Energy and Exergy Analysis of an Improved Hydrogen-Based Direct Reduction Shaft Furnace Process with Waste Heat Recovery

Featured Application

The work in this paper provides some basic theoretical and practical reference value for the energy and exergy analysis, calculation, process optimization, and energy conservation research of the hydrogen-based direct reduction shaft furnace process, which is helpful for promoting its further industrial application.

Abstract

The traditional production mode using coal as the main energy source is not conducive to the sustainable development of the iron and steel industry (ISI). The hydrogen-based direct reduction shaft furnace (HDRSF) process is a feasible technical route for promoting the green development of the ISI. However, there is a lack of comprehensive analysis with respect to the energy utilization and process flow of the HDRSF method. To address these issues, a systemic material–energy–exergy model of HDRSF is established. An improved HDRSF process incorporating waste heat recovery is also proposed, and energy consumption intensity and exergy intensity are used as assessment metrics. This study’s findings indicate that the proposed waste heat recovery can considerably lower gas demand and energy consumption intensity, but exergy intensity has little effect. The reducing gas demand drops from 2083 m³ to 1557 m³, the energy consumption intensity drops from 2.75 × 10⁷ kJ to 1.70 × 10⁷ kJ, and the exergy intensity drops from 1.08 × 10⁷ kJ to 1.05 × 10⁷ kJ when the reducing gas temperature is 900 °C, H₂:CO = 1:1; meanwhile, the recovery rate of waste heat reaches 40%. This study can serve as a reference for actual HDRSF process production.

1. Introduction

The ISI plays a crucial role in global economic advancement and industrial growth. Over recent decades, global steel consumption has experienced rapid expansion and is projected to reach 2.2 billion tons by the year 2050 [1]. The ISI is also one of the most energy-intensive and carbon-emitting industries. At present, the average energy consumption per ton of crude steel produced is 20 GJ [2], and carbon dioxide emissions are in the range of 1.8–1.9 tons [3,4]. The ISI contributes approximately 7% to global energy consumption and accounts for 7–9% of global carbon dioxide emissions [5,6]. In the context of global warming and environmental degradation, the high energy consumption and significant carbon emissions associated with traditional production pose substantial challenges to the sustainable development of the ISI [7]. As such, a critical task in the ISI is to accelerate the transformation to green and low-carbon production.

Currently, there exist two primary technical processes for steel production: the blast furnace–basic oxygen furnace (BF-BOF) process and the scrap/direct reduction iron–electric arc furnace (scrap/DRI-EAF) process. Together, these two methods account for over 95% of the world’s total steel production [8,9]. The traditional BF-BOF process is still the most widely used, accounting for about 70% of the world’s total steel production [10]. In the BF-BOF process, about 80% of carbon dioxide emissions originate from the blast furnace ironmaking stage, primarily due to the substantial coal consumption involved [11]. Because coke plays an indispensable structural role in blast furnaces, the research of carbon emission reduction in blast furnace ironmaking has nearly reached a bottleneck [12,13]. The scrap/DRI-EAF process is a typical “non-blast furnace ironmaking” process, where scrap steel or DRI is used as raw material. Compared with the BF-BOF process, the alternative process has shown clear preponderance in energy conservation and carbon emission reduction, leading to rapid development in recent years [14]. However, due to the limited availability of scrap steel resources, relying solely on scrap steel recycling cannot satisfy the rapidly growing global demand for steel [15]. Hence, there is an increasing demand for DRI produced by low-carbon technology [16].

The shaft furnace process plays an important role in DRI production, accounting for more than 72% of global DRI output [17]. The HDRSF approach integrates shaft furnace technology with hydrogen metallurgy. This approach reduces carbon emissions in DRI production at the source by using hydrogen to directly reduce iron ore, a process known as “substitution of carbon with hydrogen”. This promotes cleaner production practices in the ISI [18]. The HDRSF-EAF process, which is a more mature technical route in the practical application of hydrogen metallurgy, can significantly reduce carbon emissions [19]. The flexible mixing ratio of reducing gases such as H₂ and CO also renders the HDRSF process more affordable [20]. Owing to the above characteristics, the HDRSF process is expected to be an important route for achieving the green and low-carbon development of the ISI in line with the concept of hydrogen metallurgy [21,22,23].

In recent years, China, the United States, Europe, and many other countries and regions have conducted research on the HDRSF process [24], thereby promoting its development and improvement. Hydrogen is a clean energy source that, when used in the reduction reaction with iron ore, produces only water vapor as a gaseous byproduct. This significantly reduces carbon emissions in steel production. According to calculations by Li et al. [25], compared with the BF-BOF process, which emits 2054.33 kg of carbon per ton of steel, the carbon emissions in the hydrogen-rich shaft furnace–electric arc furnace process based on coal gasification and the pure hydrogen shaft furnace–electric arc furnace process based on renewable electricity and water electrolysis have been reduced to 1121.28 kg and 120.92 kg per ton of steel, respectively. Abhinav et al. [26] established a material and energy model for the production of steel without carbon emissions. The research results reveal that the hydrogen direct reduction iron ore–electric arc furnace process can decrease the carbon emissions of EU steel production exceeding 35%. Rechberg et al. [27] evaluated the carbon emissions of the hydrogen-based direct reduction from the perspective of the carbon flow of electricity in hydrogen production and found that when the carbon emission intensity of electricity was lower than 120 g CO₂ kWh⁻¹, the carbon emissions of the HDRSF route were less than that of the natural gas-based direct reduction in the shaft furnace route.

