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Forced periodically operated chemical reactor- Evaluation and analysis by the nonlinear frequency response method

Periodične operacije hemijskih reaktora-evaluacija i analiza primenom metode nelinearnog frekventnog odziva

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2016
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Authors
Nikolić-Paunić, Daliborka
Contributors
Petkovska, Menka
Žižović, Irena
Nikačević, Nikola
Panić, Vladimir
Seidel-Morgenstern, Andreas
Doctoral thesis (Published version)
,
Dr Daliborka Nikolić Paunić
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Abstract
Abstract The conventional way to design and operate the processes in chemical engineering is to determine the optimal steady-state design and to operate as close as possible to that steady-state. Nevertheless, many investigations have proven that periodic operations, when one or more inputs are periodically modulated, can result with better process performances, especially for chemical reactors. The origin of improvement of the reactor performance lies in fact that for nonlinear systems, the periodic modulation of one or more inputs will cause the outputs to change periodically, as well, with the mean value which is, in general, different from their steady-state values. In this work, we propose and implement the nonlinear frequency response (NFR) method for fast and easy evaluation of possible reactor improvements throughout periodic modulations. The NFR method is a relatively new method, mathematically based on Volterra series, generalized Fourier transform and the concept of highe...r-order frequency response functions (FRFs). The change of the reactor performances caused by periodic operations can be evaluated from the DC (non-periodic) component of the frequency response of the reactor, if it is a weakly nonlinear system. The DC component can be calculated exactly as a sum of an indefinite series, with members which are proportional to the asymmetrical even order FRFs. Nevertheless, based on the NFR method, the DC component can be estimated only from the first, dominant term of this series, which is proportional to the asymmetrical second order frequency response function G2(ω,-ω). In that way, for analysis of possible improvements of forced periodically operated chemical reactors, it is enough to derive and analyze asymmetrical second order FRFs G2(ω,-ω). For this reason, the NFR method is essentially approximate. In this work, the nonlinear frequency response method is applied for evaluation of possible improvements (increase of the reactant conversion or product yield) through periodic modulation of one (single input modulation) and simultaneous modulation of two inputs, when a homogeneous, simple, irreversible nth order reaction takes place in an isothermal, non-isothermal or adiabatic continuously stirred tank reactor (CSTR). The NFR method is tested on several numerical examples and the results are compared with the results calculated by numerical integration, which as considered as exact. Good agreements between the results of the NFR method and results of numerical integration are obtained, except for highly nonlinear systems around the resonant frequency, when high forcing amplitudes are used. It is concluded that, whether and to which extend is possible to achieve the improvements of the reactor performance through periodic operations, can be evaluated by the nonlinear frequency response method. The influence of the forcing parameters (frequency, amplitudes and phase shift of the input modulations) on the possible improvement can also be determined by the nonlinear frequency response method.

