Computer simulation of diffusion and reaction in zeolites

Abstract

A simple model of diffusion in a (2-D) periodic array of adsorption sites is investigated. The main microscopic assumptions are: (a) each site may contain only one molecule; and (b) transport is achieved by sorbate molecules "jumping" from one site to an adjacent site. A finite difference approximation (FDA) is set out which predicts that diffusion under this model obeys Fick's second law of diffusion with a concentration independent diffusion constant. The assumptions are also incorporated into a stochastic computer simulation. Four simulation techniques are compared with the FDA. Three of these exhibit measurable deviations from the FDA, showing that care must be taken as seemingly reasonable methods can introduce subtle correlations that have observable consequences. The fourth simulation exhibited no significant deviations from the FDA and thus, is apparently the first reported confirmation of the FDA theory by simulation. The model (FDA and simulation) is applied to diffusion in zeolite ZSM-5 and in particular the silicalite form as any effects of Al substitution have been ignored. A simple "gaseous", boundary condition is developed which, as predicted by the FDA, results in the Langmuir adsorption isotherm. Diffusion through a membrane and uptake diffusion are modelled and briefly compared with published experimental results. The continuum (large lattice) limit of the FDA predicts that Fickian diffusion theory is applicable in this limit. The FDA also correctly predicts the "collision" rate between sorbate molecules within the simulation. The "collision" rate is thought to be of fundamental importance to bi-molecular reactions in ZSM-5. It is believed that the simulations presented here provide a sound theoretical base which may be used as a first order approximation to diffusion in silicalite (and ZSM-5). Additional assumptions may be added to the simulation at a molecular level in an attempt to explain reported experimental departures from Fickian diffusion theory and to account for reactions within ZSM-5. Finally, a simulation of an extremely simplified reaction sequence that might occur in ZSM-5 is presented to show the flexibility of the simulation technique and to stimulate further research. This simulation is intended to be qualitatively similar to the methanol to gasoline process used at Motunui (N.Z.) to produce synthetic petrol. One interesting feature of the simulation is the dynamic production of "coke" within the zeolite lattice. The spatial distribution of the "coke" within a uniform lattice is found to be dependent on the pressure of the reactant molecules at constant temperature. At high pressures "coking" occurs mainly at the edges, whereas at lower pressures "coking" occurs more towards the centre of the lattice.