Numerical solutions of population balance models in preferential crystallization

Chemical Engineering Science

Volumn 63, Issue 5, 2008, Pages 1342-1352

  Qamar, S ^a   Ashfaq, A ^a   Angelov, I ^b   Elsner, M P ^b   Warnecke, G ^a   Seidel Morgenstern, A ^a,b  

^a OTTO VON GUERICKE UNIVERSITY   (Germany)

^b MAX PLANCK INSTITUTE FOR DYNAMICS OF COMPLEX TECHNICAL SYSTEMS   (Germany)

Author keywords

Fines dissolution; High resolution schemes; Method of characteristics; Nucleation and growth rates; Population balance models; Preferential crystallization of enantiomers

Indexed keywords

DISSOLUTION; ENANTIOMERS; FINITE VOLUME METHOD; NUCLEATION;

FINES DISSOLUTION; GROWTH RATES; HIGH RESOLUTION SCHEMES; POPULATION BALANCE MODELS;

CRYSTALLIZATION;

CRYSTALLIZATION; DISSOLUTION; ENANTIOMERS; FINITE VOLUME METHOD; NUCLEATION;

EID: 38149125486     PISSN: 00092509     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ces.2007.07.045     Document Type: Article

References (19)

1. Abramowitz M., and Stegun I.A. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (1972), Dover, New York p. 11
2. Angelov, I., Raisch, J., Elsner, M.P., Seidel-Morgenstern, A., 2007. Optimal operation of enantioseparation by batch-wise preferential crystallization Chemical Engineering Science, in press, doi:10.1016/j.ces.2007.07.023.
3. Elsner M.P., Fernández Menéndez D., Alonso Muslera E., and Seidel-Morgenstern A. Experimental study and simplified mathematical description of preferential crystallization. Chirality 17 (2005) 183-195
4. Gunawan R., Fusman I., and Braatz R.D. High resolution algorithms for multidimensional population balance equations. A.I.Ch.E. Journal 50 (2004) 2738-2749
5. Hounslow M.J. A discretized population balance for continuous systems at steady-state. A.I.Ch.E. Journal 36 (1990) 106-116
6. Koren, B., 1993. A robust upwind discretization method for advection, diffusion and source terms. In: Vreugdenhill, C.B., Koren, B., (Eds.), Numerical Methods for Advection-Diffusion Problems, Notes on Numerical Fluid Mechanics, vol. 45. Vieweg Verlag, Braunschweig, 1993, pp. 117-138 (Chapter 5).
7. Kumar S., and Ramkrishna D. On the solution of population balance equations by discretization-III. Nucleation, growth and aggregation of particles. Chemical Engineering Science 52 (1997) 4659-4679
8. van Leer, B., 1985. Upwind-difference methods for aerodynamic problems governed by the Euler equations, Lectures in Applied Mathematics, vol. 22 (Part 2). American Mathematical Society, Providence, RI, 1985, pp. 327-336.
9. LeVeque R.J. Finite Volume Methods for Hyperbolic Problems (2002), Cambridge University Press, New York
10. Lim Y.I., Lann J.-M.L., Meyer X.M., Joulia X., Lee G., and Yoon E.S. On the solution of population balance equation (PBE) with accurate front tracking method in practical crystallization processes. Chemical Engineering Science 57 (2002) 3715-3732
11. Ma A., Tafti D.K., and Braatz R.D. High resolution simulation of multidimensional crystal growth. Industrial and Engineering Chemistry Research 41 (2002) 6217-6223
12. Ma A., Tafti D.K., and Braatz R.D. Optimal control and simulation of multidimensional crystallization processes. Computers & Chemical Engineering 26 (2002) 1103-1116
13. Qamar S., Elsner M.P., Angelov I., Warnecke G., and Seidel-Morgenstern A. A comparative study of high resolution schemes for solving population balances in crystallization. Computers & Chemical Engineering 30 (2006) 1119-1131
14. Qamar, S., Ashfaq, A., Elsner, M.P., Angelov, I., Warnecke, G., Seidel-Morgenstern, A., 2007. Adaptive high resolution schemes for multidimensional population balances in crystallization processes. Computers & Chemical Engineering 31, 1296-1311.
15. Ramkrishna D. Statistical models of cell populations. Advances in Biochemical Engineering 11 (1979) 1-47
16. Ramkrishna D. The status of population balances. Reviews Chemical Engineering 3 1 (1985) 49-95
17. Ramkrishna D. Population Balances: Theory and Applications to Particulate Systems in Engineering (2000), Academic Press, San Diego, CA
18. Shi D., Mhaskar P., El-Farra N.H., and Christofides P.D. Predictive control of crystal size distribution in protein crystallization. Nanotechnology 16 (2005) S562-S574
19. Shi D., El-Farra N.H., Li M., Mhaskar P., and Christofides P.D. Predictive control of particle size distribution in particulate processes. Chemical Engineering Science 61 (2006) 268-281