Obtaining a reduced kinetic mechanism for Methyl Butanoate

  • A. L. De BortoliEmail author
  • F. N. Pereira
Original Paper


The computational treatment of detailed kinetic reaction mechanisms for combustion is expensive, especially in the case of biodiesel fuels. In this way, great efforts in the search of techniques for the development of reduced kinetic mechanisms have been observed. As Methyl Butanoate (MB, \(C_3H_7COOCH_3\)) is an essential model frequently used to represent the ester group of reactions in saturated methyl esters of large chain, this paper proposes a reduction strategy and uses it to obtain a reduced kinetic mechanism for the MB. The reduction strategy consists in the use of artificial intelligence to define the main chain and produce a skeletal mechanism, apply the traditional hypotheses of steady-state and partial equilibrium, and justify these assumptions through an asymptotic analysis. The main advantage of the strategy employed here is to reduce the work required to solve the system of chemical equations by two orders of magnitude for MB, since the number of reactions is decreased in the same order.


Artificial intelligence Mechanism reduction Methyl Butanoate Asymptotic analysis Biofuels 

Mathematics Subject Classification

80A25 80A30 



This research is being developed at UFRGS, Federal University of Rio Grande do Sul. Professor De Bortoli gratefully acknowledges the financial support from CNPq, Conselho Nacional de Desenvolvimento Científico e Tecnológico, under Grant 303816/2015-5.


