Industrial Crystallization Research Articles

Size-Independent Nucleation and Growth Model of Potassium Sulfate from Supersaturated Solution Produced by Stirred Crystallization.

This paper explores the kinetics of the crystallization of potassium sulfate in a stirred bed crystallizer through experimental investigation. Employing classical nucleation theory, the homogeneous and heterogeneous nucleation mechanisms of potassium sulfate were investigated. The induction time and critical nucleation parameters, including the surface tension (γ), critical nucleation radius (r*), critical nucleation free energy (ΔG*), and critical nucleation molecule number (i*), were meticulously determined under varying temperatures and supersaturation ratios. The experimental findings revealed that as the temperature and supersaturation ratio increased, the induction time, critical nucleation free energy, critical nucleation radius, and critical molecule number decreased whereas the nucleation rate increased. The crystalline shape remains relatively unaltered with respect to temperature and supersaturation ratio, yet the particle size (D10, D50, D90) increases as the supersaturation and temperature increase. The variations in the measured nucleation parameters align well with the predictions of classical nucleation theory. Furthermore, the kinetic equations of crystal nucleation and the growth rate in a stirred crystallization system were fitted using population balance equations. The results demonstrate that the growth rate increases with increasing supersaturation and stirring rates. Additionally, the effects of the parameters in the nucleation rate equation suggested that the suspension density exerted the greatest influence, followed by the supersaturation ratio and stirring rate. This extensive research provides invaluable theoretical guidance for optimizing the crystallization process and designing industrial crystallizers.

A model-based supersaturation estimator (inferential or soft-sensor) for industrial sugar crystallization process

The degree of supersaturation of the mother liquor is a key factor in improving the monitoring and control of the final stage of industrial sugar crystallization. However, the difficulty of obtaining online supersaturation measurements is one of the challenges associated with monitoring and controlling sugar crystallization. There is no direct method or single instrument for measuring supersaturation. It can only be calculated or inferred from other measurements. In the literature, estimators of mother liquor supersaturation are reported, typically focused on the first stage of crystallization. The SeedMaster series transmitters are the sole industrial instruments that provide online supersaturation information by calculating it from external measurements. The purpose of this study is to design a first-principles model-based soft-sensor as a practical alternative to obtain real-time information about supersaturation in the last stage of sugar crystallization. The proposed estimator relies on two models: a supersaturation model and a second simplified model of the last stage of crystallization. The parameters of both models were estimated based on real industrial data. The estimation is performed in three steps: 1. An Unscented Kalman Filter estimates the states of the crystallization model and their variance. 2. The estimated supersaturation value is obtained by substituting the estimated states into the supersaturation model. 3. The estimator’s bias, and variance are calculated to establish error bounds. The main characteristics of the obtained estimator are: practical unbiasedness, nearly minimum variance and robustness. The performance and behavior of the supersaturation estimator are contrasted using real data from an industrial crystallization plant (Urbano Noris factory, Holguín, Cuba). Regardless of its initial conditions, the estimator converges to the three standard deviation error band in less than three minutes. The exact time may vary depending on how much the estimator’s initial conditions deviate from those of the process. After this time (Reach Time), the estimates remain within the calculated error limits of three standard deviations. The maximum absolute errors obtained were less than 0.019 units, corresponding to a maximum relative error of less than 1.5%. These values are favorable since they are well below critical values (0.125 units of absolute error). Moreover, the error bands are much smaller than the operating zone width (approximately 0.25 units), which is a necessary condition for any supersaturation estimator to be useful. Finally, it should be noted that the errors have been reduced compared to the values reported in previous research focused on the sugar industry using other techniques.

