Distillation - Principles of Chemical Separations with Environmental Applications - page 105

D min ) corresponds to the lowest possible value of the
slope of the top operating line. On a McCabe-Thiele diagram this operating line begins
at the point y

The minimum reflux ratio ( L /

x D , and ends at the point where the feed and equilibrium lines
intersect. The slope of this operating line can then be used to find the minimum reflux
ratio.
In some cases, the operating line may intersect the equilibrium line below the inter-
section of the q and equilibrium lines. In general, the operating line corresponding to
minimum reflux can be constructed by rotating the line upward about the point y

= x =

x D
until the line contacts the equilibrium line at or above the feed line. [ Remember : slope of
top operating line

=

= R D / ( R D + 1).]

Total reflux

Total reflux is similar to minimum reflux in that it is not usually a real condition. In total
reflux, all of the overhead vapor is returned to the column as reflux, and all of the liquid
is returned as boilup, so that there are no distillate and bottom flows out of the column.
At steady-state, this means that the feed stream flowrate is also zero. Total reflux is used
in actual columns during start up and also to test their efficiency. Total reflux is useful in
a McCabe-Thiele analysis in order to find the minimum number of stages required for a
given separation.
Since all of the vapor is re fluxed , L

= V and therefore L / V = 1. The same is true in

the stripping section, so that L x line.

This is shown in Figure 4.10. The minimum number of stages required is determined by
stepping off stages using the equilibrium line and the diagonal ( y

/ V = 1. So both operating lines are now the y =

= x ) line.

y

y = x line

x B x D

x

Figure 4.10 McCabe-Thiele analysis for total reflux and minimum number of
plates.