# Simultaneous Electrochemical Removal of Selenium and Strontium from Aqueous Solution
## 2 Materials and Methods
### Design of Experiments  
The experiments were conducted following the design of experiments (DoE) method combined with the response surface methodology (RSM). This approach was utilized to understand the functional relationships between process variables and their influence on the numerical response, in this case, the Se and Sr removal efficiency. The primary advantage of the statistical design of experiments lies in significantly reducing the number of experiments required, as it allows for the prediction of variable behavior across a broad range of conditions [34; 35]. This enables obtaining a lot of data from a relatively limited dataset. Within the RSM framework, a Box-Behnken design (BBD) was adopted--a three-level optimization approach (low, medium, and high variable values) that helps refine experimental conditions and develop a polynomial regression model for predicting responses. This method proves particularly effective in scenarios with non-linear interactions between independent variables and dependent outcomes [36]. For example, the quadratic model, a second-order RSM formulation, can be expressed as  
\[Y(x)=\beta_{0}+\sum_{i=1}^{n}\beta_{i}x_{i}+\sum_{i=1}^{n}\sum_{j=1}^{n}\beta _{ij}x_{i}x_{j}+\varepsilon \tag{1}\]  
where \(Y\) represents the result derived from input variables \(x_{n}\), while \(\beta_{i}\) and \(\beta_{ij}\) denote the first- and second-order regression coefficients for individual and interactive variable effects, respectively, and \(\varepsilon\) accounts for errors in the observed response \(Y\)[36]. The goal of this study was to determine the most influential parameters and their optimal values for maximizing the efficiency of the Se and Sr removal from water. Five parameters (factors) were tested: electrode material, applied current, number of electrodes, operating time, and initial pH value of the solution. As shown in Table 2, the electric current, electrode surface, and treatment time were numeric factors tested at three levels, while the electrode material and pH value were categorical factors. The treatment times of 5, 15, or 25 min represented the EC treatment time in one phase. The total EC treatment times for both stages were 10, 30, and 50 min, respectively. The applied current was consistent across both EC reactors during the EC phase of the treatment. The active (anodic) surface of the electrodes was adjusted by varying the number of electrodes used, which means that the current density varied from 72 (5 A, 8 electrodes per EC reactor) to 720 (25 A, 4 electrodes per EC reactor) A m\({}^{-2}\). Two electrode materials were used: aluminum (Al) and iron (Fe). The pH factor in this study had three settings: unchanged initial pH (pH control stage of the treatment was skipped), a middle range, and a maximum range. For the middle range, the pH was set between 5 and 6 for acidic conditions and 8 and 9 for alkaline conditions. For the maximum range, it was set between 2.5 and 3.5 for acidic conditions and 9.5 and 10.5 for alkaline conditions. These pH levels were achieved by applying 120 V to graphite electrodes in the electrochemical pH control reactor for either 5 min (middle range) \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Factor** & **Name** & **Units** & **Type** & **Subtype** & **Minimum** & **Mean** & **Maximum** \\ \hline A & I & A & Numeric & Continuous & 5 & 15 & 25 \\ B & Electrode number & & Numeric & Continuous & 4 & 6 & 8 \\ C & t & min & Numeric & Continuous & 5 & 15 & 25 \\ D & Electrode material & & Categoric & Nominal & Al & Fe \\ E & pH & & Categoric & Nominal & No pH & Middle & Maximum \\  & & & & adjustment & range & range \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Factors used and their characteristics. or 15 min (maximum range), producing a current of 7 to 10 A. In the second phase of the treatment, adjusting the pH became more challenging due to the lower electroconductivity of the solution, which required either more time or a higher current to reach the desired pH ranges.