## 2 Materials and Methods
### Effect of Adsorbent Bed Height  
The experimental BTCs for the adsorption of the blue, red, and black dyes on the PSAC at distinct bed lengths of 2 and 4 cm, and an inlet dye concentration of 500 mg L\({}^{-1}\) for the blue and red dyes and 100 mg L\({}^{-1}\) for the black dye at a flow rate of 7.7 mL min\({}^{-1}\) are depicted in Figure 6. It is observed that both the breakthrough time and the removal efficiency increased with increasing bed height (Table 4) [25]. On the other hand, the shape of the curves was, in general, steeper for the lower bed height because of the reduced mass-transfer zone due to the decrease in adsorbent load, which can lead to a reduction in the adsorption capacity and a faster adsorption rate. By increasing the bed height, the number of active sites for adsorption also increase because of the increased surface area [1,25,33]. With the increase in the bed height, it was more difficult to reach saturation for the operation time since \(C/C_{0}\) values are lower due to the availability of higher adsorption sites. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Dye** & **Concentration** & \(t_{b}\) & \(V_{df}\) & \(t_{oper}\) & \(m\) & \(q_{bed}\) & \%_Removal_ & _MTZ_ \\ \hline Blue & 500 & 20 & 3370 & 438 & 0.5 & 1165.6 & 34.7 & 1.9 \\  & 100 & 341 & 10,407 & 1352 & 0.5 & 1139.3 & 50.9 & 1.5 \\ Red & 500 & 5 & 3445 & 447 & 0.5 & 1028.4 & 30.0 & 2.0 \\  & 100 & 50 & 8409 & 1092 & 0.4 & 863.5 & 39.7 & 1.9 \\ Black & 100 & 6 & 1347 & 175 & 0.5 & 109.3 & 43.0 & 1.9 \\  & 25 & 49 & 5088 & 661 & 0.5 & 146.5 & 57.2 & 1.8 \\ \hline \hline \end{tabular} Concentration (mg L\({}^{-1}\)); \(t_{b}\) (min): breakthrough time; \(V_{gf}\) (mL); volume of effluent; \(t_{oper}\) (min): total operating time; \(m\) (g): mass of adsorbent; \(q_{half}\) (mg g\({}^{-1}\)): adsorption capacity of the PSAC bed; \(MTZ\) (cm): mass-transfer zone.  
\end{table} 
Table 3: Estimated parameters obtained from BTCs corresponding to the adsorption of blue, red, and black dyes onto the PSAC in function of inlet concentrations (flow rate: 7.7 mL min\({}^{-1}\); bed height: 2 cm; temperature: 20 \({}^{\circ}\)C). Figure 6: BTC curves for blue (a), red (b), and black (c) dye adsorption onto the PSAC at distinct influent concentrations (initial dye concentration: 500 mg L\({}^{-1}\) for blue and red and 100 mg L\({}^{-1}\) for black dye; flow rate: 7 mL min\({}^{-1}\); temperature: 20 \({}^{\circ}\)C). Additionally, as a comparison, Figure 7 shows in more detail the dye behavior at the same adsorption conditions. It revealed, in agreement with the previous results, that the PSAC is more effective in adsorbing the blue dye since the retention time is higher during the experiment. However, for the other two dyes, especially for the black dye, the release of dye occurs in the outlet effluent in a short period of time. In addition, mass-transfer limitations within the bed, due to the dye molecular size and structure, could have an impact on their access to the microporous structure of the carbon resulting in a slower adsorption capacity, mainly for the black dye, the biggest one and with a more complex structure, preventing to reach the adsorbent saturation within the experimental time [38]. By comparing the adsorption capacity of the PSAC (Table 4) with that of other biomass-based activated carbons reported in the literature, it can be concluded that the PSAC has a high capacity for dye adsorption. As an example, the adsorption capacity of _Acacia milotica_ sawdust activated carbon for Indigo Carmine dye was 24.67 mg g\({}^{-1}\) at a bed height, an initial dye concentration, and a flow rate of 30 cm, 100 mg L\({}^{-1}\), and 250 mL h\({}^{-1}\), respectively [3]. Employing sludge-sawdust activated carbon as an adsorbent for malachite green removal, a maximum adsorption capacity of 565 mg g\({}^{-1}\) was obtained at an inlet dye concentration of 50 mg L\({}^{-1}\), a flow rate of 20 mL min\({}^{-1}\), and a bed length of 6 cm [39].