Reversible effectiveness factor

Oxidation kinetics over platinum proceeds at a negative first order at high concentrations of CO, and reverts to a first-order dependency at very low concentrations. As the CO concentration falls towards the center of a porous catalyst, the rate of reaction increases in a reciprocal fashion, so that the effectiveness factor may be greater than one. This effectiveness factor has been discussed by Roberts and Satterfield (106), and in a paper to be published by Wei and Becker. A reversal of the conventional wisdom is sometimes warranted. When the reaction kinetics has a negative order, and when the catalyst poisons are deposited in a thin layer near the surface, the optimum distribution of active catalytic material is away from the surface to form an egg yolk catalyst. 

Some deactivation processes are reversible. Deactivation by physical adsorption occurs whenever there is a gas-phase impurity that is below its critical point. It can be reversed by eliminating the impurity from the feed stream. This form of deactivation is better modeled using a site-competition model that includes the impurities—e.g., any of Equations (10.18)-(10.21)— rather than using the effectiveness factor. Water may be included in the reaction mixture so that the water-gas shift reaction will minimize the formation of coke. Off-line decoking can be... 

Effectiveness Factors for Reversible Reactions. The vast majority of the literature dealing with catalyst effectiveness factors pre-... 

Determine the effectiveness factor for the ion exchange resin at 85 °C, assuming that the reaction is reversible even though the authors presumed the reaction to be irreversible in reporting their data. They note that at 100 °C the equilibrium for the reaction corresponds to a conversion greater than 94%. If the equilibrium constant for the reaction is expressed as the ratio of the t-butanol concentration to the isobutylene concentration and corrected for the temperature change in going from 100 °C to 85 °C, a value of 16.6 may be considered appropriate for use. 

Key study Toxicity endpoint Weeks et al. 1963 1-h LC50 of 981 ppm in dogs reduced by a factor of three to 327 ppm as an estimate of a lethality threshold. Weeks et al. (1963) provided data showing that 15-min exposure of dogs at 36 100 ppm produced only minor, reversible effects (behavioral changes and mild muscle fasciculations)... 

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... 

The pathogenesis of glucocorticoid-induced glaucoma is still unknown, but there is reduced outflow, and excessive accumulation of mucopolysaccharides may be a major factor. An association with cataract and papilledema has often been observed. The rise in intraocular pressure is variable in the pediatric study of low dose cited above there was a reversible effect in only two of 23 subjects compared with controls, but in other studies serious increases in pressure have occurred, with a risk of blindness. 

The catalyst intraparticle reaction-diffusion process of parallel, equilibrium-restrained reactions for the methanation system was studied. The non-isothermal one-dimensional and two-dimensional reaction-diffusion models for the key components have been established, and solved using an orthogonal collocation method. The simulation values of the effectiveness factors for methanation reaction Ch4 and shift reaction Co2 are fairly in agreement with the experimental values. Ch4 is large, while Co2 is very small. The shift reaction takes place as direct and reverse reaction inside the catalyst pellet because of the interaction of methanation and shift reaction. For parallel, equilibrium-restrained reactions, effectiveness factors are not able to predict the catalyst internal-surface utilization accurately. Therefore, the intraparticle distributions of the temperature, the concentrations of species and so on should be taken into account. 

The effectiveness factor fen, of the methanation reaction is large, while the effectiveness factor < co2 of the WGSR is very small and nearly equal to zero. The interaction between the methanation reaction and the WGSR leads to the existence of the direct and reverse WGSR in catalyst pellet, which is called equilibrium-restrained WGSR. 

The last two factors, which cause the molar conductivity to decrease with concentration beyond the c.m.c., normally outweigh the first factor, which has the reverse effect (see Figure 4.13). When conductance measurements are made at very high field strengths the ionic atmospheres cannot re-form quickly enough (Wien effect) and some of the bound counter-ions are set free. It is interesting to note that under these conditions the molar conductivity increases with concentration beyond the c.m.c. 

