Interpretation and Utilisation of Parametric Models of Binary Distillation Columns; Relating Plant and Control Design

Previously published analytical models (1) (2) for the separation dynamics of CSTC and tubular packed distillation columns are rederived using common notation for detailed comparison purposes. The separation and total composition equations are now successfully separated at an early stage in the derivation which is thus simplified. The analyses produce parametric formulae for steady-state separation and for the transfer functions of both columns in terms of length, relative volatility, evaporation-and nominal vapour-rate, parameters only plus columns and end-vessel capacitance. A second order, nonminimum-phase structure derived from high-and low-frequency asymptotic behaviour is shown to fit all types and on the basis of this, analytic stability and critical error criteria for linear closed-loop control are derived; again requiring the substitution only of the above mentioned plant parameters. It is shown that, for equal parameters, tubular columns out perform CSTC types. However, matching of the two types for separation and stability is achievable by fictitious inflation of the CSTC length and volatility coefficient. This may permit use of an equivalent but simpler CSTC model for unified tubular plant and control design. Finally the CSTC column is formulated as a parametric, bilinear third-order, state space model having a state-dependent, input-coefficient matrix. This is derived with a view to future application of optimal control based on the on-line Riccatti solution method of Banks (3) already successfully tested on a bilinear CSTR chemical reactor model (4).