Mathematical Correlations for Volumetric (Density and Specific Gravity) Properties of Diesel/Biodiesel Blends

Biodiesel is a renewable and environmentally friendly alternative energy source to conventional diesel. The use of biodiesel blends with diesel to meet energy needs can significantly reduce greenhouse gas emissions, as biodiesel produces smaller amounts of carbon dioxide (CO2) when burned. In addition, diesel/biodiesel blends can be used as fuel in existing diesel engines without the need to modify them, and their exploitation reduces dependence on oil imports and the impact of oil prices on the economy. Since increasing the percentage of biodiesel in diesel/biodiesel blends aims to increase the environmental and economic benefits, it is necessary to know the physicochemical properties of these blends, such as density, specific gravity, etc. The aim of the present work was to use appropriate mathematical equations that can predict the physicochemical properties of mixtures under different conditions of temperature and mixing ratios. Kay’s mathematical mixing expression, the Tammann–Tait equation, and empirical equations were used to describe the dependence of the density (ρ, kg/m3) of the mixtures on the volume percentage (v%) of biodiesel mixed with diesel and the temperature variance (T, K). In addition, mathematical equations were used to predict the specific gravity (Sg) of the mixtures. Mathematical estimations were based on experimental data obtained by blending diesel and animal or vegetable biodiesel volume percentages. These data showed the effect of different mixing volume percentages of biodiesel and diesel (from 0% to 100% biodiesel) on their physicochemical characteristics under different temperatures (278 to 298 K). The accuracy of the mathematical estimations was evaluated using factors such as the Nash and Sutcliffe coefficient (E) and relative root mean squared error (MSE%). The results showed that the selected mathematical equations were able to accurately estimate (E up to 0.9988 and MSE up to 0.4%) the increased density and specific gravity as the volume percentage of biodiesel increased and temperature decreased. The present study uses mathematical tools for choosing the right blending ratios and conditions, depending on the desired features of the finished product.