Photobioreactor radiative analysis

Photobioreactor Modeling and Radiative Transfer Analysis for Engineering Purposes... 

Analysis of Multiple-Scattering Radiative Transfer Within Photobioreactors ... 

Thus, the construction of predictive models of photobioreactors requires careful formulation of radiative transfer within the reaction volume, in order to obtain the radiation field (cf step 1 in the earlier procedure). Such analysis is developed this chapter, starting in Section 2 with determination of the light scattering and absorption properties of photosynthetic-microorganism suspensions. Next, these properties are used in Section 3 for analysis of radiative transfer and in Section 4 for rigorous solution of the radiative transfer equation by the Monte Carlo method. Finally, the thermokinetic coupling between radiative transfer and photosynthesis is addressed in Section 5. It should be noted that Sections 2 and 4 mainly summarize works that have been already published elsewhere, whereas Sections 3 and 5 include extensive original work and results. 

ANALYSIS OF MULTIPLE-SCATTERING RADIATIVE TRANSFER WITHIN PHOTOBIOREACTORS APPROXIMATE SOLUTIONS FOR THE RADIATION FIELD WITHIN ONE-DIMENSIONAL CARTESIAN PHOTOBIOREACTORS... 

Let us briefly define, according to the intensity, the usual macroscopic radiative quantities used for photobioreactor analysis. Irradiance Gj,(x) is the integral of the intensity over propagation directions ... 

In this section, we introduce a set of dimensionless quantities commonly used to characterize radiative transfer in specific configurations. These quantities are necessary for a detailed understanding of radiative transfer in photobioreactors. Depending on the value of the albedo a, the asymmetry parameter of the phase function, and the optical thickness of the medium, it is possible to conduct first analysis of the scattering regime and to identify the appropriate approximations. 

During the previous radiative-transfer analysis, the following approximate solutions were obtained for the irradiance field within the typical photobioreactor configuration in Fig. 6 ... 

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