Study of Controlled Cyclic Distillation: II. Analytical Transient Solution and Asymptotic Plate Efficiencies

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Abstract
The dynamic equations of the composition variables of a controlled cycling distillation column are solved to obtain the transient solutions for the vapor-flow period. These solutions are then used to establish asymptotic expressions for the compositions at the pseudo-steady-state condition of the cycling column. Analytical expressions for the asymptotic plate efficiencies in terms of the operating conditions, equilibrium data, and local point efficiencies are derived to show quantitatively the amount of improvement in the separating ability that can be achieved in an ideal cycling column. A method of numerical iterative solution for a nonlinear equilibrium relationship is demonstrated, and a simplified graphical method for calculating the number of stages required for a given separation is presented.

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