Models mixed-product removal

The crystallizer model that led to the development of equations 44 and 45 is referred to as the mixed-suspension, mixed-product removal (MSMPR) crystallizer. 

Equation (18-31) contains no information about the ciystalhzer s influence on the nucleation rate. If the ciystaUizer is of a mixed-suspension, mixed-product-removal (MSMPR) type, satisfying the criteria for Eq. (18-31), and if the model of Clontz and McCabe is vahd, the contribution to the nucleation rate by the circulating pump can be calculated [Bennett, Fiedelman, and Randolph, Chem. E/ig, Prog., 69(7), 86(1973)] ... 

This results In a set of first-order ordinary differential equations for the dynamics of the moments. However, the population balance Is still required In the model to determine the three Integrals and no state space representation can be formed. Only for simple MSMPR (Mixed Suspension Mixed Product Removal) crystallizers with simple crystal growth behaviour, the population balance Is redundant In the model. For MSMPR crystallizers, Q =0 and hp L)=l, thus ... 

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. 

Once the theoretical yield from a crystallizer has been calculated from mass and energy balances, there remains the problem of estimating the CSD of the product from the kinetics of nucleation and growth. An idealized crystallizer model, called the mixed suspension-mixed product removal model (MSMPR), has served well as a basis for identifying the kinetic parameters and showing how knowledge of them can be applied to calculate the performance of such a crystallizer, ... 

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)... 

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. 

Figure 9.11. Mixed suspension crystallizer operating with fines destruction and classified product removal a) the R-Z model, b) population density plot...

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