## 2 Experimental Section
### Dynamic Biosorption Procedure
#### 2.3.2 Biosorption Design in the Fixed/Packed Bed Column  
In order to design an installation with a biosorption column with a solid biosorbent fixed/packed in a bed, a series of required operating parameters were determined, i.e., the mean flow of treated effluent per mass of biosorbent (\(b_{i}\)), to determine the optimal volume of treated effluent (\(V_{opt}\)), the biosorption time (\(t_{ri}\)) to the maximum admissible concentration of dye in the treated effluent (i.e., M.A.C. = 1 mg dye/L), and the size of a proposed biosorption tank or reactor (i.e., the height of fixed/packed bed (\(H_{ads}\)), the interior/inner diameter (\(D_{R}\)) and the height (\(H_{R}\)) of the biosorption reactor) working with granules of immobilized residual _Bacillus_ sp. biomass.  
Thus, the mean flow of treated effluent per mass of biosorbent, \(b_{i}\), was calculated as per Equation (2) [30]:  
\[b_{i}=\frac{V_{n}+n_{i}\cdot v}{m\cdot t_{ni}}(\text{mL/g\cdot min}) \tag{2}\]  
where \(V_{n}\) is the treated effluent volume that passes through the packed bed, collected at the bottom of the column (mL); \(n_{i}\) is the number of samples periodically analyzed for residual dye content; \(v\) is the volume of each analyzed sample (\(v\) = 5 mL); \(m\) is the immobilized biosorbent mass (g), and \(t_{ni}\) is the total biosorption time until the maximum value of residual dye concentration in the treated effluent is reached (equal to or greater than the initial dye concentration in the aqueous solution) (min).  
For each series of experiments performed at a certain effluent flow rate (\(F_{vi}\)), the biosorption time (\(t_{ri}\)) after which the treated effluent (passed through the packed biosorbent bed) has a residual dye concentration equal to the maximum admissible limit (M.A.C.) (M.A.C. = 1 mg dye/L) was established from a graphical representation of the residual dye concentration variations (mg of dye /L of solution) as a function of biosorption time (min) (i.e., \(C_{idw}\) = \(f(t_{ri})\)). Moreover, the optimal volume (\(V_{opt}\)) of treated effluent per biosorbent mass needed to be determined from the graphical representation of \(V_{i}\) = \(f(b_{i})\), where \(V_{i}\) is the volume of the treated effluent with a certain flow rate (\(F_{vi}\)) passed through the mass (\(m_{i}\)) of fixed/packed biosorbent bed until the maximum admissible concentration of residual dye is attained (M.A.C.= 1 mg dye/L) (mL), and is calculated follwing Equation (3) (mL/g). \(b_{i}\) represents the mean effluent flow rate per immobilized biosorbent mass (mL/g.min) calculated using Equation (2) [30].  
\[V_{i}=b_{i}\times t_{ri}\;(\text{mL/g}) \tag{3}\]  
Three values for \(V_{i}\) and \(b_{i}\) were calculated for each treated effluent flow rate (\(F_{vi}\) = 2.9, 4.5, and 7.3 mL/min) and were plotted; the optimal treated effluent volume per mass of fixed/packed biosorbent bed (\(V_{opt}\)) until the maximum admissible BRed dye concentration in the treated effluent were reached (dynamic regime, M.A.C. = 1 mg dye/L) was determined as the inflexion point of the graphical representation.  
If the bulk density of biosorbent (\(\rho_{ads}\)) and \(V_{opt}\) for a certain estimated flow rate of the real effluent are known (e.g., \(F_{vi}\) = 20 L/h for the treated dye-containing effluent of a cotton fabrics' manufacturing company), the main sizes of the biosorption (column) reactor can be calculated with the help of the biosorbent mass (\(M_{ads}\)), biosorbent volume in the column packed bed (\(V_{ads}\)), working flow rate (\(F_{vi}\)), biosorption time (\(t_{mi}\)), uniformity distribution coefficient (\(\beta\)) of biosorbent in the packed bed, and the estimated free space above the packed bed of biosorbent (\(\lambda\)), mainly considering the relations summarized in Table 1 [30; 31].