Nonlinear Frequency Response Method for Evaluating Forced Periodic Operations of Chemical Reactors

Abstract

Nonlinear Frequency Response (NFR) method is a relatively new method which can be used for fast evaluation of possible process improvements through periodic operations. The method is analytical and approximate. Its main task is to give an answer whether periodic modulation of one or more process inputs can result in improved process performance. The method is explained in brief and an overview of the existing applications is given. The review covers simple reactions performed in isothermal and non‐isothermal stirred tank reactors exposed to different modulated inputs (inlet concentration, flow‐rate, inlet temperature, temperature of the heating/cooling medium). Processes with two simultaneously modulated inputs and different shapes of the periodic input are also considered. The results of the NFR method are compared with the results of numerical simulation and a critical evaluation of the method is given.

Forced periodic operations of a chemical reactor for methanol synthesis – The search for the best scenario based on Nonlinear Frequency Response Method. Part II Simultaneous modulation of two inputs

“…More details can be found in our previous publications (e.g. Nikolić and Petkovska, 2013;Petkovska et al, 2018).…”

“…If one or more inputs of a weakly nonlinear systems is/are periodically modulated around a previously established steady-state, the frequency response of the system output is obtained as a sum of the output steady-state value (y s ), the basis harmonic (y I ), an infinite number of higher harmonics (y II , y III ,…) and a non-periodic (DC) term (y DC ) (Marković et al, 2006, Petkovska andSeidel-Morgenstern, 2013;Petkovska et al, 2018):…”

“…while the contribution of the cross-effect can be approximately evaluated in the following way (Nikolić and Petkovska, 2013;Petkovska et al, 2018):…”

“…The phase difference is a crucial parameter for a periodic operation with simultaneous modulations of two inputs, considering that its appropriate choice guaranties that the cross term of the DC component has the desirable sign. Furthermore, by choosing the optimal phase difference, the cross-effect can be maximized (Felischak 2020;Felischak et al 2021;Nikolić, 2016;Nikolić and Petkovska, 2013;Petkovska et al, 2018). The optimal phase difference, maximizing the DC component can be determined based only on the cross ASO FRF, in the following way (Nikolić and Petkovska, 2013):…”

Optimal periodic control of nonlinear chemical reactions with a time‐varying flow rate

“…The optimization of nonlinear chemical reactions with periodic input modulations has been discussed extensively in the literature since the late 1960's [2]. Some recent advances in this area are summarized in the book [5] and survey paper [4]. The task of maximizing the mean product of non-isothermal reactions over a given time period t ∈ [0, τ ] is treated in [7] as an isoperimetric optimal control problem with two independent inputs: the inlet concentration and the inlet temperature.…”