Intraparticle transport control

Rapid Adsorption-Desorption Cycles For rapid cycles with particle diffusion controlling, when the cycle time is much smaller than the time constant for intraparticle transport, the LDF approximation becomes inaccurate. The generalized expression... 

The film diffusion process assumes that reactive surface groups are exposed directly to the aqueous-solution phase and that the transport barrier to adsorption involves only the healing of a uniform concentration gradient across a quiescent adsorbent surface boundary layer. If instead the adsorbent exhibits significant microporosity at its periphery, such that aqueous solution can effectively enter and adsorptives must therefore traverse sinuous microgrottos in order to reach reactive adsorbent surface sites, then the transport control of adsorption involves intraparticle diffusion.3538 A simple mathematical description of this process based on the Fick rate law can be developed by generalizing Eq. 4.62 to the partial differential expression36... 

Representative rate data for 2,4,5-T and parathion for the experiments on adsorption of pesticides on active carbon are presented in Figures 1 and 2. The (C0 — C)/m values in these plots represent the amount of solute, both in micromoles and milligrams, removed from solution per gram of carbon. Good linearization of the data is observed for the experiments, in accord with expected behavior for intraparticle-transport rate control. Similar linearization was obtained also for data for the other pesticides. The linear traces facilitate comparison of relative rates of adsorption of pesticides, and such comparison is made in column 1 of Table III, using the square f the slope pf each plot as the relative rate constant for the experiment. 

To eliminate intraparticle transport limitations, the particle size and average pore size must be carefully controlled during manufacture. Other physical properties that become important in industry have to do with the physical integrity of the catalyst particles. These properties include bulk density, crush strength, resistance to abrasion, and attrition. These properties are very important when working with reactors that contain a large amount of a particular catalyst. Fig. 2 lists a number of chemical and physical properties that affect catalyst performance. 

Protonation/deprotonation reactions are among the fastest reactions in solution, and it is believed that surface protonation/deprotonation reactions are also fast. Therefore, the experimentally observed kinetics in surface protonation experiments is transport-controlled. Different models of kinetics of ion exchange with intraparticle rate control are discussed in [165]. Kinetic models based on a series of consecutive and/or branched reactions and experimental setups for kinetic measurements are reviewed in [166]. 

In a fixed-bed reactor the catalyst pellets are held in place and do not move with respect to a fixed reference frame. Material and energy balances are required for both the fluid, which occupies the interstitial region between catalyst particles, and the catalyst particles, in which the reactions occur. For heterogeneously catalyzed reactions, the effects of intraparticle transport on the rate of reaction must be considered. Catalytic systems operate somewhere between two extremes kinetic control, in which mass and energy transfer are very rapid and intra-partide transport control, in which the reaction is very rapid. Separate material and energy balances are needed to describe the concentration and temperature profile inside the catalyst pellet. The concentrations... 

Rates of adsorption and desorption in porous adsorbents are generally controlled by transport within the pore network, rather than by the intrinsic kinetics of sorption at the surface. Since there is generally little, if any, bulk flow through the pores, it is convenient to consider intraparticle transport as a diffusive process and to correlate kinetic data in terms of a diffusivity defined in accordance with Pick s first equation ... 

Since intraparticle diffiision/transport controls the species transport rate, a linear transport rate expression is sought to describe it to focilitate solution of the overall adsorption process taking place in a packed bed. The transient rate of adsorption/desorption of a species i may be described by the time rate of change of a particle-averaged species concentration defined for a spherical particle of radius tp by... 

We compare the intrinsic rate of adsorption of nitrogen with an experimentally observed rate of adsorption of nitrogen at 6 bar and 25°C (Crittenden et al. 1995). Appropriate substitution of numerical values into equation (4.1) gives the maximum intrinsic rate of adsorption as 2 x 10 kg m s" . On the other hand, the experimentally observed rate is approximately 4 x 10 kg s (c. 0.33 mol s" at 6 bar, 25°C onto a surface of 250 m g ). Thus the intrinsic rate of adsorption is some 10 times faster than the observed rate of adsorption. It is generally acknowledged throughout the literature on physical adsorption processes that the dominant rate-controlling step is not the actual physical attachment of adsorbate to adsorbent (normally referred to as very rapid) but rather intraparticle transport of gas within the porous structure of the adsorbent to its available surface. Interparticle transport from bulk fluid to the external surface of the porous adsorbent may also have an effect on the overall rate of adsorption under some circumstances. 

