## 2 Optimization Model for Process Parameters of Zinc Smelting Slag Melting Point  
### Selection of Key Process Parameters  
The process flow of zinc smelting slag treatment consists mainly of the batching stage, smelting stage, and product recovery stage, as shown in Figure 1. The specific steps are as follows:  
Batching Stage: Initially, in the batching stage, slag materials are mixed with smokeless coal and river sand is added to complete slag making, resulting in mixed slag. Figure 1: Zinc smelting slag treatment process flow chart. Smelting Stage: The mixed slag is then sent to the smelting furnace for melting treatment. During smelting, various additives are added as needed to adjust the composition, resulting in molten slag, high-silver flue ash, and dust-laden flue gas. Product Recovery Stage: The high-silver flue ash and dust-laden flue gas are directly recovered, extracting valuable metals such as gold and silver. Subsequently, the molten slag is transferred to the reduction furnace, where various additives are incorporated as necessary to optimize production. This process generates slag suitable for use as building materials and flue gas ash. Through further recovery, metals such as lead and zinc are obtained until the slag contains over 30% Fe, at which point it is discharged as flue slag, achieving resource utilization and enhancing the economic efficiency of the smelting plant. During the batching and smelting stages, different batching schemes can result in mixed slag containing different elements, thereby affecting the melting point of the mixed slag. Excessively high melting points can pose safety hazards during the production process and incur additional production costs for the smelting plant. Therefore, the practical problem that smelting plants need to address is how to adjust the batching scheme to meet production requirements while minimizing the melting point of the mixed slag as much as possible. According to relevant studies and literature, it is known that the iron-silicon ratio and the calcium-silicon ratio have a significant impact on the melting point of mixed slag [24; 25; 26]. The iron-silicon ratio refers to the weight ratio of iron to silicon in the furnace charge. In the metallurgical industry, as the iron-silicon ratio increases, the melting point of the slag tends to increase, while the viscosity decreases, and the melting performance improves. Therefore, during the smelting process, the iron-silicon ratio is usually controlled to reduce the melting point and improve the melting performance of the materials inside the furnace. The calcium-silicon ratio refers to the weight ratio of calcium to silicon. Within a certain range, as the calcium-silicon ratio increases, the melting point rises, and the fluidity also improves. Therefore, during the smelting process, an appropriate amount of silicon is usually added to the slag to reduce the calcium-silicon ratio, lower the melting point of the slag, and improve its fluidity. The specific experimental results are shown in Figure 2. The lower curve shows the variation in slag melting point with changes in the CaO/SiO\({}_{2}\) ratio within the range of 0.3 to 1.0 under constant conditions. The upper curve shows the variation in slag melting point with changes in the Fe\({}_{2}\)O\({}_{3}\)/SiO\({}_{2}\) ratio within the range of 1.8 to 2.4 under constant conditions. Additionally, the inclusion of river sand, oxygen flow, and coal also affects the melting point. Figure 2: The effect of Fe–Si ratio and Ca–Si ratio on melting point. River sand, primarily composed of silica dioxide, contains a significant amount of silicon elements, which significantly influences the iron-silicon ratio and calcium-silicon ratio, thereby affecting the melting point. The addition of oxygen alters the valence state of iron in the slag, thereby affecting the iron-silicon ratio. Elements such as ash, sulfur, and sodium in coal may form compounds with high melting points inside the furnace during combustion, thereby affecting the melting point of the mixed slag.