377543 Analysis of Crystallization Kinetics Based on CSD Estimates from PAT Tools
Nucleation and growth are the two dominating phenomena in crystallization processes. In our study, a partial crystal size distribution (CSD) was estimated for the size range from 50 µm to 500 µm by combining in situ measurements from both FBRM and ATR-FTIR. Experimental results show that the evolution of the CSD was better tracked by this framework, compared to a qualitative interpretation using chord length distribution (CLD).
To explore the process and the corresponding kinetics, seeded and unseeded batch cooling crystallization experiments were designed to start with different initial conditions and proceed through different cooling rates. The general procedure is: (1) a concentrated ethanolic solution of paracetamol is cooled to supersaturated conditions, followed by a constant-temperature plateau; (2) either seeds are added or primary nucleation occurs on the constant-temperature plateau; (3) after desupersaturation of the solution is complete, the solution is further cooled to the final temperature. The estimated CSDs from CLDs were consistent with our expectations of the design of the crystallization runs, such as initial concentrations and cooling rates. These CSDs were also verified by sieving.
A full population-balance model was solved in order to fit the experimental data and estimate kinetic parameters. A numerical method (conservation/solution element scheme) was applied to the population balance to simulate the experiments efficiently and was used in parameter estimation. Classical nucleation theory was used for primary nucleation, secondary nucleation was related to relative supersaturation and mass of crystals, and the growth rate was assumed to be size-independent.
Using the estimated parameters, the simulated runs for unseeded crystallizations suggest that the final CSD was strongly influenced by the relative importance of primary versus secondary nucleation when they occur simultaneously in the clear supersaturated solution; if secondary nucleation is dominant at that moment, then most of the crystal mass is concentrated in small size ranges. An optimal two-step cooling profile was designed to produce a final size distribution with more large crystals and it was validated experimentally.
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