Page 164 - Air pollution and greenhouse gases from basic concepts to engineering applications for air emission control

138 5 Principles for Gas Separation

ratio defined by the minimum operating line. Once it is determined, the actual oper-
ating liquid-to-gas ratio is set higher than this minimum ratio.
The minimum liquid-to-gas flow ratio can therefore be determined using the
above Eq. (5.26) based on the equilibrium value of X ,

0
Y 0 Y 1

L

G min ¼ X X 1 ð5:35Þ
0
x
0
X ¼ ð5:36Þ
0
1 x
0

and X would be the maximum possible mole ratio of the target gas in the liquid
0
phase if it were allowed to come to equilibrium with the gas entering the tower in

the gas phase. x can be taken from the equilibrium line with the inlet gas inlet y 0 or
0
determined using Eq. (5.37).
x ¼ Py 0 =H ð5:37Þ

0
Example 5.5: Absorption minimum operating line
A mixture of air and H 2 S is force to pass through a single-stage counter flow water
absorption scrubber. The inlet mole fraction of H 2 S in air is 50 ppmv. The total gas
flow rate into the scrubber is 80 mol/s and the pure water flow rate into the scrubber
is 10 mol/s. Assuming that the gas-water system is at equilibrium state at 30 °C, and
the atmospheric pressure is 101,325 Pa. Find the mole fraction of H 2 S in gas phase
at the exit. Assume that the system within the tower is air-H 2 S for gas and water-
H 2 S for liquid phases.
Solution
Since the air pollutant concentration in the air is very low and the consequent
concentration in the liquid phase should also be very low, the simplified mass

balance equation can be used to solve this problem. Substitute L = 10 mol/s,

G = 80 mol/s, x 1 = 0 mol H 2 S/mole water, y 0 = 0.00005 mol H 2 S/mole air into the
simplified mass balance equation (5.27) gives
10
5
y 1 ¼ 5 10 ð x 0 0Þ
80
The inlet mole fraction of H 2 S in the air can be determined from the assumption
of equilibrium state. Applying Henry’s law to the equilibrium state to the bottom of
the system gives

Py 0 ¼ Hx 0
where the Henry’s Law constant can be found from Table 2.4 as H = 609 × 1.
5
5
1 × 10 Pa/mole fraction in water at 30 °C and P = 1.013 × 10 Pa with y 0 =
−6
50 × 10 ,x 0 can be determined as