Crystal growth rate dispersion modeling using morphological population balance

AIChE Journal

Volumn 54, Issue 9, 2008, Pages 2321-2334

  Ma, Cai Y ^a   Wang, Xue Z ^a  

^a UNIVERSITY OF LEEDS   (United Kingdom)

Author keywords

Crystal growth; Growth rate dispersion; Morphological population balance; Morphology; Potash alum (KAl(SO4)2 12H 2O); Shape

Indexed keywords

CELL GROWTH; CRYSTAL GROWTH; CRYSTALLIZATION; CRYSTALLOGRAPHY; CRYSTALS; DISPERSION (WAVES); ECOLOGY; GRAIN BOUNDARIES; GRAIN SIZE AND SHAPE; MODEL STRUCTURES; POTASH;

CHEMICAL-; CONTROLLED PROCESS; CRYSTAL FACES; CRYSTAL GROWTH RATES; CRYSTAL SIZE DISTRIBUTION; CRYSTAL SIZES; CRYSTAL SURFACES; CRYSTAL UNIT CELL; DYNAMIC EVOLUTION; EXPERIMENTAL STUDIES; FACE DIRECTION; GROWTH RATE DISPERSION; GROWTH RATES; MOLECULAR ARRANGEMENTS; MORPHOLOGICAL POPULATION BALANCE; MORPHOLOGY; POPULATION BALANCE MODEL; POPULATION BALANCING; POTASH ALUM; RELATIVE SUPER-SATURATION; SHAPE; SHAPE EVOLUTION; SOLUTION TEMPERATURES;

POWDERS;

EID: 52649094984     PISSN: 00011541     EISSN: 15475905     Source Type: Journal    
DOI: 10.1002/aic.11549     Document Type: Article

References (52)

