Continuous crystal size distributions

Although evidence exists for both mechanisms of growth rate dispersion, separate mathematical models were developed for incorporating the two mechanisms into descriptions of crystal populations random growth rate fluctuations (36) and growth rate distributions (33,40). Both mechanisms can be included in a population balance to show the relative effects of the two mechanisms on crystal size distributions from batch and continuous crystallizers (41). 

Population balances and crystallization kinetics may be used to relate process variables to the crystal size distribution produced by the crystallizer. Such balances are coupled to the more familiar balances on mass and energy. It is assumed that the population distribution is a continuous function and that crystal size, surface area, and volume can be described by a characteristic dimension T. Area and volume shape factors are assumed to be constant, which is to say that the morphology of the crystal does not change with size. 

Preferential Removal of Crystals. Crystal size distributions produced ia a perfectiy mixed continuous crystallizer are highly constraiaed the form of the CSD ia such systems is determined entirely by the residence time distribution of a perfectly mixed crystallizer. Greater flexibiUty can be obtained through iatroduction of selective removal devices that alter the residence time distribution of materials flowing from the crystallizer. The... 

It was shown in Chapter 7 that the performance of continuous crystallizers is determined by the characteristics of a feedback loop relating the output performance expressed as crystal size distribution and to the feed concentration and residence time. Thus, an increase in crystallizer residence time, or decrease in feed concentration, reduces the working level of supersaturation. This decrease in supersaturation results in a decrease in both nucleation and crystal growth. This in turn leads to a decrease in crystal surface area. By mass balance, this then causes an increase in the working solute concentration and hence an increase in the working level of supersaturation and so on. There is thus a complex feedback loop within a continuous crystallizer, as considered in Chapter 7 and illustrated in Figure 8.11. 

Abegg, C.F., Stevens, J.D. and Larson, M.A., 1968. Crystal size distribution in continuous crystallizer when growth rate is size-dependent. American Institmte oj Chemical Engineers Journal, 41, 188. 

K. C. Lim, M. A. Hashim, B. Sen Gupta. Monte Carlo simulation of transient crystal size distribution in a continuous crystallizer using the ASL model. Cryst Res Technol 33 249, 1998. 

Except for biopolymers, most polymer materials are polydisperse and heterogeneous. This is already the case for the length distribution of the chain molecules (molecular mass distribution). It is continued in the polydispersity of crystalline domains (crystal size distribution), and in the heterogeneity of structural entities made from such domains (lamellar stacks, microfibrils). Although this fact is known for long time, its implications on the interpretation and analysis of scattering data are, in general, not adequately considered. 

Crystal nucleation and growth in a crystalliser cannot be considered in isolation because they interact with one another and with other system parameters in a complex manner. For a complete description of the crystal size distribution of the product in a continuously operated crystalliser, both the nucleation and the growth processes must be quantified, and the laws of conservation of mass, energy, and crystal population must be applied. The importance of population balance, in which all particles are accounted for, was first stressed in the pioneering work of Randolph and Larson1371. ... 

Growth and nucleation interact in a crystalliser in which both contribute to the final crystal size distribution (CSD) of the product. The importance of the population balance(37) is widely acknowledged. This is most easily appreciated by reference to the simple, idealised case of a mixed-suspension, mixed-product removal (MSMPR) crystalliser operated continuously in the steady state, where no crystals are present in the feed stream, all crystals are of the same shape, no crystals break down by attrition, and crystal growth rate is independent of crystal size. The crystal size distribution for steady state operation in terms of crystal size d and population density // (number of crystals per unit size per unit volume of the system), derived directly from the population balance over the system(37) is ... 

The number of inputs which are available for controlling crystallisation processes is limited. Possible Inputs for a continuous evaporative crystallisation process are, crystalliser temperature, residence time and rate of evaporation. These Inputs affect the crystal size distribution (CSD) through overall changes in the nucleatlon rate, the number of new crystals per unit time, and the growth rate, the increase in linear size per unit time, and therefore do not discriminate directly with respect to size. Moreover, it has been observed that, for a 970 litre continuous crystalliser, the effect of the residence time and the production rate is limited. Size classification, on the other hand, does allow direct manipulation of the CSD. 

There is a clear need for other size classifiers which combine a high separation efficiency with flexibility and compactness. Hydrocyclones have a small volume, are simple in operation and are standard size classification equipment, for example in closed circuit grinding applications. The recent development of the flat-bottom hydrocyclone, which permits classification in the coarse size range, creates an additional motive to study the use of hydrocyclones for Crystal Size Distribution (CSD) control. Furthermore, throttling of a flat botom hydrocyclone does not necessarily provoke blockage but allows continuous control of its cut size when a controlled throttling valve is used. There is a clear incentive for its use in this application since it may provide an additional process input. 

The observed transients of the crystal size distribution (CSD) of industrial crystallizers are either caused by process disturbances or by instabilities in the crystallization process itself (1 ). Due to the introduction of an on-line CSD measurement technique (2), the control of CSD s in crystallization processes comes into sight. Another requirement to reach this goal is a dynamic model for the CSD in Industrial crystallizers. The dynamic model for a continuous crystallization process consists of a nonlinear partial difference equation coupled to one or two ordinary differential equations (2..iU and is completed by a set of algebraic relations for the growth and nucleatlon kinetics. The kinetic relations are empirical and contain a number of parameters which have to be estimated from the experimental data. Simulation of the experimental data in combination with a nonlinear parameter estimation is a powerful 1 technique to determine the kinetic parameters from the experimental... 

Crystal Size Distribution and Characteristics Associated nith a Continuous Crystallizer... 

On-line particle sizing by ultrasonic (acoustic attenuation) spectroscopy was developed for use during batch crystallization processes.14 Crystallization of the alpha polymorph of (l) -glutamic acid from aqueous solution was monitored by continuously pumping the crystallizing solution through an on-line ultrasonic spectrometer. The method enabled measurement of the crystal size distribution and solid concentration throughout the... 

Batch crystallizers can be used in a campaign to produce a particular product and in a second campaign to produce another product. Generally, it is not possible to operate continuous processes in this way. Batch crystallizers can handle viscous or toxic systems more easily than can continuous systems, and interruption of batch operations for periodic maintenence is less difficult than dealing with interruptions in continuous processes. The latter factor may be especially important in biological processes that require frequent sterilization of equipment. Batch crystallizers can produce a narrow crystal size distribution, whereas special processing features are required to narrow the distribu-... 

It may be easier to operate a continuous system so that it reproduces a particular crystal size distribution than it is do reproduce crystal characteristics from a batch unit. Moreover, the coupling of several transient variables and nucleation make it difficult to model and control the operation of a batch crystallizer. 

A population balance can be used to follow the development of a crystal size distribution in batch crystallizer, but both the mathematics and physical phenomena being modeled are more complex than for continuous systems at steady state. The balance often utilizes the population density defined in terms of the total crystallizer volume, rather than on a specific basis n = nVj. Accordingly, the general population balance given by Eq. (51) can be modified for a batch crystallizer to give ... 

Crystallization from an overall viewpoint represents transfer of a material from solution (or even a gas) to a solid phase by cooling, evaporation, or a combination of both. But there is more to it. Of considerable importance are economics, crystal size distribution, purity, and the shape of the crystals. Impurities or mother solution are carried along only in the surface or occlusions in the crystals. The partical size distribution depends on the distribution of seed crystals, which are injected into the crystallizer prior to initiation of crystallization (batch) or continuously from recycled undersized particles, the mixing in the system, the crystal growth rate, and the degree of supersaturation of the mother liquor. As in shown in the figures, both batch and continuous crystallization are used in industry. 

A continuous crystallizer producing 25,000 lb/h (11,340 kg/h) of cubic solids is continuously seeded with 5000 lb/h (2270 kg/h) of crystals having a crystal size distribution as listed in Table 10.2. Predict the product crystal size distribution if nucleation is ignored. If the residence time of solids in the crystallizer is 2 h, calculate the average particle-diameter growth rate G. 

A continuous crystallization process ultimately reaches a steady state, in which the rates of nucleation and growth are constant with time. For a given set of operating conditions, crystal size distribution depends considerably upon the degree to which product classification is practiced. Figures 23 and 24 illustrate schematically the possible extremes between... 

Cycling of the crystal size in a crystallizer can be reduced by periodically or continuously injecting a slurry of crystals equivalent to 5 to 40% of the production rate in the crystallizer and having a crystal size distribution at least equivalent to the average crystal size produced in the crystallizer. 

Batch crystallizers tend to have a broader crystal size distribution than continuous crystallizers. To help narrow the crystal size distribution you must either cool slowly through the initial crystallization temperature or seed at the initial crystallization temperature. 

Crystal growth is a layer-by-layer process, and the retention time required in most commercial equipment to produce crystals of the size normally desired is often on the order of 2 to 6 h. Growth rates are usually limited to less than 1 to 2 pm/min. On the other hand, nucle-ation in a supersaturated solution can be generated in a fraction of a second. The influence of any upsets in operating conditions, in terms of the excess nuclei produced, is very short-term in comparison with the total growth period of the product removed from the crystallizer. A worst-case scenario for batch or continuous operation occurs when the explosion of nuclei is so severe that it is impossible to grow an acceptable crystal size distribution, requiring redesolution or washout of the system. In a practical sense, this means that steadiness of operation is much more important in crystallization equipment than it is in many other types of process equipment. 

As explained throughout the book, disperse multiphase systems are characterized by multiple phases, with one phase continuous and the others dispersed (i.e. in the form of distinct particles, droplets, or bubbles). The term polydisperse is used in this context to specify that the relevant properties characterizing the elements of the disperse phases, such as mass, momentum, or energy, change from element to element, generating what are commonly called distributions. Typical distributions, which are often used as characteristic signatures of multiphase systems, are, for example, a crystal-size distribution (CSD), a particle-size distribution (PSD), and a particle-velocity distribution. 

The most common method for obtaining crystal growth kinetics involving suspensions involves the use of a mixed suspension, mixed product removal continuous crystallizer operating at steady state. By using the population balance concepts developed and described by Randolph and Larson (1986), growth rates can be obtained. The population balance method and the use of the crystal size distribution in obtaining kinetic parameters will be discussed in detail in Chapter 4 of this volume. 

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