## 2 Description of the HDRSF
### Main Chemical Reactions  
The main chemical reaction in the shaft furnace is the reduction reaction between H\({}_{2}\)/CO and iron ore. Existing studies have shown that the reduction of iron ore with H\({}_{2}\)/CO is a multi-stage process [35; 36; 37]. At T \(>\) 570 \({}^{\circ}\)C, the reduction step of iron ore with H\({}_{2}\)/CO is Fe\({}_{2}\)O\({}_{3}\)\(\rightarrow\)Fe\({}_{3}\)O\({}_{4}\)\(\rightarrow\)Fe. At T \(<\) 570 \({}^{\circ}\)C, the reduction step of iron ore with H\({}_{2}\)/CO is Fe\({}_{2}\)O\({}_{3}\)\(\rightarrow\)Fe\({}_{3}\)O\({}_{4}\)\(\rightarrow\)Fe. Additionally, according to the balance curve of the reduction of iron oxide with H\({}_{2}\)/CO, at T \(>\) 820 \({}^{\circ}\)C, the capacity of H\({}_{2}\) to reduce iron oxide is higher than that of CO [38]. In order to fully utilize the advantages of H\({}_{2}\) in terms of high reduction rate and low carbon emissions, the reduction temperature in the furnace is usually maintained above 820 \({}^{\circ}\)C. At this temperature, the reduction reaction in the HDRSF is shown in Equations (1)-(6) (for simplicity, wustite is represented by FeO).  
Chemical reaction formulas of Fe\({}_{2}\)O\({}_{3}\)\(\rightarrow\)Fe with H\({}_{2}\):  
\[3\text{Fe}_{2}\text{O}_{3}+\text{H}_{2}=2\text{Fe}_{3}\text{O}_{4}+\text{H}_{ 2}\text{O} \tag{1}\]  
Figure 1: Model of the HDRSF.  
\[\text{Fe}_{3}\text{O}_{4}+\text{H}_{2}=3\text{FeO}+\text{H}_{2}\text{O} \tag{2}\]  
\[\text{FeO}+\text{H}_{2}=\text{Fe}+\text{H}_{2}\text{O} \tag{3}\]  
Chemical reaction formulas of Fe2O3\(\rightarrow\)Fe with CO:  
\[3\text{Fe}_{2}\text{O}_{3}+\text{CO}=2\text{Fe}_{3}\text{O}_{4}+\text{CO}_{2} \tag{4}\]  
\[\text{Fe}_{3}\text{O}_{4}+\text{CO}=3\text{FeO}+\text{CO}_{2} \tag{5}\]  
\[\text{FeO}+\text{CO}=\text{Fe}+\text{CO}_{2} \tag{6}\]  
Table 1 shows the thermodynamic parameters of the reduction of iron oxide with H2/CO in the step of Fe2O3\(\rightarrow\)Fe3O4\(\rightarrow\)FeO\(\rightarrow\)Fe [24; 39], including the enthalpy change, Gibbs free energy, and equilibrium constant.  
In actual operation, the reactions in the shaft furnace are reversible, and the equilibrium constant is primarily influenced by temperature. The reduction of iron ore with H2/CO occurs in three stages, following the sequence of the third stage, then the second stage, and finally the first stage after the reducing gas inlets the furnace. The demand for reducing gas varies across different stages of the process. In theory, the equilibrium between gas supply and demand is typically achieved in at most one stage, with excess reducing gas being present in the remaining stages. According to the research of [PERSON] et al. [28], the demand for reducing gas is the greatest in the third stage of the reaction (the reaction in Equations (3) and (6)). The thermodynamic utilization rate of the reducing gas in the third stage can be calculated using Equation (7).  
\[\eta_{3}=x_{H_{2}}\times\frac{K_{3,H_{2}}}{1+K_{3,H_{2}}}+x_{CO}\times\frac{K_{ 3,CO}}{1+K_{3,CO}} \tag{7}\]  
where \(K_{3,H_{2}}\) and \(K_{3,CO}\) are the equilibrium constant of the third-stage reduction reaction with H2 and CO, respectively.  
Then, the amount of reducing gas demanded for the chemical reduction reaction to generate DRI that meets the process requirement can be calculated according to Equation (8).  
\[\frac{V_{reducing gas}}{22.4}\times\eta_{3}=\frac{W_{Fe}\times M_{DRI}}{56} \tag{8}\]