This work presents a polynomial regression model for the optimization of the content of fatty acid methyl esters (FAME) and the conversion yield of waste vegetable oil to biodiesel. The equations are optimized to obtain the maximum FAME yield, which is the product of the conversion yield and the FAME content in the biodiesel. The independent variables considered are the type of catalyst used (KOH and NaOH), percentage of catalyst (0.6%, 1.0% and 1.5% w/w with respect to oil), and the methanol: oil molar ratio (6:1, 7.5:1 and 9:1). The prediction models are obtained by using nine experimental points for each catalyst. The validation is developed with four main experimental points from the mapping. A polynomial relation is obtained as a consequence, which correlates each of the experimental variables with the FAME and conversion yield. The optimization of the proposed models shows an error of 2.66% for the FAME, and an error of less than 1% for the conversion yield are obtained. This work presents a straightforward methodology to obtain the best chemical conditions in the production of biodiesel by using a small number of experiments, obtaining good results. This methodology can be applied for biodiesel production from any raw material, recalculating each of the regression constants thus allowing to obtain the highest quantity of oil to be converted in FAME.
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