Radiative transfer and batch photochemical reaction in a plane slab

A fully predictive model for one‐dimensional light attenuation by Chlamydomonas reinhardtii in a torus photobioreactor

“…For this purpose, models of various complexities are described in the literature (Acien Fernandez et al, 1997;Cornet et al, 1998;Csogör et al, 2001;Suh and Lee, 2003;Tredici and Zitelli, 1998;Yun and Park, 2003). For an accurate prediction, both absorption by pigments and scattering by cells have to be considered, and because simple models, like the Lambert-Beer law, accounting only for absorption are not adapted (Leifer, 1988;Stramigioli et al, 1982), the general theory of radiative transfer must be applied to model light energy transfer in photobioreactors (Aiba, 1982;Cornet et al, 1994). Nevertheless, solving the general form of the radiative transfer equation to a finite medium such as a photobioreactor requires complex numerical tools and long calculation time.…”

Modeling and Experimental Verification of a Flat-Plate Solar Photoreactor

“…and Cengel and Ozisik . On the other hand, radiation field modeling applied to participating and reacting systems in slab geometries was also studied by Spadoni et al, Santarelli et al, Camera Roda and Santarelli, and Stramigioli et al Additional theoretical and experimental contributions for flat-plate photoreactors, employing tubular UV sources of polychromatic energy and parabolic reflectors, can be found in Alfano et al, , Cabrera et al, , and Brandi et al…”

“…Some examples where the interactions between the solar radiation and a participating plane medium (slab geometry) have been studied can be found in the papers published by Stramigioli et al 13 and Cengel and Ozisik. 14 On the other hand, radiation field modeling applied to participating and reacting systems in slab geometries was also studied by Spadoni et al, 15 Santarelli et al, 16 Camera Roda and Santarelli, 17 and Stramigioli et al 18 Additional theoretical and experimental contributions for flat-plate photoreactors, employing tubular UV sources of polychromatic energy and parabolic reflectors, can be found in Alfano et al, 19,20 Cabrera et al, 21,22 and Brandi et al 23 Among the papers mentioned in the previous paragraph, only the work published by Stramigioli et al 13 and Cengel and Ozisik 14 have specifically considered solar radiation as an energy source of the process; nonetheless, these authors have not carried out an experimental verification of the models proposed for describing the radiation transport in these systems. In the first paper 13 only the direct component of the solar radiation incident on the flat-plate photoreactor is taken into account (i.e., the corresponding diffuse component is neglected).…”

“…As was previously said, solar energy is not considered in the rest of the literature mentioned. [15][16][17][18][19][20][21][22][23] The results presented in the first group of references [15][16][17][18] concerned with the theoretical analysis of the radiation field in a participating and reacting medium, and with the study of the radiation scattering and different boundary conditions on the reactor behavior. The second group of papers [19][20][21][22][23] are involved with the theoretical modeling and the experimental verification of flat-plate photoreactors irradiated with UV lamps and reflectors.…”

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

“…This first requires describing the radiant light transfer inside the volume of the photoreactor with appropriate accuracy. For this purpose, a great many models of ranging complexities are described in the relevant literature, from the simple Lambert-Beer monodimensional model (Ten Hoopen et al, 1981;Stramigioli et al, 1982;Frohlich et al, 1983;Leifer, 1988) to complex three-dimensional ones (Spadoni et al, 1978;Aiba, 1982;Cornet et al, 1994). The most widely used models are monodimensional as these prove more tractable, especially for dynamic simulations or model-based predictive control (Cornet et al, 1995).…”