Intracrystalline diffusion isothermal system

This methods depends on the implicit assumption that the uptake rate is controlled entirely by intracrystalline diffusion in an isothermal system, with all other resistances to either mass or heat transfer negligible. This is a valid approximation if diffusion is sufficiently slow or if the zeolite crystals are sufficiently large but the dominance of intracrystalline diffusional resistance should not be assumed without experimental verification. In many practical systems, particularly with small commercial zeolite crystals, the external heat and mass transfer resistances are in fact dominant. A detailed discussion of such effects has been given by Lee and Ruthven(5-7). 

The experimental method used in TEOM for diffusion measurements in zeolites is similar to the uptake and chromatographic methods (i.e., a step change or a pulse injection in the feed is made and the response curve is recorded). It is recommended to operate with dilute systems and low zeolite loadings. For an isothermal system when the uptake rate is influenced by intracrystalline diffusion, with only a small concentration gradient in the adsorbed phase (constant diffusivity), solutions of the transient diffusion equation for various geometries have been given (ii). Adsorption and diffusion of o-xylene, / -xylene, and toluene in HZSM-5 were found to be described well by a one-dimensional model for diffusion in a slab geometry, represented by Eq. (7) (72) ... 

In the preceding analysis we considered the diffusivity as constant but if the uptake curve is measured over a large concentration step this may be a poor approximation. In many zeolitic systems the concentration dependence of the intracrystalline diffusivity is given approximately by Eq. (5.6), with Dq independent of concentration. If the adsorption equilibrium isotherm obeys the Langmuir equation this gives as the expression for the concentration dependence of the diffusivity... 

For many zeolitic systems the equilibrium isotherm can jbe represented in an approximate way by the Langmuir model while the intracrystalline diffu-sivity varies with concentration according to Eq. (6.12). Model 2c is intended to describe the dynamic behavior of such systems under conditions of intracrystalline diffusion control. 

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