Thermodynamic Study of Energy Consumption and Carbon Dioxide Emission in Ironmaking Process of the Reduction of Iron Oxides by Carbon

Abstract

Carbon included in coke and coal was used as a reduction agent and fuel in blast furnace (BF) ironmaking processes, which released large quantities of carbon dioxide (CO₂). Minimizing the carbon consumption and CO₂ output has always the goal of ironmaking research. In this paper, the reduction reactions of iron oxides by carbon, the gasification reaction of carbon by CO_2, and the coupling reactions were studied by thermodynamic functions, which were derived from isobaric specific heat capacity. The reaction enthalpy at 298 K could not represent the heat value at the other reaction temperature, so the certain temperature should be confirmed by Gibbs frees energy and gas partial pressure. Based on Hess’ law, the energy consumption of the ironmaking process by carbon was calculated in detail. The decrease in the reduction temperature of solid metal iron has been beneficial in reducing the sensible heat required. When the volume ratio of CO to CO₂ in the top gas of the furnace was given as 1.1–1.5, the coupling parameters of carbon gasification were 1.06–1.28 for Fe₂O₃, 0.71–0.85 for Fe₃O₄, 0.35–0.43 for FeO, respectively. With the increase in the coupling parameters, the volume fraction of CO₂ decreased, and energy consumption and CO₂ output increased. The minimum energy consumption and CO₂ output of liquid iron production were in the reduction reactions with only CO₂ generated, which were 9.952 GJ/t and 1265.854 kg/t from Fe₂O₃, 9.761 GJ/t and 1226.799 kg/t from Fe₃O₄, 9.007 GJ/t and 1107.368 kg/t from FeO, respectively. Compared with the current energy consumption of 11.65 GJ/t hot metal (HM) and CO₂ output of 1650 kg/tHM of BF, the energy consumption and CO₂ of ironmaking by carbon could reach lower levels by decreasing the coupled gasification reactions, lowering the temperature needed to generate solid Fe and adjusting the iron oxides to improve the iron content in the raw material. This article provides a simplified calculation method to understand the limit of energy consumption and CO₂ output of ironmaking by carbon reduction iron oxides.

1. Introduction

Ironmaking processes are a focus area when the topic of energy consumption and CO₂ emissions is mentioned, which requires carbon (from coke and coal) as the fuel and reducing agent to convert iron oxide to hot metal at high temperatures. The CO₂ emissions from the iron and steel industry accounted for 4–7% of that of global emissions [1]. Current production processes consisting of sintering or pelletizing, coke making, and blast furnace (BF) without top gas recovery contribute to approximately 90% of the CO₂ output from BF-converter steelmaking integrated steel plants [2,3]. As the dominant primary energy source, coal (coking coal and pulverized coal) accounts for about 80% of the total energy consumption and acts as a major source of CO₂ emissions in the iron and steel industry [3]. CO₂ emissions of the BF process are around 1.650 t CO₂/tHM [4], and the energy consumption of the BF process is around ±12 GJ/tHM [5,6]. Therefore, from the point of view of carbon sources, reducing carbon usage is to reduce CO₂ emissions.

With the strict environmental policy and the recent signing of the Paris agreement, steel manufacturers are under continually increasing pressure to reduce CO₂ emissions further to near net-zero levels [7,8,9,10,11]. Several innovative technologies [1,8,12,13,14,15,16] have been used or are under development to reduce energy consumption and CO₂ emissions of BF process, for example, flue gas recycling within BF stoves, dry gas cleaning process, dry slag granulation including heat recovery, high-efficiency coal injection technology (PCI), top gas dry residual pressure power generation (TRT), hot BF flue gas double preheating technology, BF gas recovery technology, BF slag comprehensive utilization technology, BF coke oven gas injection technology, BF waste plastic injection technology, charcoal injection, top-gas recycling (TGR) with carbon capture and storage (CCS), microbiological process gas treatment, H₂ injection. According to the report [8], 1.75 GJ/t and 54.12kg CO₂/t crude steel would be reduced in the BF process. Direct reduction ironmaking technology with syngas as the reduction gas, represented by Midrex and HYL/Energiron, is also an alternative choice to reduce the energy consumption and carbon emissions of ironmaking [17,18]. Therefore, decreasing energy input or increasing energy savings are alternative ways to reduce energy consumption.

BF production is the most cost-efficient technology today [1], and is considered a highly developed process operating close to the thermodynamic limits of efficiency. There are no obvious enhancements that will fundamentally reduce its carbon demand or significantly improve its thermal efficiency [19], so there is only limited room left for improvement based on existing technologies [11,20,21]. Are BF plants now at or very close to their thermodynamic limits? This is an interesting question worthy of further consideration and research.

Although extensive research has been carried out on the low energy consumption and low emission of the BF process [7,18,22,23,24,25,26,27,28,29,30,31], research and development of the theoretical innovation for carbon reduction of iron oxides is scarce. And also, there is very limited information on a more accurate equation formula in terms of reduction and gas gasification of carbon. The simplified equations have been recognized and used in many situations [8,13,14,18,30,31,32,33,34,35,36,37,38,39,40], which facilitates the rapid use by researchers, but they are not accurate enough. In this paper, the complete temperature function expressions of enthalpy, entropy, and Gibbs free energy were derived from the isobaric specific heat capacity, which was used to analyze the reduction law and energy consumption.

The purpose of this paper was to explore the possible limit of further reducing the fuel ratio of the BF ironmaking process. Base on the existing equilibrium of chemical reactions, a thermodynamic model of carbon reduction of iron oxides was proposed. The effect of temperature and gas partial pressure on reduction reactions and gasification reactions was analyzed to confirm the reaction conditions. Furthermore, reaction enthalpy and gas yields of coupling chemical reactions were discussed to fix the energy consumption. Through the simplified model, the energy consumption of BF ironmaking was calculated, and then the minimum energy consumption would be found in basic thermodynamics.

2. Methods

2.1. Model Setting Assumptions

The heat and mass balance between income and outcome of the BF process were used in the textbook calculation, which needed to collect adequate and detailed data to match the actual BF as much as possible [41]. To simplify the calculation process, according to Hess’ law [42,43], the following assumptions were made in this study:

(1)

Carbon and iron oxides were objects of study, and other components were ignored, such as ash, volatile matter, gangue, and carbonate, etc. Carbon in coke or coal was considered as a reducing agent and fuel. Three kinds of iron oxides of Fe₂O₃, Fe₃O_4, and FeO were the main components in agglomeration or lump. The differences between various raw materials and production processes were not considered, and the common problems of reduction and energy consumption would be studied.

(2)

Energy was mainly used to provide heat to raise the temperature of solid raw materials, and met the heat needed of the reactions of reduction and gasification, and was supplied by the complete combustion of carbon. Although the heat energy in the hot air, non-recyclable heat loss, and recyclable heat of the top gas of BF could not be ignored in heat balance, they were not in the scope of this paper. Therefore, the carbon consumption included carbon for combustion, for reduction, for gasification, as shown in Equation (1). When the reduction and gasification reactions were considered simultaneously, the coupling reactions would be constructed as:

$$\begin{array}{ll}C{C}_{\mathrm{consumption}}& =C{C}_{\mathrm{combustion}}+C{C}_{\mathrm{reduction}}+C{C}_{\mathrm{gasification}}\\ & =C{C}_{\mathrm{combustion}}+C{C}_{\mathrm{coupling}}\\ & =\frac{E_{\mathrm{temperature} \mathrm{rising}}+E_{\mathrm{smelting}}+E_{\mathrm{coupling}}}{{\mathrm{\Delta }}_r{H}_{\mathrm{combustion}}^{Ө}}+C{C}_{\mathrm{coupling}}\end{array}$$

(1)

where CC referred to the quality of the carbon consumption, kg/t Fe. The subscripts “combustion”, “reduction”, “gasification”, “coupling” referred to the combustion reaction, reduction reactions, gasification reaction, and coupling reactions, respectively. E referred to the energy consumption, GJ/t Fe. The subscripts “temperature rising”, “smelting” referred to raising the temperature of solid materials to reduction temperature or smelting temperature, and the process of converting to liquid pure iron, respectively. ${\mathrm{\Delta }}_r{H}_{\mathrm{combustion}}^{Ө}$ referred to the heat value of complete combustion of carbon and oxygen at a certain temperature, which was determined by thermodynamics discussion, GJ/kg C. So, $C{C}_{\mathrm{coupling}}$ meant the carbon needed for coupling reactions based on chemical reaction equations of coupling reactions. $\frac{E_{\mathrm{coupling}}}{{\mathrm{\Delta }}_r{H}_{\mathrm{combustion}}^{Ө}}$ meant the carbon needed to provide heat for the coupling reactions based on enthalpy change of coupling reactions.

(3)

The CO₂ was produced from combustion and reduction, and its mole value was equal to the mole value of carbon consumption.

(4)

The gaseous O₂ in hot air was used for combustion with carbon and did not exist in the top gas of the actual BF [41]. The steam (gaseous H₂O) in hot air was not considered in this study to only explore the thermodynamic law of gasification between C and CO₂.

