Article pubs.acs.org/Langmuir
Mass Transfer and Adsorption Equilibrium for Low Volatility Alkanes in BPL Activated Carbon Yu Wang,† John J. Mahle,‡ Amanda M. B. Furtado,† T. Grant Glover,§ James H. Buchanan,‡ Gregory W. Peterson,‡ and M. Douglas LeVan*,† †
Department of Chemical and Biomolecular Engineering, Vanderbilt University, Nashville, Tennessee 37235, United States Edgewood Chemical Biological Center, U.S. Army, Aberdeen Proving Ground, Maryland 21010, United States § SAIC, Gunpowder, Maryland 21010, United States ‡
ABSTRACT: The structure of a molecule and its concentration can strongly influence diffusional properties for transport in nanoporous materials. We study mass transfer of alkanes in BPL activated carbon using the concentration-swing frequency response method, which can easily discriminate among mass transfer mechanisms. We measure concentration-dependent diffusion rates for n-hexane, n-octane, n-decane, 2,7-dimethyloctane, and cyclodecane, which have different carbon numbers and geometries: straight chain, branched chain, and cyclic. Micropore diffusion is determined to be the controlling mass transfer resistance except at low relative saturation for n-decane, where an external mass transfer resistance also becomes important, showing that the controlling mass transfer mechanism can change with system concentration. Micropore diffusion coefficients are found to be strongly concentration dependent. Adsorption isotherm slopes obtained from measured isotherms, the concentration-swing frequency response method, and a predictive method show reasonably good agreement.
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Cavalcante and Ruthven4 studied the diffusion of C6 alkane isomers, including several branched and cyclic molecules in silicalite with channels of 5.5−6 Å. Steric hindrance was observed with diffusivities decreasing substantially with an increase in the critical molecular diameter following the trend in magnitude of the diffusivity: linear single-branched > double(ternary C)branched > cyclic > double(quaternary C)-branched alkanes. Gorring8 performed uptake experiments for C2−C10 linear alkanes in zeolite T, an intergrowth of offretite and erionite, and reported an unexpected oscillatory trend in the variation of apparent diffusivity with carbon number, which he explained as a window effect based on the size of openings into zeolite cages. The diffusivities passed through a minimum at about C8 and a maximum at C12, corresponding to a limitation of adsorbate size relative to cage size. This behavior was critically re-examined by Ruthven,9 who suggested that the observed pattern of variation in uptake rates could be explained by accounting for isotherm nonlinearity and the intrusion of a heat transfer resistance. Because Gorring’s materials were not well characterized, lacking detailed information on the Si/Al ratio and proportions of offretite and erionite, Cavalcante et al.10 studied a series of nalkanes, from C6 to C20, in four different offretite−erionite intergrowths ranging from nearly pure offretite to nearly pure erionite. Except for one of the intermediate samples, the intracrystalline diffusivities showed a monotonic decrease with carbon number.
INTRODUCTION Activated carbon is the most commonly used of all adsorbents because of its low cost, high surface area, high micropore volume, low affinity for water vapor, and ability to adsorb a broad range of compounds, particularly molecules of low polarity. Carbons are made from various precursors, with coal, wood, coconut shells, and polymeric materials being the most common. The precursors are treated thermally and often chemically to yield microporous and graphitic regions. Applications typically involve purifications of gases and liquids, especially air and water, although many other uses exist. Mass transfer in adsorbents depends not only on the adsorbent and adsorbates constituting the system but also on operating conditions. The structure of an adsorbent affects the rate properties, and these impact the efficiency of an adsorption process. Compared to ordered adsorbents, such as zeolites, carbon nanotubes, and some of the mesoporous silicas, activated carbons as well as carbon molecular sieves, aluminas, and other silicas have largely amorphous structures, and their pore size distribution determines rate controlling mechanisms inside the adsorbents and the corresponding diffusional parameters that are useful for understanding and modeling system behavior. Most of the research on diffusion in adsorbents has focused on zeolites and related inorganic, crystalline materials and on carbon molecular sieves, which have pore openings sized during synthesis. The uniform structure of these materials is considered to provide shape-selective capabilities to separate adsorbates of different sizes and shapes, such as linear and branched alkanes. Many studies have been carried out on diffusion of hydrocarbons in zeolites,1−5 titanosilicates,6 and carbon molecular sieves7 to investigate steric effects for separation. © 2013 American Chemical Society
Received: December 13, 2012 Revised: January 23, 2013 Published: January 29, 2013 2935
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Figure 1. Adsorption equilibria apparatus with vapor concentrator.
