Photobioreactor implementation

Additional engineering studies will have to be conducted to identify the most efficient physical designs to implement for photobioreactor systems after the biological and materials challenges are solved. 

The main steps in our model and their organization within this chapter are summarized in Fig. 1. Our practice of the Monte Carlo method extends beyond the solution of the radiative transfer equation in Section 4, we also argue that the Monte Carlo method is well suited for numerical implementation of the entire model, especially in research on photobioreactors with complex geometric structure. 

Implementation of the Single Scattering Approximation for an Equivalent Transport Problem Application to a Flat-Plate Photobioreactor... 

NUMERICAL IMPLEMENTATION OF PHOTOBIOREACTOR MODELS BY THE MONTE CARLO METHOD, INCLUDING RIGOROUS SOLUTION OF THE RADIATIVE TRANSFER EQUATION FOR COMPLEX GEOMETRIC STRUCTURE... 

With the Monte Carlo method, the difficulty with the geometric complexity is reduced to calculation of the intersections between the straight rays and surfaces. In Section 4.1, this situation corresponds to calculation of the intersection between half-hnes starting at Xy in the direction (Oj and the surface R.yjJ- [Step (3) of our algorithm]. Indeed, the calculation of these intersections for the complex surface 7 . U. F of a DiCoFluV is the only additional difficulty, in contrast to the implementation for a one-dimensional Cartesian photobioreactor (see Fig. 25). 

Figure 27 Calculation time for estimating the specific rate of photon absorption A within the reaction volume of the DiCoFluV photobioreactor, as a function of the number of light-diffusing optical fibers. The results were obtained in EDStar (Delatorre et al., 2014) by implementation of the algorithm presented in Section 4.1 for different versions of the geometric structure in Fig. 26B (containing different numbers of fibers).

When a Monte Carlo algorithm is used for estimation of any physical quantity B), a simple and fast additional procedure can be implemented that simultaneously estimates sensitivity of B to any parameter (Delatorre et al., 2014). This practically means that when Monte Carlo code is available that computes B, only a few additional lines of code are needed so that partial derivatives of B are also computed with respect to all the parameters ofinter-est. We are interested either in physical analysis (how does B evolve when a parameter is modified ) or in optimal design (what is the optimal value of the parameter for a target value of E ). A general overview of sensitivity estimation is available in Delatorre et al. (2014). This methodology was implemented in Dauchet et al. (2013) and Delatorre et al. (2014) to evaluate sensitivity of the radiation field within a DiCoFluV photobioreactor (see... 

Muller-Feuga A, Pruvost J, Le Guedes R, Le Dean L, Legentilhomme P, LegrandJ Swirling flow implementation in a photobioreactor for batch and continuous cultures of Porphyridium cruentum, Biotechnol Bioeng 84(5) 544—551, 2003b. 

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