(513dj) E?ectiveness Factor in Catalytic Particulate Filters

Traditionally, a so-called 1D+1D model is used to describe catalytic monolith filter for automotive exhaust gas aftertreatment. This model assumes 1D flow along the filter channels and 1D flow, diffusion and reaction across the filter wall. A micro-scale 3D model was recently developed to calculate detailed flow, diffusion and reaction inside pores of the filter wall. This model utilizes realistic 3D structure of porous medium including washcoat distribution. The structure is obtained from X-ray microtomography. Resulting 3D profiles are averaged and effective properties of the wall are evaluated (permeability, filtration efficiency). These effective parameters are applied as input parameters for the overall 1D+1D model. The catalytic reactions occur only in coated zones inside large macropores of the wall. The catalytic sites inside the coated domains are reachable only via diffusion, which is a slow transport mechanism that may limit the achieved conversion.

To describe possible diffusion limitation and its impact on reactant conversion in the 1D+1D model, a modified concept of effectiveness factor has been developed, η = r_obs/r, where r_obs is observed reaction rate and r is reaction rate without any diffusion limitation. The effectiveness factor is estimated using Thiele modulus that depends on effective diffusion length, reaction rate constant and diffusivity of key reactant. To evaluate the effective diffusion length which characterizes the in-wall coating distribution, the 3D micro-scale simulation is performed and spatially averaged 1D concentration profile over the wall is obtained. Then, the value of the characteristic diffusion length in the 1D+1D model is fitted to match this profile (figure). To validate this approach, Thiele moduli and effectiveness factors of CO oxidation are calculated for several different wall structures of real catalytic particulate filters under various operating conditions. This study also compares the relations between Thiele modulus and effectiveness factor for pseudo-first order and Langmuir–Hinshelwood kinetics.