# Optimization Studies on Recovery of Metals from Printed Circuit Board Waste

Authors: P. Sivakumar; D. Prabhakaran; M. Thirumarimurugan
Journal: Bioinorganic Chemistry and Applications
 (2018)

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## Abstract

The aim of the study was to recover copper and lead metal from waste printed circuit boards (PCBs). The electrowinning method is found to be an effective recycling process to recover copper and lead metal from printed circuit board wastes. In order to simplify the process with affordable equipment, a simple ammonical leaching operation method was adopted. The selected PCBs were incinerated into fine ash powder at 500°C for 1 hour in the pyrolysis reactor. Then, the fine ash powder was subjected to acid-leaching process to recover the metals with varying conditions like acid-base concentration, electrode combination, and leaching time. The relative electrolysis solution of 0.1 M lead nitrate for lead and 0.1 M copper sulphate for copper was used to extract metals from PCBs at room temperature. The amount of lead and copper extracted from the process was determined by an atomic absorption spectrophotometer, and results found were 73.29% and 82.17%, respectively. Further, the optimum conditions for the recovery of metals were determined by using RSM software. The results showed that the percentage of lead and copper recovery were 78.25% and 89.1% should be 4 hrs 10 A/dm2.


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## Body

## 1. Introduction

Recycling of e-waste is an important subject not only from the point of waste treatment but also from the recovery aspect of valuable materials [1–4]. Among the resources in e-waste, metals contribute more than 95% of the materials market value. Hence, the recovery of valuable metals is the inherent motive in e-waste disposal. In the past decades, many techniques for recovering valuable metals from e-waste have been developed such as gravity separation, magnetic separation, and electrostatic separation [5] synthesis of CuCl with e-waste, separation of PCBs with organic solvent method [6, 7], cyanide and noncyanide lixiviants leaching methods, ammonium persulfate leaching bioleaching methods [8–10], or a combination of these approaches. Among those methods, hydrometallurgical methods are more accurate, predictable, and controllable [11]. Therefore, hydrometallurgical techniques are most active in the research of valuable metal recovery from electronic scraps in the past two decades. However, traditional hydrometallurgical methods are acid dependent, time-consuming, and inefficient for simultaneous recovery of precious metals. Remarkably, a large amount of corrosive or toxic reagents, such as aqua regia, nitric acid, cyanide and halide, are consumed, producing large quantities of toxic and corrosive fumes or solution [12, 13]. Therefore, it is necessary to seek a more environmental friendly method for the recovery of valuable metals from e-wastes. Hydrometallurgical methods are used in the upgrading and refining stages of the recycling chain [14–16]. In this research article, the recovery of lead and copper metals from e-waste is widely investigated. The PCBs were converted into fine ash powder and subjected to electrowinning process for the recovery of metals. The experimental results were determined by EDS and AAS, respectively. Furthermore, the experimental results are validated through RSM software at different parameters like acid-base concentration, electrode combination, and leaching time [17–22].


## 2. Materials and Methods

### 2.1. Materials

The computer PCBs were collected from various sources for the recovery of metals. The collected PCBs were crushed using roll crusher and powdered by a hammer mill. The crushed PCBs were incarnated through pyrolysis to avoid side reaction in the leaching process with the electrolyte solution. The optimum condition of the pyrolysis reactor was 500°C in atmospheric pressure for 1 h where the epoxy resins and polymers were volatized at the temperature less than 500°C. The volatized contents were condensed and collected separately. The ferrous materials present in the obtained ash were separated by a magnetic separator.


### 2.2. Electrowinning Process

The fine ash powder was treated with aqua regia solution (3 : 1 ratio of HCl and HNO3) in the incineration chamber in order to avoid the liberation of toxic fumes. Then the precipitated salts obtained from the leaching was analyzed by EDS to determine the composition of metal present in the salts (Figure 1). The electrowinning setup consists of bath arrangement and amplifier. The bath having two slots for the anode and cathode fixing and the electrode is connected with amplifier, and the current density was varied through the amplifier (Figure 2).Figure 1
Initial analysis of raw materials.Figure 2
Experimental setup of electrowinning process.


### 2.3. Extraction Process of Lead

About 25 g of incinerated fine ash was added into the acid bath followed by the addition of ammonical electrolyte solution. The current density was set to 1 to 10 (A/dm2). The solution was agitated at regular interval to get an effective electrodeposition:(1)Pb+4HCl⟶PbCl4+2H2After the stipulated time of operation, pure lead was deposited on lead cathode. The deposited elements were scrapped and stored in an air tight container. The recovered lead quantitated from the EDS method. The spent acid left with mud filtered at pH 6–10 was stored in a glass container for further treatment.


### 2.4. Extraction Process of Copper

About 25 g of incinerated fine ash was added into the acid bath followed by the addition of ammonical electrolyte solution. The current density was set to 1 to 10 (A/dm2). The solution was agitated at regular intervals to get an effective electrodeposition. After the stipulated time of operation, pure copper (cupric) was deposited on the cathode and impure copper (cuprous ion) were deposited on the anode. The deposited elements were scrapped and stored in an air tight container. The recovered copper quantitated from the EDS method. The spent acid left with mud (nonleached elements) was filtered (pH–8.4) and were stored in a glass container for further treatment (Figure 3):(2)2Cu2+aq+2H2Ol⟶2Cus+4H+aq+O2gFigure 3
Bath solutions of copper and lead.The spent solution collected from the electrodeposition was neutralized to 6.9 for the safe disposal as per the standard. Moreover, the presence of any metal in the spent solution was analyzed by Fourier-transform infrared spectroscopy. The results (Figure4) show that the metallic traces were found to be absent which confirms that all the metals recovered from the ashes deposited on the electrode.Figure 4
FTIR analysis of bath solution.


