Pore structure reaction kinetics

The simple pore structure shown in Figure 2.69 allows the use of some simplified models for mass transfer in the porous medium coupled with chemical reaction kinetics. An overview of corresponding modeling approaches is given in [194]. The reaction-diffusion dynamics inside a pore can be approximated by a one-dimensional equation... 

The reactor feed mixture was "prepared so as to contain less than 17% ethylene (remainder hydrogen) so that the change in total moles within the catalyst pore structure would be small. This reduced the variation in total pressure and its effect on the reaction rate, so as to permit comparison of experiment results with theoretical predictions [e.g., those of Weisz and Hicks (61)]. Since the numerical solutions to the nonisothermal catalyst problem also presumed first-order kinetics, they determined the Thiele modulus by forcing the observed rate to fit this form even though they recognized that a Hougen-Watson type rate expression would have been more appropriate. Hence their Thiele modulus was defined as... 

The amorphous silica matrixes are porous network structures that allow other species to penetrate [44]. Thus, the doped dye molecules have the ability to react with targets. However, the reaction kinetics is significantly different than the molecules in a bulk solution. In the synthesis of DDSNs, commonly used silicon alkoxides including TEOS and TMOS have tetrahedron structures, which allow compact polycondensation. As a result, the developed silica nanomatrix can be very dense. The small pore sizes provide limited and narrow pathways for other species to diffuse into the silica matrix. 

It is noted that the microporous effect was greater in the disproportionation of 1,2,4-TrMB than in the cracking of cumene. As shown in the previous paper [14], the disproportionation of 1,2,4-TrMB at 200°C proceeds via a bimolecular transition state and obeys the second order kinetics. In contrast, the cracking of cumene is the first order kinetics with respect to cumene concentration. Thus, it seems that the microporous effect is exerted more significantly in the second order reaction (disproportionation) than in the first order reaction (cracking) if pore structure plays an important role in localizing concentration of reactant molecules. 

Of course, certain features of overall kinetics are inaccessible via a cluster model method, such as the influence of pore structure on reactivity. The cluster model method cannot integrate reaction rates with concepts such as shape selectivity, and an alternative method of probing overall kinetics is needed. This has recently been illustrated by a study of the kinetics of the hydroisomerization of hexane catalyzed by Pt-loaded acidic mordenite and ZSM-5 (211). The intrinsic acidities of the two catalysts were the same, and differences in catalyst performance were shown to be completely understood on the basis of differences in the heat of adsorption of hexene, an intermediate in the isomerization reaction. Heats of adsorption are strongly dependent on the zeolite pore diameter, as shown earlier in this review (Fig. 11). 

Hydrodemetallation reactions require the diffusion of multiringed aromatic molecules into the pore structure of the catalyst prior to initiation of the sequential conversion mechanism. The observed diffusion rate may be influenced by adsorption interactions with the surface and a contribution from surface diffusion. Experiments with nickel and vanadyl porphyrins at typical hydroprocessing conditions have shown that the reaction rates are independent of particle diameter only for catalysts on the order of 100 /im and smaller (R < 50/im). Thus the kinetic-controlled regime, that is, where the diffusion rate DeU/R2 is larger than the intrinsic reaction rate k, is limited to small particles. This necessitates an understanding of the molecular diffusion process in porous material to interpret the diffusion-disguised kinetics observed with full-size (i -in.) commercial catalysts. 

A gas-solid reaction usually involves heat and mass transfer processes and chemical kinetics. One important factor which complicates the analysis of these processes is the variations in the pore structure of the solid during the reaction. Increase or decrease of porosity during the reaction and variations in pore sizes would effect the diffusion resistance and also change the active surface area. These facts indicate that the real mechanism of gas-solid noncatalytic reactions can be understood better by following the variations in pore structure during the reaction. 

There have been numerous studies on HDM catalyst deactivation. They differ in the mechanisn of deactivation, in the kinetics used for the HDM reaction, in the expression employed to describe diffusivity or pore structure. These different approaches can lead to quite different conclusions as to the catalyst properties that yield optimum overall activity (3-9). 

The assumption of global kinetic control is probably valid for only a handful of catalytic reaction processes. Nevertheless, some typical simulation results of the model of catalyst deactivation under kinetic control are presented here in order to emphasize some of the unique percolation-type aspects of the problem. The overall plugging time 0p, i.e., the time at which the catalyst becomes completely deactivated is shown is Figure 1, where it is plotted versus Z, the average coordination number of the network of pores, (in industrial applications, of course, the useful lifetime of the catalyst is significantly smaller than 0p). Note that as Z increases, (higher values of Z mean a more interconnected catalyst pore structure) 0p increases, i.e., the catalyst becomes more resistant to deactivation. The dependence of normalized catalytic activity (r/rQ) ([Pg.176]

Kinetic experiments in the thermo-balance carried out with ZnO as sorbent showed that the overall reaction rate at 600 C depended on the particle size in the range 50-350 pm [7] and on the pore structure of the sorbent [8]. In addition, a study of sorbent performance [9]... 

Related to their similar pore diameter and pore structure, unsurprisingly the Henry adsorption constants for linear alkanes are very close to each other on zeolite ZSM-22 and ZSM-23 (Table I). Somewhat higher constants are obtained for 2- and 3-methylbranched alkanes on ZSM-23 compared to zeolite ZSM-22. The adsorption constants of linear alkanes are obviously hi er than branched alkanes on the two cases. The separation power of a zeolite between a linear and a branched hydrocarbon may be given by the separation factor (a), which is the ratio of Henry consteints of linear and branched molecules at a certain temperature, a values at 523 K are given for both zeolites in Table 1. For comparison, values for ZSM-5 are also included, which is one of the most popular shape selective catalyst used in isomerization reactions. From this table it can be seen that both ZSM-22 and ZSM-23 have higher separation constants compared to ZSM-5. The zeolites can be listed in the following order with respect to their separation capacity between linear and 2- and 3-methylbranched alkanes ZSM-22 > ZSM-23 > ZSM-5. In narrow pore structures such as zeolites ZSM-22 and ZSM-23 it is very probable that linear alkanes with smaller kinetic diameters have more access to the available adsorption sites compared to the more bulky branched molecules. This may be regarded as the first... 

Dimensional analysis of the coupled kinetic-transport equations shows that a Thiele modulus (4> ) and a Peclet number (Peo) completely characterize diffusion and convection effects, respectively, on reactive processes of a-olefins [Eqs. (8)-(14)]. The Thiele modulus [Eq. (15)] contains a term ( // ) that depends only on the properties of the diffusing molecule and a term ( -) that includes all relevant structural catalyst parameters. The first term introduces carbon number effects on selectivity, whereas the second introduces the effects of pellet size and pore structure and of metal dispersion and site density. The Peclet number accounts for the effects of bed residence time effects on secondary reactions of a-olefins and relates it to the corresponding contribution of pore residence time. 

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