Mathematical modelling and techno-economic analysis of electric arc furnace steelmaking process with hot metal charging in China

Abstract

Comprehensively considering the raw materials availability, production technology, and economy factor, it is unclear to choose the optimal electric arc furnace (EAF) steelmaking modes with charging scrap and hot metal (HM) in China. In this paper, the mathematical modelling and techno-economic analysis is adopted to quantitatively describe the consumption level of material and energy, as well as the economic performance in EAF steelmaking process. The calculation results reveal that considering the lowest smelting time, heat loss and total energy consumption, and better economic benefit and energy saving effect, the optimal EAF steelmaking process of 50% HM ratio with carbon powder and coal gas added is suggested, and the consumption of carbon powder and natural gas should be limited within 19.58 kg and 11.63 Nm³. This research is expected to provide some theoretical and operation guidance for low consumption and high efficiency lean production in EAF steelmaking process.

Keywords

electric arc furnace steelmaking hot metal charging mathematical modelling techno-economic analysis production cost

Introduction

Steel products support the progress of science and technology, play an irreplaceable role in people's daily life.^1,2 In 2023, world crude steel production remains at a high level, reaching 1888.2 million tons. China, served as the largest steel producer and consumer of steel, contributes about 1019.1 million tons, accounts for more than 50% of the total crude steel yield.³ To maintain the normal supply and demand of steel, the energy-intensive iron and steel industries formulate a large amount of natural energy and resources consumption, greenhouse gas and pollutants emissions.⁴ These phenomena are attributed to the lower energy and material efficiency level and industrial concentration, the lack universal application of energy-saving technologies, and insufficient production capacity ratio of electric arc furnace (EAF) steelmaking.⁵ Hence, the Chinese government has proposed ambitious targets for carbon peak and carbon neutral to search for sustainable development.⁶ One of the most critical steps is the low-carbon and energy-saving transformation of the steel industry, that is, the promotion and development of short-process EAF steelmaking route.⁷

With the quick development and popularisation of ultra-high power EAF, secondary refining and continuous casting technologies, the production efficiency of EAF steelmaking has been greatly improved, and the output and proportion of EAF steel have been rapidly increased worldwide.⁸ The charge structure of EAF steelmaking is diversified, which determines the consumption level of material and energy and the emission level of pollutants and wastes. EAF mainly rely on scrap to complete the smelting process. The unique bowl-shaped structure and small height-diameter ratio design make it more conducive to holding and digesting solid charges.^9,10 Except for scrap, some typical metallic charges, such as hot metal (HM), direct reduced iron (DRI), pig iron, hot briquetted iron (HBI) and metallised pellet are also covered.⁷ Many foreign EAF mills use scrap and DRI to produce molten steel (MS).^11–14 This is due to the mature access to scrap and DRI resources with high iron grade. However, the situation in China is quite different. The scrap, especially high-quality scrap appears shortage.¹⁵ The quantity and quality of scrap cannot meet the demands of the development of EAF steelmaking process. More HM is adopted in EAF steelmaking process to keep the massive crude steel yield.^16,17 A large number of scholars have studied the charge structure of EAF steelmaking, and try to explain the internal relationships of materials and energy sources to obtain some practical energy-saving and consumption reduction measures. Kirschen et al.¹⁸ constructed an energy efficiency model of an 80t EAF with the charge structure of scrap and DRI based on the mass and energy balance, and analysed the effects of DRI properties on materials and energy consumption. Malfa et al.¹⁹ combined historical heat data and mass and energy balance calculation, investigated the influence of different quality grades of scrap on the energy efficiency and production cost in EAF steelmaking process with full scrap. Ekmekçi et al.²⁰ established the mass balance model for EAF-ladle furnace (LF) system, and investigated the element efficiencies while considering different types of scrap (production waste, heavy melting scrap and shredder), pig iron and alloys (nickel, ferromanganese, ferrosilicon, ferromolybdenum, etc.). Hassan et al.²¹ analysed the effects of metallic charges (scrap, DRI, HBI and metallised pellet) and mixing proportion on consumptions (lime, oxygen, electrode, natural gas, coke and electricity) and metal recovery rate through industry experiments in a 220t ultra-high power EAF. Erwee et al.²² collected the production data of three 180t EAF with the charge structure of mix of HM, scrap and DRI, and focused on the nitrogen removal of MS under different DRI dosage ratio. Irawan et al.²³ developed an EAF dynamic operation model with the charge structure of HM, scrap and sponge iron by mass and energy balance, and explored the EAF performance under different HM ratio. Zhang et al.²⁴ compared the material and energy consumption and carbon emissions of coal-based DRI-EAF, gas-based DRI-EAF, 100% scrap-EAF and several other steelmaking scenarios based on the historical China Steel Yearbook data. Yang et al.⁷ and Tian et al.^16,25 developed the life cycle assessment model based on the actual EAF smelting data of the charge structure of HM and scrap, and explored the environment impact and economic benefit of EAF steelmaking process with different HM ratio. Zhu et al.²⁶ displayed the production technical indicators of eight EAF mills, and compared the consumption level and cost of the selected three EAF smelting modes (100% scrap, 70% scrap + 30% HM, 40% scrap + 60% HM). Li et al.²⁷ also explored the consumption level of EAF steelmaking process by material–energy balance and statistical methods, but the selected EAF is depending on the quaternary charge structure of scrap, pig iron, HM and DRI. He et al.²⁸ conducted process and technology analysis for EAF steelmaking process with DRI and scrap to control electricity consumption, which included DRI properties and size, charging ratio, feed system, initial temperature, etc. Duan et al.²⁹ studied the influence of HM ratio on tap-to-tap time, consumption of electricity and lime, and desulphurisation and desulphurisation abilities of a 50t EAF with HM and scrap. Liu et al.³⁰ investigated the effects of electricity and oxygen supply, carbon injection and infiltrated air on energy consumption, and clarified the carbon emission and energy consumption of HM charging in EAF steelmaking process.

