Pore diffusion resistence

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 presence (or absence) of pore-diffusion resistance in catalyst particles can be readily determined by evaluation of the Thiele modulus and subsequently the effectiveness factor, if the intrinsic kinetics of the surface reaction are known. When the intrinsic rate law is not known completely, so that the Thiele modulus cannot be calculated, there are two methods available. One method is based upon measurement of the rate for differing particle sizes and does not require any knowledge of the kinetics. The other method requires only a single measurement of rate for a particle size of interest, but requires knowledge of the order of reaction. We describe these in turn. 

The rate is independent of particle size. This is an indication of neghgible pore-diffusion resistance, as might be expected for either very porous particles or sufficiently small particles such that the diffusional path-length is very small. In either case, i -> 1, and ( rA)obs = ( rA)inl for the surface reaction. 

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,... 

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). 

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. 

The activity calculated from (7) comprises both film and pore diffusion resistance, but also the positive effect of increased temperature of the catalyst particle due to the exothermic reaction. From the observed reaction rates and mass- and heat transfer coefficients, it is found that the effect of external transport restrictions on the reaction rate is less than 5% in both laboratory and industrial plants. Thus, Table 2 shows that smaller catalyst particles are more active due to less diffusion restriction in the porous particle. For the dilute S02 gas, this effect can be analyzed by an approximate model assuming 1st order reversible and isothermal reaction. In this case, the surface effectiveness factor is calculated from... 

Pore diffusion resistance which may cause the interior of the particle to be starved for reactant. 

Pore Diffusion Resistance Combined with Surface Kinetics 381... 

PORE DIFFUSION RESISTANCE COMBINED WITH SURFACE KINETICS... 

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. 

Our packed bed reactor runs the gas phase reaction A R at 10 atm and 336°C, and gives 90% conversion of a pure A feed. However, the catalyst salesman guarantees that in the absence of any pore diffusion resistance our reaction will proceed on his new improved porous catalyst e = 2 X 10 m /m cat s) with a rate given by... 

In the absence of pore diffusion resistance a particular first-order gas-phase reaction proceeds as reported below. 

The kinetics of the decomposition, when free of pore diffusion resistance, is given by... 

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 ... 

How Pore Diffusion Resistance Distorts the Kinetics of Reactions with Deactivating Catalysts... 

For no deactivation but with or without pore diffusion resistance these rate expressions become... 

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. 

EXAMPLE 21J INTERPRETING KINETIC DATA IN THE PRESENCE OF ------------ PORE DIFFUSION RESISTANCE AND DEACTIVATION... 

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

This represents poisoning by both reactant and by product, thus pore diffusion resistance does not influence the deactivation rate. 

This represents fairly strong pore diffusion resistance. 

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