Final Crystal Size Distribution Research Articles

A model-based nucleation study of the combined effect of seed properties and cooling rate in cooling crystallization

Crystallization is a widely used unit operation for the production of pharmaceuticals, fertilizers, and fine chemicals. A commonly used crystallization operational objective is to produce large crystals under minimum nucleation rates. For cooling crystallization there are two key methods for minimizing nucleation, programmed cooling and seeding. In this paper, we evaluate the cooling and seeding methods through the detailed modeling of nucleation phenomena coupled with a population balance and dynamic optimization of this mathematical formulation. Extensive simulation results showed that initial seeding parameters, as proclaimed by others, do have a significant effect on the final product crystal size distribution. It also showed the significance of a combined seeding–cooling approach where a joint cooling and seeding optimization gives superior performance to just optimizing the seed. Importantly, the developed model was highly instrumental in rapidly determining optimal combined seeding–cooling profiles via dynamic model-based optimizations.

Effect of seed loading and cooling rate on crystal size and shape distributions in protein crystallization—A study using morphological population balance simulation

A morphological population balance model is applied to crystallization of hen-egg white lysozyme for investigation of the effect of seed loading and cooling rate on supersaturation, and crystal size and shape distributions. Growth rates of individual faces and final crystal size and shape distributions were examined under varied seeding and cooling conditions. It was found that for growth only crystallization, desired crystal size and shape can be obtained by coordinative manipulation of the seed loading and cooling rate: low seed loading and high cooling rate lead to large crystals of low aspect ratio, but care has to be taken to avoid nucleation and major shape change such as width becoming larger than the length. The interesting results not only demonstrate the effectiveness of morphological population balance simulation for protein crystallization but also provide useful knowledge for process optimization and control.

Efficient solution of a batch crystallization model with fines dissolution

In this paper, an efficient and accurate numerical method is proposed for solving a batch crystallization model with fines dissolution. The dissolution of small crystals (fines dissolution) is useful for improving the quality of a product. This effectively shifts the crystal size distribution (CSD) towards larger crystal sizes and often makes the distribution narrower. The growth rate can be size-dependent and a time-delay in the dissolution unit is also incorporated in the model. The proposed method has two parts. In the first part, a coupled system of ordinary differential equations (ODEs) for moments and solute mass is numerically solved in the time domain of interest. These discrete values are used to get growth and nucleation rates in the same time domain. In the second part, the discrete growth and nucleation rates along with the initial CSD are used to construct the final CSD. The analytical expression for CSD is obtained by applying the method of characteristics and Duhamel's principle on the given population balance model (PBM). A Gaussian quadrature method, based on orthogonal polynomials, is used for approximating integrals in the ODE-system of moments and solute mass. The efficiency and accuracy of the proposed numerical method is validated by a numerical test problem.

Nucleation of Alpha lactose monohydrate induced using flow through a venturi orifice

Nucleation is a determinant of the final crystal size distribution produced during a crystallization process. Other studies in the literature have shown that mixing influences alpha lactose monohydrate nucleation. To investigate this in more detail, three different sized Venturi orifices were used to provide a point of passive mixing for supersaturated lactose solutions. This system allowed the study of different factors associated with characterising the mixing process, including cavitation, power input, Reynolds number and vortex formation. A strong relationship was found between the number of vortices created in the system and the nucleation rate. It is speculated that the vortices decrease the distance required for diffusion of molecules in the system, increasing the rate at which they can come together to form a stable nuclei.

First in situ observation of crystallization processes in a basaltic-andesitic melt with the moissanite cell

