Elsevier

Chemical Engineering Science

Volume 84, 24 December 2012, Pages 718-726
Chemical Engineering Science

Simulation of the light evolution in an annular photobioreactor for the cultivation of Porphyridium cruentum

https://doi.org/10.1016/j.ces.2012.09.017Get rights and content

Abstract

Light availability inside the reactor is often the bottleneck in microalgae cultivation and the light intensity varies with its position and time in the cultivation process. An integrated model including flow, radiation and microorganism growth is presented, in which the radiation of two complementary polychromatic light sources is resolved with the finite volume method combined with a box model. The integration of the box model into radiative transport equation (RTE) is verified first and then utilized to predict the microalgae concentration evolutions in a batch and continuous culture, respectively, which are in a good agreement with the experimental data. The evolution of light transfer in the photobioreactor (PBR) is well captured in both cultures, which provides a guideline to promote the light utilization in the PBR. The model developed and verified in this contribution has the potential to be applied as an effective tool to scale up these types of reactors and achieve an optimal biomass production with the precise control of the cultivation.

Highlights

▸ An integrated model for the cultivation of microalgae including flow, radiation and microorganism growth is presented. ▸ The evolution of light transfer in the photobioreactor (PBR) is well captured both in the batch and continuous cultures. ▸ The radiation of two polychromatic light sources is successfully predicted by the box model and corrected light/dark ratio.

Introduction

Microalgae are a new natural resource with a lot of potential industrial interests, but their production under controlled conditions requires a dedicated reactor called photobioreactors (PBRs), which differ from classic bioreactors, fermentors or enzymatic reactors, mainly by the need of a light supply in addition to classic chemical growth substrates (Pruvost et al., 2002). The culture productivity is invariably controlled by the availability of light, particularly as the scale of operation increases (Molina Grima et al., 1999, Cuaresma et al., 2011). The light attenuation in a PBR is a function of the cell concentration and the light absorption characteristics of the cellular pigments (Chrismadha and Borowitzka, 1994), while the light intensity distribution is generally non-uniform inside the reactor (Yang et al., 2004). The culture volume in a PBR can indeed be delimited schematically into two zones, namely an illuminated zone where photosynthetic activity is higher than respiration (resulting in the specific growth rate μ>0), and a dark zone where respiration is higher (μ<0). These zones may have different volumes during the process of culture cultivation. The time span that the cells reside in a specific zone is a function of the culture fluid-dynamics (Grobbelaar et al., 1996). Moreover, hydrodynamics conditions are proposed to affect the light conversion in PBRs, by modifying the light availability of suspended photosynthetic cells (Pruvost et al., 2008). Although great progresses have been achieved in modeling the hydrodynamics and radiation in PBRs (Pruvost et al., 2002, Huang et al., 2010, Huang et al., 2011), and a great deal of work has been done to develop PBRs for algal cultures, more efforts are still needed to improve PBR technologies and understand the growth mechanism of the algal culture (Ugwu et al., 2008).

A simple Lambert–Beer law has been widely adopted to predict the radiation in PBRs (e.g., Janssen et al., 2000, Suh and Lee, 2003, Benson et al., 2007, Bosma et al., 2007, Elyasi and Taghipour, 2010, Li et al., 2010). However, it is inappropriate to model the light intensity in PBRs with this oversimplified model in most cases. First, the model is correct only in dilute solutions with the monochromatic light and the light absorption independent of cells (Suh and Lee, 2003, Li et al., 2010). Second, the model cannot be used to predict the radiation distribution in an annular PBR since the lamps emit photons neither from one point source nor in parallel (Rosello Sastre et al., 2007, Imoberdorf and Mohseni, 2011). Finally, the contribution of scattered photons to neighboring volume elements is ignored in this model, while this effect should be taken into account to predict the distribution of photon flux density (PFD) properly. Even for simple geometries the errors of applying the Lambert–Beer law are often large, especially, when the scattering coefficient is big (Rosello Sastre et al., 2007). Moreover, the analysis of the PBR system based on the local available light energy presents a valid means of determining the algal cell growth rate (Suh and Lee, 2003). In recent years, the discrete ordinate method (DOM) and the finite volume method (FVM) have emerged as the two most attractive methods for modeling radiative transfer mainly due to their high accuracy, wide applicability and relatively low computational cost and computer memory requirement (Huang et al., 2011).

It is well known that photosynthesis is limited to wavelengths between 400 nm and 700 nm (photosynthetically active radiation, PAR), and microalgae is usually cultivated with polychromatic light source (Muller-Feuga et al., 2003, Berberoglu et al., 2007). However, it is very difficult to model the distribution of radiation in PBR accurately with polychromatic light due to the fact that the absorption coefficient and the scattering coefficient are both spectrally dependent. Berberoglu et al. (2007) predicted the one-dimensional steady radiation transfer in a plane-parallel PBR with a great success using a box model where the spectral dependence of the radiation was considered. However, to the best of our knowledge, there is no other published literature in predicting the polychromatic light radiation in PBRs, especially for complex structures with a two-dimensional or three-dimensional geometry. However, such occasions are frequently encountered in practice.

