Sorption, diffusion, and catalytic reaction

Sorption, Diffusion, and Catalytic Reaction in Zeolites L. Riekert... 

The TAP reactor is particularly suited to study monomolecular reactions because of the very low pressures that are applied and the high ratio of active sites to reactant concentration. For the catalytic cracking of methylcyclohexane, these conditions lead to negligible coke deposits. Moreover, it has been already been demonstrated that the TAP reactor allows the determination of sorption, diffusion and cracking parameters in for reactions over zeolite materials. ... 

Since the time constants of catalytic reactions and the sorption uptake of molecules of various types on crystalline MS, e.g. zeolites, alumlnophosphates and others, are within comparable ranges, the diffusion coefficient represents one of the important rate characteristics of both catalytic and sorptive... 

The discussion above explains why basic information on sorption and diffusion under the reaction conditions, especially at elevated pressures, is required for kinetic and mass- and heat- transfer modelling of catalytic polymerization reactors. If such information is sufficiently available, one should be able, for example, to compare the kinetics of gas-phase and slurry-processes directly by taking into account both gas solubilities in swollen polymers and the hydrocarbons used in slurry processes. 

Rieckmann and Keil (1997) introduced a model of a 3D network of interconnected cylindrical pores with predefined distribution of pore radii and connectivity and with a volume fraction of pores equal to the porosity. The pore size distribution can be estimated from experimental characteristics obtained, e.g., from nitrogen sorption or mercury porosimetry measurements. Local heterogeneities, e.g., spatial variation in the mean pore size, or the non-uniform distribution of catalytic active centers may be taken into account in pore-network models. In each individual pore of a cylindrical or general shape, the spatially ID reaction-transport model is formulated, and the continuity equations are formulated at the nodes (i.e., connections of cylindrical capillaries) of the pore space. The transport in each individual pore is governed by the Max-well-Stefan multicomponent diffusion and convection model. Any common type of reaction kinetics taking place at the pore wall can be implemented. 

A great number of studies have been published to deal with relation of transport properties to structural characteristics. Pore network models [12,13,14] are engaged in determination of pore network connectivity that is known to have a crucial influence on the transport properties of a porous material. McGreavy and co-workers [15] developed model based on the equivalent pore network conceptualisation to account for diffusion and reaction processes in catalytic pore structures. Percolation models [16,17] are based on the use of percolation theory to analyse sorption hysteresis also the application of the effective medium approximation (EMA) [18,19,20] is widely used. 

Sousa et al [5.76, 5.77] modeled a CMR utilizing a dense catalytic polymeric membrane for an equilibrium limited elementary gas phase reaction of the type ttaA +abB acC +adD. The model considers well-stirred retentate and permeate sides, isothermal operation, Fickian transport across the membrane with constant diffusivities, and a linear sorption equilibrium between the bulk and membrane phases. The conversion enhancement over the thermodynamic equilibrium value corresponding to equimolar feed conditions is studied for three different cases An > 0, An = 0, and An < 0, where An = (ac + ad) -(aa + ab). Souza et al [5.76, 5.77] conclude that the conversion can be significantly enhanced, when the diffusion coefficients of the products are higher than those of the reactants and/or the sorption coefficients are lower, the degree of enhancement affected strongly by An and the Thiele modulus. They report that performance of a dense polymeric membrane CMR depends on both the sorption and diffusion coefficients but in a different way, so the study of such a reactor should not be based on overall component permeabilities. 

The catalyst activity is influenced by the selective sorption and diffusion of the substrate in the membrane. Generally, substrates that are preferentially adsorbed, and therefore are more concentrated around the catalytic sites, increase the reaction rate on the other hand, diffusion is also an important factor for the catalytic reactions, particularly in dense membranes. Cycloheptanol is the more hydrophobic alcohol in this series and, consequently, can better interact with the PDMS by Van der Waals interactions however, it is also the more stoically constrainted, and the reaction rate is lower than for n-cyclopentanol (Fig. 27.8). 

Because of their intrinsic characteristics, mostly dense rubbery polymers have been considered for the preparation of polymeric catalytic membranes. The mass-transport mechanism considered has been the well-known sorption-diffusion model.ii Modelling the kinetics of the reaction(s) occurring at the occluded catalyst level is a much more complex task. The reaction may be carried out under special operating conditions, for example in a batch reactor where the catalyst is dispersed in a support - or directly inside the catalytic membrane, -" a reaction-rate model is assumed and the related parameters are determined by fitting the global model to the experimental data. In other cases, the kinetic models determined by other authors are used. - In some theoretical studies, a hypothetical reaction-rate model and the respective model parameters are assumed. 

The model by Yawalkar et was extended by Nagy some years later. The same geometrical distribution of the catalyst in the polymer phase and the same sorption-diffusion model for the mass transport, either in the polymer or in the catalyst, was considered. However, that author considered an irreversible first-order reaction in his model. From the study of the catalytic particles size and distribution, membrane thickness, membrane and catalyst diffusion coefficients, among other variables, the author concluded that the mass-transfer rate depends significantly on the size of the catalytic particles and the thickness of the membrane fraction between the surface and the first particles layer and, also, on the usually low diffusion coefficient through the catalytic particles. 

The Elovich model was originally developed to describe the kinetics of heterogeneous chemisorption of gases on solid surfaces [117]. It describes a number of reaction mechanisms including bulk and surface diffusion, as well as activation and deactivation of catalytic surfaces. In solid phase chemistry, the Elovich model has been used to describe the kinetics of sorption/desorption of various chemicals on solid phases [23]. It can be expressed as [118] ... 

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