Modeling and optimization of zinc recovery from enyigba sphalerite in a binary solution of acetic ac

2.1. Materials

Sphalerite sample used in this study was obtained from Enyigba mining site, in Ebonyi state of Nigeria. The ore sample was pulverized and sieved with 75µm sieve. Analytical grade reagents and deionized water were used to prepare all solutions.

2.2. Analytical methods

The chemical composition of the ore was determined with X-ray fluorescence spectroscopy (XRF) via X-supreme 60 oxford instruments. The mineralogical composition of the ore sample 590

was determined with X-ray diffraction (XRD) with ARL X’TRA X-ray Diffractometer, Thermoscientific with the serial number 197492086 using Cu Kα radiation at 45kV and 40mA. The XRD patterns were recorded in the range of 5-65o 2θ. Scanning electron microscopy (SEM) Q250 by FEI model was used to perform the SEM analysis.

2.3. Leaching procedure

The leaching experiments were performed in a 500 ml flat-bottomed flask. The flask was fitted with a condenser to prevent losses through evaporation. A magnetically-stirred hot plate was used to provide heating. The calculated volumes of CH3COOH and H2O2 solutions were added to the flask, which was then heated to the desired temperature. Subsequently, a sample with a pre-determined weight was added to the flask. At the completion of each reaction time, the undissolved materials in the suspension was allowed to settle and separated by filtration. The resulting solutions were diluted and analyzed for zinc using atomic absorption spectrophotometer (AAS) [4].

2.4. XRF analysis description

About 20g of the ore sample was dried and sieved through 2mm sieves. Samples were milled further to between 20-53 µm. About 5g homogeneous specimen of the sample was loaded into special XRF cups prepared with 4µm ultralene film. The cups were half-full with sample. The instrument was switched on and taken to measurement mode. The measurement software was opened and the desired method selected. The sample was placed on the instrument in its bench top measurement position setup and covered. The sample compartment lid was closed to prevent scattering X-ray radiation. The measurement conditions as well as the time for each condition were set. The sample details were entered. The trigger was pulled to start the measurement. All detectable elements were measured simultaneously. Raw qualitative spectra and quantified result were stored in the software.

2.5. Design of experiment for RSM modeling

A five-level-five-factor CCRD was employed in the modeling and optimization studies, which produced 32 experimental runs. The independent factors chosen for the optimization include leaching temperature, acid concentration, stirring rate, leaching time and hydrogen peroxide concentration. The response variable was chosen as % yield of zinc. The coded and uncoded levels of the independent factors are shown in Table 1. Experiments were performed according to the actual experimental design matrix shown in Table 2. The experiments were performed randomly to avoid systemic error. In order to correlate the response variable to the independent variables, multiple regressions were used to fit the coefficient of the second-order polynomial model of the response. The quality of the fit of the model was evaluated using a test of significance and analysis of variance (ANOVA). In RSM, the most widely used second-order polynomial equation developed to fit the experimental data and identify the relevant model terms is shown in Equation 3. n 1

where Y is the predicted response variable which is the % yield of zinc in this study, 𝛽0 is the constant coefficient, 𝛽𝑖 is the ith linear coefficient of the input variable 𝑥𝑖 , 𝛽𝑖𝑖 is the ith quadratic coefficient of the input variable 𝑥𝑖 , 𝛽𝑖𝑗 is the different interaction coefficients between the input

variables 𝑥𝑖 and 𝑥𝑗 and ε is the error of the model. Design Expert software package version 10.0 (Stat-Ease Inc., Minneapolis, MN, USA) was used for regression analysis and analysis of variance (ANOVA). Table 1. Experimental range of the independent variables with different levels, to study sphalerite dissolution in a binary solution of acetic acid (CH3COOH) and hydrogen peroxide (H2O2) Independent variable Leaching temperature Acid concentration Stirring rate Leaching time Hydrogen Peroxide

Table 2. Experimental design matrix for sphalerite dissolution in a binary solution of acetic acid (CH3COOH) and hydrogen peroxide (H2O2) Run 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

A:Leaching temp. Coded Real -1 60 +1 90 -2 45 0 75 0 75 0 75 0 75 -1 60 +1 90 0 75 -1 60 +1 90 +1 90 +1 90 -1 60 0 75 -1 60 +2 105 0 75 0 75 -1 60 0 75 0 75 0 75 -1 60 +1 90 0 75 0 75 -1 60 0 75 +1 90 +1 90

Coded +1 +1 0 0 0 0 0 +1 -1 -2 -1 +1 -1 +1 -1 0 -1 0 0 0 +1 0 0 0 +1 +1 +2 0 -1 0 -1 -1

Coded -1 +1 0 0 +2 0 0 -1 +1 0 -1 -1 +1 -1 +1 0 -1 0 0 0 +1 0 0 0 +1 +1 0 0 +1 -2 -1 -1