The hydrogen reduction of iron ore involves a highly endothermic reaction that necessitates adequate heat supply to sustain the reduction process at high temperatures. Due to the cost implications of using hydrogen in iron ore reduction, alongside efforts to reduce carbon emissions, several scholars have also focused on significant research into energy efficiency, consumption reduction, and process optimization for the HDRSF method. Chai et al. [28] established a thermal equilibrium model of hydrogen metallurgy and calculated that the optimal reduction temperature in hydrogen metallurgy is 1250–1350 K. The utilization of pure hydrogen for reduction can effectively raise the reaction temperature, thereby reducing overall energy consumption. Qiu et al. [29] established a mass–energy–exergy calculation model of the reduction section of HDRSFs, analyzed the influence of iron ore preheating temperature on the exergy intensity per ton of DRI, and proposed a furnace top gas recovery process. Zhang et al. [30] established a thermal equilibrium model of the reduction section in HDRSFs to explore the energy consumption per ton of DRI at different H₂ and CO ratios within a temperature range of 800–1300 °C. After the numerical simulation and calculation of the reduction section of HDRSFs, Ariyan et al. [31] and Shao et al. [32] found that double-row gas injection could enhance the utilization of reducing gas in the shaft furnace and reduce energy consumption. Qiu et al. [33] established a thermal balance model of the reduction section of HDRSFs and an optimization model for the utilization of reducing gas, where the utilization of reducing gas after process optimization increased by 26.7%.

In summary, the HDRSF process represents a significant technical pathway for the low-carbon production of DRI through hydrogen metallurgy technology, crucial for advancing the green and low-carbon development of the ISI. However, this technology is still in its early stage and requires further in-depth analysis and improvements in the energy utilization and process efficiency. Currently, most energy analysis studies of HDRSFs focus on theoretical calculations of hydrogen metallurgical energy consumption, primarily examining the reduction section while neglecting the impact analysis on the cooling section, leading to incomplete assessments of overall shaft furnace energy utilization. Furthermore, the whole HDRSF process is rarely discussed in the existing literature. Given the current high cost of hydrogen acquisition, it is imperative to design and enhance the overall HDRSF process to achieve energy savings, efficiency improvements, and production cost reductions.

Based on the described analysis, in order to further promote the development and improvement of the HDRSF process, the contributions of the present study can be summarized as follows:

• The principle of DRI production by HDRSFs is introduced. A calculation model for the energy analysis and exergy analysis of HDRSFs is established. Building upon existing research predominantly focused on the reduction section of HDRSFs, the model supplements the analysis by incorporating the cooling section of the shaft furnace. This approach aims to provide a more comprehensive assessment of energy utilization in HDRSFs.
• An improved process flow of HDRSFs with waste heat recovery is proposed. Under the premise of considering the actual production, the waste heat of top gas and high temperature cooling gas can be recovered and utilized so as to improve the energy utilization efficiency of HDRSFs.
• Combined with the practical production data of a plant, the influence of waste heat recovery on the reduction gas consumption of HDRSFs is calculated, and the energy flow and exergy flow of the improved HDRSF are analyzed. In addition, two evaluation indicators, namely energy consumption intensity and exergy intensity per ton of DRI, have been established to assess the energy utilization efficiency of the improved HDRSF.

The rest of the article is as follows: Section 2 is an overview of the HDRSF. Section 3 gives an explanation of the model and method description. In Section 4, a process flow of the HDRSF with waste heat recovery is presented. Section 5 includes the analysis and discussion. Section 6 is the conclusion.

2. Description of the HDRSF

In this section, an overview of the production process of DRI with HDRSF and the main chemical reactions in HDRSF are given. The main abbreviations in the following text are explained in Abbreviations section.

2.1. HDRSF Production Process

The shaft furnace is pivotal equipment for producing hydrogen-based DRI [34]. The HDRSF model is shown in Figure 1. Generally, an HDRSF can be divided into three sections from top to bottom: the preheating section, the reduction section, and the cooling section. During normal operation, iron ore enters the shaft furnace from the top and descends due to gravity. The reduction reaction takes place in the reduction section, where the iron ore is exposed to endothermic heat from the preheating section, which raises it to the necessary temperature for reduction. Because there is no obvious boundary between the preheating section and the reduction section, they are collectively referred to as the reduction section for the convenience of modeling and calculation.

Due to economic considerations, it is generally recommended to use the mixture of high-temperature H₂ and CO as the reducing gas in HDRSF processing. The heat brought in by the reducing gas is the main heat source of the shaft furnace. The high-temperature mixed reducing gases of H₂ and CO flow upward after entering from the middle of the shaft furnace, where there is reduction reaction with the iron ore inside to generate high-temperature DRI. The H₂O and CO₂ gases generated by the reduction reaction and the unreacted surplus H₂ and CO gases are discharged from the top of the shaft furnace. To safeguard the shell of the vertical furnace in the cooling section and prevent the re-oxidation of high-temperature DRI after discharge, it is essential to cool the DRI using gases such as N₂ or H₂. The cooling gas enters from the lower part of the cooling section and is discharged from the upper part. After the DRI product is cooled to the tap temperature, it is discharged at the bottom of the shaft furnace.

