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Design-Expert software was used to optimize the experimental results. The desired goal for each response and factors affecting the response was chosen from five options including none, maximize, minimize, target, or in range. Since various concentrations of copper tested in this study did not alter the removal efficiency of copper remarkably, this parameter was targeted at the central value. To adopt a cost-driven approach and also to save energy, current intensity was minimized. But to compensate for reduced efficiency due to the decreased current intensity and to achieve the maximum rate of copper removal, residence time was maximized. Accordingly, 3 mg L−1 copper concentration, 75.8 min electrolysis time, and 0.16 A current intensity (as minimized goal) were selected as numerical optimization option of RSM to achieve the best removal efficiency in the range of 69.9–99% (the goal was maximized) by consuming the least possible amount of energy in the range of 1.78–18 kWh m−3 (the goal was minimized). After determining the favorable criteria for factors and responses, RSM proposed four solutions to achieve the optimization goals. Table 4 presents the combinations of the factors optimized for satisfying the requirements placed on factors and responses. After numerical optimization, the point prediction option of RSM, which had predicted responses under optimal experimental conditions of each solution, was applied to verify optimization results. The program predicted 91.42% copper removal efficiency (corresponding importance: 5) and 7.28 kWh m−3 energy consumption (corresponding importance: 3) under optimal values of variables: 3 mg L−1 copper concentration, 75.81 min reaction time, and 0.18 A current intensity suggested in the solution number 1. In the point prediction option of the program, a prediction interval at confidence level of 95% was determined for every response. The low and high prediction intervals of responses were 87–95.8% for copper removal and 6.78–7.77 kWh m−3 for energy consumption. To validate the suggested optimum values, an extra experiment was performed under conditions proposed by the solution number 1. The experiment showed 91% copper removal and 7.05 kWh m−3 energy consumption; both values were quite close to the estimated values and were also between the foreseen ranges by point prediction. Based on the optimization results, only 0.27 mg L−1 copper remained in the final effluent, which is much less than what is permitted by the USEPA (1.3 mg L−1) for the presence of copper in industrial treated effluents.

Table 4

Optimization conditions predicted by CCD to achieve maximum rate of copper removal using least probable energy

SolutionX1 : Copper conc. (mg L−1)X2 : Time of electrolysis (min)X3 : Current intensity (A)Y1 : Copper removal (%)Y2 : Consumption of energy (kWh m−3)
75.81 0.18 91.42 7.28 
75.81 0.17 91.315 7.235 
75.81 0.18 91.548 7.335 
75.81 0.19 92.882 7.94 
SolutionX1 : Copper conc. (mg L−1)X2 : Time of electrolysis (min)X3 : Current intensity (A)Y1 : Copper removal (%)Y2 : Consumption of energy (kWh m−3)
75.81 0.18 91.42 7.28 
75.81 0.17 91.315 7.235 
75.81 0.18 91.548 7.335 
75.81 0.19 92.882 7.94 

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