# 5.12: Untitled Page 110

## Chapter 5

In this case we are given the inlet mole fractions, ( x )  0 and A o

( y )

0 . 010 , and the system parameters, K

 2 5

. 3 , M

90 kmol/h

A N 

1

eq,A

 

and M

30 kmol/h . For these particular values, we want to know how

 

Figure 5.9. Multi‐stage gas‐liquid contacting device

many stages, N, are required to reduce the exit mole fraction of acetone to ( y )  0 001

.

. In this case we express Eq. 5‐91 as

A 1

( y )

N

A N

0 010

.

2

3

1

1  A A A .... A

 10 . 0

(1)

( y )

0 . 001

A 1

Two‐Phase Systems & Equilibrium Stages 201

in which the value of the absorption coefficient is given by A M

M

K

 1 186

.

. This leads to the values listed in Table 5.9

eq,A

where we see that 5 stages are insufficient to achieve the desired result, ( y )  0 001

.

. In addition, the use of 6 stages reduces the exit mole A 1

fraction of acetone in the air stream to ( y )  0 00081

.

which is less than

A 1

the desired result. For this type of situation, it is the responsibility of the chemical engineer to make a judgment based on safety considerations, environmental constraints, requirements for other processing units, and economic optimization. Such matters are covered in a future course on process design, and we have alluded to some of these concerns in Sec. 1.1.

Table 5.9. Number of stages, N, versus ( y )

( y )

A N

1

A 1

Number of stages, N

1 + A + A 2 + A 3 +….+ AN

1

2.186

2

3.592

3

5.260

4

7.238

5

9.584

6

12.366

Type II: Given the inlet mole fractions, ( x ) and ( y )

, the

A o

A N1

system parameters, and the number of stages, N, we would like to determine the value of ( y ) .

A 1

In this case we consider an existing unit in which there are 7 stages. The inlet mole fractions are given by ( x )  0 and ( y )  0 . 010 , and the A o

A 8

parameters associated with the system are specified as K

 2 5

. 3 ,

eq,A

M

90 kmol/h and M

30 kmol/h . In order to determine the mole

 

 

fraction in the  ‐phase (air) leaving the cascade, we make use of Eq. 5‐91

to express ( y ) as

A 1

( y )

A 8

( y )

(2)

A 1

2

3

4

5

6

1

7

A A A A A A A This leads to the following value of the mole fraction of acetone leaving the top of the cascade illustrated in Figure 5.9:

202