Computationally efficient solution of population balance models incorporating nucleation, growth and coagulation: Application to emulsion polymerization

Chemical Engineering Science

Volumn 58, Issue 16, 2003, Pages 3681-3698

  Immanuel, Charles David ^a   Doyle III , Francis Joseph ^a  

^a University of Delaware   (United States)

Author keywords

Emulsion polymerization; Model reduction; Numerical solution; Particle size distribution; Population balance model

Indexed keywords

AGGLOMERATION; COAGULATION; COMPUTATIONAL METHODS; EMULSION POLYMERIZATION; GROWTH (MATERIALS); MATHEMATICAL MODELS; NUCLEATION; STIFFNESS;

SEMI-ANALYTICAL SOLUTIONS;

CHEMICAL ENGINEERING;

MATHEMATICAL ANALYSIS;

EID: 0041825843     PISSN: 00092509     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0009-2509(03)00216-1     Document Type: Article

References (54)

1. Adrover A. Continillo G. Crescitelli S. Giona M. Russo L. Construction of approximate inertial manifold by decimation of collocation equations of distributed parameter systems Computers and Chemical Engineering 26 2002 113-123
2. Araujo P.H.H. de la Cal J.C. Asua J.M. Pinto J.C. Modeling particle size distribution (PSD) in emulsion copolymerization reactions in a continuous loop reactor Macromolecular Theory Simulations 10 2001 769-779
3. Bandyopadhyaya R. Kumar R. Gandhi K.S. Ramkrishna D. Modeling of precipitation in reverse micellar systems Langmuir 13 1997 3610-3620
4. Behnken D.W. Horowitz J. Katz S. Particle growth processes Industrial and Engineering Chemistry Fundamentals 2 3 1963 212-216
5. Braatz, R. D., - Hasebe, S. (2001). Particle size and shape control in crystallization processes. In J. B. Rawlings, B. A. Ogunnaike, - J. W. Eaton (Eds.), AIChE symposium series: Chemical process control-VI (pp. 307-327). Vol. 98 of 326. New York: AIChE.
6. Chiu T. Christofides P.D. Nonlinear control of particulate processes A.I.Ch.E. Journal 45 6 1999 1279-1297
7. Christofides, P. D. (2002). Control of Nonlinear distributed Process Systems: An Overview and New Research Directions. Proceedings of 6th IFAC Symposium on Dynamics and Control of Process Systems, 341-346, Cheiv Island, Korea, 2001.
8. Coen E.M. Gilbert R.G. Morrison B.R. Leube H. Peach S. Modeling particle size distributions and secondary particle formation in emulsion polymerisation Polymer 39 26 1998 7099-7112
9. Crowley, T., Meadows, E., - Doyle III, F. (1999). Numerical issues in solving population balance equations for particle size distribution control in emulsion polymerization. Proceedings of the 1999 American control conference.
10. Crowley T. Meadows E. Kostoulas E. Doyle III F. Control of particle size distribution described by a population balance model of semibatch emulsion polymerization Journal of Process Control 10 2000 419-432
11. Daoutidis, P., - Henson, M. A. (2001). Dynamics and control of cell populations in continuous biorroeact. In J. B. Rawlings, B. A. Ogunnaike, - J. W. Eaton (Eds.), AIChE symposium series: Chemical process control-VI (pp. 274-289). Vol. 98 of 326. New York: AIChE.
12. Doyle III, F. J., Soroush, M., - Cordeiro, C. (2001). Control of product quality in polymerization processes. In J. B. Rawlings, B. A. Ogunnaike, - J. W. Eaton (Eds.), AIChE symposium series: Chemical process control-VI (pp. 290-306). Vol. 98 of 326. New York: AIChE.
13. Falk L. Schaer E. A PDF modeling of precipitation reactors Chemical Engineering Science 56 2001 2445-2457
14. Fredrickson A.G. Tsuchiya H.M. Continuous propagation of microorganisms A.I.Ch.E. Journal 9 4 1963 459-468
15. Gelberd F. Seinfeld J.H. Numerical solution of the dynamic equation for particulate systems Journal of Computational Physics 28 1978 357-375
16. Gerstlauer A. Mitrovic A. Motz S. Gilles E.-D. A population model for crystallization processes using two independent particle properties Chemical Engineering Science 56 2001 2553-2565
17. Godin F.B. Cooper D.G. Rey A.D. Numerical methods for a population- balance model of a periodic fermentation process A.I.Ch.E. Journal 45 6 1999 1359-1364
18. Henson M.A. Muller D. Reuss M. Cell population modelling of yeast glycolytic oscillations Biochemical Journal 368 2002 433-446
19. Hollander E.D. Derksen J.J. Bruinsma O.S.L. van den Akker H.E.A. van Rosmalen G.M. A numerical study on the coupling of hydrodynamics and orthokinetic agglomeration Chemical Engineering Science 56 2001 2531-2541
20. Hounslow M.J. Ryall R.L. Marshall V.R. A discretized population balance for nucleation, growth and aggregation A.I.Ch.E. Journal 34 1988 1821-1832
21. Hulburt H. Katz S. Some problems in particle technology: A statistical mechanical formulation Chemical Engineering Science 19 1964 555-574
22. Immanuel C.D. Cordeiro C.F. Sundaram S.S. Meadows E.S. Crowley T.J. Doyle III F.J. Modeling of particle size distribution in emulsion co-polymerization: Comparison with experimental data and parametric sensitivity studies Computers and Chemical Engineering 26 7-8 2002 1133-1152
23. Immanuel, C. D., Cordeiro, C. F., Sundaram, S. S., - Doyle III, F. J. (2002b). Population-balance Modeling of Particle Size Distribution in the Emulsion Co-Polymerization of Vinyl Acetate and Butyl Acrylate under Steric Stabilization with Non-Ionic Surfactants, and Experimental Validation. Journal of Polymer Science Part A-Polymer Chemistry, 49, 1392-1404, 2003.
