Mathematical model of the process of converting waste oils into diesel biofuel

The growing demand for renewable energy sources encourages the development of technologies for the production of biodiesel from waste, but the high content of free fatty acids in raw materials complicates transesterification, reduces fuel yield, and increases the need for purification. The purpose of the study was to develop and validate a mathematical model of the process of transesterification of used oils into diesel biofuels to optimise technological parameters. The rationalised model described in detail the patterns of triglyceride transformation in the presence of alcohol and a catalyst. It allowed tracking changes in the concentrations of reaction intermediates, in particular, diglycerides, monoglycerides, biodiesel, and glycerol, which is critical for predicting the effectiveness of the process. Stable values of the speed of the transesterification process are indicated using the Arrhenius equation, which helped to estimate the effect of temperature and the ratio of reactants on the overall kinetics of the reaction. As part of the study, numerical modelling and correlation of the model were carried out by systematising the results with the data obtained during the research and obtained from the results of the analysis of literature sources. Catalytic and non-catalytic variants of the process were analysed, which determined the most effective reaction conditions. The simulation results confirmed that an increase in temperature values to 60°C leads to an increase in the yield of diesel biofuels, so excessive heating above the boiling point of methanol causes its evaporation, which leads to a decrease in the efficiency of the process and the loss of raw materials. Optimal technological parameters that ensure the maximum yield of biodiesel with minimal material and energy costs were determined. The proposed mathematical model can be used in industrial settings to optimise the biofuel production process, helping to increase the efficiency of recycling