Parameterization of population balance models for polythermal auto seeded preferential crystallization of enantiomers

For analysis, design and model-based control of crystallization processes typically population balance models or reduced models derived therefrom are used. Usually the kinetic parameters in these models are determined analyzing measured concentration trajectories and/or particle size distributions using parameter estimation procedures. In the case of preferential crystallization of enantiomers the analysis of experiments is complex since there are two “competing” crystal populations. In this field often batch processes are performed using seeds of the desired enantiomer. Currently, it is in particular challenging to quantify and optimize a new concept: e.g. the so-called “auto seeded programmed polythermal preferential crystallization” (“as3pc” [Coquerel, G., Petit, M.-N., Bouaziz, R., 2000. Method of resolution of two enantiomers by crystallization. United States Patent, Patent number: 6,022,409]). In order to design and optimize this process the temperature dependent kinetic constants for crystal growth, nucleation and dissolution have to be known. In this work a reduced model for this auto seeded process is presented. The general identifiability of the model parameters is investigated along with some suggestions on how to reparameterize the kinetic terms involved. The values of the identified key parameters are estimated using conventional least square optimization using experimental data determined for the model system threonine/water. Parameter confidence and cross correlation are discussed and finally the model is validated using experiments not used for parameter estimation.     

A novel kinetic approach to crystallization mechanisms in polymers

Kinetics of polymer crystallization is capable of modeling the polymer crystallization processes by revealing their mechanisms. Although complexities of polymer crystallization processes are familiar, a generalized approach for their kinetic modeling has not yet been suggested. This paper presents a concise review of the pre-existing kinetic approaches to polymer crystallization, including their pros and cons, putting a special emphasis on the necessity of approaches to polymer crystallization. A systematic and advanced approach comprising an innovative kinetic framework to model polymer crystallization processes is put forward using Hoffman-Lauritzen theory. Kinetic functions are developed for predicting the crystallization mechanisms of simple as well as complicated polymer crystallization processes. The suggested kinetic approach is experimentally justified by its effective applications to non-isothermal glass and melt crystallization of poly(ethylene 2,5-furandicarboxylate). An account of the soundness of the proposed kinetic approach and its prospective applications are also discussed.     

Tools for Design and Control of Industrial Crystallizers – State of Art and Future Needs

The design and control of industrial crystallizers continues to be a tremendous challenge. The tendency to move away from base‐chemicals towards fine‐chemicals will give a new impulse to the utilisation of crystallization technology for the separation and the formulation of particulate products. This paper reviews the most recent developments in the design industrial crystallizers and the development of novel crystallization processes. Furthermore it discusses emerging modeling tools needed for a flexible design and operation of crystallizers and crystallization processes that meet rapid changing product yield and specifications. Finally a new approach towards model‐based predictive control of crystallization processes is presented.     

Efficient separation of enantiomers by preferential crystallization in two coupled vessels

The focus of this work is to study the enantioseparation of conglomerate forming systems using an innovative configuration for preferential crystallization. Two batch crystallizers are coupled by an exchange of their liquid phases. In each vessel one of the two enantiomers is seeded initially and crystallizes subsequently. Compared with conventional single batch crystallization the exchange of the crystal free liquid phases between two crystallizers leads to an increase of the concentrations of the preferred enantiomers and therefore to an increase of the driving forces for the crystallization. This enhances the productivity of the process compared with the conventional operation. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

Comparison of numerical methods for the simulation of dispersed phase systems

This contribution deals with a new numerical method for an accurate and efficient simulation of particulate processes. As an example for dispersed phase systems a detailed model for crystallization processes is considered. After the model derivation, which is based solely on physical principles, different techniques for the numerical simulation of the mathematical model are discussed. State-of-the-art finite volume schemes based on the ‘method of lines’ approach are compared to the recently published ‘Space-time conservation element and solution element method’. The presented simulation results show a strong dependence on the chosen numerical method. Guidelines for a proper selection of numerical methods for the treatment of population balance based models are given.     

