Macropores

Macropore diffusion has been widely studied in connection with its influence on the overall kinetics of heterogeneous catalytic reactions. Four distinct mechanisms of transport may be identified molecular diffusion, Knudsen diffusion, Poiseuille flow, and surface diffusion. The effective macropore diffusivity is thus a complex quantity which often includes contributions from more than one mechanism. Although the individual mechanisms are reasonably well understood, it is not always easy to make an accurate a priori prediction of the effective diffusivity since this is strongly dependent on the details of the pore structure. 

In analyzing macropore diffusion it is usually assumed that the transport occurs only through the pores and the flux through the solid can be neglected. It is therefore convenient to define a pore diffusivity D ) based on the pore cross-sectional area  

Dullien - has shown that, if the pore structure is characterized in detail, a reasonably accurate theoretical prediction of the tortuosity may be made, but this requires detailed measurement of both the pore shape and pore size distribution. However, it is generally simpler and more accurate to treat the tortuosity as an empirical constant which is determined experimentally for any particular adsorbent. 

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The simplest way of introducing Che pore size distribution into the model is to permit just two possible sizes--Tnlcropores and macropotes--and this simple pore size distribution is not wholly unrealistic, since pelleted materials are prepared by compressing powder particles which are themselves porous on a much smaller scale. The small pores within the powder grains are then the micropores, while the interstices between adjacent grains form the macropores. An early and well known model due to Wakao and Smith [32] represents such a material by the Idealized structure shown in Figure 8,2,... 

To evaluate the flux by each of Che three paths, flux relations spanning Che range between the micropore and macropore sizes are needed, and Wakao and Smith confined their attention to binary mixtures, using the equations of Scott and Dullien [4], which Cake the form... 

More recently, the Wakao-Smith type of model has been generalized by Cunningham and Geankoplis [50] to admit two different sizes of macropore. 

Case (c). The pore size distribution is strictly bimodal, with macropores... 

To be specific let us have in mind a picture of a porous catalyst pellet as an assembly of powder particles compacted into a rigid structure which is seamed by a system of pores, comprising the spaces between adjacent particles. Such a pore network would be expected to be thoroughly cross-linked on the scale of the powder particles. It is useful to have some quantitative idea of the sizes of various features of the catalyst structur< so let us take the powder particles to be of the order of 50p, in diameter. Then it is unlikely that the macropore effective diameters are much less than 10,000 X, while the mean free path at atmospheric pressure and ambient temperature, even for small molecules such as nitrogen, does not exceed... 

When a chemical reaction takes place at the solid surface, we expect a smooth variation in gas composition in the macropores on a scale comparable with the whole pellet, provided the reaction rate is not too high. 

Satterfield [52]) indicate that the macropore effectiveness factor will be... 

It arises solely because we continue Co describe micropore diffusion in terms of smooch macropore concentration fields and their gradients, even under reactive conditions where these no longer adequately describe Che actual concentration gradients in the micropores. 

The first thing to notice about these results is that the influence of the micropores reduces the effective diffusion coefficient below the value of the bulk diffusion coefficient for the macropore system. This is also clear in general from the forms of equations (10.44) and (10.48). As increases from zero, corresponding to the introduction of micropores, the variance of the response pulse Increases, and this corresponds to a reduction in the effective diffusion coefficient. The second important point is that the influence of the micropores on the results is quite small-Indeed it seems unlikely that measurements of this type will be able to realize their promise to provide information about diffusion in dead-end pores. 

Classification of pore sizes micropores, mesopores and macropores... 

The basis of the classification is that each of the size ranges corresponds to characteristic adsorption effects as manifested in the isotherm. In micropores, the interaction potential is significantly higher than in wider pores owing to the proximity of the walls, and the amount adsorbed (at a given relative pressure) is correspondingly enhanced. In mesopores, capillary condensation, with its characteristic hysteresis loop, takes place. In the macropore range the pores are so wide that it is virtually impossible to map out the isotherm in detail because the relative pressures are so close to unity. 

MesoporesJ Between 20 and 500A (2 and 50 nm) Macropores More than 500 A (50nm)... 

Mercury porosimetry is a technique which was originally developed to enable pore sizes to be determined in the macropore range where, as pointed out in... 

Whereas at the lower end of its range mercury porosimetry overlaps with the gas adsorption method, at its upper end it overlaps with photomicrography. An instructive example is provided by the work of Dullien and his associates on samples of sandstone. By stereological measurements they were able to arrive at a curve of pore size distribution, which was extremely broad and extended to very coarse macropores the size distribution from mercury porosimetry on the other hand was quite narrow and showed a sharp peak at a much lower figure, 10nm (Fig. 3.31). The apparent contradiction is readily explained in terms of wide cavities which are revealed by photomicrography, and are entered through narrower constrictions which are shown up by mercury porosimetry. 

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