1. Introduction
With continuous improvements in science and technology, the electronics industry has ushered in rapid changes. The number of eliminated electronics-related products is increasing rapidly due to the short replacement cycle of electronic products [
1,
2,
3,
4]. Currently, 20–50 million tons of e-waste are generated globally, and the average annual growth rate is three times that of other solid wastes according to an analysis report by the United Nations Environment Programme [
5,
6]. In addition, e-waste is increasing at an annual growth rate of 3% to 5% in EU countries, which will also increase more than three times in developing countries over the next five years [
7]. These will not only cause huge environmental pressure, but also provide broad prospects for the utilization of valuable resources; the economic value and environmental benefits have also become increasingly prominent.
Since the 1970s, a variety of new technologies and equipment for the comprehensive utilization of rare and precious metal renewable resources have been developed, which use anode slime, electronic waste, and industrial slag containing rare and precious metals as raw materials [
2,
8]. For instance, Bydałek. A. et al. [
9] reported a novel method of separating some metals from liquid slag; the structure of the slag in liquid state, the properties and interactions within the slag were discussed in detail. Furthermore, there are many valuable metals and organic substances in electronic waste, and its recycling and utilization can not only solve the problem of environmental pollution but also recover valuable secondary resources.
In recent years, the comprehensive recycling technology of electronic waste has become a hot topic globally and a wide variety of novel processes can be developed [
10,
11,
12,
13]. For instance, the United States uses Kaldor furnaces to smelt electronic waste, Germany and Belgium use ISA furnaces, and Japan and South Korea use Ausmelt furnaces. For China, after simple physical separation of electronic scrap, most of the rare and precious metals are enriched in the crude copper during the smelting process, realizing the separation from non-metals. Afterward, the crude copper is refined by the pyrorefining process, and then rare precious metals are recovered from the electrolytic anode slime. Nevertheless, there are lots of problems in the electrolysis process, such as serious depletion of copper ions, high cell voltage, and low current efficiency in terms of low copper grade and high impurities in crude copper [
14,
15,
16]. Moreover, the existing process of copper anode slime has defects such as long process, difficult comprehensive recovery of precious metals, temperature distribution asymmetry, incomplete low-temperature cracking of organic matter, dioxins in tail gas [
17], etc. Therefore, it can be seen that the overall treatment technology and equipment of electronic waste need to be further improved and innovated.
In view of these, the Nerin Recycling Technology (NRT), an innovative comprehensive recycling process for electronic waste, was developed and took the lead in realizing industrial applications. Similar to the Kaldor furnace, ISA furnace, and Ausmelt furnace, the NRT furnace is a high-temperature intensified top-blown bath smelting furnace, which has broad prospects for popularization and application. However, how to improve the direct recovery of valuable metals and reduce the emission of toxic and harmful gases is a key issue to realize efficient smelting and clean production of electronic waste.
The slag-gold-gas system has characteristics of great heat and mass transfer conditions and a high reaction rate due to the high-pressure swirling effect produced by the hydrocyclone based on the research of top-blowing submerged bath smelting [
18]. It can be seen that the electronic waste reacts quickly with the gas by the continuous injection of excess oxygen during the process of high-temperature molten pool smelting, which indicates good reaction kinetic conditions. At the same time, the high-temperature smelting reaction system involves different phases such as blister copper, copper matte, slag, magnetite, and flue gas. The composition of electronic waste, smelting temperature, and reaction atmosphere are constantly changing in the process of high-temperature smelting for several hours. The reaction system has obvious non-equilibrium multiphase reaction characteristics because of the continuous phase transformation and component migration, and then gradually completes complex reactions such as oxidation, combustion, slagging, copper production, etc.
It is difficult to comprehensively analyze the physical and chemical behavior of electronic waste during the smelting process in the laboratory due to the complexity of the high-temperature non-equilibrium reaction system. To solve this problem, the predecessors have made many successful explorations, carrying out the experimental research directly in an industrial furnace [
19,
20]. Wołczyński. W. et al. [
21] investigated copper droplets agglomeration/coagulation in conditions that were similar to those usually applied to the industrial process, and the influence of the liquid slag stirring on the copper droplets self-cleaning was also analysed. However, the production practice usually requires relatively stable process conditions, which makes it difficult to implement a large number of experiments in the factory. Thus, it is necessary to find a method to investigate the influence of various working situations on the physicochemical behavior of electronic waste in the smelting process.
Nowadays, digital–analog simulation technology has become an effective method for studying the laws of high-temperature pyrometallurgy with the rapid development of computer technology. For example, Wang [
22], Xu [
23], Zhang [
24], Li [
25], and the author of this work [
26] performed thermodynamic computer simulations on high-temperature molten pool smelting. It can be found that they all regard the entire smelting furnace as a closed system reaching or approaching the equilibrium of chemical reactions. Besides, the smelting furnace is regarded as a “black box”, which cannot reflect the microscopic migration and transformation behavior of materials during the smelting process.
The local-equilibrium hypothesis is an important method for solving non-equilibrium thermodynamics problems by classical thermodynamics and has been successfully applied to some fields such as metallurgy and materials. Previous studies on the melting kinetics of top-blowing immersed bath smelting provide a feasible theoretical basis for introducing the local equilibrium assumption into the modeling of a non-equilibrium multiphase system in top-blowing smelting of electronic waste. Hence, the high-temperature molten pool smelting process is regarded as a multi-phase reaction system in which electronic waste and reaction gas continuously reach a local equilibrium, and the time is discrete in millisecond order. Simultaneously, the smelting process is divided into several microelement localities of time, and then a multi-phase equilibrium mathematical model is constructed for each time microelement region according to the principle of minimum Gibbs free energy. Afterward, the local models are associated based on the transfer relationship between electronic waste and reaction gas in each micro-element local area; in this way, the mathematical model of the composition transfer and transformation of electronic waste in the smelting process is established, and the non-equilibrium multiphase reaction system of the electronic waste smelting is also analyzed.
In conclusion, based on the local equilibrium hypothesis of the non-equilibrium system and combined with the production practice of the NRT smelting industry, the local equilibrium modeling and division method of the non-equilibrium multiphase reaction system of the electronic waste top-blowing smelting process are investigated in this study. The mathematical description of the multi-phase equilibrium of each local area and the correlation method between the local areas are studied on the basis of the analysis of the relationship between valence state, phase, composition, and Gibbs free energy of each element. In addition, reaction characteristic data such as melting material, product phase, composition, temperature, atmosphere, etc. are obtained by industrial measurement experiments. It can provide production practice data for the construction, verification, and optimization of digital models, which will help to further improve the consistency between the model and production practice. Furthermore, the establishment of a local equilibrium mathematical model for the top-blowing smelting process of electronic waste can provide theoretical guidance for the development of a thermodynamic digital simulation system.