## 4 Discussions  
Figure 3a-f present the influence of two independent variables (one independent variable kept at the basic value) vs. reactive Bred dye removal (\(Y_{1}\)) (i.e., \(Y\) = \(Y_{1}\)(\(X_{1}\),\(X_{2}\),0), \(Y\) = \(Y_{1}\)(\(X_{1}\),0,\(X_{3}\)) and \(Y\) = \(Y_{1}\)(0,\(X_{2}\),\(X_{3}\))). Figure 3: Variation of Bred dye removal (\(Y_{1}\)) vs. two independent variables (one variable kept at its basic value) and its isolines. (**a**) \(Y=Y_{1}(0\),\(X_{2}\),\(X_{3}\)); (**b**) Isolines for \(Y=Y_{1}(0\),\(X_{2}\),\(X_{3}\)); (**c**) \(Y=Y_{1}(X_{1}\),\(0\),\(X_{3}\)); (**d**) Isolines for \(Y=Y_{1}(X_{1}\),\(0\),\(X_{3}\)); (**e**) \(Y=Y_{1}(X_{1}\),\(X_{2}\)); (**f**) Isolines for \(Y=Y_{1}(X_{1}\),\(X_{2}\),\(0\)). Figure 4a-f illustrate the dependence of reactive dye removal (\(Y_{2}\)) vs. two independent variables (one independent variable kept at the basic value) (i.e., \(Y=Y_{2}(X_{1}\),\(X_{2}\),0), \(Y=Y_{2}(X_{1}\),0,\(X_{3})\) and \(Y=Y_{2}(0\),\(X_{2}\),\(X_{3})\)). Figure 4: Variation of Bred dye removal (\(Y_{2}\)) vs. two independent variables (one variable kept at its basic value) and its isolines. (**a**) \(Y=Y_{2}(0\),\(X_{2}\),\(X_{3}\)); (**b**) Isolines for \(Y=Y_{2}(0\),\(X_{2}\),\(X_{3}\)); (**c**) \(Y=Y_{2}(X_{1}\),0,\(X_{3})\); (**d**) Isolines for \(Y=Y_{2}(X_{1}\),0,\(X_{3})\); (**e**) \(Y=Y_{2}(X_{1}\),\(X_{2}\),0); (**f**) Isolines for \(Y=Y_{2}(X_{1}\),\(X_{2}\),0). The graphical representations of the BRed dye removal (\(Y_{1}\), %) variation in the experimental field of two independent variables (on isolines) in Figure 3 for biosorbent 1 and Figure 4 for biosorbent 2 indicate the following aspects:  
1. The biosorbent concentration (\(X_{1}\)) had one of the highest levels of significance in obtaining a high dye removal degree, with higher values recommended than the basic (\(X_{1}>0\)) where the local maximum dye removal was no more than 23% for \(Y_{1}\) (Figure 3c,d) and 65% for \(Y_{2}\) (Figure 3a,b);
2. High local dye removal (\(Y\)) close to the value of 52% for \(Y_{1}\) function and 80% for \(Y_{2}\) function can be performed for an initial dye concentration close to 50 mg/L in the aqueous system studied (Figures 3a,b and 4c,d);
3. A biosorption time higher than 8 h (as a possible exchange period at work) is beneficial but at least 6 h (basic value of \(X_{3}\)) are obligatory for dye removals of at least 35% for \(Y_{1}\) (or \(>52.878\%\) experimentally performed, Figure 3e,f) and 50% for \(Y_{2}\), or much more than the obtained experimental value of 72.4868% (Figure 4e,f);
4. If the biosorption operating regime is discontinuous, higher values of the dye removal degree will be performed after a S/L contact time greater than 20 h (as found in a previous authors' report after 24 h) [10,11]. Other aspects can be underlined when two independent variables are constant in the biosorption process, especially at their basic values (\(X_{ij}=0\)). In this context, the increase in BRed reactive dye removal percentage (dye biosorption efficiency) can vary with the increase in each \(X_{1}\) independent value, as follows:  
* for \(Y_{1}\) function (BRed dye biosorption efficiency onto biosorbent 1): the influence of initial dye concentration (\(X_{1}\)) vs. \(Y_{1}\) is illustrated in Figure 5a. It seems that it is _no distinct maximum_ but only an _extreme local maximum_ for BRed dye removal (\(Y_{1}\)* = 35.724%) at \(X_{1}\)*= +2.00 corresponding to a BRed dye concentration of 100.00 mg/L, for a biosorbent 1 concentration of 12 g/L and t\({}_{\text{biosorption}}\) of 6 h (\(X_{2}\) and \(X_{3}\) kept constant at their basic values). The dependence of BRed dye removal (\(Y_{1}\)) vs. \(X_{2}\) (biosorbent 1 concentration) (\(X_{1}\) and \(X_{3}\) coded values are 0) indicates no _distinct minimum_ of dye removal degree; thus, an _extreme local maximum_ can be considered (\(Y\) = 31.661%) at \(X_{2}\)* = +2.00, corresponding to a biosorbent concentration of 24 g/L (0.60 g per 25 mL), a dye concentration of 50.00 mg/L and t\({}_{\text{sorption}}\) of 6 h (Figure 5b).