Thermodynamic Study on Reduction of Iron Oxides by H2 + CO + CH4 + N2 Mixture at 900 °C

The reduction gas used in the gas-based direct reduction iron-making process contains CH4 in different concentrations, which has an important effect on the gas and heat needed for the reduction of iron oxide. To investigate the influence of CH4 on gas utilization rate and heat needed at 900 °C, the initial conditions are set as H2% + CO% = 90, CH4% + N2% = 10, gas pressure 1–9 atm, and 0.5 mol Fe2O3, and the equilibrium state composition is calculated using the minimum free energy method. The utilization rate of total gas can be improved, and gas demand can be decreased by increasing CH4 concentration or H2 concentration or reducing gas pressure. For the production of per ton of Fe from 25 °C to 900 °C, 6.08–7.29 m3 of reduction gas, and 7.338–8.952 MJ of gas sensible heat can be saved by increasing 1 m3 CH4, while 10.959–11.189 MJ of reaction heat is increased. Compared with 3390.828–3865.760 MJ of the total heat of per ton of Fe for the reduction by H2 + CO, 2.174–3.703 MJ of total heat is increased by increasing 1 m3 CH4, and the increase ratio is 0.065–0.096%. This study is helpful to improve the gas efficiency and lower the pursuit of higher concentration of H2 + CO in reduction gas.

The aim of this study is to investigate the effects of CH 4 concentration, gas pressure, H 2 or CO concentration on reduction gas needed, and reaction enthalpy at 900 • C with CH 4 concentration Energies 2020, 13, 5053 3 of 18 less than 10%. This study is helpful to understand the relationship between H 2 + CO and CH 4 in the process of reducing Fe 2 O 3 and even to improve the utilization rate of reducing gas by increasing the concentration of CH 4 .

Parameters Settings
The initial state and the equilibrium state are shown in Figure 1. The reaction system is composed of solid and gas. The initial solid is 0.5 mol Fe 2 O 3 , and other gangue in the iron ore are not considered in the reaction system. The initial gas volume fraction is as shown in Table 3. The volume fraction of H 2 + CO is fixed at 90%; namely, CO% + H 2 % = 90, which is a common gas composition requirement. For comparison, CO 2 gas and H 2 O gas in initial states are neglected in the mixed gas. The volume fraction of CH 4 gas increase from 0% to 10%, and the N 2 is residual.
0%. This study is helpful to understand the relationship between H2 + CO and CH4 in s of reducing Fe2O3 and even to improve the utilization rate of reducing gas by increasing tration of CH4. hods rameters Settings he initial state and the equilibrium state are shown in Figure 1. The reaction system sed of solid and gas. The initial solid is 0.5 mol Fe2O3, and other gangue in the iron ore nsidered in the reaction system. The initial gas volume fraction is as shown in Table 3. e fraction of H2 + CO is fixed at 90%; namely, CO% + H2% = 90, which is a common sition requirement. For comparison, CO2 gas and H2O gas in initial states are neglected in gas. The volume fraction of CH4 gas increase from 0% to 10%, and the N2 is residual.   he reaction temperature is 900 °C, which is used in the MIDREX process and HYL/Energ s [9,13]. The total gas pressure total p increases from 1 atm 9 atm, and 1 atm (atmosphere  The reaction temperature is 900 • C, which is used in the MIDREX process and HYL/Energiron process [9,13]. The total gas pressure p total increases from 1 atm 9 atm, and 1 atm (atmosphere) or 1 p is 101,325 Pa. The total pressure of the reaction system is set to remain unchanged before and after reactions. In fact, the gas pressure decreases from bottom to top of the shaft furnace due to the solid bulk layer. The amount of the initial gas is 10 mol, which exceeds the amount of gas required for reduction. For the reduction of 0.5 mol Fe 2 O 3 , the demand for reduction gas, composed of different concentrations of H 2 + CO, are 4.0-4.7 mol, which has been calculated by the minimum Gibbs free energy method [7]. For the H 2 + CO + CH 4 + N 2 gas mixture, the gas demand needs to be calculated under different conditions by the minimum Gibbs free energy method.

The Minimum Gibbs Free Energy Method
The minimum Gibbs free energy method can be used to calculate the amount of the components in the equilibrium state [7,14,15], which can be obtained from the initial state conditions (amount, temperature, and pressure). Based on the principle of minimum free energy; that is, the sum of Gibbs free energy of each component in the equilibrium state is the smallest, and a calculation model is established, as shown in Formulas (22) and (23). By solving the non-linear equations with constraints, the amount of each component in the equilibrium state could be received.
In this two formulas, i, e, represent the components and elements in the equilibrium state, respectively; N, M, represent the number of components and the number of elements in the equilibrium state, respectively; n i , n e , are the amounts of the components i and elements e in the equilibrium state, respectively, mol; G i , G i , represent the Gibbs free energy and the standard Gibbs free energy of the components i, respectively, J/mol; p i , p total , p , represent the partial pressure of the components i, the total pressure of all gas, and the standard atmospheric pressure, respectively, Pa, and p = 1atm = 101,325 Pa; α ie represents the number of element e in the component i; T, represents the thermodynamic temperature of the system, K; R, is the ideal gas constant, which is equal to 8.314, J/(mol·K); a i represents the activity, when i is a gaseous state a i = p i p = n i n i · p total p , when i is a solid-state a i = 1. The software LINGO is used in the mathematics calculation of minimum values for nonlinear equations.

