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Theoretical–Experimental Methodology for Designing Hybrid Photocatalytic Reactors

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Abstract

Hybrid photocatalytic reactors (HPR) utilize combined solar and lamp illumination to carry out the degradation of pollutants, allowing for reliable operation with reduced environmental impacts. In spite of this, few studies have addressed the design and simulation of these devices. A method is introduced for HPR design, based on simulations calibrated with experimental results. A radiative transfer model, based on the P1 approximation, is used to evaluate the local volumetric rate of photons absorption in the reaction volume. The model allows to evaluate the effective radii for artificial light (when 80% of absorption is reached) and the optical depth for solar radiation and is used to develop simplified expressions for this parameter. The radiation transfer method is coupled to a first-order kinetic model to describe the evolution of pollutant concentration. The combined model is tuned with experimental results for the degradation of Reactive Blue 69 anthraquinone dye, as a function of the accumulated radiative energy, in the presence of a TiO\(_2\) catalyst. These results were obtained by separate operation with solar radiation and lamps. Based on the developed method, 20 h duration experiments were simulated for three different HPR configurations, with different solar collection areas and lamp arrangements. Several operation modes were tested: either utilizing solar radiation during the day and artificial light at night, or a hybridizing diurnal solar operation with a variable number of lamps, depending on weather conditions. The proposed methodology can be used to optimize photo-reactor configurations and operation strategies to guarantee the discoloration and can be applied to any catalyst material that absorbs in the UV–Vis range, combined with either radiatively participating or transparent pollutants.

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Abbreviations

\(A_0\) :

Model parameter

\(A_{top}\) :

Exposed area

c :

Light speed

C :

Concentration

\(\mathbb {C}\) :

Integration constant

\(e_L\) :

Energy absorbed per unit volume and time

\(e_a\) :

Absorbed photons

E :

Energy

EC:

Electric energy consumption

\(F_{\lambda }\) :

Normalized spectral radiative power

f :

Flux transmission factor

\(g _{\lambda }\) :

Spectral asymmetry parameter

\(G_{\lambda }\) :

Spectral incident radiation

h :

Planck’s constant

HPR:

Hybrid photocatalytic reactor

k :

Apparent kinetic constant

\(k'\) :

Kinetic parameter

K :

Adsorption equilibrium constant

\(\ell _{MFP}\) :

Mean free path

L :

Penetration depth

LVRPA:

Local volumetric rate of photons absorption

N :

Number of lamps

\(N_A\) :

Avogadro mole number

PR:

Photocatalytic reactor

\(q_{\lambda }\) :

Spectral radiative flux

RMSE:

Root mean square error

\(r_{dis}\) :

Instantaneous discoloration rate

\(\mathbf {r}\) :

Position vector

t :

Time

V :

Volume

\(\alpha\) :

Decaying exponent

\(\beta _{\lambda }\) :

Spectral extinction coefficient

\(\kappa _{\lambda }\) :

Spectral absorption coefficient

\(\Gamma _{max}\) :

Maximum colorant adsorbed in equilibrium per unit catalyst mass

\(\omega _{\lambda }\) :

Spectral scattering albedo

\(\Psi\) :

Adsorption parameter

\(\rho _{n,\lambda }\) :

Spectral reflectance function of order n

\(\sigma _{\lambda }\) :

Spectral scattering coefficient

\(\tau _{\lambda }\) :

Spectral transmittance function

0:

Initial

\(\lambda\) :

Spectral dependence

a :

Absorbed

ads :

Adsorbed

c :

Cumulative

cat :

Catalyst

d :

Diffusion

dye :

Dye/pollutant

eff :

Effective

in :

Incoming

N :

Normalized

T :

Total

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Acknowledgements

S. Orozco acknowledges CONACYT by Consolidation Scholarship M1 and M2 (I1200/224/2021). M. Rivero acknowledges UNAM-DGAPA-PAPIIT Project IA100621 and Alejandro Pompa for his technical support.

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Authors and Affiliations

  1. Facultad de Ingeniería Química, Edif. M-CU, Universidad Michoacana de San Nicolás de Hidalgo, 58060, Morelia, Michoacán, Mexico

    Sayra Orozco & Mercedes Téllez

  2. Instituto de Investigaciones en Materiales, Unidad Morelia, Universidad Nacional Autónoma de México, Antigua Carretera a Pátzcuaro No.8701, Col. Ex Hacienda de San José de la Huerta, 58190, Morelia, Michoacán, Mexico

    Michel Rivero

  3. Instituto de Energías Renovables, Universidad Nacional Autónoma de México, Priv. Xochicalco s/n, Col. Centro, 62580, Temixco, Morelos, Mexico

    Raúl Suárez-Parra & Camilo A. Arancibia-Bulnes

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  1. Sayra Orozco
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  2. Michel Rivero
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  5. Camilo A. Arancibia-Bulnes
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Contributions

SO: Conceptualization, Writing—original draft, Review & editing, Methodology, Investigation, Validation. MR: Software, Visualization, Writing—original draft, Review & editing. RS: Conceptualization, Review & editing, MT: Data Curation, Review. CA: Conceptualization, Writing—review & editing, Methodology, Investigation, Supervision.

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Correspondence to Sayra Orozco.

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Appendix

Appendix

1.1 \(\text {LVRPA}_{N} \left( L ,C_{cat} \right)\)

It is possible to extend the model presented in Sect. 6.2 by fitting a two-parameter exponential model to express the normalized LVRPA in terms of the distance L and \(C_{cat}\) as

$$\begin{aligned} \text {LVRPA}_{N} \left( L ,C_{cat} \right) = \exp \left( - \frac{L}{A_2} \left( 1 + B_2 C_{cat} \right) \right) \end{aligned}$$
(19)

where L is expressed in m and \(C_{cat}\) in mg L−1. For this model, the fitting parameters are given in Table 4, and is valid for \(C_{cat}\) in the range of 5–100 mg L−1. In this case \(A_2\) is given in m while \(B_2\) in L mg−1. Note that the higher the catalyst concentration, the faster the normalized LVRPA decays, which is physically consistent. It is noteworthy to mention that for a given \(C_{cat}\), Eq. (19) reduces to the model given by Eq. (17) with an error below \(2\%\).

Table 4 Fitting parameter and statistical measures for the normalized LVRPA for the TiO\(_2\) catalyst concentration for the model with two variables
Full size table

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Orozco, S., Rivero, M., Suárez-Parra, R. et al. Theoretical–Experimental Methodology for Designing Hybrid Photocatalytic Reactors. Top Catal 65, 1000–1014 (2022). https://doi.org/10.1007/s11244-022-01677-4

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