Pore diffusion resistance strong

Figure 8.10(b) shows a plot of if/ = cAlcAs as a function of z, the fractional distance into the particle, with the Thiele modulus cj) as parameter. For = 0, characteristic of a very porous particle, the concentration of A remains the same throughout the particle. For (f> = 0.5, characteristic of a relatively porous particle with almost negligible pore-diffusion resistance, cA decreases slightly as z —> 1. At the other extreme, for = 10, characteristic of relatively strong pore-diffusion resistance, cA drops rapidly as z increases, indicating that reaction takes place mostly in the outer part (on the side of the permeable face) of the particle, and the inner part is relatively ineffective. 

Strong pore-diffusion resistance (beyond point H) ... 

The asymptotic solution ( - large) for tj is [2/(n + l)]1/2/, of which the result given by 8.5-14c is a special case for a first-order reaction. The general result can thus be used to normalize the Thiele modulus for order so that the results for strong pore-diffusion resistance all fall on the same limiting straight line of slope - 1 in Figure 8.11. The normalized Thiele modulus for this purpose is... 

The rate is inversely proportional to particle size. This is an indication of strong pore-diffusion resistance, in which t) - llcp" as " - large. Since (f>" a Le for fixed other conditions (surface kinetics, De, and c ), if we compare measured rates for two particle sizes (denoted by subscripts 1 and 2), for strong pore-diffusion resistance,... 

Strong Pore-Diffusion Resistance Some Consequences... 

Here, we consider the consequences of being in the region of strong pore-diffusion resistance (77 - 11(f)" as apparent activation energy (f)" is given by equation 8.5-20b. 

Figure 18.7 Shows the limits for negligible and for strong pore diffusion resistance.

To find how pore resistance influences the rate evaluate Mj or then find from the above equations or figures, and insert < into the rate equation. Desirable processing range Fine solids are free of pore diffusion resistance but are difficult to use (imagine the pressure drop of a packed bed of face powder). On the other hand a bed of large particles have a small Ap but are liable to be in the regime of strong pore diffusion where much of the pellets interior is unused. 

A packed bed reactor converts A to R by a first-order catalytic reaction, A R. With 9-mm pellets the reactor operates in the strong pore diffusion resistance regime and gives 63.2% conversion. If these pellets were replaced by 18-mm pellets (to reduce pressure drop) how would this affect the conversion ... 

These expressions show that in the regime of strong pore diffusion resistance a decreases (see Eq. 39), causing to also decrease. This means that S rises with time, as shown in Fig. 21.6. However a decreases faster than (Arises so the reaction rate decreases with time. 

Find the kinetics of reaction and deactivation, both in the diffusion-free and in the strong pore diffusion resistance regime. 

This represents fairly strong pore diffusion resistance. 

Powders vary dramatically in particle size on the basis of their origin. It is common for catalyst manufacturers to classify powders in order to assure users of consistency from batch to batch since suspension, settling rates, filtration, and performance in slurry-phase reactions are all dependent on particle size. The effect on suspension, settling rates, and filtration is obvious. However, factors that favor these are unfavorable for kinetics. For reactions controlled by transport rates from the bulk fluid to the surface of the catalyst, the overall reaction rate is a strong function of geometric surface area and thus is favored by small particles. Pore diffusion resistance is also minimized by smaller particles since reaction paths to active sites are smaller. The only mode of reaction control not influenced by particle size is for those reactions in which rate is controlled by reaction at active sites. Therefore, a compromise for optimum filtration and maximum reaction rates must be made. 

Does the rate depend on particle size If the rate of reaction under constant conditions is inversely proportional to the radius of the particle, this is a strong indication of pore diffusion resistance. External diffusion also shows size effects, but not nearly 0 pronounced. 

Strong resistance to pore diffusion. Under these conditions we have... 

Strong resistance to pore diffusion. An analysis similar to that starting with Eq. 2 using the appropriate kinetic rate expressions gives the concentration ratio of materials in the main gas stream (or pore mouths) at any point in the reactor. Thus the differential expression (see Wheeler, 1951 for details) is... 

The first-order decomposition of A is run in an experimental mixed flow reactor. Find the role played by pore diffusion in these runs in effect determine whether the runs were made under diffusion-free, strong resistance, or intermediate conditions. 

No Resistance to Pore Diffusion Strong Resistance to Pore Diffusion ... 

Unfortunately, this value indicates strong resistance to pore diffusion. This contradicts our starting assumption, so our original guess was wrong. 

Guess That the Runs Were Made in the Regime of Strong Resistance to Pore Diffusion. Then Eq. (ii) becomes... 

Note In the strong pore diffusion regime the rate is lower but the catalyst deactivates more slowly. Actually, for the catalyst used here if we could have been free of diffusional resistances reaction rates would have been 360 times as fast as those measured. 

In the regime of strong resistance to pore diffusion we must change T with time such that... 

Figure 9.3 is a plot of Eq. (9.28), which shows that if r/> -> 0 then rj -> 1, which means there is no considerable diffusion resistance. As diffusion resistance increases, we have (j> - oo and hence rj -> 0. The latter can occur not for small diffusivity, for large pellet size L, or for very fast reaction rate, or for all three factors. This regime where the diffusion strongly affects the rate of reaction is called strong pore resistance. For a first-order reaction, a general criterion of... 

Comparing Eq. 3.8-3a with Eq. 3.8-1 shows that the effect of strong pore diffusion limitations is to change the ratio of rate constants, kjki, to the square root of the ratio. Thus, when fej exceeds k, other conditions being equal, a given selectivity ratio will be reduced by the diffusional resistance. 

---