Diffusion rates, intracrystalline

Understanding the adsorption, diffusivities and transport limitations of hydrocarbons inside zeolites is important for tailoring zeolites for desired applications. Knowledge about diffusion coefficients of hydrocarbons inside the micropores of zeolites is important in discriminating whether the transport process is micropore or macropore controlled. For example, if the diffusion rate is slow inside zeolite micropores, one can modify the post-synthesis treatment of zeolites such as calcination, steaming or acid leaching to create mesopores to enhance intracrystalline diffusion rates [223]. The connectivity of micro- and mesopores then becomes an... 

Shape-selective catalysis in zeolite requires that the reactants diffuse inwards to the active sites located at the intracrystalline volume (pores), and that products counterdif-fuse after the reaction. At the active sites, presence of a high local electric field may direct the reaction according to steric requirements to yield specific products. Thus, shape-selectivity may be achieved by virtue of geometric factors, Coulombic field at the active sites and/or difference in diffusion rates. Accordingly, three different kinds of shape-selectivity are distinguished (Dwyer, 1984). If the geometric factors are such that... 

Using the computer programs discussed above, it is possible to extract from these breakthrough curves the effective local mass transfer coefficients as a function of CO2 concentration within the stable portion of the wave. These mass transfer coefficients are shown in Figure 15, along with the predicted values with and without the inclusion of the surface diffusion model. It is seen that without the surface diffusion model, very little change in the local mass transfer coefficient is predicted, whereas with surface diffusion effects included, a more than six-fold increase in diffusion rates is predicted over the concentrations measured and the predictions correspond very closely to those actually encountered in the breakthrough runs. Further, the experimentally derived results indicate that, for these runs, the assumption that micropore (intracrystalline) resistances are small relative to overall mass transfer resistance is justified, since the effective mass transfer coefficients for the two (1/8" and 1/4" pellets) runs scale approximately to the inverse of the square of the particle diameter, as would be expected when diffusive resistances in the particle macropores predominate. 

Katzer (28) observed that counterdiffusion of benzene and cumene within the pores of H-mordenite does not occur at low temperatures. However, H-mordenite shows activity for the alkylation of benzene with propylene to form cumene under the liquid phase conditions used for the diffusion studies, and he has suggested that reaction must occur on the external crystallite surface, or just within the pore mouth. In earlier studies on the isomerization of 2,3-dimethylbutene-l at 0°-20°C over a deuterated Y-type faujasite (62), we observed that the extent of isomerization (2,3-dimethylbutene-2) was far greater than the extent of deutera-tion only a fraction of the total deuterium on catalyst OD groups was exchanged. One possible explanation—assuming a protonic isomerization mechanism—is that, because of lowered intracrystalline diffusion rates... 

ABSTRACT. The amount of published work on molecular shape-selective catalysis with zeolites is vast. In this paper, a brief overview of the general principles involved in molecular shape-selectivity is provided. The recently proposed distinction between primary and secondary shape-selectivity is discussed. Whereas primary shape-selectivity is the result of the interaction of a reactant with a micropore system, secondary shape-selectivity is caused by mutual interactions of reactant molecules in micropores. The potential of diffusion/reaction kinetic analysis and molecular graphics for rationalizing molecular shape-selectivity is illustrated, and an alternative explanation for the cage and window effect in cracking and hydrocracking is proposed. Pore mouth catalysis is a speculative mechanism advanced for some systems (a combination of a specific zeolite and a reactant), which exhibit peculiar selectivities and for which the intracrystalline diffusion rates of reactants are very low. 

Since Sh > 2 and < D /r, the minimum value of (Bi) , is given by t/3c ("-3.0). Thu, even under these rather extreme assumptions the internal concentratiort gradient is appreciably greater than the external gradient. Any additional resistance to mass transfer from either Knudsen diffusion or intracrystalline diffusion will decrease further, so one may conclude that under most practically realisable conditions the intraparticle resistance is more important than film resistance in determining the mass transfer rate. 

We also investigated the paraxylene/HZSM-S syston with the same technique. Due to the lower intracrystalline diffusion rate the "non uniform" model was not able to simulate the NMR spectra correctly. A simpler "core shrinking" model was used [9]. The crystallites are divided into two zones a core free of diffusing molecules and a shell with a uniform hydrocarbon concentration. During the adsorption there is a diffiision front in the crystallites, the shell region increases at the expense of the core. Then, the NMR spectra is simply the sum of two lines whose intensity inversely varies widi time (Fig. 3b). 

Also shown are the corresponding curves calculated for the same system assuming a diffusion model in place of the linear rate expression. For intracrystalline diffusion k = 15Dq/v, whereas for macropore diffusion k = 15e /R ) Cq/q ), in accordance with the Glueckauf approximation (21). 

