نبذة مختصرة : The main goal of this study was to determine the industrially best reductant for reduction of magnesium oxide to magnesium with wood charcoal and petroleum coke (petcoke) each in molar ratio 1:1 and 1:2 (oxidant:reductant) at high temperatures. In this study, a new and reliable combination of mathematical modeling and discrete numerical optimization theory by presenting 18 “mathematical filters” not relying only on statistical quantities of fitting (contrary to many similar researches) was introduced. The purpose of these filters was the determination of correct kinetic equation and therefore, the corresponding rate coefficient from among 18 equations most used at present in the challenging field of solid state chemical kinetics. With assistance of a new and fundamental mathematical function and the obtained values of rate coefficients, the function of rate coefficient in temperature was attained. The activation energy was then calculated as a function of temperature using the general definition of activation energy and the determined function for rate coefficient. The comparison between different reducing agents in the different conditions and with relevant previous study was accomplished to determine the best reducing agent from industry standpoint. Also, the areas under experimental data were calculated numerically and utilized for method validation and comparison. It turned out finally that relying only on fitting quantities in the solid state chemical kinetics can readily lead to wrong conclusions about the correct kinetic equation and about the most suitable reducing agent. It is obvious that the erroneous calculations and wrong decisions in the laboratory scale become significant and paramount in industry and this reveals the significance of rigorous mathematical analysis. Graphical abstract
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