Page 136 - Distillation theory

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110 Distillation Trajectories and Conditions of Mixture Separability

introduced in the works of Serafimov and coauthors (Serafimov, Timofeev, &
Balashov, 1973a, 1973b).
Numerous works (Levy, Van Dongen, & Doherty, 1985; Levy & Doherty,
1986; Julka & Doherty, 1990) in which distillation trajectory bundles of three-
and four-component mixtures for two sections of distillation column were used
at fixed product compositions and at different values of reflux (vapor) num-
ber, are of great importance. They defined the conditions of two section tra-
jectories joining in the feed cross-sections of the column in the mode of mini-
mum reflux, and they developed the methods of this mode calculation for some
splits.
However, numerous questions remained unsolved in these works: (1) the meth-
ods of prediction of possible product compositions for a given feed composition
were absent, which does not allow to calculate minimum reflux mode; (2) the
methods of calculation were good only for two special splits: direct and indirect
ones, but these methods were not good for the intermediate splits; (3) the peculiar-
ities arising in the case of availability of α-lines, surfaces, and hypersurfaces that
are characteristic of nonideal and azeotropic mixtures were not taken into con-
sideration; and (4) the sudden change of concentrations in the feed cross-section
was not taken into consideration.
Calculation investigations (Petlyuk, 1978; Petlyuk & Vinogradova, 1980; Shafir
et al., 1984) determined the conditions under which saddle and saddle-node sta-
tionary points of sections trajectory bundles at finite reflux arise inside the concen-
tration simplex, but not only at its boundary elements, promoted the development
of this trajectory bundles theory.
As far as stationary points of section trajectory bundles should be located at the
trajectories of reversible distillation, the systematic analysis of these trajectories
locations was of great importance (see Chapter 4).
The approximate calculation method of minimum reflux mode (Koehler,
Aguirre, & Blass, 1991) – the method of “the smallest angle,” which holds good
for mixtures with any component numbers and for any splits, including frequently
found at azeotropic mixtures separation cases of “tangential pinch,” is based on
the calculation of reversible distillation trajectories for the given product compo-
sitions.
The appearance of the “tangential pinch” in the mode of minimum reflux was
investigated in the works (Levy & Doherty, 1986; Fidkowski, Malone, & Doherty,
1991).
The approach to calculation of the minimum reflux mode, based on eigenvalue
theory, was introduced in the work (Poellmann, Glanz, & Blass, 1994). In contrast
to the above-mentioned works of Doherty and his collaborators this method cal-
culates the mode of minimum reflux not only for direct and indirect, but also for
intermediate split of four-component mixtures.
However,thismethodisnoteffectiveforthemixtureswithcomponentnumbers
greater than four and, besides that, does not take into consideration the leap of
concentration in feed cross-section.