Stirred tank, crystallization model

The Mixed Crystallizer. One problem that concerned our research for many years was the understanding of the cyclic behavior of some crystallization and polymerization reactors (27. 28) Under certain conditions the particle size undergoes strong cyclic fluctuations, which severely upset operation and control. To understand this behavior we set up a simple model proposed by Hulburt and Katz for a stirred tank crystallizer, which is simply a particle balance of the crystallizer as well as a mass balance of the solute For our purposes it is not necessary to go into the details of the model, but rather to deal directly with its implications. The only important kinetic parameters of this model are the linear crystal growth rate G and the nucleation rate B. The simplest assumption we can make about B and G are to assume that they are functions of supersaturation only. 

The majority of applications of crystal population balance modeling have assumed that the solution and suspension in the crystallizer are homogeneous, i.e., the Mixed-Suspension Mixed-Product Removal (MSMPR) approximation (Randolph and Larson 1988). (This is simply the analog of the Continuous Stirred Tank (CSTR) (Levenspiel 1972) approximation for systems containing particles. It means that the system is well mixed from the standpoint of the solute concentration and the particle concentration and PSD. In addition, the effluent is assumed to have the same solute concentration, particle concentration, and PSD as the tank.) This approximation is clearly not justified when there is significant inhomogeneity in the crystallizer solution and suspension properties. For example, it is well known that nucleation kinetics measured at laboratory scale do not scale well to full scale. It is very likely that the reason they do not is because MSMPR models used to define the kinetic parameters may apply fairly well to relatively uniform laboratory crystallizers, but do considerably worse for full scale, relatively nonhomogeneous crystallizers. 

Section 6.4 covers continuous stirred tank separators. Section 6.4.1 studies equilibrium separation processes most of this section is devoted to crystallization, with additional coverage of liquid extraction. Membrane separation processes/devices are sometimes modeled as CSTRs. Section 6.4.2 touches upon a few of these examples, encountered, for example, in ultrafllUation and gas permeation. There are brief treatments of batch systems that are well-stirred in Sections 6.4.1 and 6.4.2 for both equilibrium based and membrane separation processes. 

Optimization of disperse properties such as PSD, shape, or structure as a function of operation parameters of a distinct unit operation. Most work is known for optimization of crystallization processes in stirred tank reactors (Kwon et al, 2014 Shi et al, 2006 VoUmer and Raisch, 2006). For many unit operations, empirical approaches prevail due to a lack of predictive forward models. 

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