Reaction Enthalpy and Sensible Heat
For reaction enthalpy of chemical reactions and sensible heat of substance with temperature changing, these calculation formulas are the same, which are the difference between the final state and the initial state, as shown in Formula (24).
where ∆H represents the enthalpy change, kJ/mol, and a negative value is exothermic, a positive value is endothermic; i, j, signify the components after and before the state change, respectively; N and M represent the number of components after and before the state change, respectively; n i and n j represent the number of components after and before the state change, respectively, mol; T i and T j represent the thermodynamic temperature of components after and before the state change, respectively, K; H i, T i and H j, T j , represent the standard molar enthalpy of component i at the thermodynamic temperature T i and the component j at the thermodynamic temperature T j , respectively, kJ/mol. The standard molar enthalpy and standard molar Gibbs energy of pure matter are derived from the specific heat capacity data provided by previous literatures [16].

Related Definitions
All equilibrium compositions are calculated by the minimum Gibbs free energy method based on the initial conditions. According to the amount of each component in the initial and equilibrium state, some definitions are made out to search the thermodynamic law in the reduction of iron oxide by reduction gas within CH 4 at 900 • C. CO 2 /(CO + CO 2 ) and H 2 O/(H 2 O + H 2 ) are used to show the equilibrium gas ratio and the utilization rate of CO and H 2 in the reduction of iron oxide, which is shown in Formulas (25) where in the n expresses the amount of the component, and the subscript equilibrium and initial express the equilibrium state and the initial state, respectively. However, when CH 4 is in the reduction gas, Formulas (25) and (26) are meaningless. According to the mass balance of gas-solid reactions, the lost oxygen in iron oxide is the same as the increased oxygen in gas. The deoxygenation rate of Fe 2 O 3 and the utilization rate of total gas are defined as Formulas (27) and (28), respectively. Furthermore, the gas demand can be got by Formula (29). The amount of O in iron oxide is 1.5 mol for 0.5 mol Fe 2 O 3 , and 600 m 3 for Fe 2 O 3 including 1 t Fe. CH 4 can save the volume of reduction gas and increase the reaction enthalpy, compared with the reduction gas H 2 + CO, the saving volume of total gas per mol CH 4

The Equilibrium Composition
The collection of settings are taken as an example to display the law of reduction of Fe 2 O 3 by H 2 + CO + CH 4 + N 2 mixtures: the initial gas concentration is H 2 % = 45, CO% = 45, CH 4 % = 3.0, N 2 % = 7, the total pressure is 4 atm, and the reaction temperature is 900 • C. Figure 2 shows some rules, such as equilibrium products, equilibrium gas ratio, deoxygenation rate of iron oxide, gas utilization rate, and CH 4 conversion.

