5.14: Untitled Page 112

Chapter 5

To illustrate the graphical construction associated with Eqs. 5‐95 and 5‐96 we consider the Type I problem discussed in Sec. 5.6.1 and repeated here as Type I: Given the inlet mole fractions, ( x ) and ( y )

, the

A o

A N1

system parameters, and the desired value of ( y ) , we would like to A 1

determine the number of stages, N.

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

( y )

0 010

.

, and the system parameters, K

 2 2

. 5 , M



97.5 kmol/h and

A N 

1

eq,A

 

M



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

 

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

.

. The equilibrium line associated with Eq. 5‐96 is given directly by A 1

Equilibrium line:

y

 2 2

. 5 x

(5‐97)

A

A

while the construction of the operating line associated with Eq. 5‐95 requires that we assume the value of ( y ) in order to obtain

A 1

Operating line:

y

 3 25

.

x

 0 001

.

(5‐98)

A

A

This approach is comparable to our use of Eq. 5‐91 in Example 5.9 where the analysis of a Type I problem required that we specify ( y ) in our search for the A 1

number of stages associated with 1

N

 A  ...  A .

Given the operating line and the equilibrium line, we can construct the operating points and the equilibrium points and this is done in Figure 5‐15. Some of these points are identified by numbers such as

while others are identified by

solid dots such as !. In order to connect the graphical analysis shown in Figure 5‐15 with the sequential analysis given in Sec. 5.6.1, we recall Figure 5‐11 in the form given below by Figure 5‐16. There we have clearly identified Points #1,

#2 and #3 in the graphical analysis with those same pairs of values in the sequential analysis. In Figure 5‐15 and in Figure 5‐16 we see that Point #1

represents a point on the operating line, that Point #2 represents a point on the equilibrium line, and that Point #3 represents a second point on the operating line.

Two‐Phase Systems & Equilibrium Stages

205

Figure 5‐15. Graphical analysis of a cascade of equilibrium stages Figure 5‐16. Mole balance around Unit #1

206