Transport effects internal

Because of their tunable properties, supercritical solvents provide a useful medium for enzyme-catalyzed reactions.f The mechanism of enzyme-catalyzed reactions is similar to the mechanism described for solid-catalyzed reactions. External as well as internal transport effects may limit the reaction rate. Utilizing supercritical fluids enhances external transport rate due to increase in the diffusivity and therefore mass transfer coefficient. Internal transport rate depends on the fluid medium as well as the morphology of the enzyme. Supercritical fluids can alter both. 

Another characteristic of the fluidized bed is the small size and density of catalyst particles necessary to maintain proper fluidization. The particles provide a much larger external surface per unit mass of catalyst than those, in a fixed-bed unit. This results in a higher rate of reaction (per unit mass) for a nonporous catalyst. Also, internal transport effects are negligible. 

Tlie reaction is first order with respect to hydrogen peroxide and the effectiveness factor is found to be equal to 0.24. This effectiveness factor accounts only for internal transport effects. Due to the dilute feed of hydrogen peroxide, the operation can be considered isothermal. 

Baddour [26] retained the above model equations after checking for the influence of heat and mass transfer effects. The maximum temperature difference between gas and catalyst was computed to be 2.3°C at the top of the reactor, where the rate is a maximum. The difference at the outlet is 0.4°C. This confirms previous calculations by Kjaer [120]. The inclusion of axial dispersion, which will be discussed in a later section, altered the steady-state temperature profile by less than O.S°C. Internal transport effects would only have to be accounted for with particles having a diameter larger than 6 mm, which are used in some high-capacity modern converters to keep the pressure drop low. Dyson and Simon [121] have published expressions for the effectiveness factor as a function of the pressure, temperature and conversion, using Nielsen s experimental data for the true rate of reaction [119]. At 300 atm and 480°C the effectiveness factor would be 0.44 at a conversion of 10 percent and 0.80 at a conversion of 50 percent. 

Transport Criteria in PBRs In laboratory catalytic reactors, basic problems are related to scaling down in order to eliminate all diffusional gradients so that the reactor performance reflects chemical phenomena only [24, 25]. Evaluation of catalyst performance, kinetic modeling, and hence reactor scale-up depend on data that show the steady-state chemical activity and selectivity correctly. The criteria to be satisfied for achieving this goal are defined both at the reactor scale (macroscale) and at the catalyst particle scale (microscale). External and internal transport effects existing around and within catalyst particles distort intrinsic chemical data, and catalyst evaluation based on such data can mislead the decision to be made on an industrial catalyst or generate irrelevant data and felse rate equations in a kinetic study. The elimination of microscale transport effects from experiments on intrinsic kinetics is discussed in detail in Sections 2.3 and 2.4 of this chapter. 

Weisz-Prater criterion for internal transport effects... 

The effectiveness factor can be used to account for internal transport effects in the sizing and analysis of heterogeneous catalytic reactors. At this point, it is no longer necessary to assume that internal concentration gradients are negligible. 

The problem of evaluating the influence of pore diffusion on an experimental result can be simplified through some transformations of the previous equations. Suppose that a reaction rate has been measured in some kind of experimental reactor, preferably an ideal CSTR or a differential PFR. From the experimental data, a rate of reaction per unit of geometrical catalyst volume, designated —Ra,y, can be calculated. The v in the subscript indicates that this is a volumetric raLtc of reaction. The measured rate (—Ra.v) is not necessarily the same as the intrinsic rate, expressed on a volumetric basis (—rA,v)-The measured rate may reflect internal transport effects, whereas the intrinsic rate does not. 

It is also possible to use an internal standard to correct for sample transport effects, instrumental drift and short-term noise, if a simultaneous multi-element detector is used. Simultaneous detection is necessary because the analyte and internal standard signals must be in-phase for effective correction. If a sequential instrument is used there will be a time lag between acquisition of the analyte signal and the internal standard signal, during which time short-term fluctuations in the signals will render the correction inaccurate, and could even lead to a degradation in precision. The element used as the internal standard should have similar chemical behaviour as the analyte of interest and the emission line should have similar excitation energy and should be the same species, i.e. ion or atom line, as the analyte emission line. 

The mass transfer effects cause, in general, a decrease of the measured reaction rate. The heat transfer effects may lead in the case of endothermic reactions also to a decrease of the equilibrium value and the resulting negative effect may be more pronounced. With exothermic reactions, an insufficient heat removal causes an increase of the reaction rate. In such a case, if both the heat and mass transfer effects are operating, they can either compensate each other or one of them prevails. In the case of internal transfer, mass transport effects are usually more important than heat transport, but in the case of external transfer the opposite prevails. Heat transport effects frequently play a more important role, especially in catalytic reactions of gases. The influence of heat and mass transfer effects should be evaluated before the determination of kinetics. These effects should preferably be completely eliminated. 

The intraparticle transport effects, both isothermal and nonisothermal, have been analyzed for a multitude of kinetic rate equations and particle geometries. It has been shown that the concentration gradients within the porous particle are usually much more serious than the temperature gradients. Hudgins [17] points out that intraparticle heat effects may not always be negligible in hydrogen-rich reaction systems. The classical experimental test to check for internal resistances in a porous particle is to measure the dependence of the reaction rate on the particle size. Intraparticle effects are absent if no dependence exists. In most cases a porous particle can be considered isothermal, but the absence of internal concentration gradients has to be proven experimentally or by calculation (Chapter 6). 

Table IX is a collection of new data on mass effects of mobilities in salts. (See Reference 29 for earlier data.) In Table IX it can be seen that for the series of the chlorides and the nitrates of the alkali metals the internal mass effect /x+ decreases with increasing mass of the cation. This kind of behavior has been observed in many earlier examples and is qualitatively consistent with almost any model of ion transport including even the ionic gas model mentioned earlier in this article.

The external mass effects deal with mobilities with respect to the container of the salt. They are related to the internal mass effects by external transport numbers... 

Determination of exposure and toxic effects of chemicals also requires knowledge of toxicokinetics. Toxicokinetics is the study of changes in the levels of toxic chemicals and their metabolites over time in various fluids, tissues, and excreta of the body, and determines mathematical relationships to explain these processes. These processes depend upon uptake rates and doses, metabolism, excretion, internal transport, and tissue distribution. Methods for determining these processes include studies with laboratory animals, volunteer human subjects, persons accidentally exposed to high doses of chemicals, and experiments with tissue or organs cultured in the laboratory. Computer simulations of such processes are often formulated using complex mathematical equations. 

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