*3.5. Thermodynamic Equilibrium Analysis*

#### 3.5.1. The Interactions of Zn with S

The effect of S on the thermodynamic equilibrium distributions of Zn in the coke was investigated, as shown in Figure 7. When only ZnO exists in the coal, ZnO is reduced by carbon to generate metallic Zn vapor at the temperature range of 500–700 ◦C with 0.01 wt.% of Zn content (0.0019 mol/kg coal), as displayed in Figure 7a. As the Zn content is increased to 4 wt.% (0.62 mol/kg coal), the stability of ZnO is improved, which decomposes at the temperature range of 600–900 ◦C (Figure 7b). It is found that the generated amount of CO after the addition of ZnO is 0.62 mol more than that of the base coal (Figure 7c), so the reaction of ZnO and carbon produces CO gas, as described in Reaction (1). When the Zn content is 0.01 wt.% (0.0019 mol/kg coal), the presence of S (0.24 mol/kg coal) suppresses the volatilization of Zn due to the formation of ZnS, which is further reduced to gaseous Zn by carbon at 700–1000 ◦C (Figure 7d). ZnO and ZnS coexist in the coke as the Zn content is 4 wt.% (0.62 mol/kg coal). The gaseous Zn is produced at 600 ◦C by the reduction of ZnO and ZnS, which starts to decompose at 900 ◦C. Some ZnS undergo crystal phase transformation at 1000–1200 ◦C, from sphalerite ZnS(s) to wurtzite ZnS(s2) and are completely reduced to Zn vapor at 1200 ◦C (Figure 7e). The thermodynamic equilibrium distributions of Zn with the Zn contents of 0.02 wt.% (0.0052 mol/kg coal), 0.1 wt.% (0.0182 mol/kg coal) and 0.8 wt.% (0.12 mol/kg coal) are also calculated and displayed in Figure S1, further demonstrating that the thermal stabilities of ZnO and ZnS are enhanced with the increase of Zn content.

**Figure 7.** *Cont.*

**Figure 7.** The thermodynamic equilibrium distributions of Zn (**a**–**e**) and generated amount of CO (**c**) when S and Zn coexist in the coal.

$$\text{ZnO} + \text{C} \rightarrow \text{Zn(g)} + \text{CO(g)}\tag{1}$$

3.5.2. The Interactions of Zn with S and Ca

The effect of the co-existence of S and Ca on the thermodynamic equilibrium distribution of Zn was analyzed, as shown in Figure 8. When the Zn content is low (Zn/S/Ca = 0.0019/0.24/0.07), the Zn incorporates with S to form ZnS, which decomposes into gaseous Zn from 700 to 900 ◦C (Figure 8a). Additionally, Ca also combines with S to generate CaS at 400–500 ◦C, which is stable before 1500 ◦C (Figure 8b). When the amount of Zn is high (Zn/S/Ca = 0.62/0.24/0.07), CaO can react with ZnS at 800–900 ◦C to form CaS and gaseous Zn (Figure 8c,d). Meanwhile, 0.07 mol of CO gas is generated in this process (Figure 8e), as described in Reaction (2). The above results indicate that the presence of Ca reduces the stability of ZnS and promotes the volatilization of Zn from coke. Consistent with the XRD results, CaS can be detected in the coke generated at 700 ◦C when the Zn content is low (0.0019 mol/kg coal), while CaS is only formed in the coke obtained at 900 ◦C when the Zn content is high (0.62 mol/kg coal).

$$\text{CaO} + \text{ZnS} + \text{C} \to \text{CaS} + \text{Zn(g)} + \text{CO(g)}\tag{2}$$

**Figure 8.** The thermodynamic equilibrium distributions of Zn (**a**,**c**), Ca (**b**,**d**) and generated amount of CO (**e**) when S, Zn and Ca coexist in the coal.