## 2.1. Materials

The computer PCBs were collected from various sources for the recovery of metals. The collected PCBs were crushed using roll crusher and powdered by a hammer mill. The crushed PCBs were incarnated through pyrolysis to avoid side reaction in the leaching process with the electrolyte solution. The optimum condition of the pyrolysis reactor was 500°C in atmospheric pressure for 1 h where the epoxy resins and polymers were volatized at the temperature less than 500°C. The volatized contents were condensed and collected separately. The ferrous materials present in the obtained ash were separated by a magnetic separator.


## 2.2. Electrowinning Process

The fine ash powder was treated with aqua regia solution (3 : 1 ratio of HCl and HNO3) in the incineration chamber in order to avoid the liberation of toxic fumes. Then the precipitated salts obtained from the leaching was analyzed by EDS to determine the composition of metal present in the salts (Figure 1). The electrowinning setup consists of bath arrangement and amplifier. The bath having two slots for the anode and cathode fixing and the electrode is connected with amplifier, and the current density was varied through the amplifier (Figure 2).Figure 1
Initial analysis of raw materials.Figure 2
Experimental setup of electrowinning process.


## 2.3. Extraction Process of Lead

About 25 g of incinerated fine ash was added into the acid bath followed by the addition of ammonical electrolyte solution. The current density was set to 1 to 10 (A/dm2). The solution was agitated at regular interval to get an effective electrodeposition:(1)Pb+4HCl⟶PbCl4+2H2After the stipulated time of operation, pure lead was deposited on lead cathode. The deposited elements were scrapped and stored in an air tight container. The recovered lead quantitated from the EDS method. The spent acid left with mud filtered at pH 6–10 was stored in a glass container for further treatment.


## 2.4. Extraction Process of Copper

About 25 g of incinerated fine ash was added into the acid bath followed by the addition of ammonical electrolyte solution. The current density was set to 1 to 10 (A/dm2). The solution was agitated at regular intervals to get an effective electrodeposition. After the stipulated time of operation, pure copper (cupric) was deposited on the cathode and impure copper (cuprous ion) were deposited on the anode. The deposited elements were scrapped and stored in an air tight container. The recovered copper quantitated from the EDS method. The spent acid left with mud (nonleached elements) was filtered (pH–8.4) and were stored in a glass container for further treatment (Figure 3):(2)2Cu2+aq+2H2Ol⟶2Cus+4H+aq+O2gFigure 3
Bath solutions of copper and lead.The spent solution collected from the electrodeposition was neutralized to 6.9 for the safe disposal as per the standard. Moreover, the presence of any metal in the spent solution was analyzed by Fourier-transform infrared spectroscopy. The results (Figure4) show that the metallic traces were found to be absent which confirms that all the metals recovered from the ashes deposited on the electrode.Figure 4
FTIR analysis of bath solution.


## 3. Results and Discussion

### 3.1. RSM for Lead

The response surface methodology (RSM) is a statistical modeling technique employed for multiple regression analysis using quantitative data obtained from designed experiments to solve multivariable equations (Table1). The response surfaces can be visualized as three-dimensional plots that exhibit the response as a function of two factors while keeping the other factors constant. In this above plot, the red zone corresponds to the extract percentage above 85%, yellow zone shows 60 to 70%, and the blue zone confirms below 40% extraction of lead (Figures 5 and 5(a)). The regression equation for the RSM data plots for the lead is(3)Extract=66.36+9.0175∗A+7.37375∗B+6.42375∗C+1.235∗AB+0.17∗AC+−7.1525∗BC+−18.6187∗A2+−1.67125∗B2+−1.81625∗C2.Table 1
RSM parameters for lead extraction.
Std
Run
Factor 1
Factor 2
Factor 3
A: CD
B: solvent
C: time
A/dm2
ml
Hrs
1
8
1
400
2.5
2
9
19
400
2.5
3
17
1
700
2.5
4
12
19
700
2.5
5
1
1
550
1
6
14
19
550
1
7
6
1
550
4
8
5
19
550
4
9
4
10
400
1
10
10
10
700
1
11
7
10
400
4
12
11
10
700
4
13
2
10
550
2.5
14
16
10
550
2.5
15
13
10
550
2.5
16
15
10
550
2.5
17
3
10
550
2.5Figure 5
Contour plot for recovery of Lead.The model as a function of coded factor could be utilized to predict the response of each parameter within the given limit. Here, the maximum limit of process parameters (factors) is termed (coded) as +1 and minimum limit is terms (coded) as −1. The modifed equation or coded equation is very much useful in order to find the comparative effect of the process parameters by relating the coefficient of factors. The final equation in terms of actual factors is(4)Extract=−70.2665+5.06454∗CD+0.201188∗solvent+25.6766∗time+0.000914815∗CD∗solvent+0.0125926∗CD∗time+−0.0317889∗solvent∗time+−0.229861∗CD2+−7.42778e−05∗solvent2+−0.807222∗time2.Equation (4) in terms of process parameters could be utilized to predict the response for the provided levels of each parameter (Table2). In this equation, the original units of each parameters should be considered for each levels. In order to evaluate the comparative effect of each factor, the above equation should not be considered since the coefficients are balanced to embrace the units of each parameters. Also, the intercept does not fall at design space center.Table 2
Box–Behnken experimental design table for recovery of lead.
Std
Run
Factor 1
Factor 2
Factor 3
A: CD
B: solvent
C: time
A/dm2
ml
Hrs
1
8
1
400
2.5
2
9
19
400
2.5
3
17
1
700
2.5
4
12
19
700
2.5
5
1
1
550
1
6
14
19
550
1
7
6
1
550
4
8
5
19
550
4
9
4
10
400
1
10
10
10
700
1
11
7
10
400
4
12
11
10
700
4
13
2
10
550
2.5
14
16
10
550
2.5
15
13
10
550
2.5
16
15
10
550
2.5
17
3
10
550
2.5


