Diffusion effects, pore

Thus we can say that if the Thiele modulus is much less than unity, there is no pore diffusion effect on the reaction rate because the reactant concentration remains at Cas down the pore, but if the Thiele modulus is much greater than unity, then the rate is proportional to l/[Pg.287]

The conversion of cyclohexanes to aromatics is a highly endothermic reaction (AH 50 kcal./mole) and occurs very readily over platinum-alumina catalyst at temperatures above about 350°C. At temperatures in the range 450-500°C., common in catalytic reforming, it is extremely difficult to avoid diffusional limitations and to maintain isothermal conditions. The importance of pore diffusion effects in the dehydrogenation of cyclohexane to benzene at temperatures above about 372°C. has been shown by Barnett et al. (B2). However, at temperatures below 372°C. these investigators concluded that pore diffusion did not limit the rate when using in, catalyst pellets. 

The pure compound rate constants were measured with 20-28 mesh catalyst particles and reflect intrinsic rates (—i.e., rates free from diffusion effects). Estimated pore diffusion thresholds are shown for 1/8-inch and 1/16-inch catalyst sizes. These curves show the approximate reaction rate constants above which pore diffusion effects may be observed for these two catalyst sizes. These thresholds were calculated using pore diffusion theory for first-order reactions (18). Effective diffusivities were estimated using the Wilke-Chang correlation (19) and applying a tortuosity of 4.0. The pure compound data were obtained by G. E. Langlois and co-workers in our laboratories. Product yields and suggested reaction mechanisms for hydrocracking many of these compounds have been published elsewhere (20-25). 

If the reactions were not influenced by in-pore diffusion effects, the intrinsic kinetic selectivity would be kjk2(= S). When mass transfer is important, the rate of reaction of both A and X must be calculated with this in mind. From equation 3.9, the rate of reaction for the slab model is ... 

Obviously liquid residence time is not an appropriate parameter to describe pore diffusion effects in fluidized bed adsorption. This may be elucidated by assessing particle side transport by a dimensionless analysis. Hall et al. [73] described pore diffusion during adsorption by a dimensionless transport number Np according to Eq. (17), De denoting the effective pore diffusion coefficient in case of hindered transport in the adsorbent pores and Ue the... 

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. 

Each time an a-olefin readsorbs, there is a chance that it will desorb as a larger paraffin. Desorption as a paraffin is an irreversible termination step. At high carbon numbers, pore diffusion effects dominate and a-olefins do not exit the catalyst particles unreacted because of enhanced readsorption only unreactive paraffins are observed. As a result, the olefin/paraffin ratio decreases asymptotically to zero as carbon number increases. 

Relative rate constants for a-olefin readsorption decrease as follows kr c0>kr Ru> r Fe (7)- Although kr on Fe catalysts is smaller than on Ru or Co, the other parameters in Eq. (2), such as the low diffusivity of large hydrocarbon and the high site density on unsupported Fe catalysts, ultimately increase the probability of a-olefin readsorption therefore, pore diffusion effects also play a crucial role in Fe-catalyzed FT synthesis (Figures 3 and 4). Fe catalysts, however, give lower C20+ selectivity because of lower intrinsic values of kr- even though asymptotic chain termination probabilites are lower on Fe. 

A model Is presented for char gasification with simultaneous capture of sulfur In the ash minerals as CaS. This model encompasses the physicochemical rate processes In the boundary layer, In the porous char, and around the mineral matter. A description of the widening of the pores and the eventual collapse of the char structure Is Included. The modeling equations are solved analytically for two limiting cases. The results demonstrate that pore diffusion effects make It possible to capture sulfur as CaS In the pores of the char even when CaS formation Is not feasible at bulk gas conditions. The model predictions show good agreement with experimentally determined sulfur capture levels and reaction times necessary to complete gasification. 

Pore diffusion effects on the CO TPD spectra were investigated by varying the particle size of the catalyst. Figure 4 shows three spectra ranging in particle size from 60-80 mesh to 14-20 mesh, and essentially no difference in the spectra was observed. 

Pore diffusion effects can be considered in terms of a theoretical equation (ref, 6) which has been shown to describe the diffusion of petroleum asphaltene molecules,... 

Bodrov et al. (1964), investigated the steam reforming of methane on nickel foil to eliminate pore diffusion effects. A differential reactor was used at atmospheric pressure and in the temperature range 800-900 °C. The results demonstrated that the reaction rate is first order with respect to methane at 900 C, and at a lower temperature (800°C), H2O, H2 and CO, have an influence that can be described by the following expression ... 

