Article pubs.acs.org/IECR
A Study of Applicability of Nonlinear Frequency Response Method for Investigation of Gas Adsorption Based on Numerical Experiments Danica Brzić and Menka Petkovska* University of Belgrade, Faculty of Technology and Metallurgy, Department of Chemical Engineering, Karnegijeva 4, 11000 Belgrade, Serbia ABSTRACT: A study of the applicability of the Nonlinear Frequency Response (NFR) approach for investigation of equilibrium and kinetics of gas adsorption, based on numerical simulations, is presented. Pressure responses of a batch adsorber are simulated, using literature data, for a sinusoidal volume change with different input amplitudes, up to 10%, around several steady-state points. The procedure for application of the NFR approach is demonstrated step-by-step, using the simulated pressure responses. As a result, quasi-experimental first- and second-order FRFs are estimated and used for estimation of the equilibrium and kinetic parameters of the adsorption system. The estimated parameters agree well with the original ones used for simulations. Influence of noise on the accuracy of the estimated FRFs and model parameters is also analyzed. The results of this study show that the application of the NFR approach for investigation of equilibrium and kinetics of gas adsorption in a batch system is feasible. Furthermore, valuable information regarding the design of the NFR equipment and experiments is gained. of the system. A theoretical study of Petkovska and Do9 shows that the second-order FRFs have different shapes for different kinetic models and thus can be used for unambiguous model identification and estimation of the nonlinear model parameters. Moreover, from the low-frequency asymptotes of the experimental FRFs, it is possible to determine the equilibrium parameters of the adsorption system.10 A comprehensive theoretical study regarding the NFR approach, which includes the step-by-step procedure for estimation of the first and second order FRFs from experimental NFRs, as well as the detailed procedure for determination of the equilibrium and kinetic parameters from the experimental first- and second-order FRFs, can be found in the literature.10 The theoretical FRFs up to the second order for simple and several complex kinetic models have been derived. 9,11−14 However, there is still no experimental validation of the NFR method for the identification of the kinetics of gas−solid adsorption. The main challenge for the practical implementation of the NFR method is accurate experimental determination of the second-order FRF. Secondorder FRF is estimated from the second harmonic of the FR, and the accuracy of its estimation can be affected by the presence of noise and the contribution of the higher-order harmonics. Therefore, the questions regarding the magnitude of the second (and higher) harmonic and its sensitivity to the input amplitude, steady-state, and noise are very important to clarify before experimental implementation of the NFR method. Some aspects of the practical implementation of the NFR (choosing the optimal mass of adsorbent, the input amplitude,
1. INTRODUCTION One of the common approaches in the investigation of kinetics of gas adsorption is the frequency response (FR) method. It is based on a small amplitude sinusoidal excitation and determination of the frequency response function (FRF) from a single harmonic output. The kinetic parameters are determined by fitting the obtained FRF to the theoretical one, derived from a linearized model of the assumed kinetic mechanism. Over past decades, dozens of articles have been published regarding the application of the FR method for kinetic investigations of different adsorption/chemisorption systems.1−6 The main advantage of the FR method (in comparison to the uptake rate measurements in the time domain) is the ability to discriminate in a frequency spectrum between the time constants of simultaneous processes. However, the main limitation of this method is the inability to discriminate between kinetic models which have the same linearized form and accordingly the same shape of the FRF.2 Furthermore, most of the published FR kinetic data2−4 are limited to very low pressures (
