Combinatorial aspects of sharp split separation systems synthesis

✍ Scribed by Per E. Wahl; Kristian M. Lien

• Publisher: American Institute of Chemical Engineers
• Year: 1990
• Tongue: English
• Weight: 293 KB
• Volume: 36
• Category: Article
• ISSN: 0001-1541
• DOI: 10.1002/aic.690361020

✦ Synopsis

Thompson and King (1 972) presented a closed form expression for the number of different possible separation sequences arising when an n-component mixture is separated into pure products using sharp component separators with one input and two outputs. Subsequently, Shoaei and Sommerfeld (1986) pointed out that the number of sequences is the series of Catalan numbers (Alter, 1971), but they did not show how to derive the closed form formula. This paper will demonstrate that this may be done using a general mathematical technique-generating functions.

The analysis is extended to combinatorics of sequences of sharp separators with more than two outputs. Finally expressions for the number of distinct separators will be derived.

An underlying assumption throughout the paper is that the components in any stream are "sorted"; components appearing together will always appear in the same order.