# Development of a reduced mechanism for ethanol using directed relation graph and sensitivity analysis

- 221 Downloads

## Abstract

Numerical simulations involving detailed kinetic reaction mechanisms of combustion for conventional fuels are associated with computational costs prohibitive and, therefore, a lot of effort for obtaining reduced kinetic mechanisms has been observed. Among the known strategies, the Directed relation graph (DRG) method and the sensitivity analysis have proven to be very powerful tools, in addition to the traditional and efficient assumptions of steady-state and of partial equilibrium. The present work proposes a reduction strategy with these techniques for reduction of a mechanism for ethanol. Based on a mechanism of 377 reactions among 56 reactive species a skeletal mechanism, consisting of 24 species and 26 reactions, was obtained through the application of the DRG method and performing a sensitivity analysis. Using the assumptions of partial equilibrium and steady-state, which are justified by an asymptotic analysis, an additional reduction leads to a reduced mechanism of ten steps. Results of the new mechanism for a jet diffusion flame compare favorably with data found in the literature. The computational cost for simulation of jet diffusion flames with the reduced model is one order of magnitude less than necessary in the complete model, which is the principal contribution of this work.

## Keywords

Ethanol Mechanism reduction DRG Sensitivity analysis Asymptotic analysis## Mathematics Subject Classification

80A25 80A30## Notes

### Acknowledgements

This research is being developed at the Federal University of Rio Grande do Sul—UFRGS. The authors F.C.M. and C.B. thank the financial support of CAPES—*Coordination for the Improvement of Higher Education Personnel*. Prof. De Bortoli gratefully acknowledges the financial support of CNPq—*National Council for Scientific and Technological Development*, under the process \(303816/2015-5\).

