Absorption and stripping - Principles of Chemical Separations with Environmental Applications - page 164

Example 6.2: absorption column (Figure 6.4)

Problem:
Avent gas stream in a chemical plant is 15 wt% A ; the rest is air. The local pollution
authorities feel that A is a priority pollutant and require a maximum exit concentration
of 0.5 wt%. It is decided to build an absorption tower using water as the absorbent.
The inlet water is pure and at 25

◦ C. At 25 ◦ C, the laboratory has found that the

equilibrium data can be approximated by y = 0.5 x (where y and x are mass fractions

of A in vapor and liquid, respectively).
(a) Find the minimum ratio of water to air ( L / G ) min (on an A -free basis).

(b) With an L / G = 1.5( L / G ) min , find the total number of equilibrium stages.

Solution:
The first step is to plot the equilibrium curve using the given relationship (see
Figure 6.5). Since the known variables are given in mass fractions, the data will be
graphed as mass ratios instead of mole ratios. Rearranging the equilibrium equation in
terms of mass ratios

y = 0 . 5 x

y Y

Y =

y ⇒

y =

1 − 1 + Y

x X

X =

x ⇒

x =

X .

1 − 1 +

Substituting:

Y X

X .
Calculate exit concentrations as mass ratios:

Y =

0 . 5

1 + 1 +

0 . 05

y N + 1 = 0 . 05 Y N + 1 =

05 =

0 . 5

1 − 0 .

0 . 005

y 1 = 0 . 005 Y 1 =

005 =

0 . 005 .

1 − 0 .

Over this range of Y , the equilibrium line will be linear Y = 0 . 5 X .

G ) min . This is the case where the column would have
infinite stages, and corresponds to a pinch point. To draw the operating line with
minimum slope, connect ( X 0 , Y 1 ) and the point where the equilibrium line crosses the
value Y N + 1 . This second point is easily found from the equilibrium data and the two
points are used to find the slope:
L
G

The next step is to find ( L /

min =

Y N + 1 − Y 1 0 . 05 − 0 . 005 0 . 045

0 X 0 =

= = 0 . 45

X N − 0 . 1 − 0 . 1

5 L
G

min =

1 . 1 . 5(0 . 45) = 0 . 68 .