Barrie et al.11 used a tapered element oscillating microbalance to measure uptake rates for n-hexane, n-heptane, n-octane, toluene, and p-xylene adsorbed on an ion-exchanged Y zeolite. By fitting their data, they found that intracrystalline diffusion is not the limiting factor affecting the overall rates of adsorption and desorption. Instead, the transport of molecules between the adsorbed and vapor phases at the edge of zeolite crystallites limited the transport step. The controlling surface barrier was not an external mass transfer resistance based on a difference of fluidphase concentrations, but rather a resistance based on adsorption and desorption rates at the crystallite boundaries. A collaborative study of n-alkane transport in zeolite 5A compared diffusion coefficients measured using two microscopic methods, neutron spin−echo and pulsed-field gradient nuclear magnetic resonance, and a macroscopic method, the zero length column (ZLC).12 Diffusivities of C3−C8 molecules were found to decrease regularly with carbon number, and there was good agreement between the microscopic and macroscopic methods. However, at higher carbon numbers the agreement between the different techniques was less satisfactory, with the microscopic methods showing that the monotonic decrease in diffusivity does not continue beyond C8, whereas the ZLC results indicated a continuing decline before leveling off at C13 at a much lower value. Mass transfer mechanisms and rates reported in the literature vary considerably for different systems. Adsorption equilibrium and kinetics of four octane isomers, n-octane, 2-methylheptane, 2,5-dimethylhexane, and 2,2,4-trimethylpentane, in a carbon molecular sieve have been studied by Laredo et al.13 They found that transport became faster for an increasing degree of branching in the diffusing molecule, and experimental data were described well by either a micropore or macropore diffusion
model. Diffusion is typically different for zeolites, which show molecular sieving effects for straight and branched hydrocarbons as the result of uniform crystalline structures.2,3,10 Silva and Rodrigues14 used gravimetric and ZLC techniques to study the adsorption and diffusion of n-pentane in helium or N2 in pellets of 5A zeolite at temperatures between 373 and 573 K. Experiments were carried out with the same pellet size but different crystal sizes, and the results were insensitive to crystal size variations. The controlling resistance was found to be macropore diffusion. The same ZLC technique was also used to study transport of hexane isomers in pellets of zeolite β with straight 12-membered rings of 6.6 × 6.7 Å2 and zigzag 12membered rings of 5.6 × 5.6 Å2.15 For hexane isomers with a smaller kinetic diameter, such as n-hexane and 3-methylpentane, macropore diffusion was determined to be the controlling resistance. The controlling mechanism changed to a combination of macropore and micropore diffusion for 2,3-dimethylbutane and 2,2-dimethylbutane. Other studies for alkane isomers on adsorbents with pore size less than 5 Å, such as ZSM and silicalite, show micropore diffusion dominating.4,16,12 Even for light gases, a study using the volume-swing frequency response method showed that macropore diffusion can be rate controlling for CO217 and for N2 and O218 in pellets of zeolites 5A and 13X. The purpose of this work is to determine mass transfer mechanisms and quantify rate parameters over a range of concentrations for alkane vapors adsorbed on BPL activated carbon, which is a popular bituminous coal-based adsorbent designed for vapor-phase applications. Our interest is in improving the basis for properly predicting the breakthrough and pulse behavior of various chemicals in adsorption beds. We consider the n-alkanes hexane, octane, and decane, as well as C10 hydrocarbons including branched and cyclic molecules. Mass 2936