### 3.2. Analysis of Variance (ANOVA)

Analysis of variance is used to determine the significant effects of process variables on current efficiency (Table3) along with the factor coding. The sum of squares is found to be Type III—partial derived from the ANOVA quadratic model. The model F value of 4.43 implies the model is significant. A minimum value of 3.12% is possible for the F value due to noise. p values less than 0.0500 indicate model terms are significant. In this case A, A2 are significant model terms. Values greater than 0.1000 indicate the model terms are not significant. If there are many insignificant model terms (not counting those required to support hierarchy), model reduction may improve the model. The lack of fit F value of 63.27 implies the lack of fit is significant. There is only a 0.08% chance that a lack of fit F value could be large that could occur due to noise. The coefficient represents the expected change in response per unit change in the factor value, when all remaining factors were constant. The intercept in an orthogonal design is the overall average response of all the runs. The coefficients are adjustments around the average factor settings. When the factors are orthogonal, the variance inflation factors (VIFs) are 1; VIFs greater than 1 indicate multicolinearity; the higher the VIF, the more severe the correlation of factors. As a rough rule, VIFs less than 10 are tolerable. Hence, from the data obtained (Table 4), the VIF values of lead are found to be tolerable.Table 3
ANOVA quadratic model for lead.
Source
Sum of squares
DOF
Mean square
F value
p value
Model
3152.45
9
350.27
4.43
0.0312
Significant
A-CD
650.52
1
650.52
8.23
0.0240
B-solvent
434.98
1
434.98
5.51
0.0514
C-time
330.12
1
330.12
4.18
0.0802
AB
6.10
1
6.10
0.0772
0.7891
AC
0.1156
1
0.1156
0.0015
0.9706
BC
204.63
1
204.63
2.59
0.1516
A2
1459.61
1
1459.61
18.47
0.0036
B2
11.76
1
11.76
0.1489
0.7111
C2
13.89
1
13.89
0.1758
0.6876
Residual
553.05
7
79.01
Lack of fit
541.64
3
180.55
63.27
0.0008
Significant
Pure error
11.41
4
2.85
Total
3705.50
16Table 4
Coefficients in terms of coded factors for lead.
Factor
Coefficient estimate
DOF
Standard error
95% CI low
95% CI high
VIF
Intercept
66.36
1
3.98
56.96
75.76
A-CD
9.02
1
3.14
1.59
16.45
1.0000
B-solvent
7.37
1
3.14
−0.0573
14.80
1.0000
C-time
6.42
1
3.14
−1.01
13.85
1.0000
AB
1.24
1
4.44
−9.27
11.74
1.0000
AC
0.1700
1
4.44
−10.34
10.68
1.0000
BC
−7.15
1
4.44
−17.66
3.36
1.0000
A2
−18.62
1
4.33
−28.86
−8.38
1.01
B2
−1.67
1
4.33
−11.91
8.57
1.01
C2
−1.82
1
4.33
−12.06
8.43
1.01


### 3.3. Model Terms

For a standard deviation of 1, the power calculations are performed using response type “continuous,” and parameters are Δ = 2 andσ = 1. The power is evaluated over −1 to +1 coded factor space. From (Table 5), the standard errors should be similar to each other in a balanced design. The ideal VIF value should be 1, VIFs above 10 are cause for concern, and VIFs above 100 are cause for alarm, indicating coefficients are poorly estimated due to multicolinearity, where ideal Ri2 is 0.0. High Ri2 means terms are correlated with each other, possibly leading to poor models. If the design has multilinear constraints, then multicolinearity will exist to a greater degree. This inflates the VIFs and the Ri2, rendering these statistics would not perform well. Hence, FDS could be used. Power is an inappropriate tool to evaluate response surface designs. Use prediction-based metrics provided in this program via fraction of design space (FDS) statistics.Table 5
Model terms in RSM for lead.
Term
Standard error
VIF
Ri
2
Power (%)
A
0.3536
1
0.0000
68.1
B
0.3536
1
0.0000
68.1
C
0.3536
1
0.0000
68.1
AB
0.5000
1
0.0000
40.8
AC
0.5000
1
0.0000
40.8
BC
0.5000
1
0.0000
40.8
A2
0.4873
1.00588
0.0058
93.8
B2
0.4873
1.00588
0.0058
93.8
C2
0.4873
1.00588
0.0058
93.8


