Optimization of reduction leaching conditions for pyrite cinder using titanium dioxide waste acid by response surface methodology
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摘要: 采用Box-Behnken设计的响应面法，选取铁粉用量、还原时间和浸出温度三个变量，研究并优化了钛白废酸还原浸出硫酸烧渣的浸出条件。建立了拟合效果较好的浸出条件的预测模型，以预测浸出率或优化浸出变量值。回归方程模型显著可靠，相关系数R2为0.9961。浸出条件对反应平衡、浸出物溶解度及反应体系性质等有重要影响，其中铁粉用量与浸出温度的协同交互作用影响最大。验证试验表明，在铁粉用量10.347 g、还原时间2 h、浸出温度88 ℃的最佳条件下，浸出率可达83.63%以上。Abstract: The reduction leaching conditions for pyrite cinder leaching by titanium dioxide waste acid were investigated and optimized, using the response surface methodology designed by Box-Behnken method, and the iron powder dosage, reduction time, and leaching temperature were selected as the three variables. The established predictive model for leaching conditions was with good fitting results to predict leaching yields or optimize leaching variable values. The regression equation model was significantly reliable, with a correlation coefficient R2 of 0.9961. The leaching conditions had important effects on the leaching reaction equilibrium, solubility of leached materials, and properties of reaction systems, among which the synergistic interaction between iron powder dosage and leaching temperature had the greatest impact. The verification experiments confirmed that the leaching yield values could be achieved over 83.63% under the optimal conditions, with the iron powder dosage of 10.347 g, reduction time of 2 h and leaching temperature of 88 ℃.
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图 1 浸出条件对浸出率的影响
(a) 固定还原时间1.5 h，浸出温度89 ℃；(b) 固定还原铁粉用量12 g，浸出温度89 ℃；(c) 固定还原铁粉用量12 g，还原时间1.5 h
Figure 1. Effect of leaching conditions on leaching yield
图 3 因素交互作用对浸出率影响的响应面3D图和等高线
Figure 3. Response surface plots and contour lines of interaction factors on the leaching yield
图 4 烧渣还原浸出前后的XRD谱
浸出还原条件：铁粉用量12 g，还原时间1.5 h，浸出温度89 ℃
Figure 4. XRD patterns for the pyrite cinder before and after reduction leaching
图 5 烧渣还原浸取前的SEM和EDS面扫描
Figure 5. SEM images and EDS analysis for the raw pyrite cinder before reduction leaching
图 6 烧渣还原浸取后的的SEM和EDS面扫描
（浸出还原条件：铁粉用量12 g，还原时间1.5 h，浸出温度89 ℃）
Figure 6. SEM images and EDS analysis for the pyrite cinder after reduction leaching
表 1 优化浸出条件的BBD试验因素和水平
Table 1. Factors and levels of BBD method for the optimized leaching conditions
水平 因素 还原铁粉用量/g
(X1)还原时间 /h
(X2)浸出温度/ ℃
(X3)-1 10 1 86 0 12 1.5 89 1 14 2 92 
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表 2 烧渣浸出率的试验设计矩阵、试验结果及预测值
Table 2. Experimental design matrix, experimental leaching results and predicted values for pyrite cinder
序号 X1/g X2/ h X3/ ℃ Y 试验值/% Y 预测值/% 1 14 1.0 89 83.22 83.23 2 12 1.5 89 84.01 83.96 3 12 1.0 92 82.63 82.57 4 10 1.5 86 82.69 82.64 5 10 1.0 89 82.41 82.40 6 14 1.5 86 82.41 82.34 7 12 2.0 86 82.53 82.59 8 12 1.5 89 83.89 83.96 9 10 2.0 89 83.77 83.76 10 12 1.0 86 81.15 81.21 11 14 1.5 92 84.09 84.14 12 14 2.0 89 83.91 83.92 13 10 1.5 92 82.78 82.85 14 12 1.5 89 83.97 83.96 15 12 2.0 92 83.31 83.25
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表 3 硫铁矿烧渣浸出率的响应面试验结果方差分析
Table 3. Variance analysis of response surface experimental results of the leaching yield
平方和 自由度（df ） 均方 F值 P值 显著 模型 9.88 9 1.1 143.35 < 0.0001 ** X1 0.49 1 0.49 63.99 0.0005 ** X2 2.11 1 2.11 275.71 < 0.0001 ** X3 2.03 1 2.03 265.09 < 0.0001 ** X1 X2 0.1122 1 0.1122 14.65 0.0123 * X1 X3 0.632 1 0.632 82.53 0.0003 ** X2 X3 0.1225 1 0.1225 16 0.0103 * X1 ² 0.0016 1 0.0016 0.2093 0.6665 X2² 1.37 1 1.37 178.42 < 0.0001 ** X3 ² 3.29 1 3.29 429.04 < 0.0001 ** 残差 0.0383 5 0.0077 失拟合 0.0308 3 0.0103 2.75 0.2777 纯误差 0.0075 2 0.0037 总计 9.92 14 注：R²=0.9961, R 2 Adj =0.9892, R 2 Predj =0.9486。C.V= 0.1053%。
*表示对结果有显著的影响（P < 0.05）；**表示对结果有非常显著的影响（P < 0.01）。
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表 4 验证测试结果
Table 4. Verification test results
编号 铁粉加量/g 还原时间/h 浸出温度/ ℃ 浸出率/% 预测优化值 10.347 2 87.98 83.673 16 10.347 2 88 83.64 17 10.347 2 88 83.66 18 10.347 2 88 83.63
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