3.5.3. The Interactions of Zn with S and Fe

The influence of the co-existence of S and Fe on the thermodynamic equilibrium distributions of Zn is displayed in Figure 9. When the Zn content is low (Zn/S/Fe = 0.0019/0.24/0.06), ZnS is formed and reduced by carbon to gaseous Zn at the temperature range of 700–1000 ◦C (Figure 9a). Fe combines with S to form FeS2 (pyrite), FeS2 is transformed to FeS(s) (monoclinic pyrrhotite) at 200–300 ◦C, FeS(s) is converted to FeS(s2) (hexagonal pyrrhotite) at 300–400 ◦C, and FeS(s2) reacts with carbon to form Fe3C (cementite) at 1300–1500 ◦C (Figure 9b). When the Zn content is high (Zn/S/Fe = 0.62/0.24/0.06), Fe combines with partial Zn to form ZnFe2O4 (Figure 9c), as indicated in Reaction (3). ZnFe2O4 decomposes into ZnO and Fe3O4 at 400–500 ◦C. Fe3O4 is continuously reduced to FeO and elemental Fe by carbon at 500–700 ◦C, then Fe reacts with carbon at 800–900 ◦C to form Fe3C. Fe3C is further transformed to FeS at 1000–1100 ◦C, meanwhile, the ZnS is decomposed to metallic Zn gas, finally, FeS is converted to Fe3C at 1300–1500 ◦C (Figure 9d). The above results demonstrate that the presence of Fe has no effect on the interaction of Zn and S. In addition, when Fe and Ca coexist in coal, compared with the case where only Fe or Ca exists, the phase distributions of Zn and Ca do not change within 100–1500 ◦C, but the stability of FeS becomes worse. The FeS is transformed to Fe3C from 1200 ◦C, as shown in Figure S2.

$$\text{ZnO} + \text{Fe}\_2\text{O}\_3 \to \text{ZnFe}\_2\text{O}\_4\tag{3}$$

**Figure 9.** The thermodynamic equilibrium distributions of Zn (**a**,**c**) and Fe (**b**,**d**) when S, Zn and Fe coexist in the coal.

#### 3.5.4. The Interactions of Zn with Si

The thermodynamic equilibrium distributions of Zn and Si as Zn and Si coexist in the coal are displayed in Figure 10. When the Zn content is low (Zn/Si = 0.0019/0.53), partial Si combines with Zn to form Zn2SiO4 (Reaction (4)), which is further reduced to gaseous Zn by carbon at 600–800 ◦C (Reaction (5)), as shown in Figure 10a. SiO2(s) (α-quartz) is converted to SiO2(s2) (β-quartz) at 500–600 ◦C, SiO2(s2) is transformed to SiO2(s3) (tridymite) at 800–900 ◦C and partial SiO2(s3) reacts with carbon to form SiO(g) and CO(g) at 1300–1500 ◦C (Reaction (6)), and SiC(s) and CO(g) at 1400–1500 ◦C (Reaction (7)), respectively (Figure 10b). When the Zn content is high (Zn/Si = 0.62/0.53), the stability of

Zn2SiO4 is improved. It reacts with carbon to generate SiO2(s2) and Zn(g) at 700–800 ◦C and SiO2(s3) and Zn(g) at 800–900 ◦C (Reaction (5)), respectively (Figure 10c,d). The phase transitions of Si at the temperature range of 900–1500 ◦C are the same as the condition of low Zn content (Figure 10d). When S and Si coexist in the system, as shown in Figure S3, Zn preferentially reacts with S to form ZnS. When the Zn content is high (molar ratio of Zn/S > 1), the excessive Zn combines with Si to generate Zn2SiO4, which is converted to SiO2(s2) and Zn(g) at 700–800 ◦C and SiO2(s3) and Zn(g) at 800–900 ◦C. In addition, SiO2(s3) can react with S and carbon to generate SiS(g) and CO(g) at 1200 ◦C (Reaction (8)). The generated amount of CO during the above processes is shown in Figure 10e.

$$\text{2ZnO} + \text{SiO}\_2 \rightarrow \text{Zn}\_2\text{SiO}\_4 \tag{4}$$

$$2\text{Zn}\_2\text{SiO}\_4 + 2\text{C} \to \text{SiO}\_2 + 2\text{Zn(g)} + 2\text{CO(g)}\tag{5}$$

$$\text{SiO}\_2 + \text{C} \to \text{SiO(g)} + \text{CO(g)}\tag{6}$$

$$2\text{SiO}\_2 + 3\text{C} \rightarrow \text{SiC} + 2\text{CO(g)}\tag{7}$$

$$\text{SiO}\_2 + \text{S} + 2\text{C} \to \text{SiS}(\text{g}) + 2\text{CO}(\text{g}) \tag{8}$$

**Figure 10.** *Cont.*

**Figure 10.** The thermodynamic equilibrium distributions of Zn (**a**,**c**), Si (**b**,**d**) and generated amount of CO (**e**) when Zn and Si coexist in the coal.

