Complex Reactions with Pore Diffusion

As is true for many industrial situations, the question of diffusional effects on multiple reaction selectivity is equally as important as the effectiveness of conversion considerations. The basic concepts were provided by Wheeler [133], through consideration of three categories of situations. 

The simplest is that of parallel, independent reactions (Wheeler Type I)  

In the absence of pore diffusion. Chapter 1 gives the selectivity ratio as 

Now with pore diffusion, the two independent rates are each merely multiplied by their own effectiveness fiictor to give 

The diflerence between Eqs. 3.S.-2 and 3.8-1 is not readily seen, although the former is clearly the same as the latter when - 1.0. For strong pore diffusion limitations, where if, 1/01, the following is tlK situation  

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When gum formation proceeds, the minimum temperature in the catalyst bed decreases with time. This could be explained by a shift in the reaction mechanism so more endothermic reaction steps are prevailing. The decrease in the bed temperature speeds up the deactivation by gum formation. This aspect of gum formation is also seen on the temperature profiles in Figure 9. Calculations with a heterogenous reactor model have shown that the decreasing minimum catalyst bed temperature could also be explained by a change of the effectiveness factors for the reactions. The radial poisoning profiles in the catalyst pellets influence the complex interaction between pore diffusion and reaction rates and this results in a shift in the overall balance between endothermic and exothermic reactions. 

Based on the above results, ultrasonic irradiation to ion-exchanged [Pd(NH3)4]2+-zeolite powders was performed in an aqueous solution containing 2-propanol. The reduction of [Pd(NH3)4]2+-zeolite to Pd°-zeolite was confirmed by XPS analyses. However, from XPS depth analyses of the prepared samples, it was suggested that the [Pd(NH3)4]2+ complexes in the zeolite pore were not sufficiently reduced even in the presence of 2-propanol. Presumably, the reductants formed from 2-propanol sonolysis could not easily diffuse into the zeolite nano-pore (size 1.2 nm) and/or reductants undergo recombination reactions and quenching reactions with the walls. In addition, the results of XPS spectral analyses of the sonochemically prepared Pd-zeolite powders indicated that the average size of the Pd clusters on the zeolite surface is roughly estimated to be less than 1 nm and composed of several dozen Pd atoms. 

The problem is also more complex when heterogeneous catalysed reactions are considered. With porous catalyst pellets, reaction occurs at gas- or liquid-solid interfaces at the outer or inner sphere. When the reactants diffuse only slowly from the bulk phase to the exterior surface of the catalyst, gas or liquid film resistance must be taken into account. Pore diffusion resistance may be involved when the reactants move through the pores into the pellet. 

The effectiveness is a measure of the utilization of the internal surface of the catalyst. It depends on the dimensions of the catalyst particle and its pores, on the diffusivity, specific rate, and heat of reaction. With a given kind of catalyst, the only control is particle size to which the effectiveness is proportional a compromise must be made between effectiveness and pressure drop. In simple cases t] can be related mathematically to its parameters, but in such important practical cases as ammonia synthesis its dependence on parameters is complex and strictly empirical. Section 17.5 deals with this topic. 

Homogeneous catalysts are structurally well-defined complexes and because they are soluble in the reaction mix are not subject to pore diffusion limitations as are heterogeneous catalytic materials. They are almost always highly selective towards desired products. The main consideration is that the complex be stable and reactor conditions chosen such that all the gaseous reactants are adequately dissolved and mixed in the liquid phase. Homogeneous catalysts are easily characterized by standard instrumental methods for compound identification such as XRD or spectroscopy. Deactivation is associated with attack by traces of carboxylic acidic byproducts and impurities in the feed such as 02 and chlorides that attack the ligand groups. 

For non-porous catalyst pellets the reactants are chemisorbed on their external surface. However, for porous pellets the main surface area is distributed inside the pores of the catalyst pellets and the reactant molecules diffuse through these pores in order to reach the internal surface of these pellets. This process is usually called intraparticle diffusion of reactant molecules. The molecules are then chemisorbed on the internal surface of the catalyst pellets. The diffusion through the pores is usually described by Fickian diffusion models together with effective diffusivities that include porosity and tortuosity. Tortuosity accounts for the complex porous structure of the pellet. A more rigorous formulation for multicomponent systems is through the use of Stefan-Maxwell equations for multicomponent diffusion. Chemisorption is described through the net rate of adsorption (reaction with active sites) and desorption. Equilibrium adsorption isotherms are usually used to relate the gas phase concentrations to the solid surface concentrations. 

For inorganic ions, the reactions themselves can be very fast, but the ions may have to diffuse through soil pores before they reach a reaction site. The ions may also have to diffuse through the weathered surface. Diffusion processes lend themselves to kinetic treatment. With multiple diffusion and reaction processes going on simultaneously, the kinetic treatment can become very complex. 