Real 6 6 4.25 4.25 4.25 4.25 4.25 6 2.5 0.75 2.5 6 2.5 6 2.5 4.25 2.5 4.25 4.25 4.25 6 4.25 4.25 4.25 6 6 7.75 4.25 2.5 4.25 2.5 2.5

Real 230 540 385 385 695 385 385 230 540 385 230 230 540 230 540 385 230 385 385 385 540 385 385 385 540 540 385 385 540 75 230 230

D:Leaching time Coded Real -1 60 -1 60 0 90 0 90 0 90 0 90 0 90 +1 120 -1 60 0 90 +1 120 -1 60 +1 120 +1 120 +1 120 0 90 -1 60 0 90 -2 30 +2 150 +1 120 0 90 0 90 0 90 -1 60 +1 120 0 90 0 90 -1 60 0 90 +1 120 -1 60

E:Hydrogen Peroxide Coded Real -1 2.5 -1 2.5 0 4.25 0 4.25 0 4.25 +2 7.75 0 4.25 +1 6 +1 6 0 4.25 -1 2.5 +1 6 -1 2.5 -1 2.5 +1 6 0 4.25 +1 6 0 4.25 0 4.25 0 4.25 -1 2.5 0 4.25 -2 0.75 0 4.25 +1 6 +1 6 0 4.25 0 4.25 -1 2.5 0 4.25 +1 6 -1 2.5

3.1. Characterization

The results of the XRF analysis of the sphalerite sample had earlier been reported [4]. The result as shown in Figure 1 revealed that ZnO, SO3, Na2O and Fe2O3 were the major oxides present in the ore; oxides such as SiO2, CaO, Al2O3, Mn2O3 and MgO were present in minor quantities while the rest occurred in traces.

Figure 1. XRF result of Enyigba sphalerite The XRD result revealed the presence of sphalerite (ZnS) as the dominant mineral with three major peaks at 28.56, 47.50 and 56.37o, respectively. The result also revealed the presence of cerium germanium sulphide (Ce2GeS2) as an associated mineral with three major peaks at 30.15,

43.16. and 26.03o, respectively, as shown in Figure 2 [4].

Figure 2. X-ray diffraction pattern of Enyigba sphalerite The scanning electron micrograph (SEM) of sphalerite is presented in Figure 3 with magnifications of 500x, 1000x and 1500x, respectively. The results indicate that the particles are very cohesive, confirming their micrometer sized agglomerates with irregular shapes and rough edges and form microscopic flakes. The particles are highly crystalline, indicating a high level of purity of the ore. 593

Figure 3. SEM images of Enyigba sphalerite showing magnifications of 500× (a), 1000× (b) and 1500× (c), respectively.

3.2. RSM modeling

The analysis of the experimental results presented in Table 2 was done using design expert software (Design Expert 10.0). Models analyzed include: Linear model, 2FI (two factors interaction), quadratic and cubic model. Model quality (goodness of fit) can be compared based on the model’s R2 values and other parameters such as standard deviation (SD), prediction error sum of squares (PRESS), R2 adjusted, R2 predicted, model’s F-value and P-values. The closer the R2 value to unity, the better the models fit (Ameer et al., 2017b). From the model analyses presented as model summary statistics in Table 3, quadratic model with the highest regression coefficient (R2 value of 0.9913), least standard deviation of 1.29 shows better correlation between the observed and model predicted data. The PRESS is a measure of how well the model is likely to predict the responses in a new experiment. Low PRESS shows model’s reliability for predicting responses. The low PRESS value of 349.04 suggests that the quadratic model described the experimental design responses better than other models (Linear, 2FI and cubic), with the cubic model being aliased. In addition, a model is accepted as adequate if the difference between the adjusted R-Squared and the predicted R-Squared is less than 0.2. From Table 3, quadratic model has the least difference between Adjusted R2 and Predicted R2 of 0.1423. Hence, it can be inferred that the suggested model is adequate. Table 3. Model summary statistics Source Linear 2FI Quadratic Cubic

3.3. Response surface plots

The three-dimensional response surface plots, obtained as a function of two factors while maintaining all the factors constant at the mid-values, are helpful in understanding both the main effects and the interaction effects of these five factors. The model equations were solved for the various interaction effects on zinc yield considering at any instance the interaction between two factors only, assuming the other variables are set at their mean coded value of zero (0). The combined effects of adjusting the process variables within the design space were monitored using the 3D surface plots. Figure 5a shows the effects of leaching temperature and acid concentration on the percentage zinc yield. As the leaching temperature increased from 66 to 84oC, the percentage yield of zinc increased from 85 to 88.5%; while the percentage zinc yield also increased by the same margin as the acid concentration increased from 3.2 to 5.3M. The interactive effect of stirring rate and leaching temperature is shown in Figure 5b. As the stirring rate increased from 230 to 540 rpm, the percentage yield of zinc increased from 83 to 89.5%; whereas as the leaching temperature increased from 60 to 84oC, the percentage yield of zinc increased from 82.5 to 90%. Figure 5c shows the interactive effect of leaching time and leaching temperature. As the leaching temperature increased from 60 to 84oC, the percentage recovery of zinc increased from 82.5 to 90%; while the percentage recovery of zinc also increased by the same margin as the leaching time increased from 60 to 110 minutes. The combined interactive effect of leaching temperature and hydrogen peroxide concentration is given in Figure 5d. As the leaching temperature increased from 60 to 84oC, the percentage yield of zinc increased from 82.5

to 90%; whereas as the hydrogen peroxide concentration increased from 2.5 to 5.3M, the percentage recovery of zinc increased from 83 to 89.5%.

