Question

A wastewater plant needs to reduce the methane content in water in a stripping tower to 0.3 mol %. The liquid stream is entering the tower with a flow rate of 200 mole/h and contains 0.8 mol % methane. The tower uses pure air for stripping and its temperature and pressure are held constant at 300 K and 1 atm, respectively. The equilibrium relation for methane in the air-water system is ? = 1.2?. a) Find the minimum vapor flow rate required to achieve this separation. B) Find the number of stages required if the vapor flow rate is taken as 1.2 ???? ′ .

Answer 1

a)

The operating line for the stipping operation is given by:

L (x2 - x1) = V (y2 - y1)

which can be arranged to give:

L / V =  (y2 - y1) / (x2 - x1)

where :

L = Liquid flowrate

x2 = mole percent of solute in liquid stream entering

x1 = mole percent of solute in liquid stream leaving

y2 = mole percent of solute in air stream leaving

y1 = mole percent of solute in air stream entering

For minimum air flow rate; L / V ratio should be maximum. This is possible when air leaving the stipper has maximum solute in it. This maximum solute is equal to the equilibrium concentration of solute.

The equilibrium relation is given by:

y = 1.2 x

Therefore; for maximum separation or minimum flowate of air

y2 = 1.2 x2

Substituting this in the operating line equation:

L / Vmin =  (1.2 x2 - y1) / (x2 - x1)

We have;

L = 200 mol / h

x2 = 0.8

x1 = 0.3

y1 = 0 ( pure air )

Substituting these values we get:

200 / Vmin =  (1.2 X 0.8 - 0) / (0.8 - 0.3)

200 / Vmin = 1.92

Vmin = 200 / 1.92 = 104 mol / h

which is the required minimum air flow rate.

b)

To calculate the number of stages required; we need to find the actual air flowrate and actual concentration of solute in air leaving.

Given:

V = 1.2 Vmin

Therefore:

V = 1.2 X 104 = 124.8 mol / h

The actual y2 can be obtained using the equation of operating line:

L / V =  (y2 - y1) / (x2 - x1)

200 / 124.8 = (y2 - 0) / (0.8 - 0.3)

1.6 = y2 / 0.5

which gives ;

y2 = 0.8

The number of Stages can be obtained by the kremser equation which is given by:

where :

m = partition coefficient = 1.2

A = L / mV = 200 / (1.2 X 124.8) = 1.34

Subtituting all the values in the Kremser equation:

which on solving gives:

N = 2.9

which is approximately equal to 3

Therefore:

Number of stages = 3