# An Improved Dynamic Model of the Vanadium Extraction Process in Steelmaking Converters
## 3 Numerical Simulation and Discussion
At the end of vanadium extraction, the mass fraction of \([V]\) and \([\mathrm{Ti}]\) were approximately parallel to the horizontal axis, which implies that the oxidation of \([V]\) and \([\mathrm{Ti}]\) had been approximately completed. The remaining \([\mathrm{Si}]\) and \([\mathrm{Mn}]\) in the molten pool are continuously oxidized in the steelmaking process. Figure 4: The mass fractions \([1]\) of \([C]\) and \([V]\) (external production data). Figure 3c shows that the mass fraction of \(\rm[Fe]\) kept increasing with the oxidation of \(\rm[V]\), \(\rm[Ti]\), \(\rm[Si]\), and \(\rm[Mn]\). The reason for this is that a lot of \(\rm[Fe]\) is generated constantly with the consumption of \(\rm(FeO)\), which is then fed back to the molten steel. Figure 3d shows that the mass fraction of \(\rm[O]\) decreased first, then gradually rose to a higher level. This implies that some \(\rm[O]\) and \(\rm[Fe]\) combined to supply the oxidants \(\rm(FeO)\) at the beginning of vanadium extraction process. With the increase of \(\rm(FeO)\) generated by the top-blown oxygen, the \(\rm(FeO)\) decomposed to improve \(\rm[O]\); that is, the mass fraction of \(\rm[O]\) consequently increased. The composition of the slag is shown in Figure 3.0 Figure 5a shows that the curves of \(\rm(TiO_{2})\), \(\rm(SiO_{2})\), and \(\rm(V_{2}O_{3})\) quickly reached their respective maxima, then decreased gradually. However, the curve of \(\rm(MnO)\) was relatively flat, indicating that \(\rm[Ti]\), \(\rm[Si]\), and \(\rm[V]\) were more easily oxidized than \(\rm[Mn]\). Figure 5b shows that the content of \(\rm(FeO)\) was higher at first, reached its lowest level in the intermediate stage, and gradually recovered in the latter period. The reasons for this are that:  
1. At the beginning of vanadium extraction process, with the rapid formation of the gas-liquid interface of the impact pit, plenty of \(\rm(FeO)\) were generated through the oxidation reaction (1). Then, the \(\rm(FeO)\) took part in the oxidation reaction at the slag-metal interface and in the emulsion system as an oxidant. At that time, the slag-metal interface and the emulsion system were at the beginning of generation, and the contact areas of the corresponding oxidation reactions were small. So, the consumption of \(\rm(FeO)\) was not large. 2. During the vanadium extraction process, with the formation of the slag-metal interface and the emulsion system, the oxidation rates of \(\rm[C]\), \(\rm[V]\), \(\rm[Ti]\), \(\rm[Si]\), and \(\rm[Mn]\) continually increased. As \(\rm(FeO)\) was largely consumed as an oxidant, the content of \(\rm(FeO)\) reduced significantly. 3. At the end of vanadium extraction process, with a decrease of \(\rm[V]\), \(\rm[Ti]\), \(\rm[Si]\), and \(\rm[Mn]\), the consumption of \(\rm(FeO)\) also decreased. As \(\rm(FeO)\) was generated continually at the gas-liquid interface of the impact pit, the content of \(\rm(FeO)\) then recovered. The oxidation rates of each element were Figure 3.1 and the oxygen consumption ratios of each element were Figure 3.2 and Figure 3.3 and Figure 3.4 and Figure 3.5 respectively. Figure 3.6 Composition changes of the slag. Figure 3.7 Figure 3.8 Figure 3.9 \[\omega_{[C]} \geq 3.2\%,\]0  
where  
\[\omega_{[C]} \geq 3.2\%,\]1  
Figure 6 shows that:  
1. At the beginning of vanadium extraction process, the order of oxidation rates of each element was \(v_{[\mathrm{Ti}]}>v_{[\mathrm{Si}]}>v_{[\mathrm{V}]}>v_{[\mathrm{Mn}]}\). This indicates that the oxygen was mainly used to oxidize \([\mathrm{Ti}]\), \([\mathrm{Si}]\), and \([\mathrm{V}]\) in the early stage; only a small amount of oxidant was used to oxidize \([\mathrm{Mn}]\). As the Gibbs free energy of \([\mathrm{Ti}]\) can be large, its oxygen consumption ratio decreased gradually. The reason for this is that its concentration decreased rapidly, making its oxidation reaction most violent in the beginning. 2.