Figure 5. 3D plots of effects of process variables on zinc recovery

3.4. ANN modeling

In the present study, a three-layered feed-forward neural network with tangent sigmoid transfer function (tansig) at the hidden layer and linear transfer function (purelin) at the output layer was used. The model developed was used for the prediction of zinc yield. The ANN was trained using the back propagation algorithm. All calculations were carried out with MATLAB R2007b software (The mathworks, Inc., Ver. 7.5.0.342, MA, USA). This architecture was manipulated by modifying the number of neurons in the hidden layer. The topology of the developed ANN model was assigned as 5-9-1, where the 5 neurons of layer 1 correspond to the 5 input variables (leaching temperature, acid concentration, stirring rate, leaching time and hydrogen peroxide concentration); the hidden layer has 9 neurons while the output layer has one neuron, representing the target response (zinc yield). The same experimental dataset employed for RSM modeling was used for simulation by the ANN. During the training process, the whole experimental dataset (32 runs) was divided into 3 subsets, with a proportion of approximately 597

70:20:10 (%) for training, validation, and testing. The splitting of the dataset into different subsets allows evaluation of the predictive performance of the neural network with respect to the “hidden” data that is not used for the training purposes [14]. The network architecture was evaluated to achieve the lowest possible training, validation and testing errors and highest correlation coefficients. From the results obtained, the mean square error of the trained network is 8.06709e-1 with a regression coefficient of 0.997755. The performance plot for the trained network is shown in Figure 6 with 6 epochs while the regression plots for the training and validation are shown in Figure 7 (a and b).

Figure 6. Performance plot for sphalerite dissolution in CH3COOH/H2O2 ANN model

Figure 7. Regression plots for the training (a) and validation (b) for sphalerite dissolution in CH3COOH/H2O2

3.5. Performance evaluation of RSM and ANN models

A comparative study between artificial neural network (ANN) and response surface methodology (RSM) was carried out in order to assess the respective predictive performance and estimation capabilities by means of various statistical indicators, including root mean square error (RMSE), absolute average deviation (AAD), mean absolute error (MAE), coefficient of determination (R2), and standard error of prediction (SEP) observed for both models. The closer the RMSE and MAE values are to 0, the better the prediction of the model. The RMSE was 598

calculated using Equation (6). The AAD observed for both models gives an indication of how accurate the model predictions can be [15]. The lower the AAD (%) value, the better the prediction of the model. Equation (7) shows the expression for calculating the absolute average deviation (AAD); the expression for calculating the coefficient of determination (R2), is shown in Equation (8); while the expressions for calculating the mean absolute error (MAE) and the standard error of prediction (SEP) are shown in Equations (9) and (10), respectively.

 n   1  Y pred.  Y exp.   AAD (%) =      × 100  n i 1  Y exp.    

where n is the number of sample points, 𝑌𝑝𝑟𝑒𝑑. is the predicted response value of zinc dissolution and 𝑌𝑒𝑥𝑝. is the experimentally determined value for zinc dissolution [15]. The results of the statistical comparison between RSM and ANN models are presented in Table 6. The value of R2 for the ANN model was slightly higher than the value for RSM model. Also, the computed values of RMSE, AAD, MAE and SEP for both models were very low. AAD was used to measure the precision and accuracy of the models. The values obtained for both models were very low. However, the ANN model had lower error values than the RSM model, suggesting the superiority of ANN over RSM for predictability purpose.

Table 6. Predicive capacity comparison of RSM and ANN models Parameters RMSE AAD (%) R2 MAE SEP

3.6. Process optimization using CCD

The optimization exercise for the dissolution process was conducted independently using the pliability of the design expert tool. Equation 3 was solved for the best solutions such that the response was maximized within the design space. A conventional approach, which involves selecting the best solution based on economic considerations, was adopted. The optimal predicted conditions for zinc recovery include a leaching temperature of 90 oC, acid concentration of 6M, stirring rate of 540 rpm, leaching time of 120 minutes and hydrogen peroxide concentration of 6M; at which about 89.91% zinc was recovered. Experiments were performed in triplicate at the above optimum conditions to validate the RSM predicted result. An average value of 88.47% zinc recovery was recorded.