Generalized effectiveness factor

The patterns shown in the figure are typical of an adiabatic reactor for exothermic reactions. The effectiveness factor generally decreases with reactor length, but more rapidly than shown in the figure. Because of the reaction equilibrium, the decrease is much more moderate in this case. The conversion and temperature usually increase rapidly near the inlet, but these increases are moderate toward the outlet, reaching plateaus as the reactant is depleted. 

Durability. Grass-like surfaces intended for heavy-duty athletic use should have a service life of at least eight years, a common warranty period provided by suppHers. Lifetime is more or less proportional to the ultraviolet (uv) exposure (sunlight) and to the amount of face ribbon available for wear, but pile density and height also have an effect. Color is a factor generally uv absorption is highest with red fabrics and least with blue. In addition, different materials respond differendy to abrasive wear. These effects caimot be measured except in simulated field use and controlled laboratory experiments, which do not necessarily redect field conditions. 

Care should also be taken in the use of recovery factors, because these can exert a significant effect. In general, recovery paths are appropriate where there is a specific mechanism to aid error recovery, that is an alarm, a supervising check, or a routine walk round inspection. 

The RfD is derived from the NOAEL (or LOAEL) for the critical toxic effect by consistent application of uncertainty factors (UFs) and a modifying factor (ME). The uncertainty factors generally consist of multiples of 10 (although values less than 10 are sometimes used), with each factor representing a specific area of uncertainty inherent in the extrapolation from the available data. The bases for application of different uncertainty factors are explained below. 

The hydrolysis of acetals and ortho esters is governed hy the stereoelectronic control factor previously discussed (see A and B on p. 427) though the effect can generally be seen only in systems where conformational mobility is limited, especially in cyclic systems. There is evidence for synplanar stereoselection in the... 

The internal effectiveness factor is a function of the generalized Thiele modulus (see for instance Krishna and Sie (1994), Trambouze et al. (1988), and Fogler (1986). For a first-order reaction ... 

Figure 3.32. Interna effectiveness factor as a function of the generalized Thiele modulus for a first order reaction.

Microlevel. The starting point in multiphase reactor selection is the determination of the best particle size (catalyst particles, bubbles, and droplets). The size of catalyst particles should be such that utilization of the catalyst is as high as possible. A measure of catalyst utilization is the effectiveness factor q (see Sections 3.4.1 and 5.4.3) that is inversely related to the Thiele modulus (Eqn. 5.4-78). Generally, the effectiveness factor for Thiele moduli less than 0.5 are sufficiently high, exceeding 0.9. For the reaction under consideration, the particles size should be so small that these limits are met. 

The material factor is then modified to allow for the effect of general and special process and material hazards the physical quantity of the material in the process step the plant layout and the toxicity of process materials. 

All of these steps are rate processes and are temperature dependent. It is important to realize that very large temperature gradients may exist between active sites and the bulk gas phase. Usually, one step is slower than the others, and it is this rate-controlling step. The effectiveness factor is the ratio of the observed rate to that which would be obtained if the whole of the internal surface of the pellet were available to the reagents at the same concentrations as they have at the external surface. Generally, the higher the effectiveness factor, the higher the rate of reaction. 

This example illustrates calculation of the rate of a surface reaction from an intrinsic-rate law of the LH type in conjunction with determination of the effectiveness factor (rj) from the generalized Thiele modulus (G) and Figure 8.11 as an approximate representation of the 7]-Q relation. We first determine G, then 17, and finally (—rA)obs. 

In the case that the chemical reaction proceeds much faster than the diffusion of educts to the surface and into the pore system a starvation with regard to the mass transport of the educt is the result, diffusion through the surface layer and the pore system then become the rate limiting steps for the catalytic conversion. They generally lead to a different result in the activity compared to the catalytic materials measured under non-diffusion-limited conditions. Before solutions for overcoming this phenomenon are presented, two more additional terms shall be introduced the Thiele modulus and the effectiveness factor. 

Vayenas, C. G. and S. Pavlou. 1987a. Optimal catalyst distribution and generalized effectiveness factors in pellets single reactions with arbitrary kinetics. Chem. Eng. Sci. 42(11) 2633-2645. 

The fifth factor is the potential for side effects. In general, the newer antidepressants have less cumbersome side effects than the older agents. Your patients should be informed of potential side effects when selecting an antidepressant. By discussing side effects in advance, your patient may help you to decide which side effects would be most distressful to him/her. For example, dizziness may be a problem for an elderly patient at risk for falls, and sexual side effects may be more concerning to others. 

The assessment factors generally apphed in the estabhshment of a tolerable intake from the NOAEL, or LOAEL, for the critical effect(s) are apphed in order to compensate for rmcertainties inherent to extrapolation of experimental animals data to a given human situation, and for rmcertainties in the toxicological database, i.e., in cases where the substance-specific knowledge required for risk assessment is not available. As a consequence of the variabihty in the extent and nature of different databases for chemical substances, the range of assessment factors apphed in the establishment of a tolerable intake has been wide (1-10,000), although a value of 100 has been used most often. An overview of different approaches in using assessment factors, historically and currently, is provided in Section 5.2. 

Here, we consider the general case of a porous catalyst, where the internal diffusion effect is included in the effectiveness factor (//,). 

Here, issues in relation to the trickle flow regime—isothermal operation and plug flow for the gas phase—will be dealt with. Also, it is assumed that the flowing liquid completely covers the outer surface particles (/w = 1 or aLS = au) so that the reaction can take place solely by the mass transfer of the reactant through the liquid-particle interface. Generally, the assumption of isothermal conditions and complete liquid coverage in trickle-bed processes is fully justified with the exception of very low liquid rates. Capillary forces normally draw the liquid into the pores of the particles. Therefore, the use of liquid-phase diffusivities is adequate in the evaluation of intraparticle mass transfer effects (effectiveness factors) (Smith, 1981). 

As mentioned earlier, if the rate of a catalytic reaction is proportional to the surface area, then a catalyst with the highest possible area is most desirable and that is generally achieved by its porous structure. However, the reactants have to diffuse into the pores within the catalyst particle, and as a result a concentration gradient appears between the pore mouth and the interior of the catalyst. Consequently, the concentration at the exterior surface of the catalyst particle does not apply to die whole surface area and the pore diffusion limits the overall rate of reaction. The effectiveness factor tjs is used to account for diffusion and reaction in porous catalysts and is defined as... 

It is possible to combine the resistances of internal and external mass transfer through an overall effectiveness factor, for isothermal particles and first-order reaction. Two approaches can be applied. The general idea is that the catalyst can be divided into two parts its exterior surface and its interior surface. Therefore, the global reaction rates used here are per unit surface area of catalyst. 

First-order reactions without internal mass transfer limitations A number of reactions carried out at high temperatures are potentially mass-transfer limited. The surface reaction is so fast that the global rate is limited by the transfer of the reactants from the bulk to the exterior surface of the catalyst. Moreover, the reactants do not have the chance to travel within catalyst particles due to the use of nonporous catalysts or veiy fast reaction on the exterior surface of catalyst pellets. Consider a first-order reaction A - B or a general reaction of the form a A - bB - products, which is of first order with respect to A. For the following analysis, a zero expansion factor and an effectiveness factor equal to 1 are considered. 

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