# Evaluation of Agricultural Soil-Improving Zeolite for Improving Irrigation Water Quality
## 2 Materials and Methods
### Statistical Factorial Design  
Aiming to determine the optimal system configuration while minimizing the total number of experiments required, a preliminary factorial design was conducted. This design identified factors with significant effects on response and elucidated how a factor's impact varies, considering the levels of other factors. The exploration of interactions between factors necessitates the application of statistical experimental designs, as optimizing the system cannot be achieved by varying one factor at a time while keeping other factors constant [27,28]. In this sense, and aiming to optimize the process, a central composite rotatable design (CCRD) with two factorial variables (2\({}^{2}\)) was employed, where the zeolite content (g/L) and contact time (min) served as independent variables, while sodium (Na) and boron (B) concentrations constituted the dependent or response variables. A total of 12 batch experiments were conducted by the statistical design matrix and the studied factorial levels, as presented in Table 1. To minimize experimental error, the study included a quadruplicate repetition of the central point. Initial levels for the factorial setup were determined based on the literature [29, 30, 31, 32, 33]. Once the effective range of removal variables was identified through a bibliographic review, preliminary removal assays were conducted by the same scientific team (unpublished data). Building upon the outcomes of these preliminary assays, the minimum and maximum adsorbent content for use in this study were subsequently established. The values for the axial points (\(-1.4142\) and \(+1.4142\)) were determined through interpolation by the model's methodology [27,34].  
All experiments were conducted at a constant temperature of 22 \(\pm\) 2 \({}^{\circ}\)C. Each trial involved using 100 mL of liquid sample in non-sterile polypropylene Erlenmeyer flasks with a maximum capacity of 250 mL and a standardized neck (Kartell Labware, Noviglio, Italy). Cellulose acetate membranes of 0.20 \(\upmu\)m and 47 mm in diameter (Teknokroma, Barcelona, Spain) were employed for sample water filtration.  
The experimental data were analyzed using appropriate statistical methods for the applied experimental design. Mathematical models for each response were assessed through multiple linear regression analysis and were processed using STATISTICA 18 software from StatSoft (TIBCO Software Inc., Palo Alto, CA, USA). Statistically significant terms in the model, whether linear or nonlinear, were determined through analysis of variance (ANOVA) for each response, with a significance level set at \(p<0.05\) (95% confidence).  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Run** & \(\mathbf{X_{1}}\) & \(\mathbf{X_{2}}\) & **Zeolite Content (g/L)** & **Contact Time (min)** \\ \hline
1 & \(-1\) & \(-1\) & 12.43 & 194.33 \\ \hline
2 & 1 & \(-1\) & 54.84 & 194.33 \\ \hline
3 & \(-1\) & 1 & 12.43 & 765.67 \\ \hline
4 & 1 & 1 & 54.84 & 765.67 \\ \hline
5 & 0 & 0 & 33.64 & 480.00 \\ \hline
6 & 0 & 0 & 33.64 & 480.00 \\ \hline
7 & 0 & 0 & 33.64 & 480.00 \\ \hline
8 & 0 & 0 & 33.64 & 480.00 \\ \hline
9 & \(-1.4142\) & 0 & 3.64 & 480.00 \\ \hline
10 & 0 & \(-1.4142\) & 33.64 & 76.00 \\ \hline
11 & 1.4142 & 0 & 63.63 & 480.00 \\ \hline
12 & 0 & 1.4142 & 33.64 & 884.00 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Factorial design (2\({}^{2}\)) results for sodium and boron retention in waters intended for agricultural irrigation, where \(X_{1}\) and \(X_{2}\) represent the variable levels for zeolite content and contact time, respectively.  
Identifying the significant factors in the model allowed for a reliable prediction of performance through interpolation across a range of data, facilitating the construction of response surface graphs (3D). These graphs contribute to a better understanding of the investigated process [35].