Yilmaz A, Bieler G, Spertini O, Lejeune FL, Ruegg C. Pulse treatment of human vascular endothelial cells with high doses of tumor necrosis factor and interferon-gamma results in simultaneous synergistic and reversible effects on proliferation and morphology. Int J Cancer 1998 77 592-599. 

Solution The elementary reaction steps of adsorption, reaction, and desorption are now reversible. From this point on, we will set ai = a, pi = P, and so on, since the intrinsic kinetics are desired. The relationships between ai, as, and a are addressed using an effectiveness factor in Section 10.4. The various reaction steps are... 

In reality however, situations also exist where a more complex form of the rate expression has to be applied. Among the numerous possible types of kinetic expressions two important cases will be discussed here in more detail, namely rate laws for reversible reactions and rate laws of the Langmuir-Hinshelwood type. Basically, the purpose of this is to point out additional effects concerning the dependence of the effectiveness factor upon the operating conditions which result from a more complex form of the rate expression. Moreover, without going too much into the details, it is intended at least to demonstrate to what extent the mathematical effort required for an analytical solution of the governing mass and enthalpy conservation equations is increased, and how much a clear presentation of the results is hindered whenever complex kinetic expressions are necessary. 

From this expression it can be seen that the modulus rcv transforms to the standard Thiele modulus (eq 27) when the equilibrium constant approaches infinity. Additionally, it is obvious that the effectiveness factor decreases when, at a given value of the forward rate constant k+, the reverse reaction becomes increasingly important (Fig. 18). This holds for all types of reversible reactions [31, 91]. Therefore, the effectiveness factor of a truly reversible reaction might be considerably overestimated if the reaction is treated as irreversible. 

This problem arises even at low conversion, because although the product concentration may then be negligible at the external pellet surface, in general this is not the case inside the pellet, unless diffusion effects upon the effective reaction rate are absent. Therefore, a difference normally exists between the effectiveness factor of irreversible and reversible reactions which becomes increasingly important as the equilibrium constant A cq of the reaction is shifted to smaller values. 

Figure 18. Effectiveness factor rj of a first-order reversible reaction versus the Weisz modulus ip (related to the forward rate constant k+). Influence of intraparticle diffusion on the effective reaction rate (isothermal reaction in a sphere, equal diffusivitics i,e = Die, equilibrium constant as a parameter).

In Fig. 19, calculated curves of the effectiveness factor versus the Weisz modulus are shown for different values of Kpis [91]. For comparison, this diagram also contains the curves corresponding to the results which apply to simple, irreversible power rate laws of zeroth, first and second order. From this figure it is obvious that a strong adsorption of at least one of the products leads to a similar decrease of the effectiveness factor as it is observed in the case of a reversible reaction. 

The effectiveness factor versus the Weisz modulus according to Kao and Satterfield [61] is shown in Fig. 21 for C = 0.5 and different values of B. From this diagram, a similar behavior is seen as in the case of a simple, first order, reversible reaction (see Fig. 18) with decreasing value of B, the effectiveness factor is reduced. A decline of the effectiveness factor is also observed for a rise of the parameter C, which corresponds to a shift towards the chemical equilibrium, and hence to a reduction of the net reaction rate [91]. 

The subcommittee believes that its recommended SEALs might produce health effects such as moderate irritation of respiratory tract, eyes, skin, or other moderate reversible effects, but would not produce any irreversible health effects in the submariners. The subcommittee did not incorporate an uncertainty factor for hypersusceptible individuals, including asthmatics, because as discussed above, the submariner population is healthy and asthma is a disqualifying condition for submarine duty. However, it is possible that some crew members may be hypersusceptible to the effects of the irritant gases or become mildly asth... 

Example 11-6 Derive equations for the effectiveness factor for a first-order reversible reaction A B at isothermal conditions, for a spherical catalyst pellet. 

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