Research Progress in the Industrial Crystallization of Citrate—A Review

The citrate industry has a wide range of applications in food, pharmaceutical, and other fields. As a common class of food additives and functional supplements with tremendous development potential and strong core competitiveness, particles with good powder characteristics and functionalization are becoming one of the primary directions in the evolution of citrate into the high-end market. This article reviews the primary citrate crystallization techniques and examines the fundamental citrate crystallization mechanisms by describing citrate nucleation and growth during the industrial crystallization process. A variety of citrate hydrates are also summarized. The primary control conditions of the three essential product indices of purity, particle size, and grain shape are established. The need to take into account the density, fluidity, caking resistance, dissolution rate, suspension, bioavailability, and other indices of products is highlighted, along with applications for products that meet the purity and particle size requirements. While summarizing industrial citrate crystallization equipment, this paper also discusses the beneficial effect of continuous crystallization in achieving industrialization. Finally, the future development of citrate crystals is anticipated, and it is suggested that the combination of basic research and application research should be strengthened to explore the new application field of citrate crystals, and the automation and intelligence of the crystal preparation process should be realized as far as possible.

Cooling Crystallization of Paracetamol in a Slug-Flow Crystallizer with Silicone Oil as Continuous Phase

Continuous tubular crystallizers that can provide high yield and better control of crystal size would be of great interest to the industrial crystallization process. However, most continuous crystallizer designs face challenges either due to surface fouling or crystal breakage. In this paper, we explore the ability of slug-flow cooling crystallizers to continuously generate acetaminophen crystals using silicone oil as the continuous phase. Each slug acts as a crystallizer, and the crystals formed inside the dispersed phase avoid encrustation. Three crystallizer configurations were studied at a wide range of supersaturation and flow rates. It was found that a narrow crystal size distribution can be achieved at high flow rates and high supersaturation. Additionally, the average crystal size and the crystallization yield increased with supersaturation and residence time. The configuration of the tubular crystallizer was found to influence the crystallization yield by affecting the internal mixing in the slugs. With further studies, slug-flow cooling crystallizer can be developed for continuous crystallization of crystals with a narrow size distribution, polymorphic purity, and good yield.

Determination and correlation of solubility and Thermodynamic properties of allantoin in four binary solvents from 288.15 K to 333.15 K

The solid–liquid equilibrium data of allantoin were determined by gravimetric method in four binary solvents (methanol-water, ethanol-water, ethylene glycol-water and methanol-ethylene glycol) at temperatures ranging from 288.15 to 333.15 K. The allantoin exhibited high solubility in ethylene glycol-water solvents. The solubility increased and then decreased with the increasing ratio of ethanol to water above 318.15 K. Thermogravimetric analysis (TGA) and differential scanning calorimetry (DSC) indicated that allantoin would be decomposed above 505 K (T 5%). X-ray diffraction (XRD) showed that no crystalline transformation occurred in the investigated system. In the meanwhile, the experimental data were correlated by four thermodynamic models including modified Apelblat equation, Van’t Hoff equation, Jouyban–Acree model, and λh equation. All the models fitted well with the experimental data. This study can help the industrial crystallization of allantoin.

Effects of Properties of Crystalline Particles on Mother Liquor Holdup in Crystal Cake and Residue Behaviors of Impurities

In industrial crystallization, all impurity species need to be removed, regardless of the kind of impurity present in the raw materials. Removing the mother liquor is required because a crystal cake with mother liquor holdup is frequently formed by crystalline particles during solid-liquid separation in suspension-type melt crystallization. This study aims to make clear the relationship between the mother liquor holdup and the characteristics of the crystal cake, and the difference in residue behaviors of impurities based on the new concept for understanding the mother liquor holdup. As a result, the initial mother liquor holdup depended on the specific surface area of the crystal cake. Investigating the residue behavior of each impurity suggests that the impurity-based inclusion factors were different from the solvent-based inclusion factor depending on the kind of impurity. Furthermore, a certain impurity had a specific surface area dependence of the residual amount of impurity.