(5)

The process of smelting hot metal and output of top gas of BF were not considered in the chemical reaction but consumed vast amount of energy [44]. The energy consumption of pure iron smelting from solid metallic iron to liquid iron at 1809 K (1536 °C) was 349.573 kJ/mol [45], namely was 6.242 GJ/t. The sensible heat of the top gas of BF was not considered in energy consumption items in this study, because it was the result of chemical reactions and heat transfer of gases in BF, and not the direct consumption item.

Energy consumption from the initial to the final state of ironmaking by carbon would be studied, as shown in Figure 1. The influence factors of temperature and gas partial pressure on the reaction also would be studied. According to Hess’ law, the energy consumption of ironmaking included the heat needed for heating raw materials and chemical reactions, as shown in Figure 2.

In this given system, the component number was 6, namely being Fe_xO_y, C, O₂, Fe, CO, CO₂, and the element number was 3, namely being C, Fe, O. So, the number of independent chemical reactions in this system was equal to 3, which was 3 of the element numbers subtracted from 6 of the component numbers. Therefore, from the thermodynamic theory, two independent chemical reactions were used to describe the carbon reduction of iron oxides and reflected the whole process [39,40]. In BF ironmaking, the reactions of C and iron oxides were generally called direct reduction reactions. The reactions of CO or H₂ and iron oxide were called indirect reduction reactions. The possible reactions were listed in

Table 1. The possible chemical reactions between the initial state and the final state.

Reaction Type	Reaction Equation	Number
Direct reduction reaction with only CO generated	$3\mathrm{C}\left(\mathrm{s}\right)+{\mathrm{Fe}}_2{\mathrm{O}}_3\left(\mathrm{s}\right)=2\mathrm{Fe}\left(\mathrm{s}\right)+3\mathrm{CO}\left(\mathrm{g}\right)$	(2)
	$4\mathrm{C}\left(\mathrm{s}\right)+{\mathrm{Fe}}_3{\mathrm{O}}_4\left(\mathrm{s}\right)=3\mathrm{Fe}\left(\mathrm{s}\right)+4\mathrm{CO}\left(\mathrm{g}\right)$	(3)
	$\mathrm{C}\left(\mathrm{s}\right)+\mathrm{FeO}\left(\mathrm{s}\right)=\mathrm{Fe}\left(\mathrm{s}\right)+\mathrm{CO}\left(\mathrm{g}\right)$	(4)
Direct reduction reaction with only CO2 generated	$3\mathrm{C}\left(\mathrm{s}\right)+{2\mathrm{Fe}}_2{\mathrm{O}}_3\left(\mathrm{s}\right)=4\mathrm{Fe}\left(\mathrm{s}\right)+{3\mathrm{CO}}_2\left(\mathrm{g}\right)$	(5)
	$2\mathrm{C}\left(\mathrm{s}\right)+{\mathrm{Fe}}_3{\mathrm{O}}_4\left(\mathrm{s}\right)=3\mathrm{Fe}\left(\mathrm{s}\right)+{2\mathrm{CO}}_2\left(\mathrm{g}\right)$	(6)
	$\mathrm{C}\left(\mathrm{s}\right)+2\mathrm{FeO}\left(\mathrm{s}\right)=2\mathrm{Fe}\left(\mathrm{s}\right)+{\mathrm{CO}}_2\left(\mathrm{g}\right)$	(7)
Gasification reaction	$\mathrm{C}\left(\mathrm{s}\right)+{\mathrm{CO}}_2\left(\mathrm{g}\right)=2\mathrm{CO}\left(\mathrm{g}\right)$	(8)
Complete combustion reaction	$\mathrm{C}\left(\mathrm{s}\right)+{\mathrm{O}}_2\left(\mathrm{g}\right)={\mathrm{CO}}_2\left(\mathrm{g}\right)$	(9)

, including the direct reduction reaction of carbon and iron oxides (which was divided into only CO generated, only CO₂ generated, and both CO and CO₂ generated), the gasification reaction of C and CO_2, and the combustion of C and O₂. The abbreviation of (s) and (g) referred to the solid phase and gas phase, respectively.

According to the published data of a certain large BF in the reference [39], the average volume fraction of CO and CO₂ in the top gas of BF were 21.859% and 19.933%, respectively. The average value of the ratio of volume fraction of CO to that of CO₂ in a certain large BF was 1.10, as shown in Equation (10). It was to be noted that the CO and CO₂ in the top gas of BF were from the reduction reaction, gasification reaction, and combustion reaction, which provided the former two kinds of reaction. From the perspective of the initial state and the final state, the CO₂ output was from the reduction reaction, gasification reaction, and combustion reaction, as shown in Equation (11). For the coupling reaction of reduction reactions and gasification reaction, the ratio of volume fraction of CO to that of CO₂ in equilibrium state was more than 1.10, as shown in Equation (12).

The complete combustion of carbon occurred in the tuyere combustion strip of BF, so the generated CO₂ would participate in the gasification reactions and has been converted to CO. However, the follow up coupling reaction made sure that CO₂ was kept in a certain concentration in top gas. The CO₂ output was the sum generated from the combustion and coupling reactions, as shown in Equation (11).

$$\frac{{\phi }_{\mathrm{C}\mathrm{O}}}{{\phi }_{{\mathrm{C}\mathrm{O}}_2}}\approx 1.10 (\mathrm{average} \mathrm{ratio} \mathrm{in} \mathrm{the} \mathrm{top} \mathrm{gas} \mathrm{of} \mathrm{BF})$$

(10)

$$M_{\mathrm{C}{\mathrm{O}}_2,\mathrm{output}}=M_{\mathrm{C}{\mathrm{O}}_2,\mathrm{combustion}}+M_{\mathrm{C}{\mathrm{O}}_2,\mathrm{reduction}}+M_{\mathrm{C}{\mathrm{O}}_2,\mathrm{gasification}}=M_{\mathrm{C}{\mathrm{O}}_2,\mathrm{combustion}}+M_{\mathrm{C}{\mathrm{O}}_2,\mathrm{coupling}}$$

(11)

where M referred to the mass of CO₂.

$$\frac{{\phi }_{\mathrm{C}\mathrm{O}}}{{\phi }_{{\mathrm{C}\mathrm{O}}_2}}>1.10 (\mathrm{in} \mathrm{the} \mathrm{coupling} \mathrm{reactions})$$

(12)

where ${\phi }_{{\mathrm{CO}}_{}}$ and ${\phi }_{{\mathrm{CO}}_2}$ were the volume fraction of CO and CO₂, respectively.

2.2. Thermodynamic Functions

2.2.1. Basic Thermodynamic Function

The classical pure material data book [45,46,47] provided calories and kilocalories as heat units and listed the isobaric specific heat capacity, standard enthalpy, and standard entropy at 298 K, transition enthalpy, and transition entropy when the phase changes. Although the tabulated data was easy to read, an additional conversion calculation was required and the more detailed needs of scientific researchers were not being met. For this reason, the functions of standard enthalpy and standard Gibbs free energy would be derived by mathematical derived from basic data. The origin data, function expressions and calculation processes were shown in the Supplementary Sheet. The calculation methods were listed in Equations (13)–(19), and the results were shown in

Table 2. Thermodynamic parameters calculated by mathematical derivation.

