Evaluation of periodic processes with two modulated inputs based on nonlinear frequency response analysis

Abstract

One way to achieve process intensification is to operate the process in a periodic way, in order to obtain better average performance compared to the optimal steady-state operation. The source of the possible improvement lies in the process nonlinearity. Nevertheless, the improvement is obtained only in some cases, while in some others the periodic operation can be unfavourable. Testing whether a potential periodic process is favourable or unfavourable generally demands long and tedious experimental and/or numerical work. In our previous work, we have introduced a method, based on nonlinear frequency response analysis, which gives an approximate value of the average process performance directly, without numerical simulation of the complete process. The method, which was based on representing the nonlinear system by a sequence of frequency response functions of different orders, was developed for periodic operations with one modulated input. It was shown that the asymmetrical second order frequency response function corresponds to the dominant term of the non-periodic component of the periodic steady-state response and determines the average performance of the periodic process. Thus, it is enough to derive and analyse this function in order to evaluate the potential of a periodic operation. In this work this method is extended to evaluating periodic operations with forced oscillation of two modulated inputs. In this case the nonlinear system has to be defined by three sets of frequency response functions, two of them correlating the output to each of the inputs and one set of cross-functions. The general methodology for this case is developed. It is further used to analyze 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 n-th order homogeneous reaction. The analysis is performed for in-phase and out-of-phase input modulations.