Size-Dependent Growth Modeling Method for Batch Crystallization of Carbamazepine from Variable Seed Crystal Size Distributions

Abstract

Developing a crystallization model that accurately predicts crystal growth and nucleation has been an important topic in the pharmaceutical industry for the past few decades. Particularly, as the pharmaceutical industry shifts toward continuous manufacturing, modeling will both reduce the workload for experimental optimization and allow for the development of model-based control systems that 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 for solute concentration measurement by in-line Raman spectroscopy as well as for seed and product crystal size distribution (CSD) measurement by off-line laser diffraction. Based on these data, modeling was performed with MATLAB software using a combined quadrature method of moments and a method of characteristics technique in conjunction with a modified Mydlarz and Jones (MJ3) expression for size-dependent growth. This work expands upon our past work on 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 the MJ3 size-dependent growth expression, variation in seed CSD resulted in high prediction errors for product CSD especially for the D10 value [root-mean-square error (RMSE) = 29.8%]. The error was reduced by varying the size-dependent growth parameters as a function of the seed CSD (RMSE = 7.4%). This new technique provided a better understanding of how the overall CSD affects crystal growth rates. The improved model may reduce the time needed to optimize experiments and provide better control of the variation of the CSD of the system.