Distillation - Principles of Chemical Separations with Environmental Applications - page 97

equilibrium line are the mole fractions of the streams exiting each equilibrium stage.
Now the number of stages can be counted. Whenever the desired concentration falls
between two stages, the larger value is used. In this example, three stages will not quite
achieve the desired separation, but four stages will reduce the bottoms concentration
to less than 0.10 mol% solvent, which does not work with the mass balances solved
earlier. It is important to note that the graphical method is not exact, but it is much easier
than stage-by-stage calculations. The answer to the problem by the McCabe-Thiele
method is four equilibrium stages, but note that the concentrations produced by such
a column will probably not be equal to those specified in the problem statement (the
column should exceed specifications if it is operating efficiently).
The question then comes up of what do we adjust to change the design. The value
of x D is fixed so a change in the operating line means a change in slope. How would
we accomplish this? What is the limit? Why?

x -y diagram for SOLVENT/WATER

1

1

0.9

x D

0.8

0.7

2

0.6

0.5

0.4

3

0.3

0.2

x B

0.1

0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

LIQUID MOLE FRACTION SOLVENT

Figure 4.4 Graphical solution of enriching column, Example 4.2.