In summary, researchers generally adopt material conservation and energy balance modelling, industrial experiments, production data information mining and other methods to explore a series of optimal ways to reduce consumption and emission, promote smooth smelting and production efficiency in EAF steelmaking process under multiple charge structures. The charge structure not only affects the process consumption and emission, but also directly relates to the production cost.⁵ Steel products meet the requirements of market supply and demand and people's living needs, and enjoy the value in use (VIU).³¹ Steel production enterprises and managers often hope to obtain certain economic benefits while reducing consumption and costs as much as possible. Techno-economic analysis is an important method for the robust development and performance improvement of a process based on the VIU.^32,33 Yang et al.³⁴ explored the feasibility of structural bio-adhesive from glycerol using techno-economic analysis method. Results show that the optimised economic performance of the investigated process can be obtained by $3.11/kg. Wang et al.³⁵ conducted a techno-economic analysis comparison of coal-to-hydrogen process and biomass-to-hydrogen process in terms of material consumption, total capital investment, energy efficiency, carbon tax, and production cost. Results reveal the improvement for the clean hydrogen production. Yang et al.³⁶ conducted a techno-economic analysis of coal to ethylene glycol (CTEG) process, where the comparison with oil to ethylene glycol (OTEG) process and different coal gasifiers were performed. Results show that CTEG has advantage of about 16% total production cost and shortcomings in terms of exergy efficiency, greenhouse gas (GHG) emissions, and total capital investment than OTEG. Gas schwarze pumpe gasifier CTEG performs the best performance on exergy efficiency and internal rate of return, whereas has the largest GHG of 3.27 t/t. Curellas et al.³⁷ investigated the current and future perspectives techno-economic performance for oxidative coupling of methane (OCM) process. Results forecast that OCM will be competitive in around 20 years compared with traditional process. Wang et al.³⁸ studied the techno-economic analysis of hydro-processed renewable jet fuel for potential feedstocks. The results reveal that the feedstock cost, hydrogen price, hydro-processing catalyst price, has the influence level of 54%, 18%, 12% and 11% on the renewable aviation fuel selling price, respectively. In our previous study,⁵ the techno-economic analysis was performed from perspectives of production cost, raw materials cost, solar energy price and carbon tax, but the research object was limited to the EAF steelmaking with 50% HM and 50% scrap. It is necessary to expand the objects of study to cope with scenarios in EAF steelmaking with different HM ratios.

To the best knowledge of the authors, there have been no public reports about the techno-economic analysis of EAF steelmaking process under diverse HM ratio. Therefore, in this article, the mathematical models of EAF steelmaking based on the metal charge structure of HM and scrap are developed and validated. According to the calculation results, the material and energy consumptions to produce 1000 kg of MS are determined. Then the substitution effects of scrap and electricity with HM, and electricity with carbon powder and coal gas in terms of different HM ratio are further discussed. Finally, the economic analysis covering the fluctuant metal charge prices of HM and scrap, and the cost saving benefits of applying carbon powder and coal gas are conducted to determine the optimal EAF steelmaking mode with lower energy and material consumptions and production cost.

Mathematical modelling

Process description and system boundary

The HM from the blast furnace is originally liquid with higher temperature and carbon content. The application of HM in EAF steelmaking process enjoys many advantages, such as sufficient input energy, short tap-to-tap time, fast smelting rhythm and less electricity consumption.³⁹ Of course, the HM production involves many sub-systems (sintering, pelletising, coking, ironmaking, etc.), which lead to considerable indirect emissions and natural resources consumption. In contrast, scrap is one of the solid waste, and there is less additional emission and consumption during its collection and utilisation, but more electricity is consumed to complete the phase transformation and smelting of scrap.⁴⁰ To determine the optimal EAF steelmaking mode with lower energy consumption and cost, this article selects the EAF steelmaking with the charge structure of HM and scrap as the object. The system boundary of EAF steelmaking is shown in Figure 1. The purpose of EAF steelmaking process is to convert HM and scrap into MS with qualified temperature and chemical composition. Hence, a serious of chemical reactions occur, including decarbonisation, dephosphorisation and other oxidative exothermic reactions.⁷ The main elements related to the above reactions consist of C, Si, Mn, P and Fe. In addition, to make up for the energy gap in the smelting process, electricity, carbon powder, and coal gas are also usually deployed.

Calculation method

Analysing the material and energy consumption of EAF steelmaking process with the mixed charge structure of HM and scrap is complicated due to the different consumption level of HM and scrap. In the actual implementation process, the situation of a single metal charge is often analysed firstly, and then the related indicators of the composite metal charge are obtained by combining the single one.¹⁸ Therefore, the material and energy consumptions for the EAF steelmaking process with 1000 kg of HM (EAF-1000 HM) or 1000 kg of scrap (EAF-1000 scrap) are studied. The mass of the produced MS, and the corresponding consumption level is first determined.

Material consumption

EAF steelmaking process is characterised by great smelting intensity, violent chemical reaction and high molten bath temperature, which exists the losses of metal charges. In EAF steelmaking process, most of the metal charge is converted to MS $(M_{s t e e l}^{i})$ , and a small part of it forms chemical reaction loss $(M_{r e a c t i o n}^{i})$ , iron bead loss in slag $(M_{s l a g - F e}^{i})$ , splashing loss $(M_{s p l a s h}^{i})$ and iron loss in dust $(M_{d u s t - F e}^{i})$ . The conservation equation of metal charge is shown in equation (1).

M_{}^{i} = M_{r e a c t i o n}^{i} + M_{s l a g - F e}^{i} + M_{s p l a s h}^{i} + M_{d u s t - F e}^{i} + M_{s t e e l}^{i}

(1)

where i represents the type of metal charge (HM or scrap).

In the smelting process, the chemical reaction loss derives from the oxidation reaction of elements C, Si, Mn, P and Fe in HM and scrap. The content of the corresponding element except for Fe in MS will be lower than that in the raw metal charge. The chemical reaction loss can be obtained according to the difference of chemical composition data of raw metal charges and MS product. Considering the strong stirring and poor separation effect of slag and MS in molten bath, some iron beads is wrapped by slag and leave the furnace through the furnace door. The mass of iron bead loss in slag is calculated by equation (2).