The reason for this compensation is still obscure. That it is due to pore diffusion effects, a possibility considered by various workers, is made doubtful by the fact that the n-hydrocarbons with close values of rate constants and diffusivities do not show such a compensation. 

Pore-Diffusion Effects. Slow diffusion into pores can restrict the accessible internal surface to an outer shell of the aggregate it is not always avoidable because of other constraints, such as a minimum pressure drop in the system. 

P. B. Weisz Socony Mobil Oil Co.) The presence of appreciable pore diffusion effects need not necessarily present us with an unalterable situation. We can best discuss various means of favorably altering the system by observing the nature of a general criterion which defines the absence or onset of measurable diffusion effects ... 

Does the approach used above include pore diffusion effects, which seem to be of great possible import in the operation of trickle beds if not, how can we modify the analysis ... 

The major part of the book deals with nonideal reaetors. Chapter 4 on pore diffusion plus reaetion ineludes a new method for analyzing laboratory data and has a more eomplete treatment of the effeets of eomplex kineties, particle shape, and pore structure than most other texts. Catalyst design to minimize pore diffusion effects is emphasized. In Chapter 5 heat transfer correlations for tanks, particles, and packed beds, are reviewed, and the conditions required for reactor stability are discussed. Examples of unstable systems are included. The effects of imperfect mixing in stirred tanks and partial mixing in pipeline reactors are discussed in Chapter 6 with examples from the literature. Recommendations for scaleup or scaledown are presented. 

In the region of strong pore diffusion effects, the rate varies inversely with particle size, as shown by Eq. (4.34). Experimental tests with different particle sizes are often used to check for pore diffusion limitations. If the rate varies with 7 , the effectiveness factor is low, but the value of r] cannot be determined. If the rate increases less than twofold when R is halved, the data can perhaps be fitted to the appropriate curve in Figure 4.8 to determine 0 and T] for both sizes and thus obtain the true kinetic constant. However, more accurate values of k, , and r] are obtained when crushed catalyst is tested and the particle size is reduced until there is no further... 

The pore diffusion effect decreased the rate about 60%. 

If the catalyst is deposited as a thin layer on the inside or outside of a tube, the slab model can be used if the thickness of the catalyst layer is much less than the tube radius. The slab model is also used to analyze the performance of eggshell catalysts, which have a layer of active catalyst near the outer surface of the pellet, and of catalyst monoliths, which have a thin layer of catalyst on the inside of square, triangular, or hexagonal passages. Flowever, when the catalyst layer is very thin, pore diffusion effects are... 

Since the value of Eq. d is greater than 1, the criterion is not satisfied and so pore diffusion effects should be present, as Austin and Walker found. Therefore, the general criterion,. 3jSjc-1, indicated the proper situation it proves useful for similar tests for any reaction type, although for first-order reactions the original Weisz-Prater oiterion is identicaL... 

For isothermal particles, under conditions when

3, which is in the region with strong pore diffusion effects in Figure 2.10, the isothermal internal effectiveness factor r) will be inversely proportional to tp. Considering an nth order... 

Eliminating the pore diffusion resistances Pore diffusion resistances can be identified by the effect of the particle size on conversion. If the conversion is a function of the particle size, then the rate data are veiled by pore diffusion effects. To eliminate pore diffusion effects, the careful experimenter is advised to measure the conversion as a function of the particle diameter. If the conversions increase with decreasing particle diameters at constant space-time, then the data are veiled by pore diffusion limitations. The use of Arrhenius plots to elucidate the particle size temperature optimums is shown in Figure 7.7. 

For strong pore diffusion effects (approach to asymptotic solution = 1M ), we have ... 

The same information required in procedure 4 can be used directly to evaluate the Weisz-Prater criterion. Values below 0.3 imply > 0.95 and the absence of significant pore diffusion limitations for essentially all reactions of interest (reaction order n for 0 n s 2), while values above 6 indicate the strong influence of pore diffusion. It must be stressed that this criterion should be viewed as an order of magnitude estimate, thus values much less than 0.3 are desirable, and values between 0.3 and 6 must be interpreted with caution because an influence due to pore diffusion cannot be ruled out. In addition, if significant product inhibition occurs, the W-P criterion becomes inapplicable in the form presented in this chapter however, it can be modified to again provide a useful test for pore diffusion effects [64]. 

FIG. 6.11. The mimimization of external mass transfer or pore diffusion effects by operation at lower temperatures. 

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