用时空CE/SE方法求解微溶一维间歇结晶模型(英文)

This article is concerned with the numerical investigation of one-dimensional population balance models for batch crystallization process with fines dissolution. In batch crystal ization, dissolution of smaller unwanted nu-clei below some critical size is of vital importance as it improves the quality of product. The crystal growth rates for both size-independent and size-dependent cases are considered. A delay in recycle pipe is also included in the model. The space–time conservation element and solution element method, originally derived for non-reacting flows, is used to solve the model. This scheme has already been applied to a range of PDEs, mainly in the area of fluid mechanics. The numerical results are compared with those obtained from the Koren scheme, showing that the proposed scheme is more efficient.     

Modeling, simulation and stabilizing H∞-control of an oscillating continuous crystallizer with fines dissolution

In this contribution, a detailed model for a continuous crystallizer with fines dissolution is derived. The main focus of this article is the identification of physical reasons responsible for oscillations occurring in these crystallization plants. In contrast to many other crystallization models used in literature for the investigation of such limit cycles, detailed kinetic expressions for crystal growth and attrition, as well as for the separation of fines in the annular zone, are incorporated. By dynamic simulations of the model and by comparison with measured data, an undesired dissolution of larger crystals can be identified as a possible reason for the appearance of sustained oscillations. Finally, a stabilizing feedback controller is designed using H_∞-theory. It is demonstrated in simulations that this controller enables stable operation of the crystallizer even at a high fines dissolution rate.     

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.     

Optimal operation of batch enantiomer crystallization: From ternary diagrams to predictive control

In this work, the modeling and control of batch crystallization for racemic compound forming systems is addressed in a systematic fashion. Specifically, a batch crystallization process is considered for which the initial solution has been pre‐enriched in the desired enantiomer to enable crystallization of only the preferred enantiomer. A method for determining desired operating conditions (composition of the initial pre‐enriched solution and temperature to which the mixture must be cooled for maximum yield) for the batch crystallizer based on a ternary diagram for the enantiomer mixture in a solvent is described. Subsequently, it is shown that the information obtained from the ternary diagram, such as the maximum yield attainable from the process due to thermodynamics, can be used to formulate constraints for an optimization‐based control method to achieve desired product characteristics such as a desired yield. The proposed method is demonstrated for the batch crystallization of mandelic acid in a crystallizer with a fines trap that is seeded with crystals of the desired enantiomer. The process is controlled with an optimization‐based controller to minimize the ratio of the mass of crystals obtained from nuclei to the mass obtained from seeds while maintaining the desired enantioseparation. © 2017 American Institute of Chemical Engineers AIChE J, 64: 1618–1637, 2018     

FINES DESTRUCTION DURING BATCH CRYSTALLIZATION

An analysis of the use of fines destruction during batch crystallization based on the population (number) balance is presented. The effects of operating policy and fines crystal cut size and destruction rate are examined in detail for two cases viz. natural and controlled cooling respectively. It is predicted that use of fines destruction has the potential as a control aid to significantly improve the product crystal size distribution from batch crystallizers and is supported by experimental data on the programmed cooling crystallization of potassium sulphate solutions.     

Fines removal in a continuous plug flow crystallizer by optimal spatial temperature profiles with controlled dissolution

This work presents a systematic study for obtaining the optimal temperature profile in a continuous plug flow crystallizer (PFC). The proposed PFC consists of multiple segments where the temperature of each segment can be controlled individually. An optimization problem is formulated for a target crystal size distribution (without fines) with the temperature of the segments as decision variables. The results indicate that for the crystallization kinetics considered, dissolution steps are necessary for the reduction of fines due to nucleation. A systematic study on the form of growth and dissolution kinetics suggested that the key factor that determines whether the dissolution steps will be successful in reducing fines, without compromising the final size of the crystals from seed, is the size dependence of the growth and dissolution kinetics. Best fines removal is achieved when the larger crystals grow faster than the smaller ones and the smaller crystals dissolve faster than the larger ones. © 2013 American Institute of Chemical Engineers AIChE J, 59: 4582–4594, 2013     

