A Stochastic Approach for Anti-Solvent Addition Policy in Crystallization Operations: An Application to a Bench-Scale Fed-Batch Crystallizer

This work aims a stochastic approach for the calculation of robust anti-solvent addition policies for controlling the mean crystal size (MCS) in fed-batch crystallization operations. The proposed strategy is based-on a non-structured population balance where uncertainties associated with the start-up condition and random fluctuations along the fed-batch operation can be taken into account in a very natural fashion. We include and quantify the effect of the uncertainties by embedding a deterministic crystal growth model into a Fokker-Planck equation (FPE) resulting in a stochastic model for the MCS dynamics. This approach uses the Generalized Logistic equation (GLE) that has an adequate mathematical structure that suits the dynamic characteristic of the crystal growth. Thus, the numerical solution of the FPE provides the most likely MCS evolution for a given anti-solvent flow-rate. The effect of the anti-solvent is incorporated into the parameters of the FPE. The parameters of the FPE are computed as linear piece-wise interpolating functions of the anti-solvent flow-rate. The strategy uses a PID-like regulator in closed-loop fashion with the FPE to compute the anti-solvent addition flow-rates for different set-point targets in the MCS. In order to validate the stochastic model and assess the merits of the proposed strategy, the crystallization of sodium chloride in water using ethanol as anti-solvent is performed in a bench-scale fed-batch crystallizer. The implementation of the calculated anti-solvent policies resulted in a good control of the MCS despite modelling mismatch and uncertainties present during the crystallization operation