Distillation - Principles of Chemical Separations with Environmental Applications - page 113

K ' (a)

(b)

L '

J '

Reboil

Reboil

L

y

K

J

x B x F x D x B x F x D

x x

Figure 4.21 Murphree efficiencies: (a) vapor phase, E MV , (b) liquid phase, E ML .

where y n = actual composition of V phase leaving the stage

y n

=

composition of hypothetical V phase that would be in equilibrium with
L phase leaving actual stage.

This method is more meaningful than the overall efficiency because it is based on the
difference between true operating and hypothetical equilibrium vapor-phase concentra-
tions. However, Murphree efficiencies also vary from stage to stage and require difficult
measurement of process variables.
The Murphree ef ficiency i s the ratio of distance between the operating line and the
equilibrium line ( = [ JK / JL × 100]% in Figure 4.21(a)). Similarly, the Murphree liquid

efficiency is given by:

x n − x n + 1

E ML =

x n + 1 ×

100(%) ,

x n −

[J K / J L × 100]% in Figure 4.21(b)).

Note: Remember that a reboiler is an equilibrium stage, even though the other stages in a
column will not reach equilibrium if they are not 100% efficient. Therefore, the last stage
(the one which gives x B ) will appear on the graph at the solid equilibrium curve, not on
the dashed curve. The dashed curve is a “pseudo-equilibrium” which describes the two
phases when they don't have a chance to completely reach equilibrium.

( =

Example 4.6: plutonium stabilization at Los Alamos National Laboratories [4]

Problem:
Currently, the nitric acid used in plutonium stabilization operations at a particular
facility is evaporated to remove dissolved solids, assayed for radioactive content and
then sent via underground pipe to a low-level waste handling facility. The acid stream
is then neutralized with caustic to remove radioactivity and the resulting solids are
immobilized in cement as a TRU (trans-uranic waste). The filtrate is then sent for