Species	Phase	${\mathit{H}}_{{\mathit{T}}_1}^{Ө}$ /(kJ/mol)	$$\begin{gathered} {\mathit{S}}_{{\mathit{T}}_1}^{Ө} \\ /(\mathbf{J}/(\mathbf{mol}•\mathbf{K}\left)\right) \end{gathered}$$	$$\begin{gathered} {\mathit{H}}_0 \\ /(\mathbf{kJ}/\mathbf{mol}) \end{gathered}$$	I /(J/mol)	Specific Heat Capacity Parameter				Temperature Range		Transition Enthalpy /(J/mol)	Transition Entropy /(J/(mol•K))
						A1	A2	A3	A4	T1/K	T2/K
C	solid	0.000	5.740	−2106.402	6.659	0.109	38.940	−1.481	−17.385	298.150	1100.000	0.000	0.000
		13,993.972	26.590	−16,027.072	170.780	24.439	0.435	−31.627	0.000	1100.000	4073.000	0.000	0.000
Fe	solid, α	0.000	27.280	−9267.465	161.985	28.175	−7.318	−2.895	25.041	298.150	800.000	0.000	0.000
	solid, α	15,566.499	56.914	22,1874.519	−1925.185	−263.454	255.810	619.232	0.000	800.000	1000.000	0.000	0.000
	solid, α	24,402.271	66.704	31,8137.899	−4446.394	−641.905	696.339	0.000	0.000	1000.000	1042.000	0.000	0.000
	solid, α	27,302.663	69.541	−1,030,294.708	13,538.465	1946.255	−1787.497	0.000	0.000	1042.000	1060.000	0.000	0.000
	solid, α	28,519.379	70.700	−68,549.061	902.887	132.490	−77.200	0.000	0.000	1060.000	1184.000	0.000	0.000
	solid, β	34,207.458	75.784	−57.453	127.881	23.991	8.360	0.000	0.000	1184.000	1665.000	899.560	0.761
	solid, γ	0.000	27.280	−9267.465	161.985	28.175	−7.318	−2.895	25.041	1665.000	1809.000	13,807.200	7.632
FeO	solid	−272,043.680	60.752	−288,683.263	283.931	50.802	8.615	−3.310	0.000	298.150	1650.000	24,058.000	14.581
Fe3O4	solid, α	−1,118,383.200	146.440	−1,153,388.928	493.621	86.266	208.915	0.000	0.000	298.150	866.000	0.000	0.000
	solid, β	−1,000,344.110	357.057	−1,174,264.622	1202.180	200.832	0.000	0.000	0.000	866.000	1870.000	138,072.000	73.835
Fe2O3	solid, α	−825,503.200	87.446	−863,246.763	602.366	98.282	77.822	−14.853	0.000	298.150	953.000	0.000	0.000
	solid, β	−732,685.790	245.076	−876,230.462	938.770	150.624	0.000	0.000	0.000	953.000	1053.000	669.440	0.703
	solid, γ	−716,953.950	260.809	−860,742.892	802.955	132.675	7.364	0.000	0.000	1053.000	1730.000	0.000	0.000
O2	gas	0.000	205.037	−9679.104	−2.205	29.957	4.184	−1.674	0.000	298.150	3000.000	0.000	0.000
CO	gas	−110,541.280	197.552	−119,209.213	−6.029	28.409	4.100	−0.046	0.000	298.150	2500.000	0.000	0.000
CO2	gas	−393,505.200	213.660	−409,930.357	89.475	44.141	9.037	−8.535	0.000	298.150	3000.000	0.000	0.000
H2O	gas	−241,814.280	188.724	−251,122.370	15.205	29.999	10.711	0.335	0.000	298.150	2500.000	−241,814.280	188.724
H2	gas	0.000	130.583	−8110.091	52.816	27.280	3.264	0.502	0.000	298.150	3000.000	0.000	130.583

. Equation (20) was used to check the correctness of the calculation results.

$$C_T=A_1+A_2\times {10}^{-3}T+A_3\times {10}^5{T}^{-2}+A_4\times {10}^{-6}{T}^2$$

(13)

$$H_T^{Ө}={\displaystyle \underset{298.15}{\overset{T}{\int }}{\mathrm{C}}_{T}dT}=H_0+A_{1}T+\frac{A_2\times {10}^{-3}}{2}{T}^2-A_3\times {10}^5{T}^{-1}+\frac{A_4\times {10}^{-6}}{3}{T}^3$$

(14)

$$\begin{array}{c}{H}_0=H_{298.15}^{Ө}-(A_1\times 298.15+\frac{1}{2}\times A_2\times {10}^{-3}\times {298.15}^2\\ -A_3\times {10}^5\times {298.15}^{-1}+\frac{1}{3}\times A_4\times {10}^{-6}\times {298.15}^3)\end{array}$$

(15)

$$S_T^{Ө}={\displaystyle \underset{298.15}{\overset{T}{\int }}\frac{{\mathrm{C}}_T}{T}dT}=S_0+A_1\ln T+A_2\times {10}^{-3}T-\frac{1}{2}{A}_3\times {10}^5{T}^{-2}+\frac{1}{2}{A}_4\times {10}^{-6}{T}^2$$

(16)

$$\begin{array}{c}{S}_0=S_{298.15}^{Ө}-(A_1\times \ln 298.15+A_2\times {10}^{-3}\times 298.15-\\ \frac{1}{2}{A}_3\times {10}^5\times {298.15}^{-2}+\frac{1}{2}{A}_4\times {10}^{-6}\times {298.15}^2)\end{array}$$

(17)

$$G_T^{Ө}=H_T^{Ө}-T{S}_T^{Ө}{H}_0+IT-A_{1}T\ln T-\frac{1}{2}{A}_2\times {10}^{-3}{T}^2-\frac{1}{2}{A}_3\times {10}^5{T}^{-1}-\frac{1}{6}{A}_4\times {10}^{-6}{T}^3$$

(18)

$$\begin{array}{c}I=-S_{298.15}^{Ө}+A_1\times (1+\ln 298.15)+A_2\times {10}^{-3}\times 298.15\\ -\frac{1}{2}{A}_3\times {10}^5\times {298.15}^{-2}+\frac{1}{2}{A}_4\times {10}^{-6}\times {298.15}^2\end{array}$$

(19)

$$I=A_1-S_0$$

(20)

In these equations:

$C_T$, isobaric specific heat capacity at temperature T, J/(mol•K);

$H_T^{Ө}$, standard molar enthalpy at temperature T, J/mol;

$S_T^{Ө}$, standard molar entropy at temperature T, J/(mol•K);

$G_T^{Ө}$, standard molar Gibbs free energy at temperature T, J/mol;

$T$, temperature, K;

$H_0$, integration constant of standard molar enthalpy, J/mol;

$S_0$, integration constant of standard molar entropy, J/(mol•K);

$I$, integration constant of standard molar Gibbs free energy, J/mol;

A₁, A₂, A₃, A₄, coefficient of specific heat capacity, dimensionless parameter.

In Table 2, Greek symbols of α, β, γ, refer to the serial number of the crystal body. T₁ and T₂ refer to the temperature initial point and the final point when the phase of solid species changes, and the enthalpy and Gibbs free energy at these temperatures need to be dealt with carefully.

When the chemical reaction equations were confirmed, the reaction enthalpy ${\mathrm{\Delta }}_r{H}_T^{Ө}$ (J/mol) and reaction Gibbs free energy ${\mathrm{\Delta }}_r{G}_T^{Ө}$ (J/mol) could be calculated according to the Equations (21) and (22), respectively, namely that the former state was subtracted from the latter state. In other words, the functions were calculated from the addition and subtraction of parameters of thermodynamic functions. Besides, Equation (21) also was used to calculate sensible heat needed for solid raw materials.

$${\mathrm{\Delta }}_r{H}_T^{Ө}={\displaystyle \sum _i^{}{\nu }_i{H}_T^{Ө}}$$

(21)

$${\mathrm{\Delta }}_r{G}_T^{Ө}={\displaystyle \sum _i^{}{\nu }_i{G}_T^{Ө}}$$

(22)

where ${\nu }_i$ was the stoichiometric number of species $i$ in the reaction equation, and was “−” for the former state, and “+” for the latter state. The subscript $i$ refers to species $i$ that participated in the chemical reaction.

2.2.2. Single Reaction

According to theoretical isotherm equations of Gibbs free energy, as shown in Equation (23), and gas–solid reduction reaction of Equations (2)–(7), the relative gas partial pressure of CO and CO₂ in reduction reactions could be calculated by Equations (24)–(25) and Equations (26) and (27), respectively.

$${\mathrm{\Delta }}_r{G}_T^{Ө}=-RTln{K}^{Ө}$$

(23)

For the reaction Equations (2)–(4),

$${\mathrm{\Delta }}_r{G}_T^{Ө}=-RTln{K}^{Ө}=-RTln{P}_{CO}^{{\nu }_{CO}}=-RTln{\left(\frac{{P^{\prime }}_{CO}}{P^{Ө}}\right)}^{{\nu }_{CO}} {\nu }_{CO}=1, 3, 4$$

(24)

$$P_{CO}=\sqrt[{\nu }_{CO}]{\exp (-\frac{{\mathrm{\Delta }}_r{G}_T^{Ө}}{RT})} {\nu }_{CO}=1, 3, 4$$

(25)

For the reaction Equations (5) and (6),

$${\mathrm{\Delta }}_r{G}_T^{Ө}=-RTln{K}^{Ө}=-RTln{P}_{{CO}_2}^{{\nu }_{{CO}_2}}=-RTln{\left(\frac{{P^{\prime }}_{{CO}_2}}{P^{Ө}}\right)}^{{\nu }_{{CO}_2}} {\nu }_{{CO}_2} = 1, 2, 3$$

(26)

$$P_{{CO}_2}=\sqrt[{\nu }_{{CO}_2}]{\exp (-\frac{{\mathrm{\Delta }}_r{G}_T^{Ө}}{RT})} {\nu }_{{CO}_2} = 1, 2, 3$$

(27)

In these equations:

$P_{CO}$ and $P_{C{O}_2}$, were relative gas pressure of CO and CO₂, respectively, dimensionless, the ratio of absolute atmospheric pressure (namely $P_{CO}^{\prime }$ and $P_{C{O}_2}^{\prime }$, unit: Pa) to standard atmospheric pressure $P^{Ө}$ (= 101,325 Pa);

R, was ideal gas constant, 8.314 J/(mol•K);

$v_{CO}$ = 1, 3, 4 were the stoichiometric number of species CO in reduction reaction with only CO generated in Equations (2)–(4);

$v_{C{O}_2}$ = 1, 2, 3 were the stoichiometric number of species CO₂ in reduction reaction with only CO₂ generated in Equations (5)–(7).

