# Packed Bed Photoreactor for the Removal of Water Pollutants Using Visible Light Emitting Diodes
## 2 Results and Discussion
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Catalyst** & **Catalyst Size** & \begin{tabular}{c} **Initial MB** \\ **Concentration** \\ **(mg/L)** \\ \end{tabular} & \begin{tabular}{c} **Light** \\ **Source** \\ \end{tabular} & \
\begin{tabular}{c} **Treatment** \\ **Time \({}^{*}\)** \\ \end{tabular} & **Reusability** & **References** \\ \hline TiO\({}_{2}\)/plastic granules & 3.5 mm & 25 & Solar light & \textgreater{}48 h & Not reported & [34] \\ TiO\({}_{2}\)/PET TiO\({}_{2}\)/glass spheres & 5 mm & 10 & Solar simulator & \textgreater{}1.5 h & Not reported & [35] \\ TiO\({}_{2}\)/polpropylene & 3.5 mm & 25 & Solar light & 6 h & Not reported & [37] \\ N-TiO\({}_{2}\)/glass spheres & 1 cm & 10 &
\begin{tabular}{c} Visible light \\ lamps \\ \end{tabular} & \textgreater{}6.5 h & Not reported & [38] \\ \hline \hline \end{tabular}  
* Time to reach a total MB decolorization.  
\end{table} 
Table 1: Comparison with studies reported in the literature dealing with a different fixed bed photoreactor for methylene blue removal irradiated by artificial light sources, as well as with solar photocatalytic reactors using structured photocatalysts; PET (Polyethylene Terephthalate). Figure 3: Behavior of MB relative concentration as function of irradiation time at different liquid flow rate. Light sources: visible LEDs; light intensity: 78 mW/cm\({}^{2}\); initial MB concentration: 7 mg/L; photoreceptor configuration: batch mode; and total organic carbon (TOC). Photocatalytic Results on Methylene Blue Degradation with the Packed Bed photoreactor: Kinetic Evaluation and Mathematical Modelling  
The mathematical modeling of the photocatalytic system, based on the use of the developed packed bed photoreactor at semi-pilot scale, has been performed using first order kinetics for MB photodegradation [41] and neglecting the external mass transfer phenomena. In order to verify this last hypothesis, the apparent kinetic constant was estimated from the experimental data collected using different liquid flow rates when the photoreactor operated in continuous mode (Figure 5) and at steady-state condition (Table 2). Considering the plug-flow behavior inside the packed bed, the MB mass balance can be written as:  
\[Q_{0}\times\frac{dX}{dW_{cat}}=K\times(1-X) \tag{1}\]  
where:  
\(Q_{0}\) = liquid flow rate, L/min;  
\(K\) = apparent kinetic constant, L/(g min);  
\(X\) = MB conversion;  
\(W_{cat}\) = structured catalyst amount, g.  
The boundary condition for Equation (1) is:  
\(W_{cat}\) = 0 : X = 0. Equation (1) is easily integrated obtaining the following relationship:  
\[-\ln(1-X)=K\times\frac{W_{cat}}{Q_{0}} \tag{2}\]  
Figure 6 reports the behavior of (-ln(1 - \(X\))) as a function of \(W_{cat}\)/\(Q_{0}\). The slope of the obtained straight line is the value of the apparent kinetic constant \(K\) (3 \(\times\) 10\({}^{-5}\) L/(g min)), which can be seen as the product between the kinetic constant and the light intensity at the external surface of the photoreactor (Equation (3)) [38]:  
\[K=k_{kinetic}\times I, \tag{3}\]  
where:  
\(k_{kinetic}\) = kinetic constant, L cm\({}^{2}\)/(g min mW);  
\(I\) = light intensity, mW/cm\({}^{2}\). Figure 6: Evaluation of kinetic constant using photoreactor in continuous mode PFR (Plug Flow Reactor) at different liquid flow rate (in the range 6.3–74.15 mL/min). Light sources: visible LEDs; light intensity: 78 mW/cm\({}^{2}\); and initial MB concentration: 7 mg/L. Considering the light intensity of 78 mW/cm\({}^{2}\), it was possible to evaluate the value of \(k_{kinetic}\) from Equation (3), obtaining a value equal to 3.85\(\times\)10\({}^{-7}\) L cm\({}^{2}\)/(g min mW). The behaviour shown in Figure 6 confirmed the hypothesis that external mass transfer phenomena can be neglected since only one value of \(K\) is able to described the results obtained using different liquid flow rates [38; 42].