Reaction crystallization kinetics of benzoic acid

Benzoic acid was crystallized in a T-mixer by mixing hydrochloric acid and an aqueous sodium benzoate solution. Crystallization kinetics were determined by population balance modeling and parameter estimation by nonlinear optimization. The evaluation of several models showed that the model has to be carefully designed. The objective function is highly nonconvex, and the results have to be scrutinized to identify the appropriate optimum. Growth-rate dispersion needs to be accounted for to obtain a reasonable description of experimental product-size distributions. Six parameters of nucleation and growth kinetics were determined simultaneously in an optimization that includes experimental product-size distributions from 14 experiments at 8 different initial supersaturations. The interfacial energy calculated from the corresponding nucleation parameter is 0.015 J/m². The exponent of the normal power law growth-rate equation receives a value of 2.1, suggesting that growth is controlled by surface integration. The value becomes 2.9 if the logarithm of the supersaturation ratio is used as the driving force. The coefficient of variation of the growth-rate distribution depends only weakly on supersaturation and receives a value of 0.23 if this dependence is neglected. The final model describes experimental data well. The estimated parameters are physically reasonable and provide a physically reasonable description of the entire experiment.