## 2 Experimental Setup  
The overall photocatalytic degradation rate of the VOCs was calculated as follows:  
\[r=\left(\frac{Q}{S}\right)\times\frac{C_{in}}{100}\times R(\%) \tag{1}\]  
\[RE\ (\%)=\frac{C_{in}-C_{out}}{C_{in}}\times 100 \tag{2}\]  
where \(RE\) is the VOCs' removal efficiency, \(C_{in}\) and \(C_{out}\) are the inlet and outlet VOCs' concentration (mM\(\cdot\)m\({}^{-3}\)), respectively, \(Q\) is the volumetric flow rate (m\({}^{3}\cdot\)h\({}^{-1}\)), and \(S\) is the medium surface (m\({}^{2}\)). The Langmuir-Hinshelwood (L-H) model generally represents the degradation kinetics. This model is defined by the following equation [27; 28; 29]:  
\[r_{o}=\frac{k\cdot K\cdot C_{0}}{1+KC_{0}}\ \mathrm{or}\ \frac{1}{r_{0}}=\frac{1}{ kK}\cdot\frac{1}{C_{0}}+\frac{1}{k} \tag{3}\]where \(r_{0}\) is the initial reaction rate (mM\(\cdot\)m\({}^{-3}\cdot\)s\({}^{-1}\)), \(k\) is the reaction rate constant (mM\(\cdot\)m\({}^{-3}\cdot\)s\({}^{-1}\)), and \(K\) is the adsorption constant (m\({}^{3}\cdot\)mM\({}^{-1}\)). The slope of the curve C = f (time), where the influence of the by-products is assumed to be negligible, determines the initial reaction rate. The values of the L-H constants are determined from the slope and intercept of the plot \(r_{0}\)\({}^{-1}\) = f (C\({}_{0}\)\({}^{-1}\)). Assuming that the mass transfer is not the limiting step, and that the effect of the intermediate products is negligible, then the reaction rate can be expressed according to Equation (3) [29]. In this model, the adsorption and desorption reactions are neglected in comparison to the oxidation mechanism. A continuous plug flow reactor at a steady state is considered. The distribution of the pollutants along the axial direction should not be ignored. The continuity equation for a pollutant is denoted as follows:  
\[u\cdot\frac{dC}{dz}=-r \tag{4}\]  
In this equation, z is the axial position in the reactor. After integration, the previous equation becomes  
\[\frac{\ln(C_{in}/C_{out})}{C_{in}-C_{out})}=\frac{k_{app}\cdot K\cdot L}{u} \frac{1}{C_{in}-C_{out})}-K \tag{5}\]  
where \(L\) is the reactor length (m), \(u\) is the superficial gas velocity (m\(\cdot\)s\({}^{-1}\)), and \(C_{in}\) and \(C_{out}\) are the inlet and outlet concentrations. The L-H constants \(k_{app}\) and \(K\) are obtained by fitting the results of each concentration and flow rate with the linear equation. The cross-correlation coefficient is obtained by the covariance of kapp and \(K\) divided by the norm deviation of each modulus \(k_{app}\) and \(K\). The overall mass balances of the contaminant on the gaseous and solid phases in a continuous reactor result in the following relations [30; 31]. In the gas phase:  
\[u\cdot\frac{dC}{dz}+k_{m}\cdot a_{v}\cdot(C-C_{s})=0 \tag{6}\]  
In the solid phase:  
\[k_{m}\cdot a_{v}\cdot(C-C_{s})=\frac{k_{app}\cdot K\cdot C_{s}}{1+K\cdot C_{s}} \tag{7}\]  
where \(C\) and \(C_{s}\) are the concentrations in the gas phase of the overall and average surface of the VOCs (mM\(\cdot\)m\({}^{-3}\)), respectively, \(k_{m}\) is the mass transfer coefficient (m\(\cdot\)s\({}^{-1}\)), and a\({}_{v}\) is the average area per unit volume of the reactor (m\({}^{2}\cdot\)m\({}^{-3}\)). Assuming a linear transfer gradient, the material flux \(J_{f}\) through the film is written according to the Fick law, integrated over the thickness \(\delta\) of the film [32]. \[J_{f}=\frac{D}{\delta}\cdot(C_{b}-C_{s})=k_{f}\cdot(C_{b}-C_{s}) \tag{8}\]  
where \(\delta\) is the thickness of the external film, \(C_{b}\) is the core concentration of the fluid, \(Cs\) is the concentration on the surface of the adsorbent grain, \(k_{f}\) is the external mass transfer coefficient, and \(D\) is the diffusion coefficient. The film thickness \(\delta\) varies with the operating conditions, such as the turbulence, grain size, and fluid viscosity. Several semi-empirical correlations were established to obtain the external mass transfer coefficient \(k_{f}\).