The question of the applicable time regime for the steady-state approximation in the simulation of complex mechanisms

A mechanism proposed by Pilling and Noyes for ignition in carbon monoxide containing traces of water has been modeled using a complete numerical integration, and results have been compared with the steady state treatment (QSSA) of the previous authors. The numerical results were found to be in close agreement. However, the complete solution also yields the time required for the steady state to be reached, and it is shown that this is too large for the results of the QSSA to be considered applicable to this problem. This is substantiated by a further calculation in which temperature is introduced as an additional variable, and it is shown that thermal runaway is reached without any of the intermediate radicals which propagate the reaction chain ever going into a steady state. This study provides an example of the failure of QSSA to provide an adequate solution to a chemical kinetic problem for reasons which have not been previously discussed in the literature. For problems of more than a very few variables there is no practical way short of numerical integration to estimate the time regime during which the steady state applies. Practitioners of QSSA are thus advised of yet another precaution in assesing the credibility of their results.