The volume fraction sum of CO and CO₂ in the top gas of actual BF was about 41.13–42.43% [39,41], and the other parts were mainly N₂ and a small amount of H₂O and H₂. The top gas pressure of modern advanced BF was 200–300 kPa [12,41], so the sum of the relative partial pressure of CO and CO₂ could be set as 0.4–1.2. According to Equation (23) and Equation (8), the relative gas partial pressure of CO and CO₂ in gasification reaction can be calculated by Equations (28)–(33).

$${\mathrm{\Delta }}_r{G}_T^{Ө}=-RTln\frac{{(\frac{P_{CO}^{\prime }}{P^{Ө}})}^2}{(\frac{P_{{CO}_2}^{\prime }}{P^{Ө}})}=-RTln\frac{P_{CO}^2}{P_{{CO}_2}^{}} ,so \frac{P_{CO}^2}{P_{{CO}_2}^{}}=e^{\frac{{\mathrm{\Delta }}_r{G}_T^{Ө}}{-RT}}$$

(28)

$$\frac{P_{CO}^2}{P_{{CO}_2}^{}}=e^{\frac{{\mathrm{\Delta }}_r{G}_T^{Ө}}{-RT}}$$

(29)

$$P_{CO}^{}+P_{{CO}_2}^{}=z, z=0.4-1.2$$

(30)

$$e^{\frac{{\mathrm{\Delta }}_r{G}_T^{Ө}}{RT}}{P}_{CO}^2+P_{CO}^{}-z=0, z=0.4-1.2$$

(31)

$$P_{CO}^{}=\frac{-1+\sqrt{1+4z{e}^{\frac{{\mathrm{\Delta }}_r{G}_T^{Ө}}{RT}}}}{2e^{\frac{{\mathrm{\Delta }}_r{G}_T^{Ө}}{RT}}}=\frac{-e^{\frac{{\mathrm{\Delta }}_r{G}_T^{Ө}}{-RT}}+\sqrt{{(e^{\frac{{\mathrm{\Delta }}_r{G}_T^{Ө}}{-RT}})}^2+4z{e}^{\frac{{\mathrm{\Delta }}_r{G}_T^{Ө}}{-RT}}}}{2}, z=0.4-1.2$$

(32)

$$P_{{CO}_2}^{}=z-\frac{-1+\sqrt{1+4z{e}^{\frac{{\mathrm{\Delta }}_r{G}_T^{Ө}}{RT}}}}{2e^{\frac{{\mathrm{\Delta }}_r{G}_T^{Ө}}{RT}}}, z=0.4-1.2$$

(33)

where z was the sum of the relative partial pressure of CO and that of CO₂.

2.2.3. Coupling Reaction

The coupling reactions equations of the C-CO₂ gasification reaction and C-Fe_xO_y direct reduction reaction were shown in Equations (34), (37) and (40), and m, n, and p were coupling parameters for Fe₂O₃ (s), Fe₃O₄ (s), FeO (s), respectively. Due to the existence of CO₂, the variation range of m, n and p were fixed as 0 ≤ m ≤ 3, 0 ≤ n ≤ 2, 0 ≤ p ≤ 1, respectively. Equations (35), (38), and (41) were the isothermal equations between the Gibbs free energy and gas partial pressure. According to the ratio of the gas partial pressure of CO and CO₂, the Equations (36), (39), and (42) were used to calculate the equilibrium gas partial pressure and the equilibrium gas volume fraction.

From the Equations (36), (39), and (42), the volume fraction of CO and CO₂ were not a function of temperature and were affected by the coupling parameter.

When m = 3, n = 2, and p = 1, the Equations (34), (37) and (40), were equal to the Equations (2), (3) and (4), respectively. When m = 0, n = 0, and p = 0, the Equations (34), (37) and (40) were equal to the Equations (5), (6) and (7), respectively.

$$\begin{array}{l} 1\times \left\{3C(s)+{2Fe}_2{O}_3(s)=4Fe(s)+{3CO}_2(g)\right\} \\ \underset{¯}{+ m\times \left\{C(s)+{CO}_2(g)=2CO(g)\right\} ;m=0-3.0 }\\ (m+3)C(s)+{2Fe}_2{O}_3(s)=4Fe(s)+2mCO(g)+(3-m{)CO}_2(g)\end{array}$$

(34)

$${\mathrm{\Delta }}_r{G}_T^{Ө}=-RTln\left({(\frac{P_{CO}^{\prime }}{P^{Ө}})}^{2m}{(\frac{P_{{CO}_2}^{\prime }}{P^{Ө}})}^{3-m}\right)=-RTln\left(P_{CO}^{2m}{P}_{{CO}_2}^{3-m}\right)$$

(35)

$$\left\{\begin{array}{c}{P}_{CO}^{2m}{P}_{{CO}_2}^{3-m}=e^{\frac{{\mathrm{\Delta }}_r{G}_T^{Ө}}{-RT}}\\ \begin{array}{l}\frac{P_{CO}^{}}{P_{{CO}_2}^{}}=\frac{2m}{3-m}\ge 1.10\\ P_{CO}^{}+P_{{CO}_2}^{}=z \\ z=0.4-1.2\end{array}\end{array}\right.\stackrel{}{\to }\left\{\begin{array}{c}{P}_{{CO}_2}^{}=\sqrt[3+m]{(\frac{2m}{3-m}{)}_{}^{-2m}{e}^{\frac{{\mathrm{\Delta }}_r{G}_T^{Ө}}{-RT}}}=\frac{3-m}{3+m}z=z{\phi }_{{CO}_2}\\ \begin{array}{l}{P}_{CO}^{}=\sqrt[3+m]{(\frac{2m}{3-m}{)}_{}^{3-m}{e}^{\frac{{\mathrm{\Delta }}_r{G}_T^{Ө}}{-RT}}}=\frac{2m}{3+m}z=z{\phi }_{CO}\\ {\phi }_{{CO}_2}=\frac{3-m}{3+m}\\ {\phi }_{{CO}_{}}=\frac{2m}{3+m}\\ m\ne 0,m\ne 3, 1.06<m<3\\ 0.4\le P_{CO}^{} or P_{CO}^{}\le 1.2\end{array}\end{array}\right.$$

(36)

$$\begin{array}{l} 1\times \left\{2C(s)+{Fe}_3{O}_4(s)=3Fe(s)+{2CO}_2(g)\right\} \\ \underset{¯}{+ n\times \left\{C(s)+{CO}_2(g)=2CO(g)\right\} ;n=0-2.0 }\\ (n+2)C(s)+{Fe}_3{O}_4(s)=3Fe(s)+2nCO(g)+(2-n{)CO}_2(g)\end{array}$$

(37)

$${\mathrm{\Delta }}_r{G}_T^{Ө}=-RTln\left({(\frac{P_{CO}^{\prime }}{P^{Ө}})}^{2n}{(\frac{P_{{CO}_2}^{\prime }}{P^{Ө}})}^{2-n}\right)=-RTln\left(P_{CO}^{2n}{P}_{{CO}_2}^{2-n}\right)$$

(38)

$$\left\{\begin{array}{c}{P}_{CO}^{2n}{P}_{{CO}_2}^{2-n}=e^{\frac{{\mathrm{\Delta }}_r{G}_T^{Ө}}{-RT}}\\ \begin{array}{l}\frac{P_{CO}}{P_{{CO}_2}}=\frac{2n}{2-n}\ge 1.10\\ P_{CO}^{}+P_{{CO}_2}^{}=z\\ z=0.4-1.2 \end{array}\end{array}\right.\stackrel{}{\to }\left\{\begin{array}{c}{P}_{{CO}_2}^{}=\sqrt[2+n]{(\frac{2n}{2-n}{)}_{}^{-2n}{e}^{\frac{{\mathrm{\Delta }}_r{G}_T^{Ө}}{-RT}}}=\frac{2-n}{2+n}z=z{\phi }_{{CO}_2}\\ \begin{array}{l}{P}_{CO}^{}=\sqrt[2+n]{(\frac{2n}{2-n}{)}_{}^{2-n}{e}^{\frac{{\mathrm{\Delta }}_r{G}_T^{Ө}}{-RT}}}=\frac{2n}{2+n}z=z{\phi }_{CO}\\ {\phi }_{{CO}_2}=\frac{2-n}{2+n}\\ {\phi }_{{CO}_{}}=\frac{2n}{2+n}\\ n\ne 0(n\ne 2.0)0.71<n<2\\ 0.4\le P_{CO}^{} \mathrm{or} P_{\mathrm{CO}}^{}\le 1.2\end{array}\end{array}\right.$$

(39)

$$\begin{array}{l} 1\times \left\{C(s)+2FeO(s)=2Fe(s)+{CO}_2(g)\right\} \\ \underset{¯}{+ p\times \left\{C(s)+{CO}_2(g)=2CO(g)\right\} ;p=0-1.0}\\ (p+1)C(s)+2FeO(s)=2Fe(s)+2pCO(g)+(1-p){CO}_2(g)\end{array}$$

