New development in flow‐through pressure‐swing frequency response method for mass‐transfer study: Ethane in ZIF‐8

Abstract

A new pressure‐swing frequency response (PSFR) method has been developed to study mass transfer in adsorption systems as a function of temperature and pressure, from −70 to 180°C, and up to 7 bar. New in‐phase and out‐of‐phase functions have been derived for the PSFR in a general way to allow information extracted from it independent of whether the system is operated in a batch volume swing or a flow‐through pressure swing mode. A new mathematical model that considers distribution of diffusion rates has been introduced to account for diffusive transport in heterogeneous samples. Numerical simulation results have shown that a single rate diffusion model works well when heterogeneity can be described by a normal distribution, but not for asymmetrically bimodal distributions. As a test reference system, the transport of ethane in ZIF‐8 was investigated at different pressures and temperatures using the new PSFR method. The mass transfer was found to be dominated by micropore diffusion. Diffusivity was found to be weakly dependent on pressure or loading, but quite strongly dependent on temperature. The results agree very well with our independent batch volume frequency response technique experiments. © 2016 American Institute of Chemical Engineers AIChE J, 63: 1077–1090, 2017

CO2 Capture in Metal–Organic Framework Adsorbents: An Engineering Perspective

“…In addition, the governing mass transfer mechanism can be further concluded by comparing the FR data with predictions from different mathematical models. [113] Recently, concentration swing FR (CSFR) has been applied to studying CO 2 diffusion in large Cu-BTC single crystals, revealing a micropore diffusion coefficient of 1.7 × 10 −9 m 2 s −1 with negligible dependence on CO 2 concentration from 0.1 to 10%. [87]…”

“…The analytic data from the perturbed parameter and responding parameter together with the frequency of perturbation can help to obtain gas diffusion data in the porous adsorbents. In addition, the governing mass transfer mechanism can be further concluded by comparing the FR data with predictions from different mathematical models . Recently, concentration swing FR (CSFR) has been applied to studying CO 2 diffusion in large Cu‐BTC single crystals, revealing a micropore diffusion coefficient of 1.7 × 10 −9 m 2 s −1 with negligible dependence on CO 2 concentration from 0.1 to 10% …”

Identification of mass transfer resistances in microporous materials using frequency response methods

“…Also, it has the advantage of minimizing measurement errors because of its periodic process and non-dependence on initial conditions. Thus, FR has proven to be very useful for characterizing the transport of gases in adsorbent materials, such as zeolites [3][4][5][6][7][8][9][10][11][12][13][14], carbons [15][16][17][18][19][20], silicas [21], metal organic frameworks (MOFs) [22][23][24], and catalysts [25][26][27][28][29][30].…”

“…Do [39,40], Sun [41][42][43][44][45][46][47], and Rees [48][49][50][51]) have continued to improve FR in terms of experimental setup and theoretical analysis. The typical FR experimental apparatus allows for diffusivity and adsorption measurements using perturbation frequencies between 0.05 and 10 Hz [21,52] while newer versions allow perturbation frequencies up to 100 Hz [24]. Bourdin et al [41,53,54] introduced a thermal FR method to better distinguish thermal transfer from mass transfer limitation through the measurement of both the temperature and pressure of an adsorbent sample subjected to volume modulation.…”

Nonlinear Frequency Response Analysis as a Tool for Identification of Adsorption Kinetics: Case Study—Pore‐Surface Diffusion Control

“…Reliable identification of relative dominancy of the individual resistances is still a challenging issue. In the literature, a number of methods for measuring diffusion coefficients in solid adsorbents have been reported: uptake rate [2,3], piezometric method [4], chromatographic method [5], infrared spectroscopy [6], vacuum temperature-programmed desorption (TPD) [7], electrochemical impedance spectroscopy (EIS) [8], combination of TPD and EIS [9], frequency response (FR) method [10][11][12][13][14][15], and temperature FR method [16].…”