**1. Introduction**

In the flash smelting (FS) process, a mixture of sulfide-based concentrate and flux is continuously fed to the reaction shaft through a concentrate burner. Additional recycled materials, such as copper scrap and waste electrical and electronic equipment (WEEE) scrap can be used in the flash smelting feed. With the solid feed, oxygen enriched air is also blown through the burner. The air is used to create the exothermic reaction of sulfide oxidation, which creates the energy needed to melt the feed. This forms molten slag and matte phases as separate layers in the settler, with the lighter slag layer on top of the matte layer. The main functions of the slag are to protect the matte from oxygen, collect impurities such as Zn, Co, Ni, Sb, As, and Mo [1–3], and thermally insulate the matte to minimize energy losses. The slag and matte are tapped through tapping holes in the furnace wall. Unlike the feed, the tapping takes place at regular intervals, which causes variations in the thickness of the melt layers. Besides the melts, SO2 gas is also formed. The gas exits through the uptake shaft carrying dust that is collected in gas cleaning, and the gas is then used in sulfuric acid production. In addition, the thermal energy of the gas is recovered and used for heating input gases and possibly for the local community. The collected dust is then circulated back to the process [4].

The slag and matte layers are not stagnant in this continuous process. More material constantly descends from the reaction shaft and matte droplets settle through the slag layer, creating flows in the

matte and slag layers. Xia et al. studied the slag and matte flows in a FS settler [5–7]. They found that tapping of the slag and the matte creates complex turbulent flows in the settler. The flows are not uniform: the effect of the tapping flow is reduced as the distance to the tapping hole increases. Furthermore, the region affected by the tapping decreases as the flow velocity is reduced.

However, the area under the reaction shaft has strong flows as the majority of the droplets will be descending relatively directly from the concentrate burner. Similar trajectories have been reported in a study by Zhou et al. [8]. Studies by Khan and Jokilaakso, and Jylhä and Jokilaakso show a funneling effect created by drag flows in the slag [9,10]. These drag flows were caused by settling matte droplets.

Mechanical copper losses in the FS process can be traced to copper as flue dust or matte entrained in the slag. The settling of matte droplets through the slag phase in the FS furnace (FSF) as shown in Figure 1, is an important phenomenon and determines the overall copper yield in the smelting unit process. The copper losses during the settling process are due, in addition to the mechanical entrainment of the copper matte droplets, to the chemical dissolution of copper in the slag phase. This not only reveals the loss of matte droplets during the settling process, but also how quick the settling process is. The entrainment of matte droplets has been studied by many researchers [11–17] and it has been concluded that mostly droplets ≤100 μm in size are trapped in the slag phase and are ultimately carried away in the slag phase through the slag outlet.

**Figure 1.** Illustration of the Outotec flash smelting furnace.

The entrained copper losses to slag are due to, for example, solid spinels, small size, or droplets being lifted from the surface of the matte layer [18–20]. Spinels may be attached to a droplet or surround the droplet completely [21]. The attached spinel affects the settling of the droplet: the bulk density of the droplet–spinel entity is lower than that of a droplet without an attached spinel, but the size of the entity increases. Thus, the attached spinel may either increase or decrease the settling velocity of the droplet–spinel entity. However, as the droplet–spinel has better wetting with the slag than the matte, and has lower density than the matte, the droplet–spinel entity cannot enter the matte layer, and thus, droplets with spinel may be removed with the slag in tapping. Additionally, turbulence can lift parts of the surface layer of the matte to the slag [18]. Furthermore, the distance between the tapping hole and the slag–matte interface affects copper losses. In a study by Jiménez et al. [19], matte droplets were

found to form a dispersion layer above the matte surface. With too short a distance between the matte surface and the tapping hole, droplets from the dispersion layer may be sucked upwards and removed through the tapping hole. According to their study, at least 20 cm distance is needed to minimize the quantity of droplets sucked from the dispersion layer.

To limit mechanical copper losses, several parameters should be optimized [22]. The density difference between the slag and the matte should be as high as possible, while the viscosity of the slag should be as low as possible. Also, the matte droplets should be as large as possible. These three factors decrease the residence time of the matte droplets in the slag. The density difference and the slag viscosity are greatly affected by slag chemistry and variations in solid content, oxygen levels, and temperature in the slag. The droplet size is affected by coalescence and reactions, which are also affected by the properties of the slag and droplets themselves.

Mathematical and computational modeling of pyrometallurgical processes and furnaces started decades ago, as there was an increasing need for better understanding of the phenomena occurring inside them. A significant increase in modeling development has been seen since the introduction of commercially available computational fluid dynamics (CFD) software. The development of the Outotec flash smelting furnace (FSF) and process modeling has been reviewed in a recent review paper [23]. The aim of the modeling studies reported here is to find a feasible computational method by using commercial simulation software packages for gaining a better understanding of the fluid dynamics of the settling matte droplets in the slag layer. After validating the fluid dynamics behavior with physical model results, additional droplet–droplet or droplet–spinel interactions and chemical reactions between matte droplets and slag will be included in the simulation. However, as the geometries and phenomena in the models are computationally extremely intensive, the additional features have to be included one by one as a longer-term target. Finally, the models and knowledge developed will be used to help find ways to reduce copper losses and develop processes and their operational efficiency in a similar manner as has been done with the FS reaction shaft models [23]. In this paper, the fluid dynamics modeling results are presented, and the results obtained with the two software packages are compared. The settling flow behavior of the molten matte phase has been revealed, and the results from statistical (or traditional) CFD modeling and from the new CFD–DEM coupling approach are consistent, suggesting a channeling or funneling kind of flow pattern.

The software used in this study was ANSYS® Fluent 19.2 and EDEM® 2019.1 with EDEM-Fluent coupling v2.2 provided by DEM Solutions Ltd., Edinburgh, Scotland, UK [24].
