## 3 Results  
### Biosorption Process Performance  
The principal influencing factors of reactive Brilliant Red-HEB 3B dye biosorption onto residual biomass of _Saccharomyces pastorianus_ immobilized in sodium alginate by using a Buchi micro-encapsulator (with biosorbent 1) and/or by a simple dropping technique (with biosorbent 2) were studied and reported related to the significant dye removal efficiencies and highest dye biosorption capacities (i.e., \(q\) > 80-220 mg of dye/g biosorbent in the case of simple dropping technique, or 312.5-2500 mg dye/g biosorbent in the case of encapsulation with Buchi micro-encapsulator) [10; 11]. For the best experimental biosorption results, the operating conditions that must be considered are as follows: pH 3, temperature of 25-30 \({}^{\circ}\)C with a biosorbent concentration of minimum 2.60 g/L or 3.2 g/L (with 5% d.w.) according to the diameter of the biosorbent granules (in this case, 4 mm for biosorbent granules obtained by a simple dropping technique, and 1500 um for biosorbent granules obtained by using a Buchi micro-encapsulator), and an S/L phases contact time for biosorption of at least 7.4 h or 12 h at a dye concentration in the aqueous solution of 10.64-170.24 mg/L and 16.88-174.08 mg/L, respectively [10; 11]. All biosorption experiments were performed according to the experimental planning matrix (of the active central compositional rotatable design of 2\({}^{3}\) order).  
In our previous papers, it was concluded that the mechanism of biosorption process, referring the biosorption energy value (E) (8.28-11.23 KJ/mol) biosorbent 1) [11] and (8.45-13.61 KJ/mol) (biosorbent 2) [10], is based on physical bonding established between the positively charged surface of the biosorbent and the functional groups of reactive Red Brilliant HE-3B dye.  
A few new experimental data of studied dye biosorption in a static working regime were selected in Figure 2 after the S/L phases contact period of 24 h (biosorption equilibrium attained) but the reference experimental data were reported in our previous works, in which it was demonstrated by advanced analytical analysis (SEM, FTIR-EDX) that the dye was retained in the molecular structure of both biosorbents [10; 11]. In the present modeling and optimization study, the dye biosorption was evaluated at pH 3 for a period of no more than 10 h, referring to the biosorption capacity and efficiency in retaining of reactive BRed dye onto residual immobilized biomass.  
High BRed dye biosorption capacities were performed for dye concentrations more than 75 mg/L, i.e., \(>\)130.56 mg/L for biosorbent 1 (3.2 g/L of biosorbent) and \(>\)127.68 mg/L for biosorbent 2 (2.60 g/L of biosorbent). The highest dye biosorption capacity was performed at the highest dye concentration of around 130 mg/L of BRed dye (Figure 2a), i.e., a dye biosorption capacity of around 83.275 mg/g for biosorbent 1 and around 213.870 mg/g for biosorbent 2.  
As shown in Figure 2b, for the initial dye concentration of 31.95 mg/L, the dye biosorption capacity varied in the range of around 29.23-33.06 mg/g working with biosorbent 1 and 19.505-35.313 mg/g working with biosorbent 2, considering the biosorbent amount of 0.00285-0.00915 g d.w. (d.w.--dry mass of biosorbent per 25 mL of dye solution), corresponding to a biosorbent concentration of 2.4-3.2 g/L.  
Better results were performed for higher reactive BRed dye concentration in the aqueous system (\(>\)45-50 mg/L) working with the biosorbent concentration of more than 12 g/L in the same operating conditions of pH 3 and T = 20-30 \({}^{\circ}\)C (causing the residual biomass degradation to be easily controllable).