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8.2 Zeotropic Mixtures 269

8.2.4. Systematic Identification of Alternative Sequences

At automatic synthesis of the best sequence from the big number of feasible al-
ternative sequences, one of the tasks is their systematic identification. This task is
quite easily solved for the sequences of simple columns without distributed com-
ponents. In this case, any column of any sequence can be identified by the number
of components in its feeding − I, by the number of the first of these components –
J, and by the number of the top product components – K (Kafarov et al., 1975)
(i.e., column I, J, K is column [J, J + 1, ..., J + K − 1: J + K,..., J + I − 1]).
It is supposed that all components were numbered beforehand in order of
decreasing volatility.
The values of parameters I and J should not include impurity components
entering into the feeding of the column under consideration. Pseudocomponents
(fractions) that have to be obtained as one product can act as components while
setting parameters I, J, and K.
The identification of complete set of sequences starts with the first column, for
which I (1) = n (total number of components or pseudocomponents of the mixture
under separation), J (1) = 1, and K (1) = 1÷ (I (1) – 1), i.e. (1 : 2, . . . , n), (1,2 : 3, . . . ,
n), . . . , (1,2, . . . , n − 1: n).
EachvalueK (1) generatesthenumbers I (2) , J (2) , K (2) offeasiblesecondcolumns.
For example, at K (1) = 1 columns I (2) = I (1) − 1, J (2) = 2, K (2) = 2 ÷ (I (1) − 1), i.e.,
(2:3, . . . , n), (2,3 : 4, . . . , n), . . . , (2,3, . . . , n − 1: n) are feasible, at K (1) = 2
columns I (2) = 2, J (2) = 1, K (2) = 1, i.e., (1 : 2) and I (2) = I (1) − 2, J (2) =
3, K (2) = 3 ÷ (I (1) – 1), i.e., (3 : 4, . . . , n), (3,4 : 5, . . . n), . . . , (3,4, . . . n − 1: n)
are feasible, etc. It is easy to develop the general algorithm of systematic sorting
of all potential columns and their sequences.
The algorithm of systematic identification and sorting of all feasible sequences,
including not only simple columns, but also various distillation complexes with
branching of flows, is considerably more complicated. This task was solved
(Agrawal, 1996; Sargent, 1998). The general name of the approach introduced
was given in the latter work: “state-task network.” This approach assumes that
the main element of any column or distillation complex is a section. The initial mix-
ture, intermediate products, and end products are nodes of the network (states),
and the lines joining these nodes show the changes of these states with the help of
one section of the distillation column or complex (tasks). We note that section is
a main element not only at synthesis of sequences, but also at design calculation
(see Chapter 7).
For the top sections, the summary flow (the difference of vapor and liquid flows)
is directed upward, and for the bottom sections, it is directed downward. The top
sections should get liquid flow from the condenser or from the bottom of another
section, and the bottom sections should get vapor flow from the reboiler or from
the top of another section.
A sequence of simple columns can be obtained if each top section is provided
with a condenser and each bottom section is provided with a reboiler.
A section joining two nodes, including component with intermediate volatility,
is called an intermediate section. For example, for the sequence (1 : 2,3) → (2 : 3),