Transport restrictions

The ortho- and meto-isomers are bulkier than the para-iaomer and diffuse less readily in the zeolite pores. The transport restriction favours their conversion into the /lara-isomer, which is fonned in excess of the equilibrium concentration. Because the selectivity is transport influenced, it is dependent on the path length for transport, which is the length of the zeolite crystallites. 

A different kind of shape selectivity is restricted transition state shape selectivity. It is related not to transport restrictions but instead to size restrictions of the catalyst pores, which hinder the fonnation of transition states that are too large to fit thus reactions proceeding tiirough smaller transition states are favoured. The catalytic activities for the cracking of hexanes to give smaller hydrocarbons, measured as first-order rate constants at 811 K and atmospheric pressure, were found to be the following for the reactions catalysed by crystallites of HZSM-5 14 n-... 

Mass transport selectivity is Ulustrated by a process for disproportionation of toluene catalyzed by HZSM-5 (86). The desired product is -xylene the other isomers are less valuable. The ortho and meta isomers are bulkier than the para isomer and diffuse less readily in the zeoHte pores. This transport restriction favors their conversion to the desired product in the catalyst pores the desired para isomer is formed in excess of the equUibrium concentration. Xylene isomerization is another reaction catalyzed by HZSM-5, and the catalyst is preferred because of restricted transition state selectivity (86). An undesired side reaction, the xylene disproportionation to give toluene and trimethylbenzenes, is suppressed because it is bimolecular and the bulky transition state caimot readily form. 

There is good reason to believe that the potential of NMR studies of carbenium ions on solid metal halitks exceeds that of corresponding studies in superacid solutions. Of course the advantages of working in solids include Ae possibility of very low temperatures and the mass transport restrictions of frozen media. Thus, Mehre and Yannoni were able to characterize the sec-butyl cation in frozen SbF5 by NMR [20] and Schleyer and coworkers have obtained infrared evidence of the allyl cation in the same medium [21]. So far, we have been successful in every case in which we have tried to duplicate known solution carbenium ion chemistry on... 

In a study by Krishnamoorthy et al.,4s indigenous or added water led to marked increases in CO conversion for 12.7 wt% Co/Si02. The authors suggest that the water effects do not arise from new pathways introduced by water, by scavenging effects of H20 on the concentration of site-blocking unreactive intermediates, or by removing significant CO transport restrictions. As a result, they were left with only the possibility that water influences the relative concentration of the active and inactive forms of carbon, present at low concentrations on Co surfaces. The mechanism by which such effects occur was unclear. 

The catalyst activity depends not only on the chemical composition but also on the diffusion properties of the catalyst material and on the size and shape of the catalyst pellets because transport limitations through the gas boundary layer around the pellets and through the porous material reduce the overall reaction rate. The influence of gas film restrictions, which depends on the pellet size and gas velocity, is usually low in sulphuric acid converters. The effective diffusivity in the catalyst depends on the porosity, the pore size distribution, and the tortuosity of the pore system. It may be improved in the design of the carrier by e.g. increasing the porosity or the pore size, but usually such improvements will also lead to a reduction of mechanical strength. The effect of transport restrictions is normally expressed as an effectiveness factor q defined as the ratio between observed reaction rate for a catalyst pellet and the intrinsic reaction rate, i.e. the hypothetical reaction rate if bulk or surface conditions (temperature, pressure, concentrations) prevailed throughout the pellet [11], For particles with the same intrinsic reaction rate and the same pore system, the surface effectiveness factor only depends on an equivalent particle diameter given by... 

The activity calculated from (7) comprises both film and pore diffusion resistance, but also the positive effect of increased temperature of the catalyst particle due to the exothermic reaction. From the observed reaction rates and mass- and heat transfer coefficients, it is found that the effect of external transport restrictions on the reaction rate is less than 5% in both laboratory and industrial plants. Thus, Table 2 shows that smaller catalyst particles are more active due to less diffusion restriction in the porous particle. For the dilute S02 gas, this effect can be analyzed by an approximate model assuming 1st order reversible and isothermal reaction. In this case, the surface effectiveness factor is calculated from... 