Effect of Seeding on Metal Ion Recovery from Wastewater by Reactive Crystallization of Metal Carbonates

Reactive crystallization for separation and recovery of divalent metal ions from wastewater using a semi‐batch crystallizer has been developed. In this process, metal carbonates are produced by reacting metal sulfate solution with sodium carbonate solution. Nickel and copper ions are crystallized under particular initial pH conditions but the product shapes are not regular. Consequently, sphere seeds have been used as nucleus‐generating agents and their growth mechanism has been examined. When providing a particular amount of seeds before crystallization, metal substances piled up on the surface of the seeds, maintaining the form sphere, and the production of fines was restricted. The metal removal rate through reactive crystallization was ～99.9 % on average. This operation proved to be suitable for application in industrial wastewater treatment and for recycling of metal materials.     

Multi-stage crystallization for resolution of enantiomeric mixtures in a solid solution forming system

A systematic procedure for synthesizing the multi-stage crystallization process was developed for resolution of enantiomeric mixtures involving solid solutions in the crystalline phase. The model compound investigated was citalopram oxalate, which revealed a complete solid solution in the solid phase. The counter-current multi-stage batch crystallization was suggested to isolate the target enantiomer from enantiomerically enriched mixtures. The solid–liquid equilibria in the presence of a solvent and the distribution diagrams were quantified and used in designing the crystallization process and defining adequate processing conditions. Different flowsheet schemes were considered and compared with respect to the process performance. The design procedure was verified by the experimental separation of enantiomeric mixtures of citalopram.     

Control of fines suspension density in the fines loop of a continuous KCl crystallizer using transmittance measurement and an FBRM® probe

The control of crystal size distribution (CSD) is investigated in a 1.5 L laboratory cooling KCl crystallizer using fines dissolution rate as the manipulated variable. The controlled variable was either the fines suspension density in the fines withdrawal loop, measured by an innovative double‐sensor turbidity meter manufactured in‐house, or the chord length distribution (CLD) measured by the Focused Beam Reflectance Measurement (FBRM®) probe (model: Par‐Tec® 100, Lasentec®, Redmond, WA). It was shown that effective control of mean crystal size and fines suspension density in the presence of setpoint and disturbance changes is feasible with both control schemes. The double sensor turbidity sensor proved to be very rugged even in the presence of insoluble clay background particles. The FBRM® probe was more sensitive and capable of detecting particle breakage and flocculation.     

Entropic analysis of a batch-crystallization process

The analysis of crystallization processes considering an entropic perspective is the primary purpose of this paper. Although the modeling of crystallization processes is well established in the literature, the entropic representation of these processes still needs to be studied. The modeling considering the second law of thermodynamics was investigated, which resulted in a model that represents the entropy production rate of a batch-crystallization process. The results indicate that the entropy production of the batch cooling crystallization is related to the variability of the crystal size distribution. The model of the entropy production rate could be used as a restriction criterion for multi-objective optimization of the cooling temperature profile of a batch crystallizer to improve the quality of the crystal size distribution of the final product.     

Product quality improvement of batch crystallizers by a batch-to-batch optimization and nonlinear control approach

Batch crystallization is one of the widely used processes for separation and purification in many chemical industries. Dynamic optimization of such a process has recently shown the improvement of final product quality in term of a crystal size distribution (CSD) by determining an optimal operating policy. However, under the presence of unknown or uncertain model parameters, the desired product quality may not be achieved when the calculated optimal control profile is implemented. In this study, a batch-to-batch optimization strategy is proposed for the estimation of uncertain kinetic parameters in the batch crystallization process, choosing the seeded batch crystallizer of potassium sulfate as a case study. The information of the CSD obtained at the end of batch run is employed in such an optimization-based estimation. The updated kinetic parameters are used to modify an optimal operating temperature policy of a crystallizer for a subsequent operation. This optimal temperature policy is then employed as new reference for a temperature controller which is based on a generic model control algorithm to control the crystallizer in a new batch run.     

