A Short-Cut Method for the Quantification of Crystallization Kinetics. 1. Method Development

Population balance models are of high interest for the efficient design, control and optimization of crystallization processes. They usually contain mathematical submodels for the description of the relevant kinetic phenomena, such as growth, dissolution, and nucleation of particles. Commonly, component-specific parameters included in these submodels have to be determined for every substance system of interest or even for the specific experimental setup. Thus, a short-cut method is suggested that is based on analyzing the evolution of the crystal size distribution during a few batch crystallization experiments to efficiently parametrize kinetic submodels required to predict and evaluate the performance of crystallization processes. To illustrate the overall procedure and to evaluate the accuracy of the proposed approach, in silico data with predefined kinetics corresponding to hypothetical non-isothermal batch runs are analyzed. It is shown that it is possible to recover prespecified submodel parameters with a rather limited amount of input information. Subsequently, less flexible submodels and measurement errors are considered for comparison, in order to evaluate the loss of predictability. The agreement found between the results of a simulated continuous crystallization process applying both (a) the initially provided model together with the prespecified parameters or (b) parameter estimates provided by the short-cut method demonstrates the practical applicability of the latter.