Mixing MSMPR

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. 

Many industrial crystallizers operate in a weU-mixed or nearly weU-mixed manner, and the equations derived above can be used to describe their performance. Furthermore, the simplicity of the equations describing an MSMPR crystallizer make experimental equipment configured to meet the assumptions lea ding to equation 44 useful in determining nucleation and growth kinetics in systems of interest. 

GSD Characteristics for MSMPR Crystallizers. The perfectiy mixed crystallizer described ia the preceding discussion is highly constrained and the form of crystal size distributions produced by such systems is fixed. Such distributions have the foUowiag characteristics. 

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)] ... 

The mixed suspension, mixed product removai (MSMPR) crystaiiizer... 

The flow of slurry within all the agitated erystallizer vessels illustrated is elearly eomplex and mixed to a greater or lesser extent at the mieroseopie level. In order to ease theoretieal analysis a new type of vessel therefore had to be invented This idealized vessel has beeome known as the eontinuous MSMPR erystallizer, after Randolph and Lawson (1988). The MSMPR is the erystal-lization analogue of the CSTR (eontinuous stirred tank reaetor) employed in idealizations of ehemieal reaetion engineering. 

The CSD from the continuous MSMPR may thus be predicted by a combination of crystallization kinetics and crystallizer residence time (see Figure 3.5). This fact has been widely used in reverse as a means to determine crystallization kinetics - by analysis of the CSD from a well-mixed vessel of known mean residence time. Whether used for performance prediction or kinetics determination, these three quantities, (CSD, kinetics and residence time), are linked by the population balance. 

The assumption of perfeet mixing applied in the bateh and eontinuous MSMPR erystallizer models does not always apply, however, espeeially as vessel size inereases. Methods for aeeounting for imperfeet mixing and seale-up are eonsidered in the next ehapter. 

Garside, J. and Tavare, N.S., 1985. Mixing, reaction and precipitation limits of micromixing in an MSMPR crystallizer. Chemical Engineering Science, 40, 1485-1493. 

MSMPR Mixed Suspension, Mixed Product Removal PDF Probability Density Function... 

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 ... 

Figure 15.21. Population plots for a continuous mixed-suspension mixed-product removal (MSMPR)...

An MSMPR crystalliser operates with a steady nucleation rate of n = 1013/m4, a growth rate, Gd = 10-8 m/s and a mixed-product removal rate, based on clear liquor of 0.00017 m3/s. The volume of the vessel, again based on clear liquor, is 4 m3, the crystal density is 2660 kg/m3 and the volumetric shape factor is 0.7. Determine ... 

Etherton studied the growth and nucleation kinetics of gypsum crystallization from simulated stack gas liquor using a one-liter seeded mininucleator with a Mixed Suspension Mixed Product Removal (MSMPR) configuration for the fines created by the retained parent seed. The effect of pH and chemical additives on crystallization kinetics of gypsum was measured. This early fundamental study has been the basis for later CSD studies. 

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 ... 

However, the mixing of the dispersed and continuous phases is considered here, and it is possible to apply the same way of thinking for plural dispersed phases. Additionally, the newly defined mixedness can be applied to judge whether the assumption of MSMPR (mixed suspension mixed product removal) in the crystallization operation is established. 

The aim of crystallization is to separate the observed component into higher quality crystals. The crystal size and probability density distribution of its size become very important factors for the product or the following processes. Although multi-phase mixing is fairly common in industries, there have been few investigations on the mixing performance of operations/equipment. In crystallization operation, the assumption of MSMPR has been used to design a crystallizer without a detailed discussion. Therefore, the assumption of MSMPR must be studied quantitatively. 

MSMPR crystallizer A vessel operating in a continuous manner in which crystallization occurs and whose contents are perfectly mixed. As a result of perfect mixing, all variables descriptive of the mother liquor and crystals are constant throughout the vessel and are identical to corresponding variables in the product stream leaving the vessel. 

Clear-liquor advance is used for two purposes (1) to reduce the quantity of liquor that must be processed by the solid-liquid separation equipment (e.g., filter or centrifuge) that follows the crystallizer, and (2) to separate the residence time distributions of crystals and liquor. The reduction in liquor flow through the separation equipment can allow the use of smaller equipment for a fixed production rate or increased production through fixed equipment. Separating the residence time distributions of crystals and liquor means that crystals will have an average residence time longer than that of the liquor. This should, in principle, lead to the production of larger crystals, but because the crystallizer is otherwise well mixed, the crystal population density will have the same form as that for the MSMPR crystallizer (Eq. (54)). 

ANALYSIS OF DATA FROM A MIXED SUSPENSION—MIXED PRODUCT REMOVAL CRYSTALLIZER (MSMPR) 10.13... 

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. 

The simplest continuous reactor to consider is that of a constantly stirred tank reactor (CSTR) or precipitator, also called a mixed suspension, mixed product removal crystallizer (MSMPR) [98], shown in Figure 6.23. This tsrpe of precipitator has a constant volume, V, with an input flow rate equal to its output flow rate, Q. The population iJofR) in the precipitator is that which leaves as product. In this case, the population balance is used at steady state (i.e., drjfjdt — 0) ... 

Mixed suspension, mixed product removal crystallizers (MSMPR) normally have much longer operating cycles than... 

Garside, J. andN.S. Tavare (1985). Mixing, reaction, and precipitation hmits of micnimixing in an MSMPR crystallizer. Chem. Eng. Sci. 40, 1485—1493. 

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. 

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