Page 120 - Design of Simple and Robust Process Plants

4.2 The Methodology of Process Synthesis 105
4.2.2.3 Sequencing of separations
The sequencing of separation is generally considered to be a MINLP problem, the
argument being that the number of sequences to be evaluated grows progressively
with the number of products and the number of alternative separation techniques.
If it is assumed that the separation technique has been selected, the number of
sequences is still considerable. Table 4.2 shows this for a selected separation tech-
nique and an increasing number of products to be separated. In practice, the num-
ber of products to be separated after a reaction step are mostly between three and
five, and in a chemical process this might be followed by successive reaction steps
with their separation sections. The number of constraints for such a separation train
is also considerable. In the example of Koolen et al. (1999) the number of sequences
for five products was reduced from 14 to 9 due to constraints. In these situations ±
which cover most of the industrial cases ± it is more practicable to optimize and
evaluate all potential sequence alternatives rather than to define an overall optimiza-
tion problem.

Table 4.2. The number of possible sequences for using a selected separation technique versus the
number of products to be separated.

Number of products Number of separators Number of sequences
2 1 1
3 2 2
4 3 5
5 4 14
6 5 42
7 6 132
8 7 429
9 8 1430

In the previous paragraph, the separations were selected and the layout of the
sequential steps can be presented in a generic superstructure (Figure 4.15) (Douglas
and Stephanopoulos, 1995). This superstructure was compared with several flow-
sheets of well-developed processes, and the structure fitted reasonably well. The
superstructure also respects the heuristic rule of ªheterogeneous before homoge-
neousº separations.
Pre-selection of the sequence in the case of a distillation train ± which always is a
key activity during separation step 1 ± is based on the selection of a minimum vapor
flow alternative. This concept has been proposed by Porter and Momoh (1991), and
reflects operational cost as well as capital cost. These authors have also demonstrat-
ed that the rank order of the total vapor flow is similar to the rank order of the total
cost. This method is preferred to a heuristic approach. For each alternative, an over-
all mass balance is made where the separation specifications are either set by the
final product requirements or are selected arbitrarily, whereupon these last specifica-
tions will become free at a higher level of optimization. The sequences under evalua-