A sequence of distillation columns used to separate components from a multicomponent feed. Each column is required to perform a particular separation of either a pure component or a cut between two components. For example, in the separation of four components ABCD in a mixture in which A is the most volatile and D the least, then the five possible separation sequences requiring three columns are:
Separation | Column 1 | Column 2 | Column 3 |
1 | A:BCD | B:CD | C:D |
2 | A:BCD | BC:D | B:C |
3 | AB:CD | A:B | C:D |
4 | ABC:D | A:BC | B:C |
5 | ABC:D | AB:C | A:B |
Where it is required to separate a larger number of components, the number of possible separation sequences becomes much larger according to the relationship
where N is the number of sequences and n is the number of components:
Components (n) | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
Sequences (N) | 5 | 14 | 42 | 132 | 429 | 1430 | 4862 |
(p. 112) Due to the difficulty in seeking the best train sequence, enumerative or heuristic approaches are used to rapidly identify the best train.