Crystallizers unsteady-state operation

By the use of a generalized population balance the MSMPR modelf is extended to account for unsteady-state operation, classified product removal, crystals in the feed, crystal fracture, variation in magma volume, and time-dependent growth rate. These variations are not included in the following derivations. 

Zeolite membranes have the potential to selectively separate gas molecules in a mixture operating nnder steady state, unsteady state, or cyclic conditions, while fixed bed adsorbers are typically operated under transient conditions. In addition, becanse of the inorganic nature of zeolite man-branes, they have higher mechanical strength and greater thermal and chemical stability than some of their polymeric counterparts. Also, their ability to operate under very different conditions (total pressure, composition, and tan-perature) on both sides of the zeolite membrane is a great advantage compared to conventional adsorption on discrete zeolite crystals. 

For batch crystallizers, which inevitably operate in the unsteady state, the simple population balance relationship, e.g. equation 9.63, must be modified to... 

The population balance concept enables the calculation of CSD to be made from basic kinetic data of crystal growth and nucleation and the development of this has been expounded by Randolph and Larson (1988), as summarized in Chapters 2 and 3. Batch operation is, of course, inherently in the unsteady-state so the dynamic form of the equations must be used. For a well-mixed batch crystallizer in which crystal breakage and agglomeration may be neglected, application of the population balance leads to the partial differential equation (Bransom and Dunning, 1949)... 

As seen in Chapter 7, the operation of batch crystallizers is inherently unsteady-state. Transient values occur of the major operating variables such as slurry density, supersaturation, temperature and mean particle size. Methods of operational eontrol sueh as by use of seeding and temperature programming were also eonsidered in detail. 

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