Mathematical Modeling of Alkaline Methanol Oxidation for Design of Efficient Fuel Cells

  • Tanja Clees
  • Igor Nikitin
  • Lialia NikitinaEmail author
  • Sabine Pott
  • Ulrike Krewer
  • Theresa Haisch
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 947)


This paper considers the electrochemical kinetic model of alkaline methanol oxidation, the process, relevant for the design of efficient fuel cells. Fuel cells of direct methanol type have a great advantage in safety and storage compared to hydrogen-oxygen fuel cells. They possess high energy density and are especially suitable for portable applications. The oxidation of fuel in an alkaline medium allows the use of affordable electrodes.

The mathematical model of the oxidation process includes a system of non-linear differential equations of high order, describing elementary reactions. The model also possesses 14 unknown reaction constants and 6 dynamic variables describing surface coverages of the intermediates. These variables cannot be measured directly, but can be reconstructed by the parameter identification procedure. The procedure comprises numerical integration of the system of differential equations, automatic global minimization of the distance between measured and modeled cyclic voltammograms, iterative Monte Carlo search and interactive parameter study.

The developed methods have been applied to 9 cyclic voltammograms of cells with different concentrations of alkaline and fuel. The reaction constants have been reconstructed, their dependence on concentrations has been discussed. Dynamic behavior of the system in form of the reconstructed evolution of the intermediates has been presented.


Complex systems modeling and simulation Non-linear optimization Parameter identification Application in electrochemistry 



The authors are grateful to the organizers and participants of SIMULTECH 2018 conference for fruitful discussions. The authors thank also Kira Konich and Kevin Reinartz for proofreading the paper. The work has been partially supported by German Federal Ministry for Economic Affairs and Energy, project BMWI-0324019A, MathEnergy: Mathematical Key Technologies for Evolving Energy Grids and by the German Bundesland North Rhine-Westphalia using fundings from the European Regional Development Fund, grant Nr. EFRE-0800063, project ES-FLEX-INFRA.


  1. 1.
    Clees, T., Nikitin, I., Nikitina, L., Pott, S., Krewer, U., Haisch, T.: Parameter identification in cyclic voltammetry of alkaline methanol oxidation. In: Proceedings of the SIMULTECH 2018, Porto, Portugal, 29–31 July 2018, pp. 279–288 (2018)Google Scholar
  2. 2.
    Krewer, U., Vidakovic-Koch, T., Rihko-Struckmann, L.: Electrochemical oxidation of carbon-containing fuels and their dynamics in low-temperature fuel cells. ChemPhysChem 12, 2518–2544 (2011)CrossRefGoogle Scholar
  3. 3.
    Krewer, U., Christov, M., Vidakovic, T., Sundmacher, K.: Impedance spectroscopic analysis of the electrochemical methanol oxidation kinetics. J. Electroanal. Chem. 589, 148–159 (2006)CrossRefGoogle Scholar
  4. 4.
    Beden, B., Kardigan, F., Lamy, C., Leger, J.M.: Oxidation of methanol on a platinum electrode in alkaline medium: effect of metal ad-atoms on the electrocatalytic activity. J. Electroanal. Chem. 142, 171–190 (1982)CrossRefGoogle Scholar
  5. 5.
    Ciucci, F.: Revisiting parameter identification in electrochemical impedance spectroscopy: weighted least squares and optimal experimental design. Electrochimica Acta 87, 532–545 (2013)CrossRefGoogle Scholar
  6. 6.
    Gamry Instruments, Basics of Electrochemical Impedance Spectroscopy, online tutorial.
  7. 7.
    Clees, T., Nikitin, I., Nikitina, L., Steffes-lai, D., Pott, S., Krewer, U., Windorfer, T.: Electrochemical impedance spectroscopy of alkaline methanol oxidation. In: Proceedings of the INFOCOMP 2017, The Seventh International Conference on Advanced Communications and Computation, pp. 46–51, IARIA (2017)Google Scholar
  8. 8.
    Bard, A.J., Faulkner, L.R.: Electrochemical Methods: Fundamentals and Applications. Wiley, Hoboken (2000)Google Scholar
  9. 9.
    Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P.: Numerical Recipes in C. Cambridge University Press, Cambridge (1992). Chap. 15zbMATHGoogle Scholar
  10. 10.
    Strutz, T.: Data Fitting and Uncertainty: A Practical Introduction to Weighted Least Squares and Beyond. Springer (2016)Google Scholar
  11. 11.
    Wächter, A., Biegler, L.T.: On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Math. Program. 106, 25–57 (2006)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Nikitin, I., Nikitina, L., Clees, T.: Stochastic analysis and nonlinear metamodeling of crash test simulations and their application in automotive design. In: Browning, J.E. (ed.) Computational Engineering: Design, Development, and Applications, pp. 51–74. Nova Science Publishers, New York (2012)zbMATHGoogle Scholar
  13. 13.
    Clees, T., Hornung, N., Nikitin, I., Nikitina, L., Steffes-lai, D., Klimenko, S.: Focused ultrasonic therapy planning: metamodeling, optimization, visualization. J. Comput. Sci. 5(6), 891–897 (2014)CrossRefGoogle Scholar
  14. 14.
    Clees, T., Nikitin, I., Nikitina, L., Pott, S.: Quasi-Monte Carlo and RBF metamodeling for quantile estimation in river bed morphodynamics. In: Obaidat, M.S., et al. (eds.) Simulation and Modeling Methodologies, Technologies and Applications. Advances in Intelligent Systems and Computing, vol. 319, pp. 211–222. Springer, Cham (2014)CrossRefGoogle Scholar
  15. 15.
    Bäck, T.: Evolutionary Algorithms in Theory and Practice. Oxford University Press, New York (1996)zbMATHGoogle Scholar
  16. 16.
    Ilonen, J., Kamarainen, J.K., Lampinen, J.: Differential evolution training algorithm for feed forward neural networks. Neural Process. Lett. 17, 93–105 (2003)CrossRefGoogle Scholar
  17. 17.
    Otten, R.H.J.M., van Ginneken, L.P.P.P.: The Annealing Algorithm. Kluwer (1989)Google Scholar
  18. 18.
    Griffiths, P., de Hasseth, J.A.: Fourier Transform Infrared Spectrometry. Wiley-Blackwell, Hoboken (2007)CrossRefGoogle Scholar
  19. 19.
    Mathematica 11, Reference Manual.

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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Tanja Clees
    • 1
    • 2
  • Igor Nikitin
    • 2
  • Lialia Nikitina
    • 2
    Email author
  • Sabine Pott
    • 2
  • Ulrike Krewer
    • 3
  • Theresa Haisch
    • 3
  1. 1.University of Applied SciencesSankt AugustinGermany
  2. 2.Fraunhofer Institute for Algorithms and Scientific ComputingSankt AugustinGermany
  3. 3.Institute of Energy and Process Systems EngineeringTechnical UniversityBraunschweigGermany

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