An efficient numerical technique for solving one-dimensional batch crystallization models with size-dependent growth rates

Chemical Engineering Science

Volumn 64, Issue 16, 2009, Pages 3659-3667

  Qamar, Shamsul ^a,b   Mukhtar, Safyan ^b   Seidel Morgenstern, Andreas ^a   Elsner, Martin Peter ^a  

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

^b COMSATS Institute of Information Technology ^*  (Pakistan)

Author keywords

Crystallization processes; Duhamel's principle; Gaussian quadrature; High resolution finite volume schemes; Method of characteristics; Population balance models

Indexed keywords

CRYSTALLIZATION PROCESSES; DUHAMEL'S PRINCIPLE; GAUSSIAN QUADRATURE; HIGH RESOLUTION FINITE VOLUME SCHEMES; METHOD OF CHARACTERISTICS; POPULATION BALANCE MODELS;

CRYSTALLIZATION; FLUID STRUCTURE INTERACTION; FOURIER ANALYSIS; NUCLEATION; ONE DIMENSIONAL; STAINLESS STEEL; TIME DOMAIN ANALYSIS;

ORDINARY DIFFERENTIAL EQUATIONS;

EID: 67649784533     PISSN: 00092509     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ces.2009.05.006     Document Type: Article

References (32)

1. Abegg C.F., Stevens J.D., and Larson M.A. Crystal size distributions in continuous crystallizers when growth rate is size dependent. A.I.Ch.E. J. 14 (1968) 118-122
2. Barrett J.C., and Jheeta J.S. Improving the accuracy of the moments method for solving the aerosol general dynamic equation. J. Aerosol Sci. 27 (1996) 1135-1142
3. Bürger R., Karlsen K.H., and Towers J.D. Closed-form and finite difference solutions to a population balance model of grinding mills. J. Eng. Math. 51 (2005) 165-195
4. Chiu T., and Christofides P.D. Nonlinear control of particulate processes. A.I.Ch.E. J. 45 (1999) 1279-1297
5. Gunawan R., Fusman I., and Braatz R.D. High resolution algorithms for multidimensional population balance equations. A.I.Ch.E. J. 50 (2004) 2738-2749
6. Hounslow M.J., Ryall R.L., and Marshall V.R. A discretized population balance for nucleation, growth, and aggregation. A.I.Ch.E. J. 34 (1988) 1821-1832
7. Hounslow M.J., and Wynn E.J.W. Short-cut models for particulate processes. Comput. Chem. Eng. 17 (1993) 505-516
8. Hulburt H.M., and Katz S. Some problems in particle technology. Chem. Eng. Sci. 19 (1964) 555-574
9. Koren B. A robust upwind discretization method for advection, diffusion and source terms. In: Vreugdenhil C.B., and Koren B. (Eds). Numerical Methods for Advection-Diffusion Problems, Notes on Numerical Fluid Mechanics vol. 45 (1993), Vieweg Verlag, Braunschweig 117-138
10. Kumar J., Peglow M., Warnecke G., Heinrich S., and Mörl L. A discretized model for tracer population balance equation: improved accuracy and convergence. Comput. Chem. Eng. 30 (2006) 1278-1292
11. Kumar S., and Ramkrishna D. On the solution of population balance equations by discretization-I. A fixed Pivot technique. Chem. Eng. Sci. 51 (1996) 1311-1332
12. Kumar S., and Ramkrishna D. On the solution of population balance equations by discretization-III. Nucleation, growth and aggregation of particles. Chem. Eng. Sci. 52 (1997) 4659-4679
13. 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. Chem. Eng. Sci. 57 (2002) 3715-3732
14. Ma D.L., Tafti D.K., and Braatz R.D. High-resolution simulation of multidimensional crystal growth. Ind. Eng. Chem. Res. 41 (2002) 6217-6223
15. Madras G., and McCoy B.J. Reversible crystal growth-dissolution and aggregation breakage: numerical and moment solutions for population balance equations. Powder Technol. 143-144 (2004) 297-307
16. Marchisio D.L., Vigil R.D., and Fox R.O. Quadrature method of moments for aggregation-breakage processes. J. Colloid Interface Sci. 258 (2003) 322-334
17. McCoy B.J. A population balance framework for nucleation, growth, and aggregation. Chem. Eng. Sci. 57 (2002) 2279-2285
18. McGraw R. Description of aerosol dynamics by the quadrature method of moments. Aerosol Sci. Technol. 27 (1997) 255-265
19. Mcowen R.C. Partial Differential Equations: Methods and Applications. second ed (2003), Prentice-Hall, Englewood Cliffs, NJ
20. Miller S.M., and Rawlings J.B. Model identification and control strategies for batch cooling crystallizers. A.I.Ch.E. J. 40 (1994) 1312-1327
21. Motz S., Mitrović A., and Gilles E.D. Comparison of numerical methods for the simulation of dispersed phase systems. Chem. Eng. Sci. 57 (2002) 4329-4344
22. Press W.H., Teukolsky S.A., Vetterling W.T., and Flannery B.P. Numerical Recipes: The Art of Scientific Computing. third ed (2007), Cambridge University Press, Cambridge
23. 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. Comput. Chem. Eng. 30 (2006) 1119-1131
24. Qamar S., and Warnecke G. Numerical solution of population balance equations for nucleation growth and aggregation processes. Comput. Chem. Eng. 31 (2007) 1576-1589
25. Qamar S., Warnecke, Elsner M.P., and Seidel-Morgenstern A. A Laplace transformation based technique for reconstructing crystal size distribution regarding size-independent growth. Chem. Eng. Sci. 63 (2008) 2233-2240
26. Ramkrishna D. Population Balances: Theory and Applications to Particulate Systems in Engineering (2000), Academic Press, New York
27. Randolph A.D., and Larson M.A. Theory of Particulate Processes. second ed (1988), Academic Press, New York
28. Rawlings J.B., Witkowski W.R., and Eaton J.W. Modelling and control of crystallizers. Powder Technol. 69 (1992) 3-9
29. Rawlings J.B., Miller S.M., and Witkowski W.R. Model identification and control of solution crystallization processes: a review. Ind. Eng. Chem. Res. 32 (1993) 1275-1296
30. Smith M., and Matsoukas T. Constant-number Monte Carlo simulation of population balances. Chem. Eng. Sci. 53 (1998) 1777-1786
31. Tandon P., and Rosner D.E. Monte Carlo simulation of particle aggregation and simultaneous restructuring. Colloid Interface Sci. 213 (1999) 273-286
32. Vollmer, U., 2005. Control of crystallization based on population balanced. Ph.D. Thesis, Faculty of Electrical Engineering and Information Technology, Otto-von-Guericke University Magdeburg, Germany.