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Cited by 30Algal biology and biofuel productionFluid Dynamics and MixingGreenhouse Technology and Climate Control

Comprehensive Computational Model for Coupled Fluid Flow, Mass Transfer, and Light Supply in Tubular Photobioreactors Equipped with Glass Sponges

Open access
Mink, Albert, Schediwy, Kira, Posten, Clemens, Nirschl, Hermann, Simonis, Stephan, Krause, Mathias J.·2022·Energies
DOI 10.3390/en15207671
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Abstract

The design and optimization of photobioreactor(s) (PBR) benefit from the development of robust and quantitatively accurate computational fluid dynamics (CFD) models, which incorporate the complex interplay of fundamental phenomena. In the present work, we propose a comprehensive computational model for tubular photobioreactors equipped with glass sponges. The simulation model requires a minimum of at least three submodels for hydrodynamics, light supply, and biomass kinetics, respectively. First, by modeling the hydrodynamics, the light–dark cycles can be detected and the mixing characteristics of the flow (besides the mass transport) can be analyzed. Second, the radiative transport model is deployed to predict the local light intensities according to the wavelength of the light and scattering characteristics of the culture. The third submodel implements the biomass growth kinetic by coupling the local light intensities to hydrodynamic information of the CO2 concentration, which allows to predict the algal growth. In combination, the novel mesoscopic simulation model is applied to a tubular PBR with transparent walls and an internal sponge structure. We showcase the coupled simulation results and validate specific submodel outcomes by comparing the experiments. The overall flow velocity, light distribution, and light intensities for individual algae trajectories are extracted and discussed. Conclusively, such insights into complex hydrodynamics and homogeneous illumination are very promising for CFD-based optimization of PBR.

AI snapshot

Written from the paper’s full text.

TL;DR

The paper presents a coupled three-dimensional lattice Boltzmann model for tubular photobioreactors with internal glass sponges, combining fluid flow, radiative transport, CO₂ mass transfer, and biomass kinetics. It validates the light submodel against experiments and shows that the sponge structure homogenizes light and improves mixing and light exposure for algae trajectories.

Key findings

  • A coupled 3D LBM framework was implemented in OpenLB and applied to a tubular PBR with internal glass sponges, integrating hydrodynamics, light supply, mass transfer, and biomass growth kinetics.
  • The light simulation agreed well with experiments above 1% of the incident light intensity (<3 µmol/(m² s)); measurements used a biomass concentration of 9 × 10⁻⁵ g/m³.
  • The sponge structure homogenized light distribution via light dilution and focus effects, reducing dark zones and zones of light saturation or photoinhibition.
  • Without sponges, a 0.05 m diameter tubular reactor at fluid velocities of 0.01 m/s and lower showed poor radial mixing; the sponge increased both mixing and light exposure, which the authors expect to increase algal growth.

Methods

  • The model uses LBM submodels: radiative transport LBM for light, LBM for incompressible Navier–Stokes with Smagorinsky–Lilly LES, Euler–Lagrange tracking for algae trajectories, Euler–Euler advection–diffusion for CO₂, and a Monod-type photosynthesis coupling.
  • The simulated tubular PBR had diameter 0.05 m and length 1 m, with the sponge at 0.5 m; pore size was 0.02 m, grid size 5 × 10⁻⁴ m, total 1.5 × 10⁷ lattice cells, inflow mean velocity 0.01 m/s, and viscosity 1 × 10⁻⁵ kg/(ms).
  • Light validation used a diluted microalgal suspension, a planar mini quantum sensor, and a warm white LED; simulations and measurements were compared along the radius at 0°.

Limitations

  • The authors state that pore sizes were scaled up by about a factor of 10 (0.02 m vs. original ~0.003 m) due to memory and computation-time limits; bubbles are not considered; no full-scale practical implementation or geometry optimization was performed; more validation is required for complete PBR arrangements; future work could include interphase mass transfer through bubbly flow.
  • Evident from the text: biomass growth is discussed qualitatively and not quantitatively validated; the paper defers further examination of effective biomass growth to future studies.

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Integrity signals

Registry

Crossref · 10.3390/en15207671

Cites

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Statistics

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Claims the paper makes

0 of 51 cited sources checked · 0 supported · 0 flagged

  • Findingown data
    § 1. Introduction · p. 3

    The paper finds good agreement with the reference experiments.

    “Altogether, we find good agreement with the reference experiments.”
    Quote in the paperSubstantial claim
  • Findingown data
    § 3.5. Fluid Flow Regime and Gaseous Transport · p. 10

    Analyzing the algae light history along the z-direction, the sponge structure increases the general light supply clearly.

    “Analyzing the algae light history along the z -direction, the sponge structure increases the general light supply clearly.”
    Quote in the paperSubstantial claim
  • Findingown data
    § 3.6. Biomass Growth · p. 11

    The simulation data suggest that without the sponge structure, tubular reactors of a diameter of 0.05 m have poor radial mixing properties for fluid velocities of 0.01 m/s and lower.

