DETERMINATION OF APPROXIMATE LUMPING SCHEMES BY A SINGULAR PERTURBATION METHOD

A singular perturbation method is employed for the determination of an approximate nonlinear lumped model for a chemical kinetic system described by a set of first order ordinary differential equations with a group of small positive parameters corresponding to different time scales. New variables, called purely fast variables, are introduced and determined. Substituting their explicit expressions into the original kinetic equation system yields a lumped differential equation system containing the independent variable t. The lumped system can reach any desired accuracy for any initial composition. A further approximation to this lumped system, obtained by omitting transient exponential functions of t, is shown to define the dynamics of the system on a slow invariant manifold. Two simple examples are used to illustrate this approach.