Research Article
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Year 2024, Volume: 7 Issue: 2, 87 - 104, 04.10.2024
https://doi.org/10.58692/jotcsb.1450662

Abstract

Project Number

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References

  • 1. Acosta-Herazo, R., Cañaveral-Velásquez, B., Pérez Giraldo, K., Mueses, M. A., Pinzón-Cárdenas, M. H., & Machuca-Martínez, F. (2020). A MATLAB Based Application for Modeling and Simulation of Solar Slurry Photocatalytic Reactors for Environmental Applications. Water, 12(8), 2196. https://doi.org/10.3390/w12082196
  • 2. Acosta-Herazo, R., Monterroza-Romero, J., Mueses, M. Á., Machuca-Martínez, F., & Li Puma, G. (2016). Coupling the Six Flux Absorption–Scattering Model to the Henyey–Greenstein scattering phase function: Evaluation and optimization of radiation absorption in solar heterogeneous photoreactors. Chemical Engineering Journal, 302, 86-96. https://doi.org/10.1016/j.cej.2016.04.127
  • 3. Acosta-Herazo, R., Mueses, M. Á., Machuca-Martínez, F., & Li, G. (s. f.). Layer of photon absorption and apparent optical thickness. Akdemir, O., Lagendijk, A., & Vos, W. L. (2022). Breakdown of light transport models in photonic scattering slabs with strong absorption and anisotropy. Physical Review A, 105(3), 033517. https://doi.org/10.1103/PhysRevA.105.033517
  • 4. Arancibia-Bulnes, C. A., Jiménez, A. E., & Estrada, C. A. (2009). Development and Modeling of Solar Photocatalytic Reactors. En Advances in Chemical Engineering (Vol. 36, pp. 185-227). Elsevier. https://doi.org/10.1016/S0065-2377(09)00406-2
  • 5. Brandi, R. J., Alfano, O. M., & Cassano, A. E. (1996). Modeling of radiation absorption in a flat plate photocatalytic reactor. Chemical Engineering Science, 51(11), 3169-3174. https://doi.org/10.1016/0009-2509(96)00215-1
  • 6. Cassano, A. E., Martin, C. A., Brandi, R. J., & Alfano, O. M. (1995). Photoreactor Analysis and Design: Fundamentals and Applications. Industrial & Engineering Chemistry Research, 34(7), 2155- 2201. https://doi.org/10.1021/ie00046a001
  • 7. Christenson, J. G., Austin, R. A., & Phillips, R. J. (2018). Comparison of approximate solutions to the phonon Boltzmann transport equation withthe relaxation time approximation: Spherical harmonics expansions and the discrete ordinates method. Journal of Applied Physics, 123(17), 174304. https://doi.org/10.1063/1.5022182
  • 8. Colina-Márquez, J., Machuca-Martínez, F., & Li Puma,G. (2015). Modeling the Photocatalytic Mineralization in Water of Commercial Formulation of Estrogens 17-β Estradiol (E2) and Nomegestrol Acetate in Contraceptive Pills in a Solar Powered Compound Parabolic Collector. Molecules, 20(7), 13354-13373. https://doi.org/10.3390/molecules200713354
  • 9. Colina-Márquez, J., Machuca-Martínez, F., & Puma, G. L. (2010). Radiation Absorption and Optimization of Solar Photocatalytic Reactors for Environmental Applications. Environmental Science & Technology, 44(13), 5112-5120. https://doi.org/10.1021/es100130h
  • 10. Cuevas, S. A., & Arancibia-Bulnes, C. A. (s. f.). Photocatalytic Reactor by the P1 Approximation. International Journal of Chemical Reactor Engineering, 5(1). https://doi.org/10.2202/1542-6580.1589
  • 11. Fujii, H., Terabayashi, I., Aoki, T., Inoue, Y., Na, H., Kobayashi, K., & Watanabe, M. (2022). Numerical Study of Near-Infrared Light Propagation in Aqueous Alumina Suspensions Using the Steady-State Radiative Transfer Equation and Dependent Scattering Theory. Applied Sciences, 12(3), 1190. https://doi.org/10.3390/app12031190
  • 12. Ghafoori, S., Nasirian, M., Al-Jamal, R., Mallouh, F. A., & Mehrvar, M. (2020). Statistical parameter optimization and modeling of photodegradation of methyl orange using a composite photocatalyst prepared by thermal synthesis. Environmental Science and Pollution Research, 27(36), 45650-45660. https://doi.org/10.1007/s11356-020-10301-5
  • 13. Harel, R., Burov, S., & Heizler, S. I. (2021). Asymptotic P N Approximation in Radiative Transfer Problems. Journal of Computational and Theoretical Transport, 50(5), 390-406. https://doi.org/10.1080/23324309.2020.184573
  • 14. He, C., Clifton, O., Felker-Quinn, E., Fulgham, S. R., Juncosa Calahorrano, J. F., Lombardozzi, D., Purser, G., Riches, M., Schwantes, R., Tang, W., Poulter, B., & Steiner, A. L. (2021). Interactions between Air Pollution and Terrestrial Ecosystems: Perspectives on Challenges and Future Directions. Bulletin of the American Meteorological Society, 102(3), E525-E538. https://doi.org/10.1175/BAMS-D-20-0066.1