1. Klapper H, Becker RA, Schmiemann D, Faber A. Growth-sector boundaries and growth-rate dispersion in potassium alum crystals. Cryst. Res. Technol. 2002;37:747-757.
2. Ristic RI, Shekunov B, Sherwood JN, Long and short period growth rate variations in potash alum crystals. J. Cryst. Growth 1996;160: 330-336.
3. van der Heijden AEDM, van der Eerden JP. Growth rate dispersion: the role of lattice strain. J. Cryst. Growth 1992;118:14-26.
4. Garside J, Phillips VR, Shah MB. Size-dependent crystal-growth. Ind. Eng. Chem. Fundam. 1976;15:230-233.
5. Lacmann R, Herden A, Mayer C. Kinetics of nucleation and crystal growth. Chem. Eng. Technol. 1999;22:279-289.
6. Matsuoka M, Abe Y, Uchida H, Takiyama H. Mechanism of growth rate enhancement by micro-crystals for the potash alum-water system. Chem. Eng. Sci. 2001;56:2325-2334.
7. Mullin JW, Garside J. Crystallization of aluminium potassium sulphate - a study in assessment of crystallizer design data. I. Single crystal growth rates. Trans. Inst. Chem. Eng. Chem. Eng. 1967;45:T285-T290.
8. Ristic RI, Sherwood JN, Shripathi T. Strain variation in the (100) growth sectors of potash alum single-crystals and its relationship to growth-rate dispersion. J. Cryst. Growth 1990;102:245-248.
9. Briesen H. Simulation of crystal size and shape by means of a reduced two-dimensional population balance model. Chem. Eng. Sci. 2006;61:104-112.
10. Ma CY, Wang XZ, Roberts KJ. Multi-dimensional population balance modelling of the growth of rod-like L-glutamic acid crystals using growth rates estimated from in-process imaging. Adv. Powder Technol. 2007;18:707-723.
11. Ma DL, Tafti DK, Braatz RD. High-resolution simulation of multidimensional crystal growth. Ind. Eng. Chem. Res. 2002;41:6217-6223.
12. Oullion M, Puel F, Fevotte G, Righini S, Carvin P. Industrial batch crystallization of a plate-like organic product. In situ monitoring and 2D-CSD modelling. II. Kinetic modelling and identification. Chem. Eng. Sci. 2007:62:833-845.
13. Puel F, Fevotte G, Klein JP. Simulation and analysis of industrial crystallization processes through multidimensional population balance equations. I. A resolution algorithm based on the method of classes. Chem. Eng. Sci. 2003;58:3715-3727.
14. Puel F, Fevotte G, Klein JP. Simulation and analysis of industrial crystallization processes through multidimensional population balance equations. II. A study of semi-batch crystallization. Chem. Eng. Sci. 2003;58:3729-3740.
15. Zhang YC, Doherty MF. Simultaneous prediction of crystal shape and size for solution crystallization. AIChE J. 2004;50:2101-2112.
16. Gadewar SB, Doherty MF. A dynamic model for evolution of crystal shape. J. Cryst. Growth 2004;267:239-250.
17. Zhang YC, Sizemore JP, Doherty MF. Shape evolution of 3-dimensional faceted crystals. AIChE J. 2006;52:1906-1915.
18. Snyder RC, Doherty MF. Faceted crystal shape evolution during dissolution or growth. AIChE J. 2007;53:1337-1348.
19. Snyder RC, Studener S, Doherty MF. Manipulation of crystal shape by cycles of growth and dissolution. AIChE J. 2007;53:1510- 1517.
20. Ma CY, Wang XZ, Roberts KJ. Morphological population balance for modelling crystal growth in individual face directions. AIChE J. 2008;54:209-222.
21. Amara N, Ratsimba B, Wilhelm A, Delmas H. Growth rate of pot-*ash alum crystals: comparison of silent and ultrasonic conditions. Ultrason. Sonochem. 2004;11:17-21.
22. Bravais MA. Études Cristallographiques [Crystallographic studies]. Paris: Gauthier-Villars; 1866.
23. Donnay J, Harker D. A new law of crystal morphology extending the Law of Bravais. Am. Mineral. 1937;22:446-467.
24. Friedel M. Etudes sur la loi de bravais. Bull. Soc. Franc Miner. 1907;9:326.
25. Nollet S, Hilgers C, Urai JL. Experimental study of polycrystal growth from an advecting supersaturated fluid in a model fracture. Geofluids 2006;6:185-200.
26. Brunsteiner M, Price SL. Surface structure of a complex inorganic crystal in aqueous solution from classical molecular simulation. J. Phys. Chem. B 2004, 108:12537-12546.
27. Read WT, Shockley W. Dislocation models of crystal grain bounda ries. Phys. Rev. 1950;78:275-289.
28. Ristic RI, Shekunov BY, Sherwood JN. The influence of synchrotron radiation-induced strain on the growth and dissolution of brittle and ductile materials. J. Cryst. Growth 1997;179:205-212.
29. Sherwood JN, Ristic RI. The influence of mechanical stress on the growth and dissolution of crystals. Chem. Eng. Sci. 2001;56:2267-2280.
30. Jones CM, Larson MA. Using dislocations and integral strain to model the growth rates of secondary nuclei. Chem. Eng. Sci. 2000;55: 2563-2570.
31. Burton WK, Cabrera N, Frank FC. The growth of crystals and the equilibrium structure of their surfaces. Philos. Trans. R. Soc. Lond. 1951;243:299-358.
32. Garside J, Davey RJ. Secondary contact nucleation-kinetics, growth and scale-up. Chem. Eng. Commun. 1980;4:393-424.
33. Gerstlauer A, Mitrovic A, Motz S, Gilles ED. A population model for crystallization processes using two independent particle properties. Chem. Eng. Sci. 2001;56:2553-2565.
34. Matsuoka M, Kamada T, Takiyama H. Growth rate enhancement of potash alum crystals by microcrystals. J. Cryst. Growth 1996;158: 322-327.
35. Yokota M, Sato A, Kubota N. A simple method for evaluating kinetic parameters in non-isothermal batch crystallization. Chem. Eng. Sci. 2000;55:717-722.
36. David R, Marchal P, Marcant B. Modeling of agglomeration in industrial crystallization from solution. Chem. Eng. Technol. 1995;18:302-309.
37. Gerstlauer A, Gahn C, Zhou H, Rauls M, Schreiber M. Application of population balances in the chemical industry - current stutus and future needs. Chem. Eng. Sci. 2006;61:205-217.
38. Gunawan R, Fusman I, Braatz RD. High resolution algorithms for multidimensional population balance equations. AIChE J. 2004;50: 2738-2749.
39. Henson MA. Cell ensemble modeling of metabolic oscillations in continuous yeast cultures. Comput. Chem. Eng. 2005;29:645-661.
40. Kumar S, Ramkrishna D. On the solution of population balance equations by discretization. III. Nucleation, growth and aggregation of particles. Chem. Eng. Sci. 1997;52:4659-4679.
41. Pinto MA, Immanuel CD, Doyle FJ. A feasible solution technique for higher-dimensional population balance models. Comput. Chem. Eng. 2007;31:1242-1256.
42. Sotowa KI, Naito K, Kano M, Hasebe S, Hashimoto I. Application of the method of characteristics to crystallizer simulation and comparison with finite difference for controller performance evaluation. J. Process Control 2000;10:203-208.
43. Sun NF, Immanuel CD. Efficient solution of population balance models employing a hierarchical solution strategy based on a multi-level discretization. Trans. Inst. Meas. Control 2005;27:347-366.
44. Shampine LF, Watts HA. Subroutine RKF45. In: Forsythe GE, Malcolm MA, Moler CB, editors. Computer Methods for Mathematical Computations. Englewood Cliffs. N.J.: Prentice-Hall, 1977:135-147.
45. Calderon De Anda J, Wang XZ, Lai X, Roberts KJ. Classifying organic crystals via in-process image analysis and the use of monitoring charts to follow polymorphic and morphological changes. J. Process Control 2005;15:785-797.
46. Calderon de Anda J, Wang XZ, Lai X, Roberts KJ, Jennings KH, Wilkinson MJ, Watson D, Roberts D. Real-time product morphology monitoring in crystallization using imaging technique. AIChE J. 2005;51:1406-1414.
47. Wang XZ, Calderon De Anda J, Roberts KJ. Real-time measurement of the growth rates of individual crystal facets using imaging and image analysis: a feasibility study on needle-shaped crystals of I-glutamic acid. Chem. Eng. Res. Des. 2007;85A:921-927.
48. Wang XZ. Calderon Dc Anda J. Roberts KJ, Li RF. Thomson GB, White G. Advances in on-line monitoring and control of the morphological and polymorphic forms of organic crystals grown from solution (paper downloadable from www.kona.org.jp/html/tibout/index2005.html). KONA. 2005;23:69-85.
49. Wang XZ, Roberts KJ, Ma CY. Crystal growth measurement using 2D and 3D imaging and the perspectives for shape control. Chem. Eng. Sci. 2008:63:1171-1184.
50. Linkam Scientific Instruments. Available at: http://www.linkam.co.uk/.
51. IO Industries. Available at: http://www.ioindustries.com/vs.htm.
52. Yau ST, Vekilov PG. Quasi-planar nucleus structure in apoferritin crystallization. Nature. 2000;406:494-497.