Computational modeling and analysis on chemically reacting species in catalytic oxidation reaction mechanism: Novel model reduction and NSFD scheme

Abstract

Multi-step catalytic mechanisms are an important issue related to chemical kinetics to reduce, and such reduction directly affects the quality and efficiency of modeling complicated reactions. Nevertheless, the currently available literature is using the traditional fractional method that is poorly positioned to address the global non-local and fractal characteristics of catalytic systems. This paper will fill this gap by using fractal-fractional derivatives with generalized Mittag-Leffler kernels and using Nonstandard Finite Difference (NSFD) scheme to study kinetic equations. As a representative model, to study the behavior of numerical solutions, steady-state, and stability to various rate coefficients, the selection of Water-Gas Shift (WGS) reaction is made. Gibbs rule is used to reduce the higher dimensional system to a lower dimensional model by using two model reduction methods known as Spectral Quasi-Equilibrium Manifold (SQEM) and Intrinsic Low-Dimensional Manifold (ILDM). It was found that the fractal-fractional model is more representative of the memory and heterogeneity of the system whereas the NSFD model exhibits stability and positivity better than the existing approaches. Sensitivity analysis also indicates the effect of individual species to the system dynamics. The results are useful on how to effectively model the catalytic mechanism and avenue towards creating more realistic and consistent chemical simulation models.