## References

- 1.G.S.L. Andreis, F.A. Vaz, A.L. De Bortoli, Bioethanol combustion based on a reduced kinetic mechanism. J. Math. Chem.
**51**(6), 1584–1598 (2013)CrossRefGoogle Scholar - 2.A.K. Chandel, T.L. Junqueira, E.R. Morais, V.L.R. Gouveia, O. Cavalett, E.C. Rivera, V.C. Geraldo, A. Bonomi, S.S. da Silva, Techno-economic analysis of second-generation ethanol in Brazil: competitive, complementary aspects with first-generation ethanol. in
*Biofuels in Brazil*, (Springer, 2014), pp. 1–29Google Scholar - 3.A. De Bortoli, G. Andreis, Asymptotic anaysis for coupled hydrogen, carbon monoxide, methanol and ethanol reduced kinetic mechanisms. Lat. Am. Appl. Res.
**42**(3), 299–304 (2012)Google Scholar - 4.A. De Bortoli, F. Vaz, G. Lorenzzetti, I. Martins, Systematic reduction of combustion reaction mechanisms of common hydrocarbons and oxygenated fuels. in
*ICNAAM 2010: International Conference of Numerical Analysis and Applied Mathematics 2010*, vol 1281 (AIP Publishing, 2010) pp. 558–561Google Scholar - 5.A.L. De Bortoli, G.S.L. Andreis, F.N. Pereira,
*Modeling and Simulation of Reactive Flows*(Elsevier, Amsterdam, 2015)Google Scholar - 6.A. Demirbas,
*Biofuels: Securing the Planet’s Future Energy Needs*(Springer, London, 2009)CrossRefGoogle Scholar - 7.A. Goeke, S. Walcher, A constructive approach to quasi-steady state reductions. J. Math. Chem.
**52**(10), 2596–2626 (2014)CrossRefGoogle Scholar - 8.D.A. Goussis, U. Maas, Model reduction for combustion chemistry. in
*Turbulent Combustion Modeling*(Springer, 2011), pp. 193–220Google Scholar - 9.K.K. Kuo,
*Principles of combustion*, 2nd edn. (Wiley, Hoboken, 2005)Google Scholar - 10.A. Lebedev, M. Okun, V. Chorkov, P. Tokar, M. Strelkova, Systematic procedure for reduction of kinetic mechanisms of complex chemical processes and its software implementation. J. Math. Chem.
**51**(1), 73–107 (2013)CrossRefGoogle Scholar - 11.J. Li, A. Kazakov, F.L. Dryer, Experimental and numerical studies of ethanol decomposition reactions. J. Phys. Chem. A
**108**(38), 7671–7680 (2004)CrossRefGoogle Scholar - 12.T. Løvås,
*Model reduction techniques for chemical mechanisms*(INTECH Open Access Publisher, Rijeka, 2012)Google Scholar - 13.T. Lu, C.K. Law, A directed relation graph method for mechanism reduction. Proc. Combust. Inst.
**30**(1), 1333–1341 (2005)CrossRefGoogle Scholar - 14.T. Lu, C.K. Law, Linear time reduction of large kinetic mechanisms with directed relation graph: n-heptane and iso-octane. Combust. Flame
**144**(1), 24–36 (2006)CrossRefGoogle Scholar - 15.T. Lu, C.K. Law, On the applicability of directed relation graphs to the reduction of reaction mechanisms. Combust. Flame
**146**(3), 472–483 (2006)CrossRefGoogle Scholar - 16.N.M. Marinov, A detailed chemical kinetic model for high temperature ethanol oxidation. Int. J. Chem. Kinet.
**3**(2), 257–263 (1999)Google Scholar - 17.A. Masri, J. Gounder, Turbulent spray flames of acetone and ethanol approaching extinction. Combust. Sci. Technol.
**182**(4–6), 702–715 (2010)CrossRefGoogle Scholar - 18.T. Nagy, T. Turányi, Reduction of very large reaction mechanisms using methods based on simulation error minimization. Combust. Flame
**156**(2), 417–428 (2009)CrossRefGoogle Scholar - 19.K.E. Niemeyer, C. Sung, On the importance of graph search algorithms for DRGEP-based mechanism reduction methods. Combust. Flame
**158**(1), 1439–1443 (2011)CrossRefGoogle Scholar - 20.S.N. Pandis, J.H. Seinfeld, Sensitivity analysis of a chemical mechanism for aqueous-phase atmospheric chemistry. J. Geophys. Res.: Atmosp.
**94**(D1), 1105–1126 (1989)CrossRefGoogle Scholar - 21.P. Pepiot, H. Pitsch, Systematic reduction of large chemical mechanisms. in
*4th Joint Meeting of the US Sections of the Combustion Institute*, Philadelphia, PA (2005)Google Scholar - 22.P. Pepiot-Desjardins, H. Pitsch, An efficient error-propagation-based reduction method for large chemical kinetic mechanisms. Combust. Flame
**154**(1), 67–81 (2008)CrossRefGoogle Scholar - 23.N. Peters, Systematic reduction of flame kinetics- principles and details. in
*Dynamics of Reactive Systems. Part 1: Flames*, pp. 67–86 (1988)Google Scholar - 24.N. Peters,
*Turbulent Combustion*(Cambridge University Press, Cambridge, 2000)CrossRefGoogle Scholar - 25.Portal Brasil: Etanol atingiu produção recorde de 30 bilhões de litros em 2015 (2016). http://www.brasil.gov.br/economia-e-emprego/2016/05/etanol-atingiu-producao-recorde-de-30-bilhoes-de-litros-em-2015. Accesed 03 March 2017
- 26.O. Röhl, N. Peters, A reduced mechanism for ethanol oxidation. in
*4th European Combustion Meeting (ECM 2009)*, Vienna, Austria, April (2009), pp. 14–17Google Scholar - 27.P. Saxena, F.A. Williams, Numerical and experimental studies of ethanol flames. Proc. Combust. Inst.
**31**(1), 1149–1156 (2007)CrossRefGoogle Scholar - 28.W. Sun, Z. Chen, X. Gou, Y. Ju, A path flux analysis method for the reduction of detailed chemical kinetic mechanisms. Combust. Flame
**157**(7), 1298–1307 (2010)CrossRefGoogle Scholar - 29.T. Turányi, Reduction of large reaction mechanisms. New J. Chem.
**14**, 795–803 (1990)Google Scholar - 30.T. Turányi, Sensitivity analysis of complex kinetic systems: tools and applications. J. Math. Chem.
**5**(3), 203–248 (1990)CrossRefGoogle Scholar - 31.T. Turányi, Applications of sensitivity analysis to combustion chemistry. Reliabil. Eng. Syst. Saf.
**57**(1), 41–48 (1997)CrossRefGoogle Scholar - 32.T. Turányi, T. Berces, S. Vajda, Reaction rate analysis of complex kinetic systems. Int. J. Chem. Kinet.
**21**(2), 83–99 (1989)CrossRefGoogle Scholar - 33.T. Turányi, A.S. Tomlin,
*Analysis of Kinetic Reaction Mechanisms*(Springer, Berlin, 2014)CrossRefGoogle Scholar - 34.S. Vajda, P. Valko, T. Turányi, Principal component analysis of kinetic models. Int. J. Chem. Kinet.
**17**(1), 55–81 (1985)CrossRefGoogle Scholar - 35.F.A. Vaz, A. De Bortoli, A new reduced kinetic mechanism for turbulent jet diffusion flames of bioethanol. Appl. Math. Comput.
**247**, 918–929 (2014)Google Scholar - 36.H. Watanabe, R. Kurose, S. Komori, H. Pitsch, A numerical simulation of soot formation in spray flames. in
*Proceedings of the Summer Program*(Citeseer, 2006), p. 325Google Scholar - 37.X. Zheng, T. Lu, C. Law, Experimental counterflow ignition temperatures and reaction mechanisms of 1, 3-butadiene. Proc. Combust. Inst.
**31**(1), 367–375 (2007)CrossRefGoogle Scholar