#### 3.5.5. The Interactions of Zn with Al

The interactions of Zn and Al were also investigated, as shown in Figure 11. When the Zn content is low (Zn/Al = 0.0019/0.46), partial Al combines with Zn to form ZnAl2O4(s) (Reaction (9)), and ZnAl2O4 is reduced to gaseous Zn and Al2O3(s) by carbon at 600–800 ◦C (Reaction (10)), as shown in Figure 11a,b. When the Zn content is high (Zn/Al = 0.62/0.46), Zn exists as ZnO(s) and ZnAl2O4(s), which are reduced to Zn(g) by carbon at 600–900 and 900–1000 ◦C (Figure 11b,c), respectively, suggesting that the stability of ZnAl2O4 is higher than that of ZnO and that the existence of Al inhibits the volatilization of Zn from coke. The reaction of ZnAl2O4 and carbon can also produce CO gas, and the generated amount of CO is shown in Figure 11e, which is the same as the condition that only ZnO exists. When S and Al coexist in the system, as shown in Figure S4, Zn preferentially reacts with S to form ZnS. When the Zn content is high, Zn exists in the form of ZnS, ZnAl2O4 and ZnO, which are decomposed at the temperature range of 900–1200, 800–1000 and 600–800 ◦C, respectively. Consistent with the XRD results, ZnAl2O4 can be detected in the coke obtained at 900 ◦C when the Zn content is high (molar ratio of Zn/S > 1).

$$\text{ZnO} + \text{Al}\_2\text{O}\_3 \rightarrow \text{ZnAl}\_2\text{O}\_4 \tag{9}$$

$$\text{ZnAl}\_2\text{O}\_4 + \text{C} \to \text{Al}\_2\text{O}\_3 + \text{Zn(g)} + \text{CO(g)}\tag{10}$$

**Figure 11.** *Cont.*

**Figure 11.** The thermodynamic equilibrium distributions of Zn (**a**,**c**), Al (**b**,**d**) and generated amount of CO (**e**) when Zn and Al coexist in the coal.

#### 3.5.6. The Interactions of Zn with Si and Al

The effect of the co-existence of Si and Al on the thermodynamic equilibrium distributions of Zn was also investigated, as shown in Figure 12. When the Zn content is low (Zn/Si/Al = 0.0019/0.53/0.46mol), Zn combines with Al to form ZnAl2O4(s) (Figure 12a), indicating that Al is easier to react with Zn than Si. The Si and residual Al exists as (Al2O3)(SiO2)2(H2O)2(s) (kaolinite) and SiO2(s), and (Al2O3)(SiO2)2(H2O)2(s) decomposes into Al2SiO5(s) (kyanite) and SiO2(s) at 100–200 ◦C. Then Al2SiO5(s) (kyanite) transforms to Al2SiO5(s2) (andalusite) at 200–300 ◦C, and SiO2(s) (α-quartz) converts into SiO2(s2) (β-quartz) at 500–600 ◦C (Figure 12c). The Al2SiO5(s2) (andalusite) decomposes into Al6Si2O13(s) and SiO2(s2) at 700–800 ◦C (Figure 12c,e), as described in reaction (11). Additionally, Al6Si2O13(s) reacts with carbon to form Al2O3(s), SiC(s) and CO(g) at 1400–1500 ◦C (reaction (12)). When Zn content is high (Zn/Si/Al = 0.62/0.53/0.46), Zn combines with Al to form ZnAl2O4(s) and partial Si to generate Zn2SiO4(s) (Figure 12b). Zn2SiO4 is reduced by carbon to generate SiO2(s2) and gaseous Zn at 700–900 ◦C (Figure 12b,d). Additionally, ZnAl2O4 reacts with SiO2(s3) and carbon to generate Al6Si2O13(s), Zn(g) and CO(g) at 900–1000 ◦C (Figure 12b,d,f), as described in reaction (13). The generated amount of CO in the reactions (12) and (13) is shown in Figure 12g. When S is present in the system, Zn preferentially reacts with S to form ZnS and the excess Zn combines with Al and Si to generate ZnAl2O4 and Zn2SiO4, respectively, as shown in Figure S5. There is no change in the phase distributions of Al and Si except for the formation of SiS(g) at 1200 ◦C. The standard-state Gibbs free energies (Δ*rG<sup>θ</sup> <sup>m</sup>*) as a function of temperature for reactions (1)–(13) are calculated by FactSage 8.0 and listed in Table S2 and Figure S6. When the Gibbs free

energy is negative, the reaction is spontaneous. It is shown that the favored temperature ranges for different reactions are consistent with the generation sequence of corresponding products discussed above.

