Intrinsic rate constants influencing factors

Diffusion plays a major role in influencing both the activity and selectivity of many catalysts. For a first-order reaction in a spherical catalyst particle the intrinsic rate constant (k) is reduced by a factor rf (the effectiveness factor) ... 

Whereas Figure 2.20 is quite instructive, it is not of practical use for estimating the importance of the mass transfer influence from experimental data, as the intrinsic rate constant is normally unknown. Replotting the effectiveness factor as function of the ratio between observed reaction rate to the maximum mass transfer rate called as Carberry number Ca) allows estimating the external effectiveness factor plotted in Figure 2.21. 

For the uncoated catalyst, we have the highest reaction rate and thus the strongest influence of pore diffusion. To investigate the influence of pore diffusion, experiments with different particle diameters (<25 pm up to 2 mm) were conducted both with the uncoated Ni catalyst and with the SCILL catalyst for a pore filling degree of 15%. Figure 14.8 clearly shows that for the uncoated catalyst and a particle size of less than about 80 pm, an effectiveness factor of 1 is reached. For the SCILL catalyst, pore diffusion has less impact on the effective rate of COD conversion. The intrinsic rate constant is smaller and the effectiveness factor is still almost 1 up to a particle diameter of around 200 pm. 

Diffusional and Structural Parameters The influence of pore diSusion is considered by the effectiveness factor lypore, that is, (in the case of no influence of external diflusion) by the ratio of the effective rate constant to the (maximum) intrinsic rate constant (dp 0), and is given for a first-order reaction by (as evaluated in detail in Section 4.5.4 for heterogeneous catalysts) ... 

Figure 6.18.14 shows the influence of NO conversion on the pseudo-first-order intrinsic rate constant and on the effectiveness factor for pore diffusion. 

Figure 10 shows that Tj is a unique function of the Thiele modulus. When the modulus ( ) is small (- SdSl), the effectiveness factor is unity, which means that there is no effect of mass transport on the rate of the catalytic reaction. When ( ) is greater than about 1, the effectiveness factor is less than unity and the reaction rate is influenced by mass transport in the pores. When the modulus is large (- 10), the effectiveness factor is inversely proportional to the modulus, and the reaction rate (eq. 19) is proportional to k ( ), which, from the definition of ( ), implies that the rate and the observed reaction rate constant are proportional to (1 /R)(f9This result shows that both the rate constant, ie, a measure of the intrinsic activity of the catalyst, and the effective diffusion coefficient, ie, a measure of the resistance to transport of the reactant offered by the pore stmcture, influence the rate. It is not appropriate to say that the reaction is diffusion controlled it depends on both the diffusion and the chemical kinetics. In contrast, as shown by equation 3, a reaction in solution can be diffusion controlled, depending on D but not on k. 

As a rule of thumb, slow reactions are influenced only by the factors 7-10 (mostly only by factor 9). With increasing intrinsic rate and rate constant, respectively, the individual mass transfer resistances of both reactants have increasingly to be considered (Figure 4.9.2), particularly if large catalyst particles are used, such as in packed bed (trickle bed) reactors. For batch reactors or continuously operated slurry reactors with very fine suspended particles mass transfer resistances tend to play a... 

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