The Equilibrium Composition
The collection of settings are taken as an example to display the law of reduction of Fe2O3 by H2 + CO + CH4 + N2 mixtures: the initial gas concentration is H2% = 45, CO% = 45, CH4% = 3.0, N2% = 7, the total pressure is 4 atm, and the reaction temperature is 900 °C. Figure 2 shows some rules, such as equilibrium products, equilibrium gas ratio, deoxygenation rate of iron oxide, gas utilization rate, and CH4 conversion. Figure 2. The initial gas concentration is H2% = 45, CO% = 45, CH4% = 3, N2% = 7, the total pressure is 4 atm, and the temperature is 900°C. (a) the amount of equilibrium products; (b) equilibrium gas ratio; (c) deoxygenation rate of Fe2O3 and utilization rate of total gas; (d) CH4 conversion rate. Figure 2a shows the amount and kinds of equilibrium products with increasing the amount of initial reduction gas at the current setting, which demonstrates that the composition of equilibrium products is significantly affected by the quantity of reduction gas. With the increase of reduction gas, the iron oxide follows the law of gradual reduction, that is, Fe2O3→Fe3O4→Fe0.95O→Fe. When the initial amount of reduction gas is 1.5-2.5 mol and the initial iron oxide is 0.5 mol Fe2O3, the equilibrium state is Fe0.95O→Fe stage. Also, any two stages cannot exist at the same time in thermodynamics. Under the current initial conditions, Fe3C and C have not been generated. The  Figure 2a shows the amount and kinds of equilibrium products with increasing the amount of initial reduction gas at the current setting, which demonstrates that the composition of equilibrium products is significantly affected by the quantity of reduction gas. With the increase of reduction gas, the iron oxide follows the law of gradual reduction, that is, Fe 2 O 3 →Fe 3 O 4 →Fe 0.95 O→Fe. When the initial amount of reduction gas is 1.5-2.5 mol and the initial iron oxide is 0.5 mol Fe 2 O 3 , the equilibrium state is Fe 0.95 O→Fe stage. Also, any two stages cannot exist at the same time in thermodynamics. Under the current initial conditions, Fe 3 C and C have not been generated. The complete reduction of Energies 2020, 13, 5053 7 of 18 iron oxide is shown in Figure 2a that product Fe 0.95 O gradually decreases to 0, and the corresponding amount of product Fe gradually increases to a maximum of 1mol and then remains unchanged. There is a certain amount of reduction gas that is just enough for the iron oxide to be completely reduced, and the more amount of reduction gas is not needed. Besides, attention should be paid to the fact that the content of CH 4 in Figure 2a is close to 0. Figure 2b shows the equilibrium gas ratio with increasing the amount of initial reduction gas in the current setting. In the reduction stage of Fe 0.95 O→Fe stage at 900 • C, the equilibrium concentration ratios of H 2 O/(H 2 + H 2 O) and CO 2 /(CO + CO 2 ) are 37.581% and 31.450%, respectively, which are the same as that of the reduction of iron oxide by pure H 2 and pure CO. The two equilibrium concentration ratios are a function of temperature, regardless of whether CH 4 exists or not, or how much CH 4 exists. Figure 2c shows the deoxygenation rate of Fe 2 O 3 and the utilization rate of total gas with increasing the amount of initial reduction gas at the current setting. In the presence of CH 4 , the equilibrium concentrations of H 2 O/(H 2 + H 2 O) and CO 2 /(CO + CO 2 ) cannot represent the utilization rate of the gas. The ratio of the amount of oxygen loss to the amount of reduction gas should be adopted to display the utilization rate of reduction gas. In the reduction stage of Fe 0.95 O→Fe, the utilization rate does not change with the increase of the deoxygenation rate of Fe 2 O 3 . Therefore, this rule can be used to calculate the reduction gas utilization rate under different settings, such as gas concentration, gas pressure, etc. Figure 2d shows the CH 4 conversion rate with increasing the amount of initial reduction gas at the current setting. In the reduction stage of Fe 0.95 O→Fe, the CH 4 conversion rate remains unchanged with the increase of the reduction gas. The increased CH 4 has reacted with the increased H 2 O and CO 2 obtained from the reduction of Fe 0.95 O, which is shown in Figure 2a. At any reduction stage of iron oxide, CH 4 is almost completely decomposed, and the conversion rate of CH 4 is ≥99.982%. When the amount of reduction gas is more than needed, the CH 4 conversion rate decreases rapidly, and the reason is that the amount of CO 2 and H 2 O generated from the reduction of iron oxide do not increase.