Uobičajen način projektovanja procesa u hemijskom inženjerstvu podrazumeva određivanje optimalnog stacionog stanja i upravljanje procesom na način koji odezbeđuje da se uslovi održavaju što je moguće bliže tom optimalnom stacionarnom stanju. Ipak, mnoga istaživanja su pokazala da se performanse procesa, pogotovo hemijskih reaktora, mogu poboljšati ukoliko se jedan ili više ulaza periodično menja. Poboljšanje performansi hemijskih reaktora pri periodičnom režimu rada je posledica nelinearnosti sistema. Kod nelinearnih sistema, kada se periodično menja jedan ili više ulaza, izlazi iz sistema se takođe periodično menjaju, a njihova srednja vrednost se, u opštem slučaju, razlikuje od stacionarnih vrednosti. Methoda nelinearnog frekventnog odziva (NFO) je u ovom radu predložena i primenjena za brzo i lako određivanje mogućeg poboljšanja performansi reaktora primenom periodičnog režima rada. Metoda NFO je relativno nova metoda i ona je matematički bazirana na Voltera redovima, generalizova...noj Furijeovoj transformaciji i na konceptu frekventnih prenosnih funkcija (FPF) višeg reda. Uticaj periodičnih operacija na performanse reaktora se može odrediti preko DC komponente (neperiodičnog člana) frekventnog odziva nelinearnog sistema. DC komponenta se može tačno prikazati beskonačnim redom čiji su članovi proporcionalni asimetričnim FPF parnih redova. Medjutim, u predloženoj metodi NFO DC komponenta se procenjuje samo na osnovu svog dominantnog člana koji je proporcionalan asimetričnoj FPF drugog reda G2(ω,-ω), tako da je za analizu mogućeg poboljšanja performansi reaktora pri periodičnom režimu rada dovoljno izvesti i analizirati samo ovu funkciju. Zbog toga je metoda NFO po svojoj suštini približna. U ovom radu, metoda NFO je primenjena za procenu mogućeg poboljšanja (povećenja konverzije reaktanta ili prinosa proizvoda) pri periodičnoj promeni jednog ili dva ulaza izotermnih, neizotermnih ili adijabatskih protočnih reaktora sa idealnim mešanjem (PRIM) sa homogenom, jednostavnom, nepovratnom reakcijom n-tog reda. Methoda nelinearnog frekventnog odziva je primenjena na nekoliko numeričkih primera, a dobijeni rezultati su upoređeni sa rezultatima koji su izračunati primenom numeričke integracije, koji se smatraju za tačne. Postignuto je dobro slaganje između rezultata koji su dobijeni primenom metode NFO i rezultata numeričke integracije, osim u slučajevima izrazito nelinearnih sistema u okolini rezonantne frekvencije, kada su korišćene jako velike amplitude. Zaključeno je da određivanje da li je, i u kojoj meri, moguće postići poboljšanje performansi hemijskih reaktora primenom periodičnih operacija moguće primenom metode nelinearnog frekventnog odziva. Primenom ove metode se takođe može odrediti uticaj parametara periodičnih operacija (frekvencija, amplitude i fazne razlike ulaznih promenljivih) na moguće poboljšanje i usvojiti opseg ovih parametara koji treba koristiti za uspešne periodične procese.

Keywords:
Nonlinear frequency response method / Higher order frequency response functions / Volterra series / Periodically operated chemical reactors / Single input modulation / Two-input modulation / Forcing parameters / Isothermal CSTR / Non-isothermal CSTR / Adiabatic CSTR
Source:
2016
Publisher:
  • University of Belgrade, Faculty of Technology and Metallurgy
Funding / projects:
  • Nanostructured Functional and Composite Materials in Catalytic and Sorption Processes (RS-45001)
[ Google Scholar ]
Handle
https://hdl.handle.net/21.15107/rcub_nardus_6360
URI
https://nardus.mpn.gov.rs/handle/123456789/6360
http://eteze.bg.ac.rs/application/showtheses?thesesId=3686
https://fedorabg.bg.ac.rs/fedora/get/o:12496/bdef:Content/download
http://vbs.rs/scripts/cobiss?command=DISPLAY&base=70036&RID=48096783
https://cer.ihtm.bg.ac.rs/handle/123456789/3798
Collections
  • Doktorati (Nardus) / Doctoral thesis
Institution/Community
IHTM
TY  - THES
AU  - Nikolić-Paunić, Daliborka
PY  - 2016
UR  - https://nardus.mpn.gov.rs/handle/123456789/6360
UR  - http://eteze.bg.ac.rs/application/showtheses?thesesId=3686
UR  - https://fedorabg.bg.ac.rs/fedora/get/o:12496/bdef:Content/download
UR  - http://vbs.rs/scripts/cobiss?command=DISPLAY&base=70036&RID=48096783
UR  - https://cer.ihtm.bg.ac.rs/handle/123456789/3798
AB  - Abstract
The conventional way to design and operate the processes in chemical engineering is to determine the optimal steady-state design and to operate as close as possible to that steady-state. Nevertheless, many investigations have proven that periodic operations, when one or more inputs are periodically modulated, can result with better process performances, especially for chemical reactors.
The origin of improvement of the reactor performance lies in fact that for nonlinear systems, the periodic modulation of one or more inputs will cause the outputs to change periodically, as well, with the mean value which is, in general, different from their steady-state values.