Predictive control of particlesize distribution of crystallization process using deep learning based image analysis

The challenges to regulate the particle-size distribution (PSD) stem from on-line measurement of the full distribution and the distributed nature of crystallization process. In this article, a novel nonlinear model predictive control method of PSD for crystallization process is proposed. Radial basis function neural network is adopted to approximate the PSD such that the population balance model with distributed nature can be transformed into the ordinary differential equation (ODE) models. Data driven nonlinear prediction model of the crystallization process is then constructed from the input and output data and further be used in the proposed nonlinear model predictive control algorithm. A deep learning based image analysis technology is developed for online measurement of the PSD. The proposed PSD control method is experimentally implemented on a jacketed batch crystallizer. The results of crystallization experiments demonstrate the effectiveness of the proposed control method.     

A numerical bifurcation analysis of nonlinear oscillations in crystallization processes

The main aim of this work is the theoretical prediction and analysis of the nonlinear behavior of crystallization processes. As a first step towards the theoretical analysis a fairly simple population balance model including fines dissolution and classified product removal has been considered. By means of numerical bifurcation and stability analysis, regions in the parameter space of the operating conditions and the physical properties with periodic behavior have been predicted. Due to the simplicity of the underlying model the results are only of qualitative nature. Future work will focus on a quantitative prediction of the nonlinear behavior with more detailed models and an experimental verification.     

Neuro‐Fuzzy Control of a Continuous Cooled MSMPR Crystallizer

This work deals with the design and application of a neuro‐fuzzy controller of the magma density of the fine crystals for the stabilisation of the crystal size distribution (CSD) of the product from an MSMPR (Mixed Suspension, Mixed Product Removal) continuous crystallizer. The cooling crystallization of potassium sulphate from aqueous solutions in a pilot‐scale stirred vessel was investigated. A control strategy, based on the elimination of fines by using a combined sedimentation‐dissolution device, is presented. The control scheme was successfully applied to a pilot‐scale draft‐tube (DT) crystallizer and yielded promising results. The proposed process control system allowed the reduction of the fines fraction by more than 30 %, while maintaining operation stability and short transient responses.     

Effect of Crystallization Conditions on the Metastable Zone Width and Nucleation Kinetics of p-Aminobenzoic Acid in Ethanol

A detailed knowledge of the metastable zone width (MSZW) and nucleation kinetics is vital for the design of batch cooling crystallization processes. Factors such as cooling rate and impeller speed affect the MSZW and nucleation kinetics. Crystallization and dissolution temperatures were measured as a function of cooling rate and impeller speed during the batch cooling crystallization of p-aminobenzoic acid (pABA) from ethanol in a 0.5-L stirred-tank crystallizer. The polythermal experimental data were analyzed using the Nyvlt and first principles-based Kashchiev-Borissova-Hammond-Roberts (KBHR) methods. In all experimental cases, the latter model revealed that the nucleation process of pABA in ethanol was dominated by an instantaneous nucleation mechanism. The Nyvlt and KBHR analyses delivered a range of parameter values associated with a power-law model describing the nucleation rate as well as the concentration of nuclei.     

KNO3-H2O溶液间歇结晶动力学

基于ΔL定律推导了晶体线性生长速率的数学表达式,利用已建立的溶液间歇结晶动力学实验研究手段实现了溶液透光率和浓度的在线测量.利用经验模型关联线性生长速率和相对过饱和度求取了生长动力学参数,并与文献值进行了比较.结果发现：对于自发成核结晶过程,综合动态透光率、过饱和度和经验模型可对成核和生长阶段进行定性识别.     

KNO3-H2O溶液间歇结晶动力学

基于ΔL定律推导了晶体线性生长速率的数学表达式，利用已建立的溶液间歇结晶动力学实验研究手段实现了溶液透光率和浓度的在线测量.利用经验模型关联线性生长速率和相对过饱和度求取了生长动力学参数，并与文献值进行了比较.结果发现：对于自发成核结晶过程，综合动态透光率、过饱和度和经验模型可对成核和生长阶段进行定性识别.     

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 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