دانلود رایگان مقاله زمان تجزیه مقیاس در سیستم واکنش پیچیده: تحلیل نظری نمودار

Abstract

The formulation of a kinetic model for a complex reaction network typically yields reaction rates which vary over orders of magnitude. This results in time scale separation that makes the model inherently stiff. In this work, a graph-theoretic framework is developed for time scale decomposition of complex reaction networks to separate the slow and fast time scales, and to identify pseudo-species that evolve only in the slow time scale. The reaction network is represented using a directed bi-partite graph and cycles that correspond to closed walks are used to identify interactions between species participating in fast/equilibrated reactions. Subsequently, an algorithm which connects the cycles to form the pseudo-species is utilized to eliminate the fast rate terms. These pseudo-species are used to formulate reduced, non-stiff kinetic models of the reaction system. Two reaction systems are considered to show the efficacy of this framework in the context of thermochemical and biochemical processing.

4. Conclusion

A graph-theoretic framework is developed to generate non-stiff non-linear reducedmodels.Within this framework, a set of pseudospecies that evolve only in the slow time scale are generated as a linear combination of original species via a cycle identification procedure. A reduced model is formulated using these pseudospecies and algebraic constraints arising from fast/equilibrated reactions. The incorporation of complete conversion or quasiequilibrium constraints allows a reduction in the number of model parameters. The efficacy of the developed framework is illustrated through application on two chemical systems. The cracking reaction scheme of 1-butene over zeolite acids was studied and an order of magnitude reduction in the number of integration steps was observed by incorporating quasi-equilibrium constraints. Further, the trade-off between the accuracy and the computational complexity of the resulting reduced models for carbon metabolism in erythrocytes system was studied by gradually relaxing the criteria for identifying fast/equilibrated reactions. The developed graph-theoretic framework is an automatic, generic procedure that generates non-stiff reduced models of isothermal reaction systems.