An Approximate Mathematical Model for Design of Industrial Crystallizers with Elutriators
Qian Ruying and Chen Zude
(Shanghai Research Institute of Chemical Industry)
1985, 36(3):
302-311.
Abstract
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In spite of the effect of cycling on crystal size distribution(CSD) of potassium chloride in a pilot plant crystallizer, the average size can still be simulated by a steady-state mathematical model. According to this model, the CSD in the main size range for industrial crystallizers may be expressed as an exponential function of the population density n with respect to crystal size L, as for mixed-suspension-mixed-product-removal (MSMPR) crystallizers. For fine and coarse crystals, the withdrawal of fines and the classification of coarse crystals, respectively, should be taken into account as in the case of the R-Z model. For intermediate crystals, which can settle behind the baffles and can not be drawn off effectively from the elutriator, their retention time is taken to be infinite for simplification.
The resulting mathematical model is expressed by Eqs. ( 2 )-( 5 ) and illustrated in Fig. 2.
This model is a generalized form of all previous models for crystallizers. The calculated CSD in the main-size range fits well data from a 520-liter pilot-plant crystallizer. The calculated values for crystal growth rate G, dominant crystal size LD, median crystal size L50, suspension density MT, and production rate P/V, all agree, within 10%, with the corresponding experimental data. However, the MT equation, Eq. (10), is rather complicated, so a. simplified model, in which LF = 0 and Z = ∞, is derived, and a simplified MT equation, Eq. (11), is used for crystallizer design. The design Procedure for industrial crystallizers with elutriators is also given.