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Mathematical Model for Assessing New, Non-Fossil Fuel Technological Products (Li-Ion Batteries and Electric Vehicle)

Author

Listed:
  • Igor E. Anufriev

    (Higher School of Applied Mathematics and Computational Physics, Peter the Great St. Petersburg Polytechnic University, Politekhnicheskaya Ulitsa, 29, 195251 St. Petersburg, Russia)

  • Bulat Khusainov

    (Department of Science and Commercialization, Zhetysu University Named After I. Zhansugurov, St. Zhansugurov 187 A, Taldykorgan 040009, Kazakhstan)

  • Andrea Tick

    (Keleti Karoly Faculty of Business and Management, Obuda University, Tavaszmező Str. 15–17, 1084 Budapest, Hungary)

  • Tessaleno Devezas

    (Engineering Faculty, Atlântica Instituto Universitário, 2730-036 Barcarena, Portugal)

  • Askar Sarygulov

    (Department of Science and Commercialization, Zhetysu University Named After I. Zhansugurov, St. Zhansugurov 187 A, Taldykorgan 040009, Kazakhstan)

  • Sholpan Kaimoldina

    (Department of Science and Commercialization, Zhetysu University Named After I. Zhansugurov, St. Zhansugurov 187 A, Taldykorgan 040009, Kazakhstan)

Abstract

Since private cars and vans accounted for more than 25% of global oil consumption and about 10% of energy-related CO 2 emissions in 2022, increasing the share of electric vehicle (EV) ownership is considered an important solution for reducing CO 2 emissions. At the same time, reducing emissions entails certain economic losses for those countries whose exports are largely covered by the oil trade. The explosive growth of the EV segment over the past 15 years has given rise to overly optimistic forecasts for global EV penetration by 2050. One of the major obstacles to such a development scenario is the limited availability of resources, especially critical materials. This paper proposes a mathematical model to predict the global EV fleet based on the limited availability of critical materials such as lithium, one of the key elements for battery production. The proposed model has three distinctive features. First, it shows that the classical logistic function, due to the specificity of its structure, cannot correctly describe market saturation in the case of using resources with limited serves. Second, even the use of a special multiplier that describes the market saturation process taking into account the depletion (finiteness) of the used resource does not obtain satisfactory economic results because of the “high speed” depletion of this resource. Third, the analytical solution of the final model indicates the point in time at which changes in saturation rate occur. The latter situation allows us to determine the tracking of market saturation, which is more similar to the process that is actually occurring. We believe that this model can also be validated to estimate the production of wind turbines that use rare earth elements such as neodymium and dysprosium (for the production of powerful and permanent magnets for wind turbines). These results also suggest the need for oil-exporting countries to technologically diversify their economies to minimize losses in the transition to a low-carbon economy.

Suggested Citation

  • Igor E. Anufriev & Bulat Khusainov & Andrea Tick & Tessaleno Devezas & Askar Sarygulov & Sholpan Kaimoldina, 2025. "Mathematical Model for Assessing New, Non-Fossil Fuel Technological Products (Li-Ion Batteries and Electric Vehicle)," Mathematics, MDPI, vol. 13(1), pages 1-27, January.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:1:p:143-:d:1558898
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    References listed on IDEAS

    as
    1. Tessaleno Devezas & Andrea Tick & Askar Sarygulov & Polina Rukina, 2024. "The Slow Pace of Green Transformation: Underlying Factors and Implications," Energies, MDPI, vol. 17(19), pages 1-26, September.
    2. Fulton, Lewis M & Jaffe, Amy & McDonald, Zane, 2019. "Internal Combustion Engine Bans and Global Oil Use," Institute of Transportation Studies, Working Paper Series qt52j400b1, Institute of Transportation Studies, UC Davis.
    3. Monica Bonacina & Mert Demir & Antonio Sileo & Angela Zanoni, 2024. "The slow lane: a study on the diffusion of full-electric cars in Italy," Working Papers 2024.19, Fondazione Eni Enrico Mattei.
    4. Krešimir Jurlin, 2023. "How Efficient and Socially Sensitive Are Fiscal Incentives for Electric Cars in Europe?," JRFM, MDPI, vol. 16(6), pages 1-19, May.
    5. Bonacina, Monica & Demir, Mert & Sileo, Antonio & Zanoni, Angela, 2024. "The slow lane: a study on the diffusion of full-electric cars in Italy," FEEM Working Papers 344135, Fondazione Eni Enrico Mattei (FEEM).
    6. Gallagher, Kelly Sims & Muehlegger, Erich, 2011. "Giving green to get green? Incentives and consumer adoption of hybrid vehicle technology," Journal of Environmental Economics and Management, Elsevier, vol. 61(1), pages 1-15, January.
    7. Andrea Tick & Askar Akaev & Tessaleno Campos Devezas & Askar Sarygulov & Alexander Petryakov & Anufriev Igor Evgenevich, 2024. "Assessing Decarbonization Approaches across Major Economies," Energies, MDPI, vol. 17(17), pages 1-33, September.
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