A stochastic formulation for the description of the crystal size distribution in antisolvent crystallization processes

A stochastic approach to describe the crystal size distribution dynamics in antisolvent based crystal growth processes is here introduced. Fluctuations in the process dynamics are taken into account by embedding a deterministic model into a Fokker‐Planck equation, which describes the evolution in time of the particle size distribution. The deterministic model used in this application is based on the logistic model, which shows to be adequate to suit the dynamics characteristic of the growth process. Validations against experimental data are presented for the NaCl–water–ethanol antisolvent crystallization system in a bench‐scale fed‐batch crystallization unit. © 2009 American Institute of Chemical Engineers AIChE J, 2010     

Numerical solutions of population balance models in preferential crystallization

This article focuses on the implementation of numerical schemes to solve model equations describing preferential crystallization for enantiomers. Two types of numerical methods are proposed for this purpose. The first method uses high resolution finite volume schemes, while the second method is the so-called method of characteristics (MOC). On the one hand, the finite volume schemes which were derived for general system in divergence form are computationally efficient, give desired accuracy on coarse grids, and are robust. On the other hand, the MOC offers a technique which is in general a powerful tool for solving growth processes, has capability to overcome numerical diffusion and dispersion, gives highly resolved solutions, as well as being computationally efficient. Several numerical test examples for a preferential crystallization model with and without fines dissolution under isothermal and non-isothermal conditions are considered. The comparison of the numerical schemes demonstrates clear advantages of the finite volume schemes and the MOC for the current model.     

Integrated solvent and process design for continuous crystallization and solvent recycling using PC‐SAFT

Solvent usage is a major source of environmental waste in pharmaceutical industry. The current paradigm shift toward continuous manufacturing in pharmaceutical industry has renewed the interest in continuous crystallization, which offers the prospect of easy solvent recycling. However, the selection of solvents for an integrated crystallization processes is nontrivial due to the likely trade‐off between optimal solvent properties for crystallization and solvent separation and recycling. A systematic approach for the simultaneous optimization of process conditions and solvent selection for continuous crystallization including solvent recycling is presented. A unified perturbed‐chain statistical associating fluid theory model framework is applied to predict thermodynamic properties related to solubility and vapor‐liquid equilibrium, which is integrated with a process model. A continuous mapping procedure is adopted to solve the optimization problem effectively. A case study based on continuous antisolvent crystallization of paracetamol with solvent separation via flash demonstrates the approach. © 2017 American Institute of Chemical Engineers AIChE J, 64: 1205–1216, 2018     

手性药物结晶拆分的研究进展

手性是自然界和生物体中广泛存在的一种性质,约半数以上的药物活性成分含有手性中心,受手性分子的空间立体选择性影响,手性对映体药物往往较其外消旋体表现出更高的活性、更低的副作用,因而,精准制备手性单一对映体药物具有非常重要的研究意义。目前,手性外消旋体拆分是制备单一对映体的最高效、便捷的途径,而结晶拆分是实现手性单一对映体分离最为重要且广泛应用的技术。综述了近年来手性药物结晶拆分的研究进展,梳理了结晶拆分研究的发展历程,重点介绍了基于经典拆分方法（非对映体成盐拆分和优先结晶）和近年来发展的基于优先富集和Viedma熟化的对映体拆分新技术以及结晶拆分的强化方法,并简述了色谱、膜分离等其他手性外消旋体分离方法。最后,对手性药物的结晶拆分方法进行了总结和展望。     

A new method for on-line monitoring of non isothermal crystallization kinetics of polymers

