Pore diffusion resistance significant

Weisz-Prater criterion. The relative significance of pore-diffusion resistance can be assessed by a criterion, known as the Weisz-Prater (1954) criterion, which requires only a single measurement of the rate, together with knowledge of De, Le, and the order of the surface reaction (but not of the rate constant). 

POROUS REACTANT (intermediate pore-diffusion resistance) An example of this case would be a solid reactant formed by compressing nonporous particles into a porous pellet, as shown in Fig. 14-2c. The pores surrounding the particles are supposed to be small enough that the fluid reactant concentration decreases significantly toward the center of the pellet. 

The classical diagnostic experiment to test for the presence of a significant pore diffusion resistance, in the absence of an external resistance, is to vary the size of the catalyst particle Zc. The following example illustrates this approach. 

Mesostructured materials are granules containing individual platelets (crystals) associated in a fairly random manner. This type of configuration is always associated with a bi-porous structure, in which small particles (platelets) have pores, usually mesopores, different from the composite particle (secondary mesopores and macropores). The secondary pore structure controls access to the individual crystal mesoporosity. As a result, different mass transfer resistances to diffusion through bi-porous structures could be present. In order to evaluate the relative significance of both primary and secondary pore diffusion, usually two different particle sizes are employed in diffusion measurements. 

Figure 13 shows the potential and concentration distributions for different values of dimensionless potential under conditions when internal pore diffusion (s = 0.1) and local mass transport (y = 10) are a factor. As expected the concentration and relative overpotential decrease further away from the free electrolyte (or membrane) due to the combined effect of diffusion mass transport and the poor penetration of current into the electrode due to ionic conductivity limitations. The major difference in the data is with respect to the variation in reactant concentrations. In the case when an internal mass transport resistance occurs (y = 10) the fall in concentration, at a fixed value of electrode overpotential, is not as great as the case when no internal mass transport resistance occurs. This is due to the resistance causing a reduction in the consumption of reactant locally, and thereby increasing available reactant concentration the effect of which is more significant at higher electrode overpotentials. 

Ma et al. [104] attributed a decrease in diffusivity with an increase in initial concentration to pore diffusion effects. Because zeolites are bi-dispersed sorbents, both surface and pore diffusions may dominate different regions. In micropores, surface diffusion may be dominant, while pore diffusion may be dominant in macropores. This, therefore, supports the use of a lumped parameter (De). To explore further the relative importance of external mass transfer vis-a-vis internal diffusion, Biot number (NBl — kf r0/De) was considered. Table 9 summarizes the NBi values for the four initial concentrations. The NBi values are significantly larger than 100 indicating that film diffusion resistance was negligible. 

Table 6.7 displays some physical properties of zeolites. A study issued from industry [8] demonstrates the significant role of mass-transfer resistances, even for small particles below 1 mm, reporting that pore diffusion may decrease the effectiveness from low to very low values (0.4 to 0.06). The external mass-transfer resistance is much less important. In consequence, in commercial operation only a small part of the catalyst is effectively used, typically less than 10%. Since the... 

For liquid-phase diffusion of large adsorbate molecules, when the ratio = r /r of the molecule radius r to the pore radius is significantly greater than zero, the pore diffusivity is reduced by steric interactions with the pore wall and hydrodynamic resistance. When < 0.2, the following expressions derived by Brenner and Gaydos [/. Coll. Int Sci, 58,312 ( 1977)] for a hard sphere molecule (a particle) diffusing in a long cylindrical pore, can be used... 

The kinetics of actual adsorption of water on the sites of alumina is very fast. However, a substantial resistance to mass transport can be exhibited by the finite diffusivity of water molecules from the external gas phase to the adsorption sites through the porous network of the adsorbent particle. Diffusion of water vapour (molecular and Knudsen) through the pores of the alumina particle as well as the surface diffusion of adsorbed water on the pore walls [ 11-13] can contribute to the overall transport process. The presence of other non-adsorbing or adsorbing components can significantly influence both pore and surface diffusivity values for water. Table 3 shows a family of water vapour diffusivity data on Rhone-Poulenc grade A alumina in presence of N2 and He as carrier gases at a total gas pressure of 1.0 atmosphere. The water isotherm has a type IV shape [ 9,11]. Pore diffusion... 

Mass transfer resistances lead to a lower effective rate compared to the intrinsic chemical reaction, but may also significantly change the selectivity of parallel and consecutive reactions. In the following, this is discussed for two first-order reactions occurring in series or parallel, for simplification, the influence of external mass transfer is only discussed for a non-porous catalyst (to exclude pore diffusion), and the effect of pore diffusion is examined for a negligible influence of external mass transfer. Other more complicated cases are treated elsewhere (Baerns et al, 2006 Levenspiel, 1999 froment and Bischoff, 1990). 

To conclude, an overall summary of calculations based on the above results indicates that the usual order of events is to have first chemical reaction control throughout the pellet. Next, with higher intrinsic rates of reaction, internal pore diffusion begins to have an effect, followed by external heat transfer resistance. Finally, for extremely rapid reactions there is the possibility of external mass transfer resistance and temperature gradients of some significance. Only for unrealistic situations is it likely that particle instabilities might occur, and even then only for narrow ranges of temperature. 

Sometimes catalyst pores not covered by the liquid film are not filled with liquid due to evaporation phenomena caused by an excess of heat of reaction. If both reactants A and B have an appreciable vapor pressure at the working conditions, they can react as gaseous reactants after diffusing inside the catalyst pores. In this case inter-particle diffusion resistance is strongly reduced (at least 10 times) and the reaction rate can be very fast. These last phenomena are not significant in Slurry Reactors where the catalyst particles are always completely wetted and are much smaller - 0.1 mm (equivalent diameter) instead of 10-50 mm as in TBRs. 

At very low temperatures, has a low value and the value of is low. Pore diffusion is not a significant resistance and the effectiveness factor is essentially 1. Intrinsic (true) kinetics are observed. The measured activation energy is Dun-... 

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