Catalysts diffusion limitations

Diffusion-limited removal of products from catalyst pellets leads to enhanced readsorption and chain initiation by reactive a-olefins. These secondary reactions reverse chain termination steps that form these olefins and lead to heavier products, higher chain growth probabilities, and more paraffinic products. Diffusion-enhanced readsorption of a-olefins accounts for the non-Flory carbon number distributions frequently observed during FT synthesis on Co and Ru catalysts. Diffusion-limited reactant (H2/CO) arrival leads instead to lower selectivity to higher hydrocarbons. Consequently, intermediate levels of transport restrictions lead to highest selectiv-ities to C5+ products. A structural parameter containing the pellet diameter, the average pore size, and the density of metal sites within pellets, determines the severity of transport restrictions and the FT synthesis selectivity on supported Ru and Co catalysts. 

Catalyst Effectiveness. Even at steady-state, isothermal conditions, consideration must be given to the possible loss in catalyst activity resulting from gradients. The loss is usually calculated based on the effectiveness factor, which is the diffusion-limited reaction rate within catalyst pores divided by the reaction rate at catalyst surface conditions (50). The effectiveness factor E, in turn, is related to the Thiele modulus,

first-order rate constant, a the internal surface area, and the effective diffusivity. It is desirable for E to be as close as possible to its maximum value of unity. Various formulas have been developed for E, which are particularly usehil for analyzing reactors that are potentially subject to thermal instabilities, such as hot spots and temperature mnaways (1,48,51). 

The work of Thiele (1939) and Zeldovich (1939) called attention to the fact that reaction rates can be influenced by diffusion in the pores of particulate catalysts. For industrial, high-performance catalysts, where reaction rates are high, the pore diffusion limitation can reduce both productivity and selectivity. The latter problem emerges because 80% of the processes for the production of basic intermediates are oxidations and hydrogenations. In these processes the reactive intermediates are the valuable products, but because of their reactivity are subject to secondary degradations. In addition both oxidations and hydrogenation are exothermic processes and inside temperature gradients further complicate secondary processes inside the pores. 

The effectiveness of a porous catalyst T] is defined as the actual diffusion-limited reaction rate divided by the reaction rate that could have been achieved if all the internal surface had been at bulk concentration conditions. 

Pore diffusion limitation was studied on a very porous catalyst at the operating conditions of a commercial reactor. The aim of the experiments was to measure the effective diffiisivity in the porous catalyst and the mass transfer coefficient at operating conditions. Few experimental results were published before 1970, but some important mathematical analyses had already been presented. Publications of Clements and Schnelle (1963) and Turner (1967) gave some advice. 

D-Methylmalonyl-CoA, the product of this reaction, is converted to the L-isomer by methylmalonyl-CoA epunerase (Figure 24.19). (This enzyme has often and incorrectly been called methylmalonyl-CoA racemase. It is not a racemase because the CoA moiety contains five other asymmetric centers.) The epimerase reaction also appears to involve a carbanion at the a-position (Figure 24.20). The reaction is readily reversible and involves a reversible dissociation of the acidic a-proton. The L-isomer is the substrate for methylmalonyl-CoA mutase. Methylmalonyl-CoA epimerase is an impressive catalyst. The for the proton that must dissociate to initiate this reaction is approximately 21 If binding of a proton to the a-anion is diffusion-limited, with = 10 M sec then the initial proton dissociation must be rate-limiting, and the rate constant must be... 

Olefins are hydrogenated very easily, unless highly hindered, over a variety of catalysts. With active catalysts, the reaction is apt to be diffusion limited, since hydrogen can be consumed faster than it can be supplied to the catalyst surface. Most problems connected with olefin hydrogenation involve some aspect of regio- or stereoselectivity. Often the course of reduction is influenced greatly by the catalyst, by reaction variables, and by hydrogen availability at the catalyst surface. 

Suppose that catalyst pellets in the shape of right-circular cylinders have a measured effectiveness factor of r] when used in a packed-bed reactor for a first-order reaction. In an effort to increase catalyst activity, it is proposed to use a pellet with a central hole of radius i /, < Rp. Determine the best value for RhjRp based on an effective diffusivity model similar to Equation (10.33). Assume isothermal operation ignore any diffusion limitations in the central hole, and assume that the ends of the cylinder are sealed to diffusion. You may assume that k, Rp, and eff are known. 

Determine the position of the reaction front in the diffusion-limited decoking of a spherical cracking catalyst. 

Minimize the effects of transport phenomena If we are interested in the intrinsic kinetic performance of the catalyst it is important to eliminate transport limitations, as these will lead to erroneous data. We will discuss later in this chapter how diffusion limitations in the pores of the catalyst influence the overall activation energy. Determining the turnover frequency for different gas flow velocities and several catalyst particle sizes is a way to establish whether transport limitations are present. A good starting point for testing catalysts is therefore ... 

Mass transport may constitute another problem. Since many catalysts are porous systems, diffusion of gases in and out of the pores may not be fast enough in comparison to the rate of reaction on the catalytic site. In such cases diffusion limits the rate of the overall process. 

Hence, the apparent activation energy is half the value we would obtain if there were no transport limitations. Obviously it is important to be aware of these pitfalls when testing a catalyst. Indeed, apparent activation energies generally depend on the conditions employed (as discussed in Chapter 2), and diffusion limitation may further cause them to change with temperature. 

This example illustrates how the parameters of interest are derived from kinetic measurements. Of course, one should have ensured that the data are free from diffusion limitations and represent the intrinsic reaction kinetics. The data, reported by Borgna, that we used here satisfy these requirements, as the catalyst was actually a nonporous surface science model applied to a batch reactor. 

