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

Deconstructing 3D growth rates from transmission microscopy images of facetted crystals as captured in situ within supersaturated aqueous solutions

Here, a morphologically based approach is used for the in situ characterization of 3D growth rates of facetted crystals from the solution phase. Crystal images of single crystals of the β-form of l-glutamic acid are captured in situ during their growth at a relative supersaturation of 1.05 using transmission optical microscopy. The crystal growth rates estimated for both the {101} capping and {021} prismatic faces through image processing are consistent with those determined using reflection light mode [Jiang, Ma, Hazlehurst, Ilett, Jackson, Hogg & Roberts (2024 ▸). Cryst. Growth Des. 24, 3277-3288]. The growth rate in the {010} face is, for the first time, estimated from the shadow widths of the {021} prismatic faces and found to be typically about half that of the {021} prismatic faces. Analysis of the 3D shape during growth reveals that the initial needle-like crystal morphology develops during the growth process to become more tabular, associated with the Zingg factor evolving from 2.9 to 1.7 (>1). The change in relative solution supersaturation during the growth process is estimated from calculations of the crystal volume, offering an alternative approach to determine this dynamically from visual observations.

Automated Growth Rate Measurement of the Facet Surfaces of Single Crystals of the β-Form of l-Glutamic Acid Using Machine Learning Image Processing

Precision measurement of the growth rate of individual single crystal facets (hkl) represents an important component in the design of industrial crystallization processes. Current approaches for crystal growth measurement using optical microscopy are labor intensive and prone to error. An automated process using state-of-the-art computer vision and machine learning to segment and measure the crystal images is presented. The accuracies and efficiencies of the new crystal sizing approach are evaluated against existing manual and semi-automatic methods, demonstrating equivalent accuracy but over a much shorter time, thereby enabling a more complete kinematic analysis of the overall crystallization process. This is applied to measure in situ the crystal growth rates and through this determining the associated kinetic mechanisms for the crystallization of β-form l-glutamic acid from the solution phase. Growth on the {101} capping faces is consistent with a Birth and Spread mechanism, in agreement with the literature, while the growth rate of the {021} prismatic faces, previously not available in the literature, is consistent with a Burton-Cabrera-Frank screw dislocation mechanism. At a typical supersaturation of σ = 0.78, the growth rate of the {101} capping faces (3.2 × 10-8 m s-1) is found to be 17 times that of the {021} prismatic faces (1.9 × 10-9 m s-1). Both capping and prismatic faces are found to have dead zones in their growth kinetic profiles, with the capping faces (σc = 0.23) being about half that of the prismatic faces (σc = 0.46). The importance of this overall approach as an integral component of the digital design of industrial crystallization processes is highlighted.

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

Fine chemicals produced via batch crystallization with properties dependent on the crystal size distribution require precise control of supersaturation, which drives the evolution of crystal size over time. Model predictive control (MPC) of supersaturation using a mechanistic model to represent the behavior of a crystallization process requires less experimental time and resources compared with fully empirical model-based control methods. Experimental characterization of the hexamine-ethanol crystallization system was performed in order to collect the parameters required to build a one-dimensional (1D) population balance model (PBM) in gPROMS FormulatedProducts software (Siemens-PSE Ltd.). Analysis of the metastable zone width (MSZW) and a series of seeded batch cooling crystallizations informed the suitable process conditions selected for supersaturation control experiments. The gPROMS model was integrated with the control software PharmaMV (Perceptive Engineering Ltd.) to create a digital twin of the crystallizer. Simulated batch crystallizations were used to train two statistical MPC blocks, allowing for in silico supersaturation control simulations to develop an effective control strategy. In the supersaturation set-point range of 0.012-0.036, the digital twin displayed excellent performance that would require minimal controller tuning to steady out any instabilities. The MPC strategy was implemented on a physical 500 mL crystallizer, with the simulated solution concentration replaced by in situ measurements from calibrated attenuated total reflection-Fourier transform infrared (ATR-FTIR) spectroscopy. Physical supersaturation control performance was slightly more unstable than the in silico tests, which is consistent with expected disturbances to the heat transfer, which were not specifically modeled in simulations. Overall, the level of supersaturation control in a real crystallizer was found to be accurate and precise enough to consider future adaptations to the MPC strategy for more advanced control objectives, such as the crystal size.