Crystallization MSMPR crystallizer

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... 

The optimal network increases total residence time by 48 per cent when compared with an equivalent MSMPR of the same volume and throughput. This increase would translate into a similar increase in mean crystal size and a 78 per cent increase in yield. Exactly the same residence time as for the single crystallizer have been reported from simple cascade configurations previously designed for stage-wise crystallization processes for slight improvements in... 

Budz, J., Jones, A.G. and Mullin, J.W., 1987b. Agglomeration of potassium sulphate in an MSMPR crystallizer. In Fundamental aspects of crystallization and precipitation processes, American Institute of Chemical Engineers. Symposium Series, No. 253, 83, New York American Institute of Chemical Engineers, pp. 78-84. 

Garside, J. and Shah, M.B., 1980. Crystallization kinetics from MSMPR crystallizers. Industrial and Engineering Chemistry Process Design and Development, 19, 509-514. 

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

Hostomsky, J. and Jones, A.G., 1993b. Ibid., Crystallization and agglomeration kinetics of calcium carbonate and barium sulphate in the MSMPR crystallizer. Indem. pp. 2049-2054. 

Jazaszek, P. and Larson, M.A., 1977. Influence of fines dissolving on crystal size distribution in an MSMPR crystallizer. American Institution of Chemical Engineers Journal, 23, 460-468. 

Jones, A.G. and Mydlarz, I., 1989. Crystallization and subsequent solid-liquid separation of potassium sulphate. Part I MSMPR kinetics. Chemical Engineering Research and Design, 67, 283-293. 

Jones, A.G. and Mydlarz, J., 1990a. Continuous crystallization of potash alum. MSMPR kinetics. Canadian Journal of Chemical Engineering, 68, 250-259. 

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