ANALYSIS OF BATCH CRYSTALLIZATION PROCESSES

The analysis of batch crystallization processes normally requires the consideration of the time-dependent, batch conservation equations (e.g., population, mass, and energy balances), together with appropriate nucleation and growth kinetic equations. The solution of these integro-differential equations is relatively difficult, even by numerical techniques. This review outlines the advances that have been made in the experimental techniques and data analyses which can be used to study the crystallization kinetics and the crystal size distribution (CSD) in batch suspension crystallizers. Several simple and useful methods are discussed which include characterization of CSD maximum, cumulative CSD approach, SSBCR crystallizer, thermal response technique, maximum allowable growth rate, and desupersaturation curve technique.     

ANALYSIS OF BATCH CRYSTALLIZATION PROCESSES

The analysis of batch crystallization processes normally requires the consideration of the time-dependent, batch conservation equations (e.g., population, mass, and energy balances), together with appropriate nucleation and growth kinetic equations. The solution of these integro-differential equations is relatively difficult, even by numerical techniques. This review outlines the advances that have been made in the experimental techniques and data analyses which can be used to study the crystallization kinetics and the crystal size distribution (CSD) in batch suspension crystallizers. Several simple and useful methods are discussed which include characterization of CSD maximum, cumulative CSD approach, SSBCR crystallizer, thermal response technique, maximum allowable growth rate, and desupersaturation curve technique.     

Dynamic Compartmental Models of Uniformly‐Mixed and Inhomogeneously‐Mixed Gibbsite Crystallizers

The use of simple compartmentalized population balance (PB) models was investigated for describing the crystal size distributions (CSD) of two different laboratory batch gibbsite crystallizers, one uniformly‐mixed and the other inhomogeneously‐mixed with respect to particulate phase. The compartments were selected on the basis of the shear rate and solids concentration distribution maps generated by the computational fluid dynamics (CFD). In the inhomogeneously‐mixed case, the CSD predicted by the compartmental model was highly sensitive to the relationship between the agglomeration kernel and shear rate used to describe the local agglomeration rate. This observation is consistent with recent findings reported in the literature that to correctly account for the agglomeration process in crystallizers its kinetic formulation should be based on the local rather than the volume‐averaged properties.     

添加晶种的间歇结晶器数学模型

动力学参数是设计结晶器和优化过程操作的主要依据。针对添加晶种的二次成核结晶过程，采用经验方程将反映结晶固相信息的透光率数据与CSD的二阶矩量进行关联，建立了包含透光率、液相浓度和相对过饱和度的动力学模型。并以KNO3-H2O为对象，运用该模型求取了结晶成核和生长动力学参数，结果与文献值相近。     

Design of Crystallizers

It is shown how to design a crystallizer starting with data which must be determined in laboratory crystallizers and other measuring equipment. A survey on kinetic data of a large number of systems is given in order to show the range of parameters involved in crystallization.

The paper deals with the scale-up problems of crystallizers which are important when laboratory data are transferred to large-scale crystallizers.     

Auslegung und Maßstabsvergrößerung von Kristallisatoren

Design and scale-up of crystallizers . Industrial scale crystallizers have to be designed in such a way that the crystalline product has the design particle size distribution, crystal form, and purity. Data on multiphase flow, solubility, balances of mass, energy, and number of crystals, kinetics (crystal growth rate and nucleation rate), and heat transfer are required. The present article discusses problems of kinetics in greater detail than other aspects. Multiphase flow is considered only briefly and heat transfer not at all. Familiarity with the terms homogeneous and heterogeneous (primary) and secondary nucleation [1, 2] is also assumed. This contribution is based on evaluation of available literature.     

Development, analysis and validation of population models for continuous and batch crystallizers

This contribution deals with the derivation of mathematical models for continuous and batch crystallizers based on the population balance approach. Detailed kinetic expressions for primary nucleation, crystal growth and attrition are incorporated into the models. The proper mathematical formulation of these phenomena as well as their incorporation into the population balance are discussed. Subsequently, system theoretical properties (e.g. the differential index of the resulting differential-algebraic equation system) of the derived models are analysed. Finally, the models for the continuous and the batch crystallizer are validated by comparison to measurements of temperature, supersaturation and particle size distribution.     

高悬浮密度下氯化钾结晶动力学研究

本试验在2.5升MSMPR结晶器中对氯化钾从卤水中结晶过程进行了研究,得到较高悬浮密度下的二次成核动力学方程式,并为制造工业结晶器提供了科学的、精确的设计依据.     

QUANTIFICATION OF SOLID-LIQUID MIXING USING ELECTRICAL RESISTANCE AND POSITRON EMISSION TOMOGRAPHY

Tomographic measurement techniques offer new opportunities and challenges for quantifying the degree of mixing of particulate suspensions and other multiphase mixtures. This has implications for the design, operation and control of industrial mixers and batch reactors, including crystallizers. Various statistical methods for describing mixing phenomena are reviewed and selected methods are applied to electrical resistance and positron emission data. New and more robust methods of image reconstruction and interpretation are reported for electrical tomography based on discretizing the mixer volume into a small number of regions or cells. Realistic models can be proposed and reconstruction can then be performed by modification of existing (Newton- Raphson) methods or, if these become too complex, by the application of the Metropolis algorithm or Markov chain Monte Carlo methods. Reducing the number of parameters of the associated model can remove ambiguity and allow rapid reconstruction. Improvements to instrumentation hardware and the mounting of electrical resistance sensors on the impeller shaft greatly assists the analysis of regions of interest (such as the vicinity of down-comers). The resulting linked design and analysis of the entire measurement system with a Bayesian parametric-reconstruction approach is a significant advance in tomographic technology.     

crystSim: A software environment for modelling industrial batch cooling crystallization

Crystallization modelling is limited by the availability of methods to reliably predict mixing, temperature and concentration distributions, supersaturation, nucleation and growth kinetics for crystallization systems of industrial size. A new software environment for modelling batch cooling crystallization has been developed integrating crystallization and fluid dynamics. The mathematical model can reliably predict mixing in stirred vessels of a given geometry and its effect on the crystallization kinetics and crystal product properties thus reducing the cost and time required for the design and scale-up of industrial crystallizers. The paper describes the development and application of crystSim for modelling industrial crystallization in stirred tanks. The software is developed in Visual C# making full use of Object Oriented Programming (OOP) and multithreading.     

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.     

A homogeneous chemical reactor analysis and design laboratory: The reaction kinetics of dye and bleach

An experimental module for senior-level reaction engineering/reactor design students is described. The module is used to characterize the kinetics of dye (food coloring) neutralization by household bleach, and the reactor system is configurable for use in either batch reactor or continuous-stirred tank reactor (CSTR) modes. The reactor temperature, volume, reactant feed rates, and reactant concentrations may be adjusted to enable students to obtain a wide range of kinetic data. Dye concentrations in the reactor are monitored by absorbance spectroscopy, and the kinetic rate law is determined directly from the batch reactor performance data. Students use the completed kinetic rate law to compare experimental steady-state CSTR performance data to the mathematical models derived from reactor design equations. Finally, the students use the kinetic behavior of the system to design a hypothetical plug-flow reactor for the same chemical reaction and a set of stated operational goals.     

Crystallization and Precipitation: The Optimal Supersaturation

In this article optimal supersaturation for cooling and evaporation crystallization are presented. This information is based on a simplified model which describes the metastable zone width of activated nucleation. The model assumes that the nucleation step is very fast and the occurrence of the shower of nuclei which is used to define the metastable zone width is caused by the growth of activated nuclei. In future new sensors for the measurement of supersaturation will help to operate batch crystallizers at the optimal supersaturation during the entire batch time.     

Programmed cooling of batch crystallizers

An analysis of the programmed cooling of batch crystallizers, starting with the solution of the momentum equations of the population balance, is presented. Based on a general solution, conditions are discussed leading to limiting equations which had been published earlier. The model described in this paper determines the optimum cooling curve for a batch crystallizer with an arbitrary seeding and nucleation ratio, hence a more detailed analysis of the physical conditions of the process and a better comparison of the theory with experiment are possible. Kinetic data of crystallization can also be obtained from batch experiments.     

Iterative learning control for the systematic design of supersaturation controlled batch cooling crystallisation processes

The paper presents an approach to improve the product quality from batch-to-batch by exploiting the repetitive nature of batch processes to update the operating trajectories using process knowledge obtained from previous runs. The data based methodology is focused on using the linear time varying (LTV) perturbation model in an iterative learning control (ILC) framework to provide a convergent batch-to-batch improvement of the process performance indicator. The major contribution of this work is the development of a novel hierarchical ILC (HILC) scheme for systematic design of the supersaturation controller (SSC) of seeded batch cooling crystallizers. The HILC is used to determine the required supersaturation setpoint for the SSC and the corresponding temperature trajectory required to produce crystals with desired end-point property. The performance and robustness of these approaches are evaluated through simulation case studies. These results demonstrate the potential of the ILC approaches for controlling batch processes without rigorous process models.     

Modeling of growth rate dispersion of citric acid monohydrate in continuous crystallizers

A mathematical model for prediction of the crystal size distribution from a continuous crystallizer is presented. The kinetic data used for the model were obtained from batch contact nucleation experiments with citric acid monohydrate. In these experiments, the distribution of growth rates as well as the initial size distribution were estimated. Results from the model indicate that the excess number of crystals usually present at small sizes in continuous crystallizers is due to growth rate dispersion (where crystals of the same size may have different growth rates) and not size dependent growth.     

Secondary Nucleation: Mechanisms and Models

Secondary nucleation is the dominant nucleation mechanism in industrial crystallizers. This work reviews secondary nucleation as it occurs in solution-based crystallization of small organic/inorganic compounds. The review elucidates various mechanisms along with the experimental and analytical techniques used to study them. Based on the review, a refined classification of secondary nucleation mechanism is proposed. Mechanistic models for various secondary nucleation mechanisms are then discussed at length. The review ends with an overview of the metastable zone width for secondary nucleation. The review will be useful to researchers and engineers working on bulk crystallization of small molecules to gain in-depth understanding of secondary nucleation.     

Ammonium Sulfate Crystallization in a Cooling Batch Crystallizer

Abstract

Crystallization kinetics of ammonium sulfate crystals are determined in a 25-L draft tube baffled, agitated crystallizer from a series of batch cooling experiments performed in an integral mode. The method of s-plane analysis for relative nucleation kinetics and the method of initial derivatives for growth rate kinetics are used to establish conventional kinetic expressions. A simulation technique is developed to calculate the product population density functions for the same system in a seeded cooling batch crystallizer configuration.     

Modeling and kinetics study of conventional and assisted batch solvent extraction

Batch solvent extraction techniques have been widely explored. On understanding its potential significance, this article aims to review kinetics and modeling of various extraction techniques which involve assisted means including microwave-assisted extraction (MAE), ultrasonic-assisted extraction (UAE), pulse electric field (PEF) and high voltage electrical discharge (HVED). This review includes a detailed discussion of the instrumental setup, extraction mechanisms and their distinct advantages and disadvantages. Additionally, the impact of the operating parameters on the extraction kinetics of the mentioned techniques are highlighted. The review also covers the mathematical modeling based on Fick's law, chemical rate law and empirical models. The established kinetic models of various extractions are also summarized to facilitate better understanding.