Research Article| November 01, 2009 First in situ observation of crystallization processes in a basaltic-andesitic melt with the moissanite cell Federica Schiavi; Federica Schiavi 1Bayerisches Geoinstitut, Universität Bayreuth, D-95440 Bayreuth, Germany Search for other works by this author on: GSW Google Scholar Nicolas Walte; Nicolas Walte 1Bayerisches Geoinstitut, Universität Bayreuth, D-95440 Bayreuth, Germany Search for other works by this author on: GSW Google Scholar Hans Keppler Hans Keppler 1Bayerisches Geoinstitut, Universität Bayreuth, D-95440 Bayreuth, Germany Search for other works by this author on: GSW Google Scholar Geology (2009) 37 (11): 963–966. https://doi.org/10.1130/G30087A.1 Article history received: 29 Jan 2009 rev-recd: 04 Jun 2009 accepted: 07 Jun 2009 first online: 02 Mar 2017 Cite View This Citation Add to Citation Manager Share Icon Share MailTo Twitter LinkedIn Tools Icon Tools Get Permissions Search Site Citation Federica Schiavi, Nicolas Walte, Hans Keppler; First in situ observation of crystallization processes in a basaltic-andesitic melt with the moissanite cell. Geology 2009;; 37 (11): 963–966. doi: https://doi.org/10.1130/G30087A.1 Download citation file: Ris (Zotero) Refmanager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentBy SocietyGeology Search Advanced Search Abstract The evolution of texture and crystal size distribution of igneous rocks is mainly determined by processes such as nucleation, grain growth, and Ostwald ripening. However, the role played by these processes on the final crystal size distribution is difficult to quantify with conventional methods. Here we present the first direct in situ observation of a crystallizing supercooled basaltic-andesitic liquid in order to directly assess the role of grain-scale processes occurring during magma solidification. The experiments were conducted at 900 °C and 1 bar with a new moissanite cell specifically designed for long-term high-temperature experiments. The method allowed the direct continuous observation of the crystallizing melt until the crystal fraction approached 0.7. Investigation of the evolving texture revealed that individual crystals followed distinct growth histories characterized by intervals of relatively uniform free growth, abrupt size increase due to grain coalescence, and growth reduction due to impingement; the latter played a dominant role at higher crystal fractions. Despite this growth dispersion, average growth rates calculated for single grains showed only little variation (4.9 × 10−6 to 1.9 × 10−6 mm/s). No clear relation between growth rate and crystal size was observed. Crystal coarsening through a combination of overgrowth and coalescence can also account for the counterclockwise rotation and the drop-off at smaller size fractions of the recovered crystal size distributions in our experiments. These results suggest that crystal size distributions of natural rocks do not record the original nucleation rates. You do not have access to this content, please speak to your institutional administrator if you feel you should have access.

Investigation of the Crystallization Kinetics of Dextrose Monohydrate Using In Situ Particle Size and Supersaturation Monitoring

In this work, a seeded batch cooling crystallizer was used to study dextrose monohydrate crystallization using in situ techniques. Experiments were conducted to investigate the influence of cooling profile (natural, linear, and controlled cooling) and seed mass on dextrose monohydrate crystallization. Two in situ techniques, Lasentec focused beam reflectance measurement (FBRM) and an in-line process refractometer for monitoring aqueous crystallization of dextrose monohydrate, were used. The seed mass and cooling profile were focused on, in particular, determining the effect of secondary nucleation and crystal growth rate on the final crystal size distribution, the evolution of supersaturation, and yield of dextrose monohydrate. Experimental results were analyzed to evaluate the kinetic constants from growth and nucleation power law functions with supersaturation. The results showed that increasing the seed mass decreased the level and the peak of supersaturation and increased the crystal growth rate. The experiment performed with natural cooling and with high seed mass resulted in the highest yield. Furthermore, the results showed a significant increase in the final crystal size with decreasing seed mass.

An efficient numerical technique for solving one-dimensional batch crystallization models with size-dependent growth rates

In this work, an efficient numerical method is introduced for solving one-dimensional batch crystallization models with size-dependent growth rates. The proposed method consist of two parts. In the first part, a coupled system of ordinary differential equations (ODEs) for the moments and the solute concentration is numerically solved to obtain their discrete values in the time domain of interest. These discrete values are also used to get growth and nucleation rates in the same time domain. To overcome the issue of closure, a Gaussian quadrature method based on orthogonal polynomials is employed for approximating integrals appearing in the ODE system. In the second part, the discrete growth and nucleation rates along with the initial crystal size distribution (CSD) are used to construct the final CSD. The expression for CSD is obtained by applying the method of characteristics and Duhamel's principle on the given population balance model (PBM). The proposed method is efficient, accurate, and easy to implement in the computer. Several numerical test problems of batch crystallization processes are considered. For a validation, the results of the proposed technique are compared with those obtained using a high resolution finite volume scheme.

