Batch Crystallization Process Research Articles

Advancing crystal growth prediction: An adaptive kMC model spanning multiple regimes

Traditional batch crystallization processes encounter challenges like batch-to-batch variability, and difficulty in scale-up and achieving desired crystal size and morphology. These challenges stem from various growth mechanisms within crystallizers, influenced by operating conditions that dictate the dynamic surface structure of crystals. To overcome this, we developed a novel microscopic kinetic Monte Carlo model, which uses a specialized adsorption rate that adapts to different growth regimes by considering surface thermodynamic effects for different growth mechanisms. Specifically, the adaptive adsorption rate redefines the driving force of crystallization by considering the attachment energies of different adsorption sites (e.g., kink, adatom, and edge) and supersaturation. This approach enables seamless transitions across growth regimes. We use the lysozyme crystal system as a case study, demonstrating the model's superior predictive power in regime-to-regime transitions. Overall, the developed work provides a valuable new approach to understanding crystal morphology and predicting crystal growth rates in different growth regimes.

Recovery of nitrogen as struvite from swine wastewater: Comparison study of batch and continuous fluidized-bed crystallization process

The recovery of valuable compounds from waste supports the idea of a circular economy. Two systems were introduced in this study to recover nitrogen as struvite from swine wastewater, including batch stirred and fluidized-bed homogeneous crystallization (FBHC) systems. MgCl2 and NaH2PO4 were applied as precipitants to form struvite. In the batch stirred system, the removal efficiency of NH4+, Mg2+, and PO43− reached the optimum condition of 92.1 %, 75.6 %, and 91.1 %, respectively, under the operating conditions of pH 9 and an Mg/P molar ratio of 1.2. In the same operating conditions, the Crystallization ratio (CR) and Total Removal (TR) of the FBHC system reached 83.2 % and 89.1 %; 86.7 % and 90.6 %; 71.2 % and 76.1 % for NH4+, Mg2+, and PO43−, respectively. The XRD and FT-IR analyses confirmed the high purity and quality of the struvite solid product. However, the water content of the FBHC product is much lower than that of the batch-stirred system (5.8 % and 95.3 %, respectively). The great potential of swine wastewater as a nitrogen source for fertilizer production is evidenced by the high purity struvite product (>85.0 %).

Fault diagnosis with high accuracy and timeliness for semi‐batch crystallization process based on deep learning with multiple pattern representation

AbstractThe research on chemical process fault diagnosis has made significant progress, but there is still a big gap in its application to complex practical industrial processes. As for the fault diagnosis of batch crystallization processes, the recently‐proposed dynamic time warping–convolutional neural network (DTW‐CNN) model has achieved a great improvement in the fault diagnosis. However, its fault diagnosis rate (FDR) and timeliness of fault diagnosis are still low, and thus, it needs to improve further before being applied to the practical application. In this paper, a multiple pattern representation–convolutional neural network (MPR‐CNN) model is proposed and applied for the fault diagnosis of a semi‐batch crystallization process. The MPR‐CNN model enables the manual extraction of features with four pattern representation algorithms in the data pre‐processing stage, and generates a three‐dimensional matrix which is used as the training sample and input to the CNN for the formal feature extraction and weight learning. An excellent classification performance, with an average FDR of 97.5%, is achieved. This model is also applied for the fault diagnosis of process data within a shorter period of time after the occurrence of faults. The results indicate that the model could make timely fault diagnosis with a highly stable and accurate performance after the occurrence of a fault.

Recent Advancements in Continuous Crystallization of Proteins

AbstractRecently, there have been many studies and reports on various continuous protein crystallization processes. Due to the increasing demand for pharmaceutical proteins such as insulin and monoclonal antibodies, it has become essential to optimize the current industrial processes to meet these demands. There are various comparisons to be made between current batch crystallization processes and continuous processes for proteins. This review paper aims to review the recent advancements in continuous protein crystallization processes, such as slug flow crystallizers, oscillatory baffled crystallizers, and mixed suspension mixed product removal (MSMPR) crystallizers.

Investigating the Role of Citric Acid as a Natural Acid on the Crystallization of Amoxicillin Trihydrate.

