Some complements in combinatorics of sharp separation systems synthesis

The analysis of combinatorics of sequences of sharp separation systems is a problem extensively studied in chemical engineering. Thompson and King (1972) first presented a closed‐form expression for determining a number of possible sequences for separating an n‐component mixture into pure products by using simple (one input and two outputs) sharp separators. Then, Shoaei and Sommerfeld (1986) showed that this determination could be interpreted in term of Catalan numbers; recently Wahl and Lien (1990) derived this formula from a generating function. This article presents a closed‐form expression for a number of different possible separation sequences when complex (one input and three or more outputs) separators are used.