For noncoustaut diffusivity, a numerical solution of the conseiwa-tion equations is generally required. In molecular sieve zeohtes, when equilibrium is described by the Langmuir isotherm, the concentration dependence of the intracrystalline diffusivity can often be approximated by Eq. (16-72). The relevant rate equation is ... 

Introduction of PFG NMR to zeolite science and technology has revolutionized our understanding of intracrystalline diffusion [19]. In many cases, molecular uptake by beds of zeolites turned out to be limited by external processes such as resistances, surface barriers or the finite rate of sorbate supply, rather than by intracrystalline diffusion, as previously assumed [10, 20-24]. Thus, the magnitude of intracrystalline diffusivities had to be corrected by up to five orders of magnitude to higher values [25, 26],... 

While microscopic techniques like PFG NMR and QENS measure diffusion paths that are no longer than dimensions of individual crystallites, macroscopic measurements like zero length column (ZLC) and Fourrier Transform infrared (FTIR) cover beds of zeolite crystals [18, 23]. In the case of the popular ZLC technique, desorption rate is measured from a small sample (thin layer, placed between two porous sinter discs) of previously equilibrated adsorbent subjected to a step change in the partial pressure of the sorbate. The slope of the semi-log plot of sorbate concentration versus time under an inert carrier stream then gives D/R. Provided micropore resistance dominates all other mass transfer resistances, D becomes equal to intracrystalline diffusivity while R is the crystal radius. It has been reported that the presence of other mass transfer resistances have been the most common cause of the discrepancies among intracrystaUine diffusivities measured by various techniques [18]. 

The prerequisites of the evaluation of data characteristic of intracrystalline processes in the case of zeolite sorbents are discussed, along with the conditions under which diffusion can be compared to self-diffusion. Selected results of investigations carried out in the author s laboratory are given in order to demonstrate the consistency of sorption kinetic data with intracrystalline mobility data of single components on molecular sieves (HS). Various types of surface barrier which may influence the uptake rate are also described. 

If a NS monocrystal takes up a single component from a fluid phase and Intercrystalline transport does not influence the uptake rate, one should be aware of the possibility that, besides intracrystalline diffusion, the following processes may either contribute or even govern the uptake rate ... 

The concept of transport resistances localized in the outermost regions of NS crystals was introduced in order to explain the differences between intracrystalline self-diffusion coefficients obtained by n.m.r methods and diffusion coefficients derived from non-equilibrium experiments based on the assumption that Intracrystalline transport is rate-limiting. This concept has been discussed during the past decade, cf. the pioneering work [79-81] and the reviews [2,7,8,23,32,82]. Nowadays, one can state that surface barriers do not occur necessarily in sorption uptake by NS crystals, but they may occur if the cross-sections of the sorbing molecular species and the micropore openings become comparable. For indication of their significance, careful analysis of... 

Using the monomolecular rate theory developed by Wei and Prater, we have analyzed the kinetics of the liquid-phase isomerization of xylene over a zeolitic catalyst. The kinetic analysis is presented primarily in terms of the time-independent selectivity kinetics. With the establishment of the basic kinetics the role of intracrystalline diffusion is demonstrated by analyzing the kinetics for 2 to 4 zeolite catalyst and an essentially diffusion-free 0.2 to 0.4 m zeolite catalyst. Values for intracrystalline diffusivities are presented, and evidence is given that the isomerization is the simple series reaction o-xylene <= m-xylene <= p-xylene. 

The techniques of monomolecular rate theory easily transform measured reaction data into a form where we can analyze apparent kinetics and the effects of intracrystalline diffusion by the use of selectivity data. Time dependency has been eliminated. Since selectivity is extremely reproducible and is independent of short-term aging effects, the number of experimental runs is reduced while data reliability is maintained. For catalyst evaluation at any temperature, it is necessary to determine the equilibrium composition and the straight-line reaction path. With this information any catalyst can be evaluated at this temperature with simply the additional information from a curved-line reaction path. The approach used in the application of monomolecular rate theory to the xylene isomerization selectivity kinetics is as follows. Reference is made to the composition diagram, Figure 1. 

Temperature Dependence of the Activity and Selectivity of Xylene Isomerization over AP Catalyst. Based upon our analysis of the intracrystalline diffusional resistance in AP catalyst, we would expect that when the reaction temperature is increased, the selectivity would shift toward p-xylene since the diffusional effects are increased as the activity increases. A shift in selectivity toward p-xylene as the reaction temperature was increased was observed and is shown in Figure 6. The role of diffusion in changing the selectivity can be seen in the Arrhenius plot of Figure 7. The reaction rate constant for the o-xylene - p-xylene path, fc+3i, goes from an almost negligible value at 300°F to a substantial value at 600°F. Furthermore, the diffusional effects are also demonstrated by the changing... 

