**3. Results and Discussion**

#### *3.1. Comparison of Predicted and Measured Titanium Distribution Ratios*

Comparisons between the calculated titanium distribution ratio *L*Ti,cal based on the IMCT and the measured *L*Ti,mea for CaO–SiO2–Al2O3–MgO–FeO–MnO–TiO2 slags balanced with liquid steel at 1853 K in the LF process are expounded in Figure 2. It reveals that the titanium distribution ratio predicted by the developed IMCT model exhibited a dependable agreement with the industrially measured results. Moreover, the predicted *L*Ti,cal values were all higher than the measured *L*Ti,mea, which was due to the fact that the calculated values were acquired in an ideal equilibrium state, while during actual industrial production, the slag-metal reaction was in a local equilibrium or quasi-equilibrium state.

**Figure 2.** Comparisons between measured and calculated titanium distribution ratios for CaO–SiO2–Al2O3–MgO–FeO–MnO–TiO2 slags.

To verify the accuracy of the IMCT model, the mean deviations (Δ) of predictions by the IMCT model can be calculated as

$$\Delta = \frac{1}{Z} \sum\_{n=1}^{Z} \left| \frac{\log L\_{\text{Ti,mean}} - \log L\_{\text{Ti,cal}}}{\log L\_{\text{Ti,mean}}} \right| \times 100\% = 6.29\% < 6.3\% \tag{12}$$

where *L*Ti,cal and *L*Ti,mea are the calculated and measured titanium distribution ratios, respectively; and Z denotes the number of measured data. The mean deviation was lower than 6.3%, indicating that the titanium distribution ratio model can responsibly predict the maximum de-titanium potential of CaO–SiO2–Al2O3–MgO–FeO–MnO–TiO2 slags balanced with liquid steel at 1853 K in LF refining, and it can provide guidance for the design of a refining slag system.
