Jean-François Cornet

A simplified monodimensional approach for modeling coupling between radiant light transfer and growth kinetics in photobioreactors

Abstract Local information is essential to photobioreactor modeling because of medium anisotropy in radiant light energy. Local available energy can be calculated using complex equations, applying the physical laws of radiative transfer and independently accounting for light absorption and scattering in the reactor. In this paper, these equations are simplified postulating monodimensional approximation for the radiation field. This simplification is established for rectangular, cylindrical and spherical coordinates, leading to simple analytical solutions for available radiant energy profiles inside the reactor. This approach provides a method of determining working illuminated volume defined as the photobioreactor volume with sufficient radiant light energy for microorganism growth. This enables the coupling between radiant light transfer and growth kinetics to be easily studied. Physical light transfer models are used to simulate volumetric biomass growth rates in a cylindrical photobioreactor with kinetic parameters obtained from batch cultures of the cyanobacterium Spirulina platensis in rectangular photoreactors. These calculations are compared with experimental data obtained on continuous cultures in a wide range of incident radiant energy fluxes. The model is found to have a good predictability and robustness.

A Simple and reliable formula for assessment of maximum volumetric productivities in photobioreactors

This article establishes and discusses the consistency and the range of applicability of a simple but general and predictive analytical formula, enabling to easily assess the maximum volumetric biomass growth rates (the productivities) in several kinds of photobioreactors with more or less 15% of deviation. Experimental validations are performed on photobioreactors of very different conceptions and designs, cultivating the cyanobacterium Arthrospira platensis, on a wide range of volumes and hemispherical incident light fluxes. The practical usefulness of the proposed formula is demonstrated by the fact that it appears completely independent of the characteristics of the material phase (as the type of reactor, the kind of mixing, the biomass concentration…), according to the first principle of thermodynamics and to the Gauss‐Ostrogradsky theorem. Its ability to give the maximum (only) kinetic performance of photobioreactors cultivating many different photoautotrophic strains (cyanobacteria, green algae, eukaryotic microalgae) is theoretically discussed but experimental results are reported to a future work of the authors or to any other contribution arising from the scientific community working in the field of photobioreactor engineering and potentially interested by this approach.

Production, isolation and preliminary characterization of the exopolysaccharide of the cyanobacterium Spirulina platensis

SummaryThe soluble exocellular polysaccharide secreted by the filamentous cyanobacteria Spirulina platensis is a primary metabolite. It is formed by ten different types of monomer units including six neutral sugars (xylose, rhamnose, fucose, galactose, mannose and glucose in the proportions 1.3/0.3/0.7/2.7/traces/2), two unidentified sugars, two uronic acids and sulphate groups accounting for 40 % and 5 % respectively of the mass of the molecule. This polysaccharide displays a non Newtonian behaviour and a strong pseudoplastic characteristic that may originate in the polyelectrolytic property of the molecule.

Calculation of optimal design and ideal productivities of volumetrically lightened photobioreactors using the constructal approach

Abstract This article examines the optimal design and ideal kinetic performances of volumetrically lightened photobioreactors (PBR). From knowledge models developed for several years by the author, simple theoretical rules are established at first to define the optimal functioning of solar and artificially lightened PBR. The constructal approach is then used accordingly, which allows the emergence of the optimal design, or the best lighting structures assembly, in Cartesian and curvilinear geometries, with a privileged treatment for the practical case of the 2D-cylindrical geometry. The obtained results confirm the considerable potential of this approach which is applied here for the first time to the case of the radiant light transfer in participating and reactive media. This enables to define clearly, from a theoretical point of view, the concept of ideal PBR (both for solar or artificial illuminations), which is demonstrated to correspond exactly in most cases to volumetrically lightened PBR, mainly for the solar DiCoFluV (Dilution Controlee du Flux en Volume) concept developed in this article. For this last case, the results of the calculations allow to announce maximal biomass productivities as thermodynamic limits, what can contribute to clarify a today confused debate on this point. The work proposed in this article finally establishes guidelines to conceive more efficient large-scale PBR of any desired geometry and criteria like volume (for artificial illumination) or surface (for solar illumination) maximum productivities and internal or external irradiation.

Kinetic modeling of the photosynthetic growth of Chlamydomonas reinhardtii in a photobioreactor

The aim of this study was to establish and validate a model for the photosynthetic growth of Chlamydomonas reinhardtii in photobioreactors (PBRs). The proposed model is based on an energetic analysis of the excitation energy transfer in the photosynthesis apparatus (the Z‐scheme for photosynthesis). This approach has already been validated in cyanobacteria (Arthorspira platensis) and is extended here to predict the volumetric biomass productivity for the microalga C. reinhardtii in autotrophic conditions, taking into consideration the two metabolic processes taking place in this eukaryotic microorganism, namely photosynthesis and respiration. The kinetic growth model obtained was then coupled to a radiative transfer model (the two‐flux model) to determine the local kinetics, and thereby the volumetric biomass productivity, in a torus PBR. The model was found to predict PBR performances accurately for a broad set of operating conditions, including both light‐limited and kinetic growth regimes, with a variance of less than 10% between experimental results and simulations.

