Reduced order dynamical modelling of reaction systems: A singular perturbation approach

The authors address the problem of the reduction of order of natural mass-balance models which commonly describe the dynamics of reaction systems. This reduction is subordinated to the presence of slow and fast reactions. it is shown that, in natural coordinates, a convenient partition of the state leading to a two-time-scale standard form which allows the order reduction by using the singular perturbation technique does not generally exist. A convenient change of coordinates which is better suited to perform the order reduction is proposed. A systematic method is presented for transforming the natural mass-balance model of reaction systems with slow and fast reactions into the two-time-scale standard form of singular perturbation theory. The theory is illustrated by a prototype example