### 3.4. Fit Statistics

A negative predictedR2 implies that the overall mean may be a better predictor of the response than the current model. In some cases, a higher order model may also predict better. Adeq. precision measures the signal to noise ratio. A ratio greater than 4 is desirable. The ratio of 5.915 indicates an adequate signal. This model can be used to navigate the design space. The optimization of current efficiency is shown in Figure 6. From the results, it is observed that 69% of lead extract is obtained at current density = 10 A dm−2, solvent ratio = 5 : 2, and the electrolysis time = 4 hours (Figures 7 and 8). The significance of regression coefficients were analyzed using the p-test and t-test. The p values are used to check the effect of interaction among the variables. A larger magnitude of t-value and a smaller magnitude of p value are significant in the corresponding coefficient term. The coefficient of current efficiency and the corresponding t and p values are shown in Table 6. Finally, the coefficients in the interaction terms for current density-electrolysis time is significant compared to current density-solvent ratio, and current density-electrolysis time.Figure 6
Current density vs extract % for lead.Figure 7
Solvent vs extract % for lead.Figure 8
Time vs extract % for lead.Table 6
Fit statistics.
Std. dev.
8.89
Mean
55.96
CV (%)
15.88
R
2
0.8507
AdjustedR2
0.6589
PredictedR2
−1.3436
Adeq. precision
5.9146


### 3.5. RSM for Copper

The regression equation for the RSM data plots for the copper is in terms of coded factors form as follows:(5)ExtractE=48+24∗A+8.25∗B+15.5∗C+0.5∗AB+7.5∗AC+2.5∗BC+−6.5∗A2+8∗B2+1.5∗C2.The model (Equation 5) as a function of coded factor could be utilized to predict the response of each parameter within the given limit. Here, the maximum limit of process parameters (factors) is termed(coded) as +1 and minimum limit is termed (coded) as −1. The modified equation or coded equation is very much useful in order to find the comparative effect of the process parameters by relating the coefficient of factors (Table7).Table 7
RSM parameters for copper extraction.
Std
Run
Factor 1
Factor 2
Factor 3
A: CD
B: solvent
C: time
A/dm2
ml
Hrs
1
12
1
400
2
2
14
19
400
2
3
2
1
600
2
4
4
19
600
2
5
18
1
500
1
6
13
19
500
1
7
16
1
500
3
8
11
19
500
3
9
8
10
400
1
10
1
10
600
1
11
6
10
400
3
12
7
10
600
3
13
5
10
500
2
14
9
10
500
2
15
17
10
500
2
16
3
10
500
2
17
15
10
500
2The final equation in terms of actual factors is(6)Extract=191.503+2.32716∗CD+−0.773056∗solvent+−11.3333∗time+0.000555556∗CD∗solvent+0.833333∗CD∗time+0.025∗solvent∗time+−0.0802469∗CD2+0.0008∗solvent2+1.5∗time2.Equation (5) in terms of process parameters could be utilized to predict the response for the provided levels of each parameter. In this equation, the original units of each parameters should be considered for each levels. In order to evaluate the comparative effect of each factor, the above equation should not be considered since the coefficients are balanced to embrace the units of each parameters. Also, the intercept does not falls at design space center (Table8). In this contour plot, the red zone indicates extract percentages above 85%. And yellow and blue zones indicate 60 to 70% and below 40% extraction of copper (Figures 9 and 9(a)).Table 8
Box–Behnken experimental design table for recovery of copper.
Std
Run
Factor 1
Factor 2
Factor 3
A: CD
B: solvent
C: time
A/dm2
ml
Hrs
1
12
1
400
2
2
14
19
400
2
3
2
1
600
2
4
4
19
600
2
5
18
1
500
1
6
13
19
500
1
7
16
1
500
3
8
11
19
500
3
9
8
10
400
1
10
1
10
600
1
11
6
10
400
3
12
7
10
600
3
13
5
10
500
2
14
9
10
500
2
15
17
10
500
2
16
3
10
500
2
17
15
10
500
2
18
10
10
500
2Figure 9
Contour plot for recovery of copper.


### 3.6. Analysis of Variance (ANOVA)

Analysis of variance is used to determine the significant effects of process variables on current efficiency along with the factor coding. The sum of squares is found to be Type III—partial derived from the ANOVA quadratic model. The modelF value of 155.08 in the Table 9 implies the model is significant. A minimum value of 0.01% is possible for the F value due to noise. P values less than 0.0500 indicate model terms are significant. In this case, A, B, C, AC, A2, and B2 are significant model terms. Values greater than 0.1000 indicate the model terms are not significant. If there are many insignificant model terms (not counting those required to support hierarchy), model reduction may improve the model. The lack of fit F value is nil that implies the lack of fit is significant. The coefficient represents the expected change in response per unit change in factor value, when all remaining factors were constant. The intercept in an orthogonal design is the overall average response of all the runs. The coefficients are adjustments around the average factor settings. When the factors are orthogonal, the VIFs are 1; VIFs greater than 1 indicate multicolinearity; the higher the VIF, the more severe the correlation of factors. As a rough rule, VIFs less than 10 are tolerable. Hence, from the data obtained (Table 10), the VIF Values of lead are found to be tolerable.Table 9
ANOVA quadratic model for copper.
Source
Sum of squares
DOF
Mean square
F value
p value
Model
7763.50
9
862.61
155.08
<0.0001
Significant
A-CD
4608.00
1
4608.00
828.40
<0.0001
B-solvent
544.50
1
544.50
97.89
<0.0001
C-time
1922.00
1
1922.00
345.53
<0.0001
AB
1.0000
1
1.0000
0.1798
0.6827
AC
225.00
1
225.00
40.45
0.0002
BC
25.00
1
25.00
4.49
0.0668
A2
184.36
1
184.36
33.14
0.0004
B2
279.27
1
279.27
50.21
0.0001
C2
9.82
1
9.82
1.77
0.2206
Residual
44.50
8
5.56
Lack of fit
44.50
3
14.83
Pure error
0.0000
5
0.0000
Total
7808.00
17Table 10
Coefficients in terms of coded factors for copper.
Factor
Coefficient estimate
DOF
Standard error
95% CI low
95% CI high
VIF
Intercept
48.00
1
0.9629
45.78
50.22
A-CD
24.00
1
0.8339
22.08
25.92
1.0000
B-solvent
8.25
1
0.8339
6.33
10.17
1.0000
C-time
15.50
1
0.8339
13.58
17.42
1.0000
AB
0.5000
1
1.18
−2.22
3.22
1.0000
AC
7.50
1
1.18
4.78
10.22
1.0000
BC
2.50
1
1.18
−0.2193
5.22
1.0000
A2
−6.50
1
1.13
−9.10
−3.90
1.02
B2
8.00
1
1.13
5.40
10.60
1.02
C2
1.50
1
1.13
−1.10
4.10
1.02


