Page 67 - Distillation theory

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3.2 Analogy Between Residue Curves and Distillation Trajectories 41

Themodeofinfiniterefluxisinterestingforusnotonlyasoneoflimitdistillation
conditions, but also mainly as a mode to which splits achievable in real columns
at finite but quite big reflux correspond. These splits are ones of distillation for
border mode between the second and third classes of fractioning.
The question of the reflux at which these splits are achievable in real columns
and of how, along with that, the distillation trajectory is located in the concentra-
tion space is discussed in Chapter 5. Here, we investigate only the splits themselves.
Often the splits for zeotropic mixtures are ones of sharp separation without
distributed components. At practice, these splits are the most widespread because
they are the sequences with the smallest number of columns (n − 1 column for
n-component mixture, if each component is a purpose product) that correspond
to them.
For azeotropic mixtures, not all the practically interesting splits are feasible at
the infinite reflux. However, the sequencing should have the infinite reflux mode as
its starting point because these splits are the easiest to realize at finite reflux. That
is why we start systematic examination of distillation trajectories with the infinite
reflux rate. It is also proved to be correct because the regularities of trajectories’
locations for this mode are the simplest.
The analogy with the process of open evaporation favored the fact that this
mode was investigated earlier than the others. Systematic examination of distilla-
tion at the infinite reflux was initially carried out in works (Zharov & Serafimov,
1975; Balashov & Serafimov, 1984). The analysis of infinite reflux mode in the
infinite columns was made (Petlyuk, 1979; Petlyuk, Kievskii, & Serafimov, 1977;
Petlyuk & Serafimov, 1983) that allowed general regularities of separation to be
defined for the mixtures with any number of components and azeotropes. A num-
ber of important investigations was realized (Doherty, 1985; Doherty & Caldarola,
1985; Laroche et al., 1992; Bekiaris et al., 1993; Safrit & Westerberg, 1997; Rooks
et al., 1998) and others.

3.2. Analogy Between Residue Curves and Distillation Trajectories
Under Infinite Reflux

Investigations of residue curves have been conducted for over 100 years, begin-
ning Ostwald (1900) and Schreinemakers (1901). Later, close correspondence
between residue curves (i.e., curves of mixture composition change in time at the
open evaporation) and distillation trajectories at infinite reflux (i.e., lines of mix-
ture composition change at the plates of the column from top to bottom) was
ascertained.
The similarity and the difference of these lines are defined by their equations:

dx i /dt = y i − x i = x i (K i − 1) (3.1)
(For residue curves, see Chapter 1.)
(k+1) (k) (k)
x = y = K i x (3.2)
i i i
[For distillation trajectories at the infinite reflux, see Chapter 2 Thormann (1928).]