A Non-linear Wave Model with Variable Molar Flows for Dynamic Behaviour and Disturbance Propagation in Distillation Columns

A non-linear wave model for a distillation column has been extended and then examined for binary and ternary systems by including enthalpy and hold-up effects, these being significant for wide boilers and leading to variable molar flows and holdups. Application of the coherence condition to the system mass and energy balance equations confirms that, for an n-component system, any disturbance or eventual steady-state will be resolved into n-1 distinct, coherent waves (involving synchronized variations in composition, temperature, and flow-rate), provided that enthalpy and hold-up are made functions of composition. For steady states, the predictions of the wave-model and those of more rigorous plate-to-plate calculations show excellent agreement for the operating conditions required to obtain an optimal steady-state. In preliminary design calculations, the wave model thus quickly identifies an approximate, optimal steady state. For disturbance propagation, predictions of the wave model for the velocities of disturbance waves are in good agreement with those for the plate-to-plate model. For both models, “asymmetric dynamics” is predicted. The asymmetry is less than that predicted for a constant molar flow model; this agrees qualitatively with previous experimental results. In all cases, liquid and vapour flow variations across the waves are predicted correctly. When fully developed, wave theory can be used as a quick first step in design and optimisation, and its simplicity and speed offers good prospects for on-line control applications.