A stochastic approach for the prediction of PSD in crystallization processes: Analytical solution for the asymptotic behavior and parameter estimation

Recently, a novel stochastic formulation based on the Fokker–Planck equation (FPE) for the description of anti-solvent mediated crystal growth process was proposed. Here, we further expand these results by analyzing the asymptotic (end of the batch) solution of the FPE for the CSD. In this regard, the analytical solution of the stationary FPE is exploited for predicting the end of the batch CSD as function of the model parameters. Furthermore, the availability of such analytical solution is used to simplify and diminish the computational burden of the parameter estimation problem. Two alternative approaches for parameter estimation are discussed based on the use of the analytical solution of the FPE and of the dynamic of the logistic equation (deterministic component of the FPE approach). Validations against experimental data for the NaCl–water–ethanol anti-solvent crystallization system are presented.