) now becomes

and lo = 0. From equilibrium considerations for stage N, the
When multiplied and divided by (A, - I), (5-47) reduces to a
definition of the vapor-liquid equilibrium ratio or K-value
can be employed to give

Combining (5-34), (5-33, and (5-36), VN becomes Note that each component has a different A, and, therefore, a '
different value of +A. Figure 5.9 from Edmister [3] is a plot
of (5-48) with a probability scale for +A, a logarithmic scale
for A,, and N as a parameter. This plot, in linear coordinates,
was first developed by Kremser [2].
An absorption factor A, analogous to the extraction factor, E,
Consider next the countercurrent stripper shown in Fig-
for a given stage and component is defined by
ure 5.8b. Assume that the components stripped from the liq-
uid are absent in the entering vapor, and ignore condensation
or absorption of the stripping agent. In this case, stages are
numbered from bottom to top to facilitate the derivation. The
Combining (5-37) and (5-38),
pertinent stripping equations follow in a manner analogous
to the absorber equations. The results are

Substituting (5-39) into (5-33),
where
s, - 1
The internal flow rate, is eliminated by successive sub- 4% = = fraction of species in entering
stitution using material balances around successively s:+' - 1 liquid that is not stripped (5-50)
smaller sections of the top of the cascade. For stages 1
1
KV
through N - 2, S = - - = stripping factor
=
L A
~N-I = (1~-2 + VI)AN-I (5-41)
Figure 5.9 also applies to (5-50). As shown in Figure 5.10,
Substituting (5-41) into (5-40),
absorbers are frequently coupled with strippers or distil-
lation columns to permit regeneration and recycle of
absorbent. Since stripping action is not perfect, recycled
Continuing this process to the top stage, where 11 = vlAl,
absorbent entering the absorber contains species present in
ultimately converts (5-42) into the vapor entering the absorber. Vapor passing up through
the absorber can strip these as well as the absorbed species
introduced in the makeup absorbent. A general absorber
equation is obtained by combining (5-45) for absorption of
A more useful form is obtained by combining (5-43) with the
species from the entering vapor wit11 a modified form of
overall component balance
(5-49) for stripping of the same species from the entering
liquid. For stages numbered from top to bottom, as in Fig-
ure 5.8a, (5-49) becomes
to give an equation for the exiting vapor in terms of the
entering vapor and a recovery fraction:

or, since
where, by definition, the recovery fraction is

1
$A =
...
...
AIA~A~ AN+A~A~ AN+A 3...AN+...$AN+1
= fraction of species in entering vapor that is not (5-46) The total balance in the absorber for a component appearing
absorbed in both entering vapor and entering liquid is obtained by
adding (5-45) and (5-53) to give
In the group method, an average effective absorption
factor, A,, replaces the separate absorption factors for each