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Figure 2. Concentration-swing frequency response apparatus for measurement of diffusion of condensable vapors. conducted under the same conditions as the adsorption equilibrium measurement. During adsorption equilibrium operation, a sample stream was directed to the bed through a switching valve. Temperature control of the sample was maintained by immersing the tube in a water bath. All vapor carrying lines were heat traced. The VC operated by first collecting the sample on the collection tube and then concentrating the sample on a focusing trap, which was rapidly heated to achieve improved chromatography. A 4 min collection time was used on the VC sample tube. Samples were prepared by placing adsorbent in a 2 mL screw-top sample vial. The tare weight of the empty vial and net weight with the adsorbent were determined. Next, an aliquot of adsorbate was injected on the wall of the vial, which was sealed, and the final weight was measured. The vials were then placed in an oven at 90 °C for 3 days. The adsorbent loading was confirmed by placing approximately 20 mg in an aluminum pan for thermal gravimetric analysis using a TA Instruments Model Q600 instrument ramped to 400 °C. The remainder of the sample was crushed and loaded into a tube of 3.8 mm inside diameter with a glass frit to retain the particles. The tube was filled to a height of 4 cm. The flow rate through the bed of activated carbon pre-equilibrated with adsorbed hydrocarbon was 100 sccm, of which 10 sccm was directed through the sample tube in the VC. These conditions had been shown previously to be sufficient to achieve equilibrium with low volatility vapors on activated carbon.19 Calibration and adsorption equilibria analysis procedures were automated. Mass Transfer Measurement. Our CSFR apparatus for measurement of mass transfer in adsorbents has been described in a previous paper.20 A schematic of the apparatus is shown in Figure 2. Sparger vessels were placed in a temperature-controlled water bath to generate a saturated vapor at subambient temperature. This vapor was then mixed with helium, with the temperature of the water bath and flow rates adjusted to create a dilute feed with a desired concentration. The feed concentration was perturbed by varying the flow rates of the adsorbable component in helium and the inert helium streams sinusoidally with the same amplitude but reversed in phase. The effluent from the adsorption bed was sampled using a quadrupole mass spectrometer. The amplitude ratio calculated as the amplitude of the mole fraction variation leaving the adsorption bed divided by that coming into the adsorption bed was used to extract mass transfer information. A small amount of adsorbent was used in the mass transfer experiments to eliminate axial dispersion effects and reduce thermal effects present in the system.21 All measurements were performed at room temperature, 23 ± 1 °C, and atmospheric pressure. The BPL activated carbon was regenerated at 250 °C under vacuum for 6 h. About 20 mg of the regenerated carbon was then placed in the CSFR system and regenerated again under vacuum with a trickle flow of helium for
transfer rate data are measured using a concentration-swing frequency response (CSFR) apparatus. Adsorption equilibrium data, which are needed in the analysis of the rate data, are measured via a combination of techniques to cover a wide range of pressures, from 0.0001 Pa to saturation at room temperature. Vapor pressures of some of the alkanes and the pore size distribution of the adsorbent are also measured. Experimental isotherm slopes are compared with values obtained using the CSFR method and predictions of a pore filling model.
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EXPERIMENTS
The adsorbent used in this study was BPL activated carbon (Lot No. 4814-J) from Calgon Carbon Corporation in 6 × 16 mesh granular form with particle size ranging from approximately 1.0 to 3.4 mm. Equilibrium Measurement. Adsorption equilibria were measured by combining several techniques to obtain full range isotherms. At low pressures, a vapor concentrator (VC) was used in conjunction with a volumetric method. The latter consisted of a measured ballast volume connected in series with a circulating pump and a Fourier transform infrared spectrophotometer equipped with a gas cell. Liquid samples were dosed to the volume using syringe injections. For higher pressures, volumetric and gravimetric methods were used. The gravimetric method employed a stop flow technique with a Cahn microbalance. The vapor concentration was established by saturating a gas stream by passage through a gas−liquid contactor. The VC method has been developed using purge-and-trap chromatography (PTC) combined with desorption of a pre-equlibrated low volatility vapor for determination of ultralow vapor-phase concentrations.19 The sample was first pre-equlibrated with adsorbate vapor and then placed in the PTC apparatus for desorption by flowing inert gas through it. The desorbed vapor mixture exiting the sample cell was delivered to the concentrator trap, and the adsorbate was collected and concentrated in the trap to allow analysis by gas chromatography. A schematic of the apparatus is shown in Figure 1. The VC unit was a Dynatherm Model ACEM 900 thermal desorption system, which was connected to an Agilent 6890 gas chromatograph (GC) with a FID detector and 7683B autosampler. Carrier gas flows from the GC to the VC. The VC has two modes, one to prep the sample tube where carrier gas flow bypasses the sample tube, and the second to desorb the collected contents of the sample tube to the carrier flow. A vacuum was used to draw sample flow to the VC tube. Excess clean flow was provided at the vent tee to eliminate the introduction of ambient contaminants. A system calibration was performed using liquid standards in hexane. Autosampler injections were directed to the VC so that calibration was 2937
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approximately 16 h prior to performing concentration-swing frequency response experiments.
created, and the model is then used to determine the controlling mechanism and rate parameters. Plots for different rate models have different structures for the dependence of amplitude ratio on frequency, and the magnitude of the dependence is sensitive to the rate parameters. The local slope K of the isotherm can be obtained from the model simultaneously with the rate parameters. In this study, values of K were extracted together with the rate parameters and compared with values obtained from the measured isotherms and a predictive model. Thermal effects in the CSFR system were found to be negligible when comparing results from isothermal and nonisothermal models. Concentrations of hydrocarbons were low in the experiments, and an inert gas flows through a small quantity of the adsorbent, which minimizes heat effects. Previous studies on heat effects justify the use of the isothermal models here for the CSFR system.20,21
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MATHEMATICAL MODEL A detailed mathematical model for this system has been described in previous papers.20−22 For our experiments, mass transfer within adsorbent particles was modeled by using a micropore diffusion (miD) model and a linear driving force (LDF) model. It should be noted that both micropore and macropore diffusion models, when linearized, have the same functional form, although parameters contained in them incorporate different variables. The importance of macropore diffusion for low volatility adsorbates is discussed below. For one adsorbed component and spherical geometry the micropore diffusion model can be expressed by
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1 ∂ ⎛⎜ 2 ∂n ⎞⎟ ∂n = 2 Ds r ∂t ∂r ⎠ r ∂r ⎝ n = n*
at
r = rs
∂n/∂r = 0
at
r=0
RESULTS AND DISCUSSION Two types of systems were studied for their adsorption on BPL activated carbon at room temperature. The normal alkanes, nhexane, n-octane, and n-decane were studied at partial pressures from 2.8 × 10−5 to 0.04 bar. The C10 alkanes, n-decane, branched 2,7-dimethyloctane, and cyclodecane, were studied at partial pressures from 2.8 × 10−5 to 7.7 × 10−4 bar. The experimental conditions are listed in Table 1.
(1)
where n is the adsorbate concentration in the nanopore, n* is the adsorbate concentration at the outer boundary of a microparticle (i.e., the external surface of a nanoporous domain), Ds is micropore diffusivity, t is time, r is the radial coordinate for the microparticle, and rs is the radius of the microparticle, which may or may not be the radius of the adsorbent particle, depending on the size of the micropore domain. This point is considered in detail below. The LDF model, which can be used to characterize barrier resistances,23 is dn = k(n* − n) dt
Table 1. Experimental Conditions for Adsorption of nAlkanes in BPL Activated Carbon adsorbate hexane octane decane
(2)
where k is the linear driving force coefficient and n* is the adsorbate concentration in an equilibrium state. External mass transfer was also included using the film coefficient model ρb
dn = k f a(c − cs*) dt
2,7-dimethyloctane cyclodecane
partial P (bar)
P/Ps (23 °C)
40,000 3,150 4,880 28 61 120 360 406 753 63
4.04 × 10−2 3.18 × 10−3 4.94 × 10−3 2.85 × 10−5 6.20 × 10−5 1.22 × 10−4 3.64 × 10−4 4.11 × 10−4 7.62 × 10−4 6.33 × 10−5
0.22 0.19 0.30 0.019 0.042 0.082 0.25 0.13 0.25 0.093
(3)
Textural Characterization. The activated carbon sample was characterized by measuring a N2 adsorption isotherm at 77 K using a Micromeritics ASAP 2020 porosimeter. Prior to measurement, 0.112 g of carbon was degassed with heating to 120 °C under vacuum until a pressure of 10 μbar was reached, at which time the sample was heated to 150 °C under vacuum for an additional 6 h. The ASAP 2020 instrument was used to backfill the sample with helium after degassing was complete. The sample was then transferred to the analysis port and heated at 150 °C for an additional 3 h with vacuum to 2 μbar to remove the backfilled helium from the pores. A single equilibrium point at 77 K was measured to determine the warm and cold free space values associated with the sample in the analysis tube. The sample was degassed again, transferred to the analysis port, and heated at 150 °C for 3 h with vacuum to remove the backfilled helium. A complete isotherm, shown in Figure 3, was measured on the carbon sample using UHP nitrogen at 77 K. The total pore volume measured to P/P0 = 0.994 is 0.56 cm3/g on the basis of the Horvath−Kawazoe method, and the BET surface area is 1005 m2/g. The N2 isotherm shows a hysteresis loop for relative pressures P/P0 greater than 0.4. For the mass transfer measurements performed in this study, all are at relative
where kf is the external mass transfer coefficient, c and cs* are the adsorbate concentrations in the bulk and at the fluid−pellet interface, and a is the specific external surface area of the adsorbent. In some cases, other factors impacting mass transfer were considered, including axial dispersion, a surface barrier at the pore openings of the microparticles, and heat effects. The corresponding models are described in detail elsewhere.21,22,24 Because the perturbation in concentration in the frequency response system is small, the isotherm can be linearized and written n* = nref + K (P − Pref )
conc (ppmv)
(4)
where K is the local slope of the isotherm. In the CSFR theory, a total transfer function for the system can be written for each rate model and combination of rate models. Detailed information on the CSFR model and the full equation set in the Laplace domain have been presented in our previous publications.21,22 The concentration of the adsorbable component is perturbed using a sine wave, and the resulting response of the system is characterized using the amplitude of the output. A plot of amplitude ratio (outlet over inlet) at specific frequencies is 2938
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Figure 3. N2 adsorption on BPL activated carbon: (a) adsorption isotherm at 77 K; (b) pore size distribution determined by DFT.
Figure 5. Frequency response plot for adsorption of octane in BPL activated carbon at various octane pressures.