In addition to the effect of radiation, the period of the light/dark cycle is also important in microalgae growth. The fraction of time that microalgae spend in the illuminated zone versus the dark zone is defined as the light/dark ratio. It is evident that microalgae are out of the light field when they are in the dark zone inside the reactor or in the accessory equipments out of the reactor, during which the negative growth rate of the culture incurs negative influence on the performance of the PBR. As time evolves, the concentration of the culture increases and the dark zone in the reactor gradually becomes larger implying the light/dark ratio is time dependent. Since the photosynthesis rate increases linearly as the light intensity increases in the weak illumination zone (Luo and Al-Dahhan, 2004), how to define the light/dark ratio under such circumstance is a nontrivial problem. To the best of our knowledge, there are currently no studies in the available literature to predict the evolution of light in the process of cultivation, let alone a model to compute the light/dark ratio for these complex situations.

In this contribution, an integrated model including the multi-field coupling of flow, radiation and microorganism growth is presented to predict the evolution of cell concentration in the time course of cultivation. The FVM developed by Chai (1994) is adopted in present contribution to discretize the governing equation due to its favorable characteristics especially that it allows for conserving the radiant energy (Huang et al., 2011). Additionally, the box model applied by Berberoglu et al. (2007) is used to predict the two-dimensional radiation with polychromatic lights in annular chambers. Furthermore, the effect of dark zone in the PBR on the light/dark ratio is examined and a quantitative method is proposed. The focus of this contribution is to validate the box model integrated with the radiative transport equation (RTE) in the simulation of the polychromatic light transfer in a PBR and illustrates its practical applications in the cultivation of Porphyridium cruentum in the batch and continuous regimes, respectively. It is shown that the variation of light intensity in the PBR is non-linear and spatiotemporal. This work gives a clear insight into the evolution of the light intensity in the PBR and provides valuable information for the design and optimization of the PBR for a specific application.

Section snippets

Mathematical models and basic assumptions

The basic RTE with polychromatic radiation for an absorbing and scattering medium at the position r in the direction s can be written as (Hostikka and McGrattan, 2006, Jean-François, 2010):dIλ(r,s)ds=aλIλ(r,s)σλIλ(r,s)+σλ4π04πIλ(r,s)Φλ(s·s)dΩ

This equation indicates that the light intensity depends on the spatial position and angular direction. The sum of the absorption coefficient and the scattering coefficient is often called the extinction coefficient:βλ=aλ+σλ

The incident

Simulation conditions

The experimental data of Pruvost et al. (2002) with the Grolux lamp are chosen to evaluate the accuracy of the integration of the box model into RTE for modeling the transfer of polychromatic light with the method of FVM. The experimental data provided by Muller-Feuga et al. (2003) with batch and continuous cultures are chosen to compare with the predicted results and demonstrate the integrated model’s practical applicability. In the experiments, the inoculation concentration is fixed at 0.06 g

Validation of the RTE with box model for polychromatic light transfer

In the experiments of Pruvost et al. (2002), the extinction coefficients were changed across a wide range of optical thickness by increasing the concentration of the culture. The transmitted light intensities in the middle of the light chamber’s outer cylinder were measured and normalized. Comparisons of the predicted results using different models with the experimental data are illustrated in Fig. 3. It can be seen that the relative local light profiles predicted with different models agree

Conclusions

An integrated model with radiation transport, photosynthetic growth related to the local instantaneous photosynthetically active irradiance and flow for the cultivation of P. cruentum with polychromatic light has been established to predict the microorganism concentration in an annular PBR. The radiation in the reactor is solved by a validated FVM method. A box model, which considers the characteristics of both the spectrum of radiation and extinction coefficients of microalgae, is proposed and

Nomenclature

    a

    absorption coefficient (m−1)

    D

    dilution rate (d−1)

    G

    the incident intensity (μE m−2 s−1)

    r

    position vector (dimensionless)

    s

    direction vector (dimensionless)

    s

    scattering director vector (dimensionless)

    I

    radiation intensity, which depends on position (r) and direction (s) (μE m−2 sr−1 s−1)

    V

    volume (m3)

    Greek letters

    β

    extinction coefficient (m−1)

    σ

    scattering coefficient (m−1)

    Φ

    phase function (dimensionless)

    Ω

    solid angle in direction s (dimensionless)

    Ω

    solid angle in direction s (dimensionless)

    μ

    specific growth rate

Acknowledgements

This work is financially supported by the National Natural Science Foundation of China (Grant Nos.20976088, 21106169). The authors also gratefully acknowledge the support of the High Performance Computing Environment Branch of Chinese Academy of Sciences.

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