M_{s l a g - F e}^{i} = M_{slag}^{i} \times f_{s l a g - F e}^{i}

(2)

where

M_{slag}^{i}

denotes the mass of slag under EAF-1000 HM or EAF-1000 scrap, kg and

f_{s l a g - F e}^{i}

the mass ratio of iron beads pinched in the slag. The mass of slag is determined by the total mass of all the oxides charged or formed by chemical reactions. Theses oxides mainly consist of CaO, SiO₂, P₂O₅, MgO, MnO, Al₂O₃, FeO and Fe₂O₃. The appropriate content of slag is beneficial to remove harmful elements from molten steel in the steelmaking process. The mass of SiO₂, P₂O₅, MgO, MnO, Al₂O₃, FeO and Fe₂O₃ is obtained by the oxidation reaction in HM and scrap. Lime serves as the main slag former, provides CaO to neutralise acidic gangue component SiO₂, and control the alkalinity of the slag system. The mass of CaO is determined by the mass of SiO₂ while considering the binary alkalinity.

During the strong oxygen supply operation in EAF steelmaking process, violent oxidation reactions in the molten pool occur, especially the decarbonisation reaction. Abundant CO gas is formed in a short time, and result in the splashing of MS. A small amount of metal escapes from the loosely sealed furnace roof and furnace door to the outside of the furnace, and form splashing loss. The splashing loss is calculated as shown in equation (3).

M_{s p l a s h}^{i} = M_{}^{i} \times f_{s p l a s h}

(3)

where

f_{s p l a s h}

is the splashing ratio of MS.

In the high-temperature area near the arc, part of the iron is vaporised into the flue dust, and then is oxidised by the oxygen above the molten bath to obtain the corresponding iron oxides FeO and Fe₂O₃. Finally, the oxidised iron is discharged from the EAF through the dust flue together with the high-temperature furnace gas. Equation (4) displays the iron loss in dust.

M_{d u s t}^{i} = M_{}^{i} \times f_{d u s t}^{i} \times (\frac{56}{72} m_{F e O}^{d u s t} + \frac{112}{160} m_{F e_{2} O_{3}}^{d u s t})

(4)

where

f_{d u s t}^{i}

denotes the dust produced ratio;

m_{F e O}^{d u s t}

the FeO content in dust, % and

m_{F e_{2} O_{3}}^{d u s t}

the Fe₂O₃ content in dust, %.

Besides the iron loss, the remaining metal material eventually forms the product MS. The product MS in EAF steelmaking is calculated as equation (5). Therefore, the mass of raw metal charge (HM and scrap) consumption to produce 1000 kg of MS is determined by the following equation (6).

M_{S t e e l}^{i} = 1000 - M_{s l a g}^{i} - M_{s p l a s h}^{i} - M_{d u s t}^{i} - M_{r e a c t i o n}^{i}

(5)

M_{}^{i} = \frac{1000}{1000 - M_{s l a g - F e}^{i} - M_{s p l a s h}^{i} - M_{d u s t - F e}^{i} - M_{r e a c t i o n}^{i}} \times 1000

(6)

Energy consumption

The energy consumption is accompanied by the consumption, transformation and output of materials. In EAF-1000 HM or EAF-1000 scrap, the input energy consists of three parts: raw material physical heat $(Q_{p h y - i}^{i})$ , chemical reaction heat $(Q_{r e a}^{i})$ and dust oxidation heat $(Q_{r e a - d u s t}^{i})$ . Similarly, the output energy $(Q_{o u t p u t}^{i})$ includes six parts: physical heat of MS $(Q_{p h y - s t e e l}^{i})$ , physical heat of slag $(Q_{s l a g}^{i})$ , physical heat of flue gas $(Q_{p h y - g a s}^{i})$ , physical heat of dust $(Q_{d u s t}^{i})$ , physical heat of iron bead $(Q_{p h y - s l a g - F e}^{i})$ and physical heat of splashing $(Q_{s p l a s h}^{i})$ .The input energy and energy output is calculated in equations (7) and (8).

Q_{i n p u t}^{i} = Q_{p h y - i}^{i} + Q_{r e a}^{i} + Q_{r e a - d u s t}^{i}

(7)

Q_{o u t p u t}^{i} = Q_{p h y - s t e e l}^{i} + Q_{s l a g}^{i} + Q_{p h y - g a s}^{i} + Q_{d u s t}^{i} + Q_{p h y - s l a g - F e}^{i} + Q_{s p l a s h}^{i}

(8)

Input energy

The physical heats of the raw materials depend on the temperature. The reference temperature of 25°C is selected here. The physical heat of raw material is positive if the initial temperature is higher than the reference temperature. As well as sensible heat, the HM enjoys latent heat of fusion, which is different with other metal charge. The physical heat of HM and scrap is calculated as equations (9) and (10).

Q_{p h y - H M}^{H M} = 1000 \times [c_{s}^{H M} (T_{m p}^{H M} - 25) + H_{s - l}^{H M} + c_{l}^{H M} (T_{}^{H M} - T_{m p}^{H M})]

(9)

Q_{p h y}^{S c r a p} = 1000 \times [c_{s}^{S c r a p} (T_{}^{S c r a p} - 25)]

(10)

where

c_{s}^{H M}

and

c_{l}^{H M}

denote the specific heat of solid phase and liquid phase of HM, respectively, kJ/(kg•K);

H_{s - l}^{H M}

the latent heat of fusion of HM, kJ kg⁻¹;

T_{m p}^{H M}

the melting temperature of HM, °C;

T_{}^{H M}

the initial temperature of HM, °C;

c_{s}^{S c r a p}

the specific heat of scrap, kJ (kg•K)⁻¹ and

T_{}^{S c r a p}

the initial temperature of scrap, °C.

The chemical reaction heat is mainly generated by the oxidation of elements C, Si, Mn, P and Fe in HM and scrap in the EAF steelmaking process. According to the composition of HM, scrap and MS, the chemical reaction heat can be calculated by the exothermic heat of the corresponding chemical reaction. As well as the chemical reaction heat of HM and scrap, the element Fe in the dust also release a small amount of oxidation heat. The chemical reaction heat of dust is determined by equation (11).