### 3.7. Model Terms

For a standard deviation of 1 the power calculations are performed using response type “continuous,” and the parameters are Δ = 2 andσ = 1. The power is evaluated over −1 to +1 coded factor space (Table 11). The standard errors should be similar to each other in a balanced design. The ideal VIF value should be 1, VIFs above 10 are cause for concern and VIFs above 100 are cause for alarm, indicating coefficients are poorly estimated due to multicolinearity, where ideal Ri2 is 0.0. High Ri2 means terms are correlated with each other, possibly leading to poor models. If the design has multilinear constraints, then multicolinearity will exist to a greater degree. This inflates the VIFs and the Ri2, rendering these statistics would not perform well. Hence, FDS could be used. Power is an inappropriate tool to evaluate response surface designs. Use prediction-based metrics provided in this program via fraction of design space (FDS) statistics.Table 11
Model terms in RSM for copper.
Term
Standard error
VIF
Ri2
Power (%)
A
0.3536
1
0.0000
69.8
B
0.3536
1
0.0000
69.8
C
0.3536
1
0.0000
69.8
AB
0.5000
1
0.0000
42.1
AC
0.5000
1
0.0000
42.1
BC
0.5000
1
0.0000
42.1
A2
0.4787
1.01852
0.0182
95.4
B2
0.4787
1.01852
0.0182
95.4
C2
0.4787
1.01852
0.0182
95.4


### 3.8. Fit Statistics

A predictedR2 implies that the overall mean may be a better predictor of the response than the current model. In some cases, a higher order model may also predict better. Adeq. precision measures the signal to noise ratio. A ratio greater than 4 is desirable. A ratio of 44.9 indicates an adequate signal. This model can be used to navigate the design space. The optimization of current efficiency is shown in Figure 10. The optimum extraction of 69% Cu is obtained at current density = 19 A dm−2, solvent ratio = 5 : 2, and electrolysis time = 4 hour (Figures 11 and 12). The significance of regression coefficients was analyzed using the p-test and t-test. The p values are used to check the effect of interaction among the variables. A larger magnitude of t-value and a smaller magnitude of p value are significant in the corresponding coefficient term. The coefficient of current efficiency and the corresponding t and p values are shown in (Table 12). Finally, the coefficients in the interaction terms for current density-electrolysis time is significant compared to current density-solvent ratio and current density-electrolysis time.Figure 10
Current density vs extract % for copper.Figure 11
Solvent vs extract % for lead.Figure 12
Time vs extract % for lead.Table 12
Fit statistics.
Std. dev.
2.36
Mean
49.33
CV (%)
4.78
R
2
0.9943
AdjustedR2
0.9879
PredictedR2
0.9088
Adeq. Precision
44.9395


## 3.1. RSM for Lead

The response surface methodology (RSM) is a statistical modeling technique employed for multiple regression analysis using quantitative data obtained from designed experiments to solve multivariable equations (Table1). The response surfaces can be visualized as three-dimensional plots that exhibit the response as a function of two factors while keeping the other factors constant. In this above plot, the red zone corresponds to the extract percentage above 85%, yellow zone shows 60 to 70%, and the blue zone confirms below 40% extraction of lead (Figures 5 and 5(a)). The regression equation for the RSM data plots for the lead is(3)Extract=66.36+9.0175∗A+7.37375∗B+6.42375∗C+1.235∗AB+0.17∗AC+−7.1525∗BC+−18.6187∗A2+−1.67125∗B2+−1.81625∗C2.Table 1
RSM parameters for lead extraction.
Std
Run
Factor 1
Factor 2
Factor 3
A: CD
B: solvent
C: time
A/dm2
ml
Hrs
1
8
1
400
2.5
2
9
19
400
2.5
3
17
1
700
2.5
4
12
19
700
2.5
5
1
1
550
1
6
14
19
550
1
7
6
1
550
4
8
5
19
550
4
9
4
10
400
1
10
10
10
700
1
11
7
10
400
4
12
11
10
700
4
13
2
10
550
2.5
14
16
10
550
2.5
15
13
10
550
2.5
16
15
10
550
2.5
17
3
10
550
2.5Figure 5
Contour plot for recovery of Lead.The model as a function of coded factor could be utilized to predict the response of each parameter within the given limit. Here, the maximum limit of process parameters (factors) is termed (coded) as +1 and minimum limit is terms (coded) as −1. The modifed equation or coded equation is very much useful in order to find the comparative effect of the process parameters by relating the coefficient of factors. The final equation in terms of actual factors is(4)Extract=−70.2665+5.06454∗CD+0.201188∗solvent+25.6766∗time+0.000914815∗CD∗solvent+0.0125926∗CD∗time+−0.0317889∗solvent∗time+−0.229861∗CD2+−7.42778e−05∗solvent2+−0.807222∗time2.Equation (4) in terms of process parameters could be utilized to predict the response for the provided levels of each parameter (Table2). In this equation, the original units of each parameters should be considered for each levels. In order to evaluate the comparative effect of each factor, the above equation should not be considered since the coefficients are balanced to embrace the units of each parameters. Also, the intercept does not fall at design space center.Table 2
Box–Behnken experimental design table for recovery of lead.
Std
Run
Factor 1
Factor 2
Factor 3
A: CD
B: solvent
C: time
A/dm2
ml
Hrs
1
8
1
400
2.5
2
9
19
400
2.5
3
17
1
700
2.5
4
12
19
700
2.5
5
1
1
550
1
6
14
19
550
1
7
6
1
550
4
8
5
19
550
4
9
4
10
400
1
10
10
10
700
1
11
7
10
400
4
12
11
10
700
4
13
2
10
550
2.5
14
16
10
550
2.5
15
13
10
550
2.5
16
15
10
550
2.5
17
3
10
550
2.5


