Distillation - Principles of Chemical Separations with Environmental Applications - page 112

min. reflux
x D

actual L V line

F 1 :sat'd vapor ( q -line)

F 2 :subcooled liquid ( q -line)

Figure 4.20 When q -lines cross.

What if the feed lines cross?

The minimum reflux ratio is still determined by the intersection of the operating line from
x D with the q -line which intersects the equilibrium line furthest up the column.
Stepping off stages : starting from x D , step off stages until you reach a q -line, then shift
to new operating line for optimum feed location. For Example 4.5 (Figure 4.20), F 1 would
be introduced above F 2 in the column.

Stage efficiencies

In the McCabe-Thiele analysis thus far, ideal equilibrium stages, or those with per-
fect efficiencies, have been assumed. An ideal stage is one in which thermodynamic
equilibrium between vapor and liquid phases entering each stage is reached before the
streams exit the stage. Non-ideal stages, or those with less than perfect efficiencies, do
not reach thermodynamic equilibrium. Two approaches exist for determining the num-
ber of real stages required to perform a separation as a function of the number of ideal
stages.
The first method uses an overall efficiency,

η :

theoretical (equilibrium) stages
actual stages

η = × 100(%) .

The number of real stages, then, is merely the number of ideal stages divided by the overall
efficiency. While this method is simple to use, the difficulty is in obtaining a value for the
overall efficiency of a column. In addition, the efficiency often varies from stage to stage,
making a single overall value somewhat meaningless. Often, if efficiencies of individual
stages can be estimated, they are averaged to give an overall value.
The second method used is the Murphree vapor efficiency:

y n − y n − 1

E MV =

y n − 1 ×

100(%) ,

y n −