Page 162 - Air pollution and greenhouse gases from basic concepts to engineering applications for air emission control

136 5 Principles for Gas Separation

The equilibrium line can be determined as follows. Equation (5.23) gives

x ¼ X=ð1 þ XÞ and y ¼ Y=ð1 þ YÞ
Substituting them into the Henry’s law Eq. (2.76)

Py ¼ Hx

We can describe the Henry’s Law in terms of the mole ratios (X and Y) instead
of the mole fractions (x and y),

Y H X
¼ ð5:29Þ
1 þ Y P 1 þ X
Manipulation of the equation gives the mole ratio in liquid phase as

H 1 þ Y
Y ¼ X ð5:30Þ
P 1 þ X
For most air emission control by absorption, the concentration of the target gas
in air is usually very low, which means X 1; Y 1. With this critical
assumption, which is justified in most applications, Eq. (5.30) can be simplified as

H
Y ¼ X ð5:31Þ
P
In order to differentiate the equilibrium line from the operating line, we put
forward two more terms, hypothetical or equilibrium mole ratio: Y* and X*. They
are defined as

H H

Y ¼ X Y ¼ X ð5:32Þ
P P
A line can be drawn from this equation on X-Y axes. Since this equation is
derived from the equilibrium assumption, it is called equilibrium line (see Fig. 5.4).
The slope of this line is

Hð1 þ YÞ H
m ¼ ð5:33Þ
Pð1 þ XÞ P

5.2.2.2 Absorption Operating Line

In operating an absorption tower in engineering practice, the equilibrium between
gas and liquid phase cannot be established because of the short residence time when
they encounter each other. Therefore, for a given gas mole ratio Y, the corre-
sponding liquid mole ratio X should be always less than the equilibrium mole ratio.