Effectiveness factor approach simulations

The inlet conditions for the numerical simulations are based on the experimental conditions. The simulations are performed with the three different models for internal diffusion as given in Section 2.3 to analyze the effect of internal mass transfer limitations on the system. The thickness (100 pm), mean pore diameter, tortuosity (t = 3), and porosity ( = 60%) of the washcoat are the parameters that are used in the effectiveness factor approach and the reaction-diffusion equations. The values for these parameters are derived from the characterization of the catalyst. The mean pore diameter, which is assumed to be 10 nm, hes in the mesapore range given in the ht-erature (Hayes et al., 2000 Zapf et al., 2003). CO is chosen as the rate-limiting species for the rj-approach simulations, rj-approach simulations are also performed with considering O2 as the rate-hmiting species. 

Glaoguen F, Durand R. Simulations of PEFC cathodes an effectiveness factor approach. J Appl Electrochem 1997 27 1029-35. 

Gloaguen, F. and Durand, R. 1997. Simulations of PEFC cathodes An effectiveness factor approach. J. Ami. Electrochem.. 27(9). 1029-1035. 

Effectiveness factor calculations summarized in Tables 19-1 to 19-5 are consistent with Langmuir-Hinshelwood kinetics, as discussed in this chapter. E is larger and approaches 1 asymptotically in the reaction-controlled regime where the intrapellet Damkohler number is small, and E decreases in the diffusion-controlled regime at large values of A a- These trends are verified by simulations provided in Table 19-1. 

Finally, tj-approach simulations are performed for considering O2 instead of CO as the species rate-limiting species, i.e., the effectiveness factor is... 

The SFR with catalytically coated plates is an easy setup to investigate heterogeneously catalyzed gas-phase reactions. In situ invasive capillary techniques can be used to determine the gas-phase concentration in the one-dimensional boundary layer on top of the catalyst. The measurement species profiles can be compared with numerically predicted profiles to test surface reaction mechanisms, diffusion models but also gas-phase reaction schemes, CVD processes, and others (not discussed here). However, internal difiiision inside the catalytic disc has to be taken into account when thicker catalyst layers are used. Then, the choice of an adequate diffusion model can be crucial for a correct interpretation of the measured data. The computer code DETCHEM offers simulations with the following models to account for internal diffusion in stagnation flows on porous plates with reactions inside effectiveness factor model, ID reaction diffusion model (RD-approach), and DGM (not discussed here). While the RD-approach may even play a role in simple cases as discussed here, it is the model of choice when parallel reactions occur (e.g., catalytic partial oxidation, three-way... 

Notably, rj) depends on the carbon load Lc, which changes during burn-off with time and, in the case of a resistance of pore diffusion, also with the radial position in the particle. The Thide approach as given by Eqs. (6.9.5) and (6.9.6) is then no longer exactly valid, and numerical simulations are needed. Nevertheless, the initial effectiveness factor ijpore.o may be used as a descriptive measure for the pore diffusion resistance although [Pg.640]

The previous chapters taught us how to ask questions about specific enzymatic reactions. In this chapter we will attempt to look for general trends in enzyme catalysis. In doing so we will examine various working hypotheses that attribute the catalytic power of enzymes to different factors. We will try to demonstrate that computer simulation approaches are extremely useful in such examinations, as they offer a way to dissect the total catalytic effect into its individual contributions. 

A further insight is that the best workflow depends on a combination of factors that can in many cases be expressed in closed mathematical form, allowing very rapid graphical feedback to users of what then becomes a visualization rather than a stochastic simulation tool. This particular approach is effective for simple binary comparisons of methods (e.g., use of in vitro alone vs. in silico as prefilter to in vitro). It can also be extended to evaluation of conditional sequencing for groups of compounds, using an extension of the sentinel approach [24]. 

Fig. 7.7. Effects of Poisson photon noise on calculated SE and FRET values. (A) Statistical distribution of number of incoming photons for the mean fluorescence intensities of 5,10, 20, 50, and 100 photons/pixel, respectively. For n = 100 (rightmost curve), the SD is 10 thus the relative coefficient of variation (RCV this is SD/mean) is 10 %. In this case, 95% of observations are between 80 and 120. For example, n — 10 the RCY has increased to 33%. (B) To visualize the spread in s.e. caused by the Poisson distribution of pixel intensities that averaged 100 photons for each A, D, and S (right-most curve), s.e. was calculated repeatedly using a Monte Carlo simulation approach. Realistic correction factors were used (a = 0.0023,/ = 0.59, y = 0.15, <5 = 0.0015) that determine 25% FRET efficiency. Note that spread in s.e. based on a population of pixels with RCY = 10 % amounts to RCV = 60 % for these particular settings Other curves for photon counts decreasing as in (A), the uncertainty further grows and an increasing fraction of calculated s.e. values are actually below zero. (C) Spread in Ed values for photon counts as in (A). Note that whereas the value of the mean remains the same, the spread (RCV) increases to several hundred percent. (D) Spread depends not only on photon counts but also on values of the correction...

Practical design problems may need to take into account many additional factors, including the recycle of some reactants (such as hydrogen), residence time distribution, inhomogeneity of the packing, multiple reactions, approach to equilibria, and so on. All of these problems have been encountered before, and professional simulator routines for solving them are versatile, effective and as reliable as the data provided to them. At least half a dozen such computer packages are commercially available. 

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