  • 15. Howell, J. R., Mengüç, M. P., Daun, K. J., & Siegel, R.(2021). Thermal radiation heat transfer (Seventh edition). CRC Press.
  • 16. Illi, E., Bouanani, F. E., Park, K.-H., Ayoub, F., & Alouini, M.-S. (2019). An Improved Accurate Solver for the Time-Dependent RTE in Underwater Optical Wireless Communications. IEEE Access, 7, 96478-96494. https://doi.org/10.1109/ACCESS.2019.2929122
  • 17. Incropera, F. P. (s. f.). [PDF] Fundamentals Of Heat And Mass Transfer.
  • 18. Li, J., Carlson, B. E., Yung, Y. L., Lv, D., Hansen, J.,Penner, J. E., Liao, H., Ramaswamy, V., Kahn, R. A., Zhang, P., Dubovik, O., Ding, A., Lacis, A. A., Zhang, L., & Dong, Y. (2022). Scattering and absorbing aerosols in the climate system. Nature Reviews Earth & Environment, 3(6), 363-379. https://doi.org/10.1038/s43017-022-00296-7
  • 19. Li Puma, G. (2005). Dimensionless Analysis of Photocatalytic Reactors Using Suspended Solid Photocatalysts. Chemical Engineering Research and Design, 83(7), 820-826. https://doi.org/10.1205/cherd.04336
  • 20. Li Puma, G., Machuca-Martínez, F., Mueses, M., Colina Márquez, J., & Bustillo-Lecompte, C. (2020). Scale-Up and Optimization for Slurry Photoreactors. En C. Bustillo-Lecompte (Ed.), Advanced Oxidation Processes—Applications, Trends, and Prospects. IntechOpen.https://doi.org/10.5772/intechopen.91920
  • 21. Moreno-SanSegundo, J., Casado, C., & Marugán, J. (2020). Enhanced numerical simulation of photocatalytic reactors with an improved solver for the radiative transfer equation. Chemical Engineering Journal, 388, 124183. https://doi.org/10.1016/j.cej.2020.124183
  • 22. Nair, A. K., & JagadeeshBabu, P. E. (2017). Ag-TiO2 nanosheet embedded photocatalytic membrane for solar water treatment. Journal of Environmental Chemical Engineering, 5(4), 4128-4133.https://doi.org/10.1016/j.jece.2017.07.046
  • 23. Nchikou, C., Loredo-Medrano, J. Á., Hernández Ramírez, A., Colina-Marquez, J. Á., & Mueses, M.Á. (2021). Estimation of the radiation field for CPC photocatalytic reactors using a novel six flux model in two dimensions (SFM-2D). Journal of Environmental Chemical Engineering, 9(6), 106392. https://doi.org/10.1016/j.jece.2021.106392
  • 24. Ochoa-Gutiérrez, K. S., Tabares-Aguilar, E., Mueses, M. Á., Machuca-Martínez, F., & Li Puma, G. (2018). A Novel Prototype Offset Multi Tubular Photoreactor (OMTP) for solar photocatalytic degradation of water contaminants. Chemical Engineering Journal, 341, 628-638. https://doi.org/10.1016/j.cej.2018.02.068
  • 25. Otálvaro-Marín, H. L., Mueses, M. A., & Machuca Martínez, F. (2014). Boundary Layer of Photon Absorption Applied to Heterogeneous Photocatalytic Solar Flat Plate Reactor Design.International Journal of Photoenergy, 2014, 1-8. https://doi.org/10.1155/2014/930439
  • 26. Peralta Muniz Moreira, R., & Li Puma, G. (2021). Multiphysics Computational Fluid-Dynamics (CFD) Modeling of Annular Photocatalytic Reactors by the Discrete Ordinates Method (DOM) and the Six-Flux Model (SFM) and Evaluation of the Contaminant Intrinsic Kinetics Constants. Catalysis Today, 361, 77-84. https://doi.org/10.1016/j.cattod.2020.01.012
  • 27. Rizzo, L., Malato, S., Antakyali, D., Beretsou, V. G.,Đolić, M. B., Gernjak, W., Heath, E., Ivancev Tumbas, I., Karaolia, P., Lado Ribeiro, A. R., Mascolo, G., McArdell, C. S., Schaar, H., Silva, A. M. T., & Fatta-Kassinos, D. (2019). Consolidated vs new advanced treatment methods for the removal of contaminants of emerging concern from urban wastewater. Science of The Total Environment, 655, 986- 1008. https://doi.org/10.1016/j.scitotenv.2018.11.265
  • 28. Tourasse, G., & Dumortier, D. (2014). Development of a System Measuring the Solar Radiation Spectrum in 5 Planes for Daylight and PVApplications. Energy Procedia, 57, 1110-1119. https://doi.org/10.1016/j.egypro.2014.10.071
  • 29. Vaya, D., & Surolia, P. K. (2020). Semiconductor based photocatalytic degradation of pesticides: An overview. Environmental Technology & Innovation, 20, 101128. https://doi.org/10.1016/j.eti.2020.101128
  • 30. Wang, D., Mueses, M. A., Márquez, J. A. C., Machuca Martínez, F., Grčić, I., Peralta Muniz Moreira, R., & Li Puma, G. (2021). Engineering and modeling perspectives on photocatalytic reactors for water treatment. Water Research, 202, 117421. https://doi.org/10.1016/j.watres.2021.117421
  • 31. Zalazar, C. S., Romero, R. L., Martín, C. A., & Cassano, A. E. (2005). Photocatalytic intrinsic reaction kinetics I: Mineralization of dichloroacetic acid. Chemical Engineering Science, 60(19), 5240- 5254. https://doi.org/10.1016/j.ces.2005.04.050

