Page 159 - Air pollution and greenhouse gases from basic concepts to engineering applications for air emission control

5.2 Absorption 133

exits at the bottom. At any cross section within the absorption tower, all the
molecules removed from the gas phase enter the liquid phase, then the mass balance
at any cross section within the tower gives

d GyÞ ¼ d LxðÞ ð5:18Þ
ð
where L and G are the mole flow rates of the liquid and the gas, respectively (mole/s).
y and x are mole fractions of the target pollutant in gas and liquid, respectively. Note
that both the gas phase and liquid phase mole flow rates (G and L) are variables
within the tower, because gas molecules leave the gas phase enter the liquid phase.
Integration of Eq. (5.18) from any point to top (1) leads to

yG y 1 G 1 ¼ xL x 1 L 1 ð5:19Þ

The gas phase contains the adsorbate molecules and the inert carrier gas (mostly
air), and their mole fractions are, respectively, y and 1 y. The liquid phase also
contains inert liquid and the pollutants absorbed from the gas phase, and their mole
fractions are, x and 1 x, respectively. The liquid phase without contamination is
called solute free liquid.

Denote the mole flow rates of the carrier gas and solute fee liquid as G and L,
respectively, which remain constant throughout the process.

L
G
G ¼ L ¼ ð5:20Þ
1 y 1 x
In reality, there may be some evaporation of liquid phase, and extra liquid is
added as make up liquid to keep the mass balance, but we have to ignore this in the

following analysis. With Eq. (5.20), Eq. (5.19) can be rewritten in terms of G and L
as

y x 1 x y 1

L ¼
G þ G ð5:21Þ
L þ
1 y 1 x 1 1 x 1 y 1
Applying this equation to the entire tower from bottom (0) to top (1) leads to:

y 0 y 1 x 0 x 1
G ¼ L ð5:22Þ
1 y 0 1 y 1 1 x 0 1 x 1
If we define the mole ratio of target gas to that of the corresponding fluid as
x y
X ¼ Y ¼ ð5:23Þ
1 x 1 y