*3.2. Phase Equilibria*

It can be seen from Table 3 that significant amounts of Al2O3, CaO, MgO and ZnO are present in the BBF slag which can influence the liquidus temperature of the slag. Systematic studies were conducted under controlled oxygen partial pressures to evaluate the effects of these components on liquidus temperature of the copper smelting slag [32–39]. Figure 6 shows liquidus temperature as a function of Fe/SiO<sup>2</sup> weight ratio at Po<sup>2</sup> = 10−<sup>8</sup> atm [32]. The lines in the figure were calculated by FactSage 6.2 [31] and the symbols represent experimental data. It can be seen that spinel and tridymite are the primary phases in the composition range investigated for "FeO"–SiO2, "FeO"–SiO2–CaO and "FeO"–SiO2–CaO– Al2O<sup>3</sup> slags. Olivine and wustite primary phase fields replaced spinel primary phase fields when 4 wt% CaO and 4 wt% MgO are present in the slag. Additions of CaO and Al2O<sup>3</sup> move the low-liquidus region towards a low Fe/SiO<sup>2</sup> direction and increase the liquidus temperatures in the spinel primary phase field. FactSage predictions showed similar trends on the liquidus temperature as the experimental results. However, there are significant differences in liquidus temperatures between FactSage predictions and experimental results in some areas indicating that the FactSage database needs to be improved.

**Figure 5.** Proportion of liquid as a function of temperature for a typical BBF slag, in comparison between experimental results and FactSage 6.2 predictions. Reprinted with permission from ref. [7]. Copyright 2021 John Wiley and Sons.

**Figure 6.** Liquidus temperature as a function of Fe/SiO<sup>2</sup> weight ratio, Po<sup>2</sup> = 10−<sup>8</sup> atm, lines were calculated by FactSage 6.2, symbols are experimental results in spinel (1200 ◦C) and wustite (1300 ◦C) primary phase fields [32].

The phase equilibria in the system ZnO–"FeO"–SiO2–Al2O3–CaO–MgO were systematically studied under controlled oxygen partial pressure by Liu et al. [33–36]. Figure 7 shows the effects of ZnO, Al2O3, CaO and MgO on liquidus temperatures at fixed FeO/SiO<sup>2</sup> = 1.9 and Po<sup>2</sup> 10−<sup>8</sup> atm [33]. Spinel is the only primary phase at the given conditions without MgO. Olivine is the primary phase when 4 wt% MgO and less than 2 wt% ZnO are present. It can be seen from the figure that, the liquidus temperatures of the copper smelting slag always increase with increasing ZnO concentration in the slag. The introduction of 4 wt% CaO, MgO or Al2O<sup>3</sup> into the ZnO–"FeO"–SiO<sup>2</sup> slag significantly increases the liquidus temperature in the spinel primary phase field. It seems that the liquidus temperatures are more sensitive to the CaO and MgO concentrations than that of Al2O3.

**Figure 7.** Effects of 4 wt% Al2O<sup>3</sup> , CaO or MgO on liquidus temperatures of the ZnO–"FeO"–SiO<sup>2</sup> slag at fixed FeO/SiO<sup>2</sup> = 1.9 (in mass) and Po<sup>2</sup> 10−<sup>8</sup> atm. Reprinted with permission from ref. [33]. Copyright 2021 Elsevier.

An experimental technique was further developed to determine phase equilibria of the copper smelting slags under conditions closer to the smelting process. The phase equilibria in the systems "FeO"–SiO2, "FeO"–SiO2–CaO and "FeO"–SiO2–CaO–MgO were experimentally investigated at fixed P(SO2) = 0.3 and 0.6 atm and a fixed matte grade 72 wt% Cu [37–39]. Figure 8 shows the effects of 2 wt% CaO or MgO on the liquidus temperatures in the spinel primary phase field at fixed P(SO2) = 0.3 atm with a fixed matte grade of 72 wt% Cu [38]. The predictions by FactSage 7.3 were also shown in the figure for comparison. It can be seen from the figure that, both the predictions and experimental results indicate that the liquidus temperatures decrease with increasing SiO<sup>2</sup> concentration in the spinel primary phase field. The presence of 2 wt% CaO or MgO significantly increases the liquidus temperatures. To keep a constant liquidus temperature, more SiO<sup>2</sup> flux is required which will increase the slag volume. FactSage 7.3 predicted much lower liquidus or less SiO<sup>2</sup> flux than the experimental results as no experimental data were reported in such complex conditions for FactSage optimisation.

**Figure 8.** Effects of 2 wt% CaO or MgO on the liquidus temperatures in the spinel primary phase field at a fixed P(SO<sup>2</sup> ) = 0.3 atm and matte grade 72 wt% Cu, in comparison between experimental (symbols) and predicted (lines) results by FactSage 7.3. Reprinted with permission from ref. [38]. Copyright 2021 Elsevier.