2.2. Main Chemical Reactions

The main chemical reaction in the shaft furnace is the reduction reaction between H₂/CO and iron ore. Existing studies have shown that the reduction of iron ore with H₂/CO is a multi-stage process [35,36,37]. At T > 570 °C, the reduction step of iron ore with H₂/CO is Fe₂O₃→Fe₃O₄→FeO→Fe. At T < 570 °C, the reduction step of iron ore with H₂/CO is Fe₂O₃→Fe₃O₄→Fe. Additionally, according to the balance curve of the reduction of iron oxide with H₂/CO, at T > 820 °C, the capacity of H₂ to reduce iron oxide is higher than that of CO [38]. In order to fully utilize the advantages of H₂ in terms of high reduction rate and low carbon emissions, the reduction temperature in the furnace is usually maintained above 820 °C. At this temperature, the reduction reaction in the HDRSF is shown in Equations (1)–(6) (for simplicity, wüstite is represented by FeO).

Chemical reaction formulas of Fe₂O₃→Fe with H₂:

$$3\mathrm{F}{\mathrm{e}}_2{\mathrm{O}}_3+{\mathrm{H}}_2=2\mathrm{F}{\mathrm{e}}_3{\mathrm{O}}_4+{\mathrm{H}}_2\mathrm{O}$$

(1)

$$\mathrm{F}{\mathrm{e}}_3{\mathrm{O}}_4+{\mathrm{H}}_2=3\mathrm{F}\mathrm{e}\mathrm{O}+{\mathrm{H}}_2\mathrm{O}$$

(2)

$$\mathrm{F}\mathrm{e}\mathrm{O}+{\mathrm{H}}_2=\mathrm{F}\mathrm{e}+{\mathrm{H}}_2\mathrm{O}$$

(3)

Chemical reaction formulas of Fe₂O₃→Fe with CO:

$$3\mathrm{F}{\mathrm{e}}_2{\mathrm{O}}_3+\mathrm{C}\mathrm{O}=2\mathrm{F}{\mathrm{e}}_3{\mathrm{O}}_4+\mathrm{C}{\mathrm{O}}_2$$

(4)

$$\mathrm{F}{\mathrm{e}}_3{\mathrm{O}}_4+\mathrm{C}\mathrm{O}=3\mathrm{F}\mathrm{e}\mathrm{O}+\mathrm{C}{\mathrm{O}}_2$$

(5)

$$\mathrm{F}\mathrm{e}\mathrm{O}+\mathrm{C}\mathrm{O}=\mathrm{F}\mathrm{e}+\mathrm{C}{\mathrm{O}}_2$$

(6)

Table 1. Thermodynamic parameters of reduction of iron oxide.

Reaction Formula	$\Delta {\mathit{H}}_{298}^{\ominus }/\mathbf{J}\cdot {\mathbf{mol}}^{-1}$	${\Delta }_{\mathit{r}}{\mathit{G}}_{\mathbf{m}}^{\ominus }/\mathbf{J}\cdot {\mathbf{mol}}^{-1}$	$\mathbf{lg}{\mathit{K}}^{\ominus }$
$3\mathrm{F}{\mathrm{e}}_2{\mathrm{O}}_3+{\mathrm{H}}_2=2\mathrm{F}{\mathrm{e}}_3{\mathrm{O}}_4+{\mathrm{H}}_2\mathrm{O}$	−100,070	−15,547 − 74.40 T	${\displaystyle \frac{812}{T}}+3.886$
$\mathrm{F}{\mathrm{e}}_3{\mathrm{O}}_4+{\mathrm{H}}_2=3\mathrm{F}\mathrm{e}\mathrm{O}+{\mathrm{H}}_2\mathrm{O}$	60,450	71,940 − 73.62 T	$-{\displaystyle \frac{3757}{T}}+3.845$
$\mathrm{F}\mathrm{e}\mathrm{O}+{\mathrm{H}}_2=\mathrm{F}\mathrm{e}+{\mathrm{H}}_2\mathrm{O}$	30,230	23,430 − 16.16 T	$-{\displaystyle \frac{1224}{T}}+0.844$
$3\mathrm{F}{\mathrm{e}}_2{\mathrm{O}}_3+\mathrm{C}\mathrm{O}=2\mathrm{F}{\mathrm{e}}_3{\mathrm{O}}_4+\mathrm{C}{\mathrm{O}}_2$	−23,410	−52,131 − 41.00 T	${\displaystyle \frac{2723}{T}}+2.141$
$\mathrm{F}{\mathrm{e}}_3{\mathrm{O}}_4+\mathrm{C}\mathrm{O}=\mathrm{3}\mathrm{F}\mathrm{e}\mathrm{O}+\mathrm{C}{\mathrm{O}}_2$	19,290	35,380 − 40.16 T	$-{\displaystyle \frac{1848}{T}}+2.097$
$\mathrm{FeO}+\mathrm{CO}=\mathrm{Fe}+\mathrm{C}{\mathrm{O}}_2$	−10,930	−13,175 + 17.24 T	${\displaystyle \frac{688}{T}}-0.900$

shows the thermodynamic parameters of the reduction of iron oxide with H₂/CO in the step of Fe₂O₃→Fe₃O₄→FeO→Fe [24,39], including the enthalpy change, Gibbs free energy, and equilibrium constant.

