Pellet shapes

At the opposite limit of bulk diffusion control and high permeability, all flux models are required to he consistent with the Stefan-Maxwell relations (8.3). Since only (n-1) of these are independent, they are insufficient to determine all the flux vectors, and they permit the problem to be formulated in closed form only when they can be supplemented by the stoichiometric relations (11.3). At this limit, therefore, attention must be restricted from the beginning to those simple pellet shapes for ich equations (11.3) have been justified. Furthermore, since the permeability tends to infininty, pressure gradients within the pellet tend to zero and... 

The current requirements have led to the development of pellet shaped activated carbon products specifically for automotive applications. These pellets are typically generated as chemically activated, wood-based carbons. 

Rowe RC, York P, Colbourn EA, Roskilly S. The influence of pellet shape, size and distribution on capsule filling-a preliminary evaluation of three dimensional computer simulation using a Monte Carlo technique. Int J Pharm 2005 300 32-7. 

The mass fraction of nickel powder incorporated into the NP pyrolant was 0.01 and the diameter of the nickel particles was 0.1 pm. The NP pyrolants with and without nickel particles were pressed into pellet-shaped grains 1 mm in diameter and 1 mm in length. The BK pyrolant was pressed into pellet-shaped grains 3 mm in diameter and 3 mm in length. 

H. (2003). Dissociation Behavior of Pellet-Shaped Methane-Ethane Mixed Gas Hydrate Samples. Energy and Fuels, 17, 614-618. 

J.-H. Ohga, K. (2006). Dissociation behavior of pellet shaped mixed gas hydrate samples that contain propane as a guest. Energy Convers. Manage., 47 (15-16), 2491-2498. 

Figure 5. Effectiveness factor rj as a function of the Thiele modulus for different pellet shapes. Influence of intraparticle diffusion on the effective reaction rate (isothermal, first order, irreversible reaction).

Figure 5 shows the dependence of the effectiveness factor on the Thiele modulus for the different pellet shapes. At small values of 4> the effectiveness factor approaches unity in all cases. Here, the chemical reaction constitutes the rate determining step—the corresponding concentration profiles over the pellet cross-section arc flat (sec Fig. 4). This situation may occur at low catalyst activity (k is small), large pore size and high porosity (Dc is large), and/or small catalyst pellets (R is small, i.c. in fluidized bed reactors R is typically around 50 /im).

Figure 6 shows the effectiveness factor for any of the three different pellet shapes as a function of the generalized Thiele modulus p. It is obvious that for larger Thiele moduli (i.e. p > 3) all curves can be described with acceptable accuracy by a common asymptote t] — 1 / p. The largest deviation between the solutions for the individual shapes occurs around p x 1. However, even for the extremely different geometries of the flat plate and the sphere, the deviation of the efficiency... 

The above considerations can also be extended in a simple way to different reaction orders, if the modulus p is further modified. In this sense Petersen [85] defined a generalized Thiele modulus 4>pn which takes into account the effects of the pellet shape as well as the influence of the reaction order ... 

Equation 56 can be used only for spherical catalyst pellets and first order, irreversible reactions. However, for convenience, and in analogy to the Thiele modulus, a generalized modulus ij/pn can be defined as well which applies to arbitrary pellet shape and arbitrary reaction order. This is defined as... 

When the effective reaction rate is controlled by pore diffusion, then the asymptotic solution of the catalyst effectiveness factor as a function of the generalized Thiele modulus can be utilized (cq 108). This (approximate) relationship has been derived in Section 6.2.3.1. It is valid for arbitrary order of reaction and arbitrary pellet shape. 

For a pellet shape such as a sphere or a cylinder, expressions analogous to 7.107 can be derived along the same lines as for a slab geometry. 

Figure 7.11 also shows the relationship between the effectiveness factor and the Thiele modulus for other pellet shapes. In general the linear dimension L of the slab is replaced by ... 

Note that the asymptotic behaviour, Eqns. 7.108 and 7.109, is not affected by the pellet shape due to the choice of L. 

HI(R-R,) measure for the geometry of a ring-shaped catalyst pellet shape-generalized Thiele modulus for first-order kinetics of Aris... 

According to the above definitions, the effectiveness factor for any of the above shapes can adequately describe simultaneous reaction and diffusion in a catalyst particle. The equation for the effectiveness factor in a slab is the simplest in Table 6.3.1 and will be used for all pellet shapes with the appropriate Thiele modulus ... 

FIGURE 2 Cumulative distribution functions of pellet shapes using different shape factors aspect ratio, and (D) Cr. Abbreviation OPCS. one plane critical stability. Source From Ref. 76,... 

Chopra R, Podczeck F, Newton JM, et al. The influence of pellet shape and film coating on the filling of pellets into hard shell capsules. Eur J Pharm Biopharm 2002 53 327-33. 

Santos H. Veiga, Pina. ME, et al. Compaction, compression and drug relea.se characteristics of xanthan gum pellets of different compositions. Eur J Pharm Sci 2004 21 271-81. Chopra R. Alderbom G, Podczeck F, et al. The influence of pellet shape and the surface properties on the drug relea.se form uncoated and coated pellets. Int J Pharm 2002 239 171-8. 

The amount of liquid added to the dry particulate matter also influences pellet shape. As shown by Bhrany et a critical moisture exists for each material which depends on particle size and distribution, porosity and surface roughness, or, more generally, the specific surface of the powder, and the wettability of the solid(s) by the liquid. It can be determined experimentally according to proposals of Hainesand Jimeniz and increases with decreasing particle size (see also Section 3.2.3 and Figure 59). 

Some authors used a refined model, in which the original pellet shape is assumed to be an ellipsoid [23]. In this case, the impregnation depth follows from... 

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