Comparison of the accuracy and performance of quadrature-based methods for population balance problems with simultaneous breakage and aggregation

Computers and Chemical Engineering

Volumn 34, Issue 3, 2010, Pages 286-297

  Silva, L F L R ^a   Rodrigues, R C ^a   Mitre, J F ^a   Lage, P L C ^a  

^a FEDERAL UNIVERSITY OF RIO DE JANEIRO   (Brazil)

Author keywords

Aggregation; Breakage; DQMOM; Population balance; PPDC; QMOM

Indexed keywords

ANALYTICAL SOLUTIONS; CFD CODES; CLASSICAL METHODS; COMPUTATIONAL COSTS; EFFICIENT METHOD; NUMERICAL TECHNIQUES; PARTICLE BREAKAGE; POLYDISPERSES; POPULATION BALANCE EQUATION; POPULATION BALANCES; TEST CASE;

MULTIPHASE FLOW; POLYDISPERSITY;

AGGLOMERATION;

EID: 75849149996     PISSN: 00981354     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.compchemeng.2009.11.005     Document Type: Article

References (31)

1. Bove S., Solberg T., and Hjertager B.H. A novel algorithm for solving population balance equations: The parallel parent and daughter classes. Derivation, analysis and testing. Chemical Engineering Science 60 (2005) 1449
2. Campos F., and Lage P. A numerical method for solving the transient multidimensional population balance equation using an Euler-Lagrange formulation. Chemical Engineering Science 58 (2003) 2725
3. Dorao C.A., and Jakobsen H.A. A least squares method for the solution of population balance problems. Computers and Chemical Engineering 30 (2006) 535-547
4. Dorao C.A., and Jakobsen H.A. Time-space-property least squares spectral method for population balance problems. Chemical Engineering Science 62 (2007) 1323-1333
5. Dorao C.A., and Jakobsen H.A. hp-adaptive least squares spectral element method for population balance equations. Applied Numerical Mathematics 58 (2008) 563-576
6. Friedlander S. Smoke, dust and haze (1977), John Wiley & Sons Inc, New York
7. Gautschi W. Algorithm 726: ORTHPOL - A package of routines for generating orthogonal polynomials and gauss-type quadrature rules. ACM Transactions on Mathematical Software 20 1 (1994) 21-62
8. Gelbard F., and Seinfield J. Numerical solution of the dynamic equation for particulate systems. Journal of Computational Physics 28 (1978) 357
9. Gordon R. Error bounds in equilibrium statistical mechanics. Journal of Mathematical Physics 9 5 (1968) 655
10. Hounslow M., Ryall R., and Marshall V. A discrete population balance for nucleation, growth and aggregation. AIChE Journal 34 11 (1988) 1821
11. Hulburt H., and Katz S. Some problems in particle technology. A statistical mechanical formulation. Chemical Engineering Science 19 (1964) 555
12. Kumar S., and Ramkrishna D. On the solution of population balance equations by discretization - I. A fixed pivot technique. Chemical Engineering Science 51 8 (1996) 1311
13. Kumar S., and Ramkrishna D. On the solution of population balance equations by discretization - II. A moving pivot technique. Chemical Engineering Science 51 8 (1996) 1333
14. Lage P. Comments on the "An analytical solution to the population balance equation with coalescence and breakage - The special case with constant number of particles" by D.P. Patil and J.R.G. Andrews [Chemical Engineering Science 53(3) 599-601]. Chemical Engineering Science 57 (2002) 4253
15. Lage P. The quadrature method of moments for continuous thermodynamics. Computers & Chemical Engineering 31 7 (2007) 782-799
16. Lanczos C. Applied analysis (1988), Dover, New York
17. Marchisio D., and Fox R. Solution of population balance equations using the direct method of moments. Journal of Aerosol Science 36 (2005) 43
18. McCoy B., and Madras G. Analytical solution for a population balance equation with aggregation and fragmentation. Chemical Engineering Science 58 (2003) 3049
19. McGraw R. Description of aerosol dynamics by the quadrature method of moments. Aerosol Science and Technology 27 (1997) 255
20. McGraw R., and Saunders J. A condensation feedback mechanism for oscillatory nucleation and growth. Aerosol Science and Technology 3 (1984) 367
21. Patil D., and Andrews J. An analytical solution to the population balance equation with coalescence and breakage - The special case with constant number of particles. Chemical Engineering Science 53 3 (1998) 599
22. Petzold, L. (1982). A description of DASSL: A differential/algebraic system solver. Tech. rep., Sandia National Laboratories.
23. Pinto, J., & Lage, P. (2001). Métodos Numéricos em Problemas de Engenharia Química. E-papers, Rio de Janeiro.
24. Press W., Teukolsky S., and Vetterling W.F.B. Numerical recipes: The art of scientific computing, FORTRAN 77. 2nd ed. (1992), Cambridge University Press, Cambridge
25. Ramkrishna D. Population balances - Theory and applications to particulate systems in engineering (2000), Academic Press, San Diego
26. Ramkrishna D., and Borwanker J. A puristic analysis of population balance - I. Chemical Engineering Science 28 (1973) 1423
27. Ramkrishna D., and Borwanker J. A puristic analysis of population balance - II. Chemical Engineering Science 29 (1974) 1711
28. Smith B.T., Boyle J.M., Dongarra J.J., Garbow B.S., Ikebe Y., Klema V.C., et al. Matrix Eigen-system routines - EISPACK guide (1976), Springer-Verlag
29. Vanni M. Discretization procedure for the breakage equation. AIChE Journal 45 4 (1999) 916
30. Wright Jr. D.L. Numerical advection of moments of the particle size distribution in Eulerian models. Journal of Aerosol Science 38 (2007) 352-369
31. Zhu Z.J., Dorao C.A., Lucas D., and Jakobsen H.A. On the coupled solution of a combined population balance model using the least-squares spectral element method. Industrial & Engineering Chemistry Research 48 17 (2009) 7994-8006