Conference Agenda

Mathematical modeling is essential for the effective control of many chemical engineering processes, including crystallization. However, most existing continuous crystallization models used in industry and academia assume ideal mixing. As a result, the effects of imperfect mixing on crystallization are largely unexplored in the literature.

Population balance modeling (PBM) is the standard approach for crystallization processes. While PBM can be integrated within a computational fluid dynamics (CFD) framework, this method is computationally demanding, making it impractical for extensive parametric. Therefore, Alternative modeling approaches are required to address the impact of nonideal mixing in a less costly manner. In our study, we employ a simplified mixing model based on the engulfment model originally developed by Baldyga and Bourne in the context of reaction engineering [1].

We present an efficient method for nondimensionalizing the model equations. As in other areas of chemical engineering, nondimensionalization offers valuable insights by reducing the number of parameters and revealing characteristic system properties. It also provides appropriate scaling of variables, improving both the precision and efficiency of numerical computations.

Our work focuses on a theoretical study of continuous crystallization, including extensive parametric investigations including attainable regions analysis [2]. We compare the simulation results of our model with those obtained under the assumption of perfect mixing. The primary objective is to assess the effect of mixing intensity on particle size. Interestingly, we demonstrate that increasing mixing intensity can either increase or decrease the mean crystal size, in agreement with experimental observations, and we offer an explanation for this behavior.

To validate the model’s relevance, we use experimental data from the literature to fit the model parameters. Our results indicate that the simplified model performs comparably to more complex CFD-based models, providing a computationally efficient alternative for studying crystallization under non-ideal mixing conditions.

1. Bałdyga, J.; Bourne, J.; Hearn, S., Interaction between chemical reactions and mixing on various scales. Chemical Engineering Science 1997, 52 (4), 457-466.

2. Vetter, T.; Burcham, C. L.; Doherty, M. F., Regions of attainable particle sizes in continuous and batch crystallization processes. Chemical Engineering Science 2014, 106, 167-180.

Agglomeration, often undesirable in crystallization, can lead to impurity incorporation [1,2], longer filtration and drying times, and challenges in achieving uniformity in particle size and content. While controlling supersaturation and agitation rates has been shown to mitigate agglomeration [1,3], more rigorous techniques, such as thermocycles, can promote deagglomeration and dissolve fines resulting from breakage or attrition.

Optimizing thermocycles involves determining parameters like the number of heating-cooling cycles and heating-cooling rates. This presents a complex optimization challenge, where traditional quality-by-control methods relying on process analytical technology become resource-intensive [4,5]. A more efficient alternative is the use of population balance models (PBMs) to monitor and control agglomeration during crystallization [6].

In this study, we propose a model-based approach for optimizing temperature profiles to minimize agglomeration and increase crystal size. A PBM is coupled with the number density of agglomerates to monitor agglomeration during thermocycles. The hybrid PBM incorporates key mechanisms such as nucleation, growth, dissolution, agglomeration, and deagglomeration, and is applied to the crystallization of an industrial active pharmaceutical ingredient, Compound K. Most parameters were estimated through design of experiments (DoE) in a prior study, while additional thermocycle experiments were conducted to refine dissolution parameters.

Results from in-silico DoE simulations indicate that the hybrid PBM approach surpasses traditional methods in accurately evaluating process performance when agglomeration is involved. This approach provides a more robust means of assessing agglomeration control compared to methods based solely on particle bridge formation. Moreover, the simulations reveal that while thermocycles are effective in reducing agglomeration, their efficiency saturates after a certain number of cycles, which were verified through the experiments.

In conclusion, this study demonstrates the value of a model-based approach for optimizing thermocycle profiles, leading to improved control over agglomeration compared to linear cooling or quality-by-design recipes. The optimized thermocycles resulted in reduced agglomeration and shorter batch times, making this approach more efficient for crystallization process optimization.

1. Urwin, Stephanie J., et al. "A structured approach to cope with impurities during industrial crystallization development." Organic process research & development 24.8 (2020): 1443-1456.
2. Terdenge, Lisa‐Marie, and Kerstin Wohlgemuth. "Impact of agglomeration on crystalline product quality within the crystallization process chain." Crystal Research and Technology 51.9 (2016): 513-523.
3. Sun, Zhuang, et al. "Use of Wet Milling Combined with Temperature Cycling to Minimize Crystal Agglomeration in a Sequential Antisolvent–Cooling Crystallization." Crystal Growth & Design 22.8 (2022): 4730-4744.
4. Fujiwara, Mitsuko, et al. "First-principles and direct design approaches for the control of pharmaceutical crystallization." Journal of Process Control 15.5 (2005): 493-504.
5. Wu, Wei-Lee, et al. "Implementation and application of image analysis-based turbidity direct nucleation control for rapid agrochemical crystallization process design and scale-up." Industrial & Engineering Chemistry Research 61.39 (2022): 14561-14572.
6. Szilagyi, Botond, et al. "Application of model-free and model-based quality-by-control (QbC) for the efficient design of pharmaceutical crystallization processes." Crystal Growth & Design 20.6 (2020): 3979-3996.

