10 Knowledge models for the engineering and optimization of photobioreactors

Abstract

Spherical coordinates:The modeling of microalgal photosynthetic biomass production draws some support from the abundant literature on bioprocess modeling, in particular when mineral or CO 2 mass-transfer limitations on growth rates are considered in the same way as substrate and O 2 -transfer limitations in engineered bacterial cultivation. However, photosynthetic biomass growth exhibits highly specific features owing to its need for light energy: unlike dissolved nutrients, assumed to be homogeneous in well-mixed conditions, light energy is heterogeneously distributed in the culture due to absorption and scattering by cells, independently of the mixing conditions. As light is the principal energy source for photosynthesis, this heterogeneity alone sets microalgal cultivation systems apart from other classical bioprocesses, as they are generally limited by light transfer inside the culture media. Hence the design, optimization and control of photobioreactors (PBRs) require specific approaches.This chapter deals with developing useful knowledge models for engineering microalgal cultivation systems. Prerequisites and main concepts will be presented. Concrete illustrations will be given that use modeling to gain a deeper understanding of the complex influence of light transfer on the process, and to predict biomass productivities as a function of cultivation system engineering variables (especially depth of culture) and operating settings (residence time and incident light flux) in both artificial constant light and natural sunlight conditions. Theoretical background for radiation measurement and handling Main physical variablesGiven the crucial importance of radiative transfer description in photobioreactor modeling, it is essential to have a broad overview of the main physical quantities and definitions involved in radiation measurement and theory, together with a thorough knowledge of the conversion factors linking the two main practical systems of units (joules and micromoles of photons). There is often much confusion on these points in the microalgal growth modeling literature, conducive to misin-

Calculation of the radiative properties of photosynthetic microorganisms

“…The predictive normal-hemispherical transmittance of a microorganism suspension with a given homogeneous concentration C x is hereafter calculated by rigorously solving the radiative transfer equation for the radiative 6 The resolution of the light-scattering problem leads to cross-sections σ expressed in m 2 per particle. Considering the mass M (in kg) of this particle, one can define the cross-section e σ ¼ σ=M that is expressed in m 2 per kg of particles.…”

“…Such original future designs, or more basically the optimization of existing concepts, are only feasible if predictive knowledge-models of these processes are developed on a strong physical basis, giving them sufficient genericity for industrial purposes (simulation, sizing, scale-up, optimization, model-based predictive control, etc.). Assuming a proper mixing and that all physiological needs are maintained at their optimal conditions (pH, temperature, dissolved CO 2 , minerals), it has been clearly demonstrated in the past decades that photobioreactors are mainly governed by radiant light transfer inside the culture volume, determining the kinetic rates, energetic yields, biomass composition and pigment contents [1][2][3][4][5][6][7][8]. Accurate knowledge of the radiation fields is therefore required prior to any analysis of photosynthesis engineering, which is only feasible by properly solving the radiative transfer equation for any boundary condition, i.e.…”

Investigation and modeling of the effects of light spectrum and incident angle on the growth of Chlorella vulgaris in photobioreactors

“…In high absorbing conditions, a dark volume appears in the culture system ( γ < 1) with then negative impact on the biomass productivity due to respiration activity of the microalgae. In low absorbing conditions, because not all the light energy is absorbed ( γ > 1), this also results in lowered biomass productivity . Hence, maximal biomass productivity at a given incident light flux is achieved for a very precise condition of light transfer in the culture volume, where full light attenuation occurs but with no dark volume.…”

“…Hence, maximal biomass productivity at a given incident light flux is achieved for a very precise condition of light transfer in the culture volume, where full light attenuation occurs but with no dark volume. This is called the “luminostat regime” ( γ = 1).…”

Absorption and scattering by fractal aggregates and by their equivalent coated spheres

“…To achieve maximum biomass and biofuel productivities, light transfer in the PBRs must be optimized [19][20][21]. For example, a flat-plate PBR should be designed and operated such that the fluence rate at the backwall corresponds to the photosynthetic compensation point, i.e., the minimum amount of energy required to maintain cell metabolism [21].…”