    “The simulation data suggest that without the sponge structure, tubular reactors of a diameter of 0.05 m have poor radial mixing properties for fluid velocities of 0.01 m/s and lower.”
    Quote in the paperSubstantial claim
  • Findingown data
    § 5. Conclusions · p. 12

    The novel mesoscopic simulation model is successfully applied to a tubular PBR equipped with an internal sponge structure.

    “Subsequently to its methodological development, the novel mesoscopic simulation model is successfully applied to a tubular PBR equipped with an internal sponge structure.”
    Quote in the paperSubstantial claim
  • Findingown data
    § 3.3. Validation of Light Simulation · p. 8

    The agreement of the simulation results with the measured data is especially convincing above 1% of the incident light intensity being <3 μmol/(m2 s).

    “The agreement of the simulation results with the measured data is especially convincing above 1% of the incident light intensity being &lt;3 µmol/ ( m 2 s ) .”
    Quote in the paperSubstantial claim
  • May combine two claims. 31
  • Classified as probably not a substantial claim. 27

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    Findingreasoning
    § 5. Conclusions · p. 12

    By modeling the hydrodynamics, the light-dark cycles are detected and the mixing characteristics of the flow, besides the mass transport, are analyzed.

    “In particular, by modeling the hydrodynamics, the lightdark cycles are detected and the mixing characteristics of the flow (besides the mass transport) are analyzed.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingreasoning
    § 3.4. Light Simulation of Complex Geometry · p. 9

    Close to the walls, the reactor volume is partly subjected to photo-saturation, which induces light limitation in deeper zones.

    “Close to the walls, the reactor volume is partly subjected to photo-saturation, which induces light limitation in deeper zones.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingreasoning
    § 3.5. Fluid Flow Regime and Gaseous Transport · p. 10

    Before and after the sponge structure, the subjected light decreases and remains at a constant level.

    “Before and after the sponge structure, the subjected light decreases and remains at a constant level.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Findingown data
    § 3.6. Biomass Growth · p. 11

    The present data only indicate the tendency to light-dark cycles given the alternating light exposure history in Figure 10.

    “However, the present data only indicate the tendency to light-dark cycles given the alternating light exposure history in Figure 10.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingown data
    § 3.6. Biomass Growth · p. 11

    In contrast to an empty tubular geometry, including the sponge structure increases both the mixing and the light exposure.

    “Further, in contrast to an empty tubular geometry, including the sponge structure increases both the mixing and the light exposure.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data
    § 5. Conclusions · p. 12

    We found good agreement in the experimental measurements and documented various simulation results for the individual submodels and the coupled PBR processes.

    “We found good agreement in the experimental measurements and documented various simulation results for the individual submodels and the coupled PBR processes.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data
    § 3.5. Fluid Flow Regime and Gaseous Transport · p. 10

    While the fluid passes the sponge, the local constrictions lead to high velocities and a complex flow pattern develops for inlet velocities as slow as 0.01 m/s.

    “While the fluid passes the sponge, the local constrictions lead to high velocities and a complex flow pattern develops for inlet velocities as slow as 0.01 m/s, see Figure 8.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Premisecitation
    § 1. Introduction · p. 1

    Common approaches to overcome steep light gradients in photobioreactors include internal illuminations, reduction of the light path, enlargement of the reactor surface, or installation of light-diluting structures.

    “Common approaches to overcome the (steep) light gradients are internal illuminations [1], the straightforward reduction of the light path using more reactor units, the enlargement of the reactor surface, or the installation of light-diluting structures in the reactor [2].”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites [1] Cornet, 2010, Calculation of optimal design and ideal productivities of volumetrically lightened photobioreactors using the constructal approach, Chem. Eng. Sci. source

      Not checked in the free run.

    • cites [2] Jacobi, A., Bucharsky, E.C., Schell, K.G., Habisreuther, P., Oberacker, R., Hoffmann, M.J., Zarzalis, N., and Posten, C. (2012). The Application of Transparent Glass Sponge for Improvement of Light Distribution in Photobioreactors. J. Bioprocess. Biotech., 2. source

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation
    § 2.3. Light Distribution Model · p. 5

    Measurements of optical properties depend on the wavelength and growth conditions.

    “Measurements depend on the wavelength and growth conditions, e.g., see Table 1.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [49] Kandilian, 2016, Comparison of experimentally and theoretically determined radiation characteristics of photosynthetic microorganisms, J. Quant. Spectrosc. Radiat. Transf. source

      Not checked in the free run.

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    Premisecitation
    § 1. Introduction · p. 2

    An increased surface-to-volume ratio causes lower light intensities on the reactor surface and shorter light paths on average, yielding a more homogeneous light supply in the algal culture.

    “The increased ratio causes lower light intensities on the reactor surface and shorter light paths on average, which in turn yields a more homogeneous light supply in the algal culture.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [3] Nwoba, 2019, Light management technologies for increasing algal photobioreactor efficiency, Algal Res. source

      Not checked in the free run.

