Energy Optimization of Steel in Electric Arc Furnace

The aim of this work is to create a representative mathematical model of the process of steelmaking for the quantities of raw materials and energy consumption optimal for producing a ton of steel of the specific composition. The specific steel is grade 1010. The reaction enthalpies are critical in the conceptualization and the percentages of carbon and iron in the steelmaking process. There should be a maximum of FeO in slag and a bounded particle C. chemical reactions electric arc furnace enthalpies linear programming steel-making.


Introduction
Longtime has been passed to optimize the energy of the electric arc furnace (EAF), as Gordon H. Geiger [1] and Rodolfo D. Morales [2] authors have focused their efforts on this type of furnace using linear programming techniques. Steel production in EAF is adapted as an optimization problem, equations of mass and energy balance with the profit function are coupled to see if the metal load can optimally produce the desired steel ( Figure 1). Therefore, it is crucial to establish the chemical reactions that take place in the process of steelmaking to obtain reaction enthalpies. It is necessary to know where are carried out such reactions, that part of the metallic charge involves and how each contributes.
Homologation of units must be maintained because although the method allows to mix variables of different nature, the made must be coherent and consistent interpretation.
It was assumed that the reactions were not focused on the direct reduced iron. But also involved other iron present in the metallic charge, as well as ferro-alloying, slag formers, injected oxygen and carbon particles. All as a single system, a large pot subject to the physico-chemical processes.
The technical parameters of electrical and thermal efficiency are mainly due to factors such as the lining of the container, refractory or pan, tilt of the injectors, the input speed of the coal particles, the pre-heated oven and preferential area inside retaining furnace high temperature.

Mass balance
To set the mass balance must first determine what goes into the system and what comes out. Incoming masses are those from Direct Reduced Iron (DRI), the scraps, injected oxygen, injected carbon particles, coke, alloying elements and additives. The masses that come out are those formed in the slag from the trainers and additives, CO, 2 O , steel. The power here does not apply.

Energy balance
Closely related to the previous balance is energy balance. It is here that becomes relevant the determination of the chemical reactions involved in the process of steelmaking into EAF. Calculating enthalpies at 1600 C  and the reaction enthalpies were calculated from the heat capacities taken from tables of Barin and standard enthalpies of transformation. They were compared with BASEDAT and REACTION [3] programs to corroborate the calculations made in Excel at the stage of pretreatment of input data.

Profit function
It is defined as the difference between revenues and expenditures. It is assumed that the cost function of raw materials include transportation and different inputs come with well-defined costs to be prorated respect to the chemical compositions. The simplex method allows slack in the extreme exactitude in the coefficients. That is why as modeling tool has proven to be highly efficient with respect to their predictions.
The simplex method allows slack in the extreme exactitude in the coefficients. That is why as modeling tool has proven to be highly efficient with respect to their predictions.

Thermodynamics of the process
It is based on the enthalpies calculation, because it is believed that at 1600°C radiation losses are greater than dissipation. Since this model is closely related to the chemical composition, it is not considered the radiation loss, only by thermal and electrical losses. Radiation bounces off the walls of the furnace by the action of the slag and coatings ( Figure 2).
Input data: percentages of the compositions of DRI, scraps, the desired slag from additives, ferro-alloying elements, load and desired steel coke and gaseous Iron gangue. The data to be determined, or output, are the amounts of input variables to produce a ton of steel, the amount of spent fuel (electricity, particles C and oxygen). So that energy consumption and the amounts of each component to maximize the benefits of the company. Labor appears as fixed and constant cost, so it does not affect the function to maximize.

Brief state of the art
Information on energy levels, particle injection, oxygen and supplies are taken from the references [4,5].
Considerations are made to linearize own conceptualization to reach the structural form of a linear programming.
Ionas, et al. [6] by considering the preheated process takes into consideration two aspects: the heat transfer between fluid and particles and heat transfer between the gas layer and an exchange surface, thermal gradients quantizing. The objective function used is a Cobb-Douglas quality/price. It takes into account technical parameters such as the lining of the container, the optimum angle of inclination of the injectors, the inlet velocity of the coal particles, etc. Economic parameters such as exchange rates, inflation, market prices, among others. And weights that reflect the relative importance or contribution of each parameter.
This model shows that preheating has a homogeneous increase existing preferential area retains the high temperature, so that the reactions be differentiated or staggered with respect to time and temperature.
This work bases its hypotheses on which the furnace is efficient (the furnace passed the pre-heated).
Build a model that takes into account the maximum possible variables that adequately describe the physical and chemical phenomena occurring within an electric arc furnace taking into account energy and economic restrictions have been under investigation for some time.
For a detailed description of the process of steelmaking see the final report of the European Commission [5].
Geiger model considers that the reactions are performed zonally, this is, is the sponge iron in the scrap or slag, it does not consider it as a single system where the subsystems interact by exchanging energy.
In addition, energy balance considers the sum of different sources equaling the thermochemical energy and then equating to an estimate of the amount of energy for steel. The latter bound is underestimated by Geiger to considerer only Fe in sponge iron.
A model based on balances for areas was developed by Wendelstorf and Spitzer [7] which optimizes mass balance, momentum, energy and species establishing the differential equation For a conserved quantity Ψ i in the balance volume i, S Ψi is the sum over all source terms of balanced quantity Ψ i in the balance volume i and F Ψ,I,j is the interaction term for Ψ i between the balance volumes i and j. For the simple case of heat transport without mass or species transport between two balance volumes, the interaction term for the enthalpy content H is , , , The interaction area A i,j , and the heat transfer coefficient α i,j must be provided, while the actual boundary temperature boundary , , can be calculated from the symmetry/conservation relations. Whereas a new method by Duan, et al. [8] focus on improving preheating using oxygen injectors and improving slagging. Hot metal is charged into EAF in two portions or steps: firstly, 35 wt% to 40 wt% hot metal is pretreated by blowing oxygen in a specially designed reactor for decarburization, improving temperature, and melting pre-melted slag; secondly, another 35 wt% hot metal is charged into EAF with high basicity refining slags.
Li and Hong [9] used nonlinear differential equations for a dynamic model of EAF steelmaking process and assumed that the simulation Energy Process Scheme Electric energy, injected oxigen, injected carbon particles Raw materials that increasing the temperature react to from slag, CO, fume and steel. Enthalpies.
Steel + slag + CO + fume was conducted during the later stage of scarp melting process when the heat transfer from arc is supposed directly to the liquid and gaseous phases and, then from the liquid phases to the solid phases. Also, the formulation of scrap melting process was merely based on heat transfer. The heat absorbed by the solid may be utilized to heat or melt itself. The quantity of each one depended on a temperature ratio between the solid and the liquid. And, the scrap lump was dealt with as roundness approximately and assumed to be melt symmetrically.
All models are based on balances of volume, mass, energy, etc. The optimization is over balances not costs or profit.

