Model-based analysis and quality-by-design framework for high aspect ratio crystals in crystallizer-wet mill systems using GPU acceleration enabled optimization

Abstract The simultaneous control of crystal size and shape is particularly important in pharmaceutical crystallization processes. These two quantities not only influence the dissolution rate and bioavailability of final drug products, but also contribute to the manufacturability and efficiency of downstream operations. The manipulation of crystal shape, however, is difficult since it requires decoupled growth rate control of individual crystal faces. The aim of this work is to analyze and evaluate the effectiveness of wet milling for control of bivariate size distribution of high-aspect ratio crystals during solution crystallization. Three configurations are compared: the pure batch crystallizer, the crystallizer with internal wet mill (immersion mill) and crystallizer with external wet mill. Population balance models (PBMs) are employed to describe bivariate size density function dynamics, with stirring rate dependent breakage to enable the direct optimization of wet mill operation. The generated system of hyperbolic partial differential and ordinary differential equations is solved by a fully discretized high-resolution finite volume method (HR-FVM), involving graphical processing unit (GPU) acceleration, which brings up to two orders of magnitude speed-up by compared to the serial C implementation. The simulation studies revealed that wet milling significantly extends the achievable crystal size and shape domain, but it also broadens the product size distribution. The analysis of the optimized operating profiles, which include temperature, wet mill rotation (RPM) and recirculation rate, enabled the generalization of optimal operation, which can efficiently guide a QbD approach by considerably reducing the design space without compromising the process performance.