In this work, we propose and implement the nonlinear frequency response (NFR) method for fast and easy evaluation of possible reactor improvements throughout periodic modulations. The NFR method is a relatively new method, mathematically based on Volterra series, generalized Fourier transform and the concept of higher-order frequency response functions (FRFs). 
The change of the reactor performances caused by periodic operations can be evaluated from the DC (non-periodic) component of the frequency response of the reactor, if it is a weakly nonlinear system. The DC component can be calculated exactly as a sum of an indefinite series, with members which are proportional to the asymmetrical even order FRFs. Nevertheless, based on the NFR method, the DC component can be estimated only from the first, dominant term of this series, which is proportional to the asymmetrical second order frequency response function G2(ω,-ω). In that way, for analysis of possible improvements of forced periodically operated chemical reactors, it is enough to derive and analyze asymmetrical second order FRFs G2(ω,-ω). For this reason, the NFR method is essentially approximate.
In this work, the nonlinear frequency response method is applied for evaluation of possible improvements (increase of the reactant conversion or product yield) through periodic modulation of one (single input modulation) and simultaneous modulation of two inputs, when a homogeneous, simple, irreversible nth order reaction takes place in an isothermal, non-isothermal or adiabatic continuously stirred tank reactor (CSTR).
The NFR method is tested on several numerical examples and the results are compared with the results calculated by numerical integration, which as considered as exact. Good agreements between the results of the NFR method and results of numerical integration are obtained, except for highly nonlinear systems around the resonant frequency, when high forcing amplitudes are used.
It is concluded that, whether and to which extend is possible to achieve the improvements of the reactor performance through periodic operations, can be evaluated by the nonlinear frequency response method. The influence of the forcing parameters (frequency, amplitudes and phase shift of the input modulations) on the possible improvement can also be determined by the nonlinear frequency response method.
AB  - Uobičajen način projektovanja procesa u hemijskom inženjerstvu podrazumeva određivanje optimalnog stacionog stanja i upravljanje procesom na način koji odezbeđuje da se uslovi održavaju što je moguće bliže tom optimalnom stacionarnom stanju. Ipak, mnoga istaživanja su pokazala da se performanse procesa, pogotovo hemijskih reaktora, mogu poboljšati ukoliko se jedan ili više ulaza periodično menja.
Poboljšanje performansi hemijskih reaktora pri periodičnom režimu rada je posledica nelinearnosti sistema. Kod nelinearnih sistema, kada se periodično menja jedan ili više ulaza, izlazi iz sistema se takođe periodično menjaju, a njihova srednja vrednost se, u opštem slučaju, razlikuje od stacionarnih vrednosti.
Methoda nelinearnog frekventnog odziva (NFO) je u ovom radu predložena i primenjena za brzo i lako određivanje mogućeg poboljšanja performansi reaktora primenom periodičnog režima rada. Metoda NFO je relativno nova metoda i ona je matematički bazirana na Voltera redovima, generalizovanoj Furijeovoj transformaciji i na konceptu frekventnih prenosnih funkcija (FPF) višeg reda.
Uticaj periodičnih operacija na performanse reaktora se može odrediti preko DC komponente (neperiodičnog člana) frekventnog odziva nelinearnog sistema. DC komponenta se može tačno prikazati beskonačnim redom čiji su članovi proporcionalni asimetričnim FPF parnih redova. Medjutim, u predloženoj metodi NFO DC komponenta se procenjuje samo na osnovu svog dominantnog člana koji je proporcionalan asimetričnoj FPF drugog reda G2(ω,-ω), tako da je za analizu mogućeg poboljšanja performansi reaktora pri periodičnom režimu rada dovoljno izvesti i analizirati samo ovu funkciju. Zbog toga je metoda NFO po svojoj suštini približna.
U ovom radu, metoda NFO je primenjena za procenu mogućeg poboljšanja (povećenja konverzije reaktanta ili prinosa proizvoda) pri periodičnoj promeni jednog ili dva ulaza izotermnih, neizotermnih ili adijabatskih protočnih reaktora sa idealnim mešanjem (PRIM) sa homogenom, jednostavnom, nepovratnom reakcijom n-tog reda.