A model-based method for investigating bioenergetic processes in autotrophically growing eukaryotic microalgae: Application to the green algae Chlamydomonas reinhardtii

A constraint‐based modeling approach was developed to investigate the metabolic response of the eukaryotic microalgae Chlamydomonas reinhardtii under photoautotrophic conditions. The model explicitly includes thermodynamic and energetic constraints on the functioning metabolism. A mixed integer linear programming method was used to determine the optimal flux distributions with regard to this set of constraints. It enabled us, in particular, to highlight the existence of a light‐driven respiration depending on the incident photon flux density in photobioreactors functioning in physical light limitation.

Revised Technique for the Determination of Mean Incident Light Fluxes on Photobioreactors

The cultivation of photosynthetic microorganisms in photobioreactors mainly occurs under limitation by radiant light energy transfer at a rate controlled by the total radiant light energy entering the reactor. Consequently, the mean incident radiant light flux onto the reactor is a key technical quantity in both kinetic and energetic studies of such processes. In this paper, a general revised method for determining the incident radiant light flux is proposed using a chemical actinometer, Reineckes salt. New easy procedures are given for preparing the reactive salt and measuring the photoreaction rate. Additionally, a mathematical model makes it possible to apply the technique to different reactor geometries and lighting systems with no limiting operating conditions for the incident flux. The method gives accurate results and constitutes a simple, general and reliable method for evaluating the maximum performance of photobioreactors. It can also be a tool for developing monodimensional models for simulation.

Modeling photoheterotrophic growth kinetics of Rhodospirillum rubrum in rectangular photobioreactors

Based on a previously established model for radiant light transfer in photobioreactors (PBR), taking into account absorption and scattering of light, a new knowledge model for coupling radiant light energy available and local growth kinetics in PBRs for the photoheterotrophic bacteria Rhodospirillum rubrum is discussed. A revised method is presented for the calculation of the absorption and scattering coefficients. The specific characteristics of the electron‐transfer chains in such microorganisms leads to definition of three different metabolic zones in the PBR, explaining the behavior of mean kinetics observed in a wide range of incident light fluxes. The model is validated in rectangular PBRs for five different carbon sources and proved robust and fully predictive. This approach can be considered for simulation and model‐based predictive control of PBRs cultivating photoheterotrophic microorganisms.

Modeling Stability of Photoheterotrophic Continuous Cultures in Photobioreactors

Continuous cultures of the purple non‐sulfur bacterium Rhodospirillum rubrum were grown in a cylindrical photobioreactor in photoheterotrophic conditions, using acetate as carbon source. A new kinetic and stoichiometric knowledge model was developed, and its ability to simulate experimental results obtained under varying incident light fluxes and residence times is discussed. The model accurately predicts the stable, unstable, or oscillating behavior observed for the reactor productivity. In particular, the values of residence time corresponding to a subcritical bifurcation with a typical hysteresis effect are calculated and analyzed. The robustness of the proposed model allows the engineering operating domain of the photobioreactor function to be set and offers a promising tool for the design and control of such photoheterotrophic processes.

Theoretical investigation of biomass productivities achievable in solar rectangular photobioreactors for the cyanobacterium Arthrospira platensis

Modeling was done to simulate whole‐year running of solar rectangular photobioreactors (PBRs). Introducing the concept of ideal reactor, the maximal biomass productivity that could be achieved on Earth on nitrate as N‐source was calculated. Two additional factors were also analyzed with respect to dynamic calculations over the whole year: the effect of PBR location and the effects of given operating conditions on the resulting decrease in productivity compared with the ideal one. Simulations were conducted for the cyanobacterium Arthospira platensis, giving an ideal productivity (upper limit) in the range 55–60 tX ha−1 year−1 for a sun tracking system (and around 35–40 tX ha−1 year−1 for a fixed horizontal PBR). For an implantation in France (Nantes, west coast), the modification in irradiation conditions resulted in a decrease in biomass productivity of 40%. Various parameters were investigated, with special emphasis on the influence of the incident angle of solar illumination on resulting productivities, affecting both light capture and light transfer inside the bulk culture. It was also found that with appropriate optimization of the residence time as permitted by the model, productivities close to maximal could be achieved for a given location.