Model Reduction in Chemical Systems- an Alternative Method Applying Discrete Approximation

<div><div>This paper addresses model reduction in large or spatially distributed systems including diffusion of matter and chemical reactions. If diffusion is present, it would be represented by a diffusion operator (always including a spatial second derivative term). If diffusion is not present, spatial discretization is straightforward. In the latter case, applying the concept of chemical invariants, or the concept of asymptotic chemical invariants, paves the way for model reduction through elimination of the invariants. Inclusion of diffusion destroys the opportunity to obtain invariants , when numerical discretization of the diffusion term is applied. However, the paper demonstrates that application of the invariant concept may be applied even in the case of diffusion of matter in a chemical tubular reactor, if relying on an approximation in modelling of a tubular reactor by a tank-in-the series model. For nonreacting matter, the quality and numerical properties of the tanks-in-the-series model approximation of a tubular reactor is well documented in the literature. However, there is no general proof available for the quality and effectiveness of such an approximation when chemical reactions are present, although example cases show good approximation.<br></div></div><div><div><br></div></div>