Semi-batch reactive crystallisation of mono-ammonium phosphate: An experimental study

NH 4H 2PO 4, mono-ammonium phosphate (MAP) and (NH 4) 2HPO 4, di-ammonium phosphate (DAP) have become leading phosphate fertiliser products worldwide. Ammonium phosphates are produced by reactions of ammonia and phosphoric acid resulting in the formation of the mono-basic, di-basic, or tri-basic salts. Inefficiencies in the MAP/DAP production process are due to the lack of a fundamental understanding of the crystallisation–reaction mechanisms. A semi-batch reactive crystalliser equipped with a cooling jacket, a dual feed system and a turbine type agitator has been used in this study. Effects of N/P ratio, seed crystals, feeding system, feed flow rate, initial supersaturation, feeding time and mixing intensity to the real-time supersaturation, crystal yield, crystal shape (aspect ratio) and final crystal size distribution (CSD) were studied in order to understand the kinetics. This study aims to provide new insights into the MAP/DAP reaction–crystallisation mechanisms.

An efficient numerical technique for solving multi-dimensional batch crystallization models with size independent growth rates

This article introduces an efficient numerical technique for solving multi-dimensional batch models. The method requires initial crystal size distribution (CSD) and initial solute mass. The initial CSD is used to calculate the initial moments as an initial data for the reduced moments system. The solution of the moments system coupled with an algebraic equation for the mass gives moments and mass at the discrete points of the computational time domain. These values are then used to get the discrete values of growth and nucleation rates. The discrete values of growth and nucleation rates along with the initial CSD are sufficient to get the final CSD. In the derivation of current technique the Laplace transformation of the population balance equation (PBE) plays an important role. The method is efficient, accurate and easy to implement. For validation, the results of the proposed scheme are compared with those from the high resolution finite volume scheme.

The Impact of Direct Nucleation Control on Crystal Size Distribution in Pharmaceutical Crystallization Processes

The control of crystal size distribution (CSD) in pharmaceutical crystallization is of primary importance, as downstream processes such as filtration or drying are greatly affected by the properties of the CSD. It is recognized that the variability in the final CSD is mainly caused by the significant uncertainties in the nucleation rates, and therefore, a good control of nucleation events is necessary to achieve the desired CSD. In this paper, a new direct nucleation control (DNC) approach is introduced that directly controls the apparent onset of nucleation defined as the formation of new particles with detectable size using in situ instruments. The approach uses information on nucleation and dissolution, provided by focused beam reflectance measurement (FBRM), in a feedback control strategy that adapts the process variables, so that the desired quality of product is achieved, for example large crystals with a narrow CSD. In addition, DNC provides in situ fines removal through the operating protocol, rather than having additional equipment and external recycle loops. DNC does not require concentration measurement and has the advantage of being a model-free approach, requiring no information on nucleation or growth kinetics in order to design an operating curve. The DNC approach automatically and adaptively detects the boundary of the operating zone; hence it is more robust to the presence of impurities or residual solvent than the supersaturation control approach. The approach has been applied for the crystallization of glycine and experimental results demonstrate the benefits of DNC of producing larger crystals with narrower CSD compared to classical operations.

A Laplace transformation based technique for reconstructing crystal size distributions regarding size independent growth

This article introduces a technique for reconstructing crystal size distributions (CSDs) described by well-established batch crystallization models. The method requires the knowledge of the initial CSD which can also be used to calculate the initial moments and initial liquid mass. The solution of the reduced four-moment system of ordinary differential equations (ODEs) coupled with an algebraic equation for the mass gives us moments and mass at the discrete points of the given computational time domain. This information can be used to get the discrete values of size independent growth and nucleation rates. The discrete values of growth and nucleation rates along with the initial distribution are sufficient to reconstruct the final CSD. In the derivation of current technique the Laplace transformation of the population balance equation (PBE) plays an important role. The proposed technique has dual purposes. Firstly, it can be used as a numerical technique to solve the given population balance model (PBM) for batch crystallization. Secondly, it can be used to reconstruct the final CSD from the initial one and also vice versa. The method is very efficient, accurate and easy to implement. Several numerical test problems of batch crystallization processes are considered here. For validation, the results of the proposed technique are compared with those from the high resolution finite volume scheme which solves the given PBM directly.

