Combustion Chemistry and Parameter Estimation

Chapter
Part of the Contributions in Mathematical and Computational Sciences book series (CMCS, volume 4)

Abstract

Combustion processes in practical systems are marked by an huge complexity stemming from their multi-dimensional character, from the interaction of physical processes (including diffusion, flow dynamics, thermodynamics and heat transfer), and from the extremely complex chemistry potentially involving up to hundreds of species and thousands of elementary reactions. The determination of accurate parameters accounting for the chemical kinetics is an essential step for predicting the behavior of practical combustion systems. This is usually done by carrying out specific experiments in simplified systems whereby many of the physical phenomenons mentioned above can be neglected. The present paper aims at giving an overview over the approaches currently followed to estimate kinetic parameters based on experimental data originating from these simplified systems. The nature and mathematical description of such problems are presented for homogeneous systems where all variables depend on time only. The techniques for the identification of the most significant reactions (and hence parameters) are shown along with methods for mechanism reduction considerably alleviating the computational burden. As an application example, Mechacut, a C++ procedure written by the authors is employed for the reduction of a detailed reaction mechanism aiming at describing the combustion of methane CH4. In the following section, the estimation of kinetic parameters is formulated as an optimization problem and different approaches found in the current literature are examined.

Keywords

Shock Tube Sensitivity Coefficient Plug Flow Reactor Ignition Delay Time Differential Equation System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    S. Allende, C. Bouza, and I. Romero. Fitting a linear regression model by combining least squares and least absolute value estimation. QESTIIO, 19(1,2,3):107–121, 1985.Google Scholar
  2. 2.
    I.P. Androulakis. Kinetic mechanism reduction based on an integer programming approach. AIChE Journal, 46(2):361–371, 2000.MathSciNetCrossRefGoogle Scholar
  3. 3.
    I. Bauer, H. G. Bock, S. Körkel, and J. P. Schlöder. Numerical methods for optimum experimental design in DAE systems. Journal of Computational and Applied Mathematics, 120:1–25, 2000.MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    H.G. Bock. Modelling of chemical reaction systems. Proceedings of an International Workshop, 18:102–125, 1980.Google Scholar
  5. 5.
    H.G. Bock, E. Kostina, and Schloeder J. P. Numerical methods for parameter estimation in non-linear differential algebraic equations. GAMM-Mitt., 30(2):376–408, 2007.Google Scholar
  6. 6.
    M. Carlier, C. Corre, R. Minetti, J-F. Pauwels, M. Ribaucour, and L-R. Sochet. Autoignition of butane: a burner and a rapid compression machine study. Twenty-Third symposium (International) on combustion / The combustion Institute, (4):1753–1758, 1990.Google Scholar
  7. 7.
    L. Elliott, D. B. Ingham, A. G. Kyne, N. S. Mera, M. Poukashanian, and C. W. Wilson. Genetic algorithms for optimisation of chemical kinetics reaction mechanisms. Progress in Energy and Combustion Science, 30:297–328, 2004.CrossRefGoogle Scholar
  8. 8.
    Michael Frenklach. Process informatics for combustion chemistry. 31-th International Symposium on Combustion, Heidelberg, 2006.Google Scholar
  9. 9.
    R. Q. Gonzales. Evaluation of a Detailed Reaction Mechanism for Partial and Total Oxidation of C1-C4 Alkanes. PhD thesis, University of Heidelberg, 2007.Google Scholar
  10. 10.
    C. Heghes. C1-C4 Hydrocarbon Oxidation Mechanism. PhD thesis, University of Heidelberg, 2006.Google Scholar
  11. 11.
    J. C. Ianni. A comparison of the bader-deuflhard and the cash-karp runge-kutta integrators for the gri-mech 3.0 model based on the chemical kinetics code kintecus. Second MIT Conference on Computational Fluid and Solid Mechanics, pages 1368–1372, 2003.Google Scholar
  12. 12.
    S.H. Lam. Using csp to understand complex chemical kinetics. Combustion, Science and Technology, 89:375, 1993.Google Scholar
  13. 13.
    L. Liang, J.G. Stevens, J.T. Farell, P.T. Huynh, I.P. Androulakis, and M. Ierapetritou. An adaptive approach for coupling detailed chemical kinetics and multidimensional cfd. 5th US Combustion Meeting- Paper C09, pages 1–15, 2007.Google Scholar
  14. 14.
    A.E. Lutz, R.J. Kee, and J.A. Miller. Senkin: A fortran program for predicting homogeneous gas phase chemical kinetics with sensitivity analysis. SAND87-8248, Sandia National Laboratories, pages 4–30, 1988.Google Scholar