Vapor-phase alkylation of benzene by ethene and propene over HY, LaY, and REHY has been studied in a tubular flow reactor. Transient data were obtained. The observed rate of reaction passes through a maximum with time, which results from build-up of product concentration in the zeolite pores coupled with catalyst deactivation. The rate decay is related to aromatic olefin ratio temperature, and olefin type. The observed rate fits a model involving desorption of product from the zeolite crystallites into the gas phase as a rate-limiting step. The activation energy for the desorption term is 16.5 heal/mole, approximately equivalent to the heat of adsorption of ethylbenzene. For low molecular weight alkylates intracrystalline diffusion limitations do not exist. 

An intriguing aspect of these measurements is that the values of D determined from NMR and from sorption kinetics differ by several orders of magnitude. For example, for methane on (Ca,Na)-A the value of the diffusion coefficient determined by NMR is 2 x 10 5 cm2 sec-, and the value determined for sorption rates only 5 x 10"10 cm2 sec-1. The values from NMR are always larger and are similar to those measured in bulk liquids. The discrepancy, which is, of course, far greater than the uncertainty of either method, remained unexplained for several years, until careful studies (267,295,296) showed that the actual sorption rates are not determined by intracrystalline diffusion, but by diffusion outside the zeolite particles, by surface barriers, and/or by the rate of dissipation of the heat of sorption. NMR-derived results are therefore vindicated. Large diffusion coefficients (of the order of 10-6 cm2 sec-1) can be reliably measured by sorption kinetics... 

Alternatively one can in principle derive both micropore and macropore diffusivities from measurements of the transient uptake rate for a particle (or assemblage of crystals) subjected to a step change in ambient sorbate pressure or concentration. The main problem with this approach is that the overall uptake rate may be controlled by several different processes, including both heat and extraparticle mass transfer as well as intraparticle or intracrystalline diffusion. The intrusion of such rate processes is not always obvious from a cursory examination of the experimental data, and the literature of the subject is replete with incorrect diffusivities (usually erroneously low values) obtained as a result of intrusion of such extraneous effects. Nevertheless, provided that intraparticle diffusion is sufficiently slow, the method offers a useful practical alternative to the Wicke-Kallen bach method. 

Earlier studies of intracrystalline diffusion in zeolites were carried out almost exclusively by direct measurement of sorption rates but the limitations imposed by the intrusion of heat transfer and extra-crystalline mass transfer resistances were not always fully recognized. As a result the reported diffu-sivities showed many obvious inconsistencies such as differences in diffusivity between adsorption and desorption measurements(l-3), diffusivities which vary with fractional uptake (4) and large discrepancies between the values measured in different laboratories for apparently similar systems. More recently other experimental techniques have been applied, including chromatography and NMR methods. The latter have proved especially useful and have allowed the microdynamic behaviour of a number of important systems to be elucidated in considerable detail. In this paper the advantages and limitations of some of the common experimental techniques are considered and the results of studies of diffusion in A, X and Y zeolites, which have been the subject of several detailed investigations, are briefly reviewed. 

This methods depends on the implicit assumption that the uptake rate is controlled entirely by intracrystalline diffusion in an isothermal system, with all other resistances to either mass or heat transfer negligible. This is a valid approximation if diffusion is sufficiently slow or if the zeolite crystals are sufficiently large but the dominance of intracrystalline diffusional resistance should not be assumed without experimental verification. In many practical systems, particularly with small commercial zeolite crystals, the external heat and mass transfer resistances are in fact dominant. A detailed discussion of such effects has been given by Lee and Ruthven(5-7). 

These results reveal that at low temperature the rate of diffusion of Ar and N2 into the intracrystalline pore structure is extremely slow. The increase in the adsorption with temperature is not thermodynamically controlled but is instead dependent on the molecules gaining enough kinetic energy to allow their passage through some of the 4A apertures. This process is probably assisted by enhanced vibrational amplitude of the oxygen ring structure. 

Adsorption investigations (determination of equilibrium data, uptake rates, adsorption kinetics, and intracrystalline diffusion). 

The experimental method used in TEOM for diffusion measurements in zeolites is similar to the uptake and chromatographic methods (i.e., a step change or a pulse injection in the feed is made and the response curve is recorded). It is recommended to operate with dilute systems and low zeolite loadings. For an isothermal system when the uptake rate is influenced by intracrystalline diffusion, with only a small concentration gradient in the adsorbed phase (constant diffusivity), solutions of the transient diffusion equation for various geometries have been given (ii). Adsorption and diffusion of o-xylene, / -xylene, and toluene in HZSM-5 were found to be described well by a one-dimensional model for diffusion in a slab geometry, represented by Eq. (7) (72) ... 

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