Global rate expressions, validation

Evaluate the validity of the global rate expression for thermal NO formation... 

Validation of the Global Rates Expressions. In order to validate the global rate expressions employed in the model, temperature and concentration profiles determined by probing the flames on a flat flame burner were studied. Attention was concentrated on Flames B and C. The experimental profiles were smoothed, and the stable species net reaction rates were determined using the laminar flat-flame equation described in detail by Fristrom and Westenberg (3) and summarized in Reference (8). 

First-order reactions with internal mass-transfer limitations Since the following equation is valid, under the assumption made earlier, we only have to replace the right form of the global rate as expressed in eq. (5.196) ... 

Such global reaction expressions can be found for oxidation of a range of hydrocarbon fuels [107], They may be useful for engineering considerations but should be used very cautiously. Global reaction rates are only valid in a narrow range of conditions and cannot be extrapolated with any confidence. 

The reason many global reactions between stable reactants and products have complex mechanisms is that these unstable intermediates have to be produced in order for the reaction to proceed at reasonable rates. Often simplifying assumptions lead to closed-form kinetic rate expressions even for very complex global reactions, but care must be taken when using these since the simplifying assumptions are valid over limited ranges of compositions, temperature, and pressure. These assumptions can fail completely—in that case the full elementary reaction network has to be considered, and no closed-form kinetics can be derived to represent the complex system as a global reaction. 

Equation (11-86) shows that the external effect on the rate can always be treated as a separate, additive resistance. Hence from here on we shall focus on internal effects, using Eq. (11-85) for the global rate and taking bulk and surface concentrations to be equal. The internal problem can be expressed analytically if we are satisfied with examining the extreme case of large intrapellet resistance characterized by > 5 ( 7 < 0.2) where Eq. (11-54) is valid. Then Eq. (11-85) becomes... 

It must be noted that the expression for chemical reaction rates, Eq. (10), is valid strictly for elementary reactions. If a global kinetics scheme is used, the exponents for molar concentrations may differ from their stoichiometric coefficients in order to match experimental data. 

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