Effectiveness factor catalyst size effect

The second factor to consider is the catalyst conditions and the catalyst-particles, environment. From the point of view of the effectiveness factor, the size, shape, porosity, metal-loading, and other internal characteristics, must be the same. Otherwise, the intrinsic reaction rate and selectivity will be compromised. In practice there will be a trend to reduce costs by using less metal. This will change the process markedly, and other adjustments will be required. 

Figure 11. Effect of catalyst size and effectiveness factor in different reaction systems...

The ways in which reaction parameters affect a two phase batch reaction are similar to those considered above for the three phase systems. Since there is no gas phase, agitation only serves to keep the catalyst suspended making it more accessible to the dissolved reactants so it only has a secondary effect on mass transfer processes. Substrate concentration and catalyst quantity are the two most important reaction variables in such reactions since both have an influence on the rate of migration of the reactants through the liquid/solid interface. Also of significant importance are the factors involved in minimizing pore diffusion factors the size of the catalyst particles and their pore structure. 

Blue et al. have studied the dehydrogenation of butane at atmospheric pressure, using a chromia-alumina catalyst at 530°C. For a spherical catalyst size of dp = 0.32 cm the experimental data suggest a first-order rate constant of about 0.94 cm /(sec)(g catalyst). The pore radius is given as 110 A. Assuming Knudsen diffusivity at this low pressure and estimating the pore volume as 0.35 cm /g, predict an effectiveness factor for the catalyst. Use the parallel-pore model with a tortuosity factor of 2.0. 

Trickle bed reactors have grown rapidly in importance in recent years because of their application in hydrodesulfurization of naphtha, kerosene, gasoil, and heavier petroleum fractions hydrocracking of heavy gasoil and atmospheric residues hydrotreating of lube oils and hydrogenation processes. In trickle bed operation the flow rates are much lower than those in absorbers. To avoid too low effectiveness factors in the reaction, the catalyst size is much smaller than that of the packing used in absorbers, which also means that the overall void fraction is much smaller. 

Heterogeneous intra and external gradients are included and catalyst effectiveness factors are calculated continuously during the integration. The kinetic rate expressions are intrinsic rates. This is definitely the preferred model, but rigorous modelling of transport processes is tedious for all catalyst sizes and shapes in syngas processes. 

There are many factors influencing internal diffusion, such as the size of particles and pore of catalysts, molecular diffusion coefficient, temperature, pressure and other parameters in reaction kinetics etc. Among these factors, the size of catalyst particles and reaction temperature are the most important and easily adjustable parameters. The estimation and elimination of internal diffusion effect can usually use the ways as follows ... 

It seems reasonable to assume that an oxidation-reduction dynamic equilibrium is established on the catalyst surface during the reduction step and that appreciable restructuring of the catalyst surface can take place. Since the kinetics of the process are controlled by pore diffusion, particle size and shape once again play an important role in determining the initial activity of the catalyst. In fact, rate measurements conducted by the authors in the laboratory with prereduced catalysts of various particle sizes show that the initial activity of the larger catalyst particles is considerably lower than that of the smaller particles. Consequently, another corrective factor, EFsp, which takes into account the influence of the catalyst particle size on this inherent self-poisoning effect, must be included in the rate equation for use in converter calculations. Values of EFsp for various catalyst size ranges are reported in Table 6.11. 

The mass transport influence is easy to diagnose experimentally. One measures the rate at various values of the Thiele modulus the modulus is easily changed by variation of R, the particle size. Cmshing and sieving the particles provide catalyst samples for the experiments. If the rate is independent of the particle size, the effectiveness factor is unity for all of them. If the rate is inversely proportional to particle size, the effectiveness factor is less than unity and

experimental points allow triangulation on the curve of Figure 10 and estimation of Tj and ( ). It is also possible to estimate the effective diffusion coefficient and thereby to estimate Tj and ( ) from a single measurement of the rate (48). 

This conclusion was additionally confirmed by Palczewska and Janko (67) in separate experiments, where under the same conditions nickel-copper alloy films rich in nickel (and nickel films as well) were transformed into their respective hydride phases, which were proved by X-ray diffraction. The additional argument in favor of the transformation of the metal film into hydride in the side-arm of the Smith-Linnett apparatus consists of the observed increase of the roughness factor ( 70%) of the film and the decrease of its crystallite size ( 30%) after coming back from low to high temperatures for desorbing hydrogen. The effect is quite similar to that observed by Scholten and Konvalinka (9) for their palladium catalyst samples undergoing the (a — j8) -phase transformation. 

