Julien Léo Billeter
Identification of kinetic models is an important task for monitoring, control and optimization of industrial processes. Robust kinetic models are often based on first principles, which describe the evolution of states – number of moles, temperature and volume – by means of conservation and constitutive equations. Identification of reaction kinetics, namely, rate expressions and rate parameters, represents the main challenge in building first-principles models. Estimation of parameters is especially complex for fluid-fluid reaction systems where chemical species can transfer between phases. The identification task is commonly performed in one step via a simultaneous approach. In this approach, a dynamic model comprising all kinetic steps, whether physical or chemical, is postulated and the corresponding parameters are estimated by comparing the predicted and measured concentrations. The procedure is repeated for all combinations of model candidates and the combination with the best fit is selected. However, simultaneous identification can be computationally costly when several candidates are available and convergence problems can arise for poor initial guesses. Furthermore, this approach often leads to high parameters correlation, and any structural mismatch in the modeling of one part of the model leads to errors in all estimated parameters. In this contribution, the model identification over several steps via an incremental approach will be used. In this approach, the identification task is decomposed into sub-problems of lower complexity. Measured concentrations are first transformed to reaction rates or extents, which are fully decoupled from each other. Then, postulated rate expressions (and corresponding rate parameters) are estimated – one at a time – by comparing individually the predicted and experimental rate or extent of each kinetic step. This approach allows considerably reducing the computational effort and the convergence problems. Since each kinetic step is dealt individually, correlation between parameters of different physical and chemical kinetic steps disappears. The extent-based method of identification will be presented and the relevance of this incremental approach will be demonstrated via examples taken from homogeneous and heterogeneous chemistry.
2013
