(148b) Developing a Novel Size-Dependent Growth Modeling Method for the Batch Crystallization of Carbamazepine from Variable Seed Crystal Size Distributions

Developing a crystallization model that accurately predicts crystal growth and nucleation has been an important topic in the pharmaceutical industry for the last few decades. Particularly, as the industry shifts toward continuous manufacturing (CM), crystallization modeling will both reduce the workload for experimental optimization and allow for model-based control systems that can yield more consistent quality output. In this work, a unique approach for modeling size-dependent growth was applied to a set of batch cooling crystallizations. The cooling crystallization of carbamazepine (CBZ) in ethanol was monitored using in-line Raman spectroscopy for solute concentration measurement as well as off-line laser diffraction for seed and product crystal size distribution (CSD) measurement. Modeling was performed using the MATLAB software utilizing a combined quadrature method of moments and method of characteristics (QMOM-MOCH) technique in conjunction with a modified expression for size-dependent growth. This work expands upon past work done in modeling the cooling crystallization of CBZ by evaluating the effect of variable seed CSD on crystal growth rates as well as the accuracy of the model-predicted product CSD. Using typical modeling techniques, variation in seed CSD resulted in significant error in the model CSD predictions especially for the product D10 value, thus demonstrating the necessity for novel methods for modeling size-dependent growth. This error was reduced by varying the size-dependent growth parameters as a function of the seed CSD. Simpler size-dependent equations have proven accurate in the past, particularly when seed CSD was held constant. However, this new technique provides a more accurate representation of how crystal growth rates are affected by the overall distribution of crystals present in the system. This enhanced understanding will benefit future research into continuous crystallization by enabling more accurate start-up simulations as the system CSD changes from the seed to the steady state of crystallization. It will also reduce experimental optimization workload and provide better control for perturbations in either the seed or the system CSD.