$$\text{Al}\_2\text{SiO}\_5 \to \text{Al}\_6\text{Si}\_2\text{O}\_{13} + \text{SiO}\_2 \tag{11}$$

$$\text{Al}\_6\text{Si}\_2\text{O}\_{13} + 6\text{C} \to 3\text{Al}\_2\text{O}\_3 + 2\text{SiC} + 4\text{CO(g)}\tag{12}$$

$$\text{3ZnAl}\_2\text{O}\_4 + \text{2SiO}\_2 + \text{3C} \rightarrow \text{Al}\_6\text{Si}\_2\text{O}\_{13} + \text{3Zn(g)} + \text{3CO(g)}\tag{13}$$

**Figure 12.** *Cont.*

**Figure 12.** The thermodynamic equilibrium distributions of Zn (**a**,**b**), Si (**c**,**d**), Al (**e**,**f**) and generated amount of CO (**g**) when Zn, Si and Al coexist in the coal.

#### 3.5.7. The Interactions of Zn with Ca and Al

The effect of the co-existence of Ca and Al on the phase distributions of Zn was investigated, as shown in Figure 13. When the Zn content is low (Zn/Ca/Al = 0.0019/0.07/0.46), Zn combines with Al to form ZnAl2O4, which decomposes to gaseous Zn at 600–800 ◦C (Figure 13a). CaAl4O7(s) and CaAl12O19(s) are formed by the interaction between Ca and Al at 400 ◦C, which exists stably at high temperatures (Figure 13c,e). When the Zn content is high (Zn/Ca/Al = 0.62/0.07/0.46), Zn exists as ZnO and ZnAl2O4, and partial ZnAl2O4 begins to decompose at 600–700 ◦C (Figure 13b), and the generated Al species combines with Ca to form Ca3Al2O6 (Figure 13d,f). Ca3Al2O6 transforms into CaAl4O7 at 800–900 ◦C, and part of CaAl4O7 converts into CaAl12O19 at 900–1000 ◦C. The above results show that there is a competitive relationship between Ca and Zn in the interaction of Al. Below 600 ◦C, Zn preferentially reacts with Al to generate ZnAl2O4. With the increase in temperature, Ca begins to plunder Al to form Ca aluminate. When S is also present in the above system (Figure S7), ZnS is generated as the Zn content is low (Zn/S/Ca/Al = 0.0019/0.24/0.07/0.46). CaAl12O19 and CaS are formed at 400–500 ◦C, and CaAl12O19 begins to decompose and reacts with S to form CaS and Al2O3 at 700–800 ◦C. When the Zn content is high (Zn/S/Ca/Al = 0.62/0.24/0.07/0.46), Zn exists as ZnS, ZnAl2O4 and ZnO. ZnAl2O4 decomposes into ZnO at 600–700 ◦C and gaseous Zn at 700–1000 ◦C, respectively. Meanwhile, Ca3Al2O6 is generated at 600–700 ◦C, and partial Ca3Al2O6 transforms into CaAl2O4 at 700–800 ◦C, then the residual Ca3Al2O6 and CaAl2O4 converts into CaAl4O7 at 800–900 ◦C. Subsequently, part of CaAl4O7 turns into CaAl12O19 at 900–1000 ◦C, and the remaining CaAl4O7 and CaAl12O19 combine with S to form CaS and Al2O3 at 1000–1100 ◦C.

