Automatic Design of Wet-Milling-Integrated Batch Crystallization Processes by Process Analytical Technology-Based Split-Range Direct Nucleation Control

Experimental implementation of a Quality-by-Control (QbC) framework using a mechanistic PBM-based nonlinear model predictive control involving chord length distribution measurement for the batch cooling crystallization of l-ascorbic acid

Crystal size distribution (CSD) is an essential criterion for determining the production of high-quality crystals since it influences the efficiency of the crystallization process. Producing specified CSD in the crystallization process represents a main challenge as it depends on temperature control, which indirectly regulates the solution’s concentration and affects the crystal’s evolution. Different temperature profiles may influence the distribution of crystal products, and a suitable optimization algorithm is required to produce an optimum temperature trajectory that produces the desired CSD. Thus, this study aims to maximize the CSD of the grown seed crystals while minimizing the nucleus-grown crystals by employing the best optimization algorithm for the potash alum crystallization process. The crystallization process was developed and simulated in Matlab software using a potash alum in the water system. Four optimization algorithms were proposed with different objective functions, such as maximizing mean crystal size (I), minimizing coefficient of variation (II), minimizing nucleus-grown crystals (III), and maximizing CSD (IV). Based on the simulation results, optimization IV, which maximizes CSD, performs best with a large mean crystal size of 490 µm. Furthermore, the number of fine crystals was among the lowest at a volume distribution of 0.00071 m3/m compared to the linear profile at 0.00191 m3/m. Optimization IV employs a dissolution strategy, which manipulates two quality specifications in one algorithm (size of crystals and number of fines), which is considered the best optimal cooling profile for seeded batch crystallization by maximizing CSD and minimizing the generation of nucleus-grown crystals.

In this work, we focus on the development of a parametric drift detection and isolation (PDDI) method for the handling of batch-to-batch parametric drifts in a batch crystallization process used to produce hen egg-white (HEW) lysozyme crystals. We consider that the batch crystallization process is controlled by an in-batch model predictive control (MPC) system and is subject to batch-to-batch parametric drifts in the solubility, growth rates, continuous-phase mass and energy balance parameters, and nucleation rate. The proposed PDDI scheme consists of two parts: preparatory stage before batch-to-batch operation and post-batch stage during batch-to-batch operation. The goal of the preparatory stage is to compute the threshold values and signatures for each parametric drift using simulations and batch process common cause variance described by noise. During batch-to-batch operation, the proposed PDDI system monitors closed-loop process residuals, which are computed by taking the difference between the time profiles of the states obtained through in-batch and postbatch measurements from the time profiles of the states obtained from the drift-free simulation with noise. While the measurements of the protein solute concentration and the temperature in the crystallizer are available in real-time, post-batch measurements are usually available for the quality of the crystal products (e.g., number of crystals, average crystal size and shape) and this key characteristic is taken into account in the PDDI method. We then compare the residuals with signatures obtained in the preparatory stage for each parametric drift for isolation of a parametric drift. The PDDI system estimates the magnitude of the parametric drift and updates the parameters of the batch process model used in the in-batch MPC system to compute a set of jacket temperatures for the production of crystals with a desired shape distribution in the next batch. The performance of the MPC with the proposed PDDI scheme is demonstrated by applying it to a multiscale simulation of a batch crystallization process with parametric drifts in the solubility and crystal growth rates. The closed-loop system simulations demonstrate that crystals with a crystal shape distribution that is closer to a desired set-point value are produced under a parametric-drift handling scheme that integrates the in-batch MPC with the proposed PDDI system compared to those under the MPC with the nominal process model.

On-line dynamic optimization integrated with generic model control of a batch crystallizer