Q_{r e a - d u s t}^{i} = 1000 \times f_{d u s t}^{i} [\frac{56}{72} m_{F e O}^{d u s t} H_{F e - F e O} + \frac{112}{160} m_{F e_{2} O_{3}}^{d u s t} H_{F e - F e_{2} O_{3}}]

(11)

where

H_{F e - F e O}

denotes the exothermic oxidation of Fe to FeO, kJ kg⁻¹ and

H_{F e - F e_{2} O_{3}}

the exothermic oxidation of Fe to Fe₂O₃, kJ kg⁻¹.

Output energy

MS is the final product of EAF steelmaking process. The latent heat and sensible heat make up the physical heat of MS. The physical heat of MS is calculated according to mass and temperature of MS, which is shown as equation (12).

Q_{p h y - s t e e l}^{i} = M_{s t e e l}^{i} \times [c_{s}^{M S} (T_{m p}^{M S} - 25) + H_{s - l}^{M S} + c_{l}^{M S} (T_{}^{M S} - T_{m p}^{M S})]

(12)

where

c_{s}^{M S}

and

c_{l}^{M S}

denote the specific heat of solid phase and liquid phase of MS, respectively, kJ (kg•K)⁻¹;

H_{s - l}^{M S}

the latent heat of fusion of MS, kJ kg⁻¹;

T_{m p}^{M S}

the melting temperature of MS, °C and

T_{}^{M S}

the final temperature of MS, °C.

The temperature of slag is very close to that of the MS considering it floats on the surface of MS. The calculation method of physic heat of slag is shown in equation (13).

Q_{s l a g}^{i} = M_{s l a g}^{i} \times [c_{l}^{s l a g} (T_{}^{s l a g} - 25) + H_{s - l}^{s l a g}]

(13)

where

c_{l}^{s l a g}

denotes the specific heat of liquid phase of slag, kJ (kg•K)⁻¹;

H_{s - l}^{s l a g}

the latent heat of slag, kJ kg⁻¹ and

T_{}^{s l a g}

the final temperature of slag, °C.

The main components of flue gas include CO₂, CO, N₂, O₂, etc. CO and CO₂ come from the products of C reaction in MS. The rest comes from the involved air and not fully reacted oxygen from oxygen injection. The dust takes away some physical heat along with the flue gas. The temperature of dust and flue gas is basically the same. The physical heat of flue gas and dust is calculated as equations (14) and (15), respectively.

Q_{p h y - g a s}^{i} = M_{g a s}^{i} \times c_{g}^{g a s} (T_{}^{g a s} - 25)

(14)

Q_{d u s t}^{i} = M_{d u s t}^{i} \times [c_{s}^{d u s t} (T_{}^{d u s t} - 25) + H_{s - l}^{d u s t}]

(15)

where

c_{g}^{g a s}

and

c_{s}^{d u s t}

denotes the specific heat of flue gas and dust, respectively, kJ (kg•K)⁻¹;

T_{}^{g a s}

and

T_{}^{d u s t}

the final temperature of flue gas and dust, °C and

H_{s - l}^{d u s t}

the latent heat of dust, kJ kg⁻¹.

The iron beads and splashing iron are liquid phase state and the calculation of physic heats are similar with MS. The physic heat of iron beads and splashing iron is calculated as equations (16) and (17).

Q_{p h y - s l a g - F e}^{i} = M_{s l a g - F e}^{i} \times [c_{s}^{M S} (T_{m p}^{M S} - 25) + H_{s - l}^{M S} + c_{l}^{M S} (T_{}^{s l a g - F e} - T_{m p}^{M S})]

(16)

Q_{s p l a s h}^{i} = M_{s p l a s h}^{i} \times [c_{s}^{M S} (T_{m p}^{M S} - 25) + H_{s - l}^{M S} + c_{l}^{M S} (T_{}^{s p l a s h} - T_{m p}^{M S})]

(17)

where

T_{}^{s l a g - F e}

and

T_{}^{s p l a s h}

denotes the temperature of iron beads in slag and splashing iron, respectively, °C.

The surplus energy is defined to balance the input and output energy. The surplus energy is significantly influenced by the HM ratio (the mass of HM to the total mass of metal charges). The surplus energy can be calculated by equation (18).

\begin{aligned} Q_{s u r}^{i} = & Q_{i n p u t}^{i} - Q_{o u t p u t}^{i} \\ = & (Q_{p h y - i}^{i} + Q_{r e a}^{i} + Q_{r e a - d u s t}^{i}) \\ - (Q_{p h y - s t e e l}^{i} + Q_{s l a g}^{i} + Q_{p h y - g a s}^{i} + Q_{d u s t}^{i} + Q_{p h y - s l a g - F e}^{i} + Q_{s p l a s h}^{i}) \end{aligned}

(18)

Modelling simplifications and assumptions

EAF steelmaking process is specified by energy intensive and complex chemical reactions, so it is difficult to quantify consumption level of materials and energy sources. To establish the comprehensive material and energy balance model for EAF steelmaking based on the metal charge structure of HM and scrap, some simplifications and assumptions are made as follows:

The melting process of HM and scrap in EAF has no influence on each other. Besides, the MS production can be completed by using HM or scrap alone.

The input raw materials and energy sources individually act on the smelting process of HM or scrap. When the mixed charges of HM and scrap are adopted, the surplus energy of HM smelting is supplied for the scrap smelting.

The complex chemical reactions in EAF steelmaking process are simplified to several single oxidation reactions.⁷ Only the chemical reaction heat generated by oxidation reactions and slagging reactions is considered, while the energy generated by other reactions is ignored.

In decarbonisation in the molten bath, 90% of the mass of C is oxidised to CO, and the remaining 10% is oxidised to CO₂. Besides, the post combustion of flue gas is not considered. As for the combustion of carbon powder, 60% of the mass of C is oxidised to CO, and the remaining 40% is oxidised to CO_2.^41,42

Except for HM, the temperature of the remaining materials entering the EAF is regarded as the reference temperature, and no physical heat is brought into the EAF by them.

The influence of time scale on the input and output of materials and energies in steelmaking process is ignored. All inputs and outputs occur at once in a specific period of time during the EAF steelmaking process.

Based on the EAF steelmaking mechanism and characteristics, some undetermined parameters in the above equations are assumed as shown in Table 1.⁴¹

Table 1.

Values of parameters related to the material consumption equations.

