Modeling and control of extraction columns

A population-balance-equation model is employed for the analysis of liquid-liquid extraction columns. This model considers drop breakage, coalescence, and exit phenomena for the drop phase and axial mixing for the continuous phase. Drop breakage and coalescence are described for a single stirred-cell contactor. The obtained frequency functions are incorporated into a population balance model. Fitting experimental data of transient drop size distributions with calculated results of the population balance model yields appropriate values for the constant parameters of the drop frequency functions. Identical functions are then employed for the analysis of a multistage stirred-cell contactor. The predictive power of the population-balance-equation model is tested against experimental data of drop size distribution and dispersed-phase volume fraction (holdup) profiles along the contactor. The effect of mass transfer on the above parameters is studied experimentally.;An ultrasonic technique for holdup monitoring is employed for the study of the dynamic behavior and control of the process. A first-order-plus-dead-time model is assumed for the process transfer functions. The model parameters are obtained from step-response tests. The Dahlin control algorithm is employed for the design of the controller. Both, adaptive and nonadaptive control schemes are employed. The effectiveness of the controller is tested for servo and regulatory holdup control. Multivariable holdup and concentration control is also studied. A conductance measuring technique is employed for monitoring the solute concentration at the exit of the continuous phase. The performance of the controller is demonstrated for both servo and regulatory control.