In this research, response surface methodology (RSM) under Design-Expert 7 software (trial version) was applied for determining the experimental conditions and modeling the experimental results. RSM, as a multivariate technique which applies mathematical and statistical methods, can be used to fit a polynomial equation to a set of data for the final goal of finding the optimized levels of different variables when a response is influenced by several factors (Bezerra et al. 2008). Central composite design (CCD) under RSM was used to design the experiments. CCD is an ideal choice for sequential experimentation which can test lack of fit even at low number of design points. Based on specified independent variables, which were chosen based on literature review and preliminary tests and according to the selected second order experimental design, an experimental matrix was developed by RSM for carrying out the experiments. The number of experiments with three factors (initial copper concentration, 1–5 mg L−1; reaction time, 20–90 min; and current intensity, 0.1–0.4 A) at five coded levels (, 1, 0, 1, ) was 20 based on N = k2+2k+cp, where k is the number of factors and cp is the number of replicates at the central point(Bezerra et al. 2008). Therefore, 15 experiments consisting of eight factorial points and six axial points were augmented with five replications at the design center in order to evaluate the pure error. They were carried out in a randomized order as required in design procedures. Table 1 shows independent variables at coded and actual levels. Table 2 presents the experimental conditions suggested by CCD.

Table 1

Operational factors ranged at actual and coded levels

VariablesSymbolsRange of actual and coded variables
α−10+1+α
Initial copper concentration (mg L−1A(x11.81 4.19
Retention time (min) B(x220 34.19 55 75.81 90
Current intensity (A) C(x30.1 0.16 0.25 0.34 0.4
VariablesSymbolsRange of actual and coded variables
α−10+1+α
Initial copper concentration (mg L−1A(x11.81 4.19
Retention time (min) B(x220 34.19 55 75.81 90
Current intensity (A) C(x30.1 0.16 0.25 0.34 0.4
Table 2

Suggested experimental matrix by CCD based on observed and predicted results

Run orderIndependent variables
Copper removal %
Energy consumption kWh m−3
Initial copper concentration (mg L−1)Retention time (min)Current intensity (A)ActualPredictedActualPredicted
55 0.25 95 96.97 8.99 8.84
1.81 34.19 0.16 80 79.67 2.6 2.77
1.81 75.81 0.34 93 93.61 18.04 18.11
55 0.25 99 97.77 8.93 8.81
90 0.25 95 96.08 14.81 14.59
55 0.4 81 79.55 15.76 15.82
55 0.25 96.94 96.47 9.05 8.97
4.19 75.81 0.16 91 88.7 5.91 6.16
55 0.25 96 96.47 8.93 8.97
10 55 0.25 96.98 96.47 8.93 8.97
11 1.81 75.81 0.16 90 89.65 6.06 6.25
12 55 0.25 94.98 96.47 8.93 8.97
13 4.19 34.19 0.16 80 78.95 2.64 2.77
14 4.19 75.81 0.34 93.55 93.38 18.10 18.14
15 55 0.25 98 96.47 8.93 8.97
16 20 0.25 80 79.66 3.20 3.15
17 1.81 34.19 0.34 82 83.83 7.94 7.89
18 55 0.25 96 96.47 8.99 8.97
19 55 0.1 69.93 72.12 1.78 1.45
20 4.19 34.19 0.34 83.99 83.83 7.99 8.01
Run orderIndependent variables
Copper removal %
Energy consumption kWh m−3
Initial copper concentration (mg L−1)Retention time (min)Current intensity (A)ActualPredictedActualPredicted
55 0.25 95 96.97 8.99 8.84
1.81 34.19 0.16 80 79.67 2.6 2.77
1.81 75.81 0.34 93 93.61 18.04 18.11
55 0.25 99 97.77 8.93 8.81
90 0.25 95 96.08 14.81 14.59
55 0.4 81 79.55 15.76 15.82
55 0.25 96.94 96.47 9.05 8.97
4.19 75.81 0.16 91 88.7 5.91 6.16
55 0.25 96 96.47 8.93 8.97
10 55 0.25 96.98 96.47 8.93 8.97
11 1.81 75.81 0.16 90 89.65 6.06 6.25
12 55 0.25 94.98 96.47 8.93 8.97
13 4.19 34.19 0.16 80 78.95 2.64 2.77
14 4.19 75.81 0.34 93.55 93.38 18.10 18.14
15 55 0.25 98 96.47 8.93 8.97
16 20 0.25 80 79.66 3.20 3.15
17 1.81 34.19 0.34 82 83.83 7.94 7.89
18 55 0.25 96 96.47 8.99 8.97
19 55 0.1 69.93 72.12 1.78 1.45
20 4.19 34.19 0.34 83.99 83.83 7.99 8.01

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