Total effectiveness factor

The need for an average total effectiveness factor results from the variation of the total effectiveness factor with substrate concentration. 

In either case, the overall reaction rate comprises both mass transfer and bioreaction kinetics, where the former is usually the rate-limiting step. It is possible to define a total effectiveness factor, rjx, which accounts for the effects of mass transfer on the reaction rate as... 

When external or internal mass transfer resistances are negligible, ijg= 1 or i]i= 1, respectively. If intrinsic kinetic parameters (determined while using free enzymes or cells, with no mass transfer limitations) are known, the total effectiveness factor can thus be used together with the reactor design equations as... 

Figure 4.12b shows the variation of the total effectiveness factor of the CCL with current density for the polarization curves in Figure 4.12a. Fstat and F p are functions of composition and microstructure of the CCL neglecting degradation effects, these parameters should remain constant. However, the agglomerate effectiveness factor decreases with current density. The dependence of the effectiveness factor on current density is stronger at low and high current densities, jo < 0.4 A cm and jo > I A cm . Effectiveness factor values are similar over a wide range of jo for the studies of Suzuki et al. (2011) and Soboleva et al. (2011). However, the higher propensity for flooding of the GDL results in a sharper drop of the effectiveness factor at jo > I A cm in Suzuki et al. (2011).

Intraparticle mass transport resistance can lead to disguises in selectivity. If a series reaction A — B — C takes place in a porous catalyst particle with a small effectiveness factor, the observed conversion to the intermediate B is less than what would be observed in the absence of a significant mass transport influence. This happens because as the resistance to transport of B in the pores increases, B is more likely to be converted to C rather than to be transported from the catalyst interior to the external surface. This result has important consequences in processes such as selective oxidations, in which the desired product is an intermediate and not the total oxidation product CO2. 

The ortho effect may consist of several components. The normal electronic effect may receive contributions from inductive and resonance factors, just as with tneta and para substituents. There may also be a proximity or field electronic effect that operates directly between the substituent and the reaction site. In addition there may exist a true steric effect, as a result of the space-filling nature of the substituent (itself ultimately an electronic effect). Finally it is possible that non-covalent interactions, such as hydrogen bonding or charge transfer, may take place. The role of the solvent in both the initial state and the transition state may be different in the presence of ortho substitution. Many attempts have been made to separate these several effects. For example. Farthing and Nam defined an ortho substituent constant in the usual way by = log (K/K ) for the ionization of benzoic acids, postulating that includes both electronic and steric components. They assumed that the electronic portion of the ortho effect is identical to the para effect, writing CTe = o-p, and that the steric component is equal to the difference between the total effect and the electronic effect, or cts = cr — cte- They then used a multiple LFER to correlate data for orrAo-substituted reactants. 

A new or calculated point of performance is not defined until all three factors have been determined. It is not sufficient to determine one point and draw conclusions, but rather the total effect of the change must be considered. 

In this exercise we shall estimate the influence of transport limitations when testing an ammonia catalyst such as that described in Exercise 5.1 by estimating the effectiveness factor e. We are aware that the radius of the catalyst particles is essential so the fused and reduced catalyst is crushed into small particles. A fraction with a narrow distribution of = 0.2 mm is used for the experiment. We shall assume that the particles are ideally spherical. The effective diffusion constant is not easily accessible but we assume that it is approximately a factor of 100 lower than the free diffusion, which is in the proximity of 0.4 cm s . A test is then made with a stoichiometric mixture of N2/H2 at 4 bar under the assumption that the process is far from equilibrium and first order in nitrogen. The reaction is planned to run at 600 K, and from fundamental studies on a single crystal the TOP is roughly 0.05 per iron atom in the surface. From Exercise 5.1 we utilize that 1 g of reduced catalyst has a volume of 0.2 cm g , that the pore volume constitutes 0.1 cm g and that the total surface area, which we will assume is the pore area, is 29 m g , and that of this is the 18 m g- is the pure iron Fe(lOO) surface. Note that there is some dispute as to which are the active sites on iron (a dispute that we disregard here). 

The value calculated above is at variance with the value listed in Table 3 of reference 63, because the individuals cited used jS = 0.27 based on a calculation in which the total gas phase concentration was used. Consequently, they predicted an effectiveness factor of 20. 

Up to now, in the formulation of a bolometer model, only the heat capacity of itinerant carriers was considered [57], However, our measurements show that, even at 24 mK, the presence of a spurious heat capacity in the thermometer increases the expected value of the pulse rise time. We expect that the spurious contribution in Fig. 12.17 increases down to the temperature of the Schottky peak at T = k.E/khT about 10 mK. Since gc decreases at low temperatures, the total effect on pulse rise time and pulse amplitude can be dramatic at lowest temperatures. In reality, the measured rise time of CUORICINO pulses is about three times longer than that obtained from a model which neglects the spurious heat capacity of the thermistor. For the same reason, also the pulse amplitude is by a factor two smaller than the expected value (see Section 15.3.2). 

Several studies with rats support the AEGL-3 values. A 10-min exposure to aniline at 15,302 ppm resulted in no toxic effects, and a 4-h exposure at 359 ppm resulted in severe toxic effects but no deaths. Dividing these values by a total uncertainty factor of 100 and scaling across time using C%t=k results in values similar to those derived from the Kim and Carlson (1986) study. Studies with repeated exposures of rats resulted in additional effects on the blood and spleen, but concentrations up to 87 ppm, 6 h/d, 5 d/w for 2 w were not disabling or life-threatening. 

