Crystallization crystal size distribution

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... 

Batch Crystallization. Crystal size distributions obtained from batch crystallizers are affected by the mode used to generate supersaturation and the rate at which supersaturation is generated. For example, in a cooling mode there are several avenues that can be followed in reducing the temperature of the batch system, and the same can be said for the generation of supersaturation by evaporation or by addition of a nonsolvent or precipitant. The complexity of a batch operation can be ihustrated by considering the summaries of seeded and unseeded operations shown in Figure 19. 

Madsen C and Jacobsen C J FI 1999 Nanosized zeolite crystals—convenient control of crystal size distribution by confined space synthesis Chem. Commun. 673-4... 

Sepa.ra.tlon, Sodium carbonate (soda ash) is recovered from a brine by first contacting the brine with carbon dioxide to form sodium bicarbonate. Sodium bicarbonate has a lower solubiUty than sodium carbonate, and it can be readily crystallized. The primary function of crystallization in this process is separation a high percentage of sodium bicarbonate is soHdified in a form that makes subsequent separation of the crystals from the mother hquor economical. With the available pressure drop across filters that separate Hquid and soHd, the capacity of the process is determined by the rate at which hquor flows through the filter cake. That rate is set by the crystal size distribution produced in the crystallizer. 

Process. In each of the systems discussed above there is a need to form crystals, to cause the crystals to grow, and to separate the crystals from residual Hquid. There are various ways to accomplish these objectives lea ding to a multitude of processes that are designed to meet requirements of product yield, purity, and, uniquely, crystal size distribution. 

Nucleation. Crystal nucleation is the formation of an ordered soHd phase from a Hquid or amorphous phase. Nucleation sets the character of the crystallization process, and it is, therefore, the most critical component ia relating crystallizer design and operation to crystal size distributions. 

Correlations of nucleation rates with crystallizer variables have been developed for a variety of systems. Although the correlations are empirical, a mechanistic hypothesis regarding nucleation can be helpful in selecting operating variables for inclusion in the model. Two examples are (/) the effect of slurry circulation rate on nucleation has been used to develop a correlation for nucleation rate based on the tip speed of the impeller (16) and (2) the scaleup of nucleation kinetics for sodium chloride crystalliza tion provided an analysis of the role of mixing and mixer characteristics in contact nucleation (17). Pubhshed kinetic correlations have been reviewed through about 1979 (18). In a later section on population balances, simple power-law expressions are used to correlate nucleation rate data and describe the effect of nucleation on crystal size distribution. 

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. 

GSD Characteristics for MSMPR Crystallizers. The perfectiy mixed crystallizer described ia the preceding discussion is highly constrained and the form of crystal size distributions produced by such systems is fixed. Such distributions have the foUowiag characteristics. 

Although magma density is a function of the kinetic parameters fP and G, it often can be measured iadependentiy. In such cases, it should be used as a constraint ia evaluating nucleation and growth rates from measured crystal size distributions (62), especially if the system of iaterest exhibits the characteristics of anomalous crystal growth. 

A pair of kinetic parameters, one for nucleation rate and another for growth rate, describe the crystal size distribution for a given set of crystallizer operating conditions. Variation ia one of the kinetic parameters without changing the other is not possible. Accordingly, the relationship between these parameters determines the abiUty to alter the characteristic properties (such as dominant size) of the distribution obtained from an MSMPR crystallizer (7). 

As an idealization of the classified-fines removal operation, assume that two streams are withdrawn from the crystallizer, one corresponding to the product stream and the other a fines removal stream. Such an arrangement is shown schematically in Figure 14. The flow rate of the clear solution in the product stream is designated and the flow rate of the clear solution in the fines removal stream is set as (R — 1) - Furthermore, assume that the device used to separate fines from larger crystals functions so that only crystals below an arbitrary size are in the fines removal stream and that all crystals below size have an equal probabiHty of being removed in the fines removal stream. Under these conditions, the crystal size distribution is characterized by two mean residence times, one for the fines and the other for crystals larger than These quantities are related by the equations... 

Although many commercial crystallizers operate with some form of selective crystal removal, such devices can be difficult to operate because of fouling of heat exchanger surfaces or blinding of screens. In addition, several investigations identify interactions between classified fines and course product removal as causes of cycling of a crystal size distribution (7). Often such behavior can be rninirnized or even eliminated by increasing the fines removal rate (63,64). 

Control of supersaturation is an important factor in obtaining crystal size distributions of desired characteristics, and it would be useful to have a model relating rate of cooling or evaporation or addition of diluent required to maintain a specified supersaturation in the crystallizer. Contrast this to the uncontrolled situation of natural cooling in which the heat transfer rate is given by... 

The advantages of selective removal of fines from a batch crystallizer have been demonstrated (66,67). These experimental programs showed narrowiag of crystal size distributions and suggest significant reductions ia the fraction of a product that would consist of fines or undersize material. 

Eeactive crystalli tion addresses those operations ia which a reaction occurs to produce a crystallizing solute. The concentration of the solute formed generally is greater than that corresponding to solubiHty. In a subset of systems, the solubiHty is nearly zero and, concomitantly, the supersaturation produced by reaction is large. These are often referred to as precipitation operations, and crystal size distributions from them contain a large fraction of fine crystals. 

It is common practice to use a parameter characterizing crystal-size distribution called the coefficient of variation. This is defined as follows ... 

It is emphasized that the delta L law does not apply when similar crystals are given preferential treatment based on size. It fails also when surface defects or dislocations significantly alter the growth rate of a crystal face. Nevertheless, it is a reasonably accurate generahzation for a surprising number of industrial cases. When it is, it is important because it simphfies the mathematical treatment in modeling real crystallizers and is useful in predicting crystal-size distribution in many types of industrial crystallization equipment. 

General solution of the population balance is complex and normally requires numerical methods. Using the moment transformation of the population balance, however, it is possible to reduce the dimensionality of the population balance to that of the transport equations. It should also be noted, however, that although the mathematical effort to solve the population balance may therefore decrease considerably by use of a moment transformation, it always leads to a loss of information about the distribution of the variables with the particle size or any other internal co-ordinate. Full crystal size distribution (CSD) information can be recovered by numerical inversion of the leading moments (Pope, 1979 Randolph and Larson, 1988), but often just mean values suffice. 

The population balance analysis of the idealized MSMPR crystallizer is a particularly elegant method for analysing crystal size distributions at steady state in order to determine crystal growth and nucleation kinetics. Unfortunately, the latter cannot currently be predicted a priori and must be measured, as considered in Chapter 5. Anomalies can occur in the data and their subsequent analysis, however, if the assumptions of the MSMPR crystallizer are not strictly met. 

Several authors have presented methods for the simultaneous estimation of crystal growth and nucleation kinetics from batch crystallizations. In an early study, Bransom and Dunning (1949) derived a crystal population balance to analyse batch CSD for growth and nucleation kinetics. Misra and White (1971), Ness and White (1976) and McNeil etal. (1978) applied the population balance to obtain both nucleation and crystal growth rates from the measurement of crystal size distributions during a batch experiment. In a refinement, Tavare and... 

Figure 7.5 Experimental, (a) transient supersaturatiom, and (h) consequent product crystal size distributions from hatch cooling crystallizations after Jones and Mullin, 1974)...

In this case, the co-solvent dosage rate is programmed in order to control the transient level of supersaturation in an effort to improve on the product crystal size distribution from simply dumping in all the solvent at the start of the batch. An experimental crystallizer within which a programmed microcomputer determines the set point of a variable speed-dosing pump is shown in Figure 7.7. Controlled co-solvent dosing improves the product crystal size, with a consequent increase in the filterability of the product. These process concepts are developed further in Chapter 9. 

The crystal size distribution then forms two parts (Figure 7.10) given by... 

Figure 8.10 Predicted and measured (averaged) crystal size distributions for barium sulphate (Re = 30,000, C o = 0.015 kmol Cbo = 1-500 kmol Rii = 1).

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