Crystallizer 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. 

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). 

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. 

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... 

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. 

Kubota, N., Akazawa, K. and Shimizu, K., 1990. Kinetics of BaC03 precipitation in an MSMPR crystallizer. Industrial Crystallization 90. Gamiiscli-Partenkirclien, September 1990. Ed. A. Mersmann, Diisseldorf GVC.VDI, pp. 199-204. 

Mydlarz, I. and Jones, A.G., 1990. On the estimation of size-dependent crystal growth rate functions in MSMPR crystallizers. Chemical Engineering Journal, 53, 125-135. 

PloB, R., Tengler, T. and Mersmann, A., 1986. Scale-up of MSMPR-Crystallizers. German Chemical Engineering, 1, 42-48. 

Sengupta, B. and Dutta, T.K., 1990. Effect of dispersions on CSD in continuous MSMPR crystallizers. Chemical Engineering and Technology, 13(6), 426-431. 

Sheikh, A.Y. and Jones, A.G., 1996. Dynamic flow sheet model for an MSMPR crystal-liser. In Industrial Crystallization 96. Ed. B. Biscans, Toulouse, Progep, 16-19 September 1996, pp. 583-588. 

Tavare, N.S., 1986. Crystallization kinetics from transients of an MSMPR crystallizer. The Canadian Journal of Chemical Engineering, 64, 752-758. 

WHITE, E. T. and RANDOLPH, A. D. AIChE Jl 33 (1984) 686-689. Graphical solution of the material balance constraint for MSMPR crystallizers. 

The development and refinement of population balance techniques for the description of the behavior of laboratory and industrial crystallizers led to the belief that with accurate values for the crystal growth and nucleation kinetics, a simple MSMPR type crystallizer could be accurately modelled in terms of its CSD. Unfortunately, accurate measurement of the CSD with laser light scattering particle size analyzers (especially of the small particles) has revealed that this is not true. In mar cases the CSD data obtained from steady state operation of a MSMPR crystallizer is not a straight line as expected but curves upward (1. 32. 33V This indicates more small particles than predicted... 

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