Process of Copper Slag Reduction in an Electric Furnace and the Possibilities of Its Modelling ^†

1. Technological Background

Over the past several decades, numerous studies have been published on the topic of electric furnaces used in the reduction processes used for metallic slags. These studies have focused on gaining a thorough understanding of the kinetics and thermodynamics of the reduction process, as well as determining the influence of furnace design and operating parameters on their performance and the extensive potential of numerical modelling, which has become an alternative and effective method for studying and optimizing the slag reduction process in electric furnaces.

The main purpose of using an electric furnace in the primary copper industry is the reduction of valuable metals present in the slag after the finished smelting process of copper concentrates. The application and continuous improvement of the copper slag reduction process in the electric furnace stem from increasingly strict legal restrictions on slag utilization and the financial losses associated with metal loss in the oxidic phase. Key to implementing modifications aimed at improving the copper slag reduction process is a thorough understanding of its kinetics and thermodynamics. Electric resistance furnaces are used for this process, and for more intensive copper removal, arc resistance furnaces are used. The focus will be on the electric resistance furnace, in which there is no electric arc.

The article [1] delves into the theoretical foundations of the reduction process, identifying the pivotal reactions and driving and limiting factors that govern this process. Subsequently, the process is analyzed in the context of designing furnaces for slag treatment in the non-ferrous metals domain and determining operational parameters [2]. The influence of individual parameters and employed additives on the achievable efficiency of the copper slag reduction process is also examined.

The possibilities of conducting industrial experiments in furnaces for processing metallurgical slags are severely limited due to high process costs and measurement constraints of particular parameters. For this reason, computer numerical simulations have become an alternative and effective methods for studying and optimizing metallurgical slag reduction processes, as well as for designing electric furnaces [3].

Boundary conditions, initial values, and material specifications are essential for defining when conducting numerical simulations. In the absence of knowledge of particular material parameters such as the viscosity, surface tension, density, specific heat, thermal, and electrical conductivity of slags, it is necessary to conduct measurement tests, the procedures of which are presented in the next part of the article [4].

2. Modelling Methodologies

The first three-dimensional finite element analysis of fluid flow and heat transfer in a submerged electric furnace was conducted in 1983 by Szekely et al. [5]. Sheng et al. [6,7] introduced a method that uses a constant electric potential as an input parameter instead of alternating current, which contributed to a reduction in computation costs.

The development of computational numerical modelling has enabled an in-depth analysis of metallurgical slag reduction processes in electric furnaces. Tesfahunegn et al., in their studies [8,9,10] presented a numerical model of the electric current, power, and heat distribution in the particular parts of a cylindrical three-electrode submerged arc furnace used for silicon production and studied the influence of pitch circle diameter on it.

Scheepers et al. [11] developed a numerical model to investigate the influence of operating conditions on the energy distribution and the gas–solid reaction zone inside an electric arc furnace for phosphorus production. The arc region was simplified to a cylindrical conductor with a constant heat source, without solving the electromagnetic field. The developed model took into account fully developed gas product flows, energy associated with chemical reactions, heating, and phase transformations, as well as thermal conductivity and interparticle radiation.

Bezuidenhout et al. [12,13] developed a three-dimensional CFD model to study the distribution of velocity and temperature inside an electric arc furnace used for melting platinum group metals. Based on previous models, the study [14] considered the impact of CO gas bubbles formed near the electrodes on the velocity distribution of the liquid bath flow. The flow characteristics of the liquid bath in the EAF were also examined in detail in the study by G. Wei et al. [15], where the technology of injecting a CO₂-O₂ stream beneath the bath surface was discussed to enhance circulation and accelerate the reaction rate of the bath in the steel production process.

Karalis et al. [16] used a two-dimensional, stationary numerical model to investigate the impact of electrode shape, immersion depth, and slag thermal conductivity on the amount of Joule heat generated during the operation of an EAF in the ferronickel processing process. Equations for electric potential, momentum, and heat transfer were solved in four different regions (i.e., air, slag, ferronickel melt, and refractory materials), and the final slag/metal boundary profile was calculated as a function of the furnace operating parameters. Karalis et al. then presented the application of CFD numerical simulations [17] to analyze liquid flow, heat transfer, and electromagnetic phenomena occurring during the operation of an EAF used in ferronickel production. In their developed model, the relationship between slag properties and temperature was defined using a polynomial function, which increased the accuracy of the simulation results.

Warczok et al., in their studies [18,19], presented the application of numerical modelling to analyze the physicochemical phenomena occurring during slag reduction and copper recovery in crossed electric and magnetic fields.

Zhang et al. [20,21] proposed a numerical model to analyze the multiphysical field distribution in EAF used for the CaC₂ smelting process. The reaction kinetics equations were solved in conjunction with the Navier–Stokes equations, the energy conservation equation, and Maxwell’s equations.

H. Cui et al. [22] presented a multiphysical numerical model of a cylindrical, two-electrode electric arc furnace for processing titanium slag. Parameters such as velocity distribution, temperature, and electromagnetic field were analyzed. To describe the electromagnetic field and its impact on the velocity and temperature distribution in the furnace, the magnetohydrodynamic equations and the mass, momentum, and energy conservation equations were defined using user-defined functions (UDF) in the Fluent software (Fluent 6.3.26). The developed numerical model was validated by comparison with literature data.

Mathematical models of the reduction process developed over the years allow for a more precise characterization of the multiphysical field than previously possible, which can potentially contribute to the improvement and optimization of the operation of particular metallurgical slag processing electric furnaces. A literature review revealed a relatively small number of scientific publications concerning the operation of AC electric resistance furnaces used for the reduction of suspension slags resulting from the smelting of copper concentrates in the single-stage flash furnace technology. Available publications, including those on numerical simulations, mainly concern the operation of arc-resistance furnaces used for recycling steel scrap and other non-ferrous metals. However, the differences in the course and technological parameters of particular processes do not allow for the full transfer and application of the obtained results and conclusions.

3. Model of the Process

There is no software available on the market that allows for a direct simulation of this process. However, the solutions mentioned in the above review are strictly protected know-how by individual research teams. Therefore, it was necessary to build our own dedicated meta-simulation system composed of modules utilizing various software. For this purpose, a preliminary multiphysics model was developed, including the coupling of electromagnetic, hydrodynamic, and thermal fields for optimizing the process of deslagging in an electric furnace.

Figure 1 shows the software used to develop the numerical model and the method of data transfer between them.

The direct execution of a numerical model for the physical phenomena occurring inside an electric furnace operating on alternating current using Ansys Fluent software (Fluent 6.3.26) is not possible. Therefore, an external programme called GetDP was employed to calculate the effects resulting from the flow of alternating current. The use of external software required interpolating the numerical mesh used in GetDP to the Ansys Fluent format. Below (Figure 2) are the results of the volume density of Lorentz force and velocity distribution obtained from the simulation of the slag area in the decoppering process carried out in an electric resistance furnace.