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    Premisecitation
    § 1. Introduction · p. 2

    Simulation tools for light supply and algae trajectories in photobioreactors are advanced and already validate many algorithms, including the discrete ordinate method, Monte Carlo algorithm, and finite volume method for light supply, and various Euler-Lagrange models for trajectories.

    “Simulation tools for the light supply and the algae trajectories in PBR are advanced and already validate many algorithms, including the discrete ordinate method (DOM) [8], the Monte Carlo (MC) algorithm [9,10], and finite volume method (FVM) [11] for light supply, and various Euler-Lagrange models for the trajectories [5,12,13].”
    Quote in the paperSubstantial claim0 of 4 sources checked
    • cites [8] Kong, 2014, Simulation of photosynthetically active radiation distribution in algal photobioreactors using a multidimensional spectral radiation model, Bioresour. Technol. source

      Not checked in the free run.

    • cites [9] Herrenbauer, 2001, Light distribution in a novel photobioreactor—Modelling for optimization, J. Appl. Phycol. source

      Not checked in the free run.

    • cites [10] Dauchet, 2013, The practice of recent radiative transfer Monte Carlo advances and its contribution to the field of microorganisms cultivation in photobioreactors, J. Quant. Spectrosc. Radiat. Transf. source

      Not checked in the free run.

    • cites [11] Huang, 2011, Evaluation of radiative transfer using the finite volume method in cylindrical photoreactors, Chem. Eng. Sci. source

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation
    § 1. Introduction · p. 2

    In CFD simulations, turbulence promoters implemented as profiles at the inner tube wall establish better mixing behaviors at lower flow velocities, yielding a significantly reduced energy demand.

    “In computational fluid dynamics (CFD) simulations, turbulence promoters implemented as profiles at the inner tube wall establish better mixing behaviors at lower flow velocities, yielding a significantly reduced energy demand [5].”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [5] Espinosa, 2015, CFD simulation for reduced energy costs in tubular photobioreactors using wall turbulence promoters, Algal Res. source

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

    Premisenone given
    § 2.2. Mesoscopic Modeling and the Lattice Boltzmann Method · p. 4

    The law of large numbers ensures asymptotically that the mesoscopic collision rule solves macroscopic target equations.

    “The law of large numbers ensures asymptotically that the mesoscopic collision rule solves macroscopic (target) equations.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation
    § 1. Introduction · p. 2

    Novel reactor designs, such as the Taylor vortex photobioreactor, show that complex flow patterns lead to promising mixing behaviors.

    “Lastly, novel reactor designs, such as the Taylor vortex PBR, also show that complex flow patterns lead to promising mixing behaviors [7].”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [7] Gao, 2015, CFD investigation of bubble effects on Taylor–Couette flow patterns in the weakly turbulent vortex regime, Chem. Eng. J. source

      Not checked in the free run.

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    Premisecitation
    § 2.1. Description of the Glass Sponge PBR · p. 3

    Light dilution is achieved by increasing the illumination area by the surface area of the sponges and decreases the light path in the microalgal culture.

    “The so-called light dilution is achieved by increasing the illumination area by the surface area of the sponges in addition to the surface area of the PBR itself. The sponges conduct light to deeper positions (Figure 2) in the PBR and also decrease the light path in the microalgal culture.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [2] Jacobi, A., Bucharsky, E.C., Schell, K.G., Habisreuther, P., Oberacker, R., Hoffmann, M.J., Zarzalis, N., and Posten, C. (2012). The Application of Transparent Glass Sponge for Improvement of Light Distribution in Photobioreactors. J. Bioprocess. Biotech., 2. source

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation
    § 1. Introduction · p. 2

    Adopting the principle of static mixers, the cultivation efficiency in flat-plate photobioreactors has increased by optimizing the flow pattern using CFD simulations.

    “Further, adopting the principle of static mixers, the cultivation efficiency in flat-plate PBR has increased by optimizing the flow pattern using CFD simulations [6].”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [6] Huang, 2015, Improving performance of flat-plate photobioreactors by installation of novel internal mixers optimized with computational fluid dynamics, Bioresour. Technol. source

      Not checked in the free run.

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    Interpretationreasoning
    § 2.1. Description of the Glass Sponge PBR · p. 3

    Both light dilution and pore illumination cause more homogeneous or less extreme light intensities compared to liquid cultures in an analogous geometry without sponges.

    “Both effects cause more homogeneous or less extreme light intensities compared to liquid cultures in an analogous geometry without sponges since the attenuation of light shows less decay within the shorter path.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Premisecitation
    § 1. Introduction · p. 3

    LBM simulation has a particular strength in multiphysics applications and is a suitable framework for the development of a computational model for algae trajectories and mass transfer.