pressures less than 0.3. A pore size distribution, shown in the inset of Figure 3, was obtained on the basis of density functional theory for slit-shaped pores using the instrument software. The majority of pores are in the range 5−25 Å. Vapor Pressure Measurement. Antoine coefficients for calculating the vapor pressures of normal alkanes were obtained from reference sources.25 However, vapor pressure information for cyclodecane was not available. Therefore, vapor pressures for the temperature ranges used in the experiments were measured using a modified ASTM gas saturation method. Detailed information on this apparatus can be found in a previous paper.26 Vapor pressures measured for solid and liquid phases were consistent. Data are plotted in Figure 4 along with a vapor
sine wave divided by amplitude of inlet concentration sine wave) plotted versus the frequency of the cycling. The data shown are for the diffusion and adsorption of octane in BPL activated carbon at partial pressures of 0.0031 and 0.0049 bar. Also, data for a control experiment, which gives the response of the system with nonadsorptive material (stainless steel beads), are plotted in the figure. At 0.0031 bar, the figure shows the comparison between the micropore diffusion (miD) model of eq 1 (solid curve) and the LDF model of eq 2 (dashed curve). It is obvious that the miD model is the proper one, as the curve for the LDF model has a shape that is inconsistent with the data. Therefore, the controlling mass transfer resistance for octane in activated carbon at these experimental conditions is micropore diffusion. A similar trend was found at a higher concentration, and only the miD model for octane at the higher partial pressure of 0.0049 bar is plotted in Figure 5. With the increase in pressure from 0.0031 to 0.0049 bar, the diffusion time constant Ds/r2s increases from 1.9 × 10−3/s to 2.3 × 10−3/s, and the slope of the isotherm decreases from 64 to 23 mol/(kg bar). Thus, at low loadings molecules associate preferentially with high energy sites, where adsorbate−adsorbent interactions are strong, and consequently, the molecules diffuse slowly. At higher loadings, more lower energy sites are occupied statistically, and the diffusivity increases. The CSFR technique, like other FR methods, can give very repeatable data, as these experiments are performed on a linearized system via a perturbation approach, and amplitude ratios are obtained from data measured over many cycles. Thus, the initial experimental condition or some noise in the data does not affect results significantly. Normally, the data are very repeatable, with agreement to within 5% for gas phase adsorption. However, a long time is needed to obtain steady cycling for very low volatility alkanes, and results for very fast and very slow frequencies are less accurate than those in the middle of the frequency range. We show some response curves in Figure 5 for changes in the mass transfer rate parameter of ±20%. We can easily differentiate among these curves to deduce the proper parameter. Mass transfer of n-decane in BPL activated carbon was considered at several concentrations. As shown in Figure 6, for the highest concentration of 360 ppmv, the data are described well by the miD model with Ds/r2s = 1.0 × 10−3/s. The mass transfer result for the next highest concentration of 120 ppmv is
Figure 4. Vapor pressures of cyclodecane and 2,7-dimethyloctane.
pressure curve based on Antoine coefficients obtained from the data. The vapor pressure of 2,7-dimethyloctane was also measured and is compared in the figure with a correlation of Yang and Yaws.27 Of the three C10 alkanes at 25 °C, cyclodecane has the lowest vapor pressure (68 Pa) of the three, followed by decane (148 Pa) and 2,7-dimethyloctane (310 Pa). Mass Transfer Rates for n-Alkanes. The determination of the mass transfer mechanism is illustrated in Figure 5, which shows the amplitude ratio (amplitude of outlet concentration 2939
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Figure 6. Frequency response plot for adsorption of decane in BPL activated carbon at 360 ppmv.
Figure 8. Frequency response plot for adsorption of decane in BPL activated carbon at 61 ppmv.
shown in Figure 7. The data are described reasonably well using the micropore diffusion model with Ds/r2s = 1.2 × 10−4/s. To
the intrusion of external mass transfer becomes more important at dilute conditions, as will be discussed later. To confirm this, we performed an experiment at an even lower concentration of 28 ppmv, as shown in Figure 9. Again, the data are best described
Figure 7. Frequency response plot for adsorption of decane in BPL activated carbon at 120 ppmv.