The temperature profile is a critical parameter in industrial batch cooling crystallization processes which directly impacts the crystal size distribution (CSD) and subsequent down streaming operations. Conventional cooling approaches, including natural and linear cooling, often fail to achieve optimal results. Linear cooling may trigger excessive primary nucleation by crossing metastable limits, while natural cooling leads to inconsistent nucleation and growth, resulting in smaller and non-uniform crystals. Hence, optimized cooling profiles are used to achieve the desired target CSD. This study employs reinforcement learning (RL) to optimize the temperature profile for batch cooling crystallization for two systems: paracetamol in water and potassium dihydrogen phosphate (KDP) in aqueous solution. RL dynamically adjusts the cooling trajectory by iteratively interacting with a process model, aiming to maximize mean crystal size while minimizing the coefficient of variation. A comprehensive mathematical model incorporating population balance equations, mass balance, and energy balance is developed to simulate the crystallization process. For the paracetamol system, the RL-optimization strategy resulted in a 107.5 % increase in mean crystal size compared to the natural cooling profile. In the case of the KDP system, a 12 % increase in mean crystal length is achieved relative to a linear cooling profile, along with a significant reduction in the coefficient of variation, indicating improved crystal size uniformity. The optimization results obtained using RL are also compared with that from a genetic algorithm for both cases, and RL demonstrated superior performance. This work underscores the potential of RL in advancing broader applications in chemical process optimization.

Direct nucleation control (DNC) is a model-free feedback control approach based on the measurement of particle number in the crystallization process. The experimental implementation has demonstrated that this approach is efficient to produce large and uniform crystals in batch crystallization, or to reduce startup duration and suppress disturbance in continuous crystallization. In this work, five different DNC frameworks/strategies are proposed for a continuous mixed suspension mixed product removal (MSMPR) crystallization of paracetamol–water system and evaluated systematically using a model-based approach. It is found that the reverse DNC framework could provide the best control performance in terms of startup, set-point change, and disturbance suppression. In addition, an optimal heating/cooling rate of about 0.6 °C/min was determined. These observations are applicable for the model compound studied (paracetamol) and should be investigated for other systems. This study provides a general guidance of de...

Data-driven modeling has been widely studied and employed for quality prediction in batch processes. However, existing research and development of this methodology have found it not sufficiently effective in addressing challenges from the batch-to-batch uncertainty and limitation of noisy modeling data. This work proposes a quality prediction method that combines batch correlation information and dynamic data reconciliation (DDR). The method is based on Gaussian process regression and integrated with canonical correlation analysis to capture batch-to-batch characteristics through examining the correlation between batches. Furthermore, DDR is used to dynamically adjust prediction variance, reduce the impact of noisy process data, and improve the prediction accuracy. A numerical case, a batch crystallization process, and a silica modification process have verified that the proposed method is demonstrated effective performance, compared with the candidates.

Platinum-group element systematics in Mid-Oceanic Ridge basaltic glasses from the Pacific, Atlantic, and Indian Oceans

Kinetic parameter estimation for most batch crystallization processes is necessary because nucleation and crystal growth kinetic parameters are often not available. The existing identification methods are generally based on simplified population balance models such as moment equations, which contain insufficient information on the crystal size distribution (CSD). To deal with these problems, a new optimization‐based identification approach for general batch cooling seeded crystallization is proposed in this study. The final‐time CSD is directly used for identification. A novel effective method for solving the population balance equation is developed and used to identify nucleation and growth kinetic parameters. Cooling crystallization of ammonium sulfate in water was experimentally investigated, where the concentration was measured by an on‐line density meter and the final‐time CSD was analyzed by a Malvern Mastersizer 2000. Kinetics for ammonium sulfate are determined based on cooling crystallization experiments. Applying these kinetics in simulation provides a good prediction of the product CSD. © 2004 American Institute of Chemical Engineers AIChE J, 50: 1786–1794, 2004

Fault diagnosis of a semi-batch crystallization process through deep learning method

Continuous processing gains importance in the fine chemical and pharmaceutical industries where crystallization is an important downstream operation. Seeded cooling crystallization of the l-alanine/water system was investigated under similar conditions, i.e., temperature interval, cooling rate, and seed material, both in a stirred batch vessel and in a continuous plug flow crystallizer in the coiled flow inverter (CFI) design with horizontal helical tube coils (ID = 4 mm) and frequent 90° bends of the coils. Short-cut calculations based on characteristic time scales and the Damköhler number allow for comparing the batch and continuous crystallization processes. The experimental results reveal crystal growth and growth rate dispersion to be dominating on the product crystal size distribution (CSD). However, at low flow rates of approximately 31 g min–1, a moving sediment flow of the slurry was present in the CFI crystallizer, resulting in further size dispersion effects. Elevated flow rates of approximately 40 g min–1 resulted in a more homogeneous suspension flow and a product CSD comparable to batch quality. Simulation studies based on a population balance equation model strengthen the hypothesis of the solid phase residence time distribution (RTDS) to be more spread in the moving sediment flow regime, leading to a wider product CSD.