    “As an alternative approximation technique in CFD, an LBM simulation has a particular strength in multiphysics applications [19-34], and is a suitable framework for the development of a computational model for algae trajectories (LagrangeLagrange) and mass transfer (Euler-Lagrange).”
    Quote in the paperSubstantial claim0 of 10 sources checked
    • cites [19] Nathen, P., Gaudlitz, D., Krause, M., and Kratzke, J. (2013, January 24–27). An extension of the Lattice Boltzmann Method for simulating turbulent flows around rotating geometries of arbitrary shape. Proceedings of the 21st AIAA Computational Fluid Dynamics Conference, San Diego, CA, USA. source

      Not checked in the free run.

    • cites [20] Trunk, 2016, Inertial dilute particulate fluid flow simulations with an Euler–Euler lattice Boltzmann method, J. Comput. Sci. source

      Not checked in the free run.

    • cites [21] Maier, 2017, Multiscale Simulation with a Two-Way Coupled Lattice Boltzmann Method and Discrete Element Method, Chem. Eng. Technol. source

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    • cites [22] Gaedtke, 2019, Flow and heat transfer simulation with a thermal large eddy lattice Boltzmann method in an annular gap with an inner rotating cylinder, Int. J. Mod. Phys. C source

      Not checked in the free run.

    • cites [23] Haussmann, 2019, Direct numerical simulation of decaying homogeneous isotropic turbulence–numerical experiments on stability, consistency and accuracy of distinct lattice Boltzmann methods, Int. J. Mod. Phys. C source

      Not checked in the free run.

    • cites [24] Simonis, 2020, On relaxation systems and their relation to discrete velocity Boltzmann models for scalar advection–diffusion equations, Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci.

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    • cites [25] Dapelo, 2021, Lattice-Boltzmann coupled models for advection–diffusion flow on a wide range of Péclet numbers, J. Comput. Sci. source

      Not checked in the free run.

    • cites [26] Haussmann, M., Reinshaus, P., Simonis, S., Nirschl, H., and Krause, M.J. (2021). Fluid–Structure Interaction Simulation of a Coriolis Mass Flowmeter Using a Lattice Boltzmann Method. Fluids, 6. source

      Not checked in the free run.

    • cites [27] Simonis, 2021, Linear and brute force stability of orthogonal moment multiple-relaxation-time lattice Boltzmann methods applied to homogeneous isotropic turbulence, Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci.

      Not checked in the free run.

    • cites [28] Siodlaczek, 2021, Numerical evaluation of thermal comfort using a large eddy lattice Boltzmann method, Build. Environ. source

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Premisecitation
    § 2.2. Mesoscopic Modeling and the Lattice Boltzmann Method · p. 4

    LBM arises from kinetic theory and the Boltzmann equation, where collision rules are defined on a mesoscopic level.

    “Unlike traditional schemes that solve discretized macroscopic equations, the LBM arises from kinetic theory and the Boltzmann equation, where collision rules are defined on a mesoscopic level [37,38].”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites [37] Cercignani, C. (1987). The Boltzmann Equation and Its Applications, Springer. Applied Mathematical Sciences. source

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    • cites [38] Babovsky, H. (2013). Die Boltzmann-Gleichung: Modellbildung–Numerik–Anwendungen, Vieweg+Teubner Verlag. Leitfäden der angewandten Mathematik und Mechanik.

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    Premisecitation
    § 2.3. Light Distribution Model · p. 5

    RTLBM was established as a numerical tool to solve the general radiative transport equation.

    “In previous works, Mink et al. [16,17] established the radiative transport LBM (RTLBM) as a numerical tool to solve the general RTE.”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites [16] Mink, 2016, A 3D Lattice Boltzmann method for light simulation in participating media, J. Comput. Sci. source

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    • cites [17] Mink, 2020, Radiative transfer lattice Boltzmann methods: 3D models and their performance in different regimes of radiative transfer, J. Quant. Spectrosc. Radiat. Transf. source

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  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Premisecitation
    § 2.2. Mesoscopic Modeling and the Lattice Boltzmann Method · p. 4

    LBM is well-known for intuitive modeling, intrinsically parallelizable algorithms, the ability to address complex boundary conditions, and multiphysics models.

    “LBM is well-known for intuitive modeling, intrinsically parallelizable algorithms, the ability to address complex boundary conditions, and multiphysics models [39,40].”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites [39] Aidun, 2010, Lattice-Boltzmann method for complex flows, Annu. Rev. Fluid Mech. source

      Not checked in the free run.

    • cites [40] Krüger, T., Kusumaatmaja, H., Kuzmin, A., Shardt, O., Silva, G., and Viggen, E.M. (2017). The Lattice Boltzmann Method, Springer. source

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    Premisecitation
    § 2.3. Light Distribution Model · p. 5

    Scattering must be analyzed within thin suspensions to avoid multiple scattering events that would blur the analysis of one single scattering event.