(40)

$${\mathrm{\Delta }}_r{G}_T^{Ө}=-RTln\left({(\frac{P_{CO}^{\prime }}{P^{Ө}})}^{2p}{(\frac{P_{{CO}_2}^{\prime }}{P^{Ө}})}^{1-p}\right)=-RTln\left(P_{CO}^{2p}{P}_{{CO}_2}^{1-p}\right)$$

(41)

$$\left\{\begin{array}{c}{P}_{CO}^{2p}{P}_{{CO}_2}^{1-p}=e^{\frac{{\mathrm{\Delta }}_r{G}_T^{Ө}}{-RT}}\\ \begin{array}{l}\frac{P_{CO}^{}}{P_{{CO}_2}^{}}=\frac{2p}{1-p}\ge 1.10\\ P_{CO}^{}+P_{{CO}_2}^{}=z\\ z=0.4-1.2 \end{array}\end{array}\right.\stackrel{}{\to }\left\{\begin{array}{c}{P}_{{CO}_2}^{}=\sqrt[1+p]{(\frac{2p}{1-p}{)}_{}^{-2p}{e}^{\frac{{\mathrm{\Delta }}_r{G}_T^{Ө}}{-RT}}}=\frac{1-p}{1+p}z=z{\phi }_{{CO}_2}\\ \begin{array}{l}{P}_{CO}^{}=\sqrt[1+p]{(\frac{2p}{1-p}{)}_{}^{1-p}{e}^{\frac{{\mathrm{\Delta }}_r{G}_T^{Ө}}{-RT}}}=\frac{2p}{1+p}z=z{\phi }_{CO}\\ {\phi }_{{CO}_2}=\frac{1-p}{1+p}\\ {\phi }_{{CO}_{}}=\frac{2p}{1+p}\\ p\ne 0,p\ne 1.0,0.35<p<1\\ 0.4\le P_{CO}^{} or P_{CO}^{}\le 1.2\end{array}\end{array}\right.$$

(42)

3. Results and Discussion

3.1. Reduction Reactions between Carbon and Iron Oxides

3.1.1. Standard Gibbs Free Energy

According to Table 2 and Equations (2)–(7) and (13)–(20), the standard Gibbs free energy of reduction reactions between carbon and iron oxides with single gas product generation were calculated, and the graphical representation of these functions was shown in Figure 3. It should be noted that the displayed line was composed of piecewise functions according to the temperature range in Table 2. When ${\Delta }_r{G}_T^{Ө}=0$ and $P_{\mathrm{CO}}=P_{C{O}_2}=P^{Ө}$, the temperature T^′ was the lowest critical temperature at which the reaction could start. The critical reaction temperatures for the reduction reactions of iron-containing raw materials Fe₂O₃(s), Fe₃O₄(s), FeO(s) with C(s) to generated CO₂ were 872 K, 997 K, 1144 K, respectively. The critical reaction temperatures for the reduction reactions of iron-containing raw materials Fe₂O₃(s), Fe₃O₄(s), FeO(s) with C(s) to generated CO were 924 K, 983 K, 1044 K, respectively. The lowest critical temperature of carbon and iron oxides was at 872 K for the reaction 3C(s) + 2Fe₂O₃(s) = 4Fe(s) + 3CO₂(g), and the highest temperature was at 1144 K for the reaction C(s) + 2FeO(s) = 2Fe(s) + CO₂(g).

3.1.2. Equilibrium Relative Gas Partial Pressure of CO and CO₂

According to Table 2 and Equations (23)–(27), the equilibrium relative gas partial pressure of CO and CO₂ of reduction reactions between carbon and iron oxides were calculated, and the graphical representation of these functions was shown in Figure 4. Figure 4a,c displayed the global y-axis as 0–1000, and Figure 4b,d displayed the local y-axis as 0–3 to display comparative connections of different raw materials. All the curves in Figure 3 increased with rising temperature, and the y-axis coordinate values could be more than 100 when the temperature was more than 1200 K. Figure 4 shows that the equilibrium relative gas partial pressure of CO or CO₂ at the same temperature in order from high to low were Fe₂O₃(s), Fe₃O₄(s), FeO(s).

When the actual relative gas partial pressure was lower than the equilibrium relative gas partial pressure, it was more likely to produce metallic iron. In other words, making the gas partial pressure lower than the equilibrium value was beneficial for decreasing the critical reaction temperature. The equilibrium relative gas partial pressure of CO and CO₂ was set as 0.01, 0.10, 0.25, 0.50, 0.75, 1.00, which were not more than one atmosphere, and the corresponding critical reaction temperatures were clear, which were listed in

Table 3. The critical reaction temperature of reduction reactions between carbon and iron oxides with single gas product generation at one atmosphere (K).

Reaction Equation	The Relative Partial Pressure of CO						The Relative Partial Pressure of CO2
	0.01	0.10	0.25	0.50	0.75	1.00	0.01	0.10	0.25	0.50	0.75	1.00
3C(s) + Fe2O3(s) = 2Fe(s) + 3CO(g)	756	831	866	894	911	924
3C(s) + 2Fe2O3(s) = 4Fe(s) + 3CO2(g)							712	783	816	843	860	872
4C(s) + Fe3O4(s) = 3Fe(s) + 4CO(g)	798	881	919	950	969	983
2C(s) + Fe3O4(s) = 3Fe(s) + 2CO2(g)							796	885	926	960	981	997
C(s) + FeO(s) = Fe(s) + CO(g)	832	927	970	1006	1028	1044
C(s) + 2FeO(s) = 2Fe(s) + CO2(g)							877	994	1049	1094	1123	1144

. For example, the reaction temperature of 3C(s) + 2Fe₂O₃(s) = 4Fe(s) + 3CO₂(g) decreased from 872 K at $P_{\mathrm{C}{\mathrm{O}}_2} = 1$ to 712 K at $P_{\mathrm{C}{\mathrm{O}}_2} = 0.01$, and the decreased extent was 160 K.

In actual BFs, the value of relative gas partial pressure of CO and CO₂ was larger than 0.2. According to Figure 4, the lowest temperature was required to be more than 857 K for the reaction between C(s) and Fe₂O₃(s) with only CO generated and more than 808 K for the reaction between C(s) and Fe₂O₃(s) with only CO₂ generated, respectively. This was so that the possible reactions of carbon and iron oxides in the BF could be set as more than 808 K.

3.1.3. Standard Reaction Enthalpy

According to Table 2 and Equation (21), the standard enthalpy function per mole iron produced by reduction reactions was calculated, and the graphical representation of these functions was shown in Figure 5.

Table 4. The reaction energy consumption per ton metallic iron of reduction reactions with single gas product generation at 298–1650 K (GJ/t).

Reaction Equation	Temperature/(K)
	298	1173	1273	1373	1473	1573	1650
3C(s) + Fe2O3(s) = 2Fe(s) + 3CO(g)	4.410	4.210	4.174	4.138	4.103	4.069	4.044
3C(s) + 2Fe2O3(s) = 4Fe(s) + 3CO2(g)	2.100	1.940	1.919	1.898	1.878	1.860	1.848
4C(s) + Fe3O4(s) = 3Fe(s) + 4CO(g)	4.025	3.840	3.808	3.777	3.747	3.719	3.699
2C(s) + Fe3O4(s) = 3Fe(s) + 2CO2(g)	1.972	1.823	1.804	1.785	1.769	1.756	1.747
C(s) + FeO(s) = Fe(s) + CO(g)	2.884	2.820	2.793	2.764	2.734	2.706	2.684
C(s) + 2FeO(s) = 2Fe(s) + CO2(g)	1.344	1.307	1.289	1.270	1.251	1.233	1.220

demonstrates the data of the reaction energy consumption per ton metallic iron produced at the temperature range of 298–1650 K. The reduction temperatures of 1173 K, 1273 K, 1373 K, 1473 K, 1573 K, 1650 K were set to evaluate the energy consumption of reduction reactions.

From Figure 5 and Table 4, for the same kind of iron oxide, the energy consumption of the reduction reaction with only CO generated was nearly twice as much as that of the reduction reaction with generating CO₂. In the same type of reaction, energy consumption in order from high to low were Fe₂O₃ (s), Fe₃O₄ (s), FeO (s). It was important to note that the energy consumption of the above reactions reached a peak at 298K, and remained downward as a function of temperature. For instance, the reaction energy consumption per ton of iron through the reaction of 3C(s) + 2Fe₂O₃(s) = 4Fe(s) + 3CO₂(g) was decreased from 2.100 GJ/t at 298 K to 1.848 GJ/t at 1650 K, and the decreased percent was 12.01%, which should not be neglected. So, the use of the reaction enthalpy at 298 K for the heat calculation was inappropriate, and the reaction temperature should be confirmed when the reaction enthalpy was used.

3.2. Gasification Reaction between Carbon and CO₂

3.2.1. Standard Gibbs Free Energy

According to Table 2 and Equation (8), the standard Gibbs free energy of gasification reaction between carbon and CO₂ was calculated, and the graphical representation of these functions was shown in Figure 6. When $T>972\mathrm{K}$, ${\Delta }_r{G}_T^{Ө}<0$ the reaction of C(s) + CO₂(g) = 2CO(g) went forward.