With increased impurities in copper concentrates, control of the minor elements is an important issue in the copper smelting process. Based on the principle of Gibbs energy minimisation and the technological features of the BBS process, a multiphase equilibrium model SKS simulation software (SKSSIM) was developed [40,41]. Distributions of As, Bi, Sb, Pb and Zn as a function of matte grade can be calculated among slag, matte and gas. The calculated distributions in the BBS process were different from that in the Isasmelt and the flash smelting processes [42–44].

#### *3.3. Fluid Dynamic Studies*

The major difference between BBS and other bath smelting technologies is the direction of gas injection and gas pressure. High-pressure gas injected from different directions significantly influences stirring energy, surface waves, plume eye and splashing. Fluid dynamics of the molten bath is an important issue to understand the advanced performance of the BBS. Extensive studies were conducted on the fluid dynamic behaviours of the BBF using a water model and CFD (Computational Fluid Dynamic) simulation [45–68]. Mixing behaviour [45–51], surface wave [52,53], plume eye [54], bubble behaviour [55–58], fluctuating behaviour [59] were studied by water model to simulate the molten bath in BBF. Lance arrangement [60–62], gas–liquid multi-phase flows [63–65], flow and mixing behaviour [66] and multiphase interface behaviours [67,68] in the BBF were studied by the CFD method. A summary of the research on the fluid dynamic of the molten bath in BBF is presented in Table 4. Some examples are given in the following sections.


**Table 4.** Summary of the research on the fluid dynamic studies for the molten bath of BBF.

In a molten bath, the first step of the reactions is the melting of the concentrate particles and decomposition of the sulphides, such as FeS<sup>2</sup> and CuFeS2. These sulphides are then oxidised to form FeS–Cu2S matte and iron oxides (FeO, Fe2O3). The iron oxides generated by the reactions continuously react with SiO<sup>2</sup> to form slag which is insoluble to matte and floats on the top of the matte layer. On the other hand, the injected oxygen reacts with iron, copper and sulphur on the bottom of the bath to generate all heat to maintain the temperature of the molten bath. The mass and thermal transfer inside the molten bath significantly affect the reaction efficiency of the BBF. Cai et al. [69] did experiments in a physical model of a bottom-blowing lead smelting furnace to find an optimal lance arrangement and configuration. An empiric calculation formula was concluded by normal hydraulic model test:

$$\text{S } \text{/W} = 26.224 \cdot \text{(W/}D\_0\text{)}^{-0.629} \cdot \text{(Fr}^{\prime}\text{)}^{0.122} \cdot \text{(H/}D\text{)}^{0.523} \tag{1}$$

where *S* is the effective stirring diameter of the oxygen lance, *W* is the space between oxygen lances, *D<sup>0</sup>* is the inner diameter of the export oxygen lance, Fr<sup>0</sup> is the modified Froude number, *H* is the depth of bath pool, *D* is the inner diameter of the furnace. In a late study, Shui et al. [48] defined effective stirring range *D<sup>e</sup>* quantitatively and developed the 1st empiric equation to characterise the mixing behaviour of the copper BBF.

Figure 9 shows the mixing time as a function of distance from the lance at different depths of the bath [48]. In the water model experiments, 4 M KCl solution as a tracer of electric conductivity was added directly on the top of the gas injection lance. An electrode connected to a potentiostat was put in the required position to measure the electric conductivity of that location. The time to reach a stable electric conductivity was defined as "mixing time". It can be seen that within 220 mm the mixing time on the surface decreases slightly and then increases sharply with increasing the distance between the lance and electrode. However, *D<sup>e</sup>* is different at different depths of the bath and increases with increasing the depth. When the horizontal distance from the lance is greater than *D<sup>e</sup>* , the mixing time increases rapidly with increasing the distance. The maximum distance between two neighbour lances is the *D<sup>e</sup>* on the surface to ensure the whole bath in the reaction zone can be efficiently stirred.

**Figure 9.** Mixing time vs. horizontal distance, at gas flow rate 150 mL/s, bath height 10 cm. Reprinted with permission from ref. [48]. Copyright 2021 Springer Nature.

The empiric equation to characterise the mixing behaviour of the copper BBF was obtained from the experimental measurements of the water model [48]

$$
\pi = 37.5Q^{-0.39}h^{-1.08} \tag{2}
$$

where *τ* is mixing time, *Q* is gas flow rate and *h* is bath height. Several important findings from this study can be directly applied to BBS:


In copper BBF operation, molten matte is covered by a thick slag layer. The fluid dynamic studies for a single layer bath are not enough to accurately describe the molten bath of the copper BBF. Jiang et al. [50] and Shui et al. [49] studied mixing behaviours of two-layer baths by using silicon oil and water to simulate slag and matte, respectively. It can be seen from Figure 10 that the changes in mixing time are not significant when the water thickness increases from 0.07 m to 0.09 m, but there is a sharp decrease when the water thickness exceeds 0.09 m. This indicates that a minimum matte height is required to generate enough stirring energy to mix the bath efficiently. In addition, it can be seen that the trends are similar at different gas flow rates.

