# 5.12: Untitled Page 110

- Page ID
- 18243

## 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: