Application of nonlinear frequency response method for investigation of equlibrium and kinetics of gas-solid adsorption

Abstract

The understanding of complex kinetic mechanisms of gas-solid adsorption is a challenging issue. The Frequency Response (FR) method, which has commonly been used for studying the kinetics of adsorption, analyzes the frequency response of the system in a linear range, and therefore partly fails to identify and characterize the kinetics of nonlinear adsorption phenomena. In the frame of this thesis, the applicability of a new Nonlinear Frequency Response (NFR) method for characterization of kinetics and equilibria of gas adsorption, was investigated. The NFR method is based on the analysis of the frequency responses for a rather large amplitude input excitation, named Nonlinear Frequency Responses, and determination of the higher-order frequency response functions (FRFs), by applying the Volterra series and generalized Fourier transform. The applicability of the NFR method for characterization of kinetics and equilibria of pure gas adsorption was investigated both theoretically and experimentally, for the case of a batch adsorber. The critical issue regarding the applicability of the NFR method was determination of the second-order FRF on the adsorbent particle scale. The theoretical investigation comprises two parts. The first part of investigation is based on the numerical simulations of the dynamic responses of a batch adsorption system, by using mathematical models on the adsorber scale and adsorbent particle scale. As a result, the procedure for designing the NFR experiments has been established. In the second part, the theoretical FRFs up to the second-order for nonisothermal macropore diffusion (NMD) model, as one of the common mechanisms of gas-solid adsorption, have been derived and analyzed. As a result, the methodology for estimation of the parameters of NMD model, based on the characteristics of the FRFs, was established. In order to validate the NFR method experimentally, a new experimental set-up was designed and constructed. The working principle of the apparatus is modulation of the volume of the closed cell in a sinusiodal way, with variable amplitude and frequency, and measuring the pressure, adsorbent temperature and gas temperature responses. The test system was CO2/ zeolite 5A particles. The results showed that the NFR method can be applied for identification of the kinetic mechanism and estimation of equilibrium and kinetic data. It was also shown, that it is advantageous compared to the linear FR method in terms of reliability of identification of the kinetic model based on the second-order FRF, as well as in the possibility to estimate both kinetic and equilibrium data. Since this work represents the first evidence of experimental application of the NFR method for investigation of gas adsorption, it opens significant new perspectives in this field.

Razumevanje složenih kinetičkih mehanizama adsorpcije gas-čvrsto predstavlja izazov u savremenom istraživanju. Klasična Frekventna metoda, koja se uobičajeno koristi za ispitivanje kinetike adsorpcije, analizira frekventni odziv sistema u linearnoj oblasti i zato ne može u potpunosti da okarakteriše kinetiku nelinearnih procesa adsorpcije. U okviru ove disertacije ispitivana je primenljivost metode Nelinearnog Frekventnog Odziva (NFO) za karakterizaciju kinetike i ravnoteže adsorpcije gas-čvrsto. Metoda NFO se zasniva na analiziranju frekventnog odziva sistema na ulaznu pobudu relativno velike amplitude i određivanju frekventnih prenosnih funkcija (FPF) višeg reda, uz korišćenje Volterra redova i generalizovane Furijeove transformacije. Primenljivost metode NFO za karakterizaciju kinetike i ravnoteže adsorpcije čistih gasova je ispitivana teorijski i eksperimentalno u zatvorenom (šaržnom) sistemu. Ključno pitanje u pogledu primenljivosti metode NFO je mogućnost određivanja frekventne prenosne funkcije drugog reda na nivou čestice adsorbensa. Teorijsko istraživanje se sastoji od dva dela. Prvi deo se zasniva na numeričkim simulacijama dinamičkih odziva šaržnog adsorbera, uz korišćenje matematičkih modela na nivou adsorbera i na nivou čestice adsorbensa. Na osnovu dobijenih rezultata ustanovljena je procedura za planiranje nelinearnih frekventnih eksperimenata. U drugom delu, izvedene su i analizirane FPF prvog i drugog reda za model neizotermne diffuzije kroz makropore, koji je jedan od čestih mehanizama adsorpcije gasova. Na osnovu rezultata ustanovljena je procedura za određivanje parametara pomenutog modela na osnovu karakteristika FPF. Da bi se metoda eksperimentalno potvrdila, projektovan je i izgrađen novi eksperimentalni sistem. Princip rada ovog sistema je promena zapremine sistema po sinusnom zakonu, sa promenljivom amplitudom i frekvencijom, i merenje odziva pritiska gasa, temperature adsorbensa i temperature gasa. Kao test sistem za eksperimente korišćen je adsorpcioni sistem CO2/ zeolit 5A. Rezultati su pokazali da je moguće primeniti metodu NFO za utvrđivanje kinetičkog mehanizma adsorpcije gasova kao i za određivanje kinetičkih i ravnotežnih parametara. Takođe je pokazano da metoda NFO ima značajne prednosti u odnosu na klasičnu (linearnu) frekventnu metodu, i to u pogledu pouzdanosti utvrđivanja kinetičkog mehanizma na osnovu oblika FPF drugog reda kao i u pogledu mogućnosti određivanja i kinetičkih i ravnotežnih podataka iz istih eksperimentalnih podataka. U ovom radu je prvi put eksperimentalno potvrđena mogućnost ispitivanja adsorpcije gasčvrsto korišćenjem metode NFO, čime se otvaraju značajne nove perspektive u toj oblasti.