Internal transport effects defined

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. 

The analysis we have been working with has considered the case where the areas involved are the external surfaee, a, and internal area, s, for transport and reaction, respectively. Consider now the ease [W. Goldstein and J.J. Carberry, J. Catal., 28, 33 (1973)] where the contribution of the external surface (which is also catalytic) to the overall reaction is not negligible compared to the internal surface, s. This can be quite possible when the catalyst supplied is very active and is finely divided to minimize transport effects. We would like to know what the isothermal effectiveness and the point selectivity of intermediate for Type III reaction in such a situation is. Recall that the point or differential selectivity is defined as (rate of production of y)/(rate of reaction of i). 

In almost all reactors running in the chemical industry, the desired product throughput and quality are provided by catalysts, the functional materials that allow chemical synthesis to be carried out at economic scales by increasing the reaction rates. Owing to this critical feature, more than 98% of the today s industrial chemistry is involved with catalysis. Since catalysts have direct impact on reactor performance, they have to be operated at their highest possible effectiveness, which is determined by the degree of internal and external heat and mass transport resistances defined and explained in detail in Chapter 2. At this stage, the function of the reactor is to provide... 

The concept of effectiveness developed separately for external or internal transport resistances can be extended to an overall effectiveness factor for treating the general diffusion-reaction problem where both external and internal concentration and temperature gradients exist The overall effectiveness factor, D, is defined for relating the actual global rate to the intrinsic rate, that is, -Ra)p to (-Ra)6- To stun up the definitions for y, 7], and D,... 

The main difficulty with the first mode of oxidation mentioned above is explaining how the cation vacancies that arrive at the metal/oxide interface are accommodated. This problem has already been addressed in Section 7.2. Distinct patterns of dislocations in the metal near the metal/oxide interface and dislocation climb have been invoked to support the continuous motion of the adherent metal/oxide interface in this case [B. Pieraggi, R. A. Rapp (1988)]. If experimental rate constants are moderately larger than those predicted by the Wagner theory, one may assume that internal surfaces such as dislocations (and possibly grain boundaries) in the oxide layer contribute to the cation transport. This can formally be taken into account by defining an effective diffusion coefficient Del( = (1 -/)-DL+/-DNL, where DL is the lattice diffusion coefficient, DNL is the diffusion coefficient of the internal surfaces, and / is the site fraction of cations located on these internal surfaces. 

Interpreting the small differences between the data and the predictions of the exponential tail requires caution, because some of the basic assumptions of the model are not soundly based. For example, it is assumed that the transport occurs at a well-defined mobility edge, with a temperature-independent mobility, and both points are open to question. Other effects, such as the internal electric fields of the contacts and deep trapping, lead to distortions of the current pulse from its ideal form. 

For conventional analysis by ICP or DCP, liquid samples are used, which are either easily prepared or commercially available. Interference problems are reduced to a minimum if the cahbration solutions are matched to the samples with respect to their content of acids and easily ionisable elements (see above). Calibration curves obtained with sparks, arcs, and laser ablation systems are usually curved so that 8—15 calibration samples or more are needed to define a suitable calibration. In the case of liquid analysis by DCP and ICP, fewer cahbration samples can be used due to the better linearity and dynamic range and absence of selfabsorption effects. With the introduction of hquids, the spray chamber is the major source of flicker noise due to aerosol formation and transport. While shot noise can easily be compensated by longer integration times, the flicker noise is of multiplicative nature so that any element can be used as an internal standard provided that a true simultaneous measurement of the analyte and internal standard line intensity is possible. 

Obviously, the intention of manufacturing highly porous catalyst particles is to create a large internal surface where reaction can take place. Therefore, the reaction rate per unit volume of catalyst can be very high. However, the actual conversion rates are often limited by rates of transport processes. There are at least two relevant mass transport mechanisms the external mass transfer and the internal diffusion. The rate of internal diffusion cannot be separated from the reaction rate they enhance each other. This has been treated in some detail in section 5.4.3. The combined effect of both "resistances is shown in eq. (5.51). To get an idea which of the two resitances prevails, one can define the dimensionless catalyst number Ca as the ratio between the two terms in the denominator in eq. (5.51) ... 

A further, sometimes useful, quantity was originally defined by Monchick et al. (1965) and was defined in terms of effective cross sections by Viehland et al. (1978). It represents the transport of eneigy associated with internal degrees of freedom by a diffusion mechanism. This so-called internal diffusion coefficient is defined by... 

In the preceding discussions, a Ictrge number of forces, both external and internal to the separation system, have been identified and described briefly. Note that any force so identified was, for example, specific to molecules of the ith species. However, it is known that forces specific to the jA species can also affect the motion of molecules of the ith species. For the immediate objectives in the paragraphs that follow, these effects are ignored by assuming uncoupled conditions molecules of species i in a stagnant fluid move only due to forces specific to the ith species similarly for the jth species. It is further assumed that the conditions are not too far removed from equilibrium (see the introduction to Section 3.3 and Sections 3.3.1-3.3.6 for descriptions of equilibrium conditions) therefore thermodynamic quantities (defined only for equilibrium conditions) can be used to described nonequilibrium conditions where a net transport of molecules of species i exist due to external and internal forces. For illustrative purposes, an expression for the total driving force Fp on... 

The effectiveness factor was defined as the ratio of global rate to intrinsic rate. If both rates are expressed in terms of pellet surface conditions such that the effectiveness factor represents the effects of internal (intraphase) transport resistances, it is termed the internal effectiveness factor as opposed to the external effectiveness factor, which represents the effects of transport resistances external to the pellet surface. The internal effectiveness factor for various pellet shapes will now be derived. 

Microporous inorganic solids, such as zeolites, clays, and layered oxide semiconductors offer several advantages as organizing media for molecular electron transport assemblies. Because these materials are microcrystalline, their internal pore spaces have well-defined size and shape. This property can be exploited to cause self-assembly, by virtue of size exclusion effects, ion exchange equilibria, and specific adsorption, of photosensitizers, electron donors, and electron acceptors at the solid/solution interface. 

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