Electric furnace steelmaking is one of the most important steelmaking processes today. Since most of the raw materials for electric furnace steelmaking are scrap steel, it plays a good role in saving energy and protecting the environment and purifying the metallurgical environment. Electric furnace steelmaking also has the advantages of less capital investment and low operating costs. Therefore, the development of compact electric furnace short processes has become a strategic focus of many countries.
In recent years, there have been many related studies on electric furnace steelmaking. At present, the method of defining the optimal electric operating parameters of the electric arc furnace (EAF) uses foam slag practice technology, which is not only expensive, but is only used in AC EAF with good stability. Reference  proposes a new control system that can be applied to both AC EAF and DC EAF systems, and is cheaper and more stable. And through multiple verification tests, it proves that the technology shortens the working time and improves the power factor in practical applications; coherent jets are widely used in electric arc furnace (EAF) steelmaking processes to enhance chemical energy input, speed up the smelting rhythm, and promote uniformity of bath temperature and composition. A coherent jet of mixed injection of CO2 and O2 (COMI) is proposed in Reference , which shows great application potential in reducing dust generation in electric arc furnace steelmaking. At the same time, based on the conceptual model of eddy current dissipation, a computational fluid dynamics model of coherent jets with COMI was established using the overall and detailed chemical kinetic mechanism (GRI-Mech 3.0), and the concept was verified. The results show that the chemical action of CO2 has indeed played a positive role; Reference  has studied element migration during hydrothermal treatment of zinc-containing electric arc furnace dust (zinc-containing EAFD). At the same time, it was found that most of the Fe, total Cr and silicon (Si) in the leaching residue existed in the form of Fe2O3, Cr2O3 and SiO2 respectively, and could be recycled; In Reference , dust slag/lime from an electric arc furnace (EAF) was used to treat acidic wastewater in the industry. The test proves that EFA dust slag and lime can effectively remove Co, Cr, iron, nickel and zinc in wastewater, and the removal rate reaches more than 99.6%. This technical route not only recycles the dust and slag of the electric arc furnace, but also has simple operation and only requires mechanical mixing. It replaces the chemicals used in wastewater treatment, has good economy, and is environmentally friendly; In Reference , the effects of EAF steel slag on the fracture and temperature sensitivity of warm-mixed asphalt (WMA) were tested. The results show that the presence of EAF slag in modified asphalt mixtures has reduced the resistance of asphalt to fracture at low temperatures. Temperature sensitivity has a positive synergy.
It can be seen that the research on electric furnaces mainly focuses on improving the working efficiency of electric furnaces and the recycling of slag. The research on the recycling of electric furnace flue gas is relatively small. In fact, the recovery potential of electric furnace flue gas is huge. The unit energy consumption is about 12.4 GJ/ton of steel . Among them, about 13% - 20%  of energy exists in the form of flue gas waste heat during electric furnace steelmaking., For example, a major steel producer, China’s electric furnace steel output in 2018 was 105 million tons , and energy consumption was about 1.3 × 109 GJ, where the flue gas waste heat energy was not less than 1.69 × 108 GJ, how to use this part of waste heat reasonably, should be taken seriously.
There are many studies on the recovery and utilization of flue gas waste heat throughout some industrial fields for reference. Reference  put forward a novel idea, proposes and analyzes a novel integrated system for high-pressure hydrogen production from steel furnace waste heat. This study combines an industrial waste heat source with a thermochemical Cu-Cl cycle and a hydrogen compression system; Reference  proposed a compound cycle using CO2 and air as the heat exchange working medium, organic Rankine cycle as the bottom cycle, this new cycle has excellent thermodynamic performance in the temperature range of 500˚C - 700˚C; Reference  studied the use of mixed working fluids in an ORC system operating in combined heat and power (CHP) mode. The results show that when optimizing the overall performance of the ORC-CHP system provided by industrial waste heat sources, the temperature and load Patterns are a key factor affecting organic selection. Yang M  et al. proposed an economic parameter of the net power output index to obtain the maximum net power as the output index, using zero ODP and lower GWP working fluid to optimize the geothermal ORC system. The results show that under the optimization of economic performance, the performance of R600 is the best, followed by R600a, R1233zd, R1234yf, R1234ze and R290. In addition, the use of R600, R600a and R1233zd systems requires lower working pressure and lower equipment purchase costs.
Aiming at the heat recovery of electric furnace flue gas, building on research by seniors, this paper proposes a compound cycle composed of nitrogen Brayton cycle and transcritical toluene Rankine cycle.
