Light-off criterion and transient analysis of catalytic monoliths

Abstract

A one-dimensional two-phase model is used to derive an analytical light-off criterion for a straight channeled catalytic monolith with washcoat, in which the flow is laminar. For the case of uniform catalyst loading and a first order reaction, the light-off criterion is given by 1 f(δ c k v(T f, in ) D e ) E R Ωδ c( ΔT ad )k v(T f, in ) T f, in 2R g g(Pe h)L R Ω 2 u ̄ + 4eρ fc pf k fNu H,∞ >1. Here, T f,in is the inlet fluid temperature, Δ T ad is the adiabatic temperature rise, R Ω is one-half the channel hydraulic radius ( R Ω=A Ω/P Ω , A Ω , P Ω= channel cross-section area, perimeter), L is the channel length, ū is the fluid velocity, D e is the reactant effective diffusivity in the washcoat, δ c is the effective washcoat thickness, k f is the fluid thermal conductivity and k v ( T f,in ) is the first order rate constant per unit washcoat volume at the inlet fluid temperature. Nu H,∞ is the asymptotic Nusselt number in the channel. The function f accounts for diffusional limitations in the washcoat and is given by f( ϕ)=1 for ϕ<0.5 and f( ϕ)=2 ϕ for ϕ>0.5. The factor g( Pe h ) depends on the solid conductivity, or more precisely, the heat Peclet number, Pe h= u ̄ Lρ fc pfR Ω/δ wk w , where δ w ( k w ) is the effective wall thickness (thermal conductivity). The function g( Pe h ) decreases monotonically from 2.718 for Pe h =0 to unity for Pe h =∞. We also show that if the second term is negligible and the first exceeds unity, then ignition occurs at the back-end. If the second term exceeds unity then ignition occurs at the front-end. If the sum exceeds unity with the second term less than unity and not negligible compared to the first term then ignition occurs in the middle of the channel. This analytical ignition criterion is verified by numerical simulations using an accurate transient model that uses position dependent heat and mass transfer coefficients. We show that the plot of exit concentration versus time consists of two regions: kinetically controlled transient region and the mass transfer controlled steady-state asymptote. For the case of high solid conductivity, we present an analytical expression for the transient time at which the monolith shifts from the kinetically controlled to the mass transfer controlled regime. We also determine the influence of various parameters such as the washcoat thickness, channel dimensions, catalyst loading and initial solid temperature on this transient time and the cumulative emissions. Examination of the influence of solid conduction and channel geometry on cumulative emissions showed that designs that are optimum for steady-state operation lead to higher transient emissions and vice versa. Finally, we discuss the transient and steady-state behavior of the monolith for the special case of Le f <1 (hydrogen oxidation).