24. Immanuel, C. D., Cordeiro, C. F., Sundaram, S. S., - Doyle III, F. J. (2003). Population balance PSD model for emulsion polymerization with steric stabilizers. A.I.Ch.E. Journal, in press.
25. Immanuel, C. D., - Doyle III, F. J. (2003). A hierarchical strategy for control of particle size distribution using multi-objective optimization. A.I.Ch.E. Journal, in press.
26. Kumar S. Ramkrishna D. On the solution of population balance equations by discretization-II. A moving pivot technique Chemical Engineering Science 51 8 1996 1333-1342
27. Kumar S. Ramkrishna D. On the solution of population balance equations by discretization-I. A fixed pivot technique Chemical Engineering Science 51 8 1996 1311-1332
28. Liu Y. Cameron I.T. A new wavelet-based method for the solution of the population balance equation Chemical Engineering Science 56 2001 5283-5294
29. Ma D.L. Tafti D.K. Braatz R.D. High resolution simulation of multi-dimensional crystallization Industrial and Engineering Chemistry Research 41 2002 6217-6223
30. Maas U. Pope S.B. Simplifying chemical kinetics: Intrinsic low- dimensional manifolds in composition space Combustion and Flame 88 1992 239-264
31. Mahoney, A. W. (2001). Inverse problem modeling of particulate systems Ph.D. thesis, Purdue University, August.
32. Mahoney A.W. Ramkrishna D. Efficient solution of population balance equations with discontinuities by finite elements Chemical Engineering Science 57 2002 1107-1119
33. Marchisio D.L. Pikturna J. Wang L. Vigil R.D. Fox R.O. Quadratic method of moments for population balances in CFD applications: Comparison with experimental data Chemistry and Engineering Transactions 1 2002 305-310
34. Meadows E.S. Crowley T.J. Immanuel C.D. Doyle III F.J. Non-isothermal modeling and sensitivity studies for batch and semi-batch emulsion polymerization of styrene Industrial Engineering Chemistry Research 42 3 2003 555-567
35. Melis S. Kemmere M. Meuldijk J. Storti G. Morbidelli M. A model for the coagulation of polyvinyl acetate particles in emulsion Chemical Engineering Science 55 2000 3101-3111
36. Petzold L.R. Observations on an adaptive moving grid method for one-dimensional systems of partial differential equations Applied Numerical Mathematics 3 1987 347-360
37. Pope S.B. Computationally efficient implementation of combustion chemistry using in situ adaptive tabulation Combustion Theory and Modelling 1 1997 41-63
38. Prasetya A. Liu L. Litster J. Watanabe F. Mitsutani K. Ko G.H. Dynamic model development for residence time distribution control in high-impact polypropylene copolymer process Chemical Engineering Science 54 1999 3263-3271
39. Press W.H. Teukolsky S.A. Vetterling W.T. Flannery B.P. Numerical recipes in fortran 77: The art of scientific computing 2nd ed. 1992 Cambridge University Press Cambridge
40. Ramkrishna D. The status of population balances Reviews in Chemical Engineering 3 1 1985 49-95
41. Ramkrishna D. Population balances 2000 Academic Press San Diego
42. Ramkrishna D. Mahoney A.W. Population balance modeling. Promise for the future Chemical Engineering Science 57 2002 595-606
43. Randolph, A. D. (1964). A population balance for countable entities. Canadian Journal of Chemical Engineering, 42, December, 280-281.
44. Randolph A.D. Larson M.A. Transient and steady state size distributions in continuous mixed suspension crystallizers A.I.Ch.E. Journal 8 5 1962 639-645
45. Randolph A.D. Larson M.A. Theory of particulate processes 2nd ed. 1988 Academic Press San Diego, CA
46. Rawlings J.B. Miller S.M. Witkowski W.R. Model identification and control of solution crystallization processes: A review Industrial Engineering Chemistry Research 32 1993 1275-1296
47. Rawlings J. Ray W. The modeling of batch and continuous emulsion polymerization reactors. Part I: Model formulation and sensitivity to parameters Polymer Engineering and Science 28 1988 237-256
48. Rhodes, C., - Morari, M. (1997). A Computational algorithm for nonlinear model reduction. Presented at the AIChE Annual Meeting.
49. Saldivar, E. (1996). Modeling and control of emulsion copolymerization reactors. Ph.D. thesis, University of Wisconsin-Madison.
50. Saldivar E. Dafniotis P. Ray W.H. Mathematical modeling of emulsion copolymerization reactors. I. Model formulation and application to reactors operating with micellar nucleation J.M.S. Reviews in Macromolecular Chemistry and Physics C38 2 1998 207-325
51. Storti G. Carra S. Morbidelli M. Vita G. Kinetics of multimonomer emulsion polymerization. The pseudo-homopolymerization approach Journal of Applied Polymer Science 37 1989 2443-2467
52. Villadsen J. Michelsen M.L. Solution of differential equation models by polynomial approximation 1978 Prentice-Hall Englewood Cliffs, New Jersey
53. Wulkow M. Gerstlauer A. Nieken U. Modeling and simulation of crystallization processes using parsival Chemical Engineering Science 56 2001 2575-2588
54. Yiannoulakis H. Yiagopoulos A. Kiparissides C. Recent developments in the particle size distribution modeling of fluidized-bed olefin polymerization reactors Chemical Engineering Science 56 2001 917-925