Statistical analysis and optimization of recovering indium from jarosite residue with vacuum carbothermic reduction by response surface methodology (RSM)

2.1 Experimental procedure

The jarosite residue was obtained from a certain zinc smelter, and the grade of indium is 270 g/t. Jarosite residue dried at 100°C was mixed with carbon powder and calcium oxide in proportion. The mixed sample was pressed into a cylinder with a size of Φ2 cm×1 cm at 5.5 MPa. The cylinder sample was weighed and then put into crucibles. The crucible with a cover was put into a vacuum furnace. After setting the temperature, the indium volatilization experiment was conducted in a vacuum degree of 2–4 Pa. At the end of the experiment, the sample cooled with the furnace cooling. Finally, the furnace residues were weighed, and the content of indium in the obtained residues was analyzed. The indium volatilization rate was calculated by the following equation:

where w (%) is the indium volatilization rate, a (g) is the indium quantity of the cylinder sample, and b (g) is the indium quantity of residue.

2.2 Experimental design

Statistical software package (JMP 10, SAS Institute Inc., Cary, NC, USA) was used in the experiment design and subsequent data analysis. A three-level four-variable response surface design (RSM) was applied to explore the better combination of variables for the recovery of indium. The range values of four independent variables are shown in Table 1. Design and experiment results are given in Table 2.

3.1 Analysis of variance

The analysis of variance (ANOVA) was used to evaluate the influence of different factors on the volatilizing rate of indium. The results are summarized in Table 3, showing that the mean square (between groups) of temperature is six times larger than their error mean square. However, there is relatively less difference between the mean square of others and their error mean square. This indicates that the mean values at different levels of temperature are greatly different. However, as for other factors, the same conclusion cannot be reached. Furthermore, p-values <0.05 were considered to be statistically significant as the experimenter has selected α=0.05 [10], [11], [12], [13]. It can be seen in Table 3 that the p-values of temperature are <0.05 whereas other the p-values are not. That is to say the influence of temperature on the volatilizing rate of indium is statistically significant. Other factors have no significant influence.

3.2 Mean value analysis

The mean value of the indium volatilizing rate at each level was calculated. The relationship graphs between the mean value and the different levels of each factor are shown in Figure 1, indicating that the indium volatilizing rate presents a straight climb tendency with the increase in final temperature. From the point of view of thermodynamics, the increase in temperature provided a good thermodynamics condition and promoted the reduction and volatilization of indium. As far as dynamics is concerned, higher temperature could enhance the reaction speed and reduce the reaction time. This could give a reasonable explanation why the indium volatilizing rate presents a tendency of straight climb with the increase in final temperature. For the increase in carbon content, the indium volatilizing rate greatly increases and slows down subsequently. As for the reducing agent of the reaction process, the increasing content of carbon made the reduction reaction more thoroughly. However, when the reducing reaction reaches a certain extent, the influence of carbon content becomes relatively less. In calcium oxide, the indium volatilizing rate first increases and then decreases. Calcium oxide was used as a sulfur-fixing agent in the reaction process, which can decrease the partial pressure of sulfur trioxide and furthermore promote the transformation of In₂(SO₄)₃ into In₂O₃ or In₂O₃·α-Fe₂O₃ [14]. It can also prevent burden from sintering, which was favorable to the volatilization of indium. However, the overabundance of CaO could decrease the grade of indium in furnace charge and reduce the indium volatilizing rate. In terms of hold time, the indium volatilizing rate first increases and then keeps invariant. Hold time is related to the degree of reaction. Long holding time means the interaction between furnace charges will go thoroughly. However, with the holding time extension, the indium volatilizing rate maintained a stable value when the reaction went to the greatest extent.

Figure 1:

Effect of four variables on the volatilizing rate of indium.

3.3 Parameter optimization by RSM

The response surface quadratic model was applied to explore the best combination of four variables and to study the effects of their interactions on the indium volatilizing rate. The values of regression coefficients were calculated, and the response variable and the test variables are related by the following second-order polynomial equation:

where X₁, X₂, X₃, and X₄ are equal to carbon(wt.%)−3020,CaO(wt.%)−1312,temperature(°C)−900100, and hold time(min)−6030, respectively. Table 4 gives the statistics or the model summery, and Table 5 gives the ANOVA for response surface quadratic model. The R² value of 0.9997 (Table 4) and p<0.05 (Table 5) indicate that the quadratic model was adequate for prediction within the range of experimental variables. The 3-D response surface plot was used to study the effects of four variable interactions on the indium volatilizing rate. The results are shown in Figure 2.

Figure 2:

Response surface plot (3-D) of the interactions of four variables. (A) Fixed levels X₃=0, X₄=0. (B) Fixed levels X₂=0, X₄=0. (C) Fixed levels X₂=0, X₃=0. (D) Fixed levels X₁=0, X₄=0. (E) Fixed levels X₁=0, X₃=0. (F) Fixed levels X₁=0, X₂=0.

The 3-D response surface plot in Figure 2A, which gives the indium volatilizing rate as a function of the percent content of carbon and calcium oxide at fixed temperature (900°C) and hold tine (60 min), indicates that a higher indium volatilization rate could be achieved when the percent content of carbon and the percent content of calcium oxide were at the level of 30% (X₁=0) and 13% (X₂=0).

Figure 2B shows the 3-D response surface plot at varying percent content of carbon and temperature at fixed calcium oxide (13%) and hold time (60 min). It can be seen that the indium volatilization rate decreases with the increase in the percent content of carbon at a temperature of 800°C (X₃=−1), but when the temperature is higher than 800°C, it increases with the increase in the percent content of carbon. At a temperature of 1000°C (X₃=1), even 30% of the carbon can make the indium volatilization rate close to 100%.

In Figure 2C, the 3-D response surface plots were developed for the indium volatilization rate with varying percent content of carbon and hold time at fixed calcium oxide (13%) and temperature (900°C). It indicates that the indium volatilization rate decreases with the increase in the percent content of carbon when the hold time is <60 min (X₄=0), but when the holding time is between 60 and 90 min (X₄=1), it increases with the increase in the percent content of carbon.

The 3-D response surface plot based on independent variables calcium oxide and temperature is shown in Figure 2D, whereas the other two independent variables carbon and hold time are kept at 30% and 60 min, respectively, indicating that the maximum indium volatilization rate can be achieved when the percent content of calcium oxide and temperature were at the level of 13% and 1000°C, respectively.

Figure 2E gives the 3-D response surface plot at varying calcium oxide and hold time with fixed carbon (30%) and temperature (900°C). It shows that when the percent content of calcium oxide and hold time were 13% and 60 min, respectively, the indium volatilization rate could reach a maximum.

In Figure 2F, the 3-D response surface plot is developed for the indium volatilization rate with varying temperature and hold time, whereas the other two independent carbon and calcium oxide are 30% and 13%, respectively. It can be concluded that the maximum indium volatilization rate could be achieved when the temperature and hold time are 1000°C and 60 min, respectively.

3.4 Verification of optimal conditions

The selected optimal conditions of 30% carbon, 13% Ca, 1000°C temperature, and 60 min hold time for the optimum response values were tested. The experimental results indicated that the indium volatilization rate is up to 98.2% under the optimal conditions.