Comparison of the Effects of Crystalline Particle Size Modified by Crystallization on the Mother Liquor Removal Profiles of Washing and Reslurry

In industrial crystallization, the mother liquor recovered with the crystalline product causes a significant decrease in product purity. Therefore, additional purification processes, such as washing or reslurry, are often necessary to remove mother liquor from the particles to produce high-purity crystalline products. Although it is important to understand the characteristics of the purification processes for effective removal, a direct comparison between these different purification processes has rarely been reported. Therefore, the characteristics of washing and reslurry were compared using particle properties determined by crystallization. Herein, the mother liquor removal profiles of washing and reslurry were investigated considering changes in the removal ratio. We compared the profiles by normalizing the operating loads in each purification process. The purification processes were characterized by analyzing the particle-size dependency on the removal profiles. The results suggested that the removal profiles of washing and reslurry depended on the particle sizes, and the removal ratio was higher for reslurry for all ranges of loading when the particle size was identical. According to the proposed classification of mother liquors, by introducing the consideration of removability, we found that a primary cause was the ratio of mother liquor segments, which can change between different states of the particles during washing or reslurry. The effect of decreasing particle size on improving mother liquor removal in reslurry was more significant compared with that of washing. Therefore, reslurry is more beneficial for mother liquor removal by particle size modification via crystallization, compared with washing. This study provides primary knowledge on the operation design of the crystallization process for purification.

Insight into the role of ethylene glycol on thermodynamics and nucleation kinetics of dimethyl terephthalate in mixed solvent system

Dissolution and nucleation are two essential processes for industrial crystallization. This paper investigates the effect of ethylene glycol addition on the crystallization behavior of dimethyl terephthalate (DMT) in solution. The DMT solubility in mixed solvent system (methanol-ethylene glycol) was determined by isothermal satiation approach, and the solubility was associated using seven models. The model fitting results were consistent with the experimental values. Based on the results, the metastable zone width (MSZW) of DMT was detected by the polythermal approach; the modified Sangwal's theory was used to investigate the nucleation behavior, which can provide a new way of thought for better analysis of the crystallization behavior. The results demonstrated that MSZW was associated with various elements, such as cooling rate, saturation temperature and mass fraction of ethylene glycol. The addition of ethylene glycol slowed down the nucleation rate as shown by the broadening of MSZW. We derive the solid-liquid interface energy, the nucleation driving force, the critical nucleation size and the critical Gibbs free energy according to the classical nucleation theory. It is demonstrated that the nucleation driving force and the solid-liquid interface energy are dependent and jointly influence the MSZW.

Modeling and Optimization of the Para-Xylene Continuous Suspension Crystallization Separation Process via a Morphology Technique and a Multi-Dimensional Population Balance Equation

In this study, we carried out a para-xylene crystallization experiment at constant temperature and concentration levels. Throughout the process, the kinetics of nucleation, growth, breakage, and aggregation of para-xylene particles were measured and built using a morphological approach. An additional a three-stage continuous suspension crystallization separation experiment was carried out, the process for which was simulated using the population balance model based on correlated kinetic equations. The population balance equation was solved using an extended moment of classes algorithm, and the solving process was implemented in MATLAB. In this case, the predicted particle size distribution of the products matched well with the experiment. In order to provide references for the optimization of the industrial para-xylene crystallization process, a three-stage suspension crystallization separation experiment was designed and conducted, in which each crystallizer had a distinct operating temperature and mean residence time. The effects of operating parameters on the final product were investigated further. The proposed models and algorithms can also be applied in other cases and provide an alternative approach for optimizing continuous crystallization processes.

Crystallization by single diffusion through agar gel.