Typical concentration-time profiles during the 1-hexyne hydrogenation over 0.4wt.% Pd/ACF catalyst are presented in Figure 7 showing the experimental and simulated curves (Langmuir-Hinshelwood mechanism). Pd/ ACF materials with the same particle size but different Pd loading (0.4, 0.6, 1.2wt.%) show identical initial activity of 0.140 0.004 kmolHj/kgp(j/s. This indicates the absence of diffusion limitations. Selectivity to 1-hexene is 97.1 +0.4% up to 80% conversion, and 95.9 + 0.4% at 90% conversion. 

Zeolites have ordered micropores smaller than 2nm in diameter and are widely used as catalysts and supports in many practical reactions. Some zeolites have solid acidity and show shape-selectivity, which gives crucial effects in the processes of oil refining and petrochemistry. Metal nanoclusters and complexes can be synthesized in zeolites by the ship-in-a-bottle technique (Figure 1) [1,2], and the composite materials have also been applied to catalytic reactions. However, the decline of catalytic activity was often observed due to the diffusion-limitation of substrates or products in the micropores of zeolites. To overcome this drawback, newly developed mesoporous silicas such as FSM-16 [3,4], MCM-41 [5], and SBA-15 [6] have been used as catalyst supports, because they have large pores (2-10 nm) and high surface area (500-1000 m g ) [7,8]. The internal surface of the channels accounts for more than 90% of the surface area of mesoporous silicas. With the help of the new incredible materials, template synthesis of metal nanoclusters inside mesoporous channels is achieved and the nanoclusters give stupendous performances in various applications [9]. In this chapter, nanoclusters include nanoparticles and nanowires, and we focus on the synthesis and catalytic application of noble-metal nanoclusters in mesoporous silicas. 

The selectivity in a system of parallel reactions does not depend much on the catalyst size if effective diffusivities of reactants, intermediates, and products are similar. The same applies to consecutive reactions with the product desired being the final product in the series. In contrast with this, for consecutive reactions in which the intermediate is the desired product, the selectivity much depends on the catalyst size. This was proven by Edvinsson and Cybulski (1994, 1995) for. selective hydrogenations and also by Colen et al. (1988) for the hydrogenation of unsaturated fats. Diffusion limitations can also affect catalyst deactivation. Poisoning by deposition of impurities in the feed is usually slower for larger particles. However, if carbonaceous depositions are formed on the catalyst internal surface, ageing might not depend very much on the catalyst size. 

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]. 

The effect of catalyst particle size was investigated by two different catalyst particle size fractions 63-93 pm and 150-250 pm, respectively. The effect of the particle size is very clear as demonstrated by Figure 47.2. The overall hydrogenation rate was for smaller particles 0.17 mol/min/gNi while it was 0.06 mol/min/gNi, for the larger particles, showing the presence of diffusion limitation. This kind of studies can be used to determine the effectiveness factors. The conversion levels after 70 min time-on-stream were 21% and 3%, respectively, for these two cases. 

Prior to conducting the DOE (design of experiments) described in Table 3, it was established that no reaction took place in the absence of a catalyst and that the reactions were conducted in the region where chemical kinetics controlled the reaction rate. The results indicated that operating the reactor at 1000 rpm was sufficient to minimize the external mass-transfer limitations. Pore diffusion limitations were expected to be minimal as the median catalyst particle size is <25 pm. Further, experiments conducted under identical conditions to ensure repeatability and reproducibility in the two reactors yielded results that were within 5%. 

The results of the catalyst testing are shown in Table 3. The data listed in the table show, that on a per proton basis, catalyst A (based on 7% DVB) has higher activity as compared to resin materials, crosslinked with 12% DVB. This result is in accord with the finding by Petrus et al.,3 that at temperatures higher than 120 °C the hydration is under into particle diffusion limitation and as such, a more flexible polymeric matrix will provide better access to the acidic sites. On a dry weight basis, catalyst D showed the highest activity, which correlates well with the high acid site density found for this resin (Table 2). On a catalyst volume basis, catalyst A has the best performance characteristics followed by catalyst D. 

Many challenges remain to be addressed in this field. The use of immobilized catalysts can often reduce the activity of a catalyst Reduced reaction rates due to diffusion limitations through a permeable membrane capsule and the ease or practicality of the synthesis of these catalyst scaffolds are issues that may pose problems. In some cases, these issues have been resolved, but this is often at the expense of other properties of the capsule. For example, the use of thin walls to reduce mass transfer limitations can be at the expense of nanocapsule strength and stability. 

In terms of shape and size, catalysts are typically presented as extrudates (cylindrical, tri-lobes or four-lobes), in sizes of diameters from 0.8 mm to about 1.7 mm and lengths from 3 mm to about 7 mm. The effect of size and shape on operation concerns the pressure drop control, the fluid flow through the bed, the interparticle and intraparticle flow, the diffusion of the fluids from the external surface to the internal surface. The three and four lobes extrudates facilitates diffusion, but they are usually more fragile than the cylindrical extrudates increasing the risk of pressure drop build up. For operation of a trickle bed reactor with heavy feedstocks, for which the diffusion limitations are important, lobed extrudates are preferred. Meanwhile, for vapor phase reactors large cylindrical extrudates are used. 

The analysis of the literature data shows that zeolites modified with nobel metals are among perspective catalysts for this process. The main drawbacks related to these catalysts are rather low efficiency and selectivity. The low efficiency is connected with intracrystalline diffusion limitations in zeolitic porous system. Thus, the effectiveness factor for transformation of n-alkanes over mordenite calculated basing on Thiele model pointed that only 30% of zeolitic pore system are involved in the catalytic reaction [1], On the other hand, lower selectivity in the case of longer alkanes is due to their easier cracking in comparison to shorter alkanes. 

---