    “Moreover, the scattering must be analyzed within thin suspensions to avoid multiple scattering events that would blur the analysis of one single scattering event [45-47].”
    Quote in the paperNot a substantial claim0 of 3 sources checked
    • cites [45] Berberoglu, 2009, Radiation characteristics of Botryococcus braunii, Chlorococcum littorale, and Chlorella sp. used for fixation and biofuel production, J. Quant. Spectrosc. Radiat. Transf. source

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    • cites [46] Kandilian, 2016, Simple method for measuring the spectral absorption cross-section of microalgae, Chem. Eng. Sci. source

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    • cites [47] McHardy, 2018, Numerical analysis of the effects of air on light distribution in a bubble column photobioreactor, Algal Res. source

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based). May combine two claims.

    Premisenone given
    § 1. Introduction · p. 3

    LBM brings forth almost perfect parallelizability, which allows highly scalable simulations on high-performance computing machinery.

    “In addition, LBM brings forth almost perfect parallelizability, which allows highly scalable simulations on high-performance computing machinery.”
    Quote in the paperNot a substantial claim

  • Classified as probably not a substantial claim.

    Study design and conductreasoning
    § 2.1. Description of the Glass Sponge PBR · p. 3

    Due to computational limitations, the characteristics of the sponges were scaled up by a factor of 10 compared to the study with 8 pores per inch, porosity 0.9, and specific surface area 568 m2/m3.

    “Due to computational limitations, the characteristics of the sponges were scaled up by a factor of 10 compared to the above-mentioned study with 8 pores per inch, the porosity of 0.9, and the specific surface area of 568 m 2 /m 3 .”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation
    § 2.3. Light Distribution Model · p. 5

    Spectral light regimes are typically approximated by the Box model, where the radiative transport equation is solved for several wavelengths and the computed intensities are averaged.

    “Spectral light regimes are typically approximated by the Box model, where the RTE is solved for several wavelengths and the computed intensities are averaged [43,44].”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites [43] Huang, 2012, Simulation of the light evolution in an annular photobioreactor for the cultivation of Porphyridium cruentum, Chem. Eng. Sci. source

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    • cites [44] McHardy, 2018, Spectral simulation of light propagation in participating media by using a lattice Boltzmann method for photons, Appl. Math. Comput.

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    Premisenone given
    § 2.3. Light Distribution Model · p. 4

    Light transport in a spatially homogeneous medium is governed by the radiative transport equation.

    “The light transport in a spatially homogeneous medium is governed by the radiative transport equation (RTE)”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Premisecitation
    § 2.1. Description of the Glass Sponge PBR · p. 3

    Algae within the pores of the sponges become illuminated from all directions due to multiple and complex reflections in the glass sponges, focusing light and counteracting attenuation.

    “Algae grow within the pores of the sponges and become illuminated from all directions due to the multiple and complex reflections in the glass sponges. The illumination from all directions toward the center of each pore focuses the light, as shown in Figure 3. This focus effect counteracts the attenuation of light due to the scattering and absorption of algae along the light path.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [2] Jacobi, A., Bucharsky, E.C., Schell, K.G., Habisreuther, P., Oberacker, R., Hoffmann, M.J., Zarzalis, N., and Posten, C. (2012). The Application of Transparent Glass Sponge for Improvement of Light Distribution in Photobioreactors. J. Bioprocess. Biotech., 2. source

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based). May combine two claims.

    Interpretationreasoning
    § 2.6. Algae Growth Model and Coupling · p. 7

    All computational operations are strictly local and retain the perfect parallelizability of LBM.

    “All computational operations are strictly local and retain the perfect parallelizability of LBM.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationreasoning
    § 3.4. Light Simulation of Complex Geometry · p. 9

    The approach of increasing the light intensities translates the deficit to other reactor regions and barely solves the issue of heterogeneous light supply.

    “Hence, the approach of increasing the light intensities translates the deficit to other reactor regions and barely solves the issue of heterogeneous light supply.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationown data
    § 3.5. Fluid Flow Regime and Gaseous Transport · p. 10

    The constant light level before and after the sponge shows the laminar character of the flow field and how algae cells are not mixed and accordingly subjected to entirely different light regimes.

    “The latter shows the laminar character of the flow field and how algae cells are not mixed and accordingly subjected to entirely different light regimes.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationreasoning
    § 3.4. Light Simulation of Complex Geometry · p. 10

    This so-called light dilution reduces both dark zones and zones of light saturation or even photoinhibition.

    “This so-called light dilution reduces both dark zones and zones of light saturation or even photoinhibition.”
    Quote in the paperSubstantial claim
    • Rests on an assumption: The increase of the illuminating surface reduces the incident light intensity inversely proportional to the increase of the illumination surface.

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Premisecitation
    § 4. Discussion · p. 11

    Gupta studied ellipsoidal particle paths for fully resolved pipe flows in tubular PBR at Reynolds numbers of about 3400 and obtained enhanced mixing and light intensities.

    “For example, Gupta [55] studied ellipsoidal particle paths for fully resolved pipe flows in tubular PBR at Reynolds numbers of about 3400 and obtained enhanced mixing and light intensities.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [55] Gupta, A. (2019). Transport and Hydrodynamic Stresses in Turbulent Flows with Application to Photo-Bioreactors. [Ph.D. Thesis, Technische Universiteit Eindhoven].