#### 3.5.8. The Interactions of Zn with S, Ca, Al, Si and Fe

Finally, when Zn, Ca, Al, Si and Fe are simultaneously present in the coal, their phase distributions are displayed in Figure 14 and Figure S8. As the Zn content is low (Zn/S/Ca/Al/Si/Fe = 0.0019/0.24/0.07/0.46/0.53/0.06), Zn still interacts with S to generate ZnS, which turns into gaseous Zn at 700–1000 ◦C (Figure 14a). The reactions among Ca, Si and Al are complex. CaAl2Si2O7(OH)2(H2O), (CaO)2(Al2O3)2(SiO2)8(H2O)7 and (Al2O3)(SiO2)2(H2O)2 all transform into CaAl4Si2O10(OH)2 and Al2SiO5(s) (kyanite) at 100–200 ◦C, and CaAl4Si2O10(OH)2 decomposes into CaAl2Si2O8 and Al2SiO5(s2) (andalusite) at 200–300 ◦C (Figure 14b,c). Meanwhile, the Al2SiO5(s) (kyanite) also transforms into Al2SiO5(s2) (andalusite) at 200 ◦C, and Al2SiO5(s2) (andalusite) converts into Al6Si2O13(s) at 700–800 ◦C (Figure 14c). A small amount of CaAl2Si2O8 decomposes and CaS is generated from 1400 ◦C (Figure 14b–d). At 1400–1500 ◦C, Al6Si2O13 transforms into Al2O3 and SiC under the action of carbon (Figure 14c,d). The phase distribution of Fe at high temperatures is affected by the presence of Si. Fe3C turns into FeSi at 1400–1500 ◦C (Figure 14e). When the Zn content is high (Zn/S/Ca/Al/Si/Fe = 0.62/0.24/0.07/0.46/0.53/0.06), Zn exists as ZnS, ZnAl2O4 and Zn2SiO4, as shown in Figure S8. Two-step decompositions at 200–500 and 800–1000 ◦C are observed for ZnAl2O4, in which the ZnAl2O4 converts into Zn2SiO4 and gaseous Zn, respectively (Figure S8a). Ca3Fe2Si3O12 and CaFeSi2O6 are formed at 100–200 and 100–300 ◦C, respectively. Ca3Fe2Si3O12 transforms into CaFeSi2O6 and Ca3Al2Si3O12 at 200–300 ◦C with a little decrease in ZnAl2O4 (Figure S8b,c). Then Ca3Al2Si3O12 converts into CaAl2Si2O8 at 300–400 ◦C along with consumption of ZnAl2O4 and SiO2(s) (Figure S8c,d). Subsequently, CaFeSi2O6 turns into CaAl2Si2O8 and Fe2SiO4 at 400–500 ◦C, accompanied by the decomposition of ZnAl2O4. Fe2SiO4 decomposes into elemental Fe and SiO2(s2) at 700–800 ◦C (Figure S8d,e). The elemental Fe combines with carbon to produce Fe3C at 800–900 ◦C, which then transforms to FeS at 1000–1100 ◦C. The FeS decomposes and Fe3C is formed again at 1300–1400 ◦C, which finally converts into FeSi at 1400–1500 ◦C.

**Figure 13.** Thermodynamic equilibrium distributions of Zn (**a**,**b**), Ca (**c**,**d**) and Al (**e**,**f**) when Zn, Ca and Al coexist in the coal.

**Figure 14.** Thermodynamic equilibrium distributions of Zn (**a**), Ca (**b**), Al (**c**), Si (**d**) and Fe (**e**) in the coal when the Zn content is low (Zn/S/Ca/Al/Si/Fe = 0.0019/0.24/0.07/0.46/0.53/0.06).

Consistent with the XRD results, when the Zn content is low (molar ratio of Zn/S < 1), ZnS and SiO2 are the main minerals in the obtained coke, and ZnS, ZnAl2O4 and SiO2 can be detected when the Zn content is high (molar ratio of Zn/S > 1). In addition, CaS is present in the coke whatever the Zn content, which is not the situation as predicted by the thermodynamic equilibrium simulations. It is deduced that there is limited contact of Ca with Al and Si species in the coal, so the Ca preferentially combines with S dispersed in the coal matrix to generate CaS. Moreover, ZnO is found in the coke obtained at 700 ◦C, while the theoretically predicted Zn2SiO4 is not detected, which should be due to the physical

isolation of Zn from Si in the coal or the crystallite size of generated Zn2SiO4 being too small to be detected by the XRD measurement. Based on the above analysis, the Zn species in the blends of coal and waste tires can migrate to the gas products in the form of gaseous Zn via a carbothermal reduction reaction during pyrolysis. The formation temperature of gaseous Zn is dependent on the contents of Zn, S and mineral elements in coal. The S, Al and Si can interact with Zn to inhibit the volatilization of Zn from coke. The reaction sequence with Zn is S > Al > Si, and the thermal stability of products is in the order of ZnS > ZnAl2O4 > Zn2SiO4. The decomposition of ZnS, ZnAl2O4 and Zn2SiO4 can occur in the temperature range of 700–1200, 600–1000 and 600–900 ◦C, respectively. Moreover, Fe and Ca can also bind with S to form metal sulfides, but their interactions are weaker than that of Zn with S and ZnS can be preferentially formed. In actual industrial production, the central temperature of coke cake produced in the coke oven is controlled at 950–1050 ◦C to ensure sufficient strength, so most of the Zn species can escape from the coke, which may be detrimental to the refractory bricks of the coke oven. Additionally, the deposition of Zn also increases the risk of clogging of ascension pipe that is used for the discharge of coke oven crude gas.

