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

Abstract

Since private cars and vans accounted for more than 25% of global oil consumption and about 10% of energy-related CO2 emissions in 2022, increasing the share of electric vehicle (EV) ownership is considered an important solution for reducing CO2 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.

Keywords

• electric vehicles
• critical materials
• lithium
• mathematical model
• oil export
• technological diversification