2. Design of Compound Cycle
2.1. Design of Compound Cycle
At present, the power generation of flue gas waste heat boilers for steel-making electric furnaces often uses the water Rankine cycle  for heat exchange. Rankine cycle has a heat transfer pinch during the heat exchange process between the working medium and the flue gas, leading to a low waste heat recovery efficiency . Both Gas Brayton cycle and transcritical Rankine cycle, the heat exchange between the working medium and the heat source is a temperature change process, which has a good matching degree with the heat source, can avoid pinch problems. Steelmaking electric furnace flue gas emissions are intermittent , the heat storage process   is set up to solve the flue gas temperature fluctuation problem  , after the average heat storage temperature, the parameters of the waste heat have changed, and the power generation cycle needs to be re-designed  .
In the electric furnace steelmaking process, the waste heat recovery device is set in the flue gas dedusting system. After the flue gas is dedusted, the temperature is reduced from 1600˚C to about 800˚C, and has a few characteristics: high initial temperature, large temperature drop, almost constant specific heat capacity, continuous smooth enthalpy drop curve. For the heat recovery of flue gas in this temperature range, N2 is a good choice: not only suitable for high temperature flue gas of electric furnace, but also lower requirements for operating pressure of the system. Due to the limitation of exhaust pressure, the heat release temperature of the Brayton cycle is high, so the transcritical organic Rankine cycle is used as the second stage to recover this part of the waste heat. Therefore, this paper proposes a compound cycle using the nitrogen Brayton cycle as the first-stage cycle and the transcritical organic Rankine cycle as the second-stage cycle.
Configuration of compound cycle: the compression process of the Brayton cycle uses a multi-stage compression-intercooling scheme. Referece  found that this method can better improve the system efficiency, which is beneficial to reducing the exhaust temperature and improving the utilization of waste heat; there is no thermal device set in the Brayton cycle, referring to the research  on the Brayton cycle, shows that the influence of the heat recovery contrast work is faint. But a heat recovery device is provided in the transcritical organic Rankine cycle  to improve the thermal efficiency of the cycle.
2.2. Selection of Organic Working Medium
In the compound cycle, the heat source for second-order cycle is nitrogen, which is at the outlet of the Brayton cycle expander, with a temperature exceeding 400˚C. Reference  believed that toluene, benzene and cyclohexane are suitable for medium temperature organic Rankine Cycles; both aromatic hydrocarbons and silicone-based working mediums are suitable for high-temperature organic Rankine cycles, in which the performance of aromatic hydrocarbon organics is better than that of silicones and other hydrocarbon-based working mediums ; Critical temperature is an important parameter for screening organic working mediums. Reference  proposed that the working medium is generally more suitable when its critical temperature is 40˚C - 60˚C lower than the initial temperature of the heat source; Reference  carried out a comparative study of Alkanes working mediums, with benzene, toluene, and water, the results show that n-dodecane and toluene are the best working fluids at 500˚C heat source. Combining above points, in this paper toluene is selected as the working medium of the organic Rankine cycle. Heat exchange working fluid for transcritical organic cycle (Table 1).
2.3. Compound Cycle Workflow
The process flow of the compound cycle of flue gas waste heat power generation proposed in this paper is shown in Figure 1.
Figure 1. Flow chart of the compound cycle system.
Table 1. Critical parameters of organic working fluids.
A flue gas heat exchanger with heat storage function is set between 1-2. Through the heat storage heat exchanger, the intermittent and fluctuating electric furnace flue gas is converted into a heat source with continuous and stable flow, besides its temperature drop curve is smooth and continuous . It is helpful to alleviate the problem of heat transfer pinch of the thermal system and promote the smooth operation of the recovery system.
1-2 is the exothermic process of flue gas in the flue gas heat exchanger; 3-4 is the adiabatic expansion process of nitrogen in the turbine, 4-5 is the exothermic process of nitrogen in the intermediate heat exchanger, 5-6 is the constant pressure exothermic process of nitrogen in the cooler, 6-7 is the adiabatic compression process of nitrogen in the compressor, 7-3 is the constant pressure heating process of nitrogen in the flue gas heat exchanger; 8-9 is the process of adiabatic expansion of toluene in the expander, 9-10 is the exothermic process of toluene in the regenerator, 10-11 is the constant-pressure exothermic process of toluene in the condenser, 11-12 is the adiabatic compression process of toluene in working fluid pump, 12-13 is the heat absorption process of toluene in the regenerator, and 13-8 is the constant pressure heat absorption process of toluene in the intermediate heat exchanger.
