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

Abstract

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. This deduction accords well with the findings of previous authors McMoran [1], Shinskey [2], and Stainthorp [3] based on part impirical, approximate analytical by Edwards and Jassim [4], or purely simulation methods [5]. Near first-order-lag behaviour is also a feature common to the findings of these earlier investigations and the precise derivation herein reported.