Summary Detailed knowledge of polymer crystallization kinetics is a mandatory requirement in modeling of transformation processes. On the other hand, techniques for investigation of crystallization kinetics are limited to cooling rates much lower than those experienced by the materials in industrial processes. A method suitable to investigate crystallinity evolution during cooling procedures carried out adopting rates comparable with those experienced by the polymer during industrial processes is thus extremely attractive. In this work a method is proposed, based on fast cooling of thin samples by means of air/water sprays and optical detection of the crystallization phenomenon. Preliminary results of crystallization temperatures detected with a device based on such a method are presented and, in the low cooling rate range, are compared favorably with calorimetric results. The comparison of experimental crystallization temperature with results of a kinetics model previously developed leads to satisfactory agreement. Received: 26 October 2001/Revised version: 12 February 2002/ Accepted: 12 February 2002     

A different approach for the study of the crystallization kinetics in polymers. Key study: poly(ethylene terephthalate)/ SiO2 nanocomposites

Polymer crystallization is complex and difficult to model, especially when it is non‐isothermal and even more so when describing cold crystallization. In most cases, two different processes occur, so‐called primary and secondary crystallization. In the literature, two assumptions are generally made. Firstly, the validity of the Avrami model is assumed a priori. Secondly, for calculations of the kinetic parameters and activation energy, data from a single differential scanning calorimetry scan at a given heating rate are used. The other popular model, that of Ozawa, is also based on similar assumptions. In the study reported here, a different approach was adopted, which uses multiple scans at various heating rates simultaneously. Here the experimental data of the non‐isothermal cold crystallization of an in situ‐prepared poly(ethylene terephthalate)/1% SiO₂ nanocomposite were used. Data were analysed following both the ordinary procedure and the method proposed in this work. Findings showed that when the Avrami model is a priori supposed to hold and the data of different heating rates are analysed separately, results are not acceptable. The new approach involves calculation of the activation energy through use of the isoconversional methods of Ozawa–Flynn–Wall and Friedman over the whole range of the crystallization conversion. The reaction model f(a) was determined after the evaluation of 16 different models. The best fitting was achieved for the Prout–Tompkins model or for a mechanism involving two steps described by respective Avrami equations with different activation energies. Copyright © 2010 Society of Chemical Industry     

手性表面与对映异构体的结晶分离

近年来,手性表面在分离对映异构体方面的重要性引起科学工作者的很大兴趣。手性表面对手性分子的识别和区分能力成为人们最感兴趣的领域之一。文章回顾了用手性自组装单分子层做分离助剂来结晶分离外消旋物的研究进展。     

Crystallization Kinetics of Cocoa Fat Systems: Experiments and Modeling

Isothermal crystallization kinetics of unseeded and seeded cocoa butter and milk chocolate is experimentally investigated under quiescent conditions at different temperatures in terms of the temporal increase in the solid fat content. The theoretical equations of Avrami based on one-, two- and three-dimensional crystal growth are tested with the experimental data. The equation for one-dimensional crystal growth represents well the kinetics of unseeded cocoa butter crystallization of form α and β′. This is also true for cocoa butter crystal seeded milk chocolate. The sterical hindrance due to high solids content in chocolate restricts crystallization to lineal growth. In contrast, the equation for two-dimensional crystal growth fits best the seeded cocoa butter crystallization kinetics. However, a transition from three- to one-dimensional growth kinetics seems to occur. Published data on crystallization of a single component involving spherulite crystals are represented well by Avrami’s three-dimensional theoretical equation. The theoretical equations enable the determination of the fundamental crystallization parameters such as the probability of nucleation and the number density of nuclei based on the measured crystal growth rate. This is not possible with Avrami’s approximate equation although it fits the experimental data well. The crystallization can be reasonably well defined for single component systems. However, there is no model which fits the multicomponent crystallization processes as observed in fat systems.     