  15. 15.
    U. Maas and S.B. Pope. Simplifying chemical kinetics: Intrinsic low-dimensional manifolds in composition space. Combustion and Flame, 88:239, 1992.CrossRefGoogle Scholar
  16. 16.
    T. Mani, P. Murugan, and N. Mahinpey. Determination of distributed activation energy model kinetic parameters using simulated annealing optimization method for nonisothermal pyrolysis of lignin. Ind. Eng. Chem. Res., 48:1464–1467, 2009.CrossRefGoogle Scholar
  17. 17.
    M. Masoori, B. Boozarjomehry, B. Ramin, S.J. Maryam, and N. Reshadi. Application of genetic algorithm in kinetic modeling of fischer-topsch synthesis. Proceedings of an International Workshop, 27(1):25–32, 2008.Google Scholar
  18. 18.
    J. V. Michael and K. P. Lim. Shock tube techniques in chemical kinetics. Annu. Rev. Phys. Chem., 44:429–458, 1993.CrossRefGoogle Scholar
  19. 19.
    C. J. Montgomery, M.A. Cremer, J.-Y. Chen, C.K. Westbrook, and L.Q. Maurice. Reduced chemical kinetic mechanisms for hydrocarbon fuels. Journal of Propulsion and Power, 18(01), 2002.Google Scholar
  20. 20.
    I. I. Naydenova. Soot Formation Modeling during Hydrocarbon Pyrolysis and Oxidation behind Shock Waves. PhD thesis, University of Heidelberg, 2007.Google Scholar
  21. 21.
    L. Petzold and W. Zhu. Model reduction for chemical kinetics: An optimization approach. AIChE Journal, 45(4):869–886, 1999.CrossRefGoogle Scholar
  22. 22.
    W. Polifke, W. Geng, and K. Doebbeling. Optimisation of reaction rate coefficients for simplified reaction mechanisms with genetic algorithms. Combustion and Flame, 113:119–135, 1998.CrossRefGoogle Scholar
  23. 23.
    T. Russi, A. Packard, R. Feeley, and M. Frenklach. Sensitivity analysis of uncertainty in model prediction. J. Phys. Chem. A., 112(12):2579–2588, 2008.CrossRefGoogle Scholar
  24. 24.
    A. Saltelli, M. Ratto, S. Tarantola, and F. Campolongo. Sensitivity analysis for chemical models. Chemical Review C, American Chemical Society, Published on Web:A–P, 2004.Google Scholar
  25. 25.
    A. Saylam, M. Ribaucour, M. Carlier, and R. Minetti. Reduction of detailed kinetic mechanisms using analyses of rate and sensitivity of reactions: Application to iso-octane and n-heptane. Proceedings of the European Combustion Meeting 2005, pages 1–5, 2005.Google Scholar
  26. 26.
    N. Shenvi, J. M. Geremia, and H. Rabitz. Nonlinear kinetic parameter identification through map inversion. J. Phys. Chem. A, 106:12315–12323, 2002.CrossRefGoogle Scholar
  27. 27.
    M. S. Skjoeth-Rasmussen, P. Glarborg, M. Oestberg, J. T. Johannessen, H. Livbjerg, A. D. Jensen, and T.S. Christensen. Detailed modeling of pah and soot formation in a laminar premixed benzene/oxygen/argon low-pressure flame. Combustion and Flame, 136:91–128, 2004.CrossRefGoogle Scholar
  28. 28.
    G.P. Smith et.al. www.me.berkeley.edu/gri-mech.
  29. 29.
    H.S. Soyhan, F. Mauss, and C. Sorusbay. Chemical kinetic modeling of combustion in internal combustion engines using reduced chemistry. Combustion Science and Technology, 174(11,12):73–91, 2002.Google Scholar
  30. 30.
    Weiyong Tang, Libin Zhang, Andreas.A. Linninger, Robert S. Tranter, and Brezinsky. Solving kinetic inversion problems via a physically bounded gauss-mewton (pgn) method. Industrial and Engineering Chemistry Research, 44(10):3626–3637, 2005.Google Scholar
  31. 31.
    V. Vasudevan, D. F. Davidson, and R. K. Hanson. Shock tube measurements of toluene ignition times and oh concentrations time histories. Proceedings of the Combustion Institute, 30:1155–1163, 2005.CrossRefGoogle Scholar
  32. 32.
    J. Warnatz, U. Maas, and R.W. Dibble. Combustion: Physical and Chemical Fundamentals, Modeling and Simulation, Experiments, Pollutant Formation. Springer-Editions, Berlin, third edition, 2001.MATHGoogle Scholar
  33. 33.
    T. Zeuch. Reaktionskinetik von Verbrennungsprozessen in der Gasphase: Spektroskopische Untersuchungen der Geschwindigkeit, Reaktionsprodukte und Mechanismen von Elementarreaktionen und die Modellierung der Oxidation von Kohlenwasserstoffen mit detaillierten Reaktionsmechanismen. PhD thesis, University of Goettingen, 2003.Google Scholar
  34. 34.
    I. GY. Zsely, J. Zador, and T. Turanyi. On the similarity of the sensitivity functions of methane combustion models. Combustion Theory and Modelling, 9(4):721–738, 2005.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Interdisciplinary Center for Scientific Computing (IWR)University of HeidelbergHeidelbergGermany
  2. 2.Institute of Combustion TechnologyGerman Aerospace Center (DLR)StuttgartGermany

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