3.2.2. Equilibrium Relative Gas Partial Pressure of CO

According to Table 2 and Equations (28)–(33), the equilibrium relative gas partial pressure of CO and CO₂ of the reaction of C(s) + CO₂(g) = 2CO(g) was calculated, and the graphical representation of these functions was shown in Figure 7.

For the varied sum value (0.4, 0.6, 0.8, 1.0, 1.2) of the relative gas partial pressure of CO and CO₂, the equilibrium $P_{\mathrm{CO}}^{}$ was displayed in an S-shaped curve in Figure 7. The relative gas partial pressure of CO increased with the sum value increasing at the same temperature. The curves in Figure 7a increased slightly at $T<700 \mathrm{K}$ with $P_{\mathrm{CO}}^{}<0.02$ and jumped sharply at about $T=700\text{–}1100 \mathrm{K}$, and then remained stable at $T>1100 \mathrm{K}$ with $P_{\mathrm{CO}}^{}<0.02$.

Figure 7b showed the six sets of grid data of equilibrium $P_{\mathrm{CO}}^{}$ with $P_{\mathrm{CO}}^{}+P_{{\mathrm{CO}}_2}^{}=1$, to display the change of $P_{\mathrm{CO}}^{}$ and temperature in more detail. Equilibrium $P_{\mathrm{CO}}^{}$ increased with the temperature rising. When the equilibrium relative gas partial pressure of CO was set as 0.01, 0.20, 0.25, 0.50, 0.75, 0.99, the corresponding critical reaction temperature was 680 K, 853 K, 872 K, 941 K, 1010 K, 1243 K, respectively. When the actual $P_{\mathrm{CO}}^{}$ was less than the equilibrium $P_{\mathrm{CO}}^{}$, the reaction of C(s) + CO₂(g) = 2CO(g) went forward.

The relative gas partial pressure of CO and CO₂ was less than 0.2 in actual BF, so the gasification temperature of C(s) + CO₂(g) = 2CO(g) should be considered as more than 905 K.

3.2.3. Standard Reaction Enthalpy of the Gasification Reaction and Combustion Reaction

According to Table 2 and Equation (8), the standard enthalpy of the gasification reaction of C(s) + CO₂(g) = 2CO(g) was shown in Figure 8a, and increased from 172.423 kJ/mol at 298 K to 173.683 kJ/mol at 527 K, and then decreased to 163.974 kJ/mol at 1650 K. Obviously, the standard enthalpy of the gasification at the temperature more than 905 K was less than that at 298 K. For the calculation of energy consumption of the gasification reaction of C(s) + CO₂(g) = 2CO(g), it was necessary to confirm the given temperature. In the follow up energy consumption calculation, the temperature of the gasification reaction was set to the same as that of the reduction reaction, namely being 1173 K, 1273 K, 1373 K, 1473K, 1573K, 1650 K.

According to Table 2 and Equation (9), the standard enthalpy of the combustion reaction of C(s) + O₂(g) = CO₂(g) was shown in Figure 8b and decreased from −393.505 kJ/mol at 298 K to −396.631 kJ/mol at 1650 K.

The temperature of hot air injected into BF was 1413–1533 K (1140–1260 °C) [8,12], and thus the average temperatures of 1473 K could be set as the temperature of O₂ (g) and combustion reaction. The combustion enthalpy at 1473 K was −396.218 kJ/mol, namely −0.0330 GJ/kg C and 30.286 kg C/GJ.

3.3. Coupling Reaction of Reduction and Gasification

3.3.1. Standard Gibbs Free Energy

According to Table 2 and the Equations (34), (37) and (40), the standard Gibbs free energy of the coupling reaction with varied coupling parameters was shown in Figure 9 and decreased with the increasing temperature.

T’ was the critical temperature when the standard Gibbs free energy was zero, and increased with the coupling parameters increasing for the reaction (m+3)C(s) + 2Fe₂O₃(s) = 4Fe(s) + 2mCO(g) + (3 − m)CO₂(g) and the reaction (p+1)C(s) + 2FeO(s) = 2Fe(s) + 2pCO(g) + (1 − p)CO₂(g), which were shown in Figure 9a,b, respectively. The T’ decreased slightly with the coupling parameter increasing for the reaction (n + 2)C(s) + Fe₃O₄(s) = 3Fe(s) + 2nCO(g) + (2 − n)CO₂(g). It could be seen that when the temperature was more than 1144 K, all the coupling reactions could start. For the different iron oxides, Figure 9 shows that one crossover point appeared for varied coupling parameters, and the temperature was 972 K.

3.3.2. Relative Gas Partial Pressure of CO and CO₂

According to the Table 2 and Equations (36), (39), and (42), the equilibrium relative gas partial pressure of CO₂ was calculated, and the graphical representation of these functions was shown in Figure 10 for the reaction of (m + 3)C(s) + 2Fe₂O₃(s) = 4Fe(s) + 2mCO(g) + (3 − m)CO₂(g) (m = 0.5, 1.0, 1.5, 2.0, 2.5), and in Figure 11 for the reaction of (n + 2)C(s) + Fe₃O₄(s) = 3Fe(s) + 2nCO(g) + (2 − n)CO₂(g) (n = 0.5, 1.0, 1.5), and in Figure 12 for the reaction of (p + 1)C(s) + 2FeO(s) = 2Fe(s) + 2pCO(g) + (1 − p)CO₂(g) (p = 0.2, 0.4, 0.6, 0.8), respectively. The global graph was displayed when the y-axis value was greater than 10, and the local graph was displayed when the y-axis value was less than 1.2.

The equilibrium relative gas partial pressure of CO₂ increased with temperature increases and decreased with increasing coupling parameters, namely more CO₂ was converted to CO. A similar changing rule appeared in Figure 10, Figure 11, Figure 12. When the actual relative gas partial pressure of CO₂ was under the equilibrium value, the coupling reaction proceeded in the direction of producing Fe(s) + CO(g) + CO2(g).

When the equilibrium relative gas partial pressure of CO₂ was limited between 0.4 and 1.2, the local graphs were shown in Figure 10b, Figure 11b and Figure 12b. The curves were parallel in a single graph.

Figure 13a shows that the ratio of equilibrium gas partial pressure of CO and CO₂ increased with the coupling parameters increasing and displayed a similar shape. When the ratio was fixed to 1.1–1.5, the coupling parameters were m = 1.06–1.28 for Fe₂O₃, n = 0.71–0.85 for Fe₃O₄, p = 0.35–0.43 for FeO, respectively, which was shown in Figure 13b.

According to the stoichiometry of chemical Equations (36), (39), and (42), C needed per mole iron produced and equilibrium CO₂ volume fraction as a function of the coupling parameter, as shown in Figure 14a,b, respectively. The C needed per mole of Fe increased with the coupling parameters increasing and the maximum value was 1.5 mol C/mol Fe with Fe₂O₃ reduction, the minimum value was 0.5 mol C/mol Fe with FeO reduction. Figure 14b shows that the Equilibrium CO₂ volume fraction decreased with the coupling parameters increasing, and the reason was that the coupling parameters represented the amount of the gasification reaction, which consumed CO₂.

3.3.3. Standard Reaction Enthalpy

According to Table 2 and the Equations (21), (34), (37), and (40), the standard reaction enthalpy with varied coupling parameters as a function of temperature was shown in Figure 15. The standard reaction enthalpy decreased with the temperature increasing and increased with the coupling parameter increasing. Figure 15 showed that the standard reaction enthalpy increased with the coupling parameters increasing.

Table 5. The energy consumption of heating the coupling reaction per ton iron (GJ/t).

Reaction Equation	Coupling Parameter	Reduction Temperature/(K)
		1173	1273	1373	1473	1573	1650
(m + 3)C(s) + 2Fe2O3(s) = 4Fe(s) + 2mCO(g) + (3 − m)CO2(g)	m = 0.0	1.940	1.914	1.898	1.884	1.871	1.863
	m = 0.5	2.318	2.290	2.271	2.254	2.240	2.229
	m = 1.0	2.697	2.666	2.645	2.625	2.608	2.595
	m = 1.5	3.075	3.042	3.018	2.996	2.976	2.961
	m = 2.0	3.453	3.418	3.392	3.367	3.344	3.327
	m = 2.5	3.831	3.794	3.765	3.738	3.712	3.693
	m = 3.0	4.210	4.170	4.138	4.108	4.080	4.059
(n + 2)C(s) + Fe3O4(s) = 3Fe(s) + 2nCO(g) + (2 − n)CO2(g)	n = 0.0	1.823	1.804	1.785	1.769	1.756	1.747
	n = 0.5	2.327	2.305	2.283	2.264	2.246	2.235
	n = 1.0	2.832	2.806	2.781	2.758	2.737	2.723
	n = 1.5	3.336	3.307	3.279	3.253	3.228	3.211
	n = 2.0	3.840	3.808	3.777	3.747	3.719	3.699
(p + 1)C(s) + 2FeO(s) = 2Fe(s) + 2pCO(g) + (1 − p)CO2(g)	p = 0.0	1.307	1.289	1.270	1.251	1.233	1.220
	p = 0.2	1.610	1.590	1.569	1.548	1.528	1.512
	p = 0.4	1.913	1.891	1.867	1.845	1.822	1.805
	p = 0.6	2.215	2.191	2.166	2.141	2.117	2.098
	p = 0.8	2.518	2.492	2.465	2.438	2.411	2.391
	p = 1.0	2.820	2.793	2.764	2.734	2.706	2.684

showed the energy consumption of heating the coupling reactions at the reduction temperature of 1173 K, 1273 K, 1373 K, 1473 K, 1573 K, and 1650 K. When the coupling parameter was fixed, the energy consumption of heating the coupling reactions decreased with increasing temperature.