Parameter	$f_{s l a g - F e}^{i}$	$f_{s p l a s h}$	$f_{d u s t}^{i}$
Value	5%	0.8%	1.6%

Data collection and model verification

To solve the remaining unknown terms in the above equations, an EAF steel mill located in Hunan Province, China, is selected as the research object. This factory has one 100t EAF with the mixed metal charges of HM and scrap, and has been engaged in EAF steelmaking for nearly 30 years.⁵ This steel mill has abundant blast furnace (BF) gas and basic oxygen furnace (BOF) gas resources (herein refer to coal gas). The coal gas is recycled in BF ironmaking, BOF steelmaking and EAF steelmaking to provide additional thermal energy after dust removal, separation and purification. Through the field programmable logic controller communication programmes, production reports and test sheets, the actual production data from April 2023 to February 2024 is collected. Considering the requirements for modelling and model validation, the data of HM, scrap, MS, slag and dust related to the equations (1) to (11) are selected. For avoiding statistical and accidental errors, the data after screened, anomaly detected and eliminated and averaged by Python software, is displayed in Table 2. As for the specific heat and latent heat of fusion, they are displayed in Table 3.

Table 2.

Actual production data related to parameters in equations (1) to (11) in EAF steelmaking process.

Parameter	HM	Scarp	MS	Slag	Dust
C (Wt%)	4.00	0.30	0.08
Si (Wt %)	0.80	0.20	0.00
Mn (Wt %)	0.08	0.45	0.02
P (Wt %)	0.18	0.03	0.012
FeO (Wt %)				20	77
Fe₂O₃(Wt %)				2	20
Binary alkalinity				3.0
Melting temperature (°C)	1121		1520
Initial/final temperature (°C)	1300	25	1650	1650	1450

EAF: electric arc furnace; HM: hot metal; MS: molten steel.

Table 3.

Physical parameters in equations (9) to (17) in EAF steelmaking process.

Physical parameter	HM	Scarp	MS	Slag	Flue gas	Dust
Specific heat of solid phase (kJ (kg•K)⁻¹)	0.745	0.699	0.699			0.996
Specific heat of liquid phase (kJ (kg•K)⁻¹)	0.837	0.837	0.837	1.248
Specific heat of gas phase (kJ (kg•K)⁻¹)					1.137
Latent heat of fusion (kJ kg⁻¹)	218	272	272	209.2		209

EAF: electric arc furnace; HM: hot metal; MS: molten steel.

In EAF steelmaking process, elemental oxidation causes iron loss and releases massive chemical heat. According to the EAF steelmaking condition, the exothermic oxidation of fundamental chemical reactions is determined by FactSage 8.1 software. Besides, the chemical reaction loss and heat are also calculated based on EAF-1000 HM and EAF-1000 scrap, as shown in Table 4. The chemical reaction losses are 68.33 and 14.91 kg, respectively. According to the mass of the oxidised elements, the oxygen consumption and the corresponding oxidation products are obtained. By maintaining the alkalinity of the actual slag system at 3.0, the mass of lime can be identified, and then followed the mass of slag.

Table 4.

Changes of materials and energies during chemical reactions in EAF-1000 HM and EAF-1000 scrap.

Chemical reaction	ΔH (kJ kg⁻¹)	Mass of oxidising (kg)		Output chemical heat (kJ)
Chemical reaction	HM/scrap	HM	Scrap	HM	Scrap
C + 1/2O₂= CO	11639	35.28	1.98	410624	23045
C + O₂= CO₂	34834	3.92	0.22	136549	7663
Si + O₂= SiO₂	29202	8.00	2.00	233616	58404
Mn + O₂= MnO	6594	0.60	4.30	3956	28354
P + 5/4O₂= 1/2P₂O₅	18980	1.68	0.18	31886	3416
Fe + 1/2O₂= FeO	4250	17.29	5.72	73478	24310
Fe + 3/4O₂= 1/2Fe₂O₃	6460	1.56	0.51	10052	3295
SiO₂+ 2CaO = 2CaO•SiO₂	1620	17.14	4.29	27771	6943
P₂O₅+ 4CaO = 4CaO•P₂O₅	4880	3.85	0.41	18777	2012
Sum		68.33	14.91	946710	157443

EAF: electric arc furnace; HM: hot metal.

In addition to the chemical reaction loss, there are also other forms of iron loss in EAF steelmaking process. The other iron losses in EAF-1000 HM and EAF-1000 scrap are listed in Table 5. It is concluded that 1000 kg of HM or scrap only produce 906.3 and 963.5 kg of MS, respectively. Compared to the mass of MS of 903.9 and 965.1 kg reported in references (41) and (42) under the same conditions, the established mass balance model is verified within the small relative error. Hence, to produce 1000 kg of MS, 1103 kg HM or 1038 kg of scrap is consumed. HM smelting leads to more iron loss than that of scrap smelting. After quantifying the basic material consumption, the corresponding energy balance of input and output in EAF-1000 HM and EAF-1000 scrap is also obtained, and it is detailed in Table 6, and the Sankey diagram of the two patterns is shown in Figure 2.

Table 5.

Calculation results of the iron loss in EAF-1000 HM and EAF-1000 scrap.

No	Items	HM (1000 kg)	Scrap (1000 kg)
1	$M_{r e a c t i o n}^{i}$	68.3 kg	14.9 kg
2	$M_{d u s t}^{i}$	11.8 kg	11.8 kg
3	$M_{s l a g - F e}^{i}$	5.6 kg	1.8 kg
4	$M_{s p l a s h}^{i}$	8.0 kg	8.0 kg
5	$M_{s t e e l}^{i}$	906.3 kg	963.5 kg

EAF: electric arc furnace; HM: hot metal.

Table 6.

Energy balance in EAF-1000 HM and EAF-1000 scrap.

