Evaluation of the potential of periodically operated reactors based on the second order frequency response function

Abstract

A new, fast and easy method for analysing the potential for improving reactor performance by replacing steady state by forced periodic operation is presented. The method is based on Volterra series, generalized Fourier transform and the concept of higher-order frequency response functions (FRFs). The second order frequency response function, which corresponds to the dominant term of the non-periodic (DC) component, G(2)(omega, -omega), is mainly responsible for the average performance of the periodically operated processes. Based on that, in order to evaluate the potential of periodic reactor operation, it is enough to derive and analyze G(2)(omega, -omega). The sign of this function defines the sign of the DC component and reveals whether a performance improvement by cycling is possible compared to optimal steady state process. The method is used to analyze the periodic performance of a continuous stirred tank reactor (CSTR), a plug flow tubular reactor (PFTR) and a dispersive flow tubular reactor (DFTR), after introducing periodic changes of the input concentrations. A homogeneous, n-th order reaction is studied under isothermal conditions.