In actual operation, the reactions in the shaft furnace are reversible, and the equilibrium constant is primarily influenced by temperature. The reduction of iron ore with H₂/CO occurs in three stages, following the sequence of the third stage, then the second stage, and finally the first stage after the reducing gas inlets the furnace. The demand for reducing gas varies across different stages of the process. In theory, the equilibrium between gas supply and demand is typically achieved in at most one stage, with excess reducing gas being present in the remaining stages. According to the research of Chai et al. [28], the demand for reducing gas is the greatest in the third stage of the reaction (the reaction in Equations (3) and (6)). The thermodynamic utilization rate of the reducing gas in the third stage can be calculated using Equation (7).

$${\eta }_3=x_{H_2}\times {\displaystyle \frac{K_{3,H_2}}{1+K_{3,H_2}}}+x_{CO}\times {\displaystyle \frac{K_{3,CO}}{1+K_{3,CO}}}$$

(7)

where $K_{3,H_2}$ and $K_{3,CO}$ are the equilibrium constant of the third-stage reduction reaction with H₂ and CO, respectively.

Then, the amount of reducing gas demanded for the chemical reduction reaction to generate DRI that meets the process requirement can be calculated according to Equation (8).

$${\displaystyle \frac{V_{reducinggas}}{22.4}}\times {\eta }_3={\displaystyle \frac{W_{Fe}\times M_{DRI}}{56}}$$

(8)

3. Shaft Furnace System Modeling

In this section, comprehensive calculation models of the mass balance, energy balance, and exergy balance of the HDRSF are established to analyze and calculate the energy utilization of the hydrogen-based direct reduction process. It should be noted that the calculations in this study are based on the following assumptions: (1) all chemical reactions are in an equilibrium and stable state; (2) gangue does not participate in the reduction reaction; (3) reaction dynamics and material movement are not considered; (4) the interfacial pressure between the cooling section and the reduction section is balanced, and the gases are not mixed; (5) the heat loss at the reduction and cooling sections of the shaft furnace is 15% of its total heat output, respectively [29]; and (6) the standard parameters are 298 K and 0.1 MPa, respectively.

3.1. Mass Balance Model

According to the model of HDRSF in Figure 1, it can be seen that the incoming materials of the shaft furnace include iron ore, reducing gas, and low-temperature cooling gas, while the discharged materials are DRI, top gas, and high-temperature cooling gas. According to the law of conservation of mass, the mass of the materials entering the furnace should be equal to the mass of the materials leaving the furnace. Hence, the mass balance model of the HDRSF is shown in Equation (9).

$$M_{ironore}+M_{reducinggas}+M_{coolinggasin}=M_{topgas}+M_{DRI}+M_{coolinggasout}$$

(9)

In Equation (9), the mass of DRI depends on the actual production need. According to assumption (5), the mass of discharged high-temperature cooling gas should be the same as the mass of incoming low-temperature cooling gas, and the actual mass of cooling gas needs to be determined according to the DRI yield. In addition to the above three items, the other items in Equation (9) can be calculated by Equations (10)–(12).

$$M_{ironore}={\displaystyle \frac{M_{DRI}\times W_{Fe}}{TFe\times {\lambda }_{Fe}}}$$

(10)

$$M_{reducinggas}=V_{reducinggas}\times ({\rho }_{H_2}{x}_{H_2}+{\rho }_{CO}{x}_{CO})$$

(11)

$$M_{topgas}=V_{topgas}\times ({\rho }_{H_2}{X}_{H_2}+{\rho }_{H_{2}O}{X}_{H_{2}O}+{\rho }_{CO}{X}_{CO}+{\rho }_{C{O}_2}{X}_{C{O}_2})$$

(12)

In Equations (10)–(12), it can be seen that the mass of iron ore is related to its total iron content, the yield and metallization rate of DRI, and the mass percentage of Fe in DRI. The mass of the reducing gas is related to the volume of the reducing gas and the ratio of H₂ and CO in the reducing gas. The top gas includes the surplus reducing gas that is not involved in the reaction, the H₂O and CO₂ generated by the reduction reaction, and the vapor of water carried in the iron ore. According to the principle of conservation of elements, the extra oxygen in the top gas is equal to the oxygen lost in the iron ore. Based on the mass of oxygen lost in iron ore, the proportion of each component in the top gas in Equation (12) can be calculated by Equations (13)–(17).

$$X_{H_{2}O}={\displaystyle \frac{x_{H_2}{O}_{loss}/16+M_{ironore}\times w_{H_{2}O}/18}{V_{topgas}/22.4}}$$

(13)

$$X_{C{O}_2}={\displaystyle \frac{x_{CO}{O}_{loss}/16}{V_{topgas}/22.4}}$$

(14)

$$X_{H_2}={\displaystyle \frac{V_{reducinggas}\times x_{H_2}/22.4-x_{H_2}{O}_{loss}/16}{V_{topgas}/22.4}}$$

(15)

$$X_{C{O}_2}={\displaystyle \frac{V_{reducinggas}\times x_{C{O}_2}/22.4-x_{C{O}_2}{O}_{loss}/16}{V_{topgas}/22.4}}$$

(16)

The mass of oxygen lost of iron ore in the reduction reaction is the difference between Fe₂O₃ mass in iron ore and Fe mass in DRI and can be calculated by Equation (17).

$$O_{loss}=M_{ironore}\times {\displaystyle \frac{w_{F{e}_2{O}_3}}{160}}\times 16-M_{DRI}\times W_{Fe}/56\times 16$$

(17)

3.2. Energy Analysis Model

The reduction of iron ore with hydrogen is a strong endothermic effect, demanding substantial energy input to sustain the reaction. A thorough analysis of energy utilization in the HDRSF process is crucial for identifying recyclable energy sources and minimizing avoidable energy losses. This approach is essential for enhancing the general energy efficiency of the shaft furnace.

