## 3 Results and Discussion
### Calculation of Intensification Indices
Despite the laminar flow, average velocity was used neglecting the radial and axial differences in the velocity profile. The averaged fluid velocity was estimated at \(v=2.78\times 10^{-2}\) m/s in FPCR and \(v=4.99\times 10^{-2}\) m/s in CPC, which was used in all related models. The PFCR operated in total recirculation mode with the reactor outlet flow entering the inlet with the minimum retention volume in the collecting tank. In CPC,outlet flow mixed with the reaction mixture in the recirculation tank led to different inlet concentrations in different reaction times. Material balance is given for the perfectly mixed reservoir tank:  
\[V_{\text{Tank}}\frac{d\left[X_{\text{i}}\right]_{\text{Tank}}^{\text{out}}}{ \text{dt}}=Q\Big{(}\left[X_{\text{i}}\right]_{\text{Tank}}^{\text{in}}-\left[X_ {\text{i}}\right]_{\text{Tank}}^{\text{out}}\Big{)} \tag{6}\]  
and for reactors CPC, Equation (7) and FPCR (single cascade), Equation (8):  
\[v\frac{d\left[X_{\text{i}}\right]}{dH}=r_{\text{i}}(\text{H},\text{t}) \tag{7}\]  
\[v\frac{d\left[X_{\text{i}}\right]}{dH}=r_{\text{i}}(\text{H},\text{T},\text{t}) \tag{8}\]  
The numerical simulation was performed dividing the reaction space along the length and width--i.e., H and T (in FPCR) directions--in sufficiently small intervals. A small time increment (\(\Delta t\)) equal to the reactor space time (\(\tau\) = V\({}_{\text{R}}\)/Q) was introduced. The material balance in the reactor was solved at time t. The time step counter was increased and the procedure repeated. All simulations were performed in VBA module (Excel). Reaction rate constants (\(k_{\text{i}}\), s\({}^{-1}\)W\({}^{-0.5}\)m\({}^{1.5}\)) were determined by the trial and error method fitting the experimental values into the model by minimizing the variance. The results are graphically represented in Figure 7a-f. All results show a good match between experimental data and applied mathematical models. Reaction rate constants (\(k_{\text{i}}\), s\({}^{-1}\)W\({}^{-0.5}\)m\({}^{1.5}\)) were determined from experimental data obtained from experiments in FCPR with TiO\({}_{2}\)-GF (marked as \"model FPCR\"). \(k_{\text{i}}\) was kept constant in models applied to either FCPR with TiO\({}_{2}\)/CNT-GF (model FPCR+\(Y_{\text{cat}}\)) or CPC (model CPC). If \(k_{\text{i}}\) for the specific pollutant deviated in any of these models, it would have suggested that the hypotheses were erroneous. However, the used \(k\)i values resulted in predicted model values for CT, HQ and RS concentration that match well with the corresponding experimental data. The use of the modified kinetic equation (1)) with irradiation terms allowed the determination of intrinsic kinetic rate constants that accurately describe the photocatalytic kinetics under variable UVA and UVB irradiation. Results of kinetic modelling and given intensification indices are given in Tables 1 and 2. As shown in Table 1, observed reaction rate constants for CT, HQ and RS degradation in single pollutant model solutions were lower than the reaction rate constants for dihydroxybenzene degradation in binary mixtures. Although \(k_{\text{i}}\) is intrinsic value, specific for each pollutant, in such semiempirical models, it is a measure of reaction kinetics based on \(\bullet\)OH radical attack and subsequent degradation mechanism. If any other reaction intervened the pollutant degradation, the \(k_{\text{i}}\) would change since it would be no longer a measure of simple photocatalytic kinetics. The observed phenomenon was explained in the previous section; faster degradation kinetics in the binary mixture is a result of the self-catalyzed radical reaction cycle due to a large number of hydroxyl-compounds on the photocatalyst surface. The results indicate a more rapid degradation of the single dihydroxybenzene compound in mixture, whereby the existence and activity of different short-lived radicals during the photocatalytic cycle overrides the possible negative effect of competitive adsorption on active sites and competitiveness toward reactive species.