For a more detailed analysis of measured transport restrictions and reaction kinetics, a more complex reactor simulation tool developed at Haldor Topsoe was used. The model used for sulphuric acid catalyst assumes plug flow and integrates differential mass and heat balances through the reactor length [16], The bulk effectiveness factor for the catalyst pellets is determined by solution of differential equations for catalytic reaction coupled with mass and heat transport through the porous catalyst pellet and with a film model for external transport restrictions. The model was used both for optimization of particle size and development of intrinsic rate expressions. Even more complex models including radial profiles or dynamic terms may also be used when appropriate. 

Rules and Regulations for Transportation of Military Rxplosives and Hazardous Munitions by Ship , US Coast Guard, 400 7th St, NW, Washington, DC 20591 D) Tariff 6-D, "Official Air Transport Restricted Articles Tariff , published by C.C. Squire, Airline Tariff Publishers, Inc, Agent, 1825 "K ... 

Usually, there is no significant impediment to the transport of electrons, through this may not be true of some semiconductor electrodes [2—7], When there is more than one reactant, it is usually possible to adjust bulk concentrations (or adopt other experimental strategies such as buffering) so that all reactants except one are in such excess that their transport poses no difficulty. This is an analog of the isolation technique familiar to kineticists. The same is true of product species it is generally possible to arrange experimental conditions so that, at most, only one product species is subject to a transport restriction. 

Kinetic Experiments. The hydrogenation of alkene was followed by measuring the pressure as a function of time in a constant volume apparatus. The reactor was a 250 ml flask surrounded by a jacket through which thermostated water was pumped. The flask was connected to a vacuum pump, a pressure transducer, a Hg-manometer, a N2-source, and a H2 -source via a condenser. Limitation of the reaction rate because of transport restrictions from the gas phase to the liquid phase was avoided by magnetic stirring. Immediately above the reaction flask a small glass... 

The transfer of reactants from the bulk solution to the electrode interface and in the reverse direction is an ordinary feature of all electrode reactions. As the oxidation-reduction reactions advance, the accessibility of the reactant species at the electrode/electrolyte interface changes. This is because of the concentration polarization effect, that is, r c, which arises due to the limited mass transport capabilities of the reactant species toward and from the electrode surface, to substitute the reacted material to sustain the reaction [6,8,10,66,124], This overpotential is usually established by the velocity of reactants flowing toward the electrolyte through the electrodes and the velocity of products flowing away from the electrolyte. The concentration overpotential, r c, due to mass transport restrictions, can be expressed as... 

The transportation restrictions prohibiting the movement of toxic chemical munitions together with establishing that most maintenance and surveillance requirements are typically the same at storage installations, resulted in developing a standard modular facility design which could be sited at more than one installation. 

A given pollutant may penetrate in soil down to a specific depth, and therefore transport calculations need individual depth data. Owing to mass transport restrictions, residence times of many pollutants in soils are (unfortunately) much longer than those in the gas or liquid phases. In addition, partitioning effects in soils can be dramatic a case in point is the concentration effect that occurs with uranium, which sometimes reaches levels up to 104 times higher than its concentration in water with which the soil is in equilibrium. Biota plays a key role in the transport and mobilization of pollutants from soil, because for example, many of them bioaccumulate in vegetation and cattle (see Section 9.2). 

For the particle sizes used in industrial reactors (> 1.5 mm), intraparticle transport of the reactants and ammonia to and from the active inner catalyst surface may be slower than the intrinsic reaction rate and therefore cannot be neglected. The overall reaction can in this way be considerably limited by ammonia diffusion through the pores within the catalysts [211]. The ratio of the actual reaction rate to the intrinsic reaction rate (absence of mass transport restriction) has been termed as pore effectiveness factor E. This is often used as a correction factor for the rate equation constants in the engineering design of ammonia converters. 

