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8.2 Zeotropic Mixtures 271

One can get from completely coupled sequences all the other feasible se-
quences, including columns with distributed components, if top sections are sup-
plemented with condensers and bottom sections are supplemented with reboilers.
For example, the sequence shown in Fig. 6.12d (with prefractionator and complex
column) can be obtained in this way.
The general algorithm of synthesis of all feasible sequence has to be started
with the sequence containing the maximum number of sections and the maxi-
mum number of heat exchangers. Each section of this sequence has at the end
one component fewer than at the beginning (i.e., in each top section, the heaviest
component disappears and, in each bottom section, the lightest component disap-
pears). Each top section of this sequence has a condenser, and each bottom section
has a reboiler. The example of such a sequence is shown in Fig. 8.1c. Then one
by one heat exchangers are excluded from this sequence (except the condenser
of the section where the lightest component is obtained and the reboiler of the
section where the heaviest component is obtained). After that, one by one the
nodes are excluded from this sequence and, for each new sequence, one by one
heat exchangers are excluded again.
With the increase of the number of components, the total number of feasible
sequences grows very quickly. The number of feasible groupings of sections grows
evenmorequickly.Nevertheless,theabove-describedalgorithmidentifiesallthese
sequences.

8.2.5. Examples of Synthesis of Separation Flowsheets
For synthesis of separation flowsheets from simple columns, the method of dy-
namic programming was developed (Kafarov et al., 1975). This method compares
systematically all feasible flowsheets at any number of components and to ex-
clude numerous repeated calculations of identical columns entering into various
sequences. The main idea of this method consists of the synthesis of sequences
step by step, moving from the end of sequence to the beginning (i.e., starting with
the smallest groups of components or pseudocomponents [I = 2], turning to big-
ger groups [to I = 3, then to I = 4, etc.] and obtaining optimum fragments of the
sequences). S I,J,K is annual expenditures on separation in column I,J,K, and F I,J
is expenditures on complete separation of the group of components or pseudo-
components I,J at optimal sequence for this group. Because column I,J,K in the
general case divides group I,J into two smallest groups, we get:

F I,J = min (S I,J,K + F K−J+1,J + F I−K+J−1,K+1 ) (8.5)
K I,J

Applying Eq. (8.5) to the gradually augmenting groups of components or pseu-
docomponents, one can find optimal values of K I,J for all these groups and the
corresponding values of expenditures F I,J . As a result, we get the optimal value
K n,1 for the separation in the first column and minimum expenditures F n,1 for the
separation of initial mixture: