Two-dimensional model in a laminar flow slit photoreactor for the determination of surface kinetic constants considering the presence of diffusion limitations

Abstract

Narrow slit reactors are widely used in laboratory testing of photocatalytic materials, as well as for the determination of kinetic coefficients in surface photocatalyzed reactions. In this work, the behavior of a continuous laminar flow slit reactor was described by a two-dimensional model, addressing the advection–diffusion problem in the fluid phase, coupled with a first-order chemical reaction on the reactor walls. The concentration profile of the reactant, in the transverse and longitudinal directions of the reactor, depends on two parameters that characterize the system; the P´eclet number and the Damkohler ¨ number, in addition to the geometry of the reactor. Once a short distance from the reactor’s entrance has been surpassed, the relationship between the transversally averaged reactant concentration and the concentration existing on the catalytic surface becomes essentially constant, thus defining an (external) effectiveness factor. The simulations carried out for a wide range of values of the parameters characterizing the model showed that the effectiveness factor only depends on the Damkohler ¨ number, being independent of the value of the P´eclet number and of the relationship between the reactor length and the distance separating the plates. An analytical expression for the effectiveness factor as a function of the Damkohler ¨ number was proposed, which allows to determine the value of the kinetic coefficient for the surface reaction (ks), even in the presence of important limitations to mass transfer. The methodology proposed was illustrated performing experiments of photocatalytic oxidation of toluene in air (with P´eclet numbers ranging from 20 to 40), employing a paint formulated with carbon-doped TiO2 in a continuous laboratory photoreactor of flat parallel plates. The observed toluene conversions were in the range of 13 to 26 %, consequently, the calculated Damkohler ¨ number was Da = 0.0307 and the surface kinetic coefficient thus determined (for 50 % of relative humidity and 42.3 W/m2 of irradiance flux) was ks = 1.262 10-4 m/s. The significance of this work lies in the development of a comprehensive model that can be used to know the surface kinetics in photocatalytic reactions, applicable to scenarios where there are considerable mass transfer limitations or not.