Although the transformation mechanisms described above are concentrated on the co-pyrolysis process of waste tires and coal, the corresponding rules are also suitable to understand the thermochemical behaviors of Zn in systems containing C, S, Ca, Al, Si and Fe under an inert atmosphere. Particularly, except for Zn, the contents of S and other inorganic components such as Ca, Al, Si and Fe are appreciable in the waste tires [34,61–63], which is also verified by our analysis results (see Table 2). Therefore, the conclusions from this study can also provide insights into the migration characteristics of Zn during the pyrolysis of waste tires alone, which is vital to the prevention and control of Zn emission to reduce the environmental burden.

### **4. Conclusions**

In this paper, the transformation behaviors of Zn during co-pyrolysis of waste tires and coal were studied in a fixed-bed reactor system. It is shown that the relative percentage of Zn in the pyrolytic products (coke, tar and gas) obtained at different temperatures is closely related to the content of S and mineral elements (Ca, Al, Si and Fe) in the coal. When the molar ratio of Zn to S is less than 1, ZnS is formed in the coke obtained at 700 ◦C, resulting in ca. 97% of Zn residual rate in the coke. As the pyrolysis temperature increases to 900 and 1050 ◦C, ZnS is reduced to metallic Zn vapor by carbon, so the residual rate of Zn in coke decreases and the percentage of Zn in the tar increases. When the molar of Zn exceeds that of S, ZnO and ZnS coexist in the coke produced at 700 ◦C and partial ZnO is reduced to gaseous Zn by carbon, causing a small decrease in Zn residual rate in coke. Excess ZnO can react with Al2O3 to generate ZnAl2O4 at 900 ◦C, resulting in the enhancement of the Zn residual rate in coke (50%). Additionally, ZnAl2O4 can also be reduced by carbon to generate gaseous Zn at 1050 ◦C, giving rise to a reduction of the Zn residual rate in coke to 10%. The thermodynamic equilibrium simulations show that the formation temperature of gaseous Zn is dependent on the contents of Zn, S and mineral elements in coal. The S, Al and Si can interact with Zn to inhibit the volatilization of Zn from coke in the sequence of S > Al > Si, and the thermal stability of products is in the order of ZnS > ZnAl2O4 > Zn2SiO4. The decompositions of ZnS, ZnAl2O4 and Zn2SiO4 into Zn vapor occur in the temperature range of 700–1200, 600–1000 and 600–900 ◦C, respectively. Based on the above analysis, most Zn species can escape from the coke during the industrial cokemaking process, which is harmful to the refractory materials of the coke oven and brings the risk of blockage of ascension pipe due to the deposition of Zn. The Zn transformation mechanisms studied in this work are applicable not only for the co-pyrolysis of coal and waste tires but also for the pyrolysis of waste tires alone.

**Supplementary Materials:** The following supporting information can be downloaded at: https: //www.mdpi.com/article/10.3390/pr10081635/s1, Figure S1: Thermodynamic equilibrium distributions of Zn when S and Zn coexist in the coal; Table S1: Mass distributions of Zn in the pyrolytic products; Figure S2: The thermodynamic equilibrium distributions of Zn (a, b), Ca (c, d) and Fe (e, f) when S, Zn, Ca and Fe coexist in the system; Figure S3: The thermodynamic equilibrium distributions of Zn (a, c) and silicon (b, d) when S, Zn and Si coexist in the system; Figure S4: The thermodynamic equilibrium distributions of Zn (a, c) and Al (b, d) when S, Zn and Al coexist in the system; Figure S5: Thermodynamic equilibrium distributions of Zn (a, b), Si (c, d) and Al (e, f) when S, Zn, Si and Al coexist in the system; Table S2: Standard Gibbs free energies of typical reactions; Figure S6: The standard-state Gibbs free energies of reactions 1−13 as a function of temperature; Figure S7: Thermodynamic equilibrium distributions of Zn (a, b), Ca (c, d) and Al (e, f) when S, Zn, Ca and Al coexist in the system; Figure S8: Thermodynamic equilibrium distributions of Zn (a), Ca (b), Al (c), Si (d) and Fe (e) in the coal when the Zn content is high (Zn/S/Ca/Al/Si/Fe =0.62/0.24/0.07/0.46/0.53/0.06).