Figure 9. Frequency response plot for adsorption of decane in BPL activated carbon at 28 ppmv.
check whether other mass transfer mechanisms, specifically axial dispersion or an external mass transfer resistance, were important in the mass transfer process, combined resistance models were applied with these added. With the addition of an axial dispersion resistance, the description did not significantly improve the quality of the fit, which is almost the same as that for the pure micropore diffusion model. This implies that the bed is short enough to eliminate effects of axial dispersion. However, adding an external mass transfer resistance slightly improves the quality of fitting, suggesting the importance of this secondary mass transfer resistance at lower concentrations. For n-decane on BPL activated carbon at the lower concentration of 60 ppmv, we find that it is even more obvious that a pure micropore diffusion model alone cannot describe the data well, and neither does the LDF model, as shown in Figure 8. Instead, a combined resistance model of micropore diffusion and an external mass transfer resistance provides an excellent description, as shown by the solid curves in the figure. Thus,
with the two mass transfer steps, one resistance residing inside micropores and the other being the adsorbable component transferring to and from the adsorbent. The external mass transfer resistance coefficient is slightly smaller, 0.02 m/s compared to 0.03 m/s at 61 ppmv. We have also considered other mass transfer mechanisms to describe these data for n-decane at low concentrations. First, we evaluated the macropore diffusion model. However, when linearized, this model has the same mathematical form as the linearized micropore diffusion model, so it is not surprising that the macropore model cannot describe the data satisfactorily. Second, we considered the combined external mass transfer plus LDF model, and the data cannot be described well. This should also be expected, since both resistances are simple film-type differences and, when linearized, can be combined into a single LDF equation. Thus, adding the external mass transfer resistance to the LDF model does not improve the capability of the model. 2940
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Table 2. Experimental Results for Adsorption of n-Alkanes in BPL Activated Carbon adsorbate hexane octane decane
2,7-dimethyloctane cyclodecane a
conc (ppmv) 40,000 3,150 4,880 28 28a 61 120 360 406 753 63
K [mol/(kg bar)] 15 64 23 1950 1956 896 464 164 62 700
mass transfer mechanism
Ds/r2s (s−1)
kf (m/s)
est kf31 (m/s)
est kf32 (m/s)
0.017 0.012 0.03 0.02
0.036 0.063 0.033 0.035
0.018 0.024 0.014 0.014
−2
2.6 × 10 1.9 × 10−3 2.3 × 10−3 4.4 × 10−5 2.3 × 10−4 2.6 × 10−4 2.1 × 10−4 1.0 × 10−3 8.9 × 10−4 1.1 × 10−3 1.6 × 10−4
miD miD miD miD and ext film miD and ext film miD and ext film miD and ext film miD miD miD miD
Small particle size.
diffusion through it are more important for propane than for ethane, as propane is a larger molecule than ethane. Considering that the hydrocarbons studied in this paper are larger than propane, diffusion in the graphitic layer (i.e., micropore diffusion) can be dominant. The results of the mass transfer experiments are summarized in Table 2. Focusing on the results for decane, for comparison with experimentally determined values, external mass transfer coefficients were estimated in terms of the Sherwood number (Sh ≡ kfdp/Dij) and the Schmidt number (Sc ≡ ν/Dij) using the well-known correlations31
Finally, given the pore size distribution for the adsorbent as well as the variation in particle sizes, it seemed plausible that the data could be described accurately with a parallel micropore diffusion model, allowing for differences in diffusivity in micropores of different size or differences in rs. We developed a parallel diffusion model allowing for two values of Ds/r2s but found very little improvement over the model with a single value. In summary, combined micropore diffusion and external mass transfer describes experimental results for n-decane at low concentrations best. We also examined the dependence of diffusion rate on particle size. Activated carbon particles were crushed to obtain particles about half the size of the original ones. Other experimental conditions were kept the same. Results are compared in Figure 9. It is clear that the mass transfer mechanism is still combined micropore diffusion and external mass transfer. Considering that the particle size has changed by a factor of about 2, from a mean value for rs of about 2.2 mm to 1.1 mm, the micropore diffusivity obtained from the