## 3 Results and Discussion  
### Optimization of Phosphorus Adsorption in Fixed-Bed Column  
In this study, the effects of bed height and flow rate (and consequently, fluid superficial velocity) were optimized owing to their relevance to the design of a fixed-bed adsorption system. Figure 2a-c show the experimental breakthrough curves under different initial conditions, that is, different heights. From the data in Figure 2, Table 3 indicates that by increasing the flow rate (or fluid superficial velocity) at a constant bed height, the most relevant times (\(t_{bp}\), \(t_{ex}\), \(t_{st}\), and \(\Delta t_{ads}\)) decreased significantly. For example, for a bed height of 20 cm, the exhaustion time was reduced from 148 min to 87 min by doubling the flow rate. This occurred because the contact time between the adsorbent and phosphate ions decreased when the superficial velocity increased, resulting in a lower mass transfer efficiency from the wastewater to the adsorbent. In contrast, for the same flow rate, the exhaustion time increased as the bed height increased because more active sites were available to bind the phosphate ions, and consequently, a broader mass transfer zone was observed. \begin{table} \begin{tabular}{c c c c c c c c c c c} \hline \hline Run & \(Q\) & \(h\) & \(t_{bp}\) & \(t_{ex}\) & \(t_{st}\) & \(\Delta t_{ads}\) & \(FSB\) & \(q_{e}\) (mg P/kg & \(MTZ\) & \(t_{r}\) (min) & \(LIIB\) \\  & **(mL/min)** & **(cm)** & **(min)** & **(min)** & **(min)** & **(min)** & **(min)** & **(min)** & **(cm)** & **(cm)** & **(cm)** \\ \hline
1 & 5.0 & 20 & 26.1 & 148 & 84.3 & 122 & 0.309 & 107 & 16.5 & 6.66 & 13.8 \\
2 & 5.0 & 30 & 40.4 & 166 & 95.1 & 126 & 0.425 & 70.9 & 22.7 & 9.99 & 17.3 \\
3 & 5.0 & 40 & 69.4 & 266 & 159 & 196 & 0.436 & 85.8 & 29.6 & 13.3 & 22.5 \\
4 & 7.5 & 20 & 7.41 & 111 & 46.9 & 104 & 0.149 & 91.2 & 18.7 & 4.44 & 17.0 \\
5 & 7.5 & 30 & 16.5 & 147 & 69.0 & 131 & 0.239 & 72.3 & 26.6 & 6.66 & 22.8 \\
6 & 7.5 & 40 & 31.9 & 190 & 98.5 & 158 & 0.325 & 94.7 & 33.3 & 8.88 & 27.0 \\
7 & 10 & 20 & 1.78 & 86.7 & 26.6 & 84.9 & 0.067 & 58.7 & 19.6 & 3.33 & 18.7 \\
8 & 10 & 30 & 4.88 & 110 & 32.8 & 105 & 0.149 & 37.4 & 28.7 & 5.00 & 25.5 \\
9 & 10 & 40 & 9.37 & 158 & 46.5 & 148 & 0.201 & 66.6 & 37.6 & 6.66 & 31.9 \\ \hline \hline \end{tabular} 
\begin{tabular}{c c c c c c c c c} \hline \hline Run & \(Q\) & \(h\) & \(t_{bp}\) & \(t_{ex}\) & \(t_{st}\) & \(\Delta t_{ads}\) & \(FSB\) & \(q_{e}\) (mg P/kg & \(MTZ\) & \(t_{r}\) (min) & \(LIIB\) \\  & **(mL/min)** & **(cm)** & **(min)** & **(min)** & **(min)** & **(min)** & **(min)** & **(cm)** & **(cm)** & **(cm)** & **(cm)** \\ \hline
1 & 5.0 & 20 & 26.1 & 148 & 84.3 & 122 & 0.309 & 107 & 16.5 & 6.66 & 13.8 \\
2 & 5.0 & 30 & 40.4 & 166 & 95.1 & 126 & 0.425 & 70.9 & 22.7 & 9.99 & 17.3 \\
3 & 5.0 & 40 & 69.4 & 266 & 159 & 196 & 0.436 & 85.8 & 29.6 & 13. The _FSB_ increased with the bed height for the same flow rate but decreased with the flow rate for the same bed height. Indeed, the percentage ratio between _LUIB_ and \(h\) showed the highest value for the experiments with the lowest bed height (20 cm), where more than 90% of the bed was not used in the experiment at 10 mL/min. This percentage was the lowest (about 56%), with bed heights of 40 cm and 5 mL/min. Thus, the flow rate influences the bed utilization efficiency, and this parameter should not be too large to optimize the column use [32]. Regarding the adsorption capacity, the values did not exhibit a trend consistent with the change in \(h\). The maximum \(q_{e}\) values were obtained at 20 cm and 5 mL/min. Other study found that the breakthrough time and adsorption capacity decreased with increasing flow rate due to the presence of a mass transfer zone closer to the exit of the column [33]. In the present study, it was not possible to corroborate this statement for the adsorption capacity values when using 7.5 mL/min, despite the values being in the same order of magnitude. Nevertheless, the lowest adsorption capacity was observed at the highest flow rate (10 mL/min).