  1. 1.
    J.F. Griffiths, Reduced kinetic models and their application to practical combustion systems. Prog. Energy Combust. Sci. 21(1), 25–107 (1995)CrossRefGoogle Scholar
  2. 2.
    F.A. Vaz, A.L. De Bortoli, A new reduced kinetic mechanism for turbulent jet diffusion flames of bioethanol. Appl. Math. Comput. 247, 918–929 (2014)Google Scholar
  3. 3.
    A. Demirbas, Biofuels securing the planet’s future energy needs. Energy Convers. Manag. 50(9), 2239–2249 (2009)CrossRefGoogle Scholar
  4. 4.
    R. Grana, A. Frassoldati, A. Cuoci, T. Faravelli, E. Ranzi, A wide range kinetic modeling study of pyrolysis and oxidation of methyl butanoate and methyl decanoate. Note I: lumped kinetic model of methyl butanoate and small methyl esters. Energy 43(1), 124–139 (2012)CrossRefGoogle Scholar
  5. 5.
    A. Stagni, A. Cuoci, A. Frassoldati, T. Faravelli, E. Ranzi, Lumping and reduction of detailed kinetic schemes: an effective coupling. Ind. Eng. Chem. Res. 53(22), 9004–9016 (2013)CrossRefGoogle Scholar
  6. 6.
    C.K. Westbrook, W.J. Pitz, H.J. Curran, Chemical kinetic modeling study of the effects of oxygenated hydrocarbons on soot emissions from diesel engines. J. Phys. Chem. A 110, 6912–6922 (2006)CrossRefGoogle Scholar
  7. 7.
    E.M. Fisher, W.J. Pitz, H.J. Curran, C.K. Westbrook, Detailed chemical kinetic mechanisms for combustion of oxygenated fuels. Proc. Combust. Inst. 28(2), 1579–1586 (2000)CrossRefGoogle Scholar
  8. 8.
    M.S. Graboski, R.L. McCormick, Combustion of fat and vegetable oil derived fuels in diesel engines. Prog. Energy Combust. Sci. 24(2), 125–164 (1998)CrossRefGoogle Scholar
  9. 9.
    C.K. Westbrook, C.V. Naik, O. Herbinet, W.J. Pitz, M. Mehl, S.M. Sarathy, H.J. Curran, Detailed chemical kinetic reaction mechanisms for soy and rapeseed biodiesel fuels. Combust. Flame 158(4), 742–755 (2011)CrossRefGoogle Scholar
  10. 10.
    J. Coniglio, H. Bennadji, P.A. Glaude, O. Herbinet, F. Billaud, Combustion chemical kinetics of biodiesel and related compounds (methyl and ethyl esters): experiments and modeling—advances and future refinements. Prog. Energy Combust. Sci. 39(4), 340–382 (2013)CrossRefGoogle Scholar
  11. 11.
    J.Y.W. Lai, K.C. Lin, A. Violi, Biodiesel combustion: advances in the chemical kinetic modeling. Prog. Energy Combust. Sci. 37, 1–14 (2011)CrossRefGoogle Scholar
  12. 12.
    J. Yang, V.I. Golovitchev, P.R. Lurbe, J.J.L. Sánchez, Chemical kinetic study of nitrogen oxides formation trends in biodiesel combustion. Int. J. Chem. Eng. ID 898742, 22 pages (2012)Google Scholar
  13. 13.
    S.B. Hosseini, M. Ahmadvand, R.H. Khoshkhoo, H. Khosravi, The experimental and simulations effect of air swirler on pollutants from biodiesel combustion. Res. J. Appl. Sci. Eng. Tech. 5(18), 4556–4562 (2013)Google Scholar
  14. 14.
    Y. Ra, R.D. Reitz, A combustion model for IC engine combustion simulations with multi-component fuels. Combust. Flame 158(1), 69–90 (2011)CrossRefGoogle Scholar
  15. 15.
    P. Diévart, S.H. Won, J. Gong, S. Dooley, Y. Ju, A comparative study of the chemical kinetic characteristics of small methyl esters in diffusion flame extinction. Proc. Combust. Inst. 34, 821–829 (2013)CrossRefGoogle Scholar
  16. 16.
    J.L. Brakora, Y. Ra, R. Reitz, J. McFarlane, C.S. Daw, Development and validation of a reduced reaction mechanism for biodiesel fueled engine simulations. SAE Int. J. Fuels Lubr. 1(1), 675–702 (2009)CrossRefGoogle Scholar
  17. 17.
    H.K. Ng, S. Gan, J.H. Ng, K.M. Pang, Development and validation of a reduced combined biodiesel–diesel reaction mechanism. Fuel 104, 620–634 (2013)CrossRefGoogle Scholar
  18. 18.
    C. Saggese, A. Frassoldati, A. Cuoci, T. Favarelli, E. Ranzi, A lumped approach to the kinetic modeling of pyrolysis and combustion of biodiesel fuels. Proc. Combust. Inst. 34, 427–434 (2013)CrossRefGoogle Scholar
  19. 19.
    Z. Luo, M. Plomer, T. Lu, S. Som, D.E. Longman, A reduced mechanism for biodiesel surrogates with low temperature chemistry for compression ignition engine applications. Combust. Theory Model. 16(2), 369–385 (2012)CrossRefGoogle Scholar
  20. 20.
    P. Diévart, S.H. Won, S. Dooley, F.L. Dryer, Y. Ju, A kinetic model for methyl decanoate combustion. Combust. Flame 159(5), 1793–1805 (2012)CrossRefGoogle Scholar
