Product removal, crystal size distribution

As an idealization of the classified-fines removal operation, assume that two streams are withdrawn from the crystallizer, one corresponding to the product stream and the other a fines removal stream.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). 

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. 

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 ... 

Crystallizers are made more flexible by the introduction of selective removal devices that alter the residence time distributions of materials flowing from the crystallizer. Three removal functions—clear-liquor advance, classified-fines removal, and classified-product removal— and their idealized removal devices will be used here to illustrate how design and operating variables can be manipulated to alter crystal size distributions. Idealized representations of the three classification devices are illustrated in Fig. 17. 

Clear-liquor advance from what is called a double draw-off crystallizer is simply the removal of mother liquor without simultaneous removal of crystals. The primary action in classified-fines removal is preferential withdrawal from the crystallizer of crystals of a size below some specified value this may be coupled with the dissolution of the crystals removed as fines and the return of the resulting solution to the crystallizer. Classified-product removal is carried out to remove preferentially those crystals of a size larger than some specified value. In the following discussion, the effects of each of these selective removal functions on crystal size distributions will be described in terms of the population density function n. Only the ideal solid-liquid classification devices will be examined. It is convenient in the analyses to define flow rates in terms of clear liquor. Necessarily, then, the population density function is defined on a clear-liquor basis. 

The first three columns of Table 10.5 show sieve data for a 100-cc slurry sample containing 21.0 g of solids taken from a 20,000-gal (75-m3) mixed suspension-mixed product removal crystallizer (MSMPR) producing cubic ammonium sulfate crystals. Solids density is 1.77 g/cm3, and the density of the clear liquor leaving the crystallizer is 1.18 g/cm3. The hot feed flows to the crystallizer at 374,000 lb/h (47 kg/s). Calculate the residence time r, the crystal size distribution function n, the growth rate G, the nucleation density n°, the nucleation birth rate B°, and the area-weighted average crystal size L3 2 for the product crystals. 

Fig. 23. Idealized crystal size distribution for mixed product removal. After Saeman (SI).

If an elutriation leg or other product-classifying device is added to a crystallizer of the MSMPR type, the plot of the population density versus L is changed in the region of largest sizes. Also the incorporation of an elutriation leg destabilizes the crystal-size distribution and under some conditions can lead to cycling. To reduce cycling, fines destruction is usually coupled with classified product removal. The theoretical treatment of both the crystallizer model and the cycling relations is discussed by Randolph, Beer, and Keener (loc. cit.). 

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. 

This misconception is particularly common in crystallization. The hypothesis of a perfectly mixed system is, for crystallization and precipitation processes, labeled as mixed-suspension, mixed-product removal (MSMPR). With diis model the crystalUzer is modeled with a spatially homogeneous NDF, generally called the crystal-size distribution (CSD). However, the fact that the CSD is constant through the vessel does not mean that the rates of crystal nucleation, molecular growth, aggregation, and breakage are constant. 

The perfectly mixed, contineous. stendy-state mixed-suspension mixed-product removal (MSMPR) ciys-laHirer is restrictive in the degree to which characteristics of a crystal size distribution can be varied. Indeed, examination of Eqs. (11.2-32) and (11.2-40) shows that once nucleation and growth lunatics are fixed in these systems the crystal size distribution is determined in its entirety. In addition, such distributions have the following characteristics ... 

The effects of each of the selective removal functions on crystal size distributions can ha described in terms of the population density function n. If it is assumed that perfect classification of fines and product crystals is implemented, (hen the following expression for population density results ... 

Although many commercial crystallizers operate with some form of selective crystal removal, devices that implement these functions add to the complexity of the operation. In addition, Randolph et a .76 have established that classified-product removal can lead to cycling of the crystal size distribution. A review of the simulation and control of ciystal size distributions hes been provided by Randolph.77 Properties of the crystal size distribution have been given in terms of R and Z and the moments of the crystal size distribution.74... 

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. 

Another mechanism that must be mentioned in connection with nucleation in real crystallization equipment is attrition. In a classic paper by Randolph (1969), this subject is reviewed. Randolph demonstrated that crystal breakage, classified product removal, and decrease in linear growth rate with crystal size all skew the crystal size distribution, producing a narrower size range of crystals than would be expected in a mixed suspension, mixed product removal system. This skewing results in a curve of the plot of In n versus L. 

Continuous MSMPR Precipitator. The population balance, which was put forward by Randolph and Larson (1962) and Hulbert and Katz (1964), provides the basis for modeling the crystal size distribution (CSD) in precipitation processes. For a continuous mixed-suspension, mixed-product-removal (CMSMPR) precipitator with no suspended solids in the feed streams, the population balance equation (PBE) can be written as (Randolph and Larson 1988)... 

In the industrial o allization, operation design which satisfies required product specification is also important. However, methods of determining the seed crystals specifications i.e., size distribution and mass of seed cr3 tals, and the time of addition have not been considered systematically. The required time of start-up operation is known to be different by 10 residence times even in the laboratory scale depending on the seed crystals specifications(2). In the present study relations between the procedure and conditions of start-up operations and the product crystal size distributions are discussed based on the analysis of product crystal size distributions. The purpose of this study is, therefore, to obtain design strategies for start-up operation by use of a typical MSMPR (Mixed-Suspension Mixed- oduct Removal) crystsdlizer which has been used for the theoretical analysis. The ammonium-sul te water system was used. 

A crystallizer equipped with the devices for product classification and fines destruction can efficiently improve the particle size and particle size distribution. With the fines destruction, a portion of the small particles can be eliminated in such a way that the number of crystals in the crystallizer can be controlled within the required range. When this method is complemented with classified product removal, the size of the crystals in the product is controlled on the other hand, an undesired increase in the amount of small crystals is prevented. With this method, it is possible to obtain crystals of a uniform and large size. 

In this section, the principles involved in using a population balance to describe the crystal size distribution in the product from a well-mixed continuous crystallizer are illustrated. The primary objective of this treatment is to show how nucleation and growth kinetics can be evaluated from data on the crystal size distribution produced in such crystallizers. Detailed development of the theory and extensions of these principles to crystallizers that employ selective removal of crystals from the crystallizer internals or to batch or transient continuous crystallizers is provided by Randolph and Larson. ... 

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