Fitting a system of odes to experimental data

Global kinetic models for high-temperature gas-phase reactions were reviewed by Abdalla et al. [193] and Babushok and Dakdancha [194]. Empirical global kinetic schemes for the low-temperature oxidation of hydrocarbons have been recently reviewed by Griffiths [11]. Here, only some characteristic models are mentioned and for a full account the reader is referred to the review by Griffiths. 

The first empirical model for hydrocarbon ignition was created by Gray and Yang [195] in 1965. This simple model, given below, has two variables a single concentration variable x and temperature T. 

Temperature-dependent rate parameters and heat-release rates were assigned to the reactions, including different values for the two termination reactions. The concentration of the starting fuel, and therefore, the rate of initiation, was held constant. This model was found to be in close agreement with the main thermokinetic features of the experimental p — T,  

A two-step global mechanism has been derived by de Soete [198] for the description of NO and N2 generation from fuel nitrogen. Parameters of the model were fitted to concentration profiles in flames. This model is widely used in post-processor packages of commercial CFD codes, although it works poorly under fuel-rich conditions. 

The first global empirical model for moist CO combustion was created in 1956 [199]. In a more recent article, Yetter et al. [200] compared previous global models for CO oxidation and suggested a procedure for a more systematic generation of global models based on initial concentration sensitivity calculations. 

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