The Utilization Rate of Reduction Gas
The utilization rate of reduction gas for the full reduction of iron oxide is the same as that of the partial reduction stage of Fe 0.95 O→Fe. Therefore, the initial amount of reduction gas is set as 2 mol. The initial gas concentration is H 2 % + CO% = 90, CH 4 % = 0-10, the residual is N 2 , and these given initial gas concentration (volume fraction) are listed in Table 3. The total pressure is 1-9 atm and the reaction temperature is 900 • C.
The Figure 3a,b show the relationship between the utilization rate of total gas and the total gas pressure, and the former fixes the initial concentrations of both H 2 and CO at 45%, the latter fixed the initial concentration of CH 4 at 2%. As can be seen from these two figures, no matter what the initial gas concentration is, the gas utilization rate decreases with the increase of the total gas pressure, expect for single gas reduction. However, the influence of pressure on the gas utilization rate is not significant. The change of gas utilization rate from 1 atm to 9 atm is less than 1.70%, as shown in Figure 4. Also, when initial H 2 % = 60, the pressure has the greatest effect on gas utilization, which is close to 1.70%. (c) (d) Figure 3. The relationship between the utilization rate of total gas and other initial conditions at 900 °C. (a) the x-axis is the total gas pressure, and initial H2% = 45, CO% = 45, CH4% = 0-10; (b) x-axis is the total gas pressure, and initial H2% + CO% = 90, CH4% = 2; (c) x-axis is the initial CH4 volume fraction, and initial H2% = 45, CO% = 45; (d) x-axis is the total gas pressure, and initial H2% + CO% = 90, CH4% = 2. Figure 3c shows the relationship between the utilization rate of total gas and the initial CH4 volume fraction. It can be seen from these two figures, no matter what the initial gas concentration is, the gas utilization rate decreases with the increase of the total gas pressure. In other words, increasing the concentration of CH4 can greatly improve the gas utilization rate. Besides, the lines under different pressures are nearly parallel. According to the calculation of the slope, for every 1% increase in CH4 concentration, the gas utilization rate can be improved by 2.03-2.07%. Figure 3d shows the relationship between the utilization rate of total gas and the initial H2 volume fraction. As can be seen from the figure, the gas utilization rate increases as the initial H2 concentration increases also decreases as the initial CO concentration increases. Also, the two ends of all curves are approximately coincident, that is, when the gas concentration is (H2% = 90, CH4% = 2) and (CO% = 90, CH4% = 2), the pressure has little effect on the gas utilization. For other H2 concentrations, the higher the pressure is, the lower the utilization of the gas is. Based on the slope calculation, every 1% increase in H2 concentration can improve the gas utilization rate by about 0.06%. Table 4 lists the utilization rate of total gas of the selected nine groups of gas concentrations under different pressure. For single reduction gas (CO% = 90, N2% = 10) and (H2% = 90, N2% = 10), Figure 3. The relationship between the utilization rate of total gas and other initial conditions at 900 • C. (a) the x-axis is the total gas pressure, and initial H 2 % = 45, CO% = 45, CH 4 % = 0-10; (b) x-axis is the total gas pressure, and initial H 2 % + CO% = 90, CH 4 % = 2; (c) x-axis is the initial CH 4 volume fraction, and initial H 2 % = 45, CO% = 45; (d) x-axis is the total gas pressure, and initial H 2 % + CO% = 90, CH 4 % = 2. Figure 3c shows the relationship between the utilization rate of total gas and the initial CH 4 volume fraction. It can be seen from these two figures, no matter what the initial gas concentration is, the gas utilization rate decreases with the increase of the total gas pressure. In other words, increasing the concentration of CH 4 can greatly improve the gas utilization rate. Besides, the lines under different pressures are nearly parallel. According to the calculation of the slope, for every 1% increase in CH 4 concentration, the gas utilization rate can be improved by 2.03-2.07%. Figure 3d shows the relationship between the utilization rate of total gas and the initial H 2 volume fraction. As can be seen from the figure, the gas utilization rate increases as the initial H 2 concentration increases also decreases as the initial CO concentration increases. Also, the two ends of all curves are approximately coincident, that is, when the gas concentration is (H 2 % = 90, CH 4 % = 2) and (CO% = 90, CH 4 % = 2), the pressure has little effect on the gas utilization. For other H 2 concentrations, the higher the pressure is, the lower the utilization of the gas is. Based on the slope calculation, every 1% increase in H 2 concentration can improve the gas utilization rate by about 0.06%.