Crystallization is an important process in nature, various biological systems, and in industrial processes ranging from pharmaceuticals to material synthesis. In the industrial crystallization processes, common methods of crystallization include evaporative and cooling crystallization, and less frequently varying pH and addition of anti-solvents. The crucial driving force in all these techniques involves bringing the concentration of solutions to supersaturation to trigger the initial nucleation and growth of crystals. These conventional modes may not be applicable in systems where localized nucleation is required as these methods cause supersaturation throughout the bulk of solution which makes it challenging to affect crystallization at a specific desired location. In addition, these modes of reaching supersaturation cannot be used to explain or influence the crystallization in certain scenarios e.g., biological systems and in cases where the scope of temperature and a systemic pH change is very minimal. Another existing mode of crystallization involves the separation of ions into two different chambers and double diffusion through gels which is also not widely practical. Here we propose a mechanism in which we place salts in different solubility conditions on two sides of a permeable gel medium held at a steady state. Our steady state diffusion calculations predict that in certain pairings of different solubility conditions, the concentration of ions in the gel will always be above saturation concentration despite the absolute concentration decreasing along the length of the medium. We perform experiments in systems with variable solubilities in two different scenarios (pH and solvent mixtures) and we observe that the crystallization takes place in the gel indicating the supersaturation of the ions. This method offers an alternative way to get supersaturated solutions without evaporating solvents, changing temperatures, or separating the constituent ions into two different chambers across the diffusive medium.

Inclusion of the Mother Liquor of Three Different Salt Crystals Formed via Industrial Crystallization Processes

AbstractThree different salt crystals (K2SO4, KCl, and Na2SO4·10H2O) were produced via batch cooling and continuous crystallization using a bench‐scale crystallization device, in order to elucidate the mechanism of inclusion of the mother liquor as a function of crystal size. The inclusion ratio of the mother liquor was higher at small sizes and decreased with crystal growth. All results were represented by the previously proposed model of core‐aggregation and shell‐growth processes for the three different salt crystals. Crystals with small Vickers hardness aggregated with each other, and the inclusion ratio of the mother liquor of aggregated grown crystals was high for all three salt crystals tested herein.

Targeting Particle Size Specification in Pharmaceutical Crystallization: A Review on Recent Process Design and Development Strategies and Particle Size Measurements

Obtaining a particle size within the specifications for a pharmaceutical compound in an industrial crystallization can be a challenging task. The events affecting the final particle size of the product include nucleation, growth, breakage, and agglomeration, which are often convoluted. Secondary nucleation may significantly influence the particle size distribution. The strategies and techniques relevant to obtaining an in-spec particle size in crystallization are summarized and discussed from a perspective of process parameters. The effect of cooling profiles, seeding strategies, as well as mixing by agitation are reviewed, and an efficient and controlled crystallization process may be achieved using an optimized combination of these conditions. Multiple characterization methods for particle size and distribution are compared, and the discrepancies associated with the measurements are addressed.

Size-dependent growth kinetics model for potassium chloride from seeded chloride solution

Abstract It was widely known that crystallization kinetics are the basis for crystallization behavior and crystallizer scale-up design. Cooling crystallization of potassium chloride was an essential unit operation in recycling industry. Some researchers have proposed the strategy of adding seed crystals for the intermittent cooling crystallization process to control the particle size and distribution of the target product. This paper studied the complex function relation between particle size and growth rate of KCI in the crystallization process in a continuous mixed-suspension mixed-product-removal (MSMPR) crystallizer at a steady state. Using the crystallization kinetics data, the mathematical models of coupling crystallization were established based on the population balance equations and mass balance equations. Since population density distributions of products behave multiform under different conditions, based on diffusion theory. The growth rate was obtained by a least square method for the multivariate linear regression, and the reliability of the kinetics model was validated experimentally. Fitting results indicated that some classical models, including several size-independent growth models and size-dependent growth models, such as Bransom, C-R, MJ2, ASL, and MJ3, could not model the size-dependent growth accurately. Based on this situation, an exponential growth model was proposed and confirmed to describe the size-dependent growth behavior. It was found that the model parameters have definite meanings and were strongly related to particle size. Compared with the classical models, this model showed good pertinency and adaptability to experimental results when used to describe the population density distribution and the size-dependent growth rate of KCI. This research could provide a theoretical guide for optimizing the crystallization process and designing industrial crystallizers.

