Numerical simulations of seeded batch crystallization demonstrating the effect of stochastic nucleation on crystal product quality

Numerical simulations of seeded batch cooling crystallization were performed to investigate the effect of stochastic nucleation on crystal quality parameters. In a typical deterministic mathematical model for crystallization, which contains population and mass balance equations, primary and secondary nucleation are regarded as Poisson processes in order to derive a stochastic model. In this study, these stochastic model equations were repeatedly solved to achieve a stochastic simulation, and statistical analysis of the results revealed differences in product quality when the simulations were run under certain conditions. In particular, the statistics, such as the mean and the coefficient of variation, of the product crystal size distribution were found to fluctuate as a result of stochastic primary and secondary nucleation. Further, stochastic primary nucleation was also found to be the source of the differences between the statistics obtained using the deterministic and stochastic simulations when the seed-loading ratio was very low. This difference was attributed to the growth of crystals when the total number of crystals was less than one, as well as the accompanying secondary nucleation, in the standard deterministic simulation. Thus, a novel deterministic model in which secondary nucleation does not occur until the total number of crystals reaches one was used, and the results and statistics were found to agree with those obtained using the stochastic numerical simulation. In addition, a stochastic model ignoring stochastic secondary nucleation omitted to predict the significant statistical fluctuations under certain conditions. Finally, the statistical fluctuations were predicted for several crystallizer scales, and crystallizer scale-up was found to reduce the fluctuations caused by stochastic primary and secondary nucleation.