Model reduction for chemical kinetics: An optimization approach

AIChE Journal

Volumn 45, Issue 4, 1999, Pages 869-886

  Petzold, Linda ^a   Zhu, Wenjie ^b  

^a University of California   (United States)

^b University of Minnesota   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; CHEMICAL REACTIONS; LINEAR PROGRAMMING; MATHEMATICAL MODELS; NONLINEAR PROGRAMMING; NUMERICAL METHODS; OPTIMIZATION; RATE CONSTANTS;

SIMPLIFIED KINETICS MODELING;

REACTION KINETICS;

CHEMICAL ENGINEERING; MODEL; OPTIMIZATION;

ALGORITHM; ARTICLE; CHEMICAL REACTION; CHEMICAL REACTION KINETICS; MATHEMATICAL ANALYSIS; MATHEMATICAL MODEL;

EID: 0033119133     PISSN: 00011541     EISSN: None     Source Type: Journal    
DOI: 10.1002/aic.690450418     Document Type: Article

References (28)

1. Allara, D. L., and D. Edelson, "A Computational Modeling Study of the Low-Temperature Pyrolysis of n-Alkanes; Mechanisms of Propane, n-Butane, and n-Pentane Pyrolyses," Int. J. Chem. Kinet., 7, 479 (1975).
2. Bazaraa, M., and C. Shetty, Nonlinear Programming, Wiley, New York (1979).
3. Bischof, C., A. Carle, G. Corliss, A. Griewank, and P. Hovland, "ADIFOR - Generating Derivative Codes from Fortran Programs," Scientific Programming, 1, 11 (1992).
4. Brenan, K. E., S. L. Campbell, and L. R. Petzold, Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations, 2nd ed., SIAM, Philadelphia (1995).
5. Brown, N. J., G. Li, and M. L. Koszykowski, "Mechanism Reduction via Principal Component Analysis," Int. J. Chem. Kinet., 29, 393 (1997).
6. Carr, R. W., Jr., D. G. Peterson, and F. K. Smith, "Flash Photolysis of 1,3-Dichlorotetrafluoroacetone in the Presence of Oxygen, Kinetics and Mechanism of the Oxidation of the Chlorodifluoromethyl Radicals," J. of Physical Chemistry, 90, 697 (1986).
7. Edelson, D., "Computer Simulation in Chemical Kinetics," Science, 214, 981 (1981).
8. Frenklach, M., H. Wang, M. Goldenberg, G. P. Smith, D. M. Golden, C. T. Bowman, R. K. Hanson, W. C. Gardiner and V. Lissianski, "GRI-Mech - An Optimized Detailed Chemical Reaction Mechanism for Methane Combustion," Gas Research Institute, Chicago, Topical Report, No. GRI-95/0058 (1995).
9. Gautier, O., and R. W. Carr, Jr., "Variational Sensitivity Analysis of a Photochemical Smog Mechanism," Int. J. of Chemical Kinetics, 17, 1347 (1985).
10. Gill, P. E., W. Murray, M. A. Saunders, and M. H. Wright, "Model Building and Practical Aspects of Nonlinear Programming," Computational Mathematical Programming, Series F: Computer and Systems Science, 15 (1985).
11. Gill, P. E., W. Murray, and M. A. Saunders, "Large-Scale SQP Methods and Their Application in Trajectory Optimization," Int. Series of Numerical Mathematics, 115, 29, Birkhauser, Switzerland (1994).
12. Gisvold, K. M., and J. Moe, "A Method for Nonlinear Mixed-Integer Programming and Its Application to Design Problems," J. of Eng. for Industry: Trans. of ASME, 94, 353 (1972).
13. Grimme, E., "An Implicitly Restarted Lanczos Method for the Model Reduction of Stable Large-Scale Systems," MS Thesis, University of Illinois at Urbana-Champaign, Dept. of Electrical Engineering, Urbana-Champaign, IL (1994).
14. Grimme, E., D. Sorensen, and P. VanDooren, "Stable Partial Realizations via an Implicitly Restarted Lanczos Method," preprint (1994).
15. Kee, R. J., F. M. Rupley, and J. A. Miller, "Chemkin-II: A Fortran Chemical Kinetics Package for the Analysis of Gas Phase Chemical Kinetics," Sandia Report SAND89-8009B, UC-706, Sandia National Laboratories, Livermore, CA (1989).
16. Lam, S. H., "Using CSP to Understand Complex Chemical Kinetics," Combust. Sci. and Tech., 89, 375 (1993).
17. Lam, S. H., and D. A. Goussis, "Conventional Asymptotics and Computational Singular Perturbation for Simplified Kinetics Modelling," preprint, Mechanical and Aerospace Engineering, Princeton Univ., Princeton, NJ (1993).
18. Maas, U., and S. B. Pope, "Simplifying Chemical Kinetics: Intrinsic Low-Dimensional Manifolds in Composition Space," Combustion and Flame, 88, 239 (1992).
19. Maly, T., and L. R. Petzold, "Numerical Methods for Sensitivity Analysis of Differential-Algebraic Systems," Applied Numerical Mathematics, 20, 57 (1996).
20. Mims, C. A., R. Mauti, A. M. Dean, and K. D. Rose, "Radical Chemistry in Methane Oxidative Coupling: Tracing of Ethylene Secondary Reactions with Computer Models and Isotopes," J. Phys. Chem., 98, 13357 (1994).
21. Peters, N., "Numerical and Asymptotic Analysis of Systematically Reduced Reaction Schemes for Hydrocarbon Flames," Lecture Notes in Physics, 241, 90, Springer Verlag, Berlin (1985).
22. Peters, N., Reducing Mechanisms, Reduced Kinetic Mechanisms and Asymptotic Approximations for Methane-Air Flames, Springer-Verlag, Berlin-Heidelberg (1991).
23. Petzold, L., J. B. Rosen, P. E. Gill, L. O. Jay, and K. Park, "Numerical Optimal Control of Parabolic PDEs Using DASOPT," Large Scale Optimization with Applications, Part II: Optimal Design and Control, L. Biegler, T. Coleman, A. Conn and F. Santosa, eds., IMA Volumes in Mathematics and its Applications, Springer Verlag, New York, 93, 271 (1997).
24. Rosen, J. B., Personal communication (1995).
25. Seigneur, C., G. Stephanopoulos, and R. W. Carr, Jr., "Dynamic Sensitivity Analysis of Chemical Reaction Systems," Chem. Eng. Sci., 17, 845 (1982).
26. Vajda, S., P. Valko, and T. Turanyi, "Principal Component Analysis of Kinetic Models," Int. J. of Chemical Kinetics, 17, 55 (1985).
27. Williams, F. A., Combustion Theory, The Fundamental Theory of Chemically Reacting Systems, 2nd ed., Benjamin Cummings Publishing Co., Menlo Park, CA (1985).
28. Zhu, W., "Model Reduction for Chemical Kinetics: An Optimization Approach," PhD Thesis, Dept. of Computer Science, Univ. of Minnesota (1998).