## 3.2. Analysis of Variance (ANOVA)

Analysis of variance is used to determine the significant effects of process variables on current efficiency (Table3) along with the factor coding. The sum of squares is found to be Type III—partial derived from the ANOVA quadratic model. The model F value of 4.43 implies the model is significant. A minimum value of 3.12% is possible for the F value due to noise. p values less than 0.0500 indicate model terms are significant. In this case A, A2 are significant model terms. Values greater than 0.1000 indicate the model terms are not significant. If there are many insignificant model terms (not counting those required to support hierarchy), model reduction may improve the model. The lack of fit F value of 63.27 implies the lack of fit is significant. There is only a 0.08% chance that a lack of fit F value could be large that could occur due to noise. The coefficient represents the expected change in response per unit change in the factor value, when all remaining factors were constant. The intercept in an orthogonal design is the overall average response of all the runs. The coefficients are adjustments around the average factor settings. When the factors are orthogonal, the variance inflation factors (VIFs) are 1; VIFs greater than 1 indicate multicolinearity; the higher the VIF, the more severe the correlation of factors. As a rough rule, VIFs less than 10 are tolerable. Hence, from the data obtained (Table 4), the VIF values of lead are found to be tolerable.Table 3
ANOVA quadratic model for lead.
Source
Sum of squares
DOF
Mean square
F value
p value
Model
3152.45
9
350.27
4.43
0.0312
Significant
A-CD
650.52
1
650.52
8.23
0.0240
B-solvent
434.98
1
434.98
5.51
0.0514
C-time
330.12
1
330.12
4.18
0.0802
AB
6.10
1
6.10
0.0772
0.7891
AC
0.1156
1
0.1156
0.0015
0.9706
BC
204.63
1
204.63
2.59
0.1516
A2
1459.61
1
1459.61
18.47
0.0036
B2
11.76
1
11.76
0.1489
0.7111
C2
13.89
1
13.89
0.1758
0.6876
Residual
553.05
7
79.01
Lack of fit
541.64
3
180.55
63.27
0.0008
Significant
Pure error
11.41
4
2.85
Total
3705.50
16Table 4
Coefficients in terms of coded factors for lead.
Factor
Coefficient estimate
DOF
Standard error
95% CI low
95% CI high
VIF
Intercept
66.36
1
3.98
56.96
75.76
A-CD
9.02
1
3.14
1.59
16.45
1.0000
B-solvent
7.37
1
3.14
−0.0573
14.80
1.0000
C-time
6.42
1
3.14
−1.01
13.85
1.0000
AB
1.24
1
4.44
−9.27
11.74
1.0000
AC
0.1700
1
4.44
−10.34
10.68
1.0000
BC
−7.15
1
4.44
−17.66
3.36
1.0000
A2
−18.62
1
4.33
−28.86
−8.38
1.01
B2
−1.67
1
4.33
−11.91
8.57
1.01
C2
−1.82
1
4.33
−12.06
8.43
1.01


## 3.3. Model Terms

For a standard deviation of 1, the power calculations are performed using response type “continuous,” and parameters are Δ = 2 andσ = 1. The power is evaluated over −1 to +1 coded factor space. From (Table 5), the standard errors should be similar to each other in a balanced design. The ideal VIF value should be 1, VIFs above 10 are cause for concern, and VIFs above 100 are cause for alarm, indicating coefficients are poorly estimated due to multicolinearity, where ideal Ri2 is 0.0. High Ri2 means terms are correlated with each other, possibly leading to poor models. If the design has multilinear constraints, then multicolinearity will exist to a greater degree. This inflates the VIFs and the Ri2, rendering these statistics would not perform well. Hence, FDS could be used. Power is an inappropriate tool to evaluate response surface designs. Use prediction-based metrics provided in this program via fraction of design space (FDS) statistics.Table 5
Model terms in RSM for lead.
Term
Standard error
VIF
Ri
2
Power (%)
A
0.3536
1
0.0000
68.1
B
0.3536
1
0.0000
68.1
C
0.3536
1
0.0000
68.1
AB
0.5000
1
0.0000
40.8
AC
0.5000
1
0.0000
40.8
BC
0.5000
1
0.0000
40.8
A2
0.4873
1.00588
0.0058
93.8
B2
0.4873
1.00588
0.0058
93.8
C2
0.4873
1.00588
0.0058
93.8


