Crystallizers MSMPR

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... 

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. 

Moments of the distribution can be calculated for MSMPR crystallizers by the simple expression... 

The dominant crystal size is given by = 3Gr. This quantity is also the ratio mJwhich is often given the symbol 2-(J) Prom the definition of the coefficient of variation given by equation 41, cv = 50% for an MSMPR crystallizer. Such a cp may be too large for certain commercial products, which means either the crystallizer must be altered or the product must be screened to separate the desired fraction. 

A pair of kinetic parameters, one for nucleation rate and another for growth rate, describe the crystal size distribution for a given set of crystallizer operating conditions. Variation ia one of the kinetic parameters without changing the other is not possible. Accordingly, the relationship between these parameters determines the abiUty to alter the characteristic properties (such as dominant size) of the distribution obtained from an MSMPR crystallizer (7). 

Crystallizers with Fines Removal In Example 3, the product was from a forced-circulation crystallizer of the MSMPR type. In many cases, the product produced by such machines is too small for commercial use therefore, a separation baffle is added within the crystallizer to permit the removal of unwanted fine crystalline material from the magma, thereby controlling the population density in the machine so as to produce a coarser ciystal product. When this is done, the product sample plots on a graph of In n versus L as shown in hne P, Fig. 18-62. The line of steepest ope, line F, represents the particle-size distribution of the fine material, and samples which show this distribution can be taken from the liquid leaving the fines-separation baffle. The product crystals have a slope of lower value, and typically there should be little or no material present smaller than Lj, the size which the baffle is designed to separate. The effective nucleation rate for the product material is the intersection of the extension of line P to zero size. 

Although surface-cooled types of MSMPR crystalhzers are available, most users prefer crystallizers employing vaporization of solvents or of refrigerants. The primary reason for this preference is that heat transferred through the critical supersaturating step is through a boil-ing-hquid-gas surface, avoiding the troublesome solid deposits that can form on a metal heat-transfer surface. 

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. 

Figure 3.6 Schematic particle flows in the ideal MSMPR crystallizer at steady state...

Figure 3.7 Crystal population distribution from the MSMPR crystallizer...

A pilot-scale continuous MSMPR crystallizer of 10 litre capacity is used to crystallize potash alum from aqueous solution, supersaturation. This is being achieved using a 15-min residence time, a 100-ml slurry sample was taken and the crystals contained in this sample subjected to a size analysis. The results of this analysis are given below... 

The mass distribution from the idealized MSMPR crystallizer is thus a Gamma function, as shown in Figure 3.8b. 

The population balance analysis of the idealized MSMPR crystallizer is a particularly elegant method for analysing crystal size distributions at steady state in order to determine crystal growth and nucleation kinetics. Unfortunately, the latter cannot currently be predicted a priori and must be measured, as considered in Chapter 5. Anomalies can occur in the data and their subsequent analysis, however, if the assumptions of the MSMPR crystallizer are not strictly met. 

Evidence for secondary nucleation has came from the early continuous MSMPR studies. MSMPR crystallization kinetics are usually correlated with supersaturation using empirical expressions of the form... 

In the MSMPR crystallizer at steady state, the increase of particle number density brought about by particle growth and agglomeration is compensated by withdrawal of the product from the crystallizer. 

Figure 6.19 Experimental set-up continuous MSMPR reaction-crystallizer (Zauner and Jones, 2000a)...

Calculate the residence time and volume of an MSMPR crystallizer required to produce 1000 kg/li of potash alum having a dominant crystal size of 600 pm using a slurry density of 250 kg crystals/m slurry. 

The CSD from an MSMPR crystallizer with a working volume of 10 m operated with a magma density of 250 kg crystals/m slurry and a production rate of 62 500 kg crystals/h has a mass mean size of 480 pm. Calculate ... 

Figure 7.11 Information flow in an MSMPR crystallizer Randolph and Larson, 1988)...

Hostomsky and Jones (1991) described a numerical procedure for a noniterative solution of the steady-state MSMPR crystallization, where both the... 

Figure 8.25 Monte Carlo simulation of distribution of primary particle residence times (oo size) within MSMPR precipitated agglomerates of 5 and 20 crystals (Hostomsky and Jones, 1993a)...

By combining expressions from MSMPR theory above, it can be shown that the median crystal size in the absence of agglomeration and disruption is given by... 

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