Methoda nelinearnog frekventnog odziva je primenjena na nekoliko numeričkih primera, a dobijeni rezultati su upoređeni sa rezultatima koji su izračunati primenom numeričke integracije, koji se smatraju za tačne. Postignuto je dobro slaganje između rezultata koji su dobijeni primenom metode NFO i rezultata numeričke integracije, osim u slučajevima izrazito nelinearnih sistema u okolini rezonantne frekvencije, kada su korišćene jako velike amplitude. 
Zaključeno je da određivanje da li je, i u kojoj meri, moguće postići poboljšanje performansi hemijskih reaktora primenom periodičnih operacija moguće primenom metode nelinearnog frekventnog odziva. Primenom ove metode se takođe može odrediti uticaj parametara periodičnih operacija (frekvencija, amplitude i fazne razlike ulaznih promenljivih) na moguće poboljšanje i usvojiti opseg ovih parametara koji treba koristiti za uspešne periodične procese.
PB  - University of Belgrade, Faculty of Technology and Metallurgy
T1  - Forced periodically operated chemical reactor- Evaluation and analysis by the nonlinear frequency response method
T1  - Periodične operacije hemijskih reaktora-evaluacija i analiza primenom metode nelinearnog frekventnog odziva
UR  - https://hdl.handle.net/21.15107/rcub_nardus_6360
ER  - 
@phdthesis{
author = "Nikolić-Paunić, Daliborka",
year = "2016",
abstract = "Abstract
The conventional way to design and operate the processes in chemical engineering is to determine the optimal steady-state design and to operate as close as possible to that steady-state. Nevertheless, many investigations have proven that periodic operations, when one or more inputs are periodically modulated, can result with better process performances, especially for chemical reactors.
The origin of improvement of the reactor performance lies in fact that for nonlinear systems, the periodic modulation of one or more inputs will cause the outputs to change periodically, as well, with the mean value which is, in general, different from their steady-state values.
In this work, we propose and implement the nonlinear frequency response (NFR) method for fast and easy evaluation of possible reactor improvements throughout periodic modulations. The NFR method is a relatively new method, mathematically based on Volterra series, generalized Fourier transform and the concept of higher-order frequency response functions (FRFs). 
The change of the reactor performances caused by periodic operations can be evaluated from the DC (non-periodic) component of the frequency response of the reactor, if it is a weakly nonlinear system. The DC component can be calculated exactly as a sum of an indefinite series, with members which are proportional to the asymmetrical even order FRFs. Nevertheless, based on the NFR method, the DC component can be estimated only from the first, dominant term of this series, which is proportional to the asymmetrical second order frequency response function G2(ω,-ω). In that way, for analysis of possible improvements of forced periodically operated chemical reactors, it is enough to derive and analyze asymmetrical second order FRFs G2(ω,-ω). For this reason, the NFR method is essentially approximate.
In this work, the nonlinear frequency response method is applied for evaluation of possible improvements (increase of the reactant conversion or product yield) through periodic modulation of one (single input modulation) and simultaneous modulation of two inputs, when a homogeneous, simple, irreversible nth order reaction takes place in an isothermal, non-isothermal or adiabatic continuously stirred tank reactor (CSTR).
The NFR method is tested on several numerical examples and the results are compared with the results calculated by numerical integration, which as considered as exact. Good agreements between the results of the NFR method and results of numerical integration are obtained, except for highly nonlinear systems around the resonant frequency, when high forcing amplitudes are used.
It is concluded that, whether and to which extend is possible to achieve the improvements of the reactor performance through periodic operations, can be evaluated by the nonlinear frequency response method. The influence of the forcing parameters (frequency, amplitudes and phase shift of the input modulations) on the possible improvement can also be determined by the nonlinear frequency response method., Uobičajen način projektovanja procesa u hemijskom inženjerstvu podrazumeva određivanje optimalnog stacionog stanja i upravljanje procesom na način koji odezbeđuje da se uslovi održavaju što je moguće bliže tom optimalnom stacionarnom stanju. Ipak, mnoga istaživanja su pokazala da se performanse procesa, pogotovo hemijskih reaktora, mogu poboljšati ukoliko se jedan ili više ulaza periodično menja.