      Not checked in the free run.

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    Interpretationown data
    § 3.3. Validation of Light Simulation · p. 8

    The light model is validated and suitable for more complex geometries using the same optical principles and characteristics of the cells.

    “The light model is validated and suitable for more complex geometries using the same optical principles and characteristics of the cells.”
    Quote in the paperSubstantial claim
    • Rests on an assumption: The light intensities below 1% of the incident light intensity (<3 µmol/(m2 s)) are too low to sufficiently contribute to algal growth or maintain the requirements of the cells.

  • Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

    Interpretationreasoning
    § 3.4. Light Simulation of Complex Geometry · p. 10

    This effect is even more substantial in a real setup, since light gradients become steeper when illumination from the sun occurs from one side of the PBR only.

    “This effect is even more substantial in a real setup, since light gradients become steeper when illumination from the sun occurs from one side of the PBR only.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationcitation
    § 2.4. Fluid Flow Regime and Lagrangian Particles · p. 6

    Despite its simplicity, the model allows study of the time evolution of a representative population of algae in the fluid flow and to draw conclusions about trapped algae in vortices, the quality of mixing, and the induced shear stress.

    “In summary, despite its simplicity, the model allows us to study the time evolution of a representative population of algae in the fluid flow and to draw conclusions about trapped algae in vortices, the quality of mixing, and the induced shear stress [13], respectively.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [13] Lapin, 2004, Dynamic Behavior of Microbial Populations in Stirred Bioreactors Simulated with Euler–Lagrange Methods: Traveling along the Lifelines of Single Cells, Ind. Eng. Chem. Res. source

      Not checked in the free run.

    • The authors state this as an assumption: Algae do not affect the fluid flow at commonly used biomass concentrations in tubular photobioreactors.

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation
    § 2.5. Mass Transport · p. 6

    The LBM framework used here for the coupled equation system (4) and (7) has been presented and validated previously for particle flow by Trunk et al.

    “Note that the LBM framework used here for a coupled equation system, such as (4) and (7), has been presented and validated previously for particle flow by Trunk et al. [20].”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [20] Trunk, 2016, Inertial dilute particulate fluid flow simulations with an Euler–Euler lattice Boltzmann method, J. Comput. Sci. source

      Not checked in the free run.

  • May combine two claims.

    Interpretationreasoning
    § 3.4. Light Simulation of Complex Geometry · p. 9

    Increasing the light intensity might reduce dark zones, but the higher incident light intensity might expose the suspension close to the light source to photo-inhibition, possibly yielding inefficient light use or even damage to the algal cells.

    “Increasing the light intensity might reduce these dark zones. However, the higher incident light intensity might expose the suspension close to the light source to photo-inhibition, possibly yielding inefficient light use or even damage to the algal cells.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based). May combine two claims.

    Study design and conductnone given
    § 3.1. Geometry and Computational Parameters · p. 7

    When simulating tubular geometries, the hydrodynamics develop after the inlet and are required to settle to avoid numerical errors.

    “When simulating tubular geometries, the hydrodynamics develop after the inlet and are required to settle to avoid numerical errors.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationreasoning
    § 4. Discussion · p. 11

    Sponge structures uphold high mixing and light intensities but allow lower flow velocities and shorter reactor geometries.

    “From this point of view, it is again very promising to include sponge structures instead, which uphold high mixing and light intensities but allow lower flow velocities and shorter reactor geometries.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S4 (based). May combine two claims.

    Study design and conductnone given
    § 3.3. Validation of Light Simulation · p. 8

    The low biomass concentration minimizes the number of scattering and absorption events and maximizes the spatial resolution compared to the sensor's size.

    “The low biomass concentration minimizes the number of scattering and absorption events and maximizes the spatial resolution compared to the sensor's size.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S2 (checkable).

    Interpretationreasoning
    § 5. Conclusions · p. 12

    The design, as well as the optimization of such reactors, benefit directly from the robust and quantitatively accurate computational model presented here, which incorporates the complex interplay of the governing transport dynamics in PBR.

    “Conclusively, the design, as well as the optimization of such reactors, benefit directly from the robust (and quantitatively accurate) computational model presented here, which incorporates the complex interplay of the governing transport dynamics in PBR.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Study design and conductnone given
    § 4. Discussion · p. 12

    An actual practical implementation of the digital PBR twin to optimize, for example, a full-scale PBR geometry was not considered here.

    “An actual practical implementation of the digital PBR twin to optimize, for example, a full-scale PBR geometry was not considered here.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Study design and conductreasoning
    § 3.3. Validation of Light Simulation · p. 8

    To clearly differentiate the effects, the glass tube is partially covered, which prevents undesired reflection on the glass surface.

    “To clearly differentiate these effects, the glass tube is partially covered, which prevents undesired reflection on the glass surface.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Premisecitation
    § 4. Discussion · p. 11

    Algae can be damaged at too-high Reynolds numbers, which in turn reduces the overall productivity of PBR.