**Author Contributions:** Conceptualization, S.J. and M.J.; methodology, S.J. and Y.L.; software, S.J. and Y.L.; validation, S.J., Y.L. and X.W.; formal analysis, Y.L., J.W., X.W. and R.Z.; investigation, Y.L., J.W., X.W. and R.Z.; resources, J.W. and L.L.; data curation, S.J. and Y.L.; writing—original draft preparation, Y.L.; writing—review and editing, S.J.; visualization, S.J. and Y.L.; supervision, L.L. and M.J.; project administration, M.J.; funding acquisition, L.L. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the National Natural Science Foundation of China [No. U1710252].

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data used to support the findings of this study are available from the corresponding author upon request.

**Acknowledgments:** This work was financially supported by the National Natural Science Foundation of China (No. U1710252).

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

#### **References**


**Chengjian Hua, Yanping Bao \* and Min Wang**

State Key Laboratory of Advanced Metallurgy, University of Science and Technology Beijing, Beijing 100083, China

**\*** Correspondence: baoyp@ustb.edu.cn

**Abstract:** The argon-stirred ladle is a standard piece of steelmaking refining equipment. The molten steel quality will improve when a good argon-stirred process is applied. In this paper, a Multiphysics model that contained fluid flow, bubble transport, alloy transport, bubble heat flux, alloy heat flux, alloy melting, and an alloy concentration species transport model was established. The fluid model and bubble transport model that were used to calculate the fluid velocity were verified by the hydraulic model of the ladle that was combined with particle image velocimetry measurement results. The numerical simulation results of the temperature fields and steel–slag interface shape were verified by a ladle that contained 25 t of molten steel in a steel plant. The velocity difference between the hydraulic model and numerical model decreased when the *CL* (integral time-scale constant) increased from 0 to 0.3; then, the difference increased when the *CL* increased from 0.3 to 0.45. The results showed that a *CL* of 0.3 approached the experiment results more. The bubble heat flux model was examined by the industrial practice, and the temperature decrease rate was 0.0144 K/s. The simulation results of the temperature decrease rate increased when the initial bubble temperature decreased. When the initial bubble temperature was 800 ◦C, the numerical simulation results showed that the temperature decrease rate was 0.0147 K/s, and the initial bubble temperature set at 800 ◦C was more appropriate. The average melting time of the alloy was 12.49 s and 12.71 s, and the mixture time was approximately the same when the alloy was added to two slag eyes individually. The alloy concentration had fewer changes after the alloy was added in the ladle after 100 s.

**Keywords:** argon-stirred ladle; particle image velocimetry; numerical simulation; fluid flow; bubble

#### **1. Introduction**

In metallurgy, the argon-stirred ladle is a low-cost, highly efficient, and common refining method for the improvement of the molten steel temperature, the homogeneity ofmolten steel concentration [1–9], inclusion floatation [10–16], and increase in the kinetic reaction [17–20] in the ladle.

Studies on the argon-stirred ladle numerical simulation have focused on the following topics: (1) fluid-flow simulation [21], (2) bubble transport modeling, (3) temperature simulation, (4) alloy melting, (5) alloy concentration or other species transport [22], and (6) kinetic reaction in the ladle. In the fluid-flow simulation, the Euler–Euler approach [23,24], the single-phase methods by exerting an additional force on the fluid flow [25–27], the multiphase volume of fluid (VOF) method [2,28–30], and the Euler–Lagrange method [31–33] considered the bubble as a discrete phase and the molten steel and molten slag as the continuum phase. In the bubble transport modeling, Xue et al. [34] studied the effect of small bubbles on inclusion removal, and the results showed that the small bubble is beneficial to inclusion removal. Zhu et al. [35] studied the effect of an argon-stirred ladle on the inclusion removal, and the results showed that a larger size of inclusion will be removed more quickly and the difficulty of the inclusion removal will increase when the inclusion diameter decreases. In the molten steel temperature simulation, Urióstegui-Hernández [36] considered the heat transfer between the fluid and the bubble using the

