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Presented at ESCAPE'12 Symposium, The Hague, Netherlands, May 2002

Optimal Number of Stages in Distillation with respect to Controllability
Marius S. Govatsmark, and Sigurd Skogestad 
Department of Chemical Engineering, NTNU 
N-7491 Trondheim, Norway

Abstract
The central question to be examined in this paper is if it is optimal to have a large or small number of stages in a distillation column with respect to controllability when the objective is to have dual composition control. With multivariable controllers and without considering model uncertainty few stages shows somewhat better controllability than many stages because (i) the available manipulated variables have larger effect on the outputs (allowing larger changes in manipulated variables for few stages) and (ii) it is not necessary to reject the disturbances as fast as for many stages. However, in reality there will always be model uncertainty, and with uncertainty included the conclusion is reversed: it is better to have many stages. The reason is that with more stages the system is less interactive and thus less sensitive to uncertainty. Physically, with many stages a pinch zone develops around the feed stage, which tends to decouple the two column ends from each other.