Data Adequacy The key study was well designed, conducted, and documented. Values were presented graphically. Supporting data were sparse, probably because aniline is not a vapor at room temperature, and poisonings have involved contact with the liquid. Although human data are sparse, it is believed that a total uncertainty factor of 100 is protective of human health. Because aniline is absorbed through the skin, which increases the systemic toxicity, direct skin contact with the liquid would be additive and result in onset of adverse effects at airborne concentrations below the respective AEGL values. Therefore, direct skin contact with the liquid should be avoided. 

Uncertainty Factors/Rationale Total uncertainty factor 30 Interspecies 10—The 10-min LC50 value for the monkey was about 60% of the rat value and one-third the rabbit value. The mouse data were used to calculate the AEGL levels, because the data exhibited a good exposure-response relationship and the endpoint of decreased hematocrit levels can be considered a sensitive indicator of arsine toxicity. In addition, arsine has an extremely steep dose-response relationship, allowing little margin in exposure between no effects and lethality. 

The amount of heat actually taken up by the particles was an important quantity, as tubes operate under heat transfer limited conditions near the tube inlet. Fig. 30 shows a plot of Q against r, where Q was the total energy flow into the solid particles, for the entire segment. For inlet conditions, Q varied strongly at lower r, but was almost constant at higher values. As rcut/rp decreased from 0.95 to 0.0 and the effectiveness factor increased from nearly zero to one, the active solid volume increased by a factor of 7. If the solid temperature had remained the same, the heat sink would also have had to increase sevenfold. This could not be sustained by the heat transfer rate to the particles, so the particle temperature had to decrease. This reduced the heat sink and increased the driving force for heat transfer until a balance was found, which is represented by the curve for the inlet in Fig. 30. 

For the derivation of the PNEC several approaches have been proposed. Generally these can be categorised into three distinct assessments a conservative, a distributional, and a mixture toxicity approach. In conservative approaches, usually the most (realistic) sensitive endpoint such as LC50 or the known no observed effect concentration (NOEC) is taken and divided by an uncertainty factor (10-100). The selected uncertainty factor value depends on the type of endpoint and the number of available data, and is applied to account for laboratory to field extrapolations, species differences in sensitivities, and similar uncertainties. In distributional approaches, a series of, or all available, literature data are taken and a selected cut-off value is applied to the distribution of these data. The cut-off value may be, e.g., the concentration value that will protect 95% of the species (tested). In general, again an uncertainty factor (usually of 10) is then applied to take into account species differences. In the mixture toxicity approach, a similar mode of action is assumed for the assessment of the combined (additive) effect of the mixture. All relevant mixture components are scaled relative to the most potent one. This results in relative potencies for each component. The total effect of the mixture is then evaluated by... 

Intermediate-duration oral studies in humans for mirex are lacking. A review of the animal oral intermediate toxicity data for mirex indicates that the available studies are not adequate to derive intermediate oral MRL for mirex. The most suitable study provides a LOAEL of 0.25 mg/kg/day for endocrine effects-dilation of rough endoplasmic reticulum cisternae of the thyroid of weanling Sprague-Dawley rats (Singh et al. 1985). Adjusting the LOAEL of 0.25 mg/kg/day determined from this study with a total uncertainty factor of 1,000 (10 for use of a LOAEL, 10 for animal to human extrapolation, and 10 for interspecies variability) yields an intermediate oral MRL of 0.0003 mg/kg/day, which is lower than the chronic-duration oral MRL of 0.0008 mg/kg/day derived from an NTP (1990) study in rats (see chronic-duration MRL). Therefore, no oral intermediateduration MRL was developed for mirex. 

McLaughlin (23) stated that Cherelle wilt may be caused in Costa Rica by the fungus P. palmivora and an insect membracid. He admits, however, that it is not possible to separate the total effect of these two factors from physiological wilt, which also must be considered. 

In treating the simultaneous burning of both fast and slow coke, it is convenient for computation purposes to reformulate the slow-coke kinetics in terms of a new effectiveness factor t)t. The total rate of slow coke burning dyjdt)j of Eq. (12) is set equal to r)j(dyjdt)i ... 

In analogy to the definition of the total charge density, we define the total structure factor Ftotal(H), which includes both the nuclei and the electrons, and is, excluding thermal effects, given by... 

A further result of this analysis, as shown in Fig. 4, is that while the relative spectral intensities are determined by the individual site f-factors, the temperature dependence of all the sub-spectra together in the temperature range studied is determined by the motion of the center of mass of the whole Auj, cluster. This can be seen by the uniform decrease of the total intensity with increasing temperature, without any visible change in the general shape of the spectrum. In effect, this means that the f-factors for the individual sites must be multiplied by an f-factor due to the motion of the whole particle [24]. See also Refs. [95,96,97], where this concept was originally developed. The use of such an inter-cluster f-factor, in addition to the usual intra-cluster f-factor, also resolved the problem of the apparent deficiency in the total f-factor at 1.25 K when compared to bulk gold. 

Of course, more than two factors can be involved in an interaction. The number of factors involved in an interaction is called the order of the interaction. Interactions are always a source of information for the experimenter. If an unexpected interaction exists, the total effect is not the simple sum of the effects of the factors but an interaction term is included. For instance, for two factors we can establish the following equation ... 

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