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## Table 1

Kinetic models to investigate the compositional changes during the refining process [1,3,5–11,15].

Author | Research content | Parameter | Literature |
---|---|---|---|

Okuyama et al. | Calculated the MgO content change in inclusions by the unreacted core model | Diffusion coefficient of Mg in inclusion: 3.2 × 10^{−13} m^{2}/sDiffusion coefficient of Al in inclusion: 3.5 × 10 ^{−9} m^{2}/s |
[15] |

Shin-ya et al | Built a steel-slag-inclusion-refractory model to investigate the variations of steel, slag and inclusions | Mass transfer coefficient of the molten steel: Mass transfer coefficient of the slag: k_{s} = k_{m}/10where k is the mass transfer coefficient of the molten steel, m/s; _{m}k is the mass transfer coefficient of the slag, m/s; _{s}ε is the stirring energy, W/t. |
[16] |

Harada et al. | Developed a kinetic model including interactions among steel, slag, inclusion, alloy, and refractory to calculate compositional changes of steel, slag and inclusions | Mass transfer coefficient of the molten steel: Mass transfer coefficient of the slag: k_{s} = k_{m}/10where k is the mass transfer coefficient of the molten steel, m/s; _{m}k is the mass transfer coefficient of the slag, m/s; _{s}ε is the stirring energy, W/t. |
[9,10] |

Cicutti et al. | Established a kinetic model between steel and slag to investigate the influence of different parameters on the variations of inclusions | Expression of the stirring energy: Mass transfer coefficient of the molten steel: k_{s} = 0.00001ϵ^{0.5}where k is the mass transfer coefficient of the slag, m/s; _{s}ε is the stirring energy, W/t; Q is the argon flow rate, which is expressed at standard conditions, m^{3}/s; W is the weight of the molten steel, t; h is the ladle height, m; _{L}T is the absolute temperature of the argon, K; _{0}T is the absolute temperature of the molten steel, K._{S} |
[6] |

Bastida et al. | Calculated composition changes during the refining process using coupled reaction model and obtained the relationship between the mass transfer coefficient and the stirring energy dissipation | Expression of the stirring energy: Mass transfer coefficient of the molten steel: k_{m} = 0.013ϵ^{0.25} for ε < 60 W/tk_{m} = 8 × 10^{−6}ϵ^{2.1} for ε>60 W/twhere ε is the stirring energy, W/t; Q is the argon flow rate, which is expressed at standard conditions, m^{3}/s; W is the weight of the molten steel, t; h is the ladle height, m; _{L}T is the absolute temperature of the argon, K; _{0}T is the absolute temperature of the molten steel, K; _{S}k is the mass transfer coefficient of the molten steel, m/s._{m} |
[5] |

Kang et al. | Studied the SiO_{2} and Al_{2}O_{3} content changes in mold flux using double-film theory |
Mass transfer coefficient of Al in the film layer at 1773 K: 0.9 × 10 ^{−4} m/s to 1.2 × 10^{−4} m/s |
[8] |

Shin et al. | Established a refractory-slag-metal-inclusion model to predict the evolution of inclusion during the refining process | Mass transfer coefficient of MgO in slag: 5.0 × 10^{−6} m/s |
[1] |

Ende et al. | Proposed an effective equilibrium reaction zone model using Factsage macro processing to simulate the compositional changes of steel and inclusions in ladle furnace as well as in the RH degassing process | Expression of the stirring energy: Mass transfer coefficient of the molten steel: k_{m} = 0.006ϵ^{1.4}where k is the mass transfer coefficient of the molten steel, m/s; _{m}ε is the stirring energy, W/t; R is the ideal gas constant, J/(mol · K); W is the weight of the molten steel, t; n is the molar gas flow rate, mol/s; T is the temperature of the molten steel, K; P is the total gas pressure at the base of the ladle, Pa; _{t}P is the gas pressure ar the surface of the molten steel, Pa._{0} |
[3,11] |

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