An Analytical Study of the Dynamics of Binary Distillation Columns

Analytical transfer function matrices are developed for describing the dynamic behaviour of the compositions within the rectifying and stripping sections of both very short and very long distillation columns, in response to changes in energy and liquid throughout. Matrices of first-order lags are shown to describe both situations very closely and the simple structure of the models demonstrates the need to consider only steady-state operating curves for the elimination of interaction problems arising in twin product control. The models are useable directly by the plant or design engineer who merely needs to substitute basic design data to obtain good estimates of all the model parameter values. An elementary inverse Nyquist approach is presented which predicts precisely the extent of the detuning of one composition control loop by closing the other loop. The long column model is shown to have much in common with models produced by other authors who have used widely different and usually partly-empirical approaches to column modelling. The analytical approach here proves, for specified conditions, the empirical observations relied upon by these previous workers. The modelling method used here involves the solution of the process partial differential equation at high frequency and the discrete process equations at low frequency. The two resulting models join together quite naturally because of their structural similarity. It is believed that the approach could find application in separation processes generally.