A novel wet milling-based automated direct nucleation control (WMADNC) concept is proposed and implemented in two continuous cooling crystallization processes in this work. In process 1, WMADNC is implemented upstream to provide closed-loop controlled primary nucleation kinetics and produce seed crystals in situ for continuous mixed suspension mixed product removal crystallizer (MSMPRC). In process 2, WMADNC is applied downstream to achieve closed-loop controlled secondary nucleation kinetics and reduce particle size for crystals in the MSMPRC through recycling. For both processes, a focused beam reflectance measurement (FBRM)-based closed-loop control approach is successfully implemented to control the nucleation kinetics inside the wet mill therefore to control the final chord length distribution (CLD). In the proposed WMADNC approach, the process critical quality attributes (CQA) (e.g., particle number or size) can be directly controlled by the automated closed-loop control framework, which on one hand...

The paper presents an iterative, model-free Quality-by-Control (QbC) framework as a strategic enabler for crystallization process development, facilitating both the selection of process analytical technology (PAT) tools and the implementation of robust control strategies. The framework employs a mechanism-oriented decision-making approach to guide the choice between Direct Nucleation Control (DNC), Supersaturation Control (SSC), or a hybrid of the two, based on the relative significance of growth and agglomeration phenomena. A practical rule of thumb is proposed for selecting appropriate control variables, leveraging inline data quality and temperature trajectory insights. The framework is demonstrated using a case study involving a commercial active pharmaceutical ingredient (API), with the objective of enhancing crystallinity and reducing agglomeration in the final product. Offline tools such as high-performance liquid chromatography (HPLC) and differential scanning calorimetry (DSC) are used to track crystallinity changes in systems with both amorphous and crystalline content. Factorial experimental design analyses revealed key operational parameters that influenced process performance. Unseeded crystallization resulted in encrustation and poor crystallinity, while high supersaturation with slower cooling and lower seed loading produced large needlelike crystals. Increasing seed loading and applying slower cooling rates significantly improved product crystallinity. Guided by the QbC framework and implemented through turbidity-based DNC (TDNC), the process demonstrated significant improvements in batch time, crystallinity, agglomeration control, and robustness against seed variability─outperforming traditional approaches. This work highlights the effectiveness of the proposed framework in enabling informed, rapid design of enhanced and resilient crystallization processes.

In this work, a scale-up strategy based on the principles of direct design and quality-by-control (QbC) was applied and investigated using direct nucleation control (DNC). Process analytical technologies (PATs) were implemented for process monitoring and control. Antisolvent crystallization of indomethacin (IMC) was performed in a ternary solvent and antisolvent system. Mixture of acetone–methanol (66.5–33.5 wt %) was used as solvent and water as antisolvent since the mixed solvent system provides increased process yield and facilitates the suppression of the undesired acetone solvate. The effect of different process parameters, such as seed load, seed size, and initial concentration was investigated on process time, solid form and particle size distribution (PSD). The simplified solvent and antisolvent addition profiles obtained from the DNC were implemented directly in open-loop control to investigate reproducibility of the designed process. The open-loop operation was successfully scaled up by 1 order of magnitude, obtaining crystalline products with similar properties (solid form and PSD) as in the small-scale experiments. The results provide a proof-of-concept showing how the direct design approach can be applied in the rapid development of a robust crystallization process and efficient scale-up to yield the desired solid form with desired particulate properties (unimodal PSD and no agglomeration).

Crystalsize and shape can be manipulated to enhance the qualities of thefinal product. In this work the steady-state shape and size of succinicacid crystals, with and without a polymeric additive (Pluronic P123)at 350 mL, scale is reported. The effect of the amplitude of cyclesas well as the heating/cooling rates is described, and convergentcycling (direct nucleation control) is compared to static cycling.The results show that the shape of succinic acid crystals changesfrom plate- to diamond-like after multiple cycling steps, and thatthe time required for this morphology change to occur is stronglyrelated to the type of cycling. Addition of the polymer is shown toaffect both the final shape of the crystals and the time needed toreach size and shape steady-state conditions. It is shown how thisphenomenon can be used to improve the design of the crystallizationstep in order to achieve more efficient downstream operations and,in general, to help optimize the whole manufacturing process.