Simulation of flow field in silicon single-crystal growth using physics-informed neural network with spatial information

Melt convection plays a crucial role in the growth of silicon single crystals. In particular, melt flow transfers mass and heat, and it may strongly affect the crystal growth conditions. Understanding and controlling convection remains a significant challenge in industrial crystal production. Currently, numerical methods such as the finite element method and the finite volume method are mainly used to simulate melt convection in the crystal growth process. However, these methods are not suitable for most applications with real-time requirements. Physics-informed neural networks (PINNs) have the advantages of fast calculation and wide application. They provide a new concept for the numerical solutions of nonlinear partial differential equations (PDEs). This paper proposes a PINN with spatial information to solve the silicon melt flow model, which does not depend on any simulation data. As the network depth (number of layers) increases, the derivative information in the PDE loss becomes weak, which reduces the expression of the original features in the loss function. Therefore, this study introduces spatial information into the hidden layer of the network, thereby enhancing the correlation between the network and the original input and improving the expression ability of the network. Specifically, silicon melt flow models under three rotating conditions are considered. Compared with other methods, the proposed algorithm can accurately capture regions with complex local morphology. The experimental results reveal the flow characteristics of the silicon melt and confirm the effectiveness of the proposed algorithm. All codes and data attached to this manuscript are publicly available on the following websites: https://github.com/callmedrcom/SIPINN.

Solubility determination and thermodynamic model analysis of nevirapine in different organic solvents from 278.15 K to 328.15 K

Nevirapine (NVP) is the first non-nucleoside reverse transcriptase inhibitor drug to be marketed for the treatment of HIV. The solubility of NVP under atmospheric pressure in eleven pure solvents and three mixtures was measured from 278.15 to 323.15 K. XRD and DSC were used to detect the crystal form and stability of NVP in this work. Overall, the solubility of NVP gradually increases as the temperature rises. In addition, under the same temperature conditions, the solubility of NVP increases with the ratio of the positive solvents in binary solvents. In the mixture (DMF + acetonitrile), when the proportion of DMF reaches 0.8, the solubility in the binary solvent is greater than that in pure DMF. The experimental data was fitted by five thermodynamic models (Buchowski-Ksiazaczak λh model, the Modified Apelblat model, Jouyban-Acree model, SUN model, and CNIBS/R-K model). Subsequently, the largest mean square deviation value (RMSD) is only 2.31E-04, which demonstrates that the correlation of the solubility data and the five models is relatively good. Additionally, KAT-LSER model was used to explore the effects of solute–solvent interactions on solubility at 298.15 K. The analysis results indicated that the dipolarity/polarizability (π∗) of pure solvents plays a crucial role in the dissolution of NVP and its proportion of the total solvent effect reaches 30.92 %. This research was explored and developed the important systems (1-propyl alcohol and DMF + acetonitrile) for the industrial crystallization purification of NVP.

Kinetic characteristics of evaporative crystallization desalination of acidic high-salt wastewater

CLT acid (2-amino-4-methyl-5-chlorobenzenesulfonic acid) is a red organic pigment intermediate, which is widely used in textile printing and dyeing industry, but a large amount of acidic MgSO4 high-salt wastewater will be generated during the production process. Direct discharge not only wastes sulfates in wastewater, but also damages the environment. In this paper, a new treatment process is developed to separate and recover MgSO4 from high-salt wastewater by thermal evaporation crystallization method, which realizes the resource utilization and ensures the treatment effect. Through the evaporative crystallization kinetic experiment and the pilot experiment of acidic MgSO4 high-salt wastewater, the influence of operating conditions on the product crystal size and crystal size distribution was investigated. The results show that the crystal growth is completed when the residence time is 40 min, the stirring speed is 200 r/min, and the seed content is 3 g/L. In industrial production, crystallization and recrystallization should be carried out after removing organic matters. When the concentration ratio is 1.6, the purity of MgSO4 crystal reach 96 %, and the resources can be maximized.

