Abstract Transient two dimensional (2-D) and three dimensional (3-D) single channel models (SCMs) describing transport of NO x into a NaZSM-5 film and kinetics for reactions forming nitrate species were developed. The film consisted of a continuous thin layer of inter-grown NaZSM-5 crystals supported on a cordierite monolith support. The 2-D model which included a comprehensive transport model was developed for studying the adsorption kinetics, whereas the more rigorous 3-D model was used to provide a better picture of radial and axial concentration and velocity variations in the monolith channel and the film. The overall adsorption–desorption mechanism, consisting of two competing reaction schemes for nitrate formation, was sufficient to predict the dynamic development of surface nitrate species. The simulation results showed that the adsorption is strongly influenced by transport resistance in the NaZSM-5 film. Also, the effective diffusion of NO x in the NaZSM-5 film is apparently surface nitrate concentration dependent.