    “Nevertheless, algae can be damaged at too-high Reynolds numbers, which in turn reduces the overall productivity of PBR [55].”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [55] Gupta, A. (2019). Transport and Hydrodynamic Stresses in Turbulent Flows with Application to Photo-Bioreactors. [Ph.D. Thesis, Technische Universiteit Eindhoven].

      Not checked in the free run.

  • May combine two claims.

    Interpretationown data
    § 3.5. Fluid Flow Regime and Gaseous Transport · p. 10

    Along the trajectory, the algae are subjected to radial movements that indicate a non-laminar flow pattern and approve the mixing characteristics of the particular reactor design with built-in sponges.

    “Along the trajectory, the algae are subjected to radial movements that indicate a non-laminar flow pattern and approve the mixing characteristics of the particular reactor design with built-in sponges.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S4 (based).

    Interpretationnone given
    § 4. Discussion · p. 12

    For the first time, we propose a complete framework for the three-dimensional kinetic simulation of photobioreactors based on LBM.

    “For the first time, we propose a complete framework for the three-dimensional kinetic simulation of photobioreactors based on LBM.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationreasoning
    § 3.6. Biomass Growth · p. 11

    The novel geometry used here will definitely lead to increased algal growth and, thus, optimize the biomass growth of the overall PBR.

    “Conclusively, the novel geometry used here will definitely lead to increased algal growth and, thus, optimize the biomass growth of the overall PBR.”
    Quote in the paperSubstantial claim
    • Rests on an assumption: A more homogeneous light supply enables higher biomass productivity.

  • Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

    Premisenone given
    § 3.3. Validation of Light Simulation · p. 8

    Algal absorption and scattering induce additional attenuation.

    “The algal absorption and scattering induce additional attenuation.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Interpretationnone given
    § 3.6. Biomass Growth · p. 11

    The modeling of the trajectory and its coupling to the light model allows studying the light history of individual algae cells.

    “The modeling of the trajectory (and its coupling to the light model) allows studying the light history of individual algae cells.”
    Quote in the paperNot a substantial claim
49 of 49

  • The paper relies on this without support.

    The combination of models for coupling light supply with algae trajectories, eventually taking additional mass transfer into account, remains a numerical challenge.

    “Nevertheless, the combination of models for coupling the light supply with the algae trajectories (eventually taking additional mass transfer into account) remains a numerical challenge.”

  • The authors state this as an assumption.

    Algae do not affect the fluid flow at commonly used biomass concentrations in tubular photobioreactors.

    “The present Euler-Lagrange approach using (5) and (6) assumes that algae do not affect the fluid flow, which is valid for commonly used biomass concentrations in tubular PBR.”

  • The authors state this as an assumption.

    Biomass growth is light-limited.

    “Here, a Monod model that assumes a light-limited biomass growth was implemented.”

  • The authors state this as an assumption.

    Specific biomass growth is linearly connected to the photosynthesis rate.

    “Further, we expect a linear connection of specific biomass growth and photosynthesis rate (8).”

  • The paper relies on this without support.

    Optical parameter values rise with locally increased biomass concentrations and vice versa.

    “The parameter values rise with locally increased biomass concentrations and vice versa.”

  • The paper relies on this without support.

    The inaccuracy of complete photobioreactor simulations limits progress in reactor design and process development.

    “The inaccuracy of complete PBR simulations limits the progress in the reactor design and process development.”

  • The paper relies on this without support.

    The light intensities below 1% of the incident light intensity (<3 µmol/(m2 s)) are too low to sufficiently contribute to algal growth or maintain the requirements of the cells.

    “The light intensities in this order of magnitude are too low to sufficiently contribute to the algal growth or maintain the requirements of the cells.”

  • The paper relies on this without support.

    The increase of the illuminating surface reduces the incident light intensity inversely proportional to the increase of the illumination surface.

    “The increase of the illuminating surface goes along with a reduction of the incident light intensity inversely proportional to the increase of the illumination surface.”

  • The paper relies on this without support.

    A more homogeneous light supply enables higher biomass productivity.

    “A more homogeneous light supply enables higher biomass productivity.”
9 of 9

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

  • Some less commonly used models include the application of Lambert-Beers law in 2D or the Diffusion approximation of the RTE.

    “Besides, some less commonly used models include the application of Lambert-Beers law in 2D [126] or the Diffusion approximation of the RTE [21].”

    From Modeling and Simulation of Photobioreactors with Computational Fluid Dynamics—A Comprehensive Review (2022) · cites this paper as [21]

    The citation [21] is attached to the diffusion approximation of the RTE, not the 2D Lambert–Beer model. In §2.3 (p. 4), the source instead says it uses a radiative-transport lattice Boltzmann method to approximate the RTE; its stated method is not the diffusion approximation attributed to it. (LLM, conf=0.82)

    Checked by a reasoning model — may be wrong.

    Experimental — accuracy not yet measured

  • Reflection or refraction at the various interfaces cause additional heterogeneity of the light intensity distribution and even dark regions may arise in consequence.