The primary focus of existing energy analysis and research on HDRSFs has been on the reduction section, without much attention being paid to the cooling section and overall process flow. The cooling section of the shaft furnace plays a critical role in cooling high-temperature DRI to prevent re-oxidation after discharge and to protect the furnace shell. A comprehensive energy utilization analysis of both the reduction and cooling sections of the HDRSF is depicted in Figure 2, adhering to the principle of energy conservation.

According to the energy budget shown in Figure 2, at the reduction section of the shaft furnace, the energy balance is shown in Equation (18).

$$Q_{ironore}+Q_{reducinggas}=Q_{topgas}+Q_{reduction}+Q_{vapor}+Q_{loss1}+Q_{HDRI}$$

(18)

The calculation methods of the items in Equation (18) are shown in Equations (19)–(24).

$$Q_{ironore}=M_{ironore}\times {\displaystyle \sum w_i}{C}_i\times (T_{ironore}-298)$$

(19)

$$Q_{reducinggas}={\displaystyle \frac{V_{reducinggas}}{22.4}}\times (x_{H_2}{C}_{H_2}+x_{CO}{C}_{CO})\times (T_{reducinggas}-298)$$

(20)

$$Q_{topgas}={\displaystyle \frac{V_{topgas}}{22.4}}\times (X_{H_2}{C}_{H_2}+X_{H_{2}O}{C}_{H_{2}O}+X_{CO}{C}_{CO}+X_{C{O}_2}{C}_{C{O}_2})\times (T_{topgas}-298)$$

(21)

$$Q_{reduction}={\displaystyle \frac{M_{DRI}}{56}}\times (x_{H_2}\Delta H_{H_2}+x_{CO}\Delta H_{CO})$$

(22)

where $\Delta H_{H_2}$ is the reaction enthalpy per mole of DRI produced in the reduction of iron core with H₂; and $\Delta H_{CO}$ is the reaction enthalpy per mole of DRI produced in the reduction of iron core with CO.

The water carried in iron ore will be heated up in the furnace and then evaporated into vapor. The heat absorbed by this process is the sum of the heat absorbed when the water heats up to the boiling point of 373 K and the latent heat of the phase transition of evaporation. The calculation method is shown in Equation (23).

$$Q_{vapor}=M_{ironore}\times w_{H_{2}O}\times (C_{H_{2}O(l)}\times (373-298)+{\nu }_{H_{2}O}+C_{H_{2}O(g)}\times (T_{topgas}-373))$$

(23)

$$Q_{HDRI}=M_{DRI}\times {\displaystyle \sum W_i}{C}_i\times (T_{HDRI}-298)$$

(24)

According to the energy budget shown in Figure 2, for the cooling section of the shaft furnace, the energy balance is shown in Equation (25).

$$Q_{HDRI}+Q_{coolinggasin}=Q_{coolinggasout}+Q_{CDRI}+Q_{loss2}$$

(25)

The calculation methods of the items in Equation (25) are shown in Equations (26)–(29).

$$Q_{coolinggasin}=V_{coolinggas}\times C_{coolinggasin}\times (T_{coolinggasin}-298)$$

(26)

$$Q_{coolinggasout}=V_{coolinggas}\times C_{coolinggasout}\times (T_{coolinggasout}-298)$$

(27)

$$Q_{CDRI}=M_{DRI}\times {\displaystyle \sum W_i}{C}_i\times (T_{CDRI}-298)$$

(28)

The specific heat of each substance in the above equations changes with the change in temperature. The relationship between the specific heat of each substance and the temperature change is shown in Equation (29).

$$C_i(T)=a+b\times {10}^{-3}T+c\times {10}^5{T}^{-2}$$

(29)

3.3. Exergy Analysis Model

The energy conservation equation on the basis of the first law of thermodynamics focuses on the quantitative conservation of energy in various forms during conversion without distinguishing qualitative differences. Exergy, on the other hand, is a physical quantity that measures the quality or usefulness of energy, allowing for an analysis from both quantitative and qualitative perspectives, and it has been widely used in the analysis and evaluation of energy systems [40,41,42]. Figure 3 illustrates the exergy analysis of HDRSFs based on the second law of thermodynamics, which considers energy quality and efficiency.

According to the exergy budget shown in Figure 3, the equilibrium equations of exergy at the reduction and cooling sections of the shaft furnace are shown in Equations (30) and (31), respectively.

$$E{x}_{ironore}+E{x}_{reducinggas}=E{x}_{topgas}+E{x}_{HDRI}+E{x}_{loss1}$$

(30)

$$E{x}_{HDRI}+E{x}_{coolinggasin}=E{x}_{coolinggasout}+E{x}_{CDRI}+E{x}_{loss2}$$

(31)

The calculations of exergy in Equations (30) and (31) are shown in Equations (32)–(37). In the present study, exergy contains physical exergy and chemical exergy, as shown in Equation (32).

$$Ex=E{x}_{ph}+E{x}_{ch}$$

(32)

Physical exergy mainly consists of thermal exergy (related to the system temperature and latent heat of the phase transition) and mechanical exergy (related to the system pressure). The physical exergy can be calculated using Equation (33).

$$E{x}_{ph}=(H-H_0)+T_0(S_0-S)$$

(33)

where (H − H₀) and (S − S₀) represent enthalpy change and entropy change, respectively; T₀ is the reference ambient temperature, which is 298 K in the present study.

In Equation (33), (H − H₀) can be calculated by Equation (34).

$$H-H_0=m\times C_i(T_m)\times (T-T_0)$$

(34)

where T_m is the average temperature, calculated by (T + T₀)/2.

