A quasistatic asymptotic limit for reactor kinetics

Abstract

We propose a “quasistatic” asymptotic limit for reactor kinetics in which the material properties vary much more slowly in time than the solution itself. We further develop an asymptotic approximation of the solution in this limit using the method of multiple scales that, to leading order, takes the form of the product of a function that depends only on time and a function that depends on all independent variables but varies on the same time scale as the material properties. Determining when an approximation of this form is valid is of interest as several methods for performing reactor-kinetics calculation rely on such a representation of the solution. With an example reactor-kinetics problem, we demonstrate our asymptotic approximation becomes more accurate as the material properties vary more slowly in time, as expected.