## 3 Results
### Modeling of Textile WW Treatment in the Laboratory SD Setup
One can observe a minimum of suspended solids removal (\(Y_{1}\) = 35.467%) for \({X_{1}}^{*}\) = 0.6984 and a local maximum (\(Y_{1}\) = 44.351%) for a WW flowrate of 24.19 L/h, a rotational speed of 300 rpm, and a working time interval of 15 min. The dependence of the suspended solids removal (\(Y_{1}\)) on the rotational speed (\(X_{2}\)) indicates a constant value (\(Y_{1}\) = 36.190%) for all \({X_{2}}^{*}\) values (Figure 9b). The variation in\(Y_{1}\) with an increase in the working time (\(X_{3}\)) indicates a minimum removal (\(Y_{1}\) = 36.777%) for \({X_{3}}^{*}\) = +0.2659 (a local minimum for a flowrate of 20 L/h, a rotational speed of 300 rpm, and an operating time of 16.33 min (Figure 9c). One can observe the existence of a minimum discoloration degree (\(Y_{2}\) = 16.054%) for \({X_{1}}^{*}\) = 0.5025 and also of a local maximum (\(Y_{2}\) = 23.046%) for \({X_{1}}^{*}\) = -1.75 in the investigated experimental field. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Exp.** & \multirow{2}{*}{**No.**} & \multirow{2}{*}{**\(Z_{1}\)**} & \multirow{2}{*}{**\(Z_{2}\)**} & \multirow{2}{*}{**\(Z_{3}\)**} & \multirow{2}{*}{**\(X_{1}\)**} & \multirow{2}{*}{**\(X_{2}\)**} & \multirow{2}{*}{**\(X_{3}\)**} & \multirow{2}{*}{**\(Y_{2e}\)**} & \multirow{2}{*}{**\(Y_{2}\)**} \\  & & & & & & & & [\%] & [\%] \\ \hline
1 & 14 & 150 & 10 & \(-\)1 & \(-\)1 & \(-\)1 & 18.244 & 19.165 & \(-\)5.047 \\
2 & 26 & 150 & 10 & 1 & \(-\)1 & \(-\)1 & 20.058 & 16.395 & 18.263 \\
3 & 14 & 450 & 10 & \(-\)1 & 1 & \(-\)1 & 19.804 & 19.165 & 3.228 \\
4 & 26 & 450 & 10 & 1 & 1 & \(-\)1 & 17.954 & 16.395 & 8.684 \\
5 & 14 & 150 & 20 & \(-\)1 & \(-\)1 & 1 & 19.333 & 19.165 & 0.870 \\
6 & 26 & 150 & 20 & 1 & \(-\)1 & 1 & 20.711 & 16.395 & 0.164 \\
7 & 14 & 450 & 20 & \(-\)1 & 1 & 1 & 19.260 & 19.165 & 0.494 \\
8 & 26 & 450 & 20 & 1 & 1 & 1 & 17.737 & 16.395 & 7.567 \\
9 & 10 & 300 & 15 & \(-\)1.682 & 0 & 0 & 25.644 & 22.630 & 11.754 \\
10 & 30 & 300 & 15 & \(+\)1.682 & 0 & 0 & 14.509 & 17.971 & \(-\)23.859 \\
11 & 20 & 102 & 15 & 0 & \(-\)1.682 & 0 & 18.462 & 16.402 & 11.159 \\
12 & 20 & 550 & 15 & 0 & +1.682 & 0 & 15.524 & 16.402 & \(-\)5.654 \\
13 & 20 & 300 & 7 & 0 & 0 & \(-\)1.682 & 19.042 & 16.402 & 13.865 \\
14 & 20 & 300 & 24 & 0 & 0 & +1.682 & 18.498 & 16.402 & 11.332 \\
15 & 20 & 300 & 15 & 0 & 0 & 0 & 18.752 & 16.402 & 12.533 \\
16 & 20 & 300 & 15 & 0 & 0 & 0 & 18.027 & 16.402 & 9.015 \\
17 & 20 & 300 & 15 & 0 & 0 & 0 & 15.270 & 16.402 & \(-\)7.412 \\
18 & 20 & 300 & 15 & 0 & 0 & 0 & 13.819 & 16.402 & \(-\)18.690 \\
19 & 20 & 300 & 15 & 0 & 0 & 0 & 15.597 & 16.402 & \(-\)5.160 \\
20 & 20 & 300 & 15 & 0 & 0 & 0 & 17.048 & 16.402 & 3.790 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Experimental planning matrix for \(Y_{2}\) (discoloration degree). Figure 8: Variation in the WW suspended solids removal (\(Y_{1}\)) vs. two independent variables (one variable was maintained at the basic value) associated with its isoline: (**a**) \(Y_{1}=Y\)(\(X_{1}\),\(X_{2}\),0); (**a1**) isolines \(-Y_{1}\)(\(X_{1}\),\(X_{2}\),0); (**b**) \(Y_{1}=Y\)(\(X_{1}\),0,\(X_{3}\)); (**b1**) isolines \(-Y_{1}\)(\(X_{1}\),0,\(X_{3}\)); (**c**) \(Y_{1}=Y\)(0,\(X_{2}\),\(X_{3}\)); (**c1**) isolines \(-Y_{1}\)(0,\(X_{2}\),\(X_{3}\)). Overall, the application of classical optimization methodology leads to the conclusion that the \(Y_{1}\) function (suspended solids removal) has a distinct minimum (\(Y_{1}\) = 35.4677%), corresponding to \(X_{1}\)* = \(-\)0.6983, \(X_{2}\)* = 2.0005, and \(X_{3}\)* = 0. Transposed to real variables, these values correspond to a WW flowrate of 24.19 L/h, a rotational speed of 600 rpm, and a working time period of 15 min. Moreover, for the proposed empirical \(Y_{1}\) model, a local maximum exists in the investigated experimental field (\(Y_{1}\) = 45.624%), corresponding to \(X_{1}\)* = 0, \(X_{2}\)* = 0, and \(X_{3}\)* = +1.682, meaning a WW flowrate of 20 L/h, a rotation speed of 300 rpm, and a working time of 15 min.