Effect of copolymerization on crystallization kinetics of semicrystalline polyimides

Isothermal melt crystallization kinetics and nonisothermal cold crystallization kinetics of co‐PI based on 3, 3′, 4, 4′‐biphenyltetracarboxylic dianhydride (s‐BPDA)/1, 3‐bis‐(4‐aminophenoxy) benzene (TPER)/4, 4′‐oxydianiline(4, 4′‐ODA), and TPER PI (s‐BPDA/TPER) have been investigated. Avrami equation was used to analyze isothermal melt crystallization progress of TPER PI and co‐PI, primary crystallization processes was found to be changed as the introduction of 4, 4′‐ODA. Total activation energy ΔE for TPER PI and co‐PI were found to be ?404 and ?86 kJ mol^?1 by Arrhenius equation. Jeziorny's analysis, Ozawa's analysis, and Mo's approach were used to investigate nonisothermal cold crystallization progress of TPER PI and co‐PI. Activation energy ΔE_non for TPER PI and co‐PI were found to be 247 and 193 kJ mol^?1 by Kissinger equation. The result indicated that co‐PI exhibited lower crystallization rate than TPER PI when isothermally crystallized from melt, but higher crystallization rate under cold nonisothermal crystallization progress. © 2012 Wiley Periodicals, Inc. J. Appl. Polym. Sci., 2013     

Chiral separation of systems of high eutectic composition by a combined process: Case study of serine enantiomers

A concept for the chiral resolution of racemic compounds by a combination of chiral pre-enrichment by continuous multi-column chromatography and final purification using selective crystallization is presented. The system of serine enantiomers in water represents a typical racemic compound-forming system with very high eutectic compositions in the chiral system, which is generally considered as unfavorable for selective crystallization. It is shown exemplarily, how the solvent and temperature-dependent formation of hydrates can be exploited to allow efficient chiral resolution by a combined process for this and similar systems.     

Cyclic auto-seeded polythermal preferential crystallization—Effect of impurity accumulation

Preferential crystallization is a crystallization process where two enantiomers are separated into the pure chiral species. Usually the process is operated in a cyclic mode crystallizing the two species in sequel batches with an intermediate addition of fresh racemate. In this cyclic scheme reproducibility is a key issue.     

Model based robust control approach for batch crystallization product design

The paper presents a novel control approach for crystallization processes, which can be used for designing the shape of the crystal size distribution to robustly achieve desired product properties. The approach is based on a robust optimal control scheme, which takes parametric uncertainties into account to provide decreased batch-to-batch variability of the shape of the crystal size distribution. Both open-loop and closed-loop robust control schemes are evaluated. The open-loop approach is based on a robust end-point nonlinear model predictive control (NMPC) scheme which is implemented in a hierarchical structure. On the lower level a supersaturation control approach is used that drives the system in the phase diagram according to a concentration versus temperature trajectory. On the higher level a robust model-based optimization algorithm adapts the setpoint of the supersaturation controller to counteract the effects of changing operating conditions. The process is modelled using the population balance equation (PBE), which is solved using a novel efficient approach that combines the quadrature method of moment (QMOM) and method of characteristics (MOC). The proposed robust model based control approach is corroborated for the case of various desired shapes of the target distribution.     

Crystallization kinetics for simulation of processing of various polyesters

The approach to determine crystallization kinetic parameters based on the DSC nonisothermal crystallization experiments is applied to poly(butylene terephthalate) (PBT) and poly(ethylene‐2,6‐naphthalate) (PEN). The differential form of the Nakamura equation and master curve approach are used. The isothermal induction times are obtained from nonisothermal induction times according to the concept of induction time index. The correction of temperature lag between the DSC furnace and the sample is incorporated. The corrected nonisothermal crystallization kinetic data is shifted with respect to an arbitrarily chosen reference temperature to obtain the master curve. By fitting the obtained master curve with the Hoffman‐Lauritzen equation, the model parameters for the crystallization rate constant are obtained. The relative crystallinity measured at different cooling and heating rates is described by these model parameters. © 2006 Wiley Periodicals, Inc. J Appl PolymSci 102: 2847–2855, 2006