3.4. Energy Consumption of Heating Solid Materials

According to Table 2 and Equation (21), the energy consumption of heating solid materials per ton iron before smelting was calculated based on the process in Figure 16, and the result was shown in

Table 6. The energy consumption of heating solid materials per ton iron before smelting (GJ/t).

Reaction Equation	Coupling Parameter	Reduction Temperature/(K)
		1173	1273	1373	1473	1573	1650
(m + 3)C(s) + 2Fe2O3(s) = 4Fe(s) + 2mCO(g) + (3 − m)CO2(g)	m = 0.0	1.770	1.864	1.960	2.055	2.150	2.222
	m = 0.5	1.805	1.904	2.005	2.105	2.205	2.282
	m = 1.0	1.839	1.944	2.050	2.156	2.261	2.342
	m = 1.5	1.874	1.984	2.095	2.206	2.317	2.402
	m = 2.0	1.909	2.024	2.141	2.257	2.373	2.462
	m = 2.5	1.944	2.064	2.186	2.307	2.428	2.521
	m = 3.0	1.979	2.104	2.231	2.358	2.484	2.581
(n + 2)C(s) + Fe3O4(s) = 3Fe(s) + 2nCO(g) + (2 − n)CO2(g)	n = 0.0	1.696	1.780	1.865	1.948	2.030	2.093
	n = 0.5	1.742	1.833	1.925	2.015	2.105	2.173
	n = 1.0	1.789	1.887	1.985	2.083	2.179	2.252
	n = 1.5	1.835	1.940	2.045	2.150	2.253	2.332
	n = 2.0	1.882	1.993	2.106	2.217	2.327	2.412
(p + 1)C(s) + 2FeO(s) = 2Fe(s) + 2pCO(g) + (1 − p)CO2(g)	p = 0.0	1.458	1.525	1.593	1.663	1.732	1.786
	p = 0.2	1.486	1.557	1.630	1.703	1.777	1.834
	p = 0.4	1.513	1.589	1.666	1.743	1.821	1.882
	p = 0.6	1.541	1.621	1.702	1.784	1.866	1.929
	p = 0.8	1.569	1.653	1.738	1.824	1.910	1.977
	p = 1.0	1.597	1.685	1.774	1.864	1.955	2.025

. The reduction temperature in Figure 16 was set as 1173 K, 1273 K, 1373 K, 1473 K, 1573 K, and 1650 K.

In the real process, Fe was not heated up to 1809 K, and the Fe₃C generated would melt at 1500 K. Within the established system, 1809 K was set as the smelting temperature of pure Fe.

From Table 6, it could be seen that the energy consumption of heating solid materials increased with an increasing reduction temperature, and increased with increases of the coupling parameter. When the coupling parameter was fixed, the energy consumption of heating solid materials of the coupling reactions increased with the increasing temperature.

3.5. Energy Consumption Per Ton Liquid Iron

According to Equation (1) and the smelting heat per ton of pure iron, the energy consumption per ton of liquid iron was calculated, and the result was shown in

Table 7. The energy consumption per ton liquid iron (GJ/t).

Reaction Equation	Coupling Parameter	Reduction Temperature/(K)
		1173	1273	1373	1473	1573	1650
(m + 3)C(s) + 2Fe2O3(s) = 4Fe(s) + 2mCO(g) + (3 − m)CO2(g)	m = 0.0	9.952	10.021	10.100	10.181	10.263	10.328
	m = 0.5	10.365	10.436	10.518	10.602	10.687	10.753
	m = 1.0	10.778	10.852	10.937	11.023	11.111	11.179
	m = 1.5	11.191	11.268	11.356	11.444	11.535	11.605
	m = 2.0	11.604	11.684	11.774	11.866	11.958	12.031
	m = 2.5	12.017	12.100	12.193	12.287	12.382	12.457
	m = 3.0	12.431	12.516	12.611	12.708	12.806	12.883
(n + 2)C(s) + Fe3O4(s) = 3Fe(s) + 2nCO(g) + (2 − n)CO2(g)	n = 0.0	9.761	9.826	9.892	9.959	10.028	10.081
	n = 0.5	10.312	10.380	10.450	10.521	10.593	10.649
	n = 1.0	10.863	10.935	11.008	11.083	11.158	11.217
	n = 1.5	11.413	11.489	11.566	11.644	11.723	11.785
	n = 2.0	11.964	12.044	12.124	12.206	12.288	12.353
(p + 1)C(s) + 2FeO(s) = 2Fe(s) + 2pCO(g) + (1 − p)CO2(g)	p = 0.0	9.007	9.056	9.105	9.156	9.207	9.247
	p = 0.2	9.337	9.388	9.440	9.493	9.546	9.588
	p = 0.4	9.668	9.721	9.775	9.830	9.885	9.929
	p = 0.6	9.999	10.054	10.110	10.167	10.225	10.269
	p = 0.8	10.329	10.387	10.445	10.504	10.564	10.610
	p = 1.0	10.660	10.719	10.780	10.841	10.903	10.951

and Figure 17. From Table 7, it could be seen that the energy consumption per ton of liquid iron increased with increasing reduction temperatures, and increased with increasing the coupling parameter.

The energy consumption per ton of hot metal of BF was reported as 12.2 GJ/t (namely was 416.3 kgce/t) in 2007 in reference [5], and 11.65 GJ/t (namely was 392.1 kgce/t) in China’s key steel enterprises in 2018 [6], which were shown in Figure 17. Kgce was the unit of energy consumption and equaled the heat value 20,307 kJ of 1 kg stand coal. Compared with the reported values and the calculated values, the energy consumption of carbon reduction ironmaking could be further reduced by about 1 GJ/t (34.12 kgce/t).

To make the energy consumption of ironmaking process less than the reported value, the coupling parameter m < 2.0 was required for the reaction of (m + 3)C(s) + 2Fe₂O₃(s) = 4Fe(s) + 2mCO(g) + (3 − m)CO₂(g), and the coupling parameter n < 1.5 was required for the reaction of (n + 2)C(s) + Fe₃O₄(s) = 3Fe(s) + 2nCO(g) + (2 − n)CO₂(g).

When the ratio was fixed to 1.1–1.5, the energy consumption per ton liquid iron with coupling parameters m = 1.06–1.28 for Fe₂O₃, n = 0.71–0.85 for Fe₃O₄, and p = 0.35–0.43 for FeO was marked out in Figure 17, respectively, and these values were less than 11.65 GJ/t.

The minimum energy consumption was 9.952 GJ/t for Fe₂O₃, 9.761 GJ/t for Fe₃O₄, 9.007 GJ/t for FeO with the reduction reaction at 1173 K, and the maximum energy consumption was 12.883 GJ/t for Fe₂O₃, 12.353 GJ/t for Fe₃O₄, 10.951 GJ/t for FeO with the reduction reaction at 1650 K.

It should be emphasized that the energy consumption in this study was the theoretical value for pure liquid iron, and the reported values were for hot metal (also called molten pig iron) and not for pure liquid iron.

3.6. Carbon Consumption and CO₂ Output

The carbon needed for supply 1 GJ heat was 30.286 kg. The carbon consumption used as reduction agent for coupling reactions and the carbon consumption for coupling reactions per ton liquid iron was shown in

Table 8. The carbon consumption used as reduction agent for coupling reactions per ton of liquid iron (kg C/t).

