New Frequency Response Method for Measuring Adsorption Rates via Pressure Modulation:  Application to Oxygen and Nitrogen in a Carbon Molecular Sieve

Wang, Yu; Sward, and Brian K.; LeVan, M. Douglas

doi:10.1021/ie030206j

Cited by 42 publications

(105 citation statements)

References 47 publications

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“…Numerical experiments in which random noise with 0.5% amplitude (relative to the steady-state concentration) was added to the simulated concentrations, were also performed. Although 0.5% noise amplitude might seem small, it is actually overestimated, keeping in mind that in the linear FR method the amplitudes of the input modulations are kept in the range from 1% (Song and Rees 1996) to 5% (Wang et al 2003;Wang and LeVan 2007).…”

Section: Numerical Experimentsmentioning

confidence: 99%

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Nonlinear FR-ZLC method for investigation of adsorption equilibrium and kinetics

Petkovska

2007

Adsorption

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A new method for investigation of adsorption equilibrium and kinetics, named Nonlinear Frequency Response-Zero Length Column (NFR-ZLC) method, is introduced. It combines the advantages of the Nonlinear FR method (the potential to identify a model corresponding to the most probable kinetic mechanism and to estimate the equilibrium and kinetic parameters of the identified model) and of the ZLC method (the potential to derive direct information about the processes on the particle level, by eliminating the influence of the adsorber). The frequency response functions of a ZLC system, up to the third order, and for three simple kinetic mechanisms (film resistance control, micropore diffusion control and pore-surface diffusion control) are derived and simulated. The procedure for estimation of the equilibrium and kinetic parameters is defined and illustrated based on numerical simulations. Nomenclature A input amplitudẽ a c first order coefficient of the Taylor series expansion of the isotherm relation q = ϕ(c) a q first order coefficient of the Taylor series expansion of the isotherm relation c = (q) B amplitude of the output harmonic b c second order coefficient of the Taylor series expansion of the isotherm relation q = ϕ(c) M. Petkovska ( ) q second order coefficient of the Taylor series expansion of the isotherm relation c = (q) C concentration in the fluid phase, mol/m 3 C i concentration in the fluid phase within the particle pores (pore-surface diffusion model), mol/m 3 c nondimensional concentration in the fluid phase c i nondimensional concentration in the fluid phase within the particle pores (pore-surface diffusion model) c c third order coefficient of the Taylor series expansion of the isotherm relation q = ϕ(c) c qthird order coefficient of the Taylor series expansion of the isotherm relation c = (q) D eff effective diffusion coefficient, m 2 /s D p pore diffusion coefficient, m 2 /s D s surface diffusion coefficient, m 2 /s D μ micropore diffusion coefficient, m 2 /s F FRF on the particle level G FRF on the column level k m mass transfer coefficient, 1/s Q concentration in the adsorbent particle, mol/m 3 q nondimensional concentration in the adsorbent particle Q i concentration in the solid phase (pore-surface diffusion model), mol/m 3 q i nondimensional concentration in the solid phase (pore-surface diffusion model) R particle half-dimension, m R μ microparticle half-dimension, m r particle spatial coordinate, m r μ microparticle spatial coordinate, m t time, s V volume of the ZLC bed, m 3 V volumetric flow-rate, m 3 /s W function defined in (49) 224 Adsorption (2008) 14: 223-239

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Section: Numerical Experimentsmentioning

confidence: 99%

“…∼1%, Rees 1996 or 2%, Grenier et al 1999 for reservoir volume modulations and <5% for pressure and concentration variations, Wang et al 2003;Wang and LeVan 2007). As a result, a single frequency transfer function is obtained and its characteristics are used for estimation of the kinetic parameters.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear FR-ZLC method for investigation of adsorption equilibrium and kinetics

Petkovska

2007

Adsorption

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“…The system is justifiably assumed to be isothermal (Wang et al, 2003). Perturbations in pressure are kept small (<5%) to ensure that the system is appropriately linearized.…”