**Citation:** Hua, C.; Bao, Y.; Wang, M. Multiphysics Numerical Simulation Model and Hydraulic Model Experiments in the Argon-Stirred Ladle. *Processes* **2022**, *10*, 1563. https://doi.org/10.3390/pr10081563

Academic Editors: Elio Santacesaria, Riccardo Tesser and Vincenzo Russo

Received: 18 July 2022 Accepted: 3 August 2022 Published: 10 August 2022

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**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

Euler–Euler methods. Cheng et al. [37] studied the effect of the slot plug on the flow in the ladle and temperature exchange with the argon. In the alloy melting simulation, Bhattacharjee et al. [38] studied the alloy melting in the argon-stirred ladle by numerical simulation, and the results showed that dissolution rates are a function of gas flow rate and vessel dimensions and depend on the diffusivity of the alloy and initial size. In the alloy concentration or other species, Liu et al. [28] studied the species transport in the argon-stirred ladle, and monitoring the species concentration varies with solution time. In the kinetic reaction in the ladle studies, Kwon et al. [39] studied the Al-deoxidation in the argon-stirred ladle to predict the inclusion formation. Lachmund et al. [40] established a desulfurization model and predicted the desulphurization process by numerical simulation. Singh et al. [41] studied the desulfurization with kinetic data acquired from Thermo-Calc software, and the results showed that dual plugs are better than a single plug when the flow is the same.

Recently, Mantripragada [36] studied the argon plugs' position and flow rate on the argon-stirred ladle refined by numerical simulation. They pointed out a dimensional variation in the optimized ladle. Wondrak et al. [42] used Sn-Bi alloy in industrial experiments, and the results showed the 'slag eye' size and velocity magnitude in the molten alloy surface. The experimental results will benefit the numerical simulation optimization. Uriostegui-Hernandez et al. [43] studied the fluid flow and mass transfer of sulfur; the results showed that the desulfurization rates increase as the argon gas flow rate increases. Wang et al. [44] studied the effect of the argon-stirred process on the ladle refractory erosion by numerical simulation and industrial practice. The results showed that the refractory erosion will increase near the slag layer and near the bottom gas inlet. Joubert [45] studied the mass transfer of the species in the steel–slag phase in the argon-stirred ladle by a numerical simulation and a hydraulic model simulation. The results showed that the numerical simulation model of species transport showed good consistency with the hydraulic simulation. Guo et al. [16] studied the effect of plug position, argon flow rate, and inclusion size on the inclusion removal. The results showed that the inclusion removal rate will increase when the argon flow rate grows. Riabov et al. [46] studied the bubble diameter, plume area, and bubble velocity using a hydraulic model combined with particle image velocimetry technology. The results showed that the increase in the diameter of the porous plug will lead to a small bubble diameter and poorer mixing conditions. Li et al. [47] studied the bubble transport and fluid flow in an argon-stirred ladle by the volume of the fluid (VOF) model with a finer scale of mesh coupling with a sub-grid-scale large eddy simulation. The results showed that the slag eye size varies with time, and the bubble detachment frequency has a direct effect on the slag eyes. A new correlation of the slag eye and the modified Froude number was established.

In the previous work, the argon-stirred ladle that contained molten steel was 80~300 t. The tundish was applied in the argon-stirred ladle during the casting process. The tundish is helpful in the molten steel temperature, species homogeneity, and inclusion removal. However, there is no tundish in the casting process; when the argon-stirred steel that contained molten steel is about 25~30 t, the effect of molten steel temperature, species homogeneity, and fluid flow in the argon-stirred ladle is essential. In this paper, a numerical simulation model was established that contained a fluid flow simulation, bubble transport, alloy transport, alloy melting, alloy concentration species transport, and a bubble and alloy heat transfer simulation. In this paper, a random walk model was introduced to simulate the bubble transport and bubble drive flow novelty. The effect of random transport parameters on the bubble drive flow simulation was examined by particle image velocimetry results of the hydraulic model. The heat transfer model of the bubble and the molten steel was introduced for the first time, and the bubble heat transfer simulation was examined by industrial practice where the ladle contained 25 t of molten steel in a steel plant. The molten steel temperature distribution in the ladle was revealed for the first time. The effect of the alloy-added situation on the alloy concentration

diffusion was discussed. The numerical simulation model was helpful in the argonstirred ladle design and process modification.