Items	Energy (kWh)
Items	HM	Scrap
Input	608.29	59.07
$Q_{p h y - i}^{i}$	329.98	0.00
$Q_{r e a}^{i}$	262.98	43.73
$Q_{r e a - d u s t}^{i}$	15.33	15.33
Output	483.29	417.28
$Q_{p h y - s t e e l}^{i}$	358.96	381.60
$Q_{s l a g}^{i}$	68.21	22.12
$Q_{p h y - g a s}^{i}$	43.52	2.44
$Q_{d u s t}^{i}$	7.24	7.24
$Q_{p h y - s l a g - F e}^{i}$	2.20	0.71
$Q_{s p l a s h}^{i}$	3.17	3.17
$Q_{s u r}^{i}$	124.99	−358.22

EAF: electric arc furnace; HM: hot metal.

The total input energy of 608.29 kWh in EAF-1000 HM is nearly 10 times as much as that of 59.07 kWh in EAF-1000 scrap. Compared to the input energy 614.87 and 62.31 kWh reported in reference (42), the established energy balance model is verified. HM has more physical heat and chemical reaction heat, resulting in the surplus energy of 124.99 kWh after completing the production of MS. In contrast, the input energy of scrap is slightly insufficient. To provide the energy of 417.28 kWh for producing MS with appropriate temperature, there is an energy gap of 358.22 kWh. The energy gap needs to be filled with other energy sources, such as electricity, carbon powder, coal gas, as well as the surplus energy of HM.

Results and discussions

Effects of HM on scrap and electricity consumption

The surplus energy of HM can be supplied for scrap smelting. Hence, the mixed charge structure of HM and scrap is usually deployed, and the HM ratio is quite different in different factories or technologies. The relationship of HM and scrap consumption for producing 1000 kg of MS is shown in Figure 3, which reveals a linear tendency. As the increase of HM consumption, the mass of scrap decreases. With the HM consumption increased by 875.0 kg (HM ratio = 80.3%), the scrap consumption reduced by 823.1 kg. Depending on Figure 3, it is more convenient to conduct reasonable metal charge batching and improve the production efficiency in EAF steelmaking site.

The high-temperature EAF steelmaking process exists excessive heat loss from cooling water, furnace body and ambient air. The energy of HM and scrap cannot completely flow into the MS product. The heat loss is mainly influenced by the HM ratio and smelting time. With the increase of HM, the molten bath possesses lower melting time of metal charges, higher carbon content and better slag foaming effect, and the radiation heat loss of electrodes will reduce. However, the increasing higher carbon content means the longer decarburisation time, and finally increases the smelting time. Through field inspection, literature review and numerical simulation, the smelting time and heat loss in EAF steelmaking process under several typical HM ratios are obtained, which are displayed in Table 7.⁴³ With the increase of HM ratio, the heat loss of EAF steelmaking process deceases firstly and then gradually increases. When the HM ratio is 50%, the EAF steelmaking process has the shortest smelting time of 50 min, which also means the highest production efficiency.

Table 7.

Smelting time and heat loss under different HM ratios in EAF steelmaking process for producing 1000 kg of MS.

HM ratio (%)	HM (kg)	Scrap (kg)	Smelting time (min)	$Q_{h e a t - l o s s}^{t}$ (kWh t⁻¹)
0.0	0	1037.9	100.00	66.00
17.7	185.4	863.6	82.33	41.16
30.1	318.5	738.3	69.86	34.93
50.0	534.8	534.8	50.00	25.00
59.5	640.3	435.6	54.76	27.38
70.2	759.8	323.2	60.08	30.04
80.3	875.0	214.8	65.14	32.57

EAF: electric arc furnace; HM: hot metal; MS: molten steel.

The metal charge and energy balance are shown in equations (19) and (20). The electricity utilisation efficiency of electrodes in EAF steelmaking is usually 70–90%, and it is set as 88% here considering the better slag foaming effect.¹⁶ There is nearly a linear relationship between HM and electricity consumption, as shown in Figure 4. With the increase of HM consumption, the electricity consumption decreases. The Sankey diagrams of EAF steelmaking for producing 1000 kg of MS under four typical HM ratios: 0.0%, 30.1%, 59.5% and 80.3% are presented in Figure 5.

1000 \times (m_{H M} / M_{s t e e l}^{H M} + m_{S c r a p} / M_{s t e e l}^{S c r a p}) = 1000

(19)

Q_{}^{E} \times k_{E} = - Q_{s u r}^{H M} \times m_{H M} - Q_{s u r}^{S c r a p} \times m_{S c r a p} + Q_{h e a t - l o s s}^{t} + Q_{h e a t - l o s s}^{a r c}

(20)

where

Q_{h e a t - l o s s}^{t}

denotes the heat loss in EAF steelmaking process for producing 1000 kg of MS, kWh;

m_{H M}

the mass of HM consumption, kg;

m_{S c r a p}

the mass of scrap consumption, kg;

Q_{}^{E}

the electricity consumption, kWh and

k_{E}^{}

the electricity utilisation efficiency.

With the HM ratio increases by 80.3%, the surplus energy of HM increases by 109.37 kWh and the electricity consumption decreases from 497.50 to 0.18 kWh. Besides, the total energy demand per ton of MS firstly drops from 558.80 to 527.07 kWh, and finally rises to 545.12 kWh. When the HM ratio is 50%, the EAF steelmaking process possesses the lowest input energy of 527.07 kWh. The input energy acts on the smelting of HM and scrap, and finally disperse into the smelting products. Most of the input energy goes into the MS, then followed by slag and heat loss. Reducing the heat loss in EAF steelmaking process, especially the radiation heat loss, is of great significance for energy saving and emission reduction. As well as foaming slag optimisation for reducing radiation heat loss of electrodes, cutting down the radiant heat loss between the high-temperature furnace body and outside environment cannot be ignored. Installing the shielding plate in the local high-temperature area near the outer furnace improves the thermal resistance of space radiation, and limit the escape of radiation heat loss. As well as this method, stabilising the process operations, balancing the chemical reaction intensity and preventing the release of huge heat for a short time in the molten bath can also weaken the heat transfer loss by slowing down the local area overheating phenomenon and temperature of the outer furnace wall. Of course, recycling waste heat from high-temperature flue gas and dust greatly improve the energy efficiency. At present, there are also relatively mature technologies, such as heat recovery boiler for power generation and steam and hot water production, and scrap preheating by flue gas.^43,44

