Radiative transfer approach using Monte Carlo Method for actinometry in complex geometry and its application to Reinecke salt photodissociation within innovative pilot-scale photo(bio)reactors

Abstract

In this article, a complete radiative transfer approach for estimating incident photon flux density by actinometry is presented that opens the door to investigation of large-scale intensified photoreactors. The approach is based on an original concept: the analysis of the probability that a photon entering the reaction volume is absorbed by the actinometer. Whereas this probability is assumed to be equal to one in classical actinometry, this assumption can no longer be satisfied in many practical situations in which optical thicknesses are low. Here we remove this restriction by using most recent advances in the field of radiative transfer Monte Carlo, in order to rigorously evaluate the instantaneous absorption-probability as a function of conversion. Implementation is performed in EDStar, an open-source development environment that enables straightforward simulation of reactors with any geometry (directly provided by their CAD-file), with the very same Monte Carlo algorithm. Experimental investigations are focused on Reinecke salt photodissociation in two reactors designed for the study of natural and artificial photosynthesis. The first reactor investigated serves as reference configuration: its simple torus geometry allows to compare flux densities measured with quantum sensors and actinometry. Validations and analysis are carried out on this reactor. Then, the approach is implemented on a 25 L photobioreactor with complex geometry corresponding to one thousand light-diffusing optical fibers distributing incident photons within the reaction volume. Results show that classical actinometry neglecting radiative transfer can lead to 50 percent error when measuring incident flux density for such reactors. Finally, we show how this radiative transfer approach paves the way for analyzing high conversion as a mean to investigate angular distribution of incident photons. Highlights: A novel and improved extent of actinometry to determine photon flux is presented. Latest advances in Monte Carlo Method for radiative transfer have been used. Photon absorption probability by the actinometer is defined as a new tool. Complex geometries, pilot plant photo(bio)reactors can now be easily addressed.

A revised experimental protocol for implementing the actinometry method with the Reinecke’s salt

“…The absorption of the actinometer covers a wide range in the visible spectrum of light, with a maximum at 525 nm. It is important to note that the absorption of the by-product, [Cr(NH 3 ) 2 (NCS) 3 (H 2 O)], is of the same order of magnitude than the one of the actinometer, thus implying that its absorption should be taken account in the modelling [16]. Furthermore, as described by Szychlinski et al [17], under acidic condition, the by-product could react with water according to Eq.…”

“…Therefore, in some conditions more than one − NCS ion ligand could be substituted by molecules of water, and thus inducing a bias in the determination of the consumed molar quantity of the Reinecke's salt during a given irradiation time and an overestimation of the amount of − NCS produced. To limit this second reaction, Rochatte et al [16] recommended to work at low conversions χ, namely below a maximal value, noted χ max , equal to 30%.…”

“…2 were negligible at 450 nm. According to [16], the molar absorption coefficient at 450 nm of the Reinecke's salt and of the by-product were equal to 30.4 L.mol −1 . cm -1 and to 29.5 L.mol −1 .…”

“…To validate this revised protocol, specific experiments were carried out in a benchmark batch flat torus photoreactor which offered the advantage to be perfectly characterized [15,16]. This photoreactor was irradiated by a quasi-collimated blue light LED panel (λ =457 nm) of a 12.5 × 12.5 cm 2 surface (the emission spectrum of this LED panel is reported in Rochatte et al [16]).…”

“…To validate this revised protocol, specific experiments were carried out in a benchmark batch flat torus photoreactor which offered the advantage to be perfectly characterized [15,16]. This photoreactor was irradiated by a quasi-collimated blue light LED panel (λ =457 nm) of a 12.5 × 12.5 cm 2 surface (the emission spectrum of this LED panel is reported in Rochatte et al [16]). Furthermore, due to its specific design, the photoreactor could be described according to a one-dimensional Cartesian geometry enabling thus to define rigorously the specific surface of illumination as the inverse of the optical path δ (a light =40 m −1 with δ =0.025 m).…”