Poboljšanje performansi hemijskih reaktora pri periodičnom režimu rada je posledica nelinearnosti sistema. Kod nelinearnih sistema, kada se periodično menja jedan ili više ulaza, izlazi iz sistema se takođe periodično menjaju, a njihova srednja vrednost se, u opštem slučaju, razlikuje od stacionarnih vrednosti.
Methoda nelinearnog frekventnog odziva (NFO) je u ovom radu predložena i primenjena za brzo i lako određivanje mogućeg poboljšanja performansi reaktora primenom periodičnog režima rada. Metoda NFO je relativno nova metoda i ona je matematički bazirana na Voltera redovima, generalizovanoj Furijeovoj transformaciji i na konceptu frekventnih prenosnih funkcija (FPF) višeg reda.
Uticaj periodičnih operacija na performanse reaktora se može odrediti preko DC komponente (neperiodičnog člana) frekventnog odziva nelinearnog sistema. DC komponenta se može tačno prikazati beskonačnim redom čiji su članovi proporcionalni asimetričnim FPF parnih redova. Medjutim, u predloženoj metodi NFO DC komponenta se procenjuje samo na osnovu svog dominantnog člana koji je proporcionalan asimetričnoj FPF drugog reda G2(ω,-ω), tako da je za analizu mogućeg poboljšanja performansi reaktora pri periodičnom režimu rada dovoljno izvesti i analizirati samo ovu funkciju. Zbog toga je metoda NFO po svojoj suštini približna.
U ovom radu, metoda NFO je primenjena za procenu mogućeg poboljšanja (povećenja konverzije reaktanta ili prinosa proizvoda) pri periodičnoj promeni jednog ili dva ulaza izotermnih, neizotermnih ili adijabatskih protočnih reaktora sa idealnim mešanjem (PRIM) sa homogenom, jednostavnom, nepovratnom reakcijom n-tog reda.
Methoda nelinearnog frekventnog odziva je primenjena na nekoliko numeričkih primera, a dobijeni rezultati su upoređeni sa rezultatima koji su izračunati primenom numeričke integracije, koji se smatraju za tačne. Postignuto je dobro slaganje između rezultata koji su dobijeni primenom metode NFO i rezultata numeričke integracije, osim u slučajevima izrazito nelinearnih sistema u okolini rezonantne frekvencije, kada su korišćene jako velike amplitude. 
Zaključeno je da određivanje da li je, i u kojoj meri, moguće postići poboljšanje performansi hemijskih reaktora primenom periodičnih operacija moguće primenom metode nelinearnog frekventnog odziva. Primenom ove metode se takođe može odrediti uticaj parametara periodičnih operacija (frekvencija, amplitude i fazne razlike ulaznih promenljivih) na moguće poboljšanje i usvojiti opseg ovih parametara koji treba koristiti za uspešne periodične procese.",
publisher = "University of Belgrade, Faculty of Technology and Metallurgy",
title = "Forced periodically operated chemical reactor- Evaluation and analysis by the nonlinear frequency response method, Periodične operacije hemijskih reaktora-evaluacija i analiza primenom metode nelinearnog frekventnog odziva",
url = "https://hdl.handle.net/21.15107/rcub_nardus_6360"
}
Nikolić-Paunić, D.. (2016). Forced periodically operated chemical reactor- Evaluation and analysis by the nonlinear frequency response method. 
University of Belgrade, Faculty of Technology and Metallurgy..
https://hdl.handle.net/21.15107/rcub_nardus_6360
Nikolić-Paunić D. Forced periodically operated chemical reactor- Evaluation and analysis by the nonlinear frequency response method. 2016;.
https://hdl.handle.net/21.15107/rcub_nardus_6360 .
Nikolić-Paunić, Daliborka, "Forced periodically operated chemical reactor- Evaluation and analysis by the nonlinear frequency response method" (2016),
https://hdl.handle.net/21.15107/rcub_nardus_6360 .

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