To make allowance for mass transport restrictions, the equation can be modified by including a term containing the diffusion coefficient of CO. For operating pressures between 10 and 50 bar, when the reaction rate is controlled by bulk diffusion, Equation (83) can be applied ... 

Recently, we have shown that non-Flory distributions cannot arise from the higher solubility of larger olefins because thermodynamic equilibrium between the two phases requires that the fugacity, chemical potential, and kinetic driving force for each component be the same in the two phases (4,5,14,40,41,44). Transport restrictions, however, can lead to higher intrapellet concentrations and residence times of a-olefins, a feature of FT chemistry that accounts for the non-Flory distribution of reaction products and for the increasing paraffin content of larger hydrocarbons (4,5,14,40,... 

In the previous section, we described a hydrocarbon synthesis selectivity model that neglects CO and H2 concentration gradients within catalyst pellets. Under such conditions, H2 and CO concentrations decrease along the reactor but remain uniform across pellet dimensions. For larger or more reactive pellets, the Thiele moduli for CO and H2 consumption increase, causing diffiisional limitations and CO and H2 concentrations that also vary with position within catalyst pellets concentration gradients affect the local (H2/CO) ratios and cause marked changes in selectivity. In this section, we describe a kinetic-transport model that accounts for hydrocarbon rate and selectivity as a function of transport restrictions and of CO and H2 concentrations in intrapellet and interpellet voids. 

Intrapellet transport restrictions can limit the rate of removal of products, lead to concentration gradients within pellets, and prevent equilibrium between the intrapellet liquid and the interpellet gas phase. Transport restrictions increase the intrapellet fugacity of hydrocarbon products and provide a greater chemical potential driving force for secondary reactions. The rate of secondary reactions cannot be enhanced by a liquid phase that merely increases the solubility and the local concentration of a reacting molecule. Olefin fugacities are identical in any phases present in thermodynamic equilibrium thus, a liquid phase can only increase the rate of a secondary reaction if it imposes a transport restriction on the removal of reacting species involved in such a reaction (4,5,44). Intrapellet transport rates and residence times depend on molecular size, just as convective transport and bed residence time depend on space velocity. As a result, bed residence time and molecular size affect chain termination probability and paraffin content in a similar manner. 

Higher intrapellet residence times increase the contribution of chain initiation by a-olefins to chain growth pathways. This intrapellet delay, caused by the slow diffusion of large hydrocarbons, leads to non-Flory carbon number distributions and to increasingly paraffinic long hydrocarbon chains during FT synthesis. But intrapellet residence time also depends on the effective diameter and on the physical structure (porosity and tortuosity) of the support pellets. The severity of transport restrictions and the probability that a-olefins initiate a surface chain as they diffuse out of a pellet also de-... 

The lower CO2 selectivity observed on small pellets (Table V) apparently reflects the transport-limited removal of water, a product of the FT synthesis. CO2 selectivity also increases with increasing site density, CO conversion, and water concentration in the catalyst bed this suggests that CO2 forms in secondary water-gas shift reactions that become significant as intrapellet water fugacities rise because of transport restrictions. Transport rates of CO and H2O in hydrocarbon liquids are qualitatively similar and the reaction stoichiometry requires that one water molecule must be removed... 

The initial increase in C5+ selectivity as x increases arises from diffusion-enhanced readsorption of a-olefins. At higher values of CO transport restrictions lead to a decrease in C5+ selectivity. Because CO diffuses much faster than C3+ a-olefins through liquid hydrocarbons, the onset of reactant transport limitations occurs at larger and more reactive pellets (higher Ro, 0m) than for a-olefin readsorption reactions. CO transport limitations lead to low local CO concentrations and to high H2/CO ratios at catalytic sites. These conditions favor an increase in the chain termination probability (jSr, /Sh) and in the rate of secondary hydrogenation of a-olefins (j8s) and lead to lighter and more paraffinic products. 

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