## 3.4. Fit Statistics

A negative predictedR2 implies that the overall mean may be a better predictor of the response than the current model. In some cases, a higher order model may also predict better. Adeq. precision measures the signal to noise ratio. A ratio greater than 4 is desirable. The ratio of 5.915 indicates an adequate signal. This model can be used to navigate the design space. The optimization of current efficiency is shown in Figure 6. From the results, it is observed that 69% of lead extract is obtained at current density = 10 A dm−2, solvent ratio = 5 : 2, and the electrolysis time = 4 hours (Figures 7 and 8). The significance of regression coefficients were analyzed using the p-test and t-test. The p values are used to check the effect of interaction among the variables. A larger magnitude of t-value and a smaller magnitude of p value are significant in the corresponding coefficient term. The coefficient of current efficiency and the corresponding t and p values are shown in Table 6. Finally, the coefficients in the interaction terms for current density-electrolysis time is significant compared to current density-solvent ratio, and current density-electrolysis time.Figure 6
Current density vs extract % for lead.Figure 7
Solvent vs extract % for lead.Figure 8
Time vs extract % for lead.Table 6
Fit statistics.
Std. dev.
8.89
Mean
55.96
CV (%)
15.88
R
2
0.8507
AdjustedR2
0.6589
PredictedR2
−1.3436
Adeq. precision
5.9146


## 3.5. RSM for Copper

The regression equation for the RSM data plots for the copper is in terms of coded factors form as follows:(5)ExtractE=48+24∗A+8.25∗B+15.5∗C+0.5∗AB+7.5∗AC+2.5∗BC+−6.5∗A2+8∗B2+1.5∗C2.The model (Equation 5) as a function of coded factor could be utilized to predict the response of each parameter within the given limit. Here, the maximum limit of process parameters (factors) is termed(coded) as +1 and minimum limit is termed (coded) as −1. The modified equation or coded equation is very much useful in order to find the comparative effect of the process parameters by relating the coefficient of factors (Table7).Table 7
RSM parameters for copper extraction.
Std
Run
Factor 1
Factor 2
Factor 3
A: CD
B: solvent
C: time
A/dm2
ml
Hrs
1
12
1
400
2
2
14
19
400
2
3
2
1
600
2
4
4
19
600
2
5
18
1
500
1
6
13
19
500
1
7
16
1
500
3
8
11
19
500
3
9
8
10
400
1
10
1
10
600
1
11
6
10
400
3
12
7
10
600
3
13
5
10
500
2
14
9
10
500
2
15
17
10
500
2
16
3
10
500
2
17
15
10
500
2The final equation in terms of actual factors is(6)Extract=191.503+2.32716∗CD+−0.773056∗solvent+−11.3333∗time+0.000555556∗CD∗solvent+0.833333∗CD∗time+0.025∗solvent∗time+−0.0802469∗CD2+0.0008∗solvent2+1.5∗time2.Equation (5) in terms of process parameters could be utilized to predict the response for the provided levels of each parameter. In this equation, the original units of each parameters should be considered for each levels. In order to evaluate the comparative effect of each factor, the above equation should not be considered since the coefficients are balanced to embrace the units of each parameters. Also, the intercept does not falls at design space center (Table8). In this contour plot, the red zone indicates extract percentages above 85%. And yellow and blue zones indicate 60 to 70% and below 40% extraction of copper (Figures 9 and 9(a)).Table 8
Box–Behnken experimental design table for recovery of copper.
Std
Run
Factor 1
Factor 2
Factor 3
A: CD
B: solvent
C: time
A/dm2
ml
Hrs
1
12
1
400
2
2
14
19
400
2
3
2
1
600
2
4
4
19
600
2
5
18
1
500
1
6
13
19
500
1
7
16
1
500
3
8
11
19
500
3
9
8
10
400
1
10
1
10
600
1
11
6
10
400
3
12
7
10
600
3
13
5
10
500
2
14
9
10
500
2
15
17
10
500
2
16
3
10
500
2
17
15
10
500
2
18
10
10
500
2Figure 9
Contour plot for recovery of copper.


