Distillation - Principles of Chemical Separations with Environmental Applications - page 87

analysis. For a binary system we can define the relative volatility of the two species to
be separated in terms of the more volatile component, A , with respect to the less volatile
one, B :

y A / y A /

K A
K B =

x A x A

α AB =

x B = x A ) .

(4.1)

y B /

− / −

(1 y A ) (1

Higher relative volatilities correspond to easier separation by distillation. The greater
the slope of the vapor vs liquid ( y A vs x A ) equilibrium line, or the larger the difference
between y A and x A , the easier the separation. The relative volatility must exceed one but,
realistically, must be greater than 1.3 for distillation processes [2]. It is important to note
that α AB is dependent on pressure and that it is not necessarily constant over a composition

range.

4.3 Batch distillation

Batch distillation is often applied to separations in which small amounts of materials are
processed or in which the plant does not operate continuously. It is versatile, such that
the same equipment can be used for several products of varying composition at different
times. The distillate, which is typically much more volatile than the liquid from which it
is being recovered, is usually the product.
In batch distillation, a feed mixture is charged into a batch still where steam heat is
supplied. The product is removed from the top of the column until the process is complete,
after which the steam supply is discontinued and the remaining liquid in the still is removed.
Batch systems, as shown in Figure 4.1(a) and (b), can either be single staged, in which the
feed is charged into the reboiler, or multistaged, where a packed or tray column is placed
above the reboiler. Single-staged units are similar to flash distillation units, except that
feed and product streams are not continuous. In multistaged processes, reflux is returned
to the column during the duration of the run. Product can either be removed continuously
during the run or stored in the accumulator until the composition is of the desired quality.
In the unusual case where the bottoms is the desired product, inverted batch distillation is
applied. In this case, the bottoms liquid is continuously removed.
Because it is not continuous, the mathematical analysis of batch distillation is based on
the total quantities. For a binary system in which the distillate is the desired product, the
overall mass balance at the end of a batch run is

F = B + D (4.2)

where F is the mass of feed charged into the process initially and D and B are the
final masses of distillate and bottoms, respectively. For the desired component, the mass
balance is

Fx F = Bx B , f + Dx D , avg (4.3)