In Equation (33), (S − S₀) can be calculated using Equations (35) and (36). Equation (35) is employed to compute the entropy change of substances whose properties remain unaffected by pressure variations. Equation (36) is utilized to calculate the entropy change of the substances whose properties are affected by pressure changes, with appropriate corrections being applied [43].

$$S_0-S=m{\displaystyle \underset{T}{\overset{T_0}{\int }}\frac{C_i(T)}{T}dT}$$

(35)

$$S_0-S=m\left({\displaystyle \underset{T}{\overset{T_0}{\int }}\frac{C_i(T)}{T}dT}-R\ln {\displaystyle \frac{P_0}{P}}\right)$$

(36)

where T is the material temperature; T₀ is the reference ambient temperature, which is 298 K in the present study; R is the ideal gas constant, which is 8.314 J/(mol·K); P₀ is the reference ambient pressure, which is 0.1 MPa in the present study; and P is the gas pressure.

The chemical exergy of the mixture is related to its components and is not a simple addition of the standard exergy of each component. The chemical exergy of the mixture can be calculated by Equation (37) [44].

$$E{x}_{ch}={\displaystyle \sum e_i}E{x}_i+R{T}_0{\displaystyle \sum e_i\ln }{e}_i$$

(37)

where e_i is the molar percentage of the i-th component in the mixture.

4. An Improved HDRSF Process with Waste Heat Recovery

Under typical conditions, to ensure sufficient reduction reactions in the shaft furnace and achieve the required metallization rate of DRI, the amount of reducing gas introduced into the furnace often exceeds the theoretical demand for the reduction process. This leads to a significant amount of unreacted H₂ and CO in the top gas. For economic reasons, it is essential to separate and recover the unreacted reducing gas from the top gas. However, as the top gas is typically above 300 °C, it must be cooled and dehydrated before purification. This approach considers practical factors such as the technical feasibility and cost-effectiveness of gas separation and purification processes [45,46]. In addition to the required endothermic nature of chemical reactions and irreversible heat losses that cannot be recovered, the residual heat carried by the top gas exiting the reduction section and the cooling gas leaving the cooling section can be recovered.

In order to achieve the energy efficiency and consumption reduction of the HDRSF process, an improved HDRSF production process with waste heat recovery is proposed. In the proposed approach, the waste heat of top gas and discharged high-temperature cooling gas is recycled in the HDRSF process, and the surplus reducing gas in the top gas is also purified for recycling. The flow of the improved HDRSF process with waste heat recovery is shown in Figure 4. For the goal of energy efficiency and consumption reduction, the following two main enhancements are implemented:

• The top gas first enters the heat exchanger to preheat the reducing gas before entering the heating furnace so as to recover and utilize the waste heat of the top gas and reduce the energy consumption during the heating process of the reducing gas in the electric heating furnace.
• The discharged high-temperature cooling gas is used for preheating the iron ore entering the furnace, thereby realizing recovery of its waste heat and increasing the heat of the iron ore entering the furnace. According to Equation (18), it is evident that increasing the heat content of iron ore entering the furnace can reduce the external energy input required by the shaft furnace, accordingly decreasing the amount of reducing gas needed.

The improved HDRSF process with waste heat recovery operates as follows: External supplementary reducing gas is primarily heated by transferring heat with the top gas. It is then combined with the reducing gas separated from the top gas after undergoing heat transfer, cooling, dehydration, purification, and pressurization processes. Subsequently, the mixed gas is heated to the required process temperature in an electric heating furnace before entering the shaft furnace for iron ore reduction, completing the gas circulation in the reduction section of the shaft furnace. In the cooling section, cooling gas enters from the bottom of the shaft furnace and is discharged from the upper part. The high-temperature cooling gas discharged from the shaft furnace first enters a waste heat recovery device to preheat the iron ore before it enters the furnace. After cooling, purification, and pressurization, the cooling gas returns to the furnace to complete the circulation process. A gas–water heat exchanger is utilized to cool the top gas before dehydration and entry into the furnace, ensuring continuous process operation. The cooling gas after preheating the iron ore is also cooled again by a gas–water heat exchanger. After exiting the gas–water heat exchanger, the cooling water is cooled in a cooling tower and then returns to the heat exchanger to complete the circulation.

5. Results and Discussion

In this section, in terms of the model established in Section 3 and combined with the actual operation parameters of a plant [29,33], the reducing gas demand of a shaft furnace with or without heat recovery is calculated. The energy utilization of the HDRSF process with or without waste heat recovery is analyzed. Two evaluation indicators of energy consumption intensity and exergy intensity are established to estimate the energy utilization of the improved HDRSF process. As the present study focuses on the energy utilization effects of the proposed waste heat recovery improvement on the HDRSF process, the effects of other equipment unrelated to the improvement process are not discussed.

5.1. Parameter Settings

The actual main operating parameters of an HDRSF in a plant are shown in

Table 2. Main operating parameters of the HDRSF.

Parameter	Value
Temperature of top gas out/K	623
Temperature of reducing gas in/K	1173
Temperature of DRI out of reduction section/K	1123
DRI metallization rate/%	92

.

The iron ore composition is shown in

Table 3. Iron ore composition/%.

TFe	FeO	CaO	SiO2	MgO	Al2O3	H2O
66.79	0.13	1.24	1.69	0.14	0.27	1.00

.

Other relevant parameters related to the calculations of the improved process are reasonably set, and the specific values are shown in

Table 4. Other relevant parameter settings.

