Effectiveness factor micropores

The support has an internal pore structure (i.e., pore volume and pore size distribution) that facilitates transport of reactants (products) into (out of) the particle. Low pore volume and small pores limit the accessibility of the internal surface because of increased diffusion resistance. Diffusion of products outward also is decreased, and this may cause product degradation or catalyst fouling within the catalyst particle. As discussed in Sec. 7, the effectiveness factor Tj is the ratio of the actual reaction rate to the rate in the absence of any diffusion limitations. When the rate of reaction greatly exceeds the rate of diffusion, the effectiveness factor is low and the internal volume of the catalyst pellet is not utilized for catalysis. In such cases, expensive catalytic metals are best placed as a shell around the pellet. The rate of diffusion may be increased by optimizing the pore structure to provide larger pores (or macropores) that transport the reactants (products) into (out of) the pellet and smaller pores (micropores) that provide the internal surface area needed for effective catalyst dispersion. Micropores typically have volume-averaged diameters of 50 to... 

A bidisperse structure can be advantageous because the effectiveness factor in the microparticles is often close to unity (their size being three to four orders of magnitude smaller than the usual size of the industrial catalysts). It is of interest to estimate the ratio of the conversion rates with mono- and bidisperse structures, having the same size, when the porous structure of the microparticles is identical to that of a monodisperse pellet. This ratio can easily be found when the micropore effectiveness factor is close to unity, as in the case for many industrial systems. Since the external surface area of the... 

If the one-equation model of diffusion and reaction in a micropore-macropore system is not valid, one needs to proceed dovm the hierarchy of length scales to develop an analysis of the transport process in both the macropore region and the micropore region. This leads to yet another averaging volume that is illustrated as level III in Figure 1.4. Analysis at this level leads to a micropore effectiveness factor that is discussed by Carberry (1976, Sec. 9.2) and by Froment and Bischoff (1979, Sec. 3.9). 

Thus, the effect of the microparticles b to possibly have an effectiveness factor, less than unity, based on microparticle properties, Eq. 3.9,a-3. The overall effectiveness factor then consists of the product of n, and a macroeffcctivcness factor, and the latter b based on macropeUet properties plus the micro effectiveness factor—Eq. 3.941-5. Often the microparticles are sui iently small so that a 1.0 recall from above that there is usually not any micropore diffusional limitations unless these exist for the macropores. 

If capillary condensation leads to excluding the active centers in micropores from the reaction (y = 0, )3 = 1), then the effectiveness factor is determined only by Thiele modulus (tj 1/iA), and relative rate of such pellet (x = Vl — s) decreases with increasing s according... 

The mesoscale model is of significant importance in catalyst design, since it could be used to investigate the effect of size, distribution, and amount of microporous crystal particles in the catalyst pellet on the overall catalytic performance. For convenience, as Eq. (3) in microscale model, another internal effective factor is defined to quantify catalytic performance of the pellet ... 

Up to now, we have only considered particles with one size of pore. In reality, we may have a wide spread of pore sizes or a micro-macroporous material (see Example 4.5.11 for the pore effectiveness factor in this case). Pellets are often prepared by compressing a porous powder, and thus we may get at least two pore sizes, large macropores between the agglomerated particles and small micropores within each particle. The micropores can be considered to be in series with the macropores and only the latter communicate with the external particle surface and the bulk phase of the fluid. For a strong resistance to both macro- and micropore diffusion, the following equation is obtained for the maximum selectivity of the intermediate, if external mass transfer limitations are neglected (Carberry, 1962 Froment and Bischoff, 1990 Levenspiel, 84,83) ... 

To calculate the pore effectiveness factor of pellets that have macro- and micropores, we use the following simple model and respective assumptions ... 

For spherical microporous grains and an irreversible first-order reaction, the pore effectiveness factor is to a good approximation, see Table 4.5.5, given by ... 

Figure 4.5.34 shows the influence of the term (kmPmicro/Deff.micro) f the overall effectiveness factor r/p (Figure 4.5.34a) and on the factors for macro- and micropore diffusion for different values of dmicro/dp, D ff. micro/Deftmacro = 0.5, and 3 particle diameter of 1 cm. 

Some supports have a bimodal pore-size distribution consisting of macropores and micropores. Show for a first-order reaction that the isothermal, internal effectiveness factor (Mingle and Smith, 1961) is given by ... 

Like the expressions for the enhancement factor, Eq. 17.1-22 for the effectiveness factor turns out to be more valuable than expected. It is derived for a first-order, irreversible chemical reaction occurring in a flat microporous catalyst pellet. However, making the catalyst pellet cylindrical or spherical doesn t matter much, as shown in Fig. 17.1-3. Changing the reaction order has a larger effect but even that is not that dramatic. In particular, for a reaction which is of order m in the reagent 1 , the effectiveness factor does not change much, as shown in Fig. 17.1-4. Effectiveness factors are thus rehably estimated. 

Let us make an estimate of the order of magnitude of these effects. Referring to equation (9,23), the coefficient of the term relating the micropore contribution to and grad p is larger by a factor... 

Although the systems investigated here exhibited predominantly macropore control (at least those with pellet diameters exceeding 1/8" or 0.32 cm), there is no reason to believe that surface diffusion effects would not be exhibited in systems in which micropore (intracrystalline) resistances are important as well. In fact, this apparent surface diffusion effect may be responsible for the differences in zeolitic diffusion coefficients obtained by different methods of analysis (13). However, due to the complex interaction of various factors in the anlaysis of mass transport in zeolitic media, including instabilities due to heat effects, the presence of multimodal pore size distribution in pelleted media, and the uncertainties involved in the measurement of diffusion coefficients in multi-component systems, further research is necessary to effect a resolution of these discrepancies. 

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