Page 202 - Separation process principles 2

5.4 Multicomponent Vapor-Liquid Cascades 167

Single equilibrium stage 5.4 MULTICOMPONENT
~ll three arrangements give identical results for a single stage. VAPOR-LIQUID CASCADES
From (5-13,
Countercurrent cascades are used extensively for vapor-
liquid separation operations, including absorption, stripping,
and distillation. For absorption and stripping, a single-
The corresponding fractional extraction is section cascade is used to recover one selected component
from the feed. For distillation, a two-section cascade is
effective in achieving a separation between two selected
components referred to as the key components. For both
More than one equilibrium stage cases, approximate calculation procedures relate composi-
(a) Cocurrent cascade. For any number of stages, the percent tions of multicomponent vapor and liquid streams entering
extraction is the same as for one stage, 70.6%. and exiting the cascade to the number of equilibrium stages
required. These approximate procedures are called group
(b) Crosscurrent cascade. For any number of stages, (5-21) ap-
plies. For example, for two stages, assuming equal flow rates methods because they provide only an overall treatment of
of solvent to each stage, the group of stages in the cascade, without considering
detailed changes in temperature, phase compositions, and
flows from stage to stage.
and the percent extraction is 79.3%. Results for other numbers
of stages are obtained in the same manner. Single-Section Cascades by Group Methods
(c) Countercurrent cascade. For any number of stages, (5-29) Kremser [2] originated the group method by deriving an
applies. For example, for two stages, equation for the fractional absorption of a species from a gas
into a liquid absorbent for a multistage countercurrent ab-
sorber. His method also applies to strippers. The treatment
presented here is similar to that of Edmister [3] for general
and the percent extraction is 89.1%. Results for other numbers
of stages are obtained in the same manner. application to vapor-liquid separation operations. An alter-
native treatment is given by Smith and Brinkley [4].
A plot of percent extraction as a function of the number of equi-
Consider first the countercurrent cascade of N adiabatic,
librium stages for up to five stages is shown in Figure 5.7 for each
equilibrium stages used, as shown in Figure 5.8a, to absorb
of the three arrangements. The probability-scale ordinate is conve-
nient because for the countercurrent arrangement, with E r 1, 100% species present in the entering vapor. Assume that these
extraction is approached as the number of stages approaches infin- species are absent in the entering liquid. Stages are num-
ity. For the crosscurrent arrangement, a maximum percent extrac- bered from top to bottom. It is convenient to express stream
tion of 90.9% is computed from (5-23). For five stages, Figure 5.7 compositions in terms of component molar flow rates, vi and
shows that the countercurrent cascade has already achieved 99% li, in the vapor and liquid phases, respectively. However, in
extraction. the following derivation, the subscript i is dropped. A mate-
rial balance around the top of the absorber, including stages
1 through N - 1, for any absorbed species gives
I I I
- -
- -
Countercurrent flow
Entering liquid Exiting Exiting
(absorbent) vapor Entering liquid vapor
Crosscurrent

N- I
Cocurrent flow N-2
- -
- -
- -
- -
20 - - Exiting Entering vapor Exiting
10 I I I Entering vapor In' liquid > (stripping agentn'' liquid +
1 2 3 4 5 VN+l, UN+1 LN, IN vo, uo Ll, 11
Number of equilibrium stages
(a) (b)
Figure 5.7 Effect of multiple-stage cascade arrangement on
Figure 5.8 Countercurrent cascades of N adiabatic stages:
extraction efficiency.
(a) absorber; (b) stripper.