Pellet size

This treatment of reaction at the limit of bulk diffusion control is essentially the same as that presented by HugoC 69j. It is attractive computationally, since only a single two-point boundary value problem must be solved, namely that posed by equations (11.15) and conditions (11.16). This must be re-solved each time the size of the pellet is changed, since the pellet radius a appears in the boundary conditions. However, the initial value problem for equations (11.12) need be solved only once as a preliminary to solving (11.15) and (11.16) for any number of different pellet sizes. 

Table II.1 which depends on the pellet size, so the familiar plot of effectiveness factor versus Thiele modulus shows how t varies with pellet radius. A slightly more interesting case arises if it is desired to exhibit the variation of the effectiveness factor with pressure as the mechanism of diffusion changes from Knudsen streaming to bulk diffusion control [66,...

Physical properties of catalysts also may need to be checked periodically, includiug pellet size, specific surface, porosity, pore size and size distribution, and effective diffusivity. The effectiveness of a porous catalyst is found by measuring conversions with successively smaller pellets until no further change occurs. These topics are touched on by Satterfield (Heterogeneous Cataly.sls in Jndustiial Practice, McGraw-Hill, 1991). 

The effectiveness of a given size of pellet can be found experimentally by running tests of reaction conversion with a series of diminishing sizes of pellets until a hmiting rate is found. Then T will be the ratio of the rate with the pellet size in question to the limiting value. 

Our knowledge of the pellet size and shape and the bed voidage are thus suffieient to eharaeterize the bed resistanee. For the partieular ease investigated here, the resistanee ean be represented as ... 

The scheme of commercial methane synthesis includes a multistage reaction system and recycle of product gas. Adiabatic reactors connected with waste heat boilers are used to remove the heat in the form of high pressure steam. In designing the pilot plants, major emphasis was placed on the design of the catalytic reactor system. Thermodynamic parameters (composition of feed gas, temperature, temperature rise, pressure, etc.) as well as hydrodynamic parameters (bed depth, linear velocity, catalyst pellet size, etc.) are identical to those in a commercial methana-tion plant. This permits direct upscaling of test results to commercial size reactors because radial gradients are not present in an adiabatic shift reactor. 

Fig. 6. The activity and selectivity with catalytic pellet size.

For a specific comparison of the two different reactor types, channels of 300 pm diameter were considered. The equivalent pellet size for that case is 675 pm. As a characteristic quantity, the conversion at the reactor exits was computed for different flow velocities and a range of Damkohler numbers spanning three orders of magnitude. The results for the two different reactor types obtained in such a way were practically indistinguishable. This suggests that the different reactors considered in this study are equivalent as far as chemical conversion is concerned. 

Inspection of this equation shows that in the course of the snowballing growth the size distribution curves at various times are simply shifted toward the right on the pellet size scale without any change in their shape, as demonstrated by Capes (C2) for sand pellets snowballed in a pan granulator (Fig. 13). 

Actual measurements of the liquid content have shown that the larger granules have more liquid associated with them than the average and the smaller granules have less, in agreement with Eq. (98). Assuming that S and g are independent of pellet size, the liquid content may be related to the pellet size distribution in the following manner (B9) ... 

Fig. 28. Effect of the relative liquid content on the average relative pellet size. [From Butensky and Hyman (B9).]...

The packing itself may consist of spherical, cylindrical, or randomly shaped pellets, wire screens or gauzes, crushed particles, or a variety of other physical configurations. The particles usually are 0.25 to 1.0 cm in diameter. The structure of the catalyst pellets is such that the internal surface area far exceeds the superficial (external) surface area, so that the contact area is, in principle, independent of pellet size. To make effective use of the internal surface area, one must use a pellet size that minimizes diffusional resistance within the catalyst pellet but that also gives rise to an appropriate pressure drop across the catalyst bed. Some considerations which are important in the handling and use of catalysts for fixed bed operation in industrial situations are discussed in the Catalyst Handbook (1). 

Another disadvantage of fixed bed reactors is associated with the fact that the minimum pellet size that can be used is restricted by the permissible pressure drop through the bed. Thus if the reaction is potentially subject to diflfusional limitations within the catalyst pore structure, it may not be possible to fully utilize all the catalyst area (see Section 12.3). The smaller the pellet, the more efficiently the internal area is used, but the greater the pressure drop. 

How do changes in catalyst pellet size affect system behavior ... 

Effect of catalyst pellet size on reactor volume and pumping cost requirements. 

One could employ the techniques used in this example to investigate the effects of changes in tube diameter, catalyst pellet size, inlet pressure,... 

The catalyst activity depends not only on the chemical composition but also on the diffusion properties of the catalyst material and on the size and shape of the catalyst pellets because transport limitations through the gas boundary layer around the pellets and through the porous material reduce the overall reaction rate. The influence of gas film restrictions, which depends on the pellet size and gas velocity, is usually low in sulphuric acid converters. The effective diffusivity in the catalyst depends on the porosity, the pore size distribution, and the tortuosity of the pore system. It may be improved in the design of the carrier by e.g. increasing the porosity or the pore size, but usually such improvements will also lead to a reduction of mechanical strength. The effect of transport restrictions is normally expressed as an effectiveness factor q defined as the ratio between observed reaction rate for a catalyst pellet and the intrinsic reaction rate, i.e. the hypothetical reaction rate if bulk or surface conditions (temperature, pressure, concentrations) prevailed throughout the pellet [11], For particles with the same intrinsic reaction rate and the same pore system, the surface effectiveness factor only depends on an equivalent particle diameter given by... 

The pressure drop over the catalyst is measured again with a charge from the test production, since the precise pellet size distribution and settling properties may differ from those of the lab or pilot scale production. 

Table 2. The effect of catalyst pellet size on the observed activity of VK69 in feed gas containing 0.7% S02 and 7% 02.

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