The Saving Volume of Reduction Gas per m 3 CH4
The reduction gas needed for the full reduction of iron oxide to produce 1 ton of metallic Fe can be calculated by the utilization rate of reduction gas. For H2% = 45, CO% = 45, CH4% = 0-10, gas pressure is 1-9 atm, the reduction gas required for a ton of iron is shown in Figure 5. As can be seen from Figure 5, the amount of reduction gas required per ton of iron decreases with the increase of CH4 content. For example, when the initial CH4% is 0, the reduction gas (H2% = 45, CO%45, N2% = 10, gas pressure 4 atm) needed is 1937.319 m 3 ; when the initial CH4% is 5, that is 1453.959 m 3 , the reduction gas required decreases by 483.36 m 3 .  Table 4 lists the utilization rate of total gas of the selected nine groups of gas concentrations under different pressure. For single reduction gas (CO% = 90, N 2 % = 10) and (H 2 % = 90, N 2 % = 10), the utilization rate of total gas at 900 • C is 28.305% and 33.823%, respectively. Increasing CH 4 concentration and decreasing the pressure can improve the gas utilization rate. At the same temperature and pressure, pure H 2 has the highest gas utilization rate, while pure CO has the lowest gas utilization rate. The reduction gas needed for the full reduction of iron oxide to produce 1 ton of metallic Fe can be calculated by the utilization rate of reduction gas. For H 2 % = 45, CO% = 45, CH 4 % = 0-10, gas pressure is 1-9 atm, the reduction gas required for a ton of iron is shown in Figure 5. As can be seen from Figure 5, the amount of reduction gas required per ton of iron decreases with the increase of CH 4 content. For example, when the initial CH 4 % is 0, the reduction gas (H 2 % = 45, CO%45, N 2 % = 10, gas pressure 4 atm) needed is 1937.319 m 3 ; when the initial CH 4 % is 5, that is 1453.959 m 3 , the reduction gas required decreases by 483.36 m 3 . The reduction gas demand can be saved by increasing CH4 into the mixture, and the specific effect can be calculated by Formula (30), which is shown in Figure 6. As can be seen from the figure, the saving effect decreases with the increase of the initial CH4 concentration, and the decreasing trend is obvious with the increase of the pressure. However, the range of these savings due to pressure and CH4 concentration is small, with a maximum of just 0.008 m 3 /m 3 . Therefore, it can be considered that for reduction gas (H2% = 45, CO% = 45, N2% = 10, and the pressure is 1-9 atm), 1 m 3 CH4 can save 6.64-6.65 m 3 total reduction gas.  The reduction gas demand can be saved by increasing CH 4 into the mixture, and the specific effect can be calculated by Formula (30), which is shown in Figure 6. As can be seen from the figure, the saving effect decreases with the increase of the initial CH 4 concentration, and the decreasing trend is obvious with the increase of the pressure. However, the range of these savings due to pressure and CH 4 concentration is small, with a maximum of just 0.008 m 3 /m 3 . Therefore, it can be considered that for reduction gas (H 2 % = 45, CO% = 45, N 2 % = 10, and the pressure is 1-9 atm), 1 m 3 CH 4 can save 6.64-6.65 m 3 total reduction gas. The reduction gas demand can be saved by increasing CH4 into the mixture, and the specific effect can be calculated by Formula (30), which is shown in Figure 6. As can be seen from the figure, the saving effect decreases with the increase of the initial CH4 concentration, and the decreasing trend is obvious with the increase of the pressure. However, the range of these savings due to pressure and CH4 concentration is small, with a maximum of just 0.008 m 3 /m 3 . Therefore, it can be considered that for reduction gas (H2% = 45, CO% = 45, N2% = 10, and the pressure is 1-9 atm), 1 m 3 CH4 can save 6.64-6.65 m 3 total reduction gas.   Figure 7 shows the relationship between saving volume of total gas per m 3 CH 4 and the initial H 2 concentration. It can be seen from Figure 7 that the saving volume per m 3 CH 4 decreases linearly with the increase of the initial H 2 concentration. Since CH 4 concentration has little influence on the savings effect of CH 4 , the points in Figure 7 are coincide, and the coordinate values of the main nodes have been marked in the figure. For gas concentration from (H 2 % = 0, CO% = 90) to (H 2 % = 90, CO% = 0), the saving effect of CH 4 is decreased from 7.29 m 3 /m 3 to 6.08 m 3 /m 3 . Compared with pressure and CH 4 concentration, H 2 concentration has a more significant effect on the savings effect of CH 4 .
Energies 2020, 13, x FOR PEER REVIEW 11 of 18 Figure 7 shows the relationship between saving volume of total gas per m 3 CH4 and the initial H2 concentration. It can be seen from Figure 7 that the saving volume per m 3 CH4 decreases linearly with the increase of the initial H2 concentration. Since CH4 concentration has little influence on the savings effect of CH4, the points in Figure 7 are coincide, and the coordinate values of the main nodes have been marked in the figure. For gas concentration from (H2% = 0, CO% = 90) to (H2% = 90, CO% = 0), the saving effect of CH4 is decreased from 7.29 m 3 /m 3 to 6.08 m 3 /m 3 . Compared with pressure and CH4 concentration, H2 concentration has a more significant effect on the savings effect of CH4. It is important to note that the volume saving per m 3 CH4 cannot be calculated according to Formula (9) and (10). According to Formula (9), the reaction between CH4 and H2O can produce 3 m 3 H2 + 1 m 3 CO by 1 m 3 CH4. According to Formula (10), the reaction between CH4 and CO2 can get 2 m 3 H2 + 2 m 3 CO by 1 m 3 CH4. In other words, the reaction of CH4 with deoxidized products H2O and CO2 results in a mixture of 4 m 3 H2 + CO. However, this algorithm for saving effect without the iron oxide reduction system is not correct, due to the gas utilization rate for reduction is neglected. In the gas system composed of CH4 + H2O + H2 + CO2 + CO, five kinds of gases. H2O + H2, and CO2 + CO are also in equilibrium.

The Reaction Enthalpy
The reaction enthalpy of reduction of iron oxide can be calculated by Formula (24). Figure 8 shows the relationship between the reaction enthalpy and the initial gas amount, and the oblique line shows the full reduction of iron oxide. The curve that demonstrates the reduction by gas It is important to note that the volume saving per m 3 CH 4 cannot be calculated according to Formula (9) and (10). According to Formula (9), the reaction between CH 4 and H 2 O can produce 3 m 3 H 2 + 1 m 3 CO by 1 m 3 CH 4 . According to Formula (10), the reaction between CH 4 and CO 2 can get 2 m 3 H 2 + 2 m 3 CO by 1 m 3 CH 4 . In other words, the reaction of CH 4 with deoxidized products H 2 O and CO 2 results in a mixture of 4 m 3 H 2 + CO. However, this algorithm for saving effect without the iron oxide reduction system is not correct, due to the gas utilization rate for reduction is neglected. In the gas system composed of CH 4 + H 2 O + H 2 + CO 2 + CO, five kinds of gases. H 2 O + H 2 , and CO 2 + CO are also in equilibrium.

