Size distribution, continuous crystallization

Precipitated Calcium Carbonate. Precipitated calcium carbonate can be produced by several methods but only the carbonation process is commercially used in the United States. Limestone is calcined in a kiln to obtain carbon dioxide and quicklime. The quicklime is mixed with water to produce a milk-of-lime. Dry hydrated lime can also be used as a feedstock. Carbon dioxide gas is bubbled through the milk-of-lime in a reactor known as a carbonator. Gassing continues until the calcium hydroxide has been converted to the carbonate. The end point can be monitored chemically or by pH measurements. Reaction conditions determine the type of crystal, the size of particles, and the size distribution produced. 

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). 

The dominant crystal size, is most often used as a representation of the product size, because it represents the size about which most of the mass in the distribution is clustered. If the mass density function defined in equation 33 is plotted for a set of hypothetical data as shown in Figure 10, it would typically be observed to have a maximum at the dominant crystal size. In other words, the dominant crystal size is that characteristic crystal dimension at which drajdL = 0. Also shown in Figure 10 is the theoretical result obtained when the mass density is determined for a perfectiy mixed, continuous crystallizer within which invariant crystal growth occurs. That is, mass density is found for such systems to foUow a relationship of the form m = aL exp —bL where a and b are system-dependent parameters. 

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... 

Tailoring of the particle size of the crystals from industrial crystallizers is of significant importance for both product quality and downstream processing performance. The scientific design and operation of industrial crystallizers depends on a combination of thermodynamics - which determines whether crystals will form, particle formation kinetics - which determines how fast particle size distributions develop, and residence time distribution, which determines the capacity of the equipment used. Each of these aspects has been presented in Chapters 2, 3, 5 and 6. This chapter will show how they can be combined for application to the design and performance prediction of both batch and continuous crystallization. 

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. 

Hostomsky, J., 1987. Particle size distribution of agglomerated crystal product from a continuous crystallizer. Collection of Czechoslovakian Chemical Communications, 52, 1186-1197. 

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... 

The sorbitol solution produced from hydrogenation is purified in two steps [4]. The first involves passing the solution through an ion-exchange resin bed to remove gluconate and other ions. In the second step, the solution is treated with activated carbon to remove trace organic impurities. The commercial 70% sorbitol solution is obtained by evaporation of the water under vacuum. The solid is prepared by dehydration until a water-free melt is obtained which is cooled and seeded. The crystals are removed continuously from the surface (melt crystallization). The solid is sold as flakes, granules, pellet, and powder forms in a variety of particle size distributions. 

Analysis of Size Distribution Data Obtained in a CSTC Differential distribution data obtained from a continuous stirred tank crystallizer are tabulated. 

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... 

Figure 2.17 Mixing in a crystallizer considering continuous phase (upper left-hand imaginary regions partitioned the others local size distribution of dispersion particle and mixedness).

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-... 

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