Page 14 - Academic Press Encyclopedia of Physical Science and Technology 3rd Chemical Engineering

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Encyclopedia of Physical Science and Technology EN001H-01 May 7, 2001 16:18

Absorption (Chemical Engineering) 11

in such case, a large column height is required to achieve
a reasonable level of absorption.

3. Multicomponent Absorption
The above derivations can be extended to multicomponent
absorption, making use of Eqs. (8) as described by Hobler
and by Sherwood et al. (1975) and giving

y 1 dy

y fm
N OG = (19a)
1 − ty y − y ∗
y 2
and
G M
H OG = , (19b)
K ay ∗
OG fm
where y ∗ and t are given by Eqs. (8d) and (8e), respec-
fm
tively.
B. Stagewise Contactors
Tray columns and sometimes also packed and spray
columns are described in terms of a stage model. An ideal
or theoretical stage is hypothetical device in which the gas
and liquid are perfectly mixed, contacted for a sufficiently
long period of time so that equilibrium is attained, and
then separated. The gas leaving the stage is therefore in
equilibrium with the liquid leaving the stage. In practice,
complete equilibrium can never be attained, since infinite
contact time is required to achieve equilibrium. A factor
used to account for this nonideality is stage efficiency.

1. Material Balances
An absorber is often modeled as a device that contains
a finite number of ideal stages (Fig. 9), with countercur-
rent flow of vapor and liquid. As the gas rises from stage
to stage, it contains less and less of the solute, which is
transferred to the solvent.
A material balance can be written for envelope 1 in
Fig. 9. FIGURE 9 Schematic diagram of a stagewise absorber.
(20)
L M,0 x 0 + G M,n y n = L M,n−1 x n−1 + G M,1 y 1
The equation can be expressed in terms of the flows enter-
L M,0 = L M,1 = L M,2 =· · · = L M,n−1
ing the absorber, that is, the solute-free solvent entering at
the top, and the rich gas, such that = L M,n =· · ·= L M,N (23a)

y = yG M /G M (21a)
G M,0 = G M,1 = G M,2 =· · ·= G M,n−1

x = xL M /L M (21b)
= G M,n =· · ·= G M,N (23b)
Substituting Eqs. (21a) and (21b) in Eq. (20) gives
and Eq. (22) can be simplified to give

L x + G y = L x + G y (22)
M,0 0 M,n n M,n−1 n−1 M,1 1
L L

Since the feed flows G and L do not change throughout M M

M M y = x n−1 + y − x 0 (24)
1
n
the contactor, G M G M