Reaction crystallization kinetics of benzoic add

Benzoic acid was crystallized in a T-mixer by mixing hydrochloric acid and an acqueous sodium benzoate solution. Crystallization kinetics were determi ned by population balance modeling and parameter estimation by nonlinear op timization. The evaluation of several models showed that the model has to b e carefully designed. The objective function is highly nonconvex. and the r esults have to be scrutinized to identify the appropriate optimum. Growth-r ate dispersion needs to be accounted for to obtain a reasonable description of experimental product-size distribution. Six parameters of nucleation an d growth kinetics were determined simultaneously in an optimization that in cludes experimental product-size distributions from 14 experiments at 8 dif ferent initial supersaturations. The interfacial energy calculated from the corresponding nucleation parameter is 0.015 J/m(2). The exponent of the no rmal power law growth-rate equation receives a value of 2.1, suggesting tha t growth is controlled by surface integration. The becomes 2.9 if the logar ithm of the supersaturation ration is used as the driving force. The coeffi cient of variation of the growth-rate distribution depends only weakly on s upersaturation and receives a value of 0.23 if this dependence is neglected . The final model described experimental data well. The estimated parameter s are physically reasonable and provide a physically reasonable description of the entire experiment.