Modelling esterification of palm kernel, neem, and jatropha seed oils using a simplex lattice approach

¹ Department of Mechanical Engineering, Federal University of Petroleum Resources, Effurun, Delta State P.M.B 1221, Nigeria
² Department of Mechanical Engineering, CVR College of Engineering, Hyderabad, Telangana 501510, India
³ Department of Mathematics, Aliko Dangote University of Science and Technology, Wudil, Kano State, Nigeria

^* Corresponding author: samuel.david@fupre.edu.ng

Published online: 7 January 2026

Abstract

High concentrations of free fatty acids (FFAs) in many non- edible oils interfere with biodiesel conversion, causing soap formation throughout the transesterification reaction. Although esterification in single and binary oil systems has been well-researched, there is a lack of knowledge regarding ternary blends. The knowledge gap on interactions of multi-oils limits optimization of blended feedstocks for resource-efficient and scaled biodiesel generation. The investigation optimizes the pre- treatment of PKO, NSO, and JSO using SLMD. Esterification was carried out using methanol at 25 wt.% and sulfuric acid at 1 wt% for 1.5 h at 60 °C. In this study, SLMD was used to optimize blend composition to minimize FFA and improve the viability of hybrid biodiesel feedstocks. Fuel properties of ternary biodiesel (PNJO methyl ester) were determined using standard transesterification conditions, 6:1 methanol-to-oil ratio, 1 wt.% catalyst, 60 °C, according to density and viscosity requirements in diesel blends. ANOVA analysis confirmed the significance of the model by a p- value of less than 0.001, with very high values of R²: 0.9983, adjusted R²: 0.9957, and predicted R²: 0.9295. The model validation revealed an RMSE value of 0.106 and SEP of 2.37%, MAE and AAD of 0.076 and 1.72%, respectively. The best formulation-0.0112 % JSO, 0.9653 % NSO, and 0.0235 % PKO gave 1.93 % FFA and produced biodiesel that met requirements according to both ASTM D6751 and EN 14214. This novel ternary optimization demonstrates that SLMD is a reliable predictive framework for sustainable biodiesel production.