Issue
Korean Journal of Chemical Engineering,
Vol.36, No.12, 2095-2103, 2019
Modified kinetic rate equation model for cooling crystallization
The kinetic rate equation (KRE) model, unlike the population balance equation model, can describe growth, nucleation, and even Ostwald ripening simultaneously. However, the KRE model cannot be applied in cooling crystallization systems. In this work, we propose a modified KRE model to describe cooling crystallization. The modified KRE model can successfully describe crystal growth and nucleation in cooling crystallization systems. In addition, the metastable zone width was simulated using the modified KRE model and compared with the experimental data in references. The results revealed that the modified KRE model could express the effect of overheating prior to cooling on the metastable zone width. As the extent of overheating increases, the metastable zone width becomes wider, which phenomenon can be clearly simulated by the modified KRE model. This modeling capability is attributed to the behavior of particle clusters that are sized less than the size of sub-nuclei. Because the population balance equation model cannot describe the metastable zone width, the modified KRE model has certain competitive advantages in its application to various crystallization systems.
[References]
  1. Mullin JW, Crystallization, Elsevier (2001).
  2. Fujiwara M, Nagy ZK, Chew JW, Braatz RD, J. Process Control, 15(5), 493, 2005
  3. Sanzida N, Nagy ZK, Comput. Chem. Eng., 130, 106559, 2019
  4. Marcellos CFC, Durand H, Kwon JSI, Barreto AG, Lage PLD, de Souza MB, Secchi AR, Christofides PD, AIChE J., 64(5), 1618, 2018
  5. McDonald MA, Bommarius AS, Rousseau RW, Grover MA, Comput. Chem. Eng., 123, 331, 2019
  6. Kim H, Park K, Chang JW, Lee T, Kim SH, Yang DR, Cryst. Growth Des., 19, 1748, 2019
  7. Park K, Kim DY, Yang DR, Ind. Eng. Chem. Res., 55(26), 7142, 2016
  8. Leubner IH, Curr. Opin. Colloid Interface Sci., 5, 151, 2000
  9. Chiu TY, Christofides PD, AIChE J., 46(2), 266, 2000
  10. Kwon JSI, Nayhouse M, Christofides PD, Orkoulas G, Chem. Eng. Sci., 107, 47, 2014
  11. Kwon JSI, Nayhouse M, Orkoulas G, Christofides PD, Chem. Eng. Sci., 119, 30, 2014
  12. Griffin DJ, Grover MA, Kawajiri Y, Rousseau RW, Ind. Eng. Chem. Res., 55(5), 1361, 2016
  13. Li HY, Kawajiri Y, Grover MA, Rousseau RW, Ind. Eng. Chem. Res., 56(14), 4060, 2017
  14. Griffin DJ, Kawajiri Y, Grover MA, Rousseau RW, Cryst. Growth Des., 15, 305, 2014
  15. Griffin DJ, Kawajiri Y, Rousseau RW, Grover MA, Chem. Eng. Sci., 164, 344, 2017
  16. Li J, Tilbury CJ, Joswiak MN, Peters B, Doherty MF, Cryst. Growth Des., 16, 3313, 2016
  17. Ramkrishna D, Singh MR, Annu. Rev. Chem. Biomol. Eng., 5, 123, 2014
  18. Puel F, Fevotte G, Klein JP, Chem. Eng. Sci., 58(16), 3715, 2003
  19. Costa CBB, Maciel MRW, Maciel R, Comput. Chem. Eng., 31(3), 206, 2007
  20. Farias LFI, de Souza JA, Braatz RD, da Rosa CA, Comput. Chem. Eng., 123, 246, 2019
  21. Fysikopoulos D, Benyahia B, Borsos A, Nagy ZK, Rielly CD, Comput. Chem. Eng., 122, 275, 2019
  22. Szilagyi B, Agachi PS, Nagy ZK, Ind. Eng. Chem. Res., 57(9), 3320, 2018
  23. Sulttan S, Rohani S, J. Cryst. Growth, 505, 19, 2019
  24. da Rosa CA, Braatz RD, Ind. Eng. Chem. Res., 57(34), 11702, 2018
  25. Hulburt HM, Katz S, Chem. Eng. Sci., 19, 555, 1964
  26. Randolph A, Larson M, Theory of particulate technology, Academic Press, New York (1971).
  27. Vetter T, Iggland M, Ochsenbein DR, Hanseler FS, Mazzotti M, Cryst. Growth Des., 13, 4890, 2013
  28. Fu X, Zhang D, Xu S, Yu B, Zhang K, Rohani S, Gong J, Cryst. Growth Des., 18, 2851, 2018
  29. Anisi F, Kramer HJM, Chem. Eng. Res. Des., 138, 200, 2018
  30. Kashchiev D, Nucleation, Elsevier (2000).
  31. Farkas L, Z. Phys. Chemie., 125, 236, 1927
  32. Stranski I, Kaischew R, Ann. Phys., 415, 330, 1935
  33. Becker R, Doring W, Ann. Phys., 416, 719, 1935
  34. Hussain K, Thorsen G, Malthe-Sorenssen D, Chem. Eng. Sci., 56(7), 2295, 2001
  35. Nordstrom FL, Svard M, Malmberg B, Rasmuson AC, Cryst. Growth Des., 12, 4340, 2012
  36. Sugimoto T, Mori A, Inoue T, J. Cryst. Growth, 292(1), 108, 2006
  37. Lignos I, Maceiczyk R, deMello AJ, Accounts Chem. Res., 50, 1248, 2017
  38. Tahri Y, Kozisek Z, Gagniere E, Chabanon E, Bounahmidi T, Mangin D, Cryst. Growth Des., 16, 5689, 2016
  39. Chang J, Cooper G, J. Comput. Phys., 6, 1, 1970
  40. Iggland M, Mazzotti M, Cryst. Growth Des., 12, 1489, 2012
  41. Trifkovic M, Sheikhzadeh M, Rohani S, J. Cryst. Growth, 311(14), 3640, 2009
  42. Lenka M, Sarkar D, J. Cryst. Growth, 408, 85, 2014
  43. Hu Q, Rohani S, Wang DX, Jutan A, AIChE J., 50(8), 1786, 2004
  44. Yang DR, Lee KS, Lee JS, Kim SG, Kim DH, Bang YK, Ind. Eng. Chem. Res., 46(24), 8158, 2007
  45. Kadam SS, Kulkarni SA, Ribera RC, Stankiewicz AI, ter Horst JH, Kramer HJM, Chem. Eng. Sci., 72, 10, 2012
  46. Kobari M, Kubota N, Hirasawa I, CrystEngComm, 15, 1199, 2013
  47. Kim KJ, Mersmann A, Chem. Eng. Sci., 56(7), 2315, 2001
  48. Ulrich J, Strege C, J. Cryst. Growth, 237, 2130, 2002
  49. Qi S, Avalle P, Saklatvala R, Craig DQ, Eur. J. Pharm. Biopharm., 69, 364, 2008