Intraparticle diffusion resistance

Polymer-supported catalysts often have lower activities than the soluble catalysts because of the intraparticle diffusion resistance. In this case the immobilization of the complexes on colloidal polymers can increase the catalytic activity. Catalysts bound to polymer latexes were used in oxidation reactions, such as the Cu-catalyzed oxidation of ascorbic acid,12 the Co-catalyzed oxidation of tetralin,13 and the CoPc-catalyzed oxidation of butylphenol14 and thiols.1516 Mn(III)-porphyrin bound to colloidal anion exchange resin was... 

The employment of small particles results in effectiveness factors near unity. In other words, the intraparticle diffusion resistance is low. 

In previous studies, Sooter (2) and Satchell (3) observed that reducing the particle size of the Nalcomo 474 catalyst from 8-10 mesh to 40-48 mesh did not have any significant effect on the desulfurization and denitrogenation of Raw Anthracene Oil under similar experimental conditions as employed in this study. This suggests that the fluid distribution and hence the fluid dynamic effects, were not important in the trickle bed reactors as operated for this work. If these effects were important then the reduction in particle size should increase conversion of the HDS and HDN by improving fluid distribution and reducing the intraparticle diffusion resistances. 

A simplification is often employed for effectiveness factor calculations in the asymptotic limit of strong intraparticle diffusion resistance (12,13). In this situation, an alternative form of the key component mass balance can be written as follows ... 

Effect of Intraparticle Diffusion for Reaction Networks For multiple reactions, intraparticle diffusion resistance can also affect the observed selectivity and yield. For example, for consecutive reactions intraparticle diffusion resistance reduces the yield of the intermediate (often desired) product if both reactions have the same order. For parallel reactions diffusion resistance reduces the selectivity to the higher-order reaction. For more details see, e.g., Carberry, Chemical and Catalytic Reaction Engineering, McGraw-Hill, 1976 and Fevenspiel, Chemical Reaction Engineering, 3d ed., Wiley, 1999. 

For more complex reactions, the effect of intraparticle diffusion resistance on rate, selectivity, and yield depends on the particulars of the network. Also, the use of the Thiele modulus-effectiveness factor relationships is not as easily applicable, and numerical solution of the diffusion-reaction equations may be required. 

Intraparticle Diffusion and External Mass-Transfer Resistance For typical industrial conditions, external mass transfer is important only if there is substantial intraparticle diffusion resistance. This subject has been discussed by Luss, Diffusion-Reaction Interactions in Catalyst Pellets, in Carberry and Varma (eds.), Chemical Reaction and Reactor Engineering, Dekker, 1987. This, however, may not be the case for laboratory conditions, and care must be exerted in including the proper data interpretation. For instance, for a spherical particle with both external and internal mass-transfer limitations and first-order reaction, an overall effectiveness factor r, can be derived, indicating the series-of-resistances nature of external mass transfer followed by intraparticle diffusion-reaction ... 

Intraparticle diffusion resistance may become important when the particles are larger than the powders used in slurry reactors, such as for catalytic packed beds operating in trickle flow mode (gas and liquid downflow), in upflow gas-liquid mode, or countercurrent gas-liquid mode. For these the effectiveness factor concept for intraparticle diffusion resistance has to be considered in addition to the other resistances present. See more details in Sec. 19. 

Hence the effectiveness factor is the ratio of the actual rate to that if the reactions were to occur at the external surface concentration, i.e., in absence of intraparticle diffusion resistance ... 

The effects of particle size and temperature clearly demonstrated that the reaction was controlled by intraparticle diffusion resistance. Thus, the initial rates were plotted against dp (inverse of particle diameter) to find that a straight line passing through origin was obtained (Fig.7). This confirms that the reaction was intraparticle diffusion limited". 

Often an important reason to avoid intraparticle diffusion resistances is from selectivity considerations. To maximize the intermediate product in a consecutive reaction scheme, we should avoid intraparticle diffusional resistances. For butene dehydrogenation it can be seen in Fig. 14 that... 

On the contrary, particles without pores enable fast, efficient separation of proteins due to the absence of intraparticle diffusion resistance. The absence of pores reduces the available surface area and thereby the loading capacity. Silica- [49] and polymer-based [50] nonporous particles have been applied for biomolecule separations. Also hybrid particles have been described that have a non/porous core and a 0.25-pm porous layer, composed of colloidal silica particles [51]. 

In (5.51), r stands for the intrinsic reaction rate at liquid bulk conditions. For worst-case-estimations, one should use a highest rate value possible in the considered RD column. In this respect it should be kept in mind that the reaction rates under RD conditions strongly depends on the operating pressure that influences the boiling temperatures, that is the reaction temperature. D g/ represents the effective diffusion coefficient of a selected reaction component inside the catalyst particles. One should use the component with the lowest mole fraction Xj in the liquid bulk mixture as key component [35]. Its effective diffusion coefficient can be estimated from the diffusion coefficient at infinite dilution Dg((/ = (sfr)D with the total porosity e and the tortuosity r of the applied catalyst. Based on (5.51) one can say that intraparticle diffusion resistances will be negligible, if 1. 

The catalyst particles are so small (< 10 om) that intraparticle diffusion resistance can be neglected (ti = l). 

However, for amorphous Al, Fe, and Mn oxides, the microposous structure results in significant intraparticle diffusion resistance [10-12,26]. For Fe oxides. Axe and Anderson [24] showed that film transfer resistance is negligible compared to intra-particle diffusion resistance. 

Activated carbon fibers (ACFs) are a fibrous form of activated carbon with carbon content more than 90%. ACFs are relatively new adsorbents for filtration or purification techniques. The unique characteristics of ACFs compared with GAC and RAC could increase the application of activated carbons in various areas. The fiber shape of ACFs can significantly improve the intraparticle adsorption kinetics as compared with RAC and GAC, which are commonly employed in gas-phase and aqueous-phase adsorption. Therefore, ACFs adsorption is a promising technique used for designing adsorption units where intraparticle diffusion resistance is the dominant adsorption factor. As a consequence, the size of adsorption units can be decreased by using ACFs (Yue et al. 2001). 

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