## 2 Materials and Methods
### Experimental coagulation-Flocculation Protocol  
Laboratory evaluation of coagulation-flocculation was conducted using a VELP SCIENTIFICA Jar Test apparatus, a standard 4-station rotational device with speeds ranging from 20 to 200 rpm. Tests were performed in 1000 mL beakers following the standard protocol of coagulation-flocculation-sedimentation, after adjusting the solution pH using HCl (1 mol/L) or NaOH (1 mol/L). After settling, the supernatant was sampled, and pollution parameters including COD, turbidity, UV 254, and phosphates were measured.  
In this study, the response surface method (RSM) based on Box-Behnken design (BBD) was used as the experimental methodology using Minitab 18 software (Minitab, LLC, State College, PA, USA). The RSM is used to determine optimal ranges based on statistical techniques, and determine whether a process condition leads to an optimal value of a response variable. Through RSM, a quadratic polynomial equation was developed to predict the response as a function of the independent variables involving their interactions. This enables second-order response surfaces to be modeled. The most commonly used designs at this stage are the Box-Behnken design (BBD) and the central composite design (CCD). All these optimization designs were used to obtain and fit experimental data with a polynomial multiple linear regression model to characterize the response surface.  
[PERSON] and [PERSON] introduced an alternative type of experimental design for second-order models that allows for the estimation of certain interactions [26]. The BBD has the following properties: (i) it requires three levels for each of the factors; \(-1\), 0 and \(+1\) to ensure the orthogonality condition; (ii) it possess the sequentiality property; (iii) prediction errors are lower than experimental errors. According to [PERSON] et al., this model offers greater efficiency and cost effectiveness than other three-level models, namely the central composite design, because it allows for the selection of points in a three-level factorial arrangement [27]. According to the BBD, three factors (k = 3) were taken into account in the coagulation-flocculation performance, namely pH, the organic coagulant dosage (PSE) and a chemical coagulant dosage (FeCl3). This design required 15 experiments with three central points, as mentioned in Table 2, and mathematical models for each response (turbidity, COD, UV 254, and phosphate) were obtained using Equation (1).  
\[\mathrm{Y_{i}}=\mathrm{B_{0}}+\sum\
olimits_{i=1}^{k}\mathrm{B_{i}}*\mathrm{X_ {i}}+\sum\
olimits_{i=1}^{k}\mathrm{B_{ii}}*\mathrm{X_{i}^{2}}+\sum\
olimits_{ i}^{k}=1\mathrm{B_{ij}}*\mathrm{X_{i}}*\mathrm{X_{j}}+\varepsilon \tag{1}\]  
\[\begin{array}{l}j=2\\ i\
eq j\end{array}\]  
where \(\mathrm{Y_{i}}\) is the response variable; K: the number of factors (K = 3); \(\mathrm{X_{i}}\): the parameters studied; \(\mathrm{\beta_{0}}\): the constant value; and \(\mathrm{\beta_{i}}\), \(\mathrm{\beta_{ii}}\), \(\mathrm{\beta_{ij}}\): the regression coefficients.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Value** & **Algerian Standards [25]** \\ \hline Turbidity (NTU) & 250 & / \\ COD (mg/L) & 640 & 120 \\ UV 254 & 0.893 & / \\ Temperature (\({}^{\circ}\)C) & 24 & 30 \\ Phosphate (mg/L) & 0.115 & / \\ Salinity (mg/L) & 5.5 & / \\ Conductivity (mS/cm) & 9.15 & \\ pH & 8.25 & 6.5-8.5 \\ Sulfate (mg/L) & 2.35 & / \\ TAC (mg/L CaCO\({}_{3}\)) & 100 & / \\ Chloride (mg/L) & 4.2 & / \\ \hline \hline \end{tabular}
\end{table}
Table 1: Raw water characterization.