Pellet size calculation

Two pellets, of porosities 0.41 and 0.48 respectively, were made by means of coaxial compaction of Alumina powder consisting of non porous spherical particles of size ca. 200A in diameter. Each pellet consists of 11 sections, and the compaction pressures of those sections were selected in such a way that no macroscopic porosity inhomogeneities would be present on the final pellet. The BET specific surface area of the pellets was calculated 100 15 m /gr. 

At this time it had become possible to determine experimentally total surface area and the distribution of sizes and total volume of pores. Wheeler set forth to provide the theoretical development of calculating the role of this pore structure in determining catalyst performance. In a very slow reaction, reactants can diffuse to the center of the catalyst pellet before they react. On the other hand, in the case of a very active catalyst containing small pores, a reactant molecule will react (due to collision with pore walls) before it can diffuse very deeply into the pore structure. Such a fast reaction for which diffusion is slower than reaction will use only the outer pore mouths of a catalyst pellet. An important result of the theory is that when diffusion is slower than reaction, all the important kinetic quantities such as activity, selectivity, temperature coefficient and kinetic reaction order become dependent on the pore size and pellet size with which a pellet is prepared. This is because pore size and pellet size determine the degree to which diffusion affects reaction rates. Wheeler saw that unlike many aspects of heterogeneous catalysis, the effects of pore structure on catalyst behavior can be put on quite a rigorous basis, making predictions from theory relatively accurate and reliable. 

It should be noted that a large difference exists between the value of final conversion degree, Xra(T obtained for the optimum distribution of the pellet size R (r) and the selected constant values of R. A relatively large difference also appears between the values of calculated for the intervals [Rmm,RmaJ with the different values of R m. 

The flow and mixing in the reaction zone is approximated by a backflow cell model (BCM) with forward flow of the liquid and a back flow of vapour in the reactive part of RD zone (Roemer and Durbin, 1967). The BCM consists in a series of five perfectly mixed cells of equal size. This number of cells was estimated from the RTD data measured on KATAPAK packing (R. Dima et al., 2003). In each cell the conversion increase was calculated considering uniform distribution of the catalyst in the cells and vapour-liquid equilibrium. The influence of the internal diffusion on the process kinetics was evaluated by integrating the mass balance equations inside the catalyst pellets and calculating the effectiveness factor value. The estimated average value of the... 

Figure 8.34. Calculation of impact between depleted UOj cylinder and steel pellet at 0.7 km/s. (a) Damaged regions, (b) Fragment size contours.

The reactor volume is calculated from Mj and the bulk density of the catalyst material, (-r ) depends not only on composition and temperature, but also on the nature and size of the catalyst pellets and the flow velocity of the mixture. In a heterogeneous reaction where a solid catalyst is used, the reactor load is often determined by the term space velocity, SV. This is defined as the volumetric flow at the inlet of the reactor divided by the reaction volume (or the total mass of catalyst), that is... 

The calculation of C according to (6) shows (95) that if the catalyst splitting results in the formation of catalyst pellets about 1000 A in size, then even under the most unfavorable conditions (the concentration of the active centers is equal to the total chromium content in the catalyst, 2r2 = ) the diffusional restriction on the primary particle level is negligible. 

The pellets of the commercial catalyst were crushed to grain size from 0.5 to 1 mm. A calculation on the basis of the measurements of the effective diffusion coefficient showed that the reaction proceeded in the kinetic region. Bed density of the catalyst was 1.23 g/cm3, specific surface after kinetic experiments was 36 m2/g. In the temperature range of 150-225°C reaction (342) is practically irreversible. The experiments proved (348) to be valid thus, the kinetics on low- and high-temperature catalysts is the same. 

Figure 11. Comparison of the experimental data with the calculated values for pellets with size of 1.5 x 6.0 mm.

Figure 16 shows an effectiveness factor diagram for a first order, irreversible reaction which has been calculated from eq 95 for various values of the modified Prater number / . From this figure, it can be seen that for exothermal reactions (/ > 0) effectiveness factors above unity may be observed when the catalyst operates at a temperature substantially above the bulk fluid phase temperature. This is caused by the limited heat transfer between the pellet and the surrounding fluid. The crucial parameters controlling occurrence and size of this effect are again the modified Prater number and the Arrhenius number. 

In order to evaluate the right side of Eq. 37, we will calculate the mass loss for a single pellet due to reaction and sum up such losses for all particles present in the fluidized bed. Upon combustion, char leaves behind a layer of ash having a different density than that of coke. Thus, the mass of a single char particle, w, of size in the bed is given by ... 

Cylindrical pellets of four industrial and laboratory prepared catalysts with mono- and bidisperse pore structure were tested. Selected pellets have different pore-size distribution with most frequent pore radii (rmax) in the range 8 - 2500 nm. Their textural properties were determined by mercury porosimetry and helium pycnometry (AutoPore III, AccuPyc 1330, Micromeritics, USA). Description, textural properties of catalysts pellets, diameters of (equivalent) spheres, 2R, (with the same volume to geometric surface ratio) and column void fractions, a, (calculated from the column volume and volume of packed pellets) are summarized in Table 1. Cylindrical brass pellets with the same height and diameter as porous catalysts were used as nonporous packing. 

In Figure 6 calculated mean transport pore radii, , from both methods are compared with pore-size distribution from mercury porosimetry. It is seen that the obtained mean transport pore radii either agree with porosimetric peak, or, for bidispersed pellets, with the porosimetric peak of wider pores, or, are positioned between porosimetric peaks closer to the peak for wider pores. It was confirmed that the gas diffusion transport takes place predominantly through wider pores and the role of narrower pores depends on their size and amount. 

---