Further Recent Approaches to the Selection of QSS-Species

The relationship between the QSSA and the calculated concentrations of the important species was handled in a different way by Lpv and co-workers (Lpvas et al. 2000, 2002a, b Lpvas 2009), who introduced the level of importance (LOl) index. This index is the product of the lifetime of a species and a local sensitivity term  

The summation refers to all the Nr reaction steps. For the calculation of lifetime not only the chemical lifetime t,- is taken into account but also the residence time in a reactor and the species rate of diffusion. The half-normalised local sensitivity coefficient 3T,/3 In A shows the effect of perturbing the A-factor of reaction step I on concentration T and Vy is the corresponding stoichiometric coefficient. The index (LOI)jy estimates the error of the calculadcHi of the concentration of species j due to the application of the QSSA on species i. 

Montgomery et al. (2006) used a genetic algorithm for the selection of QSS-species. Based on the difference between the simulation results without and with the application of the QSSA, the selection of the QSS-species was optimised until the simulation error decreased below a certain threshold. CSP analysis can also be used for the selection of QSS-species and is covered in more detail in Sects. 6.4 and 7.9. The validity of the QSSA in solution-phase bimolecular reactions was also studied in Tzafriri and Edelman (2005). 

Vora and Daoutidis (2001) developed a nonlinear model reduction method for non-isothermal reaction systems that exhibit dynamics on two different timescales. The method identifies the independent algebraic constraints (possibly of QSSA origin) that define the low-dimensional state space where the slow dynamics of the reaction system are constrained to evolve. 

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