(385a) Probing Stochastic and Deterministic Methods to Estimate Primary Crystal Nucleation Rates

We report novel insights into how to accurately estimate primary and secondary crystal nucleation rates from experimental data. Knowledge on these rates is a prerequisite for model-based process design and optimization of industrial crystallization processes. In stirred crystallizers, primary and secondary nucleation are strongly correlated, rendering it challenging to obtain accurate estimates for both rates. For primary nucleation, the literature reports that different methods to measure its rate applied to the same system result in widely divergent parameter estimates. To understand this behavior, we developed a novel conceptual validation methodology for the comparative assessment of nucleation rate estimation methods.

To this end, we simulated a crystallization process for a well-studied model component considering stochastic primary nucleation, stochastic secondary nucleation, and deterministic crystal growth. Nucleation rates were estimated from the simulated data through multiple methods and the results were compared with the true values. Among the methods considered in this work, no one was able to estimate the rates accurately under general conditions. Two deterministic methods were found to overestimate primary nucleation rates in the presence of secondary nucleation. We generalized this finding and showed that deterministic methods conceptually are unable to accurately estimate primary nucleation rates under conditions where process attributes are dominated by secondary nucleation.

Conversely, two stochastic methods were found to provide accurate primary nucleation rates independent of whether secondary nucleation is present. Their accuracy, however, is limited to process conditions where only a small absolute number of primary nuclei form: if many primary nuclei are born, they underestimate the primary nucleation rate. We hence proposed a criterion to probe the accuracy of stochastic methods for arbitrary data sets, thus providing the theoretical foundations required for their rational use.

All in all, this work provides practitioners with the conceptual framework to select appropriate methods for the measurement of nucleation rates and to understand differences in their performances.

References:

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