(369a) Comparison of Models for Coarse Particle Shape Evolution during Attrition in a Stirred Vessel
Particle breakage in stirred vessels is usually modeled using population balance equations (PBEs) to describe the evolution in particle size with time. Although shape has a strong effect on the particle properties and final product quality, changes in the particle shape distribution are often neglected. To account for changes in both size and shape simultaneously, a bivariate population balance must be used. This requires a bivariate breakage distribution function that accounts for the observed size and shape evolution in actual systems. Although bivariate breakage distribution functions have been developed that meet the constraints of mass conservation and exchangeability , they are not based on the fundamental physics of particle attrition. It is necessary to develop breakage distribution functions based on fracture mechanics that meet the constraints.
Two models have been developed ? one by Gahn and Mersmann [2-3] and one by Ghadiri and Zhang [4-5] ? that use fracture mechanics to predict the total particle volume lost due to attrition. The objective of this research is to test and compare the two theories to determine if they can explain the changes in particle size and shape due to attrition. This work focuses only on the larger particles, not the fines. This information is incorporated into the PBEs by including it in the breakage distribution function. Starting with the original coarse particle size and shape, the model accounts for the material removed from the parent particles due to attrition. The approach is to model the breakage distribution function as a bivariate function of the particle volume and the shape factor. A comparison of both models with experimental results for several systems is presented.
This work has wide applicability in that it directly affects any unit operation involving solids breakage in stirred vessels. This includes both stirred reactors with solid particles as well as crystallizers.
1. P. J. Hill, "Statistics of Multiple Particle Breakage Accounting for Particle Shape", AIChE J., 50, 937-952 (2004).
2. Gahn, C., and A. Mersmann, ?Theoretical prediction and experimental determination of attrition rates?, Trans. I. Chem. Eng., 75, Part A, 125-131 (1997).
3. Gahn, C., and A. Mersmann, ?Brittle Fracture in Crystallization Processes. Part A. Attrition and abrasion of brittle solids?, Chem. Eng. Sci., 54, 1273-1282 (1999a).
4. Ghadiri, M. and A. Zhang, ?Impact attrition of particulate solids. Part 1: A theoretical model of chipping,? Chem. Eng. Sci., 57, 3659-3669 (2002).
5. Zhang, A. and M. Ghadiri, ?Impact attrition of particulate solids. Part 2: Experimental work,? Chem. Eng. Sci., 57, 3671-3686 (2002).
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