Estimation and Optimization of the Radiant Field in Flat Plate Heterogeneous Photoreactors with the P1-approximation of the Radiative Transfer Equation (RTE).

Year 2024, Volume: 7 Issue: 2, 87 - 104, 04.10.2024
https://doi.org/10.58692/jotcsb.1450662

Abstract

In this work, the P1-approximation of the radiative transfer equation (RTE) was used for the description and optimization of the radiant field in a flat plate photoreactor under solar radiation with three commercial brands of titanium dioxide photocatalysts. The boundary layer of photon absorption (δ_abs), the average volumetric rate of photon absorption (VRPA), and a new apparent optical thickness (ζ_app1) were used as design parameters for optimization. A simple mathematical expression for the calculation of δ_abs also called the best reactor thickness was formulated. For the three catalysts, varying the reactor height (L), it was found a decrease in the local volumetric rate of photon absorption (LVRPA) from the top side until the bottom of the reactor for any value of the catalyst loading (Ccat). It was also observed that when Ccat increases the VRPA increases exponentially until a fixed value where it remains almost constant. With L= 1 cm, the optimum Ccat (Ccatop) was 0.2 g/l in 0.85 cm of thickness, 0.3 g/l in 0.82 cm of thickness, and 0.4 g/l in 0.89 cm of thickness for the photocatalysts Degussa P-25, Aldrich, and Hombitak respectively. The optimum apparent optical thickness (ζ_(app1,op)) was 4.03, 4.62, and 3.7 for the photocatalysts Degussa P-25, Aldrich, and Hombitak respectively. These results are in good agreement with the literature. Results found in this work give predictions on radiation absorption in flat plate photocatalytic reactors with different heights.