different particle sizes has a value of approximately 2.5 × 10−10 m2/s. Clearly, the appropriate diffusion length is the particle size, not some smaller microporous domain. The radius of the microparticle, rs, is the radius of the adsorbent particle in this paper. The isotherm slopes obtained from the CSFR data for the two experiments are the same, which is expected because the experimental pressure is the same. The result that the relevant microporous domain encompasses the entire particle is consistent with the structure of BPL activated carbon. This adsorbent is a bituminous coal-based product activated at high temperature in a steam atmosphere. As part of the manufacturing process, the coal is pulverized and reagglomerated using a carbonaceous binder. Activation of the resulting material creates micropores and mesopores, including within the binder, whereas macropores result from irregularities in the starting material.28 A common carbonaceous binder is petroleum pitch, which itself is a common starting material for the manufacture of activated carbons, as it produces controllable microporosity upon activation.29 Activated carbon is composed of many graphite-like microcrystalline structures with lengths on the order of 10 nm and graphite layers with spacings of 0.335 nm. The orientations of the microcrystalline units are random, which results in gaps between graphitic units that can accommodate molecules. Do30 suggests that diffusion in activated carbon can occur along two parallel paths. One is through the spaces between the graphitic units, and the other is through the graphitic units. Results obtained for ethane and propane on activated carbon show that the penetration into the graphitic layer and the
Sh = 2.0 + 1.1Re 0.6Sc 0.33
and
(5)
32
⎛ Re ⎞0.6 Sh = 1.15⎜ ⎟ Sc 0.33 ⎝ ϵ⎠
(6)
where dp is particle diameter, Dij is gas-phase molecular diffusion coefficient, ν is fluid kinematic viscosity, and Re is Reynolds number. The extracted kf from the experiments has a value similar to that estimated using the empirical correlations. The observation that the external mass transfer resistance becomes more important at low concentrations has been made in previous studies.33,34 For an adsorbable component of low volatility such as decane, as the vapor-phase concentration is decreased and prior to the attainment of a linear isotherm in the Henry’s law region, the isotherm slope increases, and the component is partitioned more and more in the adsorbed phase relative to the vapor phase. External mass transfer becomes more and more important in bringing the adsorbable component to the adsorbent, as micropore diffusion becomes relatively more efficient in transferring the adsorbate throughout the particle. Within a class of adsorbable components, as volatility decreases and less of the adsorbable component is present in the vapor phase relative to the adsorbed phase, it should be expected that external mass transfer becomes more important. Carried to the obvious extreme, for a largely nonvolatile component, although micropore diffusion persists, external mass transfer is unable to deliver the adsorbable component to the adsorbent at a reasonable rapid rate, and it becomes the dominant resistance. We have examined previously the adsorption of hexane on single granules of BPL activated carbon at several different concentrations using the CSFR method.20 We repeated an experiment at a partial pressure of 0.04 bar with more sample (0.0146 g), and the results agree with the previous study. The extracted diffusivity constant of Ds/r2s = 2.6 × 10−2/s compares well with the prior result of Ds/r2s = 2.3 × 10−2/s at this 2941
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concentration.20 Given the good agreement, our previous results for n-hexane are used to compare diffusivities with those for octane and decane, as shown in Figure 10. It is obvious that the
Mass Transfer Rates for C10 Alkanes. The adsorption of C10 hydrocarbons on BPL activated carbon was studied for ndecane, 2,7-dimethyloctane, and cyclodecane. Mass transfer rates were measured at a concentration of 63 ppmv for cyclodecane, as shown in Figure 11, and concentrations of 406 and 753 ppmv for
Figure 11. Frequency response plot for adsorption of cyclodecane in BPL activated carbon at 63 ppmv.
Figure 10. Comparison of diffusivities for alkanes as functions of (a) partial pressure and (b) relative saturation.
diffusion coefficients decrease with increasing carbon number for the n-alkanes at a given relative partial pressure P/Ps. Also, diffusion coefficients show a concentration dependence for these three n-alkanes. Diffusional behