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               108                                                                                Crystallization Processes


               It is defined by:                                  tion obtained from a continuous crystallizer. The effects
                                        σ                        of operating variables on crystal size distributions will be
                                  c.v. =                 (41)    discussed in Section VI.
                                        L D
                                                                   The throughput per unit crystallizer volume is greater
               and estimated from the moments of the distribution:
                                                                 for a continuous system. Batch units have several operat-
                                  
           1/2                ing steps in a cycle—charging, heating or cooling, crystal-
                                    m 3 m 5
                             c.v. =   2  − 1             (42)    lizing, discharging, and cleaning—and the unit production
                                     m
                                      4
                                                                 rate is based on the total cycle time, even though the for-
               This is especially useful for systems that cannot be de-  mation of crystals may occur only during a small portion
               scribed by an analytical distribution function.   of the cycle.
                                                                   It may be easier to operate a continuous system so that
                                                                 it reproduces a particular crystal size distribution than it
               V. CRYSTALLIZER CONFIGURATION                     is do reproduce crystal characteristics from a batch unit.
                  AND OPERATION                                  Moreover, the coupling of several transient variables and
                                                                 nucleation make it difficult to model and control the op-
               Crystallization equipment can vary in sophistication from  eration of a batch crystallizer.
               a simple stirred tank to a complicated multiphase column,
               and the protocol can range in complexity from simply al-
                                                                 A. Relationship of Solubility
               lowing a vat of liquor to cool to the careful manipulation
                                                                    to Mode of Operation
               required of batch cyclic operations. In principle, the objec-
               tives of these systems are the same: to produce a product  The driving force for crystal formation can be generated
               meeting specifications on quality at an economical yield.  through a variety of means, including cooling or heating
               This section will examine some of the considerations that  to reduce or increase the system temperature, evaporating
               go into the selection of a crystallizer so as to meet these  solvent, evaporative (flash) cooling, inducing a chemical
               objectives.                                       reaction (when the reaction product is sparingly soluble,
                 One of the first decisions that must be made is whether  the process is called precipitation), adjusting pH, salting
               the crystallizer operation is to be batch or continuous. In  out through the addition of a nonsolvent, direct-contact
               general, the advantages of each type of operation should  cooling with a refrigerant, or some other means. All of
               be weighed in choosing one over the other, but more often  these modes of operation can be implemented in either a
               the decision rests on whether the other parts of the process  batch or a continuous process. In addition, two or more of
               are batch or continuous. If they are batch, then it is likely  the modes may be combined to enhance the product yield.
               that the crystallizer also should be batch.         As discussed in an earlier section, solubility is intrinsic
                 The equipment required for batch crystallization can be  to the solute-solvent system, and the relationship of solu-
               very simple. For example, some crystalline materials are  bility to temperature often determines the mode by which a
               produced by simply allowing a charge of hot liquor to cool.  crystallizerisoperated.Recallforexamplethatthesolubil-
               After the crystals have formed, the magma is discharged  ity of NaCl (see Fig. 2) is essentially independent of tem-
               through a filter or the liquor may be decanted and the set-  perature, while Na 2 SO 4 · 10H 2 O has a solubility that ex-
               tled slurry filtered. Very large crystals can be obtained by  hibits a strong dependence on temperature. Consequently,
               allowing encrustations formed on the walls of these crys-  cooling a sodium chloride solution cannot generate sig-
               tallizers to grow undisturbed; after the system has come  nificant product yield; solvent evaporation is the primary
               to equilibrium, the liquor is drained and the crystals are  mode of NaCl production. On the other hand, reducing
               removed by scraping them from the surface.        the temperature of a saturated solution of sodium sulfate
                 Batch crystallizers can be used in a campaign to produce  generates substantial product and may be used alone or in
               a particular product and in a second campaign to produce  combination with evaporation.
               another product. Generally, it is not possible to operate  Cooling crystallizers utilize a heat sink to remove both
               continuous processes in this way. Batch crystallizers can  the sensible heat from the feed stream and the heat of crys-
               handle viscous or toxic systems more easily than can con-  tallization released or, in some cases absorbed, as crystals
               tinuous systems, and interruption of batch operations for  are formed. The heat sink may be no more than the am-
               periodic maintenence is less difficult than dealing with in-  bient surroundings of a batch crystallizer, or (as is more
               terruptions in continuous processes. The latter factor may  likely) it may be cooling water or another process stream.
               beespeciallyimportantinbiologicalprocessesthatrequire  Evaporative crystallizers generate supersaturation by
               frequentsterilizationofequipment.Batchcrystallizerscan  removing solvent from the mixture, thereby increasing
               produce a narrow crystal size distribution, whereas special  the solute concentration. They may be operated under vac-
               processing features are required to narrow the distribu-  uum, and in those circumstances it is necessary to have a
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