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of the selected parameter on the total number of stages in
the column. This graphical method is highly intuitive, fast
and efficient. However, if there is more than one degree of
freedom, the more efficient NLP or MINLP optimization
method should be applied to find the best solution.
In this paper, we show how the examination of the
overall separation space can help in the creation of feasibleseparation schemes. We focus on the design of complex het-
erogeneous azeotropic distillation columns with decanters,
multiple feeds, and side stream draws, where an extra degree
of freedom requires a one-parameter optimization in order
to find the optimal solution among several feasible ones.
2. Getting feasible designs by examining separation
space
Let us consider separation spaces for two examples of
ternary azeotropic mixtures by labeling the azeotropes,
distillation boundaries, two-liquid phase regions and the
corresponding vapor lines. In Fig. 1, the water–acetic
acid–n-butyl acetate system shows one azeotrope and one
distillation region (the azeotrope is an unstable node, n-butyl
acetate is a stable node and the other components are sad-
dles). In the water–butanol–n-butyl acrylate system, shown
in Fig. 2, there are three binary azeotropes and one ternary
azeotrope. These azeotropes give rise to three distillation
regions (the ternary azeotrope is an unstable node, all bi-
nary azeotropes are saddles, and all pure components are
stable nodes).
In order to characterize a system, one requires knowledge
of the nature of all the azeotropes and pure components in
the system. This information is also necessary for distilla-
tion boundary calculation [3] since, for ternary systems, the
distillation boundaries are special residue curves that con-
nect azeotropes. The boundaries between distillation regions
restrict the products that can be obtained from a simple
distillation column (one feed, two products). As a rule, both
products should lie in the same distillation region [4,5].
Distillation boundaries can be crossed by mixing streams
or by decanting if the mixture forms multiple liquid phases
(e.g. the water–butanol–n-butyl acrylate system in Fig. 2).Fig. 2. Separation space for water–butanol–n-butyl acrylate as predicted by
a NRTL-Dimer model at 26.34 kPa. The system’s azeotropes, distillation
boundaries, liquid–liquid equilibrium region and vapor line has been
labeled.
The information about all azeotropes among a consid-
ered component set is of critical importance to the design
of azeotropic distillation systems. We compute tempera-
tures, compositions and stabilities (stable node, unstable
node or saddle) of azeotropes predicted by thermodynamic
models for multicomponent mixtures at a specific pressure
by the most reliable homotopy method combined with an
arc-length continuation [6]. In this method, we exploit an
efficient scheme for finding all stationary points of the boil-
ing surface, starting from pure component solutions for a
hypothetical ideal mixture described by the Raoult Law at
the beginning of the homotopy path (homotopy parameter
hD0). Then, we gradually ‘add non-idealities’ to our model
by increasing the homotopy parameter and, eventually, end-
ing with the rigorous model for hD1 [7]. This calculation
approach is very robust, since all solution branches are
connected. The eigenvalues of the Jacobian calculated at
stationary points give the stabilities of azeotropes and pure
components. Thereafter, we check the topological consis-
tency of the residue curve map via the Zharov and Serafi-
mov topological constraint [8]. The homotopy continua-