Effects of carbon powder and coal gas on electricity consumption

The carbon powder and coal gas injection provide the molten bath with input energy by combustion to enhance EAF smelting. The chemical reaction of carbon powder is a typical carbon–oxygen reaction, as shown in Table 4, while the chemical reaction of coal gas is shown in equation (21). The calculation methods of chemical reaction heat of carbon powder and coal gas are shown in equations (22) and (23). The energy substitution relationships between carbon powder, coal gas and electricity are shown in equations (24) and (25). The main components of carbon powder and gas are C and CO, respectively. The presence of other impurities will reduce the input energy, and their influences on input energy are attributed to the energy efficiency of carbon powder and coal gas. Here the parameters $k_{C P}^{}$ and $k_{C G}^{}$ are set to 90% and 95%.⁴⁵ The excessive carbon powder and coal gas injection increase the oxygen consumption and carbon content of molten bath, and affect the decarburisation reaction. According to reference(45), the consumptions of carbon powder and coal gas in EAF steelmaking processes are controlled within 25 kg and 20 Nm³ per ton of MS, respectively.

The relationship between carbon powder, coal gas and electricity consumption is displayed in Figure 6. With the increase of carbon powder and coal gas, the electricity consumption shows a linear trend of decline. The maximum mass of carbon powder and coal gas is 24.8 kg and 17.0 Nm³. The Sankey diagrams of EAF steelmaking with the metal charge structure of full scrap under different mass of carbon powder and coal gas for producing 1000 kg of MS are shown in Figures 7 and 8. In EAF steelmaking process with full scrap, the injection of auxiliary fuels strengthens the input chemical energy and reduces the electricity consumption. With the mass of carbon powder and coal gas increase to 24.8 kg and 17.0 Nm³, the electricity consumption decreases from 497.5 to 350.5 kWh, and the total energy demand decreases from 558.8 to 555.5 and 547.9 kWh, respectively. The electricity loss reduces by 17.7 kWh, while the chemical heat loss of carbon powder and coal gas increases by 14.42 and 6.83 kWh. It is concluded that coal gas enjoys better electricity saving and chemical heat loss reduction effects than carbon powder.

CO + 1 / 2 O_{2} = {CO}_{2}

(21)

Q_{C P} = \frac{0.6 \times 11639 + 0.4 \times 34834}{3600} M_{C P}

(22)

Q_{C G} = \frac{23195}{3600} \times V_{C G} \times \frac{28}{22.4}

(23)

\begin{aligned} Q_{E}^{} \times k_{E} + \frac{0.6 \times 11639 + 0.4 \times 34834}{3600} M_{C P} \times k_{C P} = Q_{R} \end{aligned}

(24)

Q_{E} \times k_{E} + \frac{23195}{3600} \times V_{C G} \times \frac{28}{22.4} \times k_{C G} = Q_{R}

(25)

where $M_{C P}$ denotes the mass of carbon powder used per ton of MS, kg; $V_{C G}$ the volume of coal gas used ton of MS, Nm³; $Q_{C P}$ and $Q_{C . G}$ the chemical reaction heat of carbon powder and coal gas, kWh; $Q_{R}$ the total input energy demand per ton of MS, kWh; and $k_{C P}^{}$ and $k_{C G}^{}$ the utilisation efficiency of carbon powder and coal gas, respectively.

Economic analysis of EAF steelmaking process under different HM ratio

The economic performance of EAF steelmaking process is highly depend on the price of HM, scrap, electricity, carbon powder and coal gas. Their price is constantly changing according to the market demand. Hence, the unit price ranges for each material and energy items during the data collection period described in the Data collection and model verification section are collected, as shown in Table 8.

Table 8.

Unit prices of HM, scrap, electricity, carbon powder and coal gas.

Item	$P_{H M}$	$P_{S c r a p}$	$P_{E}$	$P_{C P}$	$P_{C G}$
Unit	CNY kg⁻¹	CNY kg⁻¹	CNY kWh⁻¹	CNY kg⁻¹	CNY m⁻³
Price range	2.17–2.36	1.94–2.21	0.425–1.025	0.85–1.08	2.92–3.99
Price	2.20	2.15	0.70	0.95	3.50

HM: hot metal.

Effects of HM and scrap price on production cost

The proportion of HM and scrap, as well as their unit prices influence the production cost in EAF steelmaking process. It is assumed that the external energy is supplied by electricity in this sub-section. The electricity price and scrap price is selected as 0.7 CNY kWh⁻¹ and 2.0 CNY kg⁻¹. The production cost of EAF steelmaking process is expressed as equation (26).

\begin{aligned} P C_{s u m} = m_{H M} \times P_{H M} + m_{S c r a p} \times P_{S c r a p} + Q_{}^{E} \times P_{E} \end{aligned}

(26)

The relationship between HM price, HM consumption and production cost is shown in Figure 9. The x-coordinate represents the mass of HM consumption and the y-coordinate the production cost of EAF steelmaking process. The initial production cost of EAF steelmaking process with full scrap is 2423 CNY t⁻¹ MS. When the HM price varies from 2.22 to 2.36 CNY kg⁻¹, the changing trend of production cost is inconsistent. The overall production cost decreases firstly and then increase with the increase of HM consumption. There are turning points where production cost rises or falls in each line. The lowest production cost under eight HM prices is 2361, 2377, 2392, 2404, 2413, 2419, 2422 and 2423 CNY t⁻¹ MS. Hence, the optimal consumption of HM at the lowest production cost exists under different HM price, which is shown in Figure 10; where the x-coordinate represents the HM price and the y-coordinate the HM consumption. As the increase of HM price, the optimal HM consumption decreases.

Different from Figure 9, the HM price is fixed at 2.3 CNY kg⁻¹, and the variable is the scrap price in Figure 11. When the scrap price varies 1.94–2.08 CNY kg⁻¹, the overall production cost also decreases firstly and then increase with the increase of HM consumption. The connection between optimal HM consumption and scrap price based on the lowest production cost is shown in Figure 12; where the x-coordinate represents the scrap price and the y-coordinate the HM consumption. The lowest production cost under eight scrap prices is 2361, 2381, 2398, 2413, 2425, 2435, 2442 and 2448 CNY t⁻¹ MS. As the increase of scrap price, the optimal HM consumption decreases.