The Reaction Enthalpy
The reaction enthalpy of reduction of iron oxide can be calculated by Formula (24). Figure 8 shows the relationship between the reaction enthalpy and the initial gas amount, and the oblique line shows the full reduction of iron oxide. The curve that demonstrates the reduction by gas without CH 4 is at the bottom of all curves and reaches a maximum value of 8.3 kJ/mol when the iron oxide is completely reduced; due to reverse reaction of Formulas (9) and (10), the curve starts to go down. For the reduction by gas included CH 4 , the reaction enthalpy increases with the increase of the amount of reduction gas. Energies 2020, 13, x FOR PEER REVIEW 12 of 18 Figure 8. the relationship between the reaction enthalpy and the initial gas amount at 900 °C under 4 atm with H2% = 45, CO% = 45, CH4% = 0-10. Figure 9 shows the relationship between the reaction enthalpy and the initial CH4 concentration. As shown in the figure, reaction enthalpy is linearly correlated with the initial CH4 concentration. The initial reduction gas volume is set as 1.5 mol, 2.0 mol, and 2.5 mol, respectively, so the equilibrium state is in the stage of Fe0.95O→Fe. According to the calculation by Formula (33), the change of reaction enthalpy brought by 1 mol CH4 is the same at the same pressure. Increasing the pressure can reduce the change value of reaction enthalpy. The change of reaction enthalpy caused by 1 mol CH4 at 4 atm, 5 atm, and 6 atm is 249.79 kJ/mol, 249.31 kJ/mol, and 248.72 kJ/mol, respectively.  Figure 9 shows the relationship between the reaction enthalpy and the initial CH 4 concentration. As shown in the figure, reaction enthalpy is linearly correlated with the initial CH 4 concentration. The initial reduction gas volume is set as 1.5 mol, 2.0 mol, and 2.5 mol, respectively, so the equilibrium state is in the stage of Fe 0.95 O→Fe. According to the calculation by Formula (33), the change of reaction enthalpy brought by 1 mol CH 4 is the same at the same pressure. Increasing the pressure can reduce the change value of reaction enthalpy. The change of reaction enthalpy caused by 1 mol CH 4 at 4 atm, 5 atm, and 6 atm is 249.79 kJ/mol, 249.31 kJ/mol, and 248.72 kJ/mol, respectively. ∆H 1173K = slope of reaction enthalpy increment of the initial amount of CH 4 (33) Energies 2020, 13, 5053 13 of 18 the pressure can reduce the change value of reaction enthalpy. The change of reaction enthalpy caused by 1 mol CH4 at 4 atm, 5 atm, and 6 atm is 249.79 kJ/mol, 249.31 kJ/mol, and 248.72 kJ/mol, respectively. (c) Figure 9. The relationship between the reaction enthalpy and the initial CH4 volume fraction at 900 °C with H2% = 45, CO% = 45. (a) the total pressure is 4 atm; (b) total pressure is 5 atm; (c) total pressure is 6 atm.

The Increased Reaction Enthalpy Per m 3 CH4
Comparing the reduction of iron oxide by gas within CH4 and by gas without CH4, the reaction enthalpy increases under the same initial concentration of H2 and CO and pressure.

The Increased Reaction Enthalpy Per m 3 CH 4
Comparing the reduction of iron oxide by gas within CH 4 and by gas without CH 4 , the reaction enthalpy increases under the same initial concentration of H 2 and CO and pressure. Figure 10 shows the relationship between the increased reaction enthalpy per m 3 CH 4 and the total gas pressure and the initial H 2 concentration. As shown in the figure, the increased reaction enthalpy decreases with the increase of the total gas pressure, or with the increase of the initial H 2 concentration. For the gas (H 2 % = 0, CO% = 90, the pressure is 1atm), the increased reaction enthalpy per m 3 CH 4 is the maximum of 11.189 MJ/m 3 . For the gas (H 2 % = 90, CO% = 0, the pressure is 9atm) the increased reaction enthalpy per m 3 CH 4 is the smallest of 10.959 MJ/m 3 . According to the reduction reaction and methane conversion reaction, the reaction between CH4 and iron oxide is obtained by coupling, as shown in Formulas (34) and (35). The released heat of chemical reaction in the production of 1 mol of Fe with CO is 18.445 kJ, the absorption heat of chemical reaction in the production of 1 mol of Fe with H2 is 31.747 kJ, and the absorption heat of chemical reaction in the production of 1 mol of Fe with CH4 is 373.061 kJ.
When the initial CH4 concentration is set to be 10% at most, the amount of CO2 and H2O in the system are excessive relative to that of CH4; that is, the conversion reaction of CH4 is relatively sufficient, as shown in Figure 2d. When the initial concentration of CO and H2 in the gas phase changes, the concentration of CO2 and H2O generated by the reduction reaction also changes along with it, thus making the reaction enthalpy of CH4 conversion different. The reduction utilization rate of H2 is higher than that of CO at 900 °C. Increasing the initial H2 concentration can increase the overall gas utilization rate and the concentration of H2O in the gas phase. In addition, the reaction enthalpy of H2O + CH4 is lower than that of CO2 + CH4, which reduces the increased reaction enthalpy of the system.
The transformation reaction of CH4 are reactions in which the amount of substance increases. Increasing the gas pressure can decrease the amount of forwarding reaction and the gas utilization rate, which lowers the increased reaction enthalpy of the system. For the gas (H 2 % = 0, CO% = 90, N 2 % = 10), the reaction enthalpy for producing a ton of iron is −330.280 MJ. For the gas (H 2 % = 90, CO% = 0, N 2 % = 10), and the reaction enthalpy for the production of a ton of iron is 568.471 MJ. The addition of 30 m 3 CH 4 in the gas phase can make the reaction enthalpy of the former gas system zero, and the latter gas system more heat supply needed.
According to the reduction reaction and methane conversion reaction, the reaction between CH 4 and iron oxide is obtained by coupling, as shown in Formulas (34) and (35). The released heat of chemical reaction in the production of 1 mol of Fe with CO is 18.445 kJ, the absorption heat of chemical reaction in the production of 1 mol of Fe with H 2 is 31.747 kJ, and the absorption heat of chemical reaction in the production of 1 mol of Fe with CH 4 is 373.061 kJ. When the initial CH 4 concentration is set to be 10% at most, the amount of CO 2 and H 2 O in the system are excessive relative to that of CH 4 ; that is, the conversion reaction of CH 4 is relatively sufficient, as shown in Figure 2d. When the initial concentration of CO and H 2 in the gas phase changes, the concentration of CO 2 and H 2 O generated by the reduction reaction also changes along with it, thus making the reaction enthalpy of CH 4 conversion different. The reduction utilization rate of H 2 is higher than that of CO at 900 • C. Increasing the initial H 2 concentration can increase the overall gas utilization rate and the concentration of H 2 O in the gas phase. In addition, the reaction enthalpy of H 2 O + CH 4 is lower than that of CO 2 + CH 4 , which reduces the increased reaction enthalpy of the system.
The transformation reaction of CH 4 are reactions in which the amount of substance increases. Increasing the gas pressure can decrease the amount of forwarding reaction and the gas utilization rate, which lowers the increased reaction enthalpy of the system.

