An Asymptotic Solution for Washcoat Pore Diffusion in Catalytic Monoliths

When modeling monolithic exhaust aftertreatment reactors, washcoat pore diffusion resistance is often neglected with satisfactory results, but interest in the effect remains, especially for dual layer catalysts where the intention is to explicitly exploit the effect, for example, to enhance selectivity. To bring analyses that include washcoat pore diffusion resistance into convenient and everyday usage, an asymptotic solution based on small dimensionless washcoat pore diffusion resistance is derived and presented herein. When this solution is integrated within a common formulation for modeling monolithic exhaust aftertreatment reactors, it solves the leading-order reaction–diffusion equations within the washcoat analytically so the computational burden associated with discretizing and numerically solving along the washcoat thickness dimension is avoided. No further ad hoc approximations are required; in particular, the full complexity and nonlinearity of the reaction system is preserved. Catalytic surface coverages and dual layer catalysts are included. The method can be implemented in a manner that generalizes but is similar to the more standard solution method for no pore diffusion resistance. Although the asymptotic solution cannot substitute for the full solution in all cases, we argue that this asymptotic regime includes the most practical applications.