(463a) Modelling the Internal Resonanse Effect in Counter-Current Processes
AIChE Annual Meeting
Wednesday, November 10, 2010 - 12:30pm to 12:50pm
Counter-current ﬂow is a commonly used conﬁguration of industrial processes. Although these processes have been widely studied in literature by using different models, little has been published on the resonance eﬀect in their dynamic behaviour. Resonance eﬀects are well known and have been extensive studied in e.g.mechanics and electrics. Two common counter-current ﬂow processes are the heat exchanger and the distillation column, whose dynamic behaviour is studied in this report. The dynamic behaviour of the heat exchanger was studied before by using a distributed model (Xian Hua Ma PhD 1993 UNSW, Australia). In these studies an internal resonance eﬀect for high frequent input temperature changes were reported. This internal resonance eﬀect was reported earlier in other applications by Profos in 1943 (PhD ETH-Zuerich) and Friedly 1972 (Dynamic Behaviour of Processes, Prentice Hall 1972).
The purpose of this presentation is to demonstrate that lumped models show a similar behaviour by comparing the distributed model I/O behaviour of the distributed model with various lumped models. The comparison is done in the frequency domain. A very, very simplified model of a distillation column is used to demonstrate that the resonance effect is most likely also to observed there.
The dynamic properties change gradually as the number of lumps increases towards the distributed systems: In all cases an internal resonance eﬀect for high frequencies evolves and the envelope reﬂects a low order behaviour, which is independent of the number of lumps. Finally, it is observed that the normed system matrix eigenvalues lie on the border of a circle in the complex plane.
A simple physical explanation can be given for the development of an internal resonance effect, which is not dependent on the system to be linear.