The analytical modelling and dynamic behaviour of tray-type binary distillation columns (Q1196514)

A completely original, parametric transfer-function matrix (TFM) model for a binary distillation column, is derived. From the ordinary differential equations describing the individual trays of a multitray column, a partial differential equation (PDE) representation is derived together with the necessary boundary conditions. Large-signal steady- state solutions are derived to provide parametric data for a small-signal PDE model obtained by linearization. The small-signal PDEs are solved analytically for sinusoidal inputs to produce the parametric TFM model for the system. The plant parameters and operating conditions are chosen to produce a physically symmetrical system which, in turn, yields a completely diagonal TFM choosing input and output vectors as the ``sum and difference'' of the circulating vapour and liquid flows within the column and the ``difference and sum'' of the top and bottom compositions, respectively.