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Abstract <p>In this paper, a kinetic model for the reduction process by solid carbon of MnO in high-carbon ferromanganese slags using fractional differential equations (FDE) was developed, the relationship between fractional order, fractional rate constant and temperature was determined, and the accuracy of the fractional order model was verified. The fractional order <i>q</i> is 0.892, 0.808, and 0.522, at 1450, 1500, and 1600°C respectively, and the fractional rate constant <i>k</i><sub><i>q</i></sub> 1.176E-03, 2.856E-03, and 3.477E-02. A linear relationship exists between the fractional order and the temperature and an exponential relationship exists with the fractional rate constant. Comparing the conversion factors calculated from the FDE and previous model with the experimental values, the RMSE were 0.005 and 0.029, respectively, and the <i>r</i><sup>2</sup> 0.999 and 0.980. This means the FDE model is more accurate. The apparent activation energy of the MnO reduction process calculated using the model was 181.1 kJ/mol.</p>

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Kinetic Analysis of Reduction Reaction of MnO from High Carbon Ferromanganese Slag Using Fractional Differential Equations (FDE)

  • 期刊论文

  • 发表日期：

    2025年9月1日

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  • Kim UnDok,
  • Kim MyongJae,
  • Ju IlChol

摘要

Abstract

In this paper, a kinetic model for the reduction process by solid carbon of MnO in high-carbon ferromanganese slags using fractional differential equations (FDE) was developed, the relationship between fractional order, fractional rate constant and temperature was determined, and the accuracy of the fractional order model was verified. The fractional order q is 0.892, 0.808, and 0.522, at 1450, 1500, and 1600°C respectively, and the fractional rate constant kq 1.176E-03, 2.856E-03, and 3.477E-02. A linear relationship exists between the fractional order and the temperature and an exponential relationship exists with the fractional rate constant. Comparing the conversion factors calculated from the FDE and previous model with the experimental values, the RMSE were 0.005 and 0.029, respectively, and the r2 0.999 and 0.980. This means the FDE model is more accurate. The apparent activation energy of the MnO reduction process calculated using the model was 181.1 kJ/mol.