Dynamics and stability of continuous MSMPR agglomerative precipitation: Numerical analysis of the dual particle coordinate model

Computers and Chemical Engineering

Volumn 22, Issue 4-5, 1998, Pages 535-545

  Wójcik, Janusz A ^a,b   Jones, Alan G ^a  

^a UNIVERSITY COLLEGE LONDON   (United Kingdom)

^b SILESIAN UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

AGGLOMERATION; FINITE DIFFERENCE METHOD; MATHEMATICAL MODELS; PARTICLE SIZE ANALYSIS; SUPERSATURATION; SUSPENSIONS (FLUIDS);

DUAL PARTICLE COORDINATE POPULATION BALANCE APPROACH;

PRECIPITATION (CHEMICAL);

EID: 0032041187     PISSN: 00981354     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0098-1354(97)00239-1     Document Type: Article

References (34)

1. Ames, W. F. (1992) Numerical Methods for Partial Differential Equations, Third Edition. Academic Press, Boston.
2. Beckman, J. R. and Farmer, R. W. (1987) Bimodal CSD barite due to agglomeration in an MSMPR crystallizer. AIChE Symp. Ser. 83(253), 85-94.
3. Carnahan, B., Luther, H. A. and Wilkes, J. O. (1969) Applied Numerical Methods, John Wiley, New York.
4. Chang, R. Y. and Wang, M. L. (1984) Shifted Legendre function approximation of differential equations; application to crystallization processes. Comp. Chem. Engng. 8(2), 117-125.
5. Chakraborty, D., Agarwal, V. K., Bhatia, S. K. and Bellare, J. (1994) Steady-state transitions and polymorph transformations in continuous precipitation of calcium carbonate. Ind. Eng. Chem. Res. 33, 2197
6. David, R., Marchai, P., Klein, J. P. and Villermaux, J. (1991) Crystallization and precipitation engineer-ing - III. A discrete formulation of the agglomeration rate of crystals in a crystallization process. Chem. Engng. Sci. 46(1), 205-213.
7. Drake, R. L. (1972) General mathematical survey of the coagulation equation. In Topics in Current Aerosol Research (Edited by G. H. Hidy and J. R. Brock). Pergamon Press. Oxford.
8. Erasmus, L. D., Eyre, D. and Everson, R. C. (1994) Numerical treatment of the population balance equation using a spline-Galerkin method. Comp. Chem. Engng 18(9), 775-783.
9. Farrell, R. J. and Tsai, Y-C. (1994) Modeling, simulation and kinetic parameter estimation in batch crystallization processes. AIChEJ. 40(4), 586-593.
10. Fridrickson, A. G. and Tsuchiya, H. M. (1963) Continuous propagation of microorganisms. AIChE J. 9(4), 459-468.
11. Gelbard, F. and Seinfeld, J. W. (1978) Numerical solution of the dynamic equation for paniculate systems. J. Comp. Phys. 28, 357
12. Halfen, A. and Kaliaguine, S. (1976) Alumina trihydrate crystallization. Part 2: a model of agglomeration. Can. J. Chem. Eng. 54, 168-172.
13. Hartel, R. W. and Randolph, A. D. (1986) Mechanisms and kinetic modelling of calcium oxalate crystals in urine-like liquor: part II, kinetic modelling. AIChE J. 32, 1186-1195.
14. Hostomský, J. and Jones, A. G. (1991) Calcium carbonate crystallization kinetics, agglomeration and form during continuous precipitation from solution. J. Phys. D. 24, 165-170.
15. Hounslow, M. J., Ryall, R. L. and Marshall, V. R. (1988) A discretized population balance for nucleation, growth and aggregation. AIChE J. 34(11), 1821-1832.
16. Hulburt, H. M. and Katz, S. (1964) Some problems in particle technology. A statistical mechanical formulation. Chem. Engng. Sci. 19, 555-574.
17. Hwang, C. and Shih, Y. P. (1982) Solution of population balance via block pulse functions. Chem. Eng. J. 25, 39-45.
18. Jones, A. G., Wachi, S. and Delannoy, C-C. (1992) Precipitation of calcium carbonate in a fluidized bed reactor. In Proceedings of the Seventh Engineering Foundation Conference on Fluidization (Edited by O. E. Potter and D. J. Nicklin), Engineering Foundation, New York, pp. 407-414.
19. Lapidus, L. and Pinder, F. P. (1982) Numerical Solution of Partial Differential Equations in Science and Engineering. John Wiley, New York.
20. Marchai, P., David, R., Klein, J. P. and Villermaux, J. (1988) Crystallization and precipitation engineering-I. An efficient method for solving population balance in crystallization with agglomeration. Chem. Engng. Sci. 43, 59-67.
21. Press, W. H., Teukolsky, S. A., Vetterilng, W. T. and Flannery, B. P. (1992) Numerical Recipes in FORTRAN. The Art of Scientific Computing, Second Edition. Cambridge University Press, Cambridge.
22. Randolph, A. D. and Larson, M. A. (1962) Transient and steady-state size distributions in continuous mixedsuspension crystallizers. AIChE J. 8(5), 639-645.
23. Randolph, A. D. (1969) Effect of crystal breakage on crystal size distribution from a mixed-suspension crystallizer. Ind. Eng Chem. Fundam. 8, 58
24. Randolph, A. D. and Larson, M. A. (1988) Theory of Particulate Processes, Second Edition. Academic Press, New York.
25. Sherwin, M. B., Shinnar, R. and Katz, S. (1967) Dynamic behaviour of the well-mixed isothermal crystallizer. AIChE J. 13(6), 1141-1154.
26. Singh, P. N. and Ramkrishna, D. (1977) Solution of population balance equations by MWR. Comp. Chem. Engng. 1, 23-31.
27. Smoluchowski, M. (1916) Drei Vortrǎge ǔber Diffusion, Brownsche Molekularbewegung und Koagulation von Kolloidteilchen, Phisik. Z. XVII, 557-571; 585-599.
28. Sǒhnel, O., Mullin, J. W. and Jones, A. G. (1988) Crystallization and agglomeration kinetics in the batch precipitation of strontium molibdate. Ind. Eng. Chem. Res. 27, 1721-1728.
29. Sǒhnel, O. and Mullin, J. W. (1992) Agglomeration in batch precipitated suspensions. AIChE Symp. Ser. 87(284), 182-189.
30. Synowiec, P., Jones, A. G. and Ayazi Shamlou, P. (1993) Crystal break-up in dilute turbulently agitated suspensions. Chem. Engng. Sci. 48, 3485-3495.
31. Tai, C. Y. and Chen, P. C. (1995) Nucleation, agglomeration and crystal morphology of calcium carbonate. AIChE J. 41(1), 68-77.
32. Thompson, P. D. (1968) A Transformation of a stochastic equation for droplet coalescence, Proc. Int. Conf. Cloud Phys., Toronto, pp. 115-126.
33. Wachi, S. and Jones, A. G. (1991) Effect of gas-liquid mass transfer on crystal size distribution during the batch precipitation of calcium carbonate. Chem. Engng. Sci. 46, 3289-3293.
34. Wachi, S. and Jones, A. G. (1992) Dynamic modelling of particle size and degree of agglomeration during precipitation. Chem. Engng. Sci. 47, 3145-3148.