CRYSTAL GROWTH LIMITATION IN AQUEOUS FOAM CRYSTALLIZATION

We present results concerning the limitation of maximum crystal size by pre-foaming an aqueous supersaturated solution, followed by its crystallization. Foams are generated by adding specific surface active agents to the solution and by air injection under continuous high shear agitation, leading to a gas-liquid stable dispersion having polyhedral internal structures with thin separating liquid films. This spatial dispersion structuration, by locally reducing the amount of solute available for each crystal growth, permits the limitation of the resulting crystal sizes. It is shown that, under these conditions, the initial film thickness and mean bubble radius, obtained for a given volume fraction of gas in the foam, can control the final crystal size distribution. The foam expansion ratio thus appears to be a new operating parameter for crystal growth limitation when using a foam crystallization technique.

Crystallization of Monohydrate Citric Acid. 1. In Situ Monitoring through the Joint Use of Raman Spectroscopy and Image Analysis

Seeded batch crystallizations of monohydrate citric acid were performed under isothermal conditions (15 °C). Continuous monitoring of the overall solid concentration during the crystallization process was developed using in situ Raman spectroscopy. Quantitative estimation of the crystal size distribution (CSD) was made possible thanks to in situ image acquisition: off-line CSD measurements were further computed from the recorded pictures. The growth rate of monohydrate citric acid was estimated from solid concentration. Through in situ particle size visualization and quantitative analysis of the pictures, activated surface secondary nucleation was also shown to significantly impact the final CSD. It is underlined that, in addition to continuous Raman in situ spectroscopic concentration measurements, image acquisition yields highly valuable data on the dispersed phase. Advantages and drawbacks of the technique for the monitoring of solution crystallization are discussed.

Optimization in seeded cooling crystallization: A parameter estimation and dynamic optimization study

In this solution crystallization study, a population balance model that predicts the crystal size distribution (CSD) is used for targeting, by optimization, the product mean size and the coefficient of variation of the final CSD. The model is robust over a wide range of conditions and predicts the effects of heating during a batch since the kinetics of dissolution have been identified and incorporated into the model. The dynamic temperature profile and the initial seed size distribution are optimized while the initial seed induction time is conferred through knowledge of saturation conditions. This is quite a highly developed method that provides a systematic approach towards optimal operation. Results from optimizations under different objective functions are presented and validated experimentally.

Organic-free synthesis of ZSM-5 with narrow crystal size distribution using two-step temperature process

The MFI type of highly silica zeolite, ZSM-5 with well-defined crystal morphology was successfully synthesized in the absence of organic template using two-step temperature process. In this process, the crystallization process was conducted at two different temperatures by separating the nucleation and crystallization stage; that is, the nucleation stage at higher temperature (190 °C) to accelerate the nucleation followed by the crystallization stage at lower temperature (150 or 165 °C) so as to control the crystal size and size distribution. The effect of nucleation rate on the final crystal size and size distribution adopting higher temperature of the first stage for nucleation than that of the second stage for crystallization was investigated. The results show that two-step temperature process could control the crystal size and size distribution of ZSM-5. The result also shows that the time duration at higher temperature for the acceleration of nucleation strongly affects the crystal size and size distribution. It implies that rapid nucleation at higher temperature forms large number of nuclei followed by slow crystal growth probably due to the lack of energy at lower temperature. It is very critical, therefore that the optimum time duration at higher temperature should be chosen to accelerate the nucleation within initial stage.

Growth Kinetics of Manganese Sulphate from Heating and Salting‐out Batch Crystallisation

AbstractManganese sulphate crystals can be produced in laboratory‐scale batch crystallisers by either heating or by salting‐out crystallisation. However, manganese sulphate produced through heating forms monohydrate while salting‐out mode will form the tetrahydrate. The effects of various operating conditions including supersaturation, temperature and seed dosage on growth rate of these hydrates were studied. The crystal size distribution of manganese sulphate crystals was determined by Malvern Mastersizer laser diffraction and by using a Nikon microscope with digital camera attached. The growth rate was determined from the time shft of the crystal size distribution expressed in population density numbers and by the moments method. The measurements of the growth of the crystals from ex situ microscopy supported the calculated growth rate. Salting‐out crystallisation resulted in relatively large cubic crystals, and their size and size distribution can be improved by careful control of the operating conditions. However, heating crystallisation produced irregular crystals where controlling the operating conditions has little effect on the final crystal size and size distribution with almost no observable growth.