Section: Theorymentioning

confidence: 99%

“…These models include micropore diffusion, surface barrier described by a LDF, distribution of LDF transfer rates, and a combined resistance model, which considers a surface barrier to exist at the opening of micropores and surface diffusion to occur inside the micropores. Details have been published in a previous paper (Wang et al, 2003) on pure-component systems. Based on the information from the pure system, N 2 and O 2 on CMS, the combined resistance model provides an excellent fit and is used to describe the mixture behavior.…”

Section: Theorymentioning

confidence: 99%

New Developments in Flow-Through Apparatus for Measurement of Adsorption Mass-Transfer Rates by Frequency Response Method

Wang

LeVan

2005

Adsorption

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A new flow-through 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 N 2 and O 2 gases in carbon molecular sieve are investigated for different pressures and particle sizes by this method. Also, this apparatus has been extended to measure data for mixtures at different compositions at atmospheric pressure and room temperature. This is the first application of the flow FR system for a mixture. A negative cross-term diffusivity is reported. It shows that for co-diffusion, the fast diffusing molecule O 2 is decelerated by the slow diffusing molecule N 2 , and the slower moving molecule N 2 is sped up by the faster moving O 2 . The main-term diffusivities agree with the pure component diffusivities.

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“…Due to some advantages in comparison to other classical methods, the FR method is used to study adsorption, not only theoretically, but also experimentally (Boniface and Ruthven 1985;Grzegorczyk and Carta 1997;Naphtali and Polinski 1963;Park et al 1998aPark et al , 1998bRees and Song 2000;Sward and LeVan 2003;Wang et al 2003). Although most adsorption systems are nonlinear, in almost all these investigations system linearity is assumed.…”

Section: Introductionmentioning

confidence: 99%

Theoretical investigation of the adsorption of a binary mixture in a chromatographic column using the nonlinear frequency response technique

2007

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The nonlinear frequency response of a chromatographic column for the adsorption of two dissolved components is analyzed using the concept of higher order frequency response functions (FRFs) which is based on the Volterra series and generalized Fourier transform. By applying this concept a nonlinear model of a system is replaced by an infinite series of the FRFs of the first, second, etc. order. The FRFs up to the third order are derived theoretically starting from the equilibrium-dispersive model, which is used for description of a chromatographic column, and applying the harmonic probing method. The functions that relate outlet concentration changes of each component to the corresponding inlet concentration changes are derived. At the inlet of a chromatographic column, it is considered: (a) the concentration change of one of the components keeping the concentration of the other component constant and (b) the concentration change of both components keeping their ratio constant. The FRFs are calculated numerically for different steady-state concentrations and relative mixture compositions. It has been found that, despite certain differences in initial conditions, the FRFs exhibit similar behavior. For higher frequencies, the amplitudes of the FRFs tend to zero and phases to −∞. In the low frequency range, which is A. Seidel-Morgenstern Otto von Guericke University, Chair of Chemical Process Engineering, Magdeburg, Germany of interest for investigation of equilibrium parameters, these functions have similar behavior, but tend to different asymptotic values. Correlations between coefficients of competitive adsorption isotherms, i.e. partial isotherm derivatives, and the derived FRFs are established. This theoretical result offers the potential to use the analysis of the nonlinear frequency response of a chromatographic column for estimation of competitive adsorption isotherms.Keywords Binary mixture · Competitive adsorption isotherm · Nonlinear frequency response · Higher order frequency response functions Abbreviations a ij

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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

Cited by 42 publications

References 47 publications

Nonlinear FR-ZLC method for investigation of adsorption equilibrium and kinetics

Nonlinear FR-ZLC method for investigation of adsorption equilibrium and kinetics

New Developments in Flow-Through Apparatus for Measurement of Adsorption Mass-Transfer Rates by Frequency Response Method

Theoretical investigation of the adsorption of a binary mixture in a chromatographic column using the nonlinear frequency response technique

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