Model reduction for chemical kinetics: an optimization approach

The kinetics of a detailed chemically reacting system can potentially be very complex. Although the chemist may be interested in only a few species, the reaction model almost always involves a much larger number of species. Some of those species are radicals, which are very reactive species and can be important intermediaries in the reaction scheme. A large number of elementary reactions can occur among the species; some of these reactions are fast and some are slow. The aim of simplified kinetics modeling is to derive the simplest reaction system which retains the essential features of the full system. An optimization-based method for reduction of the number of species and reactions in chemical kinetics models is described. Numerical results for several reaction mechanisms illustrate the potential of this approach.

[1]  K. M. Gisvold,et al.  A Method for Nonlinear Mixed-Integer Programming and its Application to Design Problems , 1972 .

[2]  D. Allara,et al.  A computational modeling study of the low-temperature pyrolysis of n-alkanes; mechanisms of propane, n-butane, and n-pentane pyrolyses , 1975 .

[3]  M. S. Bazaraa,et al.  Nonlinear Programming , 1979 .

[4]  D. Edelson,et al.  Computer Simulation in Chemical Kinetics , 1981, Science.

[5]  George Stephanopoulos,et al.  Dynamic sensitivity analysis of chemical reaction systems: A variational method , 1982 .

[6]  Peter P. Valko,et al.  Principal component analysis of kinetic models , 1985 .

[7]  N. Peters Numerical and asymptotic analysis of systematically reduced reaction schemes for hydrocarbon flames , 1985 .

[8]  P. Gill,et al.  Model Building and Practical Aspects of Nonlinear Programming , 1985 .

[9]  Christian Seigneur,et al.  Variational sensitivity analysis of a photochemical smog mechanism , 1985 .

[10]  L. Petzold,et al.  Numerical methods and software for sensitivity analysis of differential-algebraic systems , 1986 .

[11]  R. Carr,et al.  Flash photolysis of 1,3-dichlorotetrafluoroacetone in the presence of oxygen. Kinetics and mechanism of the oxidation of the chlorodifluoromethyl radicals , 1986 .

[12]  J. Robert,et al.  CHEMKIN-II: A FORTRAN Chemical Kinetics Package for the Analysis of Gas-Phase Chemical Kinetics , 1989 .

[13]  S. H. Lam,et al.  Conventional asymptotics and computational singular perturbation for simplified kinetics modelling , 1991 .

[14]  Andreas Griewank,et al.  ADIFOR - Generating Derivative Codes form Fortran Programs , 1992, Sci. Program..

[15]  Ulrich Maas,et al.  Simplifying chemical kinetics: Intrinsic low-dimensional manifolds in composition space , 1992 .

[16]  S. H. Lam,et al.  Using CSP to Understand Complex Chemical Kinetics ∗ , 1992 .

[17]  E. Grimme An Implicitly Restarted Lanczos Method for the Model Reduction of Stable, Large-Scale Systems , 1993 .

[18]  A. Dean,et al.  Radical Chemistry in Methane Oxidative Coupling: Tracing of Ethylene Secondary Reactions with Computer Models and Isotopes , 1994 .

[19]  P. Gill,et al.  Large-scale SQP methods and their application in trajectory optimization , 1994 .

[20]  E. Grimme,et al.  Stable partial realizations via an implicitly restarted Lanczos method , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[21]  Michael Frenklach,et al.  GRI-MECH: An optimized detailed chemical reaction mechanism for methane combustion. Topical report, September 1992-August 1995 , 1995 .

[22]  Linda R. Petzold,et al.  Numerical solution of initial-value problems in differential-algebraic equations , 1996, Classics in applied mathematics.

[23]  Nancy J. Brown,et al.  Mechanism reduction via principal component analysis , 1997 .

[24]  Kihong Park,et al.  Numerical Optimal Control of Parabolic PDES Using DASOPT , 1997 .

[25]  S. H. Lam,et al.  CONVENTIONAL ASYMPTOTICS AND COMPUTATIONAL SINGULAR PERTURBATION FOR SIMPLIFIED KINETICS MODELLING , 1999 .