**1. Introduction**

The electric arc furnace (EAF) process is the main process for recycling of ferrous scrap [1] and the second most important steelmaking process route in terms of global steel production [2]. EAF process models have proven to be useful for improving process understanding and control as well as resource and energy efficiency by providing information that cannot be measured directly during the process due to the extreme conditions inside the furnace. Numerous models have been developed using different approaches both for the complete process as well as local phenomena or single process phases. However, few simulators allow for real-time manipulation of simulations by the user. Logar et al. [3] describe a simulator based on their process model and the World Steel Association provides an online EAF simulator on their website [4]. The simulator of Logar et al. [3] is based on a previously developed process model considering detailed heat transfer [5,6] and thermochemical equations [7] as well as an electrical model [8], whereas the World Steel Association gives only limited information about the workings of their model [9]. Other published models run simulations based on predetermined input data and although they can be used to study different scenarios, they do not adapt to current simulation results or user inputs.

In order simulate the process independent of plant data and cover extreme cases that may occur with unusual user input, a comprehensive mechanistic modelling approach is necessary. Several such models are available in the literature such as those of Bekker et al. [10–12] and MacRosty et al. [13–15] who introduced some of the simplifications and assumptions that Logar et al. based their model on, as well as several others that have been published with a varying degree of detail [16–31]. Both Meier et al. [32–37] and Fathi et al. [38] have published models developed on the basis of the work of Logar et al. [3,5–8]. With the exception of Logar et al., all these models rely on predetermined

input from measured data and, as far as can be determined from the published information, no other simulators that provide direct feedback and control for the user are available. Meier implemented the automatic control of the model on the basis of current simulation results [35], but his model does not allow direct user input during the simulation. The model and simulator presented here are based on a further development of the model proposed by Meier [39]. Although the general model structure and most of the assumptions and simplifications from Logar et al. [3,5–8] remain, the model has been adjusted for a different solver algorithm [36] and substantially modified [32–34,36,37,39] making it one of the most comprehensive and up-to-date EAF process models currently available. The differences compared to the model published by Logar et al. include a more efficient numerical method for solving the model equations [36], increased detail in the gas phase with additional species and reactions [34,37], a more comprehensive model of the radiative heat transfer considering the influence of the gas phase [32,37], the treatment of different carbon carriers [33], and the refinement of the thermochemical model for the interaction of slag and melt with each other as well as the injected oxygen and carbon [39].

#### **2. Process Model**

The model presented here as a basis for the simulator is essentially the state of development documented in a previous publication [39]. The model is executed in the MATLAB environment. Within the model there are eight different zones (i.e., control volumes), each of which is homogeneous in terms of composition and temperature. Separate energy and mass balances are defined for each zone. The zones are the (1) solid scrap, (2) liquid metal, (3) solid slag formers, (4) liquid slag, (5) gas phase, (6) water cooled wall and roof, and (8) the electrode(s). The electric arc is treated simply as a heat source whereas the air-cooled bottom vessel and lower wall section are represented as heat sinks. Figure 1 shows a schematic illustration of all zones and heat sinks/sources within the model.

**Figure 1.** Model zones.

Relevant phenomena such as heat exchange through radiation and direct contact, phase changes and mass transfer between zones, chemical reactions, as well as the change in geometry during meltdown, are considered in the model. Simulation results have been validated using extensive data from industrial furnaces [32–34,37,39].

The operation of the furnace is characterized by continuous as well as discontinuous mass and energy flows. For the charging of scrap baskets, the amount and composition of scrap, slag formers, and coal charged with each basket can be considered with an unlimited number of baskets per heat. The charging in bulk of coal, slag formers, or alloys without scrap can be accounted for as well by defining the desired amount and composition and charging it independently. Due to the discontinuous change of conditions inside the furnace resulting from charging of material in bulk, the integration is stopped and restarted with new initial values adjusted according to the added material for each charging event.

The time-dependent model input or operation chart consists of the electric energy input characterized by voltage and current as well as the mass flows of oxygen for lances, burners and post-combustion, natural gas for burners, coal for carbon lancing, slag former injection, and off-gas extraction. The cooling of the wall and roof is determined on the basis of the mass flows and inlet temperature of the respective cooling water flows. For the simulation based on plant data, these inputs are determined from measured values or estimates and stored for each heat at the beginning of the simulation to be evaluated at every time step of the simulation. Additional parameters describing furnace-specific properties such as the geometry and empirical factors adjusted for each individual plant are stored in a separate Excel file. Different parameter sets can be defined and automatically simulated in succession. By comparing the results for different parameter settings, empirical parameters can be adjusted for different furnaces or process conditions and the impact of parameters such as the composition of slag formers or coal and gases can be evaluated. For the automatic control of the simulation as implemented by Meier [35], the masses charged in bulk are predetermined while the time of charging, mass flows, and electric energy input are determined on the basis of the progress of the simulation and rules derived from the operation of a real-life furnace. For the simulator, the operation chart and charging of baskets can be determined by the user during the simulation.

Figure 2 shows the structure of the model with its different modules and the exchange of information between them. Essentially, the main model runs independent from the type of data use and the change between the three running modes (measurement-based simulations, automatic control, and user-input-controlled simulations) affects only the data module and its interaction with the main model.

**Figure 2.** Model structure (translated from [37]). EAF: electric arc furnace.

The data module determines both the initial conditions for each basket that are calculated in the input mass module and the time-dependent input during the simulation that is transferred to the energy distribution module for each time step. Figure 3 shows how the structure of the data module and the data that is exchanged with the EAF model when measured data is used. The input is predetermined for each point of time and together with the geometry and other furnace-specific parameters determines the input for the model. The validation data is not used directly as model input but can be compared to model results and to adjust empirical parameters.

**Figure 3.** Data module with measured data.

Figure 4 shows the structure of the data model for the automatic control (left) and simulator (right) modes. Because the input is no longer predetermined for the full simulation, the time and current state have to be passed back to the data module for each step. In the case of the automatic control mode, the current input is then determined on the basis of the current set of parameters, rules, and minimum/maximum values and passed back to the EAF model. In the simulator mode, the user interface is updated with the current model results and the input for the model is updated with those set in the interface so that any changes made by the user since the last update are carried over to the EAF model. Furthermore, for the simulator mode, the selected speed is passed to the model as an additional input parameter, whereas in all other cases the model always runs with the highest attainable speed by default.

**Figure 4.** Data module for automatic control and simulator modes.