Effects of electricity, carbon powder and coal gas on production cost

According to Figure 6, with the increase of carbon powder and coal gas, the electricity consumption decreases with a linear trend. It is obtained that the electricity consumption decreased by 5.94 kWh and 8.69 kWh t⁻¹ when the dosages of carbon powder and coal gas are 1 kg and 1 Nm³ per ton of MS, respectively. It is assumed that the prices of carbon powder and coal gas are 0.95 CNY kg⁻¹ and 3.50 CNY m⁻³.⁵ Combined with the electricity price of 0.70 CNY kWh⁻¹ described in Table 8, the production cost will be reduced by 3.21 or 2.58 CNY per ton of MS while consuming 1 kg of carbon powder or 1 m³ of coal gas. From the view of economic analysis, the carbon powder and coal gas should be used as much as possible to replace electricity consumption. However, the mass of added carbon powder and coal gas is limited according to the Effects of carbon powder and coal gas on electricity consumption section.

From the above description, the EAF steelmaking process with the HM ratio of 50% enjoys the lowest smelting time and input energy, and it is suggested the optimal smelting mode while considering the production efficiency and energy saving effect. As for the economic performance, more carbon powder and coal gas are suggested. However, the mass of carbon powder and coal gas consumed is limited by the following four factors. In EAF steelmaking process with the HM ratio of 50%, the largest replaced energy by carbon powder and coal gas is equal to the electricity consumption of 170.16 kWh. The first constraint condition, as shown in equation (27), represents the maximum energy substitution. Equation (28) refers to the second constraint condition, which is committed to obtaining better economic benefits. The third and fourth constraint conditions, as displayed in equations (29) and (30), are determined by reference(45). The influence of four constraint conditions on the mass of caron powder and coal gas is shown in Figure 13. Where the green and red lines denote the constraint condition of production cost and electricity substitution displayed in equations (28) and (27), respectively. Besides, the purple dashed lines represent the constraint conditions considered in reference(45). Therefore, systematically considering the four constraint conditions, the region that overlaps with each other is the shadow area. The optimal dosages of carbon powder and coal gas are displayed in the shadow area. The maximum consumption of carbon powder and coal gas should be less than 19.58 kg and 11.63 Nm³, respectively, and the EAF steelmaking process with the HM ratio of 50% can achieve great economic benefits.

5.94 M_{C P} + 8.69 V_{C G} \leq 170.16

(27)

M_{C P} \geq V_{C G}

(28)

M_{C P} \leq 25

(29)

V_{C G} \leq 20

(30)

Conclusions

The metal charge structure of hot metal and scrap is widely used in current EAF steelmaking process in China. It is important to determine the basic material and energy consumption level and production cost for low consumption, high efficiency, and lean production based on steelmaking mechanism. In this article, the consumption level of metal charges and energy sources, and the corresponding production cost are systematically researched by mathematical modelling and techno-economic analysis. The main conclusions are summarised as follows:

The mathematical models for describing the metal charges and energy consumption are established and verified. In EAF steelmaking process with 1000 kg of HM or scrap, 906.3 or 963.5 kg of MS is produced, and there exists the positive surplus energy of 124.99 kWh and negative surplus energy of 358.22 kWh, respectively. The surplus energy of HM can be used for scrap smelting.

The HM charged in EAF steelmaking process can reduce consumption of scrap and electricity in a straight line. With the HM ratio increases by 80.3%, the surplus energy increased by 109.37 kWh, and consumption of scrap and electricity reduces by 823.1 kg and 497.32 kWh. When the HM ratio is 50%, the EAF steelmaking process possesses the lowest input energy, smelting time and heat loss of 527.07 kWh, 50 min and 25.00 kWh, respectively. The heat loss reduction and waste heat recycling of flue gas, dust and slag is of great significance for improving energy utilisation efficiency and energy saving in EAF steelmaking process.

The addition of carbon powder and coal gas causes electricity consumption to plummet. With the consumption of carbon powder and coal gas increase to 24.8 kg and 17.0 Nm³, the electricity consumption decreases by 147 kWh, and the total energy consumption in EAF steelmaking process decreases by 3.3 and 10.9 kWh, respectively. Coal gas takes advantages of electricity saving and chemical heat loss reduction.

As the prices of HM and scrap fluctuate 2.22–2.36 and 1.94–2.08 CNY kg⁻¹, the production cost shows a trend of first decreasing and then rising. Each point under the HM and scrap prices exists a minimum production cost and optimal mass of HM consumption. The production cost per ton of MS will be reduced by 3.21 or 2.58 CNY while consuming 1 kg of carbon powder or 1 Nm³ of coal gas. Considering the smelting time, economic benefit and energy saving effect, the consumption of carbon powder and natural gas should be limited within 19.58 kg and 11.63 Nm³.

However, with the increasing attention of energy conservation and emission reduction of iron and steel industry, new requirements have been put forward for the charge structure adjustment of EAF steelmaking process. More DRI and scrap are consumed instead of HM. The material-energy consumption analysis production cost accounting of EAF steelmaking process with multiple charge structure has gradually attracted the attention of researchers. These contents will be further investigated in the future research work.

Footnotes

Acknowledgements

The authors are grateful for financial support from the National Natural Science Foundation of China (No. 52174328) and the Fundamental Research Funds for the Central Universities of Central South University (No. 2024ZZTS0062, and No. 2022ZZTS0084).

Authors’ contributions

HH contributed to methodology, software, validation, investigation, data curation, writing original draft, writing – review & editing, visualisation, and funding acquisition. LY was involved in conceptualisation, methodology, formal analysis, resources, writing – review & editing, funding acquisition, and project administration. YZ was involved in software, validation, visualisation, and funding acquisition; BX was involved in investigation, validation, visualisation, and data curation. FC was involved in visualisation and project administration; SW was involved in validation, formal analysis, and project administration; YG was involved in conceptualisation, resources, writing – review & editing and Supervision.

Data availability

Data will be made available on request.

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the National Natural Science Foundation of China (grant number 52174328), the Fundamental Research Funds for Central Universities of the Central South University (grant number 2024ZZTS0062, 2022ZZTS0084).

ORCID iDs

Hang Hu

Lingzhi Yang

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