Parameter	Value
Temperature of cooling gas (N2) in/K	323
Temperature of cooling gas (N2) out/K	573
Temperature of DRI out of furnace/K	353
Recovery rate of waste heat/%	40
Electric heating furnace efficiency/%	95

. Considering the cost, N₂ is used as cooling gas. The heat recovery rate is dependent on the equipment and technology used and is set at 40% in the calculations.

Moreover, the regression coefficients of the relationship between molar heat capacity at level pressure and temperature of the substances are shown in

Table A1. Regression coefficients of the molar heat capacity at level pressure and temperature values for the components.

Chemical Component	a/(J·mol−1·K−1)	b/(J·mol−1·K−2)	c/(J·mol−1·K)	Temperature Range/K
H2	27.28	3.26	0.50	298–3000
H2O	30.00	10.71	0.34	298–2500
CO	28.41	4.10	−0.46	298–2500
CO2	44.14	9.04	−8.54	298–2500
N2	27.87	4.63	0	298–2500
Fe	28.18	−7.32	−2.90	298–800
	−561.93	334.14	2912.10	1060–1184
FeO	50.79	8.62	−3.31	298–1650
Fe2O3	98.29	77.82	−14.85	298–953
	132.68	7.36	0	1053–1730
CaO	49.62	4.52	−6.95	298–2888
MgO	48.95	3.14	−11.42	298–3048
SiO2	43.89	38.79	−9.67	298–847
	58.91	10.04	0	847–1696
Al2O3	103.85	26.27	−29.09	298–800
	120.52	9.19	−48.37	800–2327

in Appendix A [39]. The values of the standard chemical exergy of the components are shown in

Table A2. Values of the standard chemical exergy of the components.

Chemical Component	Value (kJ/mol)
H2 (g)	236.1
H2O (l)	0.9
H2O (g)	9.5
CO (g)	275.1
CO2 (g)	19.9
N2 (g)	0.72
Fe (s)	376.4
FeO (s)	127.0
Fe2O3 (s)	16.5
CaO (s)	110.2
MgO (s)	66.8
SiO2 (s)	2.8
Al2O3 (s)	200.4

in Appendix A [47].

5.2. Comparison of Reducing Gas Demand in a Shaft Furnace with or without Waste Heat Recovery

The reduction gas demand in the shaft furnace must satisfy both the requirements of the reduction reaction and the heat demand necessary to sustain continuous reduction reactions. This demand is calculated using Equations (8) and (18), respectively, with the theoretical minimum demand for reduction gas being the greater of the two values. The necessity of reducing gas to meet the reduction reaction is affected by the reaction temperature and the composition of the reducing gas. According to Equation (18), the heat source of the shaft furnace originates from the thermal energy carried by both the reduction gas and the iron ore. In the improved process setup, the iron ore is preheated by high-temperature cooling gas before entering the furnace, increasing the thermal energy delivered by the iron ore and consequently reducing the heat brought in by the reduction gas. Therefore, with waste heat recovery, the thermal balance can be achieved with a reduced volume of reduction gas required at the same temperature. Under the temperature condition of 900 °C, the impact of the shaft furnace on the demand for reduction gas with or without waste heat recovery, under various compositions, is illustrated in Figure 5. Obviously, iron ore preheating can effectively reduce the demand for reducing gas in the shaft furnace.

5.3. Mass Balance

The amount of cooling gas in the cooling section can be calculated according to the energy balance of the cooling section in Equation (38).

$$C_{coolinggas}\times V_{reducinggas}\times {\rho }_{N_2}\times \Delta T_{coolinggas}=C_{DRI}\times M_{DRI}\times \Delta T_{DRI}$$

(38)

where ${\rho }_{N_2}$ is the nitrogen density; $\Delta T_{coolinggas}$ is the temperature difference between the cooling gas in and the cooling gas out; and $\Delta T_{DRI}$ is the temperature difference between the DRI out of the reduction section and the DRI out of the furnace.

In the remaining calculations in this section, the reducing gas composition entering the furnace is set as H₂:CO = 1:1. According to Figure 5, the reduction gas demand of shaft furnace in the production of per ton of DRI decreases from 2083 m³ to 1557 m³, which decreases by 25.3%. In addition, 1623.05 kg of iron ore and 2277 m³ of cooling gas need to be put into production. The mass balance of HDRSF without or with heat recovery are shown in

Table 5. Mass balance of the HDRSF without waste heat recovery.

Input			Output
Item	Mass/kg	Percentage/%	Item	Mass/kg	Percentage/%
Iron ore	1623.05	27.68	DRI	1000	17.05
Reducing gas	1394.7	23.78	Top gas	1963.54	33.48
Cooling gas in	2846.25	48.54	Cooling gas out	2846.25	48.54
			Gangue	54.21	0.93
Total	5864	100	Total	5864	100

and

Table 6. Mass balance of the HDRSF with waste heat recovery.

Input			Output
Item	Mass/kg	Percentage/%	Item	Mass/kg	Percentage/%
Iron ore	1623.05	29.45	DRI	1000	18.14
Reducing gas	1042.2	18.91	Top gas	1611.04	29.23
Cooling gas in	2846.25	51.64	Cooling gas out	2846.25	51.64
			Gangue	54.21	0.99
Total	5511.5	100	Total	5511.5	100

, respectively.

5.4. Comparison of the Energy Utilization of the Shaft Furnace System with or without Waste Heat Recovery

5.4.1. Energy Flow Analysis

The control of energy consumption is one of the most pivotal aspects in the HDRSF process, which is directly related to the production cost of DRI. The energy flow of the HDRSF process without or with waste heat recovery are shown in Figure 6 and Figure 7, respectively.