The Heat Needed per Ton Fe
The total heat needed of reduction of iron oxide by gas at 900 • C consists of three parts: reaction heat, the sensible heat of solid Fe 2 O 3 from 25 • C to 900 • C, and sensible heat of gas mixture from 25 • C to 900 • C. MJ/tFe represents heat unit per ton Fe. Figure 11 shows the relationship between reduced sensible heat of reduction gas and CH 4 concentration, gas pressure, and H 2 concentration, which is compared with the reduction without CH 4 . As can be seen from Figure 11a, the reduced sensible heat of reduction gas increases with the increase of CH 4 concentration and has little been influenced by the gas pressure in the range of 1-9 atm. As can be seen from Figure 11b, under the same gas pressure and CH 4 concentration, the reduced sensible heat of reduction gas decreases with the increase of H 2 concentration.
Energies 2020, 13, x FOR PEER REVIEW 15 of 18 CH4. As can be seen from Figure 11a, the reduced sensible heat of reduction gas increases with the increase of CH4 concentration and has little been influenced by the gas pressure in the range of 1-9 atm. As can be seen from Figure 11b, under the same gas pressure and CH4 concentration, the reduced sensible heat of reduction gas decreases with the increase of H2 concentration.
In addition, according to the sensible heat calculation Formula (24) and gas composition, it can be obtained that the saved sensible heat of gas per m 3 CH4 is 7.338-8.952 MJ. The former corresponds to gas mixture H2% = 90, CO% = 00, CH4% + N2% = 10, and gas pressure = 9atm. The latter corresponds to gas mixture H2% = 0, CO% = 90, CH4% + N2% = 10, and gas pressure = 1atm. Figure 12 shows the relationship between increased reaction heat and CH4 concentration, gas pressure, and H2 concentration, which is compared with the reduction without CH4. As can be seen from Figure 12a, the increased reaction heat goes up with the increase of CH4 concentration and has been little influenced by the gas pressure in the range of 1-9atm. As can be seen from Figure 12b, under the same gas pressure and CH4 concentration, the increased reaction heat decreases with the increase of H2 concentration. Figure 11. The relationship between the reduced sensible heat of total gas and the initial CH 4 volume fraction at 900 • C. (a) H 2 % = 45, CO% = 45, total pressure is 1-9 atm; (b) H 2 % + CO% = 90, total pressure is 4 atm.
In addition, according to the sensible heat calculation Formula (24) and gas composition, it can be obtained that the saved sensible heat of gas per m 3 CH 4 is 7.338-8.952 MJ. The former corresponds to gas mixture H 2 % = 90, CO% = 00, CH 4 % + N 2 % = 10, and gas pressure = 9atm. The latter corresponds to gas mixture H 2 % = 0, CO% = 90, CH 4 % + N 2 % = 10, and gas pressure = 1atm. Figure 12 shows the relationship between increased reaction heat and CH 4 concentration, gas pressure, and H 2 concentration, which is compared with the reduction without CH 4 . As can be seen from Figure 12a, the increased reaction heat goes up with the increase of CH 4 concentration and has been little influenced by the gas pressure in the range of 1-9atm. As can be seen from Figure 12b, under the same gas pressure and CH 4 concentration, the increased reaction heat decreases with the increase of H 2 concentration. Figure 12 shows the relationship between increased reaction heat and CH4 concentration, gas pressure, and H2 concentration, which is compared with the reduction without CH4. As can be seen from Figure 12a, the increased reaction heat goes up with the increase of CH4 concentration and has been little influenced by the gas pressure in the range of 1-9atm. As can be seen from Figure 12b, under the same gas pressure and CH4 concentration, the increased reaction heat decreases with the increase of H2 concentration.  The sensible heat of the solid Fe 2 O 3 is 1123.381 MJ/tFe, which is a constant under certain temperature change conditions. Therefore, increased total heat can be defined by the difference of gas sensible heat and reaction heat, as shown in Formula (36).