**Figure 10.** Effect of water height on mixing time at different gas flow rates, 0.03 m thick oil with viscosity 5 <sup>×</sup> <sup>10</sup>−<sup>5</sup> <sup>m</sup>2/s on the top, symbols are experimental points. Reprinted with permission from ref. [49]. Copyright 2021 Springer Nature.

An empiric equation was also generated for a two-layer bath in copper BBF [49]. Four variables *H*, *Q*, *h*, *ν<sup>s</sup>* were converted into SI units and correlated with the experimental mixing time in an overall multiple regression:

$$
\pi = 7.31 \times 10^{-5} H^{-3.10} Q^{-2.29} h^{2.32} \nu\_s^{0.27} \tag{3}
$$

where *τ* is mixing time, *Q* is gas flow rate, *H* is water height, *h* is oil height and *ν<sup>s</sup>* is oil viscosity.

The waves formed on the bath surface play important role in the BBF operations. Tapping of the viscous slag, corrosion of the refractory around the surface and settlement of the matte droplets in the slag are all associated with the bath waves. Simulation experiments were carried out to investigate the features of the waves formed on the bath surface of the BBF [52,53]. It was found that the ripples, the 1st asymmetric standing wave and the 1st symmetric standing wave can occur in the BBF bath. Empirical occurrence boundaries were determined from water model experiments. The amplitude of the 1st asymmetric standing wave was found to be much greater than the 1st symmetric standing wave and the ripples. The amplitudes increase with increasing bath height and flow rate but decrease with blowing angle. The frequency of the 1st asymmetric standing wave was found to increase with increasing bath height but be independent of gas flowrate and blowing angle. The dimensionless number *We* can be expressed as

$$\mathcal{W}e = \frac{\rho\_L Q\_g^2}{\sigma D^3} \tag{4}$$

where *ρ<sup>L</sup>* is liquid density (kg/m<sup>3</sup> ), *σ* is the surface tension of the liquid (dyn/cm), *D* is container inner diameter (mm), *Q<sup>g</sup>* is gas flowrate (mL/s).

Figure 11 shows the conditions for the occurrence of the 1st asymmetric standing waves [53]. The solid curves show the correlated boundaries while the points show the experimental results. It can be seen that, in general, the boundaries of different blowing angles are similar in shape. On the right side of the boundary, the 1st asymmetric standing wave is present, while on the left side only minor ripples occur.

**Figure 11.** Occurrence condition of the 1st asymmetric standing wave at lance angle 7◦ , symbols are experimental points. Reprinted with permission from ref. [53]. Copyright 2021 Springer Nature.

During the Fangyuan BBF operation, it was observed from the feeding mouth that a plume eye was formed on the surface of the bath. The plume eye was initially observed and reported in the steelmaking process to describe the exposure of the lower liquid as the upper-level liquid was pushed away by the bottom injected gas. Through the water model experiments, it was found that the sizes of the plume eyes increase with increasing gas flow rate and lower liquid thickness, decrease with increasing upper liquid thickness [54]. Figure 12 shows the effects of gas flow rate and water height on the plume eye area at a fixed oil thickness.

**Figure 12.** Effects of gas flow rate and water height on the plume eye area at a fixed oil thickness 4 cm. Reprinted with permission from ref. [54]. Copyright 2021 Springer Nature.

A modified model was developed in this study from the experimental data to predict the size of the plume eye [54]. Formation of the plume eye is important to understand the rapid reaction of the BBF. The presence of a plume eye below the feeding mouth means that the dropped copper concentrate (considered as low-grade matte) can enter and melt rapidly inside the matte layer where the oxygen partial pressure is relatively high. The formed iron and sulphur oxides in the matte raise to the slag layer.

#### **4. Conclusions**

Commercialised bottom-blowing copper smelting technology started in 2008. In less than 15 years this new technology has been developed rapidly to be the second-largest copper smelting technology. Development history and features of the new technology were reviewed from extensive publications. It is demonstrated that fundamental studies on slag chemistry and bath fluid dynamics have played an important role in supporting the development of this new technology. High-pressure gas injected from the bottom of the molten bath showed several advantages: (1.) generating a plume eye to allow the copper concentrate to react with matte directly; (2.) the surface waves assist in the tapping of the viscus slag so that low-temperature operation to produce high-grade matte with high Fe/SiO<sup>2</sup> slag is possible; (3.) strong stirring energy to enable fast reactions in the molten bath resulting in high capacity and low-copper in the slag; (4.) high efficiency of oxygen utilization and heat absorption. The flexibility of the BBS on feeding materials and productivity is expected to not only increase its application in the copper industry to treat more complicated concentrates but also to enable the exploration of more applications of this technique in other high-temperature processes.

**Author Contributions:** Conceptualization, B.Z.; resources, B.Z.; data curation, B.Z. and J.L.; writing original draft preparation, B.Z.; writing—review and editing, B.Z.; All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.