  21. 21.
    S. Turns, An Introduction to Combustion: Concepts and Applications, 2nd edn. (McGraw-Hill, New York, 2000)Google Scholar
  22. 22.
    K.K. Kuo, Principles of Combustion, 2nd edn. (Wiley, Hoboken, 2005)Google Scholar
  23. 23.
    A.L. De Bortoli, G.S.L. Andreis, F.N. Pereira, Modeling and Simulation of Reactive Flows (Elsevier, Amsterdam, 2015)Google Scholar
  24. 24.
    T. Turányi, Sensitivity analysis of complex kinetic systems: tools and applications. J. Math. Chem. 5(3), 203–248 (1990)CrossRefGoogle Scholar
  25. 25.
    N. Peters, Turbulent Combustion (Cambridge University Press, Cambridge, 2000)CrossRefGoogle Scholar
  26. 26.
    Y.Y. Wu, C.K. Chan, L.X. Zhou, Large eddy simulation of an ethylene–air turbulent premixed V-flame. J. Comput. Appl. Math. 235, 3768–3774 (2011)CrossRefGoogle Scholar
  27. 27.
    H. Watanabe, R. Kurose, S.M. Hwang, F. Akamatsu, Characterisitcs of flamelets in spray flames formed in a laminar counterflow. Combust. Flame 148, 234–248 (2007)CrossRefGoogle Scholar
  28. 28.
    D.S.S. Shieh, Y. Chang, G. Carmichael, The evaluation of numerical techniques for solution of stiff ordinary differential equations arising from chemical kinetic problems. Environ. Soft. 3(1), 28–38 (1998)CrossRefGoogle Scholar
  29. 29.
    R.C. Aiken, Stiff Computation (Oxford University Press, Oxford, 1985)Google Scholar
  30. 30.
    A. Sandu, J.G. Verwer, J.G. Blom, E.J. Spee, G.R. Carmichael, F.A. Potra, Benchmarking stiff ODE solver for atmospheric chemistry problems II: Rosenbrock solvers. Atmos. Environ. 31(20), 3459–3472 (1997)CrossRefGoogle Scholar
  31. 31.
    T.D. Bui, T.R. Bui, Numerical methods for extremely stiff systems of ordinary differential equations. Appl. Math. Model. 3, 355–358 (1979)CrossRefGoogle Scholar
  32. 32.
    T.D. Bui, A note on the Rosenbrock procedure. Math. Comput. 33, 971–975 (1979)CrossRefGoogle Scholar
  33. 33.
    J.H. Mathews, K.D. Fink, Numerical Methods Using MATLAB (Pearson, Prentice Hall, 2004)Google Scholar
  34. 34.
    B. Kovács, J. Tóth, Estimating reaction rate constants with neural networks. Int. J. Appl. Math. Comput. Sci. 4(1), 7–11 (2007)Google Scholar
  35. 35.
    B.A. Sen, S. Menon, Artificial neural networks based chemistry-mixing subgrid model for LES. 47th AIAA conference (2009), pp. 1–17Google Scholar
  36. 36.
    J.A. Blasco, N. Fueyo, J.C. Larroya, C. Dopazo, Y.J. Chen, A single-step time-integrator of a methane–air chemical system using artificial neural networks. Comput. Chem. Eng. 23, 1127–1133 (1999)CrossRefGoogle Scholar
  37. 37.
    B.A. Sen, S. Menon, Representation of chemical kinetics by artificial neural networks for large eddy simulations. In: 43rd AIAA/ASME/SAE/ASEE joint propulsion conference & exhibit, No. AIAA 2007-5635 (2007), pp. 1–15Google Scholar
  38. 38.
    Z.J. Zhou, Y. Lu, Z.H. Wang, Y.W. Xu, J.H. Zhou, K.F. Cen, Systematic method of applying ANN for chemical kinetics reduction in turbulent premixed combustion modeling. Chin. Sci. Bull. 58, 486–492 (2013)CrossRefGoogle Scholar
  39. 39.
    K.C. Lin, H. Tao, F.H. Kao, C.T. Chiu, A minimized skeletal mechanism for methyl butanoate oxidation and its application to the prediction of C3–C4 products in non-premixed flames: A base model of biodiesel fuels. Energy Fuels 30(2), 1354–1363 (2016)Google Scholar
  40. 40.
    Z.M. Nikolaou, J.Y. Chen, N. Swaminathan, A 5-step reduced mechanism for combustion of \(CO\)/\(H_2\)/\(H_2O\)/\(CH_4\)/\(CO_2\) mixtures with low hydrogen/methane and high \(H_2O\) content. Combust. Flame 160, 56–75 (2013)CrossRefGoogle Scholar
  41. 41.
    U. Niemann, R. Seiser, K. Seshadri, Ignition and extinction of low molecular weight esters in nonpremixed flows. Combust. Theory Model. 14(6), 875–891 (2010)CrossRefGoogle Scholar
  42. 42.
    Y. Chang, M. Jia, Y. Li, Y. Zhang, M. Xie, H. Wang, R.D. Reitz, Development of a skeletal oxidation mechanism for biodiesel surrogate. Proc. Combust. Inst. 35, 3037–3044 (2015)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Graduate Program in Applied Mathematics (PPGMAp)UFRGSPorto AlegreBrazil
  2. 2.Graduate Program in Chemical Engineering (PPGEQ)UFRGSPorto AlegreBrazil

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