Separation Power ◾  17
performance with cyclohexane and n-heptane would have 49.3
mol% cyclohexane in the distillate and 10.0 mol% cyclohexane
in the bottoms, that is, the separation power = (49.3/50.7)/
(10/90) = 8.75.
The Fenske 2 equation gives the minimum number of theoretical stages required to achieve a desired separation power at
total reflux for a constant relative volatility (Equation 3.3):
N = Ln [(x 1 /x 2 ) D /(x 1 /x 2 ) B ]/Ln α
(3.3)
where:
N = Number of theoretical stages at total reflux
For example, Ln[(49.3/50.7)/(10/90)]/Ln 1.72 = 4.0 for the
cyclohexane/n-heptane distillation at total reflux shown in
Table 3 .2.
In the control of distillation columns, the distillate composition is often close to 100% light component 1, and the bottoms is close to 100% heavy component 2, so the key impurity
separation power can be calculated for control purposes from
Equation 3.4.
Key Impurity Separation Power =
10 , 000
(3.4)
(wt% hea avy key in Distillate × wt% light key in Bott toms)
In other words, the key impurity separation power is indicated by the reduction of heavy key impurity from the distillate and the reduction of light key impurity from the bottoms.
The maximum separation power that a distillation tower
can achieve would be at total reflux, that is, total boilup and
reflux with zero feed rate. One rule of thumb for an economical design of a distillation column is to use 2.0 times the
minimum number of theoretical stages. This generally coincides with a design for about 1.3 to 1.5 times the minimum