Macro void pores

Modelling physical properties has many common points with that of the textile mechanics. First of all, the structural arrangements at micro- (fibre), meso- (yarn), and macro-levels (fabric) need to be modelled. Similar to Section 1.6, the structure can be considered at different levels of detail and a choice should be made between discrete and continuous models. In contrast to modelling the textile mechanics where the structure modelling is concentrated on fibres and yams, the distribution of dimensions and orientation of voids (pores) between the fibres and yams is important for models of fluid flow. Closely related to this are models of filtration where in addition to the distribution of dimensions and shapes of particles, their interactions with the fibrous structure should be considered (Chemyakov et al, 2011). 

The random pore model, or macro- micro-pore model, of Wakao and Smith [1962, 1964] is intended for application to pellets manufactured by compression of small particles. The void fraction and pore radius distributions are each replaced by two averaged values 8m, I m for the macro and for the micro distribution (often a pore radius of -100 A is used as the dividing point between macro and micro). The particles which contain the micro-pores are randomly positioned in the pellet space. The interstices are the macro-pores of the pellet (see Fig. 3.5.2.1-1). The diffusion flux consists of three parallel contributions the first through the macro-pores, the second through the micro-pores and the third through interconnected macro-micro-pores in which the dominant resistance lies in the latter. The contributions to the diffusivity are added up to yield ... 

However, a pelletized or extruded catalyst prepared by compacting fine powder typically exhibits a bimodal (macro-micro) pore-size distribution, in which case the mean pore radius is an inappropriate representation of the micropores. There are several analytical approaches and models in the literature which represent pelletized catalysts, but they involve complicated diffusion equations and may require the knowledge of diffusion coefficients and void fractions for both micro- and macro-pores [31]. An easier and more pragmatic approach is to consider the dimensional properties of the fine particles constituting the pellet and use the average pore size of only the micropore system because diffusional resistances will be significantly higher in the micropores than in the macropores. This conservative approach will also tend to underestimate Detr values and provide an upper limit for the W-P criterion. 

Figure 29. Schematic illustration for different types of PS and the current distributions (a) void macro pore (b) micro PS (c) macro pore filled with micro PS (d) macro pore partially filled with micro PS. 

Wakao and Smith [20] originally developed the random pore model to account for the behaviour of bidisperse systems which contain both micro- and macro-pores. Many industrial catalysts, for example, when prepared in pellet form, contain not only the smaller intraparticle pores, but also larger pores consisting of the voids between compressed particles. Transport within the pellet is assumed to occur through void regions... 

In order to utilize the absorption properties or the synthetic zeolite crystals in processes, the commercial materials arc prepared as pelleted aggregates combining a high percentage of the crystalline zeolite with an inert binder. The formation of these aggregates introduces macro pores in the pellet which may result in some capillary condensation at high adsorhate concentrations. In commercial materials, the inacropores contribute diffusion paths. However, the main pan of the adsorption capacity is contained in the voids within the crystals. 

The Random-pore Model This model was originally developed for pellets containing a bidisperse pore system, such as the alumina described in Chap. 8 (Table 8-5 and Fig. 8-10). It is supposed that the pellet consists of an assembly of small particles. When the particles themselves contain pores (micropores), there exists both a macro and a micro void-volume distribu-... 

It is evident from the concepts presented that no tortuosity factor is involved in this model. The actual path length is equal to the distance coordinate in the direction of diffusion. To apply Eq. (11-25) requires void fractions and mean pore radii for both macro and micro regions. The mean pore radii can be evaluated for the micro region by applying Eq. (11-21) to this region. However, must be obtained from the pore-volume distribution, as described in Sec. 8-7. The mean pore radii are necessary in order to calculate 2>k)m om Eq. (11-27). 

The basic mathematical model for a calculation of concentration vs. time dependences in sorbent beds accounts for non-isothermal sorption in biporous sorbent particles. It considers mass and energy balances in the interparticle void space of the bed and in the macro- and micropores of sorbent particles. Thus, it comprises three spatial coordinates, besides time, (0 < t < co) (i) the height z along the bed, (0 < z < L) (ii) the radial direction r in macropores of particles, (0 < r < Rp) and (hi) the radial direction p in their micropores, (0 < p < Rzi). Different geometries may exist in each single direction but in each of those geometries the transport equations are one-dimensional. For zeolite-based biporous particles, sorption in the macropores is negligible. These pores serve as transport pores, only. Sorption takes place, exclusively, in micropores. 

The macro-scale physical character of catalysts refers to the characteristics of volume, shape and size distribution as well as related mechanical strength formed by the size, shape and void structure of particles and pellets. Industrial catalyst should have good macro-scale physical character, including surface area, pore volume, pore size and distribution, packing density, favorable particle size and shape and good mechanical strength. These properties not only influence the behavior of mass transfer, heat transfer and hydrodynamics (three transferee), but also directly influence the process of catalytic reaction kinetics. Therefore, macro-scale physical behaviours of catalysts is very important in the research of industrial catalyst. 

The cement paste formed by the hydration reactions always contains interconnected pores of different diameters (Fig. 8-2). These pores can be divided into macro-pores, originating from compaction voids or entrained air with diameters in the order of... 

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