The pressure-enthalpy diagram describing the thermodynamic process of this workflow is shown in Figure 2.
Figure 2 shows the pressure and enthalpy change curves of the two working mediums in the compound cycle, and the respective gas-liquid saturation lines are given for reference. Among them, curve 3-7 is the pressure enthalpy change curve of nitrogen in the first cycle, curve 8-13 is the pressure enthalpy change curve of toluene in the second cycle. With reference to Figure 2, the properties of the nitrogen Brayton cycle and the toluene transcritical organic Rankine cycle can be understood more intuitively.
Figure 2. h-lgP diagram of the compound cycle system.
3. Mathematical Model of Compound Circulation System and Optimization Goals
3.1. Mathematical Model
This article explores the superiority of the compound cycle by adopting a method of establishing a mathematical model for calculation and verification. Several assumptions need to be made when calculating: It is assumed that both the flue gas and the heat exchange working medium are steady state and steady flow; Ignore the influence of the working medium’s gravity potential energy; Ignore the macro kinetic energy changes of the working medium except for the expansion; Ignore the friction loss of the working medium except for the expansion and compression; Ignore the heat loss of the shell of each component in the cycle.
Exothermic heat of flue gas:
Mass flow of nitrogen in the first-cycle:
Turbine power of the first-cycle:
Compressor power of the first-cycle:
Net output work of the first-cycle:
Heat exchanger capacity of the second-cycle:
Mass flow of toluene in the second-cycle:
Expander power of the second-cycle:
Pump power of the second-cycle:
Net output work of the second-cycle:
Net output work of the compound cycle:
· my = Mass flow of flue gas (kg/s);
· Cpy = Constant pressure specific heat capacity of flue gas (kJ/kg·K);
· h1 − h2 = The enthalpy of flue gas at the inlet and outlet of the flue gas heat exchanger (kJ/kg);
· h3 − h7 = The enthalpy of the state point of nitrogen in the first-cycle (kJ/kg);
· h8 − h13 = The enthalpy of the state point of toluene in the second-cycle (kJ/kg).
3.2. Optimization Goals and Methods
Optimize the main parameters of the compound cycle, including the state points 3 and 4 of the first cycle, and the state point 8 of the second cycle. With the maximum net output work as the goal, explore the influence of the main variables of the compound cycle on the net output work.
4. Electric Furnace Flue Gas and Equipment Parameters
4.1. Physical Parameters of Flue Gas
4.1.1. Specific Heat of Constant Pressure of Flue Gas
The physical parameters of the heat source are the basis of the calculation.
The electric furnace waste heat recovery device is located in the middle of the flue gas dust removal system, the inlet is connected to the combustion sedimentation chamber, and the outlet is connected to the dust removal equipment. The composition of the flue gas passing through the combustion sedimentation chamber changes, and its composition is shown in Table 2 .
Table 2. Composition of electric furnace flue gas.
Under cyclic conditions, each component in Table 2 can be treated as an ideal gas. The constant pressure specific heat capacity regression Equation (13) of the flue gas can be obtained by Equation (12).
· Cp = Constant pressure specific heat capacity of mixed gas (kJ/kg·K);
· Cpy = Constant pressure specific heat capacity of flue gas (kJ/kg·K);
· Cpi = Constant pressure specific heat capacity of each component (kJ/kg·K);
· xi = The volume fraction of each component.
4.1.2. Calculation of Flue Gas Dew Point
The acid dew point of the flue gas will affect the setting of parameters at the flue gas heat exchanger, in this paper, the acid dew point of the electric furnace flue gas is calculated according to Equation (14) , and the acid dew point of the flue gas is calculated to be 84.15˚C.
· PH2O = Partial pressure of water vapor in flue gas (Pa);
· PSO3 = Partial pressure of SO3 gas in flue gas, there is no SO3 in electric furnace flue gas (Pa).
4.2. Parameter Setting of Compound Circulation System
For some equipment parameters are set here. According to the influence of the narrow point temperature difference on the waste heat boiler  and reference to the general waste heat power generation engineering situation  , the heat exchange temperature difference of the heat exchanger in the compound cycle is set to be 15˚C, and the condenser temperature difference is set to be 15˚C. Set the condensing temperature is 35˚C, both the isentropic efficiency of the turbine and expander are 0.9, and the isentropic efficiency of the compressor is 0.8. The physical parameters of the flue gas-related gas and the compound cycle heat exchanger working mediums are obtained from the Refprop 9.1  physical property database.
