Pore diffusion, limiting process

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. 

Figure 7-15 Plots of r versus T and log i versus 1/r. We expect the rate to exhibit breaks on the 1/r plot as the reaction process goes from reaction limited at low temperature, pore diffusion limited at intermediate temperature, and external mass transfer limited at high temperature.

Another important catalyst characteristic is porosity. Particularly when heavy feeds are processed, high pore volumes and pore diameters are required to reduce pore diffusion limitations. These limitations occur when the intrinsic rate of reaction is high compared with the rate of diffusion of the reactants through the catalyst particle to the active surface. The catalyst is then not used effectively, and reaction rates and selectivity become functions of particle size. If the kinetics of the reaction are known, it is possible to estimate from theory the reaction rate or threshold above which a catalyst of known size will begin to exhibit diffusion limitations. 

From the foregoing dicussion it is apparent that residuum hydroconversion processes can be influenced adversely by pore diffusion limitations. Increasing the catalyst porosity can alleviate the problem although increased porosity is usually accompanied by a decrease in total catalytic surface area. Decreasing the catalyst particle size would ultimately eliminate the problem. However, a different type of reaction system would be required since the conventional fixed bed would experience excessive pressure drops if very fine particles were used. A fluidized system using small particles does not suffer from this limitation. However, staging of the fluidized reaction system is required to minimize the harmful effects that backmixing can have on reaction efficiency and selectivity. 

Another example of gas-solid separation is the adsorption process. The regeneration of adsorbent is often not complete due to pore diffusion limitations and other factors. Furthermore, the eventual replacement of spent adsorbent leads to solid wastes. Optimization of adsorbent pore structure is one option that can be examined here. The process of regeneration also leads to waste formation and needs to be set at optimum conditions. 

There are two types of diffusion limitations in fluid/solid interactions boundary layer diffusion and pore diffusion. Both processes are weakly temperature dependent but the operating conditions that reveal their presence are different. 

The coking and regeneration of a reforming catalyst was studied by physical characterization methods (pore volume, tortuosity, porosity, carbon distribution) as well as by kinetic investigations on the reaction rate of coke bum-off. For temperatures of industrial relevance for the Pt/Re-A Os catalyst, i.e. below 550°C (deactivation), the bum-off rate is determined by the interplay of chemical reaction and pore diffusion limitation by external mass transfer can be excluded. Based on the kinetic parameters, the process of the regeneration of a technical reactor is discussed. 

The integral product yield as function of conversion for different values of the Thiele modulus is shown in Figure 2.28 for k = k /k = 1/4. It is obvious that internal diffusional resistance leads to a drastic decrease of the target product selectivity and yield. In the domain of practical interest with k <1, the maximum obtainable yield for strong diffusion resistance ( 3, Equation 2.194) drops roughly to 50% of the value reached in the kinetic regime (Equation 2.187). At the same time the efficiency factor in the porous catalyst drops to r p<0.2 as indicated. This demonstrates the dramatic impact of pore diffusion limitation on the overall productivity of the catalytic process. 

Ferric-ion complexes are important in acid-sulfate leaching because ferric ion can be generated from fenous ion using air or oxygen in situ. The reduction of ferric iron to ferrous occurs as the ferric-ion complex diffuses through fluid-filled pores and channels in the rock matrix and encounters reactive metals or sulfides. In most instances, as already discussed, the rate of ferric ion reduction is a diffusion-limited process. The oxidation of ferrous iron to ferric in aqueous solution becomes of primary importance because of its in situ regeneration capacity under appropriate oxidation potentials. 

Fluid-Bed Processes. For the very exothermic and pore diffusion-limited synthesis reaction, a fluid-bed mode of operation would seem ideal on account of the feasibility of high heat transfer coefficients and small catalyst particles. However, the presence of relatively heavy compounds in the product spectrum may cause deposition of these compounds on the catalyst, leading to agglomeration of particles and fluidization problems. 

From what has been said, it is clear that both physical and mathematical aspects of the limiting processes require more careful examination, and we will scare this by examining the relative values of the various diffusion coefficients and the permeability, paying particular attention to their depec dence on pore diamater and pressure. 

The former usually involves process temperature or isolation. Sohds surface characteristics are important in that they control the extent to which an operation is diffusion-limited, i.e., diffusion into and out of the pores of a given sohds particle, not through the voids among separate particles. The size of the solids parti(des, the surface-to-mass ratio, is also important in the evaluation of surface characteristics and the diffusion problem. 

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. 

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 key to obtaining pore size information from the NMR response is to have the response dominated by the surface relaxation rate [19-26]. Two steps are involved in surface relaxation. The first is the relaxation of the spin while in the proximity of the pore wall and the other is the diffusional exchange of molecules between the pore wall and the interior of the pore. These two processes are in series and when the latter dominates, the kinetics of the relaxation process is analogous to that of a stirred-tank reactor with first-order surface and bulk reactions. This condition is called the fast-diffusion limit [19] and the kinetics of relaxation are described by Eq. (3.6.3) ... 

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. 

The most difficult problem to solve in the design of a Fischer-Tropsch reactor is its very high exothermicity combined with a high sensitivity of product selectivity to temperature. On an industrial scale, multitubular and bubble column reactors have been widely accepted for this highly exothermic reaction.6 In case of a fixed bed reactor, it is desirable that the catalyst particles are in the millimeter size range to avoid excessive pressure drops. During Fischer-Tropsch synthesis the catalyst pores are filled with liquid FT products (mainly waxes) that may result in a fundamental decrease of the reaction rate caused by pore diffusion processes. Post et al. showed that for catalyst particle diameters in excess of only about 1 mm, the catalyst activity is seriously limited by intraparticle diffusion in both iron and cobalt catalysts.1... 

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