Ethical Statement

Hereby, I Clovis Nchikou consciously assure that for the manuscript ´´Estimation and Optimization of the Radiant Field in Flat Plate Heterogeneous Photoreactors with the P1-approximation of the Radiative Transfer Equation (RTE)¨ the following is fulfilled: 1) This material is the authors' original work, which has not been previously published elsewhere. 2) The paper is not currently being considered for publication elsewhere. 3) The paper reflects the author's own research and analysis truthfully and completely. 4) The paper properly credits the meaningful contributions of co-authors and co-researchers. 5) The results are appropriately placed in the context of prior and existing research. 6) All sources used are properly disclosed (correct citation). Copying of text must be indicated as such by using quotation marks and giving proper references. The violation of the Ethical Statement rules may result in severe consequences. I agree with the above statements and declare that this submission follows the policies of Solid State Ionics as outlined in the Guide for Authors and in the Ethical Statement. Date: 11/03/2024 Clovis Nchikou

Project Number

There is no project number

References

  • 1. Acosta-Herazo, R., Cañaveral-Velásquez, B., Pérez Giraldo, K., Mueses, M. A., Pinzón-Cárdenas, M. H., & Machuca-Martínez, F. (2020). A MATLAB Based Application for Modeling and Simulation of Solar Slurry Photocatalytic Reactors for Environmental Applications. Water, 12(8), 2196. https://doi.org/10.3390/w12082196
  • 2. Acosta-Herazo, R., Monterroza-Romero, J., Mueses, M. Á., Machuca-Martínez, F., & Li Puma, G. (2016). Coupling the Six Flux Absorption–Scattering Model to the Henyey–Greenstein scattering phase function: Evaluation and optimization of radiation absorption in solar heterogeneous photoreactors. Chemical Engineering Journal, 302, 86-96. https://doi.org/10.1016/j.cej.2016.04.127
  • 3. Acosta-Herazo, R., Mueses, M. Á., Machuca-Martínez, F., & Li, G. (s. f.). Layer of photon absorption and apparent optical thickness. Akdemir, O., Lagendijk, A., & Vos, W. L. (2022). Breakdown of light transport models in photonic scattering slabs with strong absorption and anisotropy. Physical Review A, 105(3), 033517. https://doi.org/10.1103/PhysRevA.105.033517
  • 4. Arancibia-Bulnes, C. A., Jiménez, A. E., & Estrada, C. A. (2009). Development and Modeling of Solar Photocatalytic Reactors. En Advances in Chemical Engineering (Vol. 36, pp. 185-227). Elsevier. https://doi.org/10.1016/S0065-2377(09)00406-2
  • 5. Brandi, R. J., Alfano, O. M., & Cassano, A. E. (1996). Modeling of radiation absorption in a flat plate photocatalytic reactor. Chemical Engineering Science, 51(11), 3169-3174. https://doi.org/10.1016/0009-2509(96)00215-1
  • 6. Cassano, A. E., Martin, C. A., Brandi, R. J., & Alfano, O. M. (1995). Photoreactor Analysis and Design: Fundamentals and Applications. Industrial & Engineering Chemistry Research, 34(7), 2155- 2201. https://doi.org/10.1021/ie00046a001
  • 7. Christenson, J. G., Austin, R. A., & Phillips, R. J. (2018). Comparison of approximate solutions to the phonon Boltzmann transport equation withthe relaxation time approximation: Spherical harmonics expansions and the discrete ordinates method. Journal of Applied Physics, 123(17), 174304. https://doi.org/10.1063/1.5022182
  • 8. Colina-Márquez, J., Machuca-Martínez, F., & Li Puma,G. (2015). Modeling the Photocatalytic Mineralization in Water of Commercial Formulation of Estrogens 17-β Estradiol (E2) and Nomegestrol Acetate in Contraceptive Pills in a Solar Powered Compound Parabolic Collector. Molecules, 20(7), 13354-13373. https://doi.org/10.3390/molecules200713354
