Formulation of the Kinetic Model

It is important that different reaction schemes can lead to the same apparent rate expression. Thus, even if reaction kinetics data were collected without experimental errors, the reaction scheme still would not be determined by fitting the data to various rate expressions. In other words, the rate expression can be determined from the reaction scheme, but the 

A feasible reaction scheme includes all the reactants and products, and it generally includes a variety of reaction intermediates. The validity of an elementary step in a reaction sequence is often assessed by noting the number of chemical bonds broken and formed. Elementary steps that involve the transformation of more than a few chemical bonds are usually thought to be unrealistic. However, the desire to formulate reaction schemes in terms of elementary processes taking place on the catalyst surface must be balanced with the need to express the reaction scheme in terms of kinetic parameters that are accessible to experimental measurement or theoretical prediction. This compromise between molecular detail and kinetic parameter estimation plays an important role in the formulation of reaction schemes for analyses. The description of a catalytic cycle requires that the reaction scheme contain a closed sequence of elementary steps. Accordingly, the overall stoichiometric reaction from reactants to products is described by the summation of the individual stoichiometric steps multiplied by the stoichiometric number of that step, ai. 

Rate Constant Estimation 1. Transition State Theory 

Transition-state theory allows details of molecular structure to be incorporated approximately into rate constant estimation. The critical assumption of transition-state theory is that quasi-equilibrium is established between the reactants and an activated complex, which is a reactive chemical species that is in transition between reactants and products. The application of transition-state theory to the estimation of rate constants can be illustrated by the bimolecular gas-phase reaction 

The rate of the chemical reaction per unit volume, tab, is equal to the concentration of activated complex multiplied by a frequency factor equal to A- j77//, where h is Planck s constant. The thermodynamic activity of the activated complex is equal to 

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The chemisorbed molecules, whether on the external surface for non-porous pellets or the internal surface for porous catalyst pellets, undergo surface reaction producing chemisorbed product molecules. This surface reaction is the truly intrinsic reaction step. However, in chemical reaction engineering it is usual practice to consider that intrinsic kinetics include this surface reaction step coupled with the chemisorption steps. This is due to the difficulty of separating these steps experimentally and the ease by which they are combined mathematically in the formulation of the kinetic model. 

These processes can occur in parallel or subsequently, depending strongly on the process configuration. All of them would require dedicated kinetic expressions. In practice, assumptions are taken to simplify the formulation of the kinetic model (e.g., neglecting tars, inert ash, one pyrolysis gross reaction). 

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