The rapid population growth and escalating economic burden of human diseases suggest a potential rise in pharmaceutical waste, necessitating proper management strategies to address this challenge effectively. Sources of unused drugs can go beyond consumer waste products that have exceeded their shelf life and may exist anywhere in the supply chain, as well as the failed batches created during drug product manufacture. Previous research has highlighted the presence of pharmaceutical pollutants in water, soil, and surface environments.^1,2

Regardless of the source of unused drugs, it is imperative to ensure appropriate waste management. Given the significant health and environmental impacts of active pharmaceutical ingredients (APIs) in pharmaceutical formulations, prioritizing their separation from various excipients in their formulations is a strategic approach to address this challenge. When recycling APIs, it is crucial to ensure that the recovered APIs possess the desired critical quality attributes (CQAs), such as purity and particle size distribution, while adhering to strict FDA regulations. Traditionally, APIs, after synthesis, are purified through crystallization.³ Solvent selection is the primary step in obtaining high-purity APIs post-synthesis. Likewise, solvent selection plays a crucial role in recovering the APIs from tablets containing a variety of excipients and selectively dissolving and re-crystallizing them.⁴

This study proposes a robust solvent selection framework to recycle the APIs that conceptualizes different solvent selection metrics such as solubility, percentage recovery, and process mass intensity. The framework is demonstrated using paracetamol as a model API with six common excipients, and ten commonly used solvents in crystallization studies. Firstly, a process flowsheet is modeled to simulate the steady-state recovery process. Next, temperature-dependent equilibrium solubility curves are generated of the API for all the solvents, followed by the generation of excipient-solvent solubility curves. Having obtained the solubility curves, the framework is executed to select solvents based on each metric. Selecting solvent based on solubility involved mapping the relative solubilities of the API and excipients over a range of temperatures for all the solvents, while recovery-based selection targeted maximizing recovery in the final stage of re-crystallization of API. Further, a sustainability-based selection included calculating the process mass intensity for each solvent. All the solvents in each metric were ranked. The results enable solvent selection for each metric while encapsulating the associated tradeoffs. The framework also enables solvent selection by incorporating multiple metrics as objectives, allowing for a more comprehensive and optimized approach to identifying a suitable solvent. This multi-objective consideration ensures that the chosen solvent balances various factors, such as solubility, recovery, and environmental impact, leading to a more effective and sustainable recovery process. The developed solvent selection framework lays a foundation for creating a process to recover APIs from their formulations.

Mechanistic population-balance modeling (PBM)-based digital design has gained significant traction in the pharmaceutical industry, facilitating the design of crystallization processes to consistently produce active pharmaceutical ingredient (API) crystals with targeted critical quality attributes (CQAs), such as purity, crystal size distribution (CSD), and yield. However, developing accurate PBM models for specific API-solvent systems presents challenges due to the need for well-designed design of experiments (DoE) to decouple crystallization mechanisms, as well as high-quality real-time process data (e.g., concentration, CSD) from process analytical technology tools or offline analyses. The substantial resources—time, material, and labor—required to obtain such measurements, along with fast-paced pharmaceutical process development timelines, make PBM model development resource-intensive and impractical for numerous active compounds studied during clinical and development phases.¹

In response, this research explores data-driven modeling as an alternative for building ‘fit-for-purpose’ digital twins of crystallization processes, aiding process development using a quality-by-digital design (QbD²) framework. While data-driven strategies have been actively researched, many existing frameworks have limited industrial applicability due to a lack of training on experimental data or reliance on real-time process measurements, which are not always available.² A key contribution of this research is the development of a machine learning (ML)-based modeling workflow that leverages industrially available DoE data to link operating conditions with CQAs, addressing the knowledge gap and enhancing process development for industrially relevant API systems.

Given the absence of real-time measurements, this study operates within a low-data regime, making ML model development particularly challenging. To address this challenge, this research explores the augmentation of original experimental DoE data with synthetic data (generated from DoE data) to improve the ML model’s predictive performance. Synthetic data generation techniques, including Generative Adversarial Networks (GANs) and Variational Autoencoders (VAEs), are employed to enrich the dataset and improve model training. Additionally, model-informed active learning is integrated to generate new, strategically designed DoEs, further improving model accuracy and robustness. This iterative workflow continues until the models achieve the desired accuracy, after which they are used within optimization frameworks to inversely design operating conditions that meet the target CQAs.

The effectiveness of this workflow is demonstrated using industrial data for a commercial API facing challenges related to crystallinity, severe agglomeration tendencies, and slow growth kinetics, which are CQAs that are difficult to describe using mechanistic modeling approaches. The proposed workflow enables the efficient digital design of the crystallization process, identifying operating conditions that achieve the desired CQAs.

References:

1. Nagy, Z. K. & Braatz, R. D. Advances and new directions in crystallization control. Annu. Rev. Chem. Biomol. Eng. 3, 55–75 (2012).

2. Xiouras, C., et al., Vlachos, D. G. & Stefanidis, G. D. Applications of Artificial Intelligence and Machine Learning Algorithms to Crystallization. Chem. Rev. 122, 13006–13042 (2022).

The pharmaceutical industry is a highly specialized field where strict quality control and accelerated time-to-market are essential for maintaining competitive advantage. Spherical crystallization has emerged as a promising approach in pharmaceutical manufacturing, offering significant potential to reduce equipment and operating costs, enhance drug bioavailability, and facilitate compliance with product quality regulations. Emulsions, as an enabling technology for spherical crystallization, present unique advantages. However, the quality of spherical crystallization products derived from emulsions is significantly influenced by the intricate interactions between crystallization phenomena, formulation variables, and solution hydrodynamics. These complexities pose substantial challenges in determining optimal operational conditions to achieve the desired product characteristics.

In this study, Bayesian optimization (BO) is employed to refine and optimize the operational conditions for the spherical crystallization of a representative drug, ibuprofen. The primary goal is to improve product flowability, measured by a reduced angle of repose, while maintaining the D50 particle size within a specified range. The optimization process focuses on key variables such as temperature, stirring speed, duration, and BSA concentration. With the help of acquisition functions, BO enhances control over crystal growth and aggregation, enabling the identification of a high-quality product with fewer experimental trials compared with traditional design of experiments (DoE) methods.

Biomacromolecules have intricate crystallisation behaviour due to their size and many interactions in solution, and can often only crystallise in narrow ranges of experimental conditions [1]. High solute concentrations are needed for crystal nucleation and growth, exceeding those eluted upstream and therefore preventing the adoption of crystallisation in downstream separation steps [2]. By promoting molecular aggregation and nucleation via a lowered energy barrier, heterogeneous surfaces or templates can relax the supersaturation requirements and widen the crystallisation operating space [3].

Though templates are promising candidates for process optimisation, their experimental testing has generally been limited to small-volume experiments, and quantification of their impact on process intensification and quality metrics at higher volumes remains unexplored [4]. Computational crystallisation models can support in-vitro experiments and accelerate process development as virtual experiments can be performed quicker and with reduced material costs [5].

To address the knowledge gap, a model-based investigation of template-induced protein crystallisation systems through evaluation of key metrics is presented. Porous silica nano-particles with three chemical functionalisations (hydroxyl, carboxyl and butyl) are added to batch lysozyme crystallisation experiments at 40ml. Crystallisation population balance models are parametrised with an experimentally-validated parameter estimation methodology and and further experiments are simulated. The templates appear to lower the estimated interfacial energy compared to the homogeneous case, leading to nucleation rate profiles which are less dependent on supersaturation. For this reason, the templates can crystallize quicker than the homogeneous system, particularly at lower initial concentrations. The simulation results highlight the ability of heteronucleants to alter nucleation rate profiles, and their potential to be used as process optimisation and intensification tools for biomacromolecule purification.

Acknowledgements: This work was supported by the Engineering and Physical Sciences Research Council (EPSRC) for the Imperial College London Doctoral Training Partnership (DTP) and by AstraZeneca UK Ltd through a CASE studentship award.

1. Hekmat D (2015) Large-scale crystallization of proteins for purification and formulation. Bioprocess Biosyst Eng 38:1209–1231. https://doi.org/10.1007/s00449-015-1374-y

2. McCue C, Girard H-L, Varanasi KK (2023) Enhancing Protein Crystal Nucleation Using In Situ Templating on Bioconjugate-Functionalized Nanoparticles and Machine Learning. ACS Appl Mater Interfaces 15:12622–12630. https://doi.org/10.1021/acsami.2c17208

3. Govada L, Rubio N, Saridakis E, et al (2022) Graphene-Based Nucleants for Protein Crystallization. Adv Funct Mater 32:2202596. https://doi.org/10.1002/adfm.202202596

4. Chen W, Cheng TNH, Khaw LF, et al (2021) Protein purification with nanoparticle-enhanced crystallisation. Sep Purif Technol 255:117384. https://doi.org/10.1016/j.seppur.2020.117384

5. Orosz Á, Szilágyi E, Spaits A, et al (2024) Dynamic Modeling and Optimal Design Space Determination of Pharmaceutical Crystallization Processes: Realizing the Synergy between Off-the-Shelf Laboratory and Industrial Scale Data. Ind Eng Chem Res 63:4068–4082. https://doi.org/10.1021/acs.iecr.3c03954