Reaction Equation	Coupling Parameter	Reduction Temperature/(K)
		1173	1273	1373	1473	1573	1650
(m + 3)C(s) + 2Fe2O3(s) = 4Fe(s) + 2mCO(g) + (3 − m)CO2(g)	m = 0.0	160.714	160.714	160.714	160.714	160.714	160.714
	m = 0.5	187.500	187.500	187.500	187.500	187.500	187.500
	m = 1.0	214.286	214.286	214.286	214.286	214.286	214.286
	m = 1.5	241.071	241.071	241.071	241.071	241.071	241.071
	m = 2.0	267.857	267.857	267.857	267.857	267.857	267.857
	m = 2.5	294.643	294.643	294.643	294.643	294.643	294.643
	m = 3.0	321.429	321.429	321.429	321.429	321.429	321.429
(n + 2)C(s) + Fe3O4(s) = 3Fe(s) + 2nCO(g) + (2 − n)CO2(g)	n = 0.0	142.857	142.857	142.857	142.857	142.857	142.857
	n = 0.5	178.571	178.571	178.571	178.571	178.571	178.571
	n = 1.0	214.286	214.286	214.286	214.286	214.286	214.286
	n = 1.5	250.000	250.000	250.000	250.000	250.000	250.000
	n = 2.0	285.714	285.714	285.714	285.714	285.714	285.714
(p + 1)C(s) + 2FeO(s) = 2Fe(s) + 2pCO(g) + (1 − p)CO2(g)	p = 0.0	107.143	107.143	107.143	107.143	107.143	107.143
	p = 0.2	128.571	128.571	128.571	128.571	128.571	128.571
	p = 0.4	150.000	150.000	150.000	150.000	150.000	150.000
	p = 0.6	171.429	171.429	171.429	171.429	171.429	171.429
	p = 0.8	192.857	192.857	192.857	192.857	192.857	192.857
	p = 1.0	214.286	214.286	214.286	214.286	214.286	214.286

and

Table 9. The carbon consumption for coupling reactions per ton liquid iron (kg C/t).

Reaction Equation	Coupling Parameter	Reduction Temperature/(K)
		1173	1273	1373	1473	1573	1650
(m + 3)C(s) + 2Fe2O3(s) = 4Fe(s) + 2mCO(g) + (3 − m)CO2(g)	m = 0.0	462.116	464.201	466.602	469.050	471.546	473.500
	m = 0.5	501.414	503.582	506.064	508.593	511.169	513.183
	m = 1.0	540.713	542.962	545.526	548.136	550.791	552.866
	m = 1.5	580.011	582.343	584.989	587.679	590.413	592.549
	m = 2.0	619.309	621.724	624.451	627.222	630.036	632.232
	m = 2.5	658.607	661.105	663.913	666.764	669.658	671.915
	m = 3.0	697.906	700.486	703.376	706.307	709.280	711.598
(n + 2)C(s) + Fe3O4(s) = 3Fe(s) + 2nCO(g) + (2 − n)CO2(g)	n = 0.0	438.478	440.447	442.452	444.492	446.566	448.187
	n = 0.5	490.875	492.955	495.068	497.216	499.396	501.098
	n = 1.0	543.273	545.463	547.685	549.939	552.226	554.009
	n = 1.5	595.671	597.970	600.301	602.663	605.056	606.919
	n = 2.0	648.068	650.478	652.918	655.387	657.886	659.830
(p + 1)C(s) + 2FeO(s) = 2Fe(s) + 2pCO(g) + (1 − p)CO2(g)	p = 0.0	379.932	381.409	382.912	384.442	385.998	387.214
	p = 0.2	411.370	412.913	414.482	416.077	417.696	418.960
	p = 0.4	442.809	444.418	446.052	447.711	449.394	450.707
	p = 0.6	474.247	475.923	477.622	479.345	481.092	482.453
	p = 0.8	505.686	507.427	509.192	510.979	512.790	514.200
	p = 1.0	537.125	538.932	540.762	542.614	544.488	545.946

, respectively.

The carbon consumption as reduction agent per ton hot metal of BF was reported as 482kg/t, and 414 kg/t was considered to be the minimum value in the reference [48], which was shown in Figure 18. Compared with the 475–544 kg/tHM of fuel ratio of advanced BF [6], the actual values were less than the calculated values in this study, which included the combustion consumption, gasification consumption, and reduction consumption. Compared with the values in Table 8 and Table 9, the carbon used for combustion was larger than for reduction and gasification.

From Table 9, the minimum carbon consumption was 462.116 kg/t for Fe₂O₃, 438.478 kg/t for Fe₃O₄, 379.932 kg/t for FeO with the reduction reaction at 1173 K, and the maximum carbon consumption was 711.598 kg/t for Fe₂O₃, 659.830 kg/t for Fe₃O₄, 545.946 kg/t for FeO with the reduction reaction at 1650 K.

The CO₂ output per ton liquid iron was shown in

Table 10. The CO₂ output per ton of liquid iron (kg/t).

Reaction Equation	Coupling Parameter	Reduction Temperature/(K)
		1173	1273	1373	1473	1573	1650
(m + 3)C(s) + 2Fe2O3(s) = 4Fe(s) + 2mCO(g) + (3 − m)CO2(g)	m = 0.0	1265.854	1273.498	1282.301	1291.280	1300.431	1307.595
	m = 0.5	1284.948	1292.894	1301.997	1311.270	1320.713	1328.099
	m = 1.0	1304.041	1312.291	1321.692	1331.261	1340.995	1348.604
	m = 1.5	1323.135	1331.687	1341.387	1351.251	1361.277	1369.108
	m = 2.0	1342.228	1351.084	1361.083	1371.241	1381.559	1389.613
	m = 2.5	1361.322	1370.480	1380.778	1391.232	1401.841	1410.117
	m = 3.0	1380.416	1389.877	1400.473	1411.222	1422.123	1430.622
(n + 2)C(s) + Fe3O4(s) = 3Fe(s) + 2nCO(g) + (2 − n)CO2(g)	n = 0.0	1226.799	1234.020	1241.371	1248.851	1256.458	1262.400
	n = 0.5	1252.257	1259.882	1267.632	1275.505	1283.501	1289.740
	n = 1.0	1277.715	1285.744	1293.892	1302.159	1310.543	1317.079
	n = 1.5	1303.173	1311.606	1320.153	1328.813	1337.586	1344.418
	n = 2.0	1328.631	1337.468	1346.413	1355.467	1364.629	1371.758
(p + 1)C(s) + 2FeO(s) = 2Fe(s) + 2pCO(g) + (1 − p)CO2(g)	p = 0.0	1107.368	1112.784	1118.298	1123.908	1129.613	1134.070
	p = 0.2	1122.643	1128.301	1134.054	1139.900	1145.838	1150.473
	p = 0.4	1137.918	1143.819	1149.810	1155.892	1162.064	1166.877
	p = 0.6	1153.193	1159.336	1165.567	1171.885	1178.290	1183.280
	p = 0.8	1168.468	1174.853	1181.323	1187.877	1194.515	1199.684
	p = 1.0	1183.743	1190.370	1197.079	1203.869	1210.741	1216.088

. From Table 10, the minimum CO₂ output was 1265.854 kg/t for Fe₂O₃, 1226.799 kg/t for Fe₃O₄, 1107.368kg/t for FeO with the reduction reaction at 1173 K, and the maximum energy consumption was 1430.622 kg/t for Fe₂O₃, 1371.758 kg/t for Fe₃O₄, 1216.088 kg/t for FeO with the reduction reaction at 1650 K.

The CO₂ output per ton of hot metal of BF was reported as 1650 kg/t without CCS, and 790 kg/t with CCS in reference [4], which was shown Figure 19. Obviously, the calculated values in this study were much less than the actual values without CCS. In other words, the CO₂ output could be generated at a lower level.

3.7. Discussion

From the minimum energy consumption point of view, the ideal thermodynamic model for the reduction of iron oxide by carbon was shown in Figure 20, namely only CO₂ was generated.

In actual BFs, this ideal model does not exist due to the presence of the gasification reaction of C and CO₂. The coupling parameter of the C–CO₂ reaction was the key point to adjust the energy consumption and composition of products. The more the gasification reaction occurred, the more energy consumption and CO₂ output there was, and the lower the ratio of volume fraction of CO₂ to that of CO.

As all reactions were in one furnace, such as a blast furnace, it was very difficult to control reactions in detail, though these reactions appeared in different areas. Another way of dividing the reduction and gasification reactions, such as a gas-based direct reduction ironmaking, was shown in Figure 21. This method can control the amount of the C–CO₂ reaction, but this may need more heat to increase the gas temperature.

4. Conclusions

Through the thermodynamic functions, standard Gibbs free energy, standard reaction enthalpy, the relative gas partial pressure of CO and CO₂, energy consumption, and carbon consumption were calculated, and some interesting conclusions were obtained.

(1)

The equilibrium relative gas partial pressure of CO₂ was limited between 0.4 and 1.2, and the volume fraction of CO₂ decreased as the coupling parameters increased.

(2)

According to the actual volume ratio of CO to CO₂, the coupling parameters of carbon gasification by CO₂ and reduction of iron oxides by carbon were 1.06–1.28 for Fe₂O₃, 0.71–0.85 for Fe₃O₄, 0.35–0.43 for FeO, respectively.

(3)

Under the same conditions, the energy consumption of ironmaking of iron oxides increased with increases in the amount of carbon gasification by CO₂.

(4)

The minimum energy consumption, carbon consumption, and CO₂ output occurred in the reduction reaction with only CO₂ generated, and the maximums of these items were by the reduction reaction with only CO generated.

(5)

Compared with current production levels, the energy consumption and CO₂ of ironmaking by carbon could be lower by decreasing the coupling parameter of the C–CO₂ reaction, or by lowering the generated temperature of solid Fe, or increasing the iron content in the raw material though changing the iron oxides, though these were very difficult to operate.