Lysozyme crystallization in hydrogel media under ultrasound irradiation

Sonocrystallization implies the application of ultrasound radiation to control the nucleation and crystal growth depending on the actuation time and intensity. Its application allows to induce nucleation at lower supersaturations than required under standard conditions. Although extended in inorganic and organic crystallization, it has been scarcely explored in protein crystallization. Now, that industrial protein crystallization is gaining momentum, the interest on new ways to control protein nucleation and crystal growth is advancing. In this work we present the development of a novel ultrasound bioreactor to study its influence on protein crystallization in agarose gel. Gel media minimize convention currents and sedimentation, favoring a more homogeneous and stable conditions to study the effect of an externally generated low energy ultrasonic irradiation on protein crystallization avoiding other undesired effects such as temperature increase, introduction of surfaces which induce nucleation, destructive cavitation phenomena, etc. In-depth statistical analysis of the results has shown that the impact of ultrasound in gel media on crystal size populations are statistically significant and reproducible.

Deep learning-based on-line image analysis for continuous industrial crystallization processes

In situ microscopic imaging is a useful tool in monitoring crystallization processes, including crystal nucleation, growth, aggregation and breakage, as well as possible polymorphic transition. To convert the qualitative information to be quantitative for the purpose of process optimization and control, accurate analysis of crystal images is essential. However, the accuracy of image segmentation with traditional methods is largely affected by many factors, including solid concentration and image quality. In this study, the deep learning technique using mask region-based convolutional neural network (Mask R-CNN) is investigated for the analysis of on-line images from an industrial crystallizer of 10 m3 operated in continuous mode with high solid concentration and overlapped particles. With detailed label points for each crystal and transfer learning technique, two models trained with 70,908 and 7,709 crystals respectively are compared for the effect of training data amount. The former model effectively segments the aggregated and overlapped crystals even at high solid concentrations. Moreover, it performs much better than the latter one and traditional multi-scale method both in terms of precision and recall, revealing the importance of large number of crystals in deep learning. Some geometrical characteristics of segmented crystals are also analyzed, involving equivalent diameter, circularity, and aspect ratio.

Solubility of Organic Salts in Solvent-Antisolvent Mixtures: A Combined Experimental and Molecular Dynamics Simulations Approach.

We combine molecular dynamics simulations with experiments to estimate solubilities of an organic salt in complex growth environments. We predict the solubility by simulations of the growth and dissolution of ions at the crystal surface kink sites at different solution concentrations. Thereby, the solubility is identified as the solution’s salt concentration, where the energy of the ion pair dissolved in solution equals the energy of the ion pair crystallized at the kink sites. The simulation methodology is demonstrated for the case of anhydrous sodium acetate crystallized from various solvent–antisolvent mixtures. To validate the predicted solubilities, we have measured the solubilities of sodium acetate in-house, using an experimental setup and measurement protocol that guarantees moisture-free conditions, which is key for a hygroscopic compound like sodium acetate. We observe excellent agreement between the experimental and the computationally evaluated solubilities for sodium acetate in different solvent–antisolvent mixtures. Given the agreement and the rich data the simulations produce, we can use them to complement experimental tasks, which in turn will reduce time and capital in the design of complicated industrial crystallization processes of organic salts.

Evolutionary neural architecture search for surrogate models to enable optimization of industrial continuous crystallization process

Optimal performance of the crystallization process is of utmost importance for industries handling bulk commodity chemicals to pharmaceuticals. Such an optimization exercise becomes extremely time expensive as the mathematical models mimicking such complex processes involve the solution of Integro-Differential Population Balance Equations using High Resolution Finite Volume Methods. In order to build a fast and robust data based alternative model, a surrogate assisted approach using Artificial Neural Networks has been proposed here. To overcome the heuristics-based estimation of the hyper-parameters in ANNs, we aim to contribute a novel Neural Architecture Search strategy for the auto-tuning of hyper-parameters integrated with sample size determination techniques. While solving a multi-objective optimization of crystallization process ensuring maximum productivity, the results from surrogates are compared with those of a high-fidelity physics driven model, which reports five order of magnitude speed improvement without sacrificing much on accuracy.