    “It is also often neglected that reflection or refraction at the various interfaces cause additional heterogeneity of the light intensity distribution and even dark regions may arise in consequence [21,85].”

    From Modeling and Simulation of Photobioreactors with Computational Fluid Dynamics—A Comprehensive Review (2022) · cites this paper as [21]

    The Light Distribution Model (p. 5) describes reflection and refraction at surfaces and the resulting attenuation of light. The Light Simulation of Complex Geometry (p. 9) reports a heterogeneous distribution with dark zones, but attributes those zones to a steep radial light gradient, not specifically to reflection or refraction at interfaces. (LLM, conf=0.82)

    Experimental — accuracy not yet measured

  • In complex geometries, an accurate estimation of the light distribution requires three-dimensional computations.

    “In complex geometries, an accurate estimation of the light distribution requires three-dimensional computations [21].”

    From Modeling and Simulation of Photobioreactors with Computational Fluid Dynamics—A Comprehensive Review (2022) · cites this paper as [21]

    The Introduction (p. 2) describes a three-dimensional model for light supply in a tubular photobioreactor with sponges, and the Validation section (p. 8) reports agreement with measured light intensities. The paper supports the use of 3D computation for this complex geometry, but does not establish that accurate estimates in complex geometries require 3D computation rather than another approach. (LLM, conf=0.85)

    Experimental — accuracy not yet measured

  • The purpose of the listed models covers a variety of applications, including mechanistic understanding, investigations on flashing-light effect, design optimization, and optimization of operating conditions.

    “The purpose of the listed models covers a variety of applications, including the mechanistic understanding of photobioreactors [17-21], investigations on the flashing-light effect [22-31], photobioreactor design optimization [21,22,29,32-42] and optimization of operating conditions [26,34-36,43-45].”

    From Modeling and Simulation of Photobioreactors with Computational Fluid Dynamics—A Comprehensive Review (2022) · cites this paper as [21]

  • Some researchers selected solving the full RTE numerically in one or more dimensions.

    “Instead of using simplified or analytical models, some researchers selected the second approach, which is solving the full RTE numerically in one or more dimensions [18,21,26-28,34].”

    From Modeling and Simulation of Photobioreactors with Computational Fluid Dynamics—A Comprehensive Review (2022) · cites this paper as [21]

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

Each contradiction between two passages listed here was confirmed by an independent check.

  • Light-dark cycles are described as detected and only suggested

    Minor

    The conclusion says the light-dark cycles are detected, but the results section says the data only indicate a tendency toward them.

  • Simulated reactor length is given as both 0.05 m and 1 m

    Minor

    Section 2.1 gives the simulated geometry a length of 0.05 m, whereas Section 3.1 gives the simulated tubular PBR a length of 1 m.

2 of 2

Cites

Flagged first, then by citations

Research works printed but not linked: 1

  1. Mink, A. (2022). A Comprehensive Computational Model for Coupled Fluid Flow, Mass Transfer and Light Supply in Photobioreactors with Lattice Boltzmann Methods. [Ph.D. Thesis, Karlsruher Institut für Technologie (KIT)].

Cited by

Sorted by citations

Related

Authors
Mink, A., Schediwy, K., Posten, C., Nirschl, H., Simonis, S., & Krause, M. J.
Affiliations
Karlsruhe Institute of Technology (DE)
Corresponding author
Simonis, Stephan
ORCID
Venue
Energies
Publisher
MDPI AG
Published
2022-10-18
Volume
15
Issue
20
Pages
7671
ISSN
1996-1073 (ISSN-L)
DOI
10.3390/en15207671
OpenAlex
W3183274829
Semantic Scholar
79bb965b5faa89eb1544fd929a09f8bd7c88ff19
Cited by
30
References
56
Citations by year
2026: 7 · 2025: 13 · 2024: 3 · 2023: 4 · 2022: 3
FWCI
1.04
Type
journal article
Language
en
Open access
Licence
Locations
  • Energies (publishedVersion, cc-by)
  • Repository KITopen (Karlsruhe Institute of Technology) (publishedVersion, cc-by)
  • RePEc: Research Papers in Economics (submittedVersion)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
  • KITopen (cc-by)
Funders
Deutsche Forschungsgemeinschaft (DFG) (322739165)
Topics
  • Physical Sciences › Energy › Renewable Energy, Sustainability and the Environment › Algal biology and biofuel production
  • Physical Sciences › Engineering › Biomedical Engineering › Fluid Dynamics and Mixing
  • Life Sciences › Agricultural and Biological Sciences › Plant Science › Greenhouse Technology and Climate Control
Keywords
tubular photobioreactor, Hexactinellida, computational fluid dynamics, mass transfer, light distribution, radiative transfer modeling, algal growth kinetics, hydrodynamics, light-dark cycle, CO2 concentration

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Claims read by deepseek-v4.1-flash under definition version 3 (extract-v3) on 2026-10-07.

Classified by jev-1.13-20260917 (gold-guideline-v0.2) on 2026-10-07.

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