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

Nikolić, Daliborka; Petkovska, Menka

doi:10.1016/j.ces.2013.09.009

Cited by 20 publications

(88 citation statements)

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“…If multiple inputs in a nonlinear system are modulated, its dynamic model is defined by several sets of FRFs. A block diagram, representing a nonlinear system with two inputs, x and z , is shown in Figure . The complete model for this case is defined by three sets of FRFs: two of them relating the output to each of the inputs, and one set of cross‐functions, relating the output to both inputs .…”

Section: Introductionmentioning

confidence: 99%

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

Petkovska

Nikolić

Seidel‐Morgenstern

2018

Israel Journal of Chemistry

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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.

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Section: Introductionmentioning

confidence: 99%

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

Petkovska

Nikolić

Seidel‐Morgenstern

2018

Israel Journal of Chemistry

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“…The details about application of the NFR method for systems with two modulated inputs can be found in (Nikolić-Paunić and Petkovska, 2013), where it was shown that the interaction of two modulated inputs will give the highest contribution to a possible process improvement when the two inputs are modulated with equal forcing frequencies.…”

Section: Nonlinear Frequency Response Methods For Evaluating Periodic mentioning

confidence: 99%

“…In our previous publications we applied the NFR method for fast evaluation of chemical reactors (Marković et al, 2008;Petkovska et al, 2010;Petkovska and Seidel-Morgenstern 2013;Nikolić-Paunić and Petkovska 2013;Nikolić et al, 2014aNikolić et al, , 2014b. It was explained that, for a reaction of the type A→ product(s), when one or more inputs are periodically modulated, the difference between the mean outlet concentration of the reactant c A m and the corresponding steady-state outlet concentration…”

Section: Nonlinear Frequency Response Methods For Evaluating Periodic mentioning

confidence: 99%

“…Furthermore, it is possible to determine the optimal phase difference for which the first derivative of the cross second order asymmetrical term * 2, / xz G ϕ ∂ ∂ is equal to zero, and consequently, the cross DC term has a minimum. This optimal phase difference is a function of the forcing frequency ω (Nikolić-Paunić, Petkovska, 2013):…”

Section: Nonlinear Frequency Response Methods For Evaluating Periodic mentioning

confidence: 99%

“…Inlet concentration (Marković et al, 2008;Petkovska et al, 2010;Nikolić-Paunić and Petkovska 2013;Nikolić et al, 2014a), flow-rate (Nikolić-Paunić and Petkovska 2013;Nikolić et al, 2014a), inlet temperature and temperature of the cooling/heating medium (Nikolić et al, 2014b) were used as periodically modulated inputs, separately (Marković et al, 2008;Petkovska et al, 2010;Nikolić et al, 2014a;Nikolić et al 2014b) or two of them simultaneously (Nikolić-Paunić and Petkovska 2013). …”

Section: Introductionmentioning

confidence: 99%

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Nonlinear frequency response analysis of forced periodic operation of non-isothermal CSTR with simultaneous modulation of inlet concentration and inlet temperature

Nikolić

Seidel‐Morgenstern

Petkovska

2015

Chemical Engineering Science

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The nonlinear frequency response (NFR) method is applied for evaluation of possible improvement through simultaneous periodic modulation of two inputs of a non-isothermal continuously stirred tank reactor (CSTR) in which homogeneous nth order reaction A→product(s) takes place. The two modulated inputs are the concentration of the reactant in the feed steam and the temperature of the feed stream. The cross asymmetrical second order FRF which correlates the outlet concentration with both modulated inputs is derived and analyzed. The optimal phase difference which should be used in order to maximize the conversion is determined. The method is tested on three numerical examples of non-isothermal CSTRs: (a) one which is oscillatory stable with strong resonant behavior, (b) one which is oscillatory stable with weak resonant behavior and (c) one which is nonoscillatory stable. Good agreement between the results of the approximate NFR method and the results of “exact” numerical integration is obtained except for the reactor with strong resonance for forcing frequencies which are close to the resonant frequency and for the reactor with weak resonant behavior for forcing frequency equal to the resonant one in case of high forcing amplitudes

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Periodic Operation with Modulation of Inlet Concentration and Flow Rate. Part I: Nonisothermal Continuous Stirred‐Tank Reactor

2016

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The nonlinear frequency response (NFR) method, which is an analytical, fast, and easy method for evaluating the performance of forced periodically operated chemical reactors, was used to investigate possible improvements to a nonisothermal continuous stirred tank reactor (CSTR) when inlet concentration and/or flow rate is periodically modulated. The product yield corresponding to periodic operation is defined, expressions for its estimation, based on the NFR method, are derived, and it is used to evaluate the performance improvements due to periodic operation. Part I considers the general nonisothermal case. In Part II, these results are applied to an adiabatic CSTR and used to evaluate possible improvements for the case of the hydrolysis reaction of acetic anhydride.

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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

Cited by 20 publications

References 20 publications

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

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

Nonlinear frequency response analysis of forced periodic operation of non-isothermal CSTR with simultaneous modulation of inlet concentration and inlet temperature

Periodic Operation with Modulation of Inlet Concentration and Flow Rate. Part I: Nonisothermal Continuous Stirred‐Tank Reactor

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