  • 9. Colina-Márquez, J., Machuca-Martínez, F., & Puma, G. L. (2010). Radiation Absorption and Optimization of Solar Photocatalytic Reactors for Environmental Applications. Environmental Science & Technology, 44(13), 5112-5120. https://doi.org/10.1021/es100130h
  • 10. Cuevas, S. A., & Arancibia-Bulnes, C. A. (s. f.). Photocatalytic Reactor by the P1 Approximation. International Journal of Chemical Reactor Engineering, 5(1). https://doi.org/10.2202/1542-6580.1589
  • 11. Fujii, H., Terabayashi, I., Aoki, T., Inoue, Y., Na, H., Kobayashi, K., & Watanabe, M. (2022). Numerical Study of Near-Infrared Light Propagation in Aqueous Alumina Suspensions Using the Steady-State Radiative Transfer Equation and Dependent Scattering Theory. Applied Sciences, 12(3), 1190. https://doi.org/10.3390/app12031190
  • 12. Ghafoori, S., Nasirian, M., Al-Jamal, R., Mallouh, F. A., & Mehrvar, M. (2020). Statistical parameter optimization and modeling of photodegradation of methyl orange using a composite photocatalyst prepared by thermal synthesis. Environmental Science and Pollution Research, 27(36), 45650-45660. https://doi.org/10.1007/s11356-020-10301-5
  • 13. Harel, R., Burov, S., & Heizler, S. I. (2021). Asymptotic P N Approximation in Radiative Transfer Problems. Journal of Computational and Theoretical Transport, 50(5), 390-406. https://doi.org/10.1080/23324309.2020.184573
  • 14. He, C., Clifton, O., Felker-Quinn, E., Fulgham, S. R., Juncosa Calahorrano, J. F., Lombardozzi, D., Purser, G., Riches, M., Schwantes, R., Tang, W., Poulter, B., & Steiner, A. L. (2021). Interactions between Air Pollution and Terrestrial Ecosystems: Perspectives on Challenges and Future Directions. Bulletin of the American Meteorological Society, 102(3), E525-E538. https://doi.org/10.1175/BAMS-D-20-0066.1
  • 15. Howell, J. R., Mengüç, M. P., Daun, K. J., & Siegel, R.(2021). Thermal radiation heat transfer (Seventh edition). CRC Press.
  • 16. Illi, E., Bouanani, F. E., Park, K.-H., Ayoub, F., & Alouini, M.-S. (2019). An Improved Accurate Solver for the Time-Dependent RTE in Underwater Optical Wireless Communications. IEEE Access, 7, 96478-96494. https://doi.org/10.1109/ACCESS.2019.2929122
  • 17. Incropera, F. P. (s. f.). [PDF] Fundamentals Of Heat And Mass Transfer.
  • 18. Li, J., Carlson, B. E., Yung, Y. L., Lv, D., Hansen, J.,Penner, J. E., Liao, H., Ramaswamy, V., Kahn, R. A., Zhang, P., Dubovik, O., Ding, A., Lacis, A. A., Zhang, L., & Dong, Y. (2022). Scattering and absorbing aerosols in the climate system. Nature Reviews Earth & Environment, 3(6), 363-379. https://doi.org/10.1038/s43017-022-00296-7
  • 19. Li Puma, G. (2005). Dimensionless Analysis of Photocatalytic Reactors Using Suspended Solid Photocatalysts. Chemical Engineering Research and Design, 83(7), 820-826. https://doi.org/10.1205/cherd.04336
  • 20. Li Puma, G., Machuca-Martínez, F., Mueses, M., Colina Márquez, J., & Bustillo-Lecompte, C. (2020). Scale-Up and Optimization for Slurry Photoreactors. En C. Bustillo-Lecompte (Ed.), Advanced Oxidation Processes—Applications, Trends, and Prospects. IntechOpen.https://doi.org/10.5772/intechopen.91920
  • 21. Moreno-SanSegundo, J., Casado, C., & Marugán, J. (2020). Enhanced numerical simulation of photocatalytic reactors with an improved solver for the radiative transfer equation. Chemical Engineering Journal, 388, 124183. https://doi.org/10.1016/j.cej.2020.124183
  • 22. Nair, A. K., & JagadeeshBabu, P. E. (2017). Ag-TiO2 nanosheet embedded photocatalytic membrane for solar water treatment. Journal of Environmental Chemical Engineering, 5(4), 4128-4133.https://doi.org/10.1016/j.jece.2017.07.046