## 3.6. Analysis of Variance (ANOVA)

Analysis of variance is used to determine the significant effects of process variables on current efficiency along with the factor coding. The sum of squares is found to be Type III—partial derived from the ANOVA quadratic model. The modelF value of 155.08 in the Table 9 implies the model is significant. A minimum value of 0.01% is possible for the F value due to noise. P values less than 0.0500 indicate model terms are significant. In this case, A, B, C, AC, A2, and B2 are significant model terms. Values greater than 0.1000 indicate the model terms are not significant. If there are many insignificant model terms (not counting those required to support hierarchy), model reduction may improve the model. The lack of fit F value is nil that implies the lack of fit is significant. The coefficient represents the expected change in response per unit change in factor value, when all remaining factors were constant. The intercept in an orthogonal design is the overall average response of all the runs. The coefficients are adjustments around the average factor settings. When the factors are orthogonal, the VIFs are 1; VIFs greater than 1 indicate multicolinearity; the higher the VIF, the more severe the correlation of factors. As a rough rule, VIFs less than 10 are tolerable. Hence, from the data obtained (Table 10), the VIF Values of lead are found to be tolerable.Table 9
ANOVA quadratic model for copper.
Source
Sum of squares
DOF
Mean square
F value
p value
Model
7763.50
9
862.61
155.08
<0.0001
Significant
A-CD
4608.00
1
4608.00
828.40
<0.0001
B-solvent
544.50
1
544.50
97.89
<0.0001
C-time
1922.00
1
1922.00
345.53
<0.0001
AB
1.0000
1
1.0000
0.1798
0.6827
AC
225.00
1
225.00
40.45
0.0002
BC
25.00
1
25.00
4.49
0.0668
A2
184.36
1
184.36
33.14
0.0004
B2
279.27
1
279.27
50.21
0.0001
C2
9.82
1
9.82
1.77
0.2206
Residual
44.50
8
5.56
Lack of fit
44.50
3
14.83
Pure error
0.0000
5
0.0000
Total
7808.00
17Table 10
Coefficients in terms of coded factors for copper.
Factor
Coefficient estimate
DOF
Standard error
95% CI low
95% CI high
VIF
Intercept
48.00
1
0.9629
45.78
50.22
A-CD
24.00
1
0.8339
22.08
25.92
1.0000
B-solvent
8.25
1
0.8339
6.33
10.17
1.0000
C-time
15.50
1
0.8339
13.58
17.42
1.0000
AB
0.5000
1
1.18
−2.22
3.22
1.0000
AC
7.50
1
1.18
4.78
10.22
1.0000
BC
2.50
1
1.18
−0.2193
5.22
1.0000
A2
−6.50
1
1.13
−9.10
−3.90
1.02
B2
8.00
1
1.13
5.40
10.60
1.02
C2
1.50
1
1.13
−1.10
4.10
1.02


## 3.7. Model Terms

For a standard deviation of 1 the power calculations are performed using response type “continuous,” and the parameters are Δ = 2 andσ = 1. The power is evaluated over −1 to +1 coded factor space (Table 11). The standard errors should be similar to each other in a balanced design. The ideal VIF value should be 1, VIFs above 10 are cause for concern and VIFs above 100 are cause for alarm, indicating coefficients are poorly estimated due to multicolinearity, where ideal Ri2 is 0.0. High Ri2 means terms are correlated with each other, possibly leading to poor models. If the design has multilinear constraints, then multicolinearity will exist to a greater degree. This inflates the VIFs and the Ri2, rendering these statistics would not perform well. Hence, FDS could be used. Power is an inappropriate tool to evaluate response surface designs. Use prediction-based metrics provided in this program via fraction of design space (FDS) statistics.Table 11
Model terms in RSM for copper.
Term
Standard error
VIF
Ri2
Power (%)
A
0.3536
1
0.0000
69.8
B
0.3536
1
0.0000
69.8
C
0.3536
1
0.0000
69.8
AB
0.5000
1
0.0000
42.1
AC
0.5000
1
0.0000
42.1
BC
0.5000
1
0.0000
42.1
A2
0.4787
1.01852
0.0182
95.4
B2
0.4787
1.01852
0.0182
95.4
C2
0.4787
1.01852
0.0182
95.4


## 3.8. Fit Statistics

A predictedR2 implies that the overall mean may be a better predictor of the response than the current model. In some cases, a higher order model may also predict better. Adeq. precision measures the signal to noise ratio. A ratio greater than 4 is desirable. A ratio of 44.9 indicates an adequate signal. This model can be used to navigate the design space. The optimization of current efficiency is shown in Figure 10. The optimum extraction of 69% Cu is obtained at current density = 19 A dm−2, solvent ratio = 5 : 2, and electrolysis time = 4 hour (Figures 11 and 12). The significance of regression coefficients was analyzed using the p-test and t-test. The p values are used to check the effect of interaction among the variables. A larger magnitude of t-value and a smaller magnitude of p value are significant in the corresponding coefficient term. The coefficient of current efficiency and the corresponding t and p values are shown in (Table 12). Finally, the coefficients in the interaction terms for current density-electrolysis time is significant compared to current density-solvent ratio and current density-electrolysis time.Figure 10
Current density vs extract % for copper.Figure 11
Solvent vs extract % for lead.Figure 12
Time vs extract % for lead.Table 12
Fit statistics.
Std. dev.
2.36
Mean
49.33
CV (%)
4.78
R
2
0.9943
AdjustedR2
0.9879
PredictedR2
0.9088
Adeq. Precision
44.9395


## 4. Conclusion

The ammonia-lead nitrate and ammonia-copper sulphate system have been employed as a leaching agent for recovery of lead and copper from scraped printed circuit board wastes. A two-stage leaching was employed, wherein the first stage consisted of leaching the scrap board with 0.1 M Pb(NO3)2 and 0.1 M CuSO4 which results in the selective dissolution of lead and copper leaching rate, and other metals was found in lower amounts, respectively. The undissolved residue portion from the leaching stage containing nickel, tin, and silica were leached out in respective treatments. The current efficiency was found to increase with current density and concentration ratio with the contact time in acid bath. Hence, 73.29% lead and 82.17% copper have been successfully recovered from the electrolysis process. And, also by RSM Software prediction, the recovery of lead and copper are as 78.25% and 89.1%, respectively. In addition to the quadratic model equation, ANOVA, model terms, and fit statistics were also tested for the experimental conditions.



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*Source: 1067512-2018-11-01.xml*