As observed in Figure 6, the sole source of heat that keeps the shaft furnace’s heat consumption stable is the heat brought in by the high-temperature reduction gas. In the absence of waste heat recovery, 2083 m³ of reducing gas is needed to manufacture one ton of DRI at process parameters of 900 °C and H₂:CO = 1:1. The energy of reducing gas entering the furnace is 2.62 × 10⁷ kJ. The electric heating furnace provides the energy needed to heat up the reducing gas. Given the electric heating furnace’s conversion efficiency, the amount of external energy required to be input in the absence of waste heat recovery is 2.75 × 10⁷ kJ, which is comparable with the calculation result of Zhang et al. [30]. Furthermore, the primary energy-consuming components of the shaft furnace are the cooling gas heat and the top gas heat, excluding the required energy consumption of reduction reaction heat absorption and furnace body heat dissipation. Figure 7 depicts the HDRSF process’s energy flow following the top gas recovery and high-temperature cooling gas residual heat. Because of the extra energy income from preheating the iron ore, the amount of gas required to produce one ton of DRI decreases to 1557 m³, and the amount of gas energy entering the shaft furnace decreases to 1.96 × 10⁷ kJ. In addition, heating gas in the electric heating furnace uses less energy when the reduction gas is preheated using top gas. Following waste heat recovery, the energy needed is lowered to 1.70 × 10⁷ kJ.

5.4.2. Exergy Flow Analysis

The exergy flow of the HDRSF process without or with waste heat recovery are shown in Figure 8 and Figure 9, respectively.

Overall, the exergy income of the HDRSF process comes from two sources: chemical exergy brought in by external reducing gas and physical exergy brought in by high-temperature reducing gas leaving the electric heating furnace. According to the conservation of elements, whether or not there is waste heat recovery does not change the reducing gas consumed by the reduction reaction in the shaft furnace. Therefore, when there is a reduction gas purification and recovery process, the chemical exergy of the reducing gas consumed in the production process is unchanged, while the chemical exergy is the main source of the overall exergy income of the process. The process’s exergy income has not changed much in comparison with the energy consumption induced by waste heat recovery, and its exergy investment has decreased from 1.08 × 10⁷ kJ in the absence of waste heat recovery to 1.05 × 10⁷ kJ. However, it is essential to note that after waste heat recovery, the shaft furnace’s energy income decreased from 2.48 × 10⁷ kJ to 1.86 × 10⁷ kJ due to a decrease in the demand for reducing gas in the stove. Lowering the volume of gas and top gas also has a positive effect on HDRSF cost reduction.

5.5. Evaluation Indicators

The energy consumption intensity and exergy intensity per ton of DRI are adopted as the evaluation indicators of energy utilization of the improved HDRSF process.

The energy intensity per ton of DRI is calculated according to Equation (39).

$$E_{DRIconsumption}={\displaystyle \frac{E_{Input}}{M_{DRI}}}$$

(39)

where E_Input represents the net energy input of the process to produce M_DRI.

The exergy intensity per ton of DRI is calculated according to Equation (40).

$$E{x}_{DRIconsumption}={\displaystyle \frac{E{x}_{Input}}{M_{DRI}}}$$

(40)

where Ex_Input represents the net exergy input of the process to produce M_DRI.

In terms of overall process flow, the energy intensity of HDRSF production per ton of DRI reduced from 2.75 × 10⁷ kJ to 1.70 × 10⁷ kJ, while the exergy intensity decreased from 1.08 × 10⁷ kJ to 1.05 × 10⁷ kJ.

6. Conclusions

The process uses hydrogen metallurgy to produce DRI and reduce fossil fuel consumption in the steel production process, which is an essential technical route to promote the green and sustainable development of the ISI. The study presented in this paper can support the commercialization of HDRSFs and offer some theoretical and practical references for their growth. The main conclusions are as follows:

• According to the law of conservation of mass and the first and second laws of thermodynamics, a calculation model of the overall material–energy–exergy analysis of HDRSFs has been established. The model comprehensively considers the input and output of the shaft furnace reduction and cooling sections and realizes a more comprehensive analysis and calculation of the energy utilization of HDRSFs.
• An improved HDRSF process with waste heat recovery is proposed. In the improved process flow, the waste heat recovery of top gas and high-temperature cooling gas is realized by preheating reducing gas and iron ore. In addition, the process of purifying and recovering furnace top gas is rationally designed. The improved HDRSF process has the conditions for practical industrial application.
• The calculation results show that the waste heat recovery process proposed in this paper can reduce the reducing gas demand for the per-ton DRI produced by the shaft furnace. When the temperature of reducing gas is 900 °C and H₂:CO = 1:1, the reducing gas demand per ton of DRI produced by the shaft furnace decreases from 2083 m³ to 1557 m³, which decreases by 25.3%.
• In terms of the energy analysis and exergy analysis of the HDRSF process, when the recovery rate of waste heat reaches 40%, the energy consumption intensity per ton of DRI decreases from 2.75 × 10⁷ kJ to 1.70 × 10⁷ kJ, showing a remarkable energy-saving effect. The exergy intensity reduces from 1.08 × 10⁷ kJ to 1.05 × 10⁷ kJ, while the exergy input of the shaft furnace reduces from 2.48 × 10⁷ kJ to 1.86 × 10⁷ kJ. In general, the process proposed in this paper can realize the goal of energy conservation and consumption reduction in HDRSF production.