Page 160 - Air pollution and greenhouse gases from basic concepts to engineering applications for air emission control

134 5 Principles for Gas Separation

then the mass balance Eqs. (5.21) and (5.22) above can be simplified as

ð
ð Y Y 1 ÞG ¼ X X 1 ÞL ð5:24Þ

ð Y 0 Y 1 ÞG ¼ X 0 X 1 ÞL ð5:25Þ
ð
where Y and X are the mole ratio of pollutant to the corresponding fluid with unit of
(mole of pollutant per mole of solute free fluid). They are different from y and x: y
and x must be less than one but Y and X can be any values, although most often they
are also less than one.
Equation (5.25) can be rewritten as

L ð Y 0 Y 1 Þ

G ¼ ð X 0 X 1 Þ ð5:26Þ

The term on the left-hand side is called liquid to gas mole flow rate ratio. In a
design process, the mole ratio of the pollutant in gas phase, Y 0 , the carrier gas flow

rate G are likely known from the source of the air emission. The mole ratio of the
pollutant in liquid phase at the inlet, X 1 , is usually provided by the solvent supplier.
The two unknown parameters are the mole ratio of pollutant in the liquid phase X 0

and that is determined by the mole flow rate of the solute-free liquid (L).
Example 5.4: Liquid to gas ratio in absorption tower
A mixture of air and H 2 S is forced to pass through a single-stage counter flow water
absorption scrubber. The inlet mole fraction of H 2 S in air is 50 ppmv and outlet
being 10 ppmv. Outlet H 2 S in water is 20 ppmv. The total pure air flow rate into the
scrubber is 80 mol/s. What is the pure water flow rate into the scrubber?

Solution
From the problem description, we can get the following known parameters. For the
gas phase, the incoming mole fraction of H 2 S in the air is y 0 =50 × 10 −6 (mole
H 2 S/mole air) and the exiting mole fraction of H 2 S in the air is y 1 =10 × 10 −6 (mole
H 2 S/mole air). Then we can get the corresponding mole ratios as
50 10 6
y 0 6
Bottom/gas:Y 0 ¼ ¼ 6 50 10
1 y 0 1 50 10
10 10 6
y 1 6
Top/gas:Y 1 ¼ ¼ 6 10 10
1 y 1 1 10 10
Similarly for the liquid phase, the mole fraction of H 2 S in the incoming liquid
phase is x 1 = 0 (mole H 2 S/mole water) and exiting pollutant mole fraction in the
−6
liquid is x 0 =20 × 10 (mole H 2 S/mole water). The corresponding mole ratios are