In particular, for the synthesis of optically pure chemicals, several immobilization techniques have been shown to give stable and active chiral heterogeneous catalysts. A step further has been carried out by Choi et al. [342] who immobilized chiral Co(III) complexes on ZSM-5/Anodisc membranes for the hydrolytic kinetic resolution of terminal epoxides. The salen catalyst, loaded into the macroporous matrix of Anodise by impregnation under vacuum, must exit near the interface of ZSM-5 film to contact with both biphasic reactants such as epoxides and water. Furthermore, the loading of chiral catalyst remains constant during reaction because it cannot diffuse into the pore channel of ZSM-5 crystals and is insoluble in water. The catalytic zeolite composite membrane obtained acts as liquid-liquid contactor, which combines the chemical reaction with the continuous extraction of products simultaneously (see Figure 11.28) the... 

The first examples of molecular shape-selective catalysis in zeolites were given by Weisz and Frilette in 1960 [1]. In those early days of zeolite catalysis, the applications were limited by the availability of 8-N and 12-MR zeolites only. An example of reactant selectivity on an 8-MR zeolite is the hydrocracking of a mixture of linear and branched alkanes on erionite [4]. n-Alkanes can diffuse through the 8-MR windows and are cracked inside the erionite cages, while isoalkanes have no access to the intracrystalline catalytic sites. A boom in molecular shape-selective catalysis occurred in the early eighties, with the application of medium-pore zeolites, especially of ZSM-5, in hydrocarbon conversion reactions involving alkylaromatics [5-7]. A typical example of product selectivity is found in the toluene all lation reaction with methanol on H-ZSM-5. Meta-, para- and ortho-xylene are made inside the ZSM-5 chaimels, but the product is enriched in para-xylene since this isomer has the smallest kinetic diameter and diffuses out most rapidly. Xylene isomerisation in H-ZSM-5 is an often cited example of tranSition-state shape selectivity. The diaryl type transition state complexes leading to trimethylbenzenes and coke cannot be accommodated in the pores of the ZSM-5 structure. 

Sharma and co-workers compared several heterogeneous immobilized Co complexes for the oxidation of 2,6-di-ferf-butylphenol in acetonitrile, SCCO2, and C02-expanded acetonitrile (120). They attribute the higher conversions obtained in SCCO2 to complete O2 miscibility in the medium as well as enhanced pore diffusion. These results complement other studies with homogeneous catalysts that favor the use of expanded liquids (121), underscoring the need to match catalysts and reaction conditions to achieve the desired results. 

This reaction consists of several steps starting with the diffusion of CH3 I from the gas flow to the surface of the charcoal grains and from there into the pores, adsorption of CH3 I and isotopic exchange with the KI impregnant, followed by desorption of CH3 I and diffusion of this compound out of the pores and away from the grain surface. Due to the complexity of this process, which generally is an irreversible reaction of (pseudo)-first order, its progress may be influenced by several parameters. 

Step 2 At the aqueous-organic interface, the solute of the aqueous phase reacts with the carrier present in the organic phase in the membrane pore to form the solute-extractant complex species. The ions released to the aqueous phase boundary layer by the chemical reaction with the carrier diffuse to the bulk of the aqueous phase. 

At the beginning of Section 5.1 we have briefly discussed two alternative mechanisms for transport of a substrate, neutral molecule or ion, across a membrane, namely, pores or carriers. In both cases, the substrate is transported across the membrane as a complex either with the pore or with the carrier. What distinguishes the two mechanisms from each other is that the pores are visualized as having fixed positions with the substrate moving within them whereas the actually observed carrier molecules are known to be mobile within the membrane, either empty or loaded by a substrate molecule which can be picked up at one side of the membrane and released at the opposite side. Consequently, we design a network for a carrier mechanism by combining capacitances for empty and loaded carriers at each side of the membrane by two diffusion 2-ports, for empty and D for loaded carriers, and two identical reaction 2-ports R for the formation and dissociation of the substrate-carrier complex, one for each side of the membrane ... 

In this section we shall consider the diffusion of a binary gas mixture in a porous medium, in the absence of chemical reaction, because the understanding of this process is an important component of the more complex real life situations where pore diffusion occurs simultaneously with chemical reaction. These problems will be discussed in Chapters 3 and 4. 

Pore diffusion encountered in gas-solid reaction systems is generally rather more complex, because the solid structure may change in the course of the reaction. Moreover, the actual nature of the porous matrix may also be less well defined. In selecting pore diffusion models for the description of gas-solid reaction systems care should be taken that the sophistication of the model is consistent with the accuracy of the information available on the behavior of the system. 

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