Digital Design of Batch Cooling Crystallization Processes: Computational Fluid Dynamics Methodology for Modeling Free-Surface Hydrodynamics in Agitated Crystallizers

Abstract

A framework for the digital design of batch cooling crystallization processes is presented comprising three stages, which are based on different levels of process complexity, integrating crystallizer hydrodynamics with crystallization kinetics and consequently with expected crystal size distribution. In the first stage of the framework, a computational fluid dynamics methodology is developed to accurately assess hydrodynamics in a typical batch crystallizer configuration, comprising a 20 L scale dish-bottom vessel with a single beavertail baffle agitated by a retreat curve impeller, used in the pharmaceutical as well as in the fine chemical industries. The hydrodynamics of crystallizers with such configurations is characterized by vortex formation on the free liquid surface. It is therefore important to model the free surface using the Volume-of-Fluid (VoF) method. Comparison of the predicted mean velocity components with experimental measurements using laser Doppler anemometry reveals that improved predictions are obtained using a differential Reynolds-stress transport model for turbulence coupled with the VoF for modeling the gas-liquid interface compared with those using the Shear-stress transport model and with a flat liquid surface. This study demonstrates that an accurate treatment of the liquid free surface for capturing vortex formation is essential for reliable predictions of the crystallizer's flow field. While the vortex depth is predicted to increase with increasing impeller Reynolds number, the dependence of hydrodynamic macroparameters, including power number, impeller flow number, and secondary circulation flow number, on Reynolds number reveals that they are essentially constant within the turbulent regime but fluctuate when the flow is in the transitional and laminar regimes as fluid viscosity increases.

Development of a Digital Twin for the Prediction and Control of Supersaturation during Batch Cooling Crystallization

“…Szilaǵyi and Nagy 25 showed how parallel GPUs running a high-resolution finite volume technique improved calculation speed significantly, enough for real-time resolution of a multidimensional PBM. Camacho Corzo et al 26 used computational fluid dynamics (CFD) to investigate the hydrodynamics inside a batch crystallizer, suggesting that these simulations could be paired with a morphological PBM to create a more robust representation of the process. 27 Another recent advancement for MPC of crystallization processes is the use of open-loop simulations with the PBM to train machine-learning control algorithms, such as in the study by Zheng et al 28 They demonstrated how a recurrent neural network (RNN) model trained using a semiempirical PBM could improve the computational efficiency of MPC to achieve an optimal target product yield and crystal size.…”

“…Szilágyi and Nagy showed how parallel GPUs running a high-resolution finite volume technique improved calculation speed significantly, enough for real-time resolution of a multidimensional PBM. Camacho Corzo et al used computational fluid dynamics (CFD) to investigate the hydrodynamics inside a batch crystallizer, suggesting that these simulations could be paired with a morphological PBM to create a more robust representation of the process …”

Rapid, Automated Measurement of Dynamic Size Distributions and Size-Dependent Growth Rates of Crystal Ensembles within Microfluidic Flow Cells

“…First, such in situ probe-based measurements are point-based methods where the local environment at which the measurements are made may not be representative of the entire crystallization volume. Second, the FBRM-based chord length distributions (CLDs), which are indirect CSD measurements, require sophisticated conversion matrices for nonspherical crystals. , The growth kinetics obtained, obscured by secondary nucleation, is dependent on scale and process parameters (i.e., impeller and tank geometry) due to the spatially inhomogeneous hydrodynamic fields within the crystallizer, resulting in local variation in concentration and mixing rates. − Such inherent scale-dependency can cause significant differences between lab, pilot, and industrial manufacturing scales. Furthermore, the growth kinetics data obtained are average values obtained from crystals in constant motion and therefore do not shed detailed quantitative insights into crystal growth phenomena such as the presence of size-dependent growth. , …”

Application of a Statistical Approach to Process Development of Futibatinib by Employing Quality-by-Design Principles. Part 3: Development of Design Space for Control of Particle Size Distribution

“…In other words, it is important to identify critical process parameters (CPPs) appropriately and to control them sufficiently in the manufacturing process. Therefore, much research has been conducted on the crystal habit, particle size, and polymorphism of APIs. − …”