  • 23. Nchikou, C., Loredo-Medrano, J. Á., Hernández Ramírez, A., Colina-Marquez, J. Á., & Mueses, M.Á. (2021). Estimation of the radiation field for CPC photocatalytic reactors using a novel six flux model in two dimensions (SFM-2D). Journal of Environmental Chemical Engineering, 9(6), 106392. https://doi.org/10.1016/j.jece.2021.106392
  • 24. Ochoa-Gutiérrez, K. S., Tabares-Aguilar, E., Mueses, M. Á., Machuca-Martínez, F., & Li Puma, G. (2018). A Novel Prototype Offset Multi Tubular Photoreactor (OMTP) for solar photocatalytic degradation of water contaminants. Chemical Engineering Journal, 341, 628-638. https://doi.org/10.1016/j.cej.2018.02.068
  • 25. Otálvaro-Marín, H. L., Mueses, M. A., & Machuca Martínez, F. (2014). Boundary Layer of Photon Absorption Applied to Heterogeneous Photocatalytic Solar Flat Plate Reactor Design.International Journal of Photoenergy, 2014, 1-8. https://doi.org/10.1155/2014/930439
  • 26. Peralta Muniz Moreira, R., & Li Puma, G. (2021). Multiphysics Computational Fluid-Dynamics (CFD) Modeling of Annular Photocatalytic Reactors by the Discrete Ordinates Method (DOM) and the Six-Flux Model (SFM) and Evaluation of the Contaminant Intrinsic Kinetics Constants. Catalysis Today, 361, 77-84. https://doi.org/10.1016/j.cattod.2020.01.012
  • 27. Rizzo, L., Malato, S., Antakyali, D., Beretsou, V. G.,Đolić, M. B., Gernjak, W., Heath, E., Ivancev Tumbas, I., Karaolia, P., Lado Ribeiro, A. R., Mascolo, G., McArdell, C. S., Schaar, H., Silva, A. M. T., & Fatta-Kassinos, D. (2019). Consolidated vs new advanced treatment methods for the removal of contaminants of emerging concern from urban wastewater. Science of The Total Environment, 655, 986- 1008. https://doi.org/10.1016/j.scitotenv.2018.11.265
  • 28. Tourasse, G., & Dumortier, D. (2014). Development of a System Measuring the Solar Radiation Spectrum in 5 Planes for Daylight and PVApplications. Energy Procedia, 57, 1110-1119. https://doi.org/10.1016/j.egypro.2014.10.071
  • 29. Vaya, D., & Surolia, P. K. (2020). Semiconductor based photocatalytic degradation of pesticides: An overview. Environmental Technology & Innovation, 20, 101128. https://doi.org/10.1016/j.eti.2020.101128
  • 30. Wang, D., Mueses, M. A., Márquez, J. A. C., Machuca Martínez, F., Grčić, I., Peralta Muniz Moreira, R., & Li Puma, G. (2021). Engineering and modeling perspectives on photocatalytic reactors for water treatment. Water Research, 202, 117421. https://doi.org/10.1016/j.watres.2021.117421
  • 31. Zalazar, C. S., Romero, R. L., Martín, C. A., & Cassano, A. E. (2005). Photocatalytic intrinsic reaction kinetics I: Mineralization of dichloroacetic acid. Chemical Engineering Science, 60(19), 5240- 5254. https://doi.org/10.1016/j.ces.2005.04.050
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Details

Primary Language English
Subjects Water Treatment Processes
Journal Section Full-length articles
Authors

Clovis Nchikou 0000-0003-0773-363X

Project Number There is no project number
Publication Date October 4, 2024
Submission Date March 12, 2024
Acceptance Date May 4, 2024
Published in Issue Year 2024 Volume: 7 Issue: 2

Cite

APA Nchikou, C. (2024). Estimation and Optimization of the Radiant Field in Flat Plate Heterogeneous Photoreactors with the P1-approximation of the Radiative Transfer Equation (RTE). Journal of the Turkish Chemical Society Section B: Chemical Engineering, 7(2), 87-104. https://doi.org/10.58692/jotcsb.1450662

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J. Turk. Chem. Soc., Sect. B: Chem. Eng. (JOTCSB)