Dynamic Characteristics of Counter-Current Flow Processes

In industry counter-current flow processes are common. Although these processes have been widely studied in literature, relatively little has been published on their dynamic behaviour. Two very common counter-current flow processes are heat exchangers and distillation columns. Ma's study based on dynamic models of heat exchanger's dynamic behaviour [1] reports an internal resonance effect, also earlier reported by Profos in 1943 [4] and Friedly in 1972 [3]. Here the study is extended to lumped models, first for heat exchangers and thereafter for an extremely simplified distillation column. Not unexpectedly, the dynamic properties change gradually as the number of lumps increases towards the distributed systems and for high frequencies similar internal resonance effects evolve with the envelopes showing a very low-order behaviour, which though somewhat surprisingly is independent of the number of lumps. Finally we show that the eigenvalues of the normed system matrix lie on a circle in the complex plane.