5. Optimization Results and Analysis
5.1. Effect of Compound Cycle Parameters on Net Output Power
In order to analyze the influence of the main variables of the composite system on the net output work, it is assumed that the temperature of the electric furnace flue gas at the inlet of the circulation system is 800˚C and the mass flow rate is 1 kg/s after the heat storage’s equal temperature treatment.
Figure 3 is under the working condition of P3 = 1.3 MPa, the relationship between P3, P4, and net output power/ΔWnet. As can be seen from Figure 3, ΔWnet varies with P3 increases, and within a certain range of P3 and P4, the larger P4, the higher the rate of change of ΔWnet with the increase of P3. The pressure ranges of P3 and P4 are determined by the overall lower working pressure of the Brayton system and the appropriate pressure ratio of the expander.
The influence of the working fluid state on the Wnet of the compound cycle system at the inlet of the secondary circulation expander was studied. The pressure of P8 was not set too high, because the excessively high working pressure had an impact on system safety and work efficiency. The requirements for the quality pump pressure ratio are more demanding.
Figure 5 is the influence curve of T8 and P8 on ΔWnet. It was found that when T8 is the same, the change trend of ΔWnet between the pressure gradients of P8 is roughly the same and the value of Wnet is small. The curve of P8 = 6 MPa shows different trends. Because the value of ΔWnet is small too, this should be a normal phenomenon caused by the physical properties of the working medium itself.
Figure 6 is the corresponding curve of T8 and net output work Wnet under the condition of P8 = 8 MPa. It was found that Wnet is positively correlated with T8, and the larger T8 is, the larger Wnet The larger the increase is steady.
Figure 3. Curve of the influence of P3 and P4 on ΔWnet.
Figure 4. Curve of P4 effect on Wnet under P3 = 1.3 MPa.
Figure 5. Curve of the influence of T8 and P8 on ΔWnet.
Figure 6. Curve of T8 effect on Wnet under P8 = 8 MPa.
5.2. Compound Cycle Optimization Parameters
With Equations (1)-(11) as the calculation criterion and the maximum net output work as the goal, the main variables of the composite system were optimized and calculated. The optimization results are shown in Table 3. The physical property parameters of the heat exchange working fluid are obtained from the Refprop 9.1 physical property database obtain.
5.3. Comparison of Compound Cycle and Water Rankine Cycle
In order to evaluate this compound cycle, the main indexes of the traditional water Rankine cycle and the compound cycle system as two types of waste heat recovery of the steelmaking electric furnace flue gas recovery were compared. The waste heat recovery efficiency is shown in Equation (15), and the results are shown in Table 4.
Table 3. Optimization parameters of the compound cycle.
Table 4. Comparison of result of recovery of waste heat form.
· Wnet = Net output power of the circulation system (kW);
· Qy = Exothermic heat of flue gas (kJ).
It can be known from Table 4 that the net output power and waste heat recovery efficiency of the composite cycle proposed in this paper are 22.52% and 21.02% higher than those of the traditional Water Rankine cycle (calculated in ref ).
6. Effect of Cycle Parameters on Exhaust Temperature
Exhaust temperature is a non-negligible index parameter in waste heat recovery. Excessive exhaust temperature will cause inconvenience to the subsequent exhaust process, not only increase costs, but also cause adverse effects on the environment. The influence of the operating conditions of the compound cycle system on the exhaust temperature is shown in Figure 7.
It can be seen from Figure 7 that the t2 increases with the increase of P3 and the decrease of P4. Combining Figure 3, t2 and Wnet is positively correlated, so when determining the compound cycle operating conditions in actual engineering, it is necessary to consider the comprehensive consideration of the effect of the exhaust temperature.
Figure 7. Curve of the influence of P3 and P4 on exhaust temperature/t2.
Aiming at the characteristics of flue gas waste heat from steelmaking electric furnaces, this paper proposed a compound cycle consisting of a nitrogen Brayton cycle and a transcritical toluene Rankine cycle for waste heat power generation.
Under the optimal working conditions of the compound cycle, the net output power and waste heat recovery efficiency are respectively 22.52% and 21.02% higher than the traditional Water Rankine cycle, which reflects the superiority of the compound cycle.
The net output power Wnet of the compound cycle increases with the increase of P3, P8, t8, and decreases with the increase of P4. Among them, P8 has a smaller impact.
The increase of P3 and the decrease of P4, while bringing higher Wnet, also lead to an increase in the temperature of the electric furnace flue gas.
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