Gaseous Diffusion in Single Cylindrical Pores

Basic Equations For many catalysts and reaction conditions (especially pressure) both bulk and Knudsen diffusion contribute to the mass-transport rate within the pore volume. For some years the proper combination of the two mechanisms was in doubt. About 1961 three independent investigations proposed identical equations for the rate of diffusion (in a binary gaseous mixture of A and B) in terms of the bulk diffusivity and Knudsen diffusivity If is the molal flux of A, it is convenient to represent the result as 

For the reaction A B, reaction and diffusion (at steady state) in a pore would require equimolal counterdiffusion that is, Ng = — Then a = 0, and the effective diffusivity is 

When the pore radius is large, Eqs. (11-1) and (11-2) reduce to the conventional constant-pressure form for bulk diffusion. For this condition k)a Then combining Eqs. (11-1) to (11-3) gives 

This equation is the usual one expressing Knudsen diffusion in a long capillary. 

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SECTION 11-1 GASEOUS DIFFUSION IN SINGLE CYLINDRICAL PORES... 

Wheeler s treatment of the intraparticle diffusion problem invokes reaction in single pores and may be applied to relatively simple porous structures (such as a straight non-intersecting cylindrical pore model) with moderate success. An alternative approach is to assume that the porous structure is characterised by means of the effective diffusivity. (referred to in Sect. 2.1) which can be measured for a given gaseous component. In order to develop the principles relating to the effects of diffusion on reaction selectivity, selectivity in isothermal catalyst pellets will be discussed. 

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