Comparison of two different expressions of the kinetic equation for a photocatalytic reaction

GUADALUPE B. ORTIZ DE LA PLATA; ORLANDO M. ALFANO; ALBERTO E. CASSANO; FRANCESCO SANTARELLI; GIOVANNI CAMERA RODA

Mendoza

Congreso; 21st Inter-American Photochemical Society Conference; 2011

Inter-American Photochemical Society

Considering that the initial step of a photocatalytic reaction is the absorption of the photons, for a photocatalytic process the local rate of the reaction is strongly affected by the photon flux in that point of the reactor. Unfortunately not all the absorbed photons are effectively utilized for the reaction and, as a consequence, the quantum yield is typically low. Furthermore it has been experimentally observed and, under some assumptions, it has been theoretically demonstrated that the higher is the rate of absorption of photons the lower is the quantum yield. This phenomenon complicates the analysis and the design of photocatalytic reactors since, when the quantum yield is not constant, it becomes necessary to get a detailed appraisal of the photon flux, that is of the intensity of the radiation, inside the reactor. Actually in a photocatalytic reactor the intensity of the radiation varies very much not only with the position but also with the direction due to absorption and scattering. It must be observed that it is almost impossible to acquire experimentally the intensity distribution, so it is a common practice to obtain it by numerically solving the integro-differential equation which expresses the radiant energy balance. Then from the knowledge of the values of the intensities in a point coming from all the directions the LVREA (local volumetric rate of radiant energy absorption), or equivalently the LVRPA (local volumetric rate of photon absorption), can be estimated through the relationship: LVREA= where k is the absorption coefficient, so that the integration considers the intensities on all the solid angle.Generally the constitutive equation for the rate of reaction, R,, assumes an order, a, of reaction with respect to the LVREA which possibly can vary between 0 and 1 according to the value of the intensity of the radiation. By following this approach .  However, from a theoretical point of view, it would be more rigorous to assume that . Bearing in mind that the intensities in a given point may vary very much with the direction, it is obvious that  whenever a¹1. In the present work the consequence of using the approximate expression of the constitutive equation of the rate of reaction in substitution of the more rigorous one are examined for an annular photocatalytic reactor at different values of all the intervening parameters.  Some rules are derived which establish the conditions for which the substitution gives negligible errors.