Spacer chain catalysts 3, 4, and 19 have been investigated under carefully controlled conditions in which mass transfer is unimportant (Table 5)80). Activity increased as chain length increased. Fig. 7 shows that catalysts 3 and 4 were more active with 17-19% RS than with 7-9% RS for cyanide reaction with 1-bromooctane (Eq. (3)) but not for the slower cyanide reaction with 1-chlorooctane (Eq. (1)). The unusual behavior in the 1-bromooctane reactions must have been due to intraparticle diffusional effects, not to intrinsic reactivity effects. The aliphatic spacer chains made the catalyst more lipophilic, and caused ion transport to become a limiting factor in the case of the 7-9 % RS catalysts. At > 30 % RS organic reactant transport was a rate limiting factor in the 1-bromooctane reations80), In contrast, the rate constants for the 1 -chlorooctane reactions were so small that they were likely limited only by intrinsic reactivity. (The rate constants were even smaller than those for the analogous reactions of 1-bromooctane and of benzyl chloride catalyzed by polystyrene-bound benzyl-... 

In this study the ratio of the particle sizes was set to two based on the average value for the two samples. As a result, if the diffusion is entirely controlled by secondary pore structure (interparticle diffusion) the ratio of the effective diffusion time constants (Defl/R2) will be four. In contrast, if the mass transport process is entirely controlled by intraparticle (platelet) diffusion, the ratio will become equal to unity (diffusion independent of the composite particle size). For transient situations (in which both resistances are important) the values of the ratio will be in the one to four range. Diffusional time constants for different sorbates in the Si-MCM-41 sample were obtained from experimental ZLC response curves according to the analysis discussed in the experimental section. Experiments using different purge flow rates, as well as different purge gases... 

The major difference between the various GRM models is due to the mechanism of intraparticle diffusion that they propose, namely pore diffusion, siuface diffusion or a combination of both, independent or competitive diffusion. The pore diffusion model assumes that the solute diffuses into the pore of the adsorbent mainly or only in the free mobile phase that impregnates the pores of the particles. The surface diffusion model considers that the intraparticle resistance that slows the mass transfer into and out of the pores proceeds mainly through surface diffusion. In the GRM, diffusion within the mobile phase filling the pores is usually assumed to control intraparticle diffusion (pore diffusion model or PDM). This kind of model often fits the experimental data quite well, so it can be used for the calculation of the effective diffusivity. If this model fails to fit the data satisfactorily, other transport formulations such as the Homogeneous Surface Diffusion Model (HSDM) [27] or a model that allows for simultaneous pore and siuface diffusion may be more successful [28,29]. However, how accurately any transport model can reflect the actual physical events that take place within the porous... 

The same steps as discussed above for the case of isotope exchange (diffusion in liquid film, surface reaction, intraparticle diffusion) were considered in a kinetic model [771] of metal ion adsorption from solution. This model was presented in a book with diskettes (FORTRAN program, rate controlled by reaction, by transport or mixed control). 

Natural attenuation is controlled by numerous processes, which include sorption, intraparticle diffusion as weU as biological and chemical degradation. In order to be able to quantify respectively predict the fate and transport of contaminants, appropriate models that are able to deal with the complexity and interactions of the involved processes need to be developed. Due to insufficient information on the spatial distribution of transport parameters in the subsurface, stochastic methods are a preferred alternative to deterministic approaches. In the present paper a one-dimensional Lagrangian streamtube model is used to describe the reactive transport of acenaphthene as a sample organic compoimd at field scale. As the streamtube model does not consider the heterogeneity of hydrogeochemical parameters but only hydraubc heterogeneity, model results from the streamtube model are compared in a Monte Carlo approach to results of a two-dimensional Eulerian model. 

Table 4.3 lists some typical gas-liquid hydrogenation reactions investigated in order to explore the features of three-phase catalytic membrane reactors. An example of the application of three-phase catalytic membrane reactors to the hydrogenation of sunflower seed oil can be found in Veldsmk (2001), where it was shown that for this hydrogenation running under kinet-ically controlled conditions the interfacial transport resistances and intraparticle diffusion limitations did not have any effect. Unfortunately the catalyst underwent a serious deactivation process. 

Sample particle size has to be controlled. Particles that are too small can result in the creation of back pressure and consequent problems in maintaining constant flow along the sample, while too large particles can result in intraparticle diffusion problems, causing distorted peaks. Mass transport processes, both inter- and intraparticles, are characterized by low-activation energies and they can thus alter... 

There were no effects of pore dimension on the deactivation rates (due to coke formation) of fresh catalyst over the range investigated. Further studies of deactivation rates after one and two hours of utilization at 205 C also revealed no influence on pore structure. This would rule out intraparticle mass transport as controlling deactivation rates as well as the occurrence of any pore blockage resulting from coking in this reaction. 

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