The Dynamic Behaviour of Packed and Tray-Type Binary Distillation Columns Described by Lumped-Parameter Models

Parametric transfer-function matrix (T.F.M) models are derived from the differential equations describing the variation of liquid and vapour compositions within symmetrical distillation columns separating binary mixtures. Both packed and tray-type columns are considered, the models developed having minimal order 6 and 4 respectively, (implying perfectly-stirred mixtures and minimum number of trays in each column section) so removing the complications introduced by spatial variations encountered in earlier studies 1,2 of longer columns. The T.F.M's obtained are are again shown to diagonal with the same choice of input and output vectors as were employed in the "long" column studies. Furthermore, the fundamental behavioural differences between packed and tray-type columns are again revealed using these low- order physical models as were demonstrated in the previous studies. In particular, the sign of the static gain of packed-columns, responding to total flow changes is again shown to be parameter-sensitive and the sign of the total-flow gain at high-frequency is shown to be the reverse of that for tray-type columns, so again causing nonminimum-phase behaviour in packed-columns in some circumstances. Because of their behavioural and parametric similarities, it is proposed that the minimal-order models developed in this report be used as a future basis for control system design studies for spatially-distributed and multi-tray columns in situations where travelling-wave phenomena are unimportant.