*3.2. Application of the Model*

The charging matrix determines the surface profile and internal structure of the burden column in the furnace. In this section, three different charging matrixes are used to study the effect of charging pattern on the burden distribution. Detailed data of the charging matrixes are listed in Table 4. The on-site charging pattern can be classified into three categories, including inner coal and outer ore (e.g., Case 1#), outer coal and inner ore (e.g., Case 2#), and co-location of coal ore (e.g., Case 3#).


**Table 4.** Data of charging matrixes.

The evolution of burden profiles under various charging matrixes is shown in Figure 9, where the respective initial stable burden surfaces are determined according to the physical experiment as described above. Taking Case 1 as an example, one charging period including two coal dumps and two DRI dumps, that is, the first coal dump is charged from center to wall, followed by the first DRI charging from center to wall, and then the second coal dump is charged from wall to center, followed by the second DRI charging from wall to center. As can be seen from the figure, the burden surface profile is higher in the center and lower near the wall. As the charging position of Case 3 is farther from the wall than that of Case 1 and Case 2, the original burden surface does not have a flat platform near by the wall. Therefore, the burden profile of Case 3 is relatively flat in the radial direction, and more material gets to the wall region, while the middle area thickness of the burden pile in Case 1 and Case 2 is relatively greater than that in Case 3.

The results of the ore/coal mass ratio distribution for different charging matrixes are shown in Figure 10. It can be seen from the figure that the charging pattern has a great influence on the radial ore/coal ratio distribution.

**Figure 9.** Evolution of burden surface profiles under different charging patterns. (**a**) Burden surface profile in Case 1; (**b**) Burden surface profile in Case 2; and (**c**) Burden surface profile in Case 3.

For Case 1, the charging region of coal is in the range of 2.0~4.5 m, and that of DRI is in the range of 3.0~4.5 m. Since the starting position of coal charging is closer to the furnace center than DRI, there is an ore-free region in the central area. The ore/coal ratio is zero before approximately 2.0 m, and then increases rapidly along the radial direction till *R* ≈ 4.75 m, and finally decreases in the wall region.

For Case 2, the charging region of coal is in the range of 2.5~4.5 m and that of DRI is in the range of 2.0~4.5 m. Therefore, the volume of ore distributed before the radial distance of 1.0 m (the DRI left ends of *R*2.0 in Table 3) is more than that of coal, and the ore/coal ratio is larger in this region than Case 1. In the region of 2.5~3.0 m, the relative coal increase rate is greater than DRI, so the ore/coal ratio decreases along radial direction. However, due to larger size and lighter mass, the coal particles tend to roll and are easily pushed to the descending region near the wall, so the ore/coal ratio is decreased near the furnace wall.

For Case 3, the charging regions of both coal and ore are in the same range of 2.0~4.0 m. Since the starting positions of coal and ore charging are the same, the ore/coal ratio distribution in the radial direction is relatively uniform in Case 3. In Case 1 and Case 2, the ore/coal ratio is relatively higher in the wall area, so the ore content or the coal load is larger, which may lead to a poor permeability of the burden bed.

**Figure 10.** Calculated radial ore/coal ratio distribution with different charging patterns.

#### **4. Conclusions and Future Perspectives**

Based on the previous physical experiment, a new approach was proposed to characterize the growing mechanism of burden surface with the width of burden flow arriving at the burden surface in the COREX MG. The validity of the model is demonstrated by comparing the simulated burden layer structure with the corresponding results obtained by physical experiments. The usefulness of the mathematical model is illustrated by performing a set of simulation cases under various charging matrixes. The main conclusions are as follows.

(1) A mathematical model for characterizing the layer structure has been established based on the burden flow width. Compared with physical experiment, the model prediction is reasonably reliable, and the model can be used to predict the burden distribution with the complicated charging system of gimbal and flaps.

(2) The model can be used to predict the radial distribution of ore/coal mass ratio with different charging matrixes. It can be seen that the charging matrix has a great influence on the radial ore/coal ratio distribution. The co-location charging of coal and ore results in the most uniform distribution of the ore/coal ratio in the radial direction.

In the future, the mathematical model will be further improved by considering the influences of coal pushing, mixing between layers, and burden column descending. It is hoped that the model can be used as a what-if tool in practice for the COREX operator to gain a better understanding of burden distribution in the COREX MG and to supply boundary conditions for a mathematical model of the COREX MG to be developed.

**Author Contributions:** Conceptualization, H.L., Z.L., and Z.Z.; data curation, H.L., Z.L., and W.L.; funding acquisition, Z.Z.; investigation, W.L. and L.S.; methodology, W.L.; project administration, Z.Z.; resources, Z.Z.; software, H.L. and W.L.; supervision, Z.Z.; writing—original draft, H.L.; writing—review and editing, Z.Z. and L.S.

**Funding:** This research was funded by the National Science Foundation of China grant number 51604068, 51574064 And the APC was funded by China Scholarship Council (CSC No. 201706085021).

**Acknowledgments:** Financial supports from the National Science Foundation of China (Grants 51604068, 51574064) and China Scholarship Council (CSC No. 201706085021) are gratefully acknowledged.

**Conflicts of Interest:** The authors declare no conflict of interest.
