## 3 Results and Discussion  
### Evaluation of Hydraulic Parameters  
Table 2 reports the number of adsorption cycles carried out in the different columns that allowed us to obtain a visually colorless permeate, together with the respective total volume of treated solution. The adsorption columns C1, C2, C3, and C4 showed a total decolorization of the solution already at the first adsorption cycle, while for the C5 column, a colored permeate was observed, even if the solution in any case presented a certain degree  
Figure 2: Scheme of the adsorption system. of discoloration. Increasing the amount of MWCNTs in the columns increased the number of repeatable cycles that allowed for a colorless permeate. In fact, the C1 column, with the highest quantity of nanotubes (2.5 g), reached the highest number of cycles, corresponding to 38, while the C4 column, with 0.5 g of MWCNTs, needed only one adsorption cycle. The total volume of solution that can be treated by column C1 was the highest (3.8 L), while that which could be treated with column C4 was the lowest (0.1 L), excluding column C5, which, as already mentioned, already presented, at the first cycle, no ability to completely decolorize the solution. Columns C4 and C5, however, allowed us to define the minimum quantity of MWCNTs necessary to perform at least one adsorption cycle, which was found to be equal to 0.5 g. Figure 3 reports the permeation times for each cycle performed on columns C1, C2, and C3. The permeation time was calculated as the sum of the times used by each single adsorption cycle up to the last cycle; that is, until the solution was no longer colorless. Since the time for column C4 related to a single cycle and was equal to 12 min, and since the C5 column did not produce a decolored solution in the first cycle, they were not graphed. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Adsorption Column** & **Number of Adsorption Cycles** & **Total Volume Treated [L]** \\ \hline C1 & 38 & 3.8 \\ C2 & 9 & 0.9 \\ C3 & 6 & 0.6 \\ C4 & 1 & 0.1 \\ C5 & 0 & 0.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Number of adsorption cycles of 100 mL of Reactive Black 5 [37 mg/L] solution and total volume treated. Figure 3: Permeation times as a function of number of cycles for different columns. It is evident that in column C1, the most representative in terms of adsorption cycles carried out, there was an increase in permeation times as a function of the cycles carried out, even if characterized by a swinging sawtooth trend. This behavior of the C1 column can be associated with an alternation of clogging and rupture of the MWCNT layer, due to the creation of preferential pathways in it, which were subsequently recompacted in consecutive cycles. For columns C2 and C3, the trend remained substantially constant, settling on an average value for the permeation times of between 65 and 70 min. Table 3 reports the carbon usage rate (CUR) values calculated using the following Equation (1):  
\[CUR=\frac{M_{ads}}{Q\cdot t} \tag{1}\]  
where \(Q\) is the average flow rate, \(M_{ads}\) is the weight of the adsorbent layer of nanotubes, and \(t\) is total permeation time (as the sum of the permeation times of each single cycle) until the colorless permeate is maintained. The data obtained show that the CUR decreased as the amount of nanotubes in the column increased. The highest value was obtained for column C4 (5.0 g/L), while the lowest value was obtained for column C1 (0.66 g/L). The flux (_J_, Equation (2)) and the empty bed contact time (EBCT, Equation (3)) were calculated as:  
\[J=\frac{Q}{A} \tag{2}\]  
\[EBCT=\frac{V_{ads}}{Q} \tag{3}\]  
where \(Q\) is the average flow rate crossing the transversal section of column, A is the area of the section, and \(V_{ads}\) is the volume filled by MWCNTs. Table 3 reports the flux and EBCT for different adsorption columns. The reported data show that there was a decrease in flow (_J_) and a decrease in the EBCT as the amount of nanotubes in the column increased.