Interactions of Precipitation and Fluid Mixing with Model Validation by Electrical Tomography

Extensive new tomographic results are reported for barium sulphate precipitation in a stirred vessel under semi-batch operation exhibiting imperfect fluid mixing. An ITS System-2000 was utilized and a linear-back-projection algorithm employed for the creation of 3-D process images. It can be concluded that electrical resistance tomography (ERT) successfully captured the sequential electrical conductivity field behaviour with both sufficient spatial and temporal resolution. It also visualized the changes in the electrical conductivity field within the vessel when changing reactant feed locations. In addition, the mixing effects on the final crystal size distributions (CSD) were also experimentally investigated. Furthermore, it is confirmed that the data obtained by ERT is effective to validate a detailed precipitation process model. A new precipitation model has been developed and combined and hybridized with a networks-of-zones model which can represent imperfect mixing in a stirred vessel. The multi-zone mixing model with order 10 3 zones is commensurate with the vessel sub-division used for tomographic imaging. The images predicted by the 3-D hybridized model are compared with the tomographic measured results, including both temporal and spatial distributions, and they show good agreement.

Evaluation of optimisation techniques and control variable formulations for a batch cooling crystallization process

The mathematical optimisation of a batch cooling crystallization process is considered in this work. The objective is to minimize the standard deviation of the final crystal size distribution (CSD), which is an important feature in many industrial processes. The results with the problem written as a nonlinear programming and solved with the successive quadratic programming (SQP) coupled with the discretization of the control variable are compared with those obtained when SQP coupled with the parameterisation of the control variable is applied. Also it is proposed the implementation of the genetic algorithm (GA) coupled with parameterisation of the control variable. Extensive evaluations show that the SQP method is sensitive both to the parameterisation formulation and to the initial estimate. The solution with GA provided the control variable profile that leads to the minimum standard deviation of the final CSD. Nevertheless, it is a very time-consuming technique, which hampers its utilization in real time applications. However, its feature of global searching suggests its suitability in solving offline problems, in order to provide initial setup profiles. Bearing this in mind, it is proposed an algorithm which allows for the implementation of GA solution in a real time fashion, taking advantage of its robustness to find out the optimal solution.

Cooling and seeding effect on supersaturation and final crystal size distribution (CSD) of ammonium sulphate in a batch crystallizer

Different cooling policies (natural (NCP), linear (LCP), controlled (CCP), as well as a proposed cooling policy; impulse changes in natural cooling policy (IC-NCP)) and seeding policies (with two different mean seed size and various seed loadings) were employed to investigate the effect of cooling and seeding on the final CSD of ammonium sulphate grown in a batch-cooling crystallizer. The crystallizer was equipped with an on-line density meter for the estimation of supersaturation. By increasing the amount of the seeds, the supersaturation peak was reduced and a uni-modal final CSD was obtained, irrespective of the cooling policy. At high seed loading ( C s), greater than theoretical critical seed loading ( C s , c theo ) predicted by the seed chart, the cooling policy had no significant effect on the final CSD. However, at low C s, controlled cooling policy was needed in order to ensure uni-modal and narrow final CSD with large mean size. With the help of a simple on-off control, the IC-NCP was applied to overcome the mathematical complexities associated with the controlled cooling policy. All CSD results of the IC-NCP mode were between the linear and controlled cooling policies, and closer to the controlled cooling profile.

Batch cooling crystallization study based on in-line measurement of supersaturation and crystal size distribution

The in-line information of supersaturation and crystal size distribution is very important for the controlling and optimization of batch cooling crystallizations. Based on the in-line measurements of supersaturation with an attenuated total reflectance-Fourier transform infrared spectrophotometer and chord length distribution with an MTS laser reflection analyzer, the batch cooling crystallization of an organic compound, labeled as C15 is studied in this work. The crystal size distribution of the final product was also analyzed with a laser diffraction analyzer to verify the data obtained from the in-line instrument. Various cooling modes are tested, and the seeding policy is applied to improve the final crystal size distribution. The effects of the cooling modes and seeding are analyzed based on the obtained in-line supersaturation and off-line crystal size distribution data. Improved operation conditions are proposed in terms of large mean crystal size and narrow crystal size distribution. The result of this work shows that the spectrophotometer gave accurate solution concentration results with high resolution; the MTS in-line analyzer can be used to monitor chord length distribution and count rate trends.