Abstract
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
Highlights
The magnesium (Mg) element is one of metals in our universe with some interesting properties [1]
Calculation of activation energy (Ea) After detecting the correct kinetic equation and finding the corresponding rate coefficient, it should be noted that all actions performed are for reaction at one certain temperature
The reactions in solid state chemical kinetics (SSCK) are particular reactions and occurred at high temperatures and on the other hand, it is completely possible to obtain the values of k at different temperatures from different kinetic equations, it is a logical action to take into account the possibility of change of activation energy with temperature
Summary
The magnesium (Mg) element is one of metals in our universe with some interesting properties [1]. Because of many problems such as greenhouse effect resulting from fossil fuels and the decrease of these fuels in the future, a striking endeavor has started for producing clean energies from renewable resources [2,3,4,5,6,7]. Among various types of renewable energies, solar energy is an attractive subject for many researchers. It can be said that the human being noticed the importance of solar energy a little late but the subject of solar energy has seen a substantial amount of research projects in various fields [8,9,10,11,12,13,14,15,16,17]. It is obvious that the combination of magnesium production and utilizing renewable energies can be very beneficial for human being in this era
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