The presence of catalysts markedly changes the deflagration rate. The greatest rate increase is produced by copper chromite, a well-known hydrogenation catalyst. Some additives which catalyze the process at higher pressures may inhibit it strongly at lower pressures. The catalyst effect is related to catalyst particle-size and concentration, but these factors have not been studied extensively. 

The effectiveness factor depends, not only on the reaction rate constant and the effective diffusivity, but also on the size and shape of the catalyst pellets. In the following analysis detailed consideration is given to particles of two regular shapes ... 

A quantitative investigation of the influence exerted by a substrate on the properties of disperse catalysts is hampered by the distorting effects of many other factors, particularly the macrokinetic limitations and the size effects mentioned in Section 28.5.4. 

Recently, however, the development of nanotechnology may provide the changes on the research and development of practical catalysts. As mentioned in the previous section we can now design and synthesize a metal nanoparticle with not only various sizes and shapes, but also with various combinations of elements and their locations. Thus, we can now design the synergetic effect of two elements. In the case of core/shell structured bimetallic nanoparticles, the shell element can provide a catalytic site and the core element can give an electronic effect (a ligand effect) on the shell element. Since only the atoms on the surface can be attached by substrates, the thickness of the shell should be an important factor to control the catalytic performance. 

An apparent particle size effect for the hydrodechlorination of 2-chlorophenol and 2,4-dichlorophenol was observed by Keane et al. [147], Investigating silica supported Ni catalysts (derived from either nickel nitrate or nickel ethane-diamine) with particles in the size range between 1.4 and 16.8 nm, enhanced rates for both reactions were observed with increased size over the full range (Figure 13). As electronic factors can be ruled out in this dimension, the observed behavior is traced back to some sort of ensemble effect, known from CFC transformations over Pd/Al203... 

The size of the cataly.st particle influences the observed rate of reaction the smaller the particle, the less time required for the reactants to move to the active catalyst sites and for the products to diffuse out of the particle. Furthermore, with relatively fast reactions in large particles the reactants may never reach the interior of the particle, thus decreasing the catalyst utilization. Catalyst utilization is expressed as the internal effectiveness factor //,. This factor is defined as follows ... 

In order for diffusional limitations to be negligible, the effectiveness factor must be close to 1, i.e. nearly complete catalyst utilization, which requires that the Thiele modulus is suffieiently small (< ca. 0.5), see Figure 3.32. Therefore, the surface-over-volume ratio must be as large as possible (particle size as small as possible) from a diffusion (and heat-transfer) point of view. There are many different catalyst shapes that have different SA/V ratios for a given size. 

Microlevel. The starting point in multiphase reactor selection is the determination of the best particle size (catalyst particles, bubbles, and droplets). The size of catalyst particles should be such that utilization of the catalyst is as high as possible. A measure of catalyst utilization is the effectiveness factor q (see Sections 3.4.1 and 5.4.3) that is inversely related to the Thiele modulus (Eqn. 5.4-78). Generally, the effectiveness factor for Thiele moduli less than 0.5 are sufficiently high, exceeding 0.9. For the reaction under consideration, the particles size should be so small that these limits are met. 

Inspection of Fig. 15.3 reveals that while for jo 0.1 nAcm , the effectiveness factor is expected to be close to 1, for a faster reaction with Jo 1 p,A cm , it will drop to about 0.2. This is the case of internal diffusion limitation, well known in heterogeneous catalysis, when the reagent concentration at the outer surface of the catalyst grains is equal to its volume concentration, but drops sharply inside the pores of the catalyst. In this context, it should be pointed out that when the pore size is decreased below about 50 nm, the predominant mechanism of mass transport is Knudsen diffusion [Malek and Coppens, 2003], with the diffusion coefficient being less than the Pick diffusion coefficient and dependent on the porosity and pore stmcture. Moreover, the discrete distribution of the catalytic particles in the CL may also affect the measured current owing to overlap of diffusion zones around closely positioned particles [Antoine et ah, 1998]. 

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