Dimensionless Analysis of Photocatalytic Reactors Using Suspended Solid Photocatalysts

Photocatalytic oxidation (PCO) over suspended solid photocatalysts (e.g., titanium dioxide) has been proposed as a sustainable process for treatment and purification of water and wastewater. However, the application of this process requires the development of mathematical models that can be readily applied to reactor design, scale-up and optimization. The rigorous modelling of photocatalytic reactors requires a complex analysis of the radiation field in the photoreactor. This analysis, linked to the modelling of the fluid-dynamics and the reaction kinetics, results in integro-differential equations which almost invariably require demanding numerical solutions. As a result these models are difficult to apply to the analysis of photocatalytic reactors. This paper presents a dimensionless analysis of steady-state, continuous flow, photocatalytic reactors using suspended solid photocatalysts that still retains the essential elements of a rigorous approach, whilst providing simple solutions. The models developed are applicable to either ‘thin-film’ or ‘geometrically thick’ flat plate and annular photoreactors, of (a) falling film design or (b) double-skin design, operating with three ideal flow conditions: (1) falling film laminar flow (FFLF); (2) plug flow (PF); and (3) slit flow (SF). The radiation field in the photoreactor is modelled with either a ‘two-flux’ absorption-scattering model, i.e., scattered photons are purely back scattered, or a ‘six-flux’ absorption-scattering model, i.e., scattered photons follow the route of the six directions of the Cartesian coordinates. Four different dimensionless parameters appear in the models. These are the Reynolds number, the Damkohler number, the optical thickness of the photoreactor and the scattering albedo of the photocatalyst. The above dimensionless parameters should be maintained constant during scale-up of photocatalytic reactors by dimensional analysis. Model simulations show that at a scattering albedo higher than 0.3, radiation scattering can significantly affect conversions obtained at different values of optical thickness. The conversions with the idealized flow systems follow the sequence: FFLF > PF > SF. The models estimate the optimum value of apparent optical thickness that maximizes conversion in a photocatalytic reactor, which was found to be in the range from 1.8 to 3.4 depending on flow conditions and reaction kinetics.