Conceptualization of Model
The mass and energy balances are established using a set of linear equations. The inputs to solve the system of equations take into account: 1. Chemical processes of raw materials such as scrap, direct reduced iron (DRI), coke, ferro-alloys, the desired composition of steel and slag; 2. Physical processes: required energy levels, reduced energy losses, phase transformations. The outputs are, per ton of steel, the specific energy consumption (electricity, gas, rubber, coke, etc.), optimum amount of raw materials, oxygen and chemical composition.
The model and its application to steel grade 1010 appear together. It should be noted that there may be more equations and they must be added if it can be determined, and there is information about them.
The steelmaking process analysis identifies three main phenomena: The management of carbon and oxygen levels throughout the process and the presence of Fe in raw materials. This leads to establish the first four restrictions: To calculate the enthalpies are considered the following reactions at 1600°C: Restriction for coal (carbon). It includes coke: Restriction for Fe (balance of Fe): , , There must be balance between additives Restriction for CaO (balance of CaO): Restriction for S: The composition of raw materials is critical in the production of steel.
Restriction on the mass of DRI: Restrictions on impurities: Restriction mass balance: Restriction for desired steel: Equation (49) is used instead of the (50) proposed by Gordon H. Geiger [1] since his scheme breaks the balance in assuming that the sum of the thermal and electrical energies are those that produce steel in the DRI. The logic in this work is that the incoming power to the system (electrical) is transformed into thermal energy, do not overlap, this is transformed, so the total energy is not the sum but an equality of power with thermal more losses. Also to estimate it and not take into account the contributions of the other components would be a lower bound not equality. The electrical energy would not adding, but subtracting, and consequently would have to adjust the dimension for the difference.
These equations must be coupled to an objective function. This function is the link between the steelmaking process physical-chemical variables and economic world as it usually evaluates financial or accounting issues (Tables 1 and 2).
The proper function, since the input data is the desired chemical composition of steel, is the benefits and not the cost. The cost function explicitly considers only variables associated with the process and raw materials. This is the price that has been paid by forcing optimization to obtain, from the chemical composition, the desired steel under the constraint of energy consumption.
Objetive fuction: 1 2  Table 3 shows enter data for steel grade 1010. The system was solved using the simplex method. For this, the LP GAMS solver was applied.

Code Variable Code Variable Code Variable
Al O in the DRI SiO in the slag X 45 EC part injected C particle

Analysis and Discussion
From Tables 4 and 5, the Figures 3-6 were built. As seen from Figure 3, the behavior of the components of DRI for percent carbon is similar to impurities, FeO, Al 2 O 3 and SiO 2 . The same applies for Fe and Fe 3 C. The optimum is between 14-15% of C in coke.
Also, the behavior between the two groups is reversed, that is, for example, while the impurities are increased Fe decreases after 15% C.
From Figure 4, the benefits are increased as the % Fe in the DRI is increased to 70.89% in the optimal. After drastically decrease the benefits. The price of the gangue or metallic charge is substantially increased compared to its quality.
For a poor gangue in Fe, profits are negative or very low. For higher amounts of 2%C steel becomes brittle.
From Figure 5 and Table 5, profits will be obtained 70.18% at full load of 0.571% C respect to 0%C in coke (2.01086085 Kg C).
From Figure 6, a quick slagging occurs between 60 and 70% Fe in the DRI (0.16 kg / ton steel /%Fe in DRI). The maximum slagging is carried out between 70 and 70.89% at a rate of 0.2247 [kg / ton steel /% Fe in DRI]. After between 80 and 90% is stabilized.
From Table 4, the remaining compounds of the slag Al 2 O 3 , SiO 2 decrease as the %Fe in the DRI is increased while that calcium oxide remains constant.

Conclusions
1. Reducing energy costs in the steel-making process can only be significant in managing the composition of the slag and the cost of getting rid of it ecologically. The same applies to the fume.
2. Costs are sensitive to the composition of the DRI and the metal charge.
3. From feasibility analysis, a minimum percentage of injected particles C to be carry out reactions and this is 0.8 kg / ton of steel. 4. The model is sensitive to the definition of chemical reactions that take place in the steelmaking process more than just the energy electrical bounds, particles C and, electrical and thermal efficiencies.
5. Maximum profit is 0.059$/Ton of steel respect to 70.89%Fe in the DRI. In this optimum the production of slag (FeO) is stabilized.