Effects of Diffusion within Catalyst Particles

The resistance to mass transfer of reactants within catalyst particles results in lower apparent reaction rates, due to a slower supply of reactants to the catalytic reaction sites. Ihe long diffusional paths inside large catalyst particles, often through tortuous pores, result in a high resistance to mass transfer of the reactants and products. The overall effects of these factors involving mass transfer and reaction rates are expressed by the so-called (internal) effectiveness factor f, which is defined by the following equation, excluding the mass transfer resistance of the liquid film on the particle surface [1, 2]  

If there is no mass transfer resistance within the catalyst particle, then Ef is unity. However, it will then decrease from unity with increasing mass transfer resistance within the particles. The degree of decrease in f is correlated with a dimensionless parameter known as the Thiele modulus [2], which involves the relative magnitudes ofthe reaction rate and the molecular diffusion rate within catalyst particles. The Thiele moduli for several reaction mechanisms and shapes of catalyst particles have been derived theoretically. 

The Thiele modulus tfi for the case of a spherical catalyst particle of radius R (cm), in which a first-order catalytic reaction occurs at every point within the particles, is given as 

The radial distribution of the reactant concentrations in the spherical catalyst particle is theoretically given as  

Under steady state conditions the rate of reactant transfer to the outside surface of the catalyst particles should correspond to the apparent reaction rate within catalyst particles. Thus, the effectiveness factor Ef is given by the following equation  

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