## 3 Results and Discussion
### Calculation of Intensification Indices  
To unbiasedly estimate the intensification possibility using different reactor designs and sensitized photocatalytic film, kinetics of photocatalytic degradation of model compounds in studied reactors must be properly modeled. The basic kinetic equation (\(r=k\left[\text{X}\right]^{n}\)) was firstly modified to give more intrinsic parameters related to photocatalytic degradation of selected pollutants over irradiated TiO\({}_{2}\) film. An irradiation term was introduced to basic kinetic equations:  
\[r_{\text{i}}=-k_{\text{i}}\Big{(}\big{(}\mu I_{0}(\text{T,H})\big{)}_{\text{ UVB}}+\big{(}\mu I_{0}(\text{T,H})\big{)}_{\text{UVA}}\Big{)}^{m}[\text{X}_{ \text{i}}]^{n} \tag{2}\]  
The \(I_{0}\)(T,H) (W m\({}^{-2}\)) stands for the incident photon flux at the film surface along the cascade width and length, \(\mu\) (m\({}^{-1}\)) is the absorption coefficient averaged over the spectrum of incident irradiation (in UVB and UVA region) and m is the order of reaction with respect to irradiation absorption. By introducing the (\(\mu I_{0}\) (T,H))\({}^{m}\) into the kinetic model, resulting reaction rate constants became independent of irradiation condition and applied catalyst [48]. Note that \(k_{\text{i}}\) stands for the intrinsic degradation rate constant of selected pollutants (i). The intensification by reactor design was quantified using intensification index, \(Y_{\text{RD}}\). \[r_{\text{i}}=-k_{\text{i}}\Big{(}Y_{\text{RD}}\Big{(}\mu I_{0}(\text{T,H}) \big{)}_{\text{UVB}}+\big{(}\mu I_{0}(\text{T,H})\big{)}_{\text{UVA}}\Big{)}^{ m}[\text{X}_{\text{i}}]^{n} \tag{3}\]  
The intensification by photocatalyst formulation modification was quantified using intensification index, \(Y_{\text{cat}}\)  
\[r_{\text{i}}=-k_{\text{i}}Y_{\text{cat}}\Big{(}\big{(}\mu I_{0}(\text{T,H}) \big{)}_{\text{UVB}}+\big{(}\mu I_{0}(\text{T,H})\big{)}_{\text{UVA}}\Big{)}^{ m}[\text{X}_{\text{i}}]^{n} \tag{4}\]  
Note that \(Y_{\text{RD}}\) multiplies the equation terms related to photon absorption rate, while \(Y_{\text{cat}}\) multiplies the whole kinetic equation. The explanation is rather simple. In CPC, which is assumed as an optimal solar reactor design, irradiation conditions inside the reaction space are better than in FPCR, since the total incident irradiation is composed of incident irradiation at the reactor wall and reflected radiation. In that manner, \(Y_{\text{RD}}\) represents the ratio between the total irradiation inside the reaction tubes and the incident irradiation at the outer reactor wall:  
\[Y_{\text{RD}}=\frac{I_{0}(\text{CPC})}{I_{0}(\text{FPCR})}=\frac{I_{0}+I_{ refl}}{I_{0}}=1+\psi^{g} \tag{5}\]  
Having in mind a variety of models [45; 46] which can give the exact number of reflections (g) from collectors depending on the reactor inclination toward irradiation source, \(Y_{\text{RD}}\) can be simply calculated from g and known material reflectivity (\(\psi\)), and introduced in different kinetic models. In another words, \(Y_{\text{RD}}\) in this study was determined by semiempirical models, while it can be also calculated from different ray optics models. The predicted \(Y_{\text{RD}}\) in CPC type reactors can lead to simple simulation of degradation extents for various pollutants and various hydrodynamic conditions, thus representing the solid base for scale up. The \(Y_{\text{cat}}\) assumes the enhancement in light absorption by photocatalysts, both in the UVA and UVB region but also in the visible part of applied irradiation. It can be used for facile determination of total intensification for new improved photocatalyst formulations. The reaction kinetic model was further combined with the material balance for plug flow reactor in recirculation. The Reynolds number was estimated using the hydraulic diameter equal to the wetted perimeter of a rectangular open channel (FPCR) and a pipe (CPC). Calculated Reynolds numbers for maintained flow in FPCR and CPC were 25.9 and 134.8, respectively.