Evaluation of periodic processes with two modulated inputs based on nonlinear frequency response analysis. Case study: CSTR with modulation of the inlet concentration and flow-rate

Abstract

In our previous work, a new, fast and easy, nonlinear frequency response method for analysing potential improvements of reactor performance by forced periodic operation was presented. This method, which is based on Volterra series, generalized Fourier transform and the concept of higher-order frequency response functions (FRFs), gives an approximate value of the average process performance directly, without numerical simulation of the complete process. It was shown that the asymmetrical second order frequency response function, (G(2)(omega, -omega)) corresponds to the dominant term of the non-periodic (DC) component of the periodic steady-state response and determines the average performance of the periodic process. Thus, in order to evaluate the potential of a periodic reactor operation, it is enough to derive and analyse this function. In this work this method is extended to evaluating periodic operations with forced oscillations of two modulated inputs. In this case the nonlinear system has to be defined by three sets of frequency response functions, two of thorn correlating the output to each of the inputs and one set of cross-FRFs. The general methodology for this case is developed. It is further used to analyse the time-average performance of an isothermal continuous stirred tank reactor (CSTR) with forced periodic modulation of the inlet concentration and flow-rate, for a simple nth order homogeneous reaction. The analysis is performed for cases when the inlet concentration and flow-rate are modulated simultaneously. The optimal choice of the phase shift between the two inputs is discussed in detail.