Ind. Eng. Chem. Res. 2003, 42, 4213-4222
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New Frequency Response Method for Measuring Adsorption Rates via Pressure Modulation: Application to Oxygen and Nitrogen in a Carbon Molecular Sieve Yu Wang, Brian K. Sward, and M. Douglas LeVan* Department of Chemical Engineering, Vanderbilt University, Nashville, Tennessee 37235
A new frequency response method based on a sinusoidal modulation of pressure is developed to measure gas adsorption equilibria and kinetics simultaneously. The transfer phenomena of pure N2 and O2 gases on carbon molecular sieve are investigated for different pressures and particle sizes by this method. The mass-transfer mechanism for N2 can be explained by a surface barrier using a linear driving force model, but that for O2 requires a combination of a surface barrier and micropore diffusion using a combined resistance model. Alternatively, a distribution of surface barrier resistances is introduced to take into account heterogeneity of the surface and describes the experimental data well. The linear driving force mass-transfer coefficients increase with increasing pressure but depend on the particle size only slightly. The effects of pressure on the transfer coefficients for N2 are less pronounced than those for O2. The apparatus is shown to be useful in providing accurate and rapid transfer coefficient measurements and in identifying the rate-controlling adsorption mechanism. Introduction Knowledge of adsorption dynamics is important for the design of adsorption processes. Mass transfer in adsorbents can be a complex phenomenon because it is strongly influenced by the structure of the solid, the system, and the precise process conditions. A variety of methods for the investigation of such phenomena have been presented in the literature, and they can be grouped into two basic categories: macroscopic and microscopic.1 The frequency response (FR) method is one of the best macroscopic techniques. Because of its potential for discriminating between different ratelimiting mechanisms, the FR method has been widely used to investigate the kinetic behavior of gas-solid systems. Most theoretical and experimental aspects have been studied for a batch system in which the gas pressure is changed by a forced periodic volume fluctuation.2-11 Yasuda and co-workers applied this technique to study physical and chemical phenomena on zeolites including adsorption,2,3 diffusion-controlling processes,4-6 combinations of adsorption-diffusion processes,11 and reactions.12,13 Rees’ group used a square-wave volume perturbation to investigate hydrocarbons on silicate adsorbents.14-16 In addition to studies in batch systems, there are other applications in flow systems involving concentration or temperature variations. 17-21 Park et al.21 investigated a semibatch and continuous-flow adsorber using modulation of the inlet molar flow rate perturbed by four modes: sinusoidal, square wave, triangular, and sawtooth. This technique was also applied to sorption kinetics of methane, ethane, and propane on activated carbon systems.22 For solids having high internal surface areas such as activated carbon, surface diffusion may dominate the total rate. Sward and LeVan23 utilized a new apparatus to examine the adsorption of * To whom correspondence should be addressed. Tel.: (615) 322-2441. Fax: (615) 343-7951. E-mail: m.douglas.levan@ vanderbilt.edu.
carbon dioxide on BPL activated carbon, which is a type of activated carbon manufactured from selected grades of bituminous coal combined with suitable binders. The pressure of the system was perturbed in a sinusoidal wave, and the outlet flow rate was measured simultaneously. A nonisothermal surface diffusion model described the experimental data well. Carbon molecular sieve (CMS) is a modified form of activated carbon that has both a high internal surface area and molecular sieving capability. An important feature of CMS is that it provides molecular separations based on the rates of adsorption rather than on the differences in adsorption capacity.24 A typical application of CMS is the separation of air into N2 and O2 by pressure-swing adsorption. Many research groups have studied the diffusion of pure N2 and O2 in CMS using conventional approaches including gravimetric, volumetric, chromatographic, and other methods.25 CMS has a bidisperse pore structure with distinguishable macropore and micropore resistances to the transport of adsorbate. However, it is also believed to have “ink bottles” produced by carbon deposition at micropore entrances. Previous adsorption kinetics studies on CMS showed that the transport mechanisms are not fully understood, with some CMS samples obeying a Fickian diffusion law,26-29 whereas others show non-Fickian behavior that may contribute to pore-mouth constriction,25,30-32 and still others suggest a combination of both effects.33-37 Farooq et al.32 ascribed the extent of agreement between the barrier and diffusion models to the operating conditions. They suggested that the transfer mechanism of N2 and O2 in CMS is controlled by a barrier resistance, but in the range C/C0 ) 0.91.0, some pore diffusion resistance is present. Nguyen and Do33 proposed a dual Langmuir kinetic model, which considered nonselective adsorption in mesosupermicropores followed by selective movement of such adsorbed molecules into micropores through the pore mouth. Reid and Thomas35 investigated a series of planar and tetrahedral molecules on CMS and concluded that adsorption kinetics obeys a linear driving
10.1021/ie030206j CCC: $25.00 © 2003 American Chemical Society Published on Web 08/02/2003
4214 Ind. Eng. Chem. Res., Vol. 42, No. 18, 2003
Figure 1. Experimental apparatus.
force (LDF), combined barrier resistance/diffusion, or Fickian diffusion model depending on the adsorptive and experimental conditions. Huang et al.37 volumetrically measured the differential uptake of gases in CMS. Their results suggest that the transport is controlled by a combination of barrier resistance at the micropore mouth followed by an interior micropore resistance. In this research, we investigate the kinetics of N2 and O2 adsorption on CMS materials by a FR method. This builds on Sward and LeVan’s earlier work.23 In the configuration of their experimental apparatus, there existed a pressure drop in the system, which caused difficulty in extracting kinetic parameters at high frequencies because the pressure drop had a similar effect on the response as did mass transfer in the adsorbent. Construction of a new apparatus is reported here for which the undesirable pressure drop is no longer present. The effects of different pressures and particle sizes on mass transfer rates are studied. Micropore diffusion (MD), LDF, and combined resistance models are used to describe the experimental data. Additionally, we adopt a distribution of rates for the LDF model.
Figure 2. Block diagram of the FR system.
the mass flowmeter, is the response variable for pressure perturbation. We define the following deviation variables to simplify the material balance:
n′ ) n - n0
(2)
P′ ) P - P0
(3)
F′ ) Fout - Fin
(4)
Theory Consider flow through an adsorption bed subjected to a sinusoidal pressure perturbation of frequency ω and amplitude ∆P. The flow-rate response in the periodic state is also a sinusoidal wave with the same frequency but a different amplitude ∆F. The amplitude ratio (∆F/ ∆P) and phase shift (φ) of the response wave relative to the input are used to extract mass-transfer rates from models. The temperature in the system is assumed to be constant; this assumption will be analyzed in detail in the Discussion section. The perturbations in pressure are kept small (
