Complex kinetic models, rigorous analysis

RIGOROUS ANALYSIS OF COMPLEX KINETIC MODELS NON-LINEAR REACTION MECHANISMS... 

Nowadays, improved computing facilities and, more importantly, the availability of the Chemkin package (Kee and Rupley, 1990) and similar kinetic compilers and processors have made these complex kinetic schemes more user-friendly and allows the study of process alternatives as well as the design and optimization of pyrolysis coils and furnaces. In spite of their rigorous, theoretical approach, these kinetic models of pyrolysis have always been designed and used for practical applications, such as process simulation, feedstock evaluations, process alternative analysis, reactor design and optimization, process control and so on. Despite criticisms raised recently by Miller et al. (2005), these detailed chemical kinetic models constitute an excellent tool for the analysis and understanding of the chemistry of such systems. 

The parameter a in Equation (11.6) is positive for electrophobic reactions (5r/5O>0, A>1) and negative for electrophilic ones (3r/0Oelectrochemical promotion behaviour is frequently encountered, leading to volcano-type or inverted volcano-type behaviour. However, even then equation (11.6) is satisfied over relatively wide (0.2-0.3 eV) AO regions, so we limit the present analysis to this type of promotional kinetics. It should be remembered thatEq. (11.6), originally found as an experimental observation, can be rationalized by rigorous mathematical models which account explicitly for the electrostatic dipole interactions between the adsorbates and the backspillover-formed effective double layer, as discussed in Chapter 6. 

The model proposed by Short et al. (1998) has been rigorously tested by site-directed mutagenesis and kinetic analysis of the mutant enzymes. It has been shown to be consistent with all of the results from these studies and therefore it may indeed represent the physiological complex formed between flavocytochrome 4 2 cytochrome c. 

Chapter 3 dealt with the problem of the reaction kinetics for different gas-solid reactions, while chapter 5 dealt with the mass and heat transfer problems for porous as well as non-porous catalyst pellets. In chapter 5 different degrees of complexities and rigor were used. In chapter 5, the analysis started with the simplest case of non-porous catalyst pellets where the only mass and heat transfer Coefficients are those at the external surface which depend mainly on the flow conditions around the catalyst pellet and the properties of the reaction mixture. It was shown clearly that j-factor correlations are adequate for the estimation of the external mass and heat transfer coefficients (k, h) associated with these resistances. For the porous catalyst pellets different models with different degrees of rigor have been used, starting from the simplest case of Fickian diffusion with constant diffusivity, to the rigorous dusty gas model based on the Stefan-Maxwell equations for multicomp>onent diffusion. 

Rigorous procedures for the design and analysis of fixed-bed reactors based on heterogeneous models have been treated in Chapter 9. While such procedures can be used to solve the design and analysis problem in principle, the time and effort involved is often too costly. This is particularly so when the kinetics are too complex to yield an analytical expression for the effectiveness factor. The stability of the numerical scheme may also pose a problem. This chapter describes the use of reactor point effectiveness as an alternative to the rigorous design procedures of Chapter 9. For a fixed-bed reactor, the reactor conservation equations are ... 

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