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Two-dimensional P1 approximation (P1-2D) for the evaluation of the radiant field in annular and tubular photocatalytic reactors.

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Title: Two-dimensional P1 approximation (P1-2D) for the evaluation of the radiant field in annular and tubular photocatalytic reactors.
Authors: Nchikou, Clovis.1 (AUTHOR) clovis.nchikou@uanl.edu.mx
Source: Chemical Engineering Communications. 2025, Vol. 212 Issue 3, p422-440. 19p.
Subjects: Radiative transfer equation, Tubular reactors, Light absorption, Constants of integration, Literary sources
Abstract: The local volumetric rate of photon absorption (LVRPA) was formulated by solving the radiative transfer equation (RTE) in two dimensions using the P1 approximation approach (P1-2D) to describe the radiant field in annular and tubular photocatalytic reactors. The radiant sources employed were assumed to be periodic when applying the boundary conditions to facilitate the determination of the integration constants in the RTE solution. Three different systems were considered: S1 and S2 consisted of annular reactors, while S3 consisted of a tubular reactor. Simulations were conducted using commercial TiO2 P25 and anatase TiO2 as photocatalyst models, with their optical properties sourced from the literature. The linear source spherical emission (LSSE), Gaussian emission (GE), and uniform emission (UE) models were used as radiant sources. The LVRPA was found to decrease from the inner to the outer wall of the reactor for S1 and S2, and from the wall to the center of the reactor for S3; it was close to the values obtained using the Monte Carlo (MC) procedure in S2. The overall volumetric rate of photon absorption (OVRPA) increased exponentially with catalyst loading until a point where no significant increase was observed for each reactor. The apparent optical thickness τ App 1 ​formulated was a more reliable optimization parameter than the optical thickness. [ABSTRACT FROM AUTHOR]
Copyright of Chemical Engineering Communications is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Two-dimensional P1 approximation (P1-2D) for the evaluation of the radiant field in annular and tubular photocatalytic reactors.
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  Data: <searchLink fieldCode="JN" term="%22Chemical+Engineering+Communications%22">Chemical Engineering Communications</searchLink>. 2025, Vol. 212 Issue 3, p422-440. 19p.
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  Data: The local volumetric rate of photon absorption (LVRPA) was formulated by solving the radiative transfer equation (RTE) in two dimensions using the P1 approximation approach (P1-2D) to describe the radiant field in annular and tubular photocatalytic reactors. The radiant sources employed were assumed to be periodic when applying the boundary conditions to facilitate the determination of the integration constants in the RTE solution. Three different systems were considered: S1 and S2 consisted of annular reactors, while S3 consisted of a tubular reactor. Simulations were conducted using commercial TiO2 P25 and anatase TiO2 as photocatalyst models, with their optical properties sourced from the literature. The linear source spherical emission (LSSE), Gaussian emission (GE), and uniform emission (UE) models were used as radiant sources. The LVRPA was found to decrease from the inner to the outer wall of the reactor for S1 and S2, and from the wall to the center of the reactor for S3; it was close to the values obtained using the Monte Carlo (MC) procedure in S2. The overall volumetric rate of photon absorption (OVRPA) increased exponentially with catalyst loading until a point where no significant increase was observed for each reactor. The apparent optical thickness τ App 1 ​formulated was a more reliable optimization parameter than the optical thickness. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Chemical Engineering Communications is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1080/00986445.2024.2414177
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      – Code: eng
        Text: English
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        PageCount: 19
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      – SubjectFull: Radiative transfer equation
        Type: general
      – SubjectFull: Tubular reactors
        Type: general
      – SubjectFull: Light absorption
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      – SubjectFull: Constants of integration
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              Text: 2025
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