increased total heat = increased reaction heat − reduced gas sensible heat (36) The relationship between increased total heat with CH 4 concentration, gas pressure, and H 2 concentration is shown in Figure 13. It can be seen that the increased total heat increases with the increase of CH 4 concentration, and has been little influenced by the gas pressure in the range of 1-9 atm. As can be seen from Figure 13b, under the same gas pressure and CH 4 concentration, the increased reaction heat increases with the increase of H 2 concentration. The sensible heat of the solid Fe2O3 is 1123.381 MJ/tFe, which is a constant under certain temperature change conditions. Therefore, increased total heat can be defined by the difference of gas sensible heat and reaction heat, as shown in Formula (36).
increased total heat = increased reaction heat -reduced gas sensible heat The relationship between increased total heat with CH4 concentration, gas pressure, and H2 concentration is shown in Figure 13. It can be seen that the increased total heat increases with the increase of CH4 concentration, and has been little influenced by the gas pressure in the range of 1-9 atm. As can be seen from Figure 13b, under the same gas pressure and CH4 concentration, the increased reaction heat increases with the increase of H2 concentration.
According to Formula (36), increasing 1 m 3 CH 4 can increase the total heat by 2.174-3.703 MJ. The former corresponds to gas mixture H 2 % = 0, CO% = 90, CH 4 % = 1, N 2 % = 9, and gas pressure = 9 atm. The latter corresponds to gas mixture H 2 % = 90, CO% = 0, CH 4 % = 1, N 2 % = 9, and gas pressure = 1 atm. Figure 14 shows the relationship between the total heat and CH 4 concentration, gas pressure, and H 2 concentration, and its variation trend is the same as that of the increased total heat. Taking the reduction by H 2 % = 45, CO% = 45, CH 4 % = 0, N 2 % = 10 gas mixture as an example, as shown in Figure 14a, the total heat needed is 3649.223 MJ/tFe (gas pressure = 1 atm) and 3636.249 MJ/tFe (gas pressure = 9 atm), and the slight difference is due to the lower reaction heat caused by the increase in pressure. When the gas pressure = 4 atm, as shown in Figure 14b, the total heat needed is 3865.76 MJ/tFe for the reduction by H 2 % = 0, CO% = 90, CH 4 % = 0, N 2 % = 10 gas mixture and 3390.828 MJ/tFe for the reduction by H 2 % = 90, CO% = 0, CH 4 % = 0, N 2 % = 10 gas mixture, and the huge difference is due to the exothermic reaction of CO + Fe 2 O 3 .
The maximum increase rate in total heat caused by the presence of CH4 is 10.582% (H2% = 90, CH4% =10, gas pressure = 1 atm) compared to the reducing gas without CH4. An appropriate increase in total heat is acceptable since it saves the amount of H2 + CO and reduces the purity limit of H2 + CO. However, the addition of CH4 requires more heat supply for gas reduction and may increase the carbon content.

Conclusions
The minimum free energy method was used to calculate the equilibrium state composition of the reduction of iron oxide by gas with H2% + CO% = 90 and CH4% + N2% = 10 at 900 °C under 1-9 atm, and the following conclusions were obtained: (1) Increasing CH4 concentration, increasing H2 concentration, or reducing gas pressure can improve the utilization rate of total gas, reduce the reduction gas demand, and increase the total heat needed. (2) Under the condition of 900 °C and 1-9 atm, increasing 1 m 3 CH4 can reduce the gas demand of 6.08-7.29 m 3 , the gas sensible heat needed to be 7.338-8.952 MJ, and the increase in the reaction heat needed to be 10.959-11.189 MJ.  The maximum increase rate in total heat caused by the presence of CH 4 is 10.582% (H 2 % = 90, CH 4 % =10, gas pressure = 1 atm) compared to the reducing gas without CH 4 . An appropriate increase in total heat is acceptable since it saves the amount of H 2 + CO and reduces the purity limit of H 2 + CO. However, the addition of CH 4 requires more heat supply for gas reduction and may increase the carbon content.