Sensitivity of intrinsic low-dimensional manifolds with respect to kinetic data

Abstract

In this paper, a mathematical model is introduced for the calculation of sensitivities of Intrinsic Low-Dimensional Manifolds (ILDMs) with respect to kinetic data. This model allows treatment of questions that have not yet been discussed in sufficient detail in the context of ILDM: Which reactions are governing the ILDM, are they the same reactions that govern the detailed mechanism, and how does the ILDM change due to changes in the kinetic data in the underlying detailed mechanism? Based on the governing equation for the ILDMs, sensitivity equations are derived by partial differentiation with respect to kinetic parameters. Special numeric techniques are applied to allow a scaling-invariant calculation of the underlying Jacobian matrices. Some sample calculations are introduced for the stoichiometric CO/H 2/O 2/N 2-system to validate the approach. The examples shown in the paper also give some first impressions of the values of the sensitivities for some important reactions and they show the sensitive reactions within the sample system. In this context of results, the sensitivity of an ILDM is compared to the sensitivity of a Perfectly Stirred Reactor (PSR).