## 3 Results
### Modeling of Textile WW Treatment in the Laboratory SD Setup  
Efficient modeling and monitoring methods are becoming very important in each rigorous industrial WW treatment system organized in any processing/manufacturing industry. Therefore, improving the WW treatment performance requires an accumulation of accurate knowledge of existing or newly designed WW treatment systems, and also demands mathematical modeling and optimization. The issue of modeling associated with optimization is very problematic due to model complexity (i.e., several variables, kinetic and stoichiometric parameters, etc.). Therefore, the key operating parameters (namely, the three independent variables) influencing the removal efficiency were selected, and the prediction model efficiency and sensitivity analysis by known statistics methodology was performed, because it is difficult to simultaneously consider all selected variables while predicting the results. The designing and modeling of the WW treatment process in the SD setup was performed by using an empirical experimental planning with an active central composite rotatable 2\({}^{3}\) order design, considering three independent variables (\(z_{1}\), \(z_{2}\), \(z_{3}\)) and two response functions or optimization criteria--i.e., suspended solids removal (\(Y_{1}\)) and discoloration (\(Y_{2}\)). The real (\(z_{i0}\)) and coded basic (\(X_{i0}\)) values of the three studied independent variables are shown in Table 3, together with their variation steps (\(\Delta z_{i0}\)). The experimental variation field for the operating time (\(X_{3}\)) was short (no more than 25-30 min) due to two main reasons: (i) energy cost minimization and (ii) if additional chemical oxidative processes are applied (e.g., Fenton oxidation, especially for organics removal); these operate efficiently and attain high removals after a short period of time (frequently no more than 20-30 min). The experimental planning design is presented in Tables 4 and 5, with the experimental design matrixes for \(Y_{1}\) and \(Y_{2}\) associated with their experimental values (\(Y_{i\epsilon}\)) and calculated with the proposed model values (\(Y_{i}\)). The experimental results from Tables 4 and 5 enabled the proposal of the mathematical models after the significance evaluation of the model coefficients, using the Student's test:  
\[Y_{1}=36.1903-2.0696X_{1}+1.4709X_{3}+1.4819{X_{1}}^{2}+2.7659{X_{3}}^{2}+1.594 6X_{1}X_{3}-1.2919X_{2}X_{3}, \tag{4}\]  
\[Y_{2}=16.4018-1.3847X_{1}+1.377{X_{1}}^{2}. \tag{5}\]  
The average deviation value of the experimental data from the calculated data with the proposed model was \(-0.390\%\) for \(Y_{1}\) and \(+3.379\%\) for \(Y_{2}\), which was within the acceptable limits (\(\pm 10\%\)). The validation of the models was carried out by an appropriate analysis of variance by Fisher constant (F), correlation coefficients (R\({}_{\rm{Y}x_{1}x_{2}x_{3}}\)), and Fisher test (F\({}_{\rm{C}}\)). The calculated values of F constant were F(\(Y_{1}\)) = 45.383 for \(Y_{1}\) and F(\(Y_{2}\)) = 28.371 for \(Y_{2}\), higher than F\({}_{\rm{tab,critical}}\) = 4.6, underlining the possible influence of the independent variables on the response functions \(Y_{1}\) and \(Y_{2}\). Moreover, the calculated correlation coefficients for both response functions were high enough--namely, R\({}_{\rm{Y}1,x_{1}x_{2}x_{3}}\) = 0.8839 for \(Y_{1}\) and R\({}_{\rm{Y}2,x_{1}x_{2}x_{3}}\) = 0.530 for \(Y_{2}\)--indicating a relative good correlation between the experimental and the modeled data. Thus, the important influence of the independent variables on each response function (especially \(Y_{1}\) and only of one independent variable (\(X_{1}\)) in the case of \(Y_{2}\)) was sustained.