This study investigates the use of environmentally friendly citric acid as the main player in the process, rather than as an additive, to remove impurities from amoxicillin trihydrate (AMCT) crystals, aiming to optimize their purity and yield. By manipulating the concentration of citric acid, mixing speed, crystallization time, and pH, the researchers conducted experiments using a full factorial design. The dissolution stage was analyzed in both batch and continuous crystallization processes, emphasizing the significance of citric acid in enhancing crystallization. HPLC analyses were performed on the resulting crystals, and the data were analyzed using the Multi-Vari Chart program. The findings demonstrated that higher citric acid concentrations positively affected the yield, while factors such as crystallization time, mixing speed, and pH also contributed to the increased yield. The crystals obtained exhibited desirable dimensions sought after in the pharmaceutical industry, eliminating the need for additional purification steps. This study showcased the potential of citric acid in AMCT crystallization, offering advantages in product design, purification, and synthesis. The optimized conditions included a citric acid concentration of 2.0 M, mixing speed of 1000 rpm, crystallization time of 120 min, and pH of 5.5. Notably, the developed process proved to be environmentally friendly by avoiding the use of harmful chemicals, serving as a green alternative for crystallization processes, and producing purer AMCT products. Overall, this research contributes to the existing literature by highlighting the efficacy of citric acid in impurity removal and the optimization of AMCT crystal purity and yield.

Studies on crystallization process for pharmaceutical compounds using ANN modeling and model based control

Solvent selection and Controlling of operating parameters play a crucial role in batch cooling crystallization process. Choosing a best solvent for crystallization process involves more experimentation and time. To overcome this problem, an Artificial Neural Network (ANN) model technique is used to predict the carbamazepine form Ⅲ solubility by considering the thermodynamic properties of different solvents i.e. critical temperature, critical pressure, temperature, molecular weight, and acentric factor. The ANN model was trained and evaluated for solubility at various input data sets using experimental solubility data available in the literature. The ANN model with 20 hidden neurons has given the R2 value of 0.9943 which shows that the developed ANN model can be used for the selection of best solvent for batch crystallization process. Further, to determine the optimal cooling profile of batch cooling crystallization process, a multi-objective optimization problem is formulated by considering objectives as minimizing the coefficient of variation (CV) and maximizing the Number mean size (NMS) of crystals subjected to population balance equations using “method of moments” technique. Two types of temperature strategies i.e., piece-wise constant and piece-wise linear are developed and solved using NSGA-Ⅱ dynamic optimization procedure. The optimal NMS value attained through piece-wise linear strategy was 197.1 µm. This value has been increased by 28.3 µm from the nominal case (without optimization) and the coefficient of variation has decreased from 0.951 to 0.76. Further, optimal NMS value attained through piece-wise constant strategy was 205 µm. The value has been increased by 36.2 µm and the coefficient of variation has decreased from 0.951 to 0.73. This proves that the crystal attributes can be improved by optimal cooling temperature profile obtained by multi-objective optimization framework. For implementing the optimal cooling profile an advanced model-based control, i.e., Generic Model Control (GMC) was developed. It was observed that the GMC controller has the good tracking profile with no offset with/without disturbances and small value of root mean square error (RMSE) of 0.0016 using piece-wise constant as set point temperature. Using piece-wise linear as set point temperature, the RMSE value was 0.0018. In particular, it is advantageous to operate the batch cooling crystallization process with piece-wise linear strategy for set point trajectory tracking problems.

Rapid Assessment of Crystal Nucleation and Growth Kinetics: Comparison of Seeded and Unseeded Experiments.

In this work, we outlined an experimental workflow enabling the rapid assessment of primary and secondary nucleation and crystal growth kinetics. We used small-scale experiments in agitated vials with in situ imaging for crystal counting and sizing to quantify nucleation and growth kinetics of α-glycine in aqueous solutions as a function of supersaturation at isothermal conditions. Seeded experiments were required to assess crystallization kinetics when primary nucleation is too slow, especially at lower supersaturations often encountered in continuous crystallization processes. At higher supersaturations, we compared results from seeded and unseeded experiments and carefully analyzed interdependencies of primary and secondary nucleation and growth kinetics. This approach allows for the rapid estimation of absolute values of primary and secondary nucleation and growth rates without relying on any specific assumptions about functional forms of corresponding rate expressions used for estimation approaches based on fitting population balance models. Quantitative relationships between nucleation and growth rates at given conditions provide useful insights into crystallization behavior and can be explored to rationally manipulate crystallization conditions for achieving desirable outcomes in batch or continuous crystallization processes.

Protein Nucleation and Crystallization Process with Process Analytical Technologies in a Batch Crystallizer.

Protein crystallization has drawn great attention to replacing the traditional downstream processing for protein-based pharmaceuticals due to its advantages in stability, storage, and delivery. Limited understanding of the protein crystallization processes requires essential information based on real-time tracking during the crystallization process. A batch crystallizer of 100 mL fitted with a focused beam reflectance measurement (FBRM) probe and a thermocouple was designed for in situ monitoring of the protein crystallization process, with simutaneously record of off-line concentrations and crystal images. Three stages in the protein batch crystallization process were identified: long-period slow nucleation, rapid crystallization, and slow growth and breakage. The induction time was estimated by FBRM, i.e., increasing numbers of particles in the solution, which could be half of the time required for detecting the decrease of the concentration, by offline measurement. The induction time decreased with an increase in supersaturation within the same salt concentration. The interfacial energy for nucleation was analyzed based on each experimental group with equal salt concentration and different concentrations of lysozyme. The interfacial energy reduced with an increase in salt concentration in the solution. The yield of the experiments was significantly affected by the protein and salt concentrations and could achieve up to 99% yield with a 26.5 μm median crystal size upon stabilized concentration readings.

Effects of different seed forms on crystal size distribution for seeded batch crystallization process

The effects of different seed forms on crystal product distribution are presented for optimizing crystal size distribution (CSD) in the case of seeded batch cooling crystallization process. Three different seed distributions and quality are introduced as variable parameter for CSD control of seeded batch crystallization process via simulation in Matlab software. Similar implementation is conducted in the experimental study using the same operating conditions and parameters. Cubic cooling profile is adapted as the temperature profile for potash alum crystallization system due to its ability to control secondary nucleation. The experimental data obtained from laboratory works are validated the simulation results from Matlab where good agreement has been achieved. In terms of mean crystal size of the final CSD, the seed profile with 0.29 standard deviation labelled Sieved Seed 2, produces the best seed profile for seeded batch potash alum crystallization process because it has the largest size of crystals at mean crystal size of 500 μm grown from 90 μm of seed crystals. However, considerable fine crystals at mean crystal size of 30 μm are also obtained indicating trade-off between large size of crystals and fine crystals are needed. In conclusion, this work highlights the effects of different seed quality in terms of distribution and shape on crystal size distribution as one of the important quality specifications in crystallization process and demonstrates narrow distribution of seed crystals as recommendation on the best seed quality for producing desired CSD.

Optimal Control of Batch Crystallization Processes with Primary Nucleation

Multi-objective optimization problems for batch crystallization processes with primary nucleation are presented and solved using optimal control theory. The mass of the nucleated crystals is tracked and included in the material balance. The resulting two-point boundary-value problems are difficult to solve because the expressions for the derivatives of the states and costates are highly non-linear. Conventional shooting methods usually fail to converge. Therefore, a gradient-based algorithm is applied instead. The method is illustrated by computing Pareto fronts for multi-objective optimization problems. An inherent trade-off is observed between the competing objectives of minimizing the number of nucleated crystals and the nucleated mass or the weight mean size. The algorithm is found to be both fast and robust, suggesting that it might be suitable for online model-based control.

Algorithms for solving boundary value problems in optimal control of seeded batch crystallization processes with temperature-dependent kinetics

Algorithms for solving boundary value problems in optimal control of seeded batch crystallization processes with temperature-dependent kinetics

Physics-informed machine learning for MPC: Application to a batch crystallization process

This work presents a framework for developing physics-informed recurrent neural network (PIRNN) models and PIRNN-based predictive control schemes for batch crystallization processes. The population balance model of the aspirin crystallization process is first developed to describe the formation of crystals through nucleation and growth. Then, the PIRNN modeling scheme is introduced to integrate observational data and mechanistic models for the development of machine learning models. Additionally, the physical constraints on process states are embedded in the machine learning models to prevent physically unreasonable predictions. Subsequently, the PIRNN model that captures the dynamic behavior of the batch crystallization process is utilized in the design of model predictive controller that optimizes the operation of the crystallizer. Through open-loop and closed-loop simulations, it is demonstrated that the PIRNN models using less training data achieve prediction accuracy and closed-loop performance comparable to the purely data-driven model.

Machine Learning-Based MPC of Batch Crystallization Process Using Physics-Informed RNNs

This work presents a framework for developing physics-informed recurrent neural network (PIRNN) models and PIRNN-based predictive control schemes for batch crystallization processes. The population balance model of aspirin crystallization process is first developed to describe the formation of crystals through nucleation and growth. Then, the PIRNN modeling scheme is introduced to integrate observational data and mechanistic models for the development of machine learning models. Subsequently, the PIRNN model that captures the dynamic behavior of the batch crystallization process is utilized in the design of model predictive control. Through open-loop and closed-loop simulations, it is demonstrated that the PIRNN models using less training data achieve prediction accuracy and closed-loop performance comparable to the purely data-driven model.

Just-In-Time Learning Based Functional Spectral Data Modeling for In-Situ Measurement of Slurry Component Concentrations via Infrared Spectroscopy

For using the infrared spectroscopy to conduct in-situ measurement of slurry component concentrations during batch crystallization or fermentation process in engineering practice, a novel just-in-time learning (JITL) based functional modelling method is proposed for spectral data analysis in this paper to improve on-line measurement accuracy, by addressing engineering issues of very limited assay samples, spectral absorption nonlinearity and high-dimensional spectral variables. The traditional univariate or multivariate partial least-squares (PLS) model is subtly extended to the corresponding functional form for describing the relationship between the measured spectra and slurry component concentrations, such that the salient problem of only a small number of slurry component concentration samples available in practice for spectral data modeling could be effectively solved. The wavelet functions are adopted to properly approximate the measured spectral curves owing to their multi-scale and orthogonal properties. Accordingly, a functional spectral data model is established by wavelet functional PLS for on-line measurement of single and multiple component concentrations, respectively. Meanwhile, a JITL strategy is introduced to select the most representative samples for such modeling, which could efficiently handle the disparity issue involved with real-time samples and guarantee the model validity. Experimental results show that root mean square error of model prediction on the solution concentration during L-glutamic acid cooling crystallization process and multiple componts of ethanol fermentation process, could be evidently reduced over 40% and 50%, respectively, compared with the traditional PLS and support vector regression methods.

Primal–dual differential dynamic programming: A model-based reinforcement learning for constrained dynamic optimization

The main objective of this study is to develop primal–dual differential dynamic programming (DDP), a model-based reinforcement learning (RL) framework that can handle constrained dynamic optimization problems. DDP has advantages of being able to provide a closed-loop policy and having computational complexity that grows linearly with respect to the time horizon. To take advantage, the DDP should consider optimality and feasibility for the disturbed state during closed-loop operations. Previous DDPs consider the feasibility only for the nominal state condition and can handle limited types of constraints. In this paper, we propose a primal–dual DDP incorporating modified augmented Lagrangian that can handle general nonlinear constraints. We pay special attention to obtain the feasible policy when active set changes due to the state perturbations, using path-following predictor–corrector approach. The developed framework method was applied to van der Pol oscillator and batch crystallization process, thereby validating the key aspects of this study.

Process intensification of atorvastatin calcium crystallization for target polymorph development via continuous combined cooling and antisolvent crystallization using an oscillatory baffled crystallizer

In this paper, continuous crystallization of Atorvastatin calcium (ASC) using a continuous oscillatory baffled crystallizer (COBC) has been investigated. Like most API manufacturing, ASC is manufactured batchwise and the pure API is recovered via batch combined cooling and antisolvent crystallization (CCAC) process, which has the challenges of low productivity, wide crystal size distribution (CSD) and sometimes polymorphic form contamination. To overcome the limitations of the batch crystallization, continuous crystallization of ASC was studied in a NiTech (United Kingdom) DN15 COBC, manufactured by Alconbury Weston Ltd. (AWL, United Kingdom), with the aim to improve productivity and CSD of the desired polymorph. The COBC has the advantage of high heat transfer rates and improved mixing that significantly reduces the crystallization time. It also has the advantage of spatial temperature distribution and multiple addition ports to control supersaturation and hence the crystallization process. This work uses an array of process analytical technology (PAT) tools to assess key process parameters that affect the polymorphic outcome and CSD. Two parameters were found to have significant impact on the polymorph, they are ratio of solvent to antisolvent at the point of mixing of the two streams and presence of seeds. The splitting of antisolvent into two addition ports in the COBC was found to give the desired form. The CCAC of ASC in COBC was found to be -30-fold more productive than the batch CCAC process. The cycle time for generating 100 g of desired polymorphic form of ASC also significantly reduced from 22 h in batch process to 12 min in the COBC. The crystals obtained using a CCAC process in a COBC had a narrower CSD compared to that from a batch crystallization process.

Development of a recurrent neural networks-based NMPC for controlling the concentration of a crystallization process

Crystallization is a separation and purification process relevant to industrial sectors, such as pharmaceuticals. The maximum possible recovery of solute amount is one of its goals, and the temperature profile is crucial to achieve this. In this work, neural networks-based models were developed to predict the solute concentration of a batch crystallization process and used as internal model in a nonlinear model predictive controller. Three different neural network architectures were considered: the multilayer perceptron (MLP) network, the echo state network (ESN), and the long short-term memory (LSTM). The dataset used for training and testing applied a co-teaching learning algorithm, which uses simulated and experimental data from the batch crystallization of the potassium sulfate (K2SO4). The three network structures were trained to predict the solute concentration one step ahead, using the current temperature and concentration values as feed, and the predictive performances were evaluated for larger prediction horizons. A nonlinear model predictive controller (NMPC) based on the ESN, the most efficient neural network design, was successfully applied to the batch crystallization process to maintain the solute concentration on its desired trajectories by manipulating the operating temperature. The controller's behavior was studied for three different set-points of concentration and supersaturation, varying the initial concentration. The performance of the proposed NMPC was compared to a controller based on a more traditional approach, using the MLP network as internal model.

External fine particle removal for crystallization processes: Introduction and systematic comparison with the temperature cycling-based fines removal

Intermittent small particle removal is frequently used for particle property improvement in batch crystallization processes. This is generally solved by partial dissolution cycles, which for a cooling crystallization translates to temperature cycles - well suited for small-scale experimentation. However, implementing temperature cycles on a larger scale may face technical difficulties. This paper investigates a concept for fine particle removal, namely, the controlled external fines removal. Here, controlled dissolution is achieved in an external environment being attached to the crystallizer via a recirculation stream. Simulation-based external and internal fines removal is compared. The population balance model involves primary and secondary nucleation as well as crystal growth and dissolution. A two-level control system is developed: the low-level PI controller sets the vessel's temperature, whereas direct nucleation control (DNC) alternates between growth and dissolution cycles based on the actual particle number density. The paper demonstrates that the external fines’ removal results in slightly but consistently larger particles and a narrower size distribution in the majority of cases. Under optimal conditions, external fines’ removal leads to shorter batch times, and its convergence is significantly less sensitive to the DNC settings e.g., heating/cooling rates. From an energy utilization perspective, the internal fines removal requires less cooling and heating energy than the external configuration. The external configuration has great energy saving potential through heat integration as during the constant temperature recirculation the simultaneous heating and cooling duties in the crystallizer and heat exchanger match each other.

COOLING PROFILE OF POTASSIUM HYDROGEN TARTRATE BATCH CRYSTALLIZATION

Batch crystallization is an important chemical unit operation. So, large numbers of published works were focused on batch crystallization modelization, simulation, optimization, control and parameter estimation. In this work, an optimization is made with the objective to obtain the optimal cooling temperature strategy of a batch crystallizer realized in our laboratory. The potassium hydrogenotartarate (cream of tartar) subject of our study is recovered from wine tartar, a solid byproduct of winemaking, using batch cooling crystallization. To determine the optimum cooling temperature profile with a maximum yield of cream of tartar, we used coupled population, material and energy balance model. This model can describe the dynamics of the batch crystallization process. Based on this model, an optimal cooling temperature profile is calculated, using method of moments and the solubility data of cream tartar in water

A novel linear hybrid model predictive control design: application to a fed batch crystallization process

This paper addresses the problem of enabling the use of complex first principles model information as part of a linear Model Predictive Control implementation for improved control. This is achieved by building a hybrid model that uses an approximate implementation of a first principle model and a Subspace Identification (SID) State Space model to explain the error (the residual) between the first principle implementation and the process outputs. The key idea is to utilize the first principles model with the initial conditions consistent with a particular batch, but using a constant value of the control action. Thus, even though the first principles model may be intractable from an optimization perspective, the approximate implementation allows the hybrid model to be linear (in the control input), while allowing the nonlinear dependence on the initial conditions to be captured. The proposed hybrid model based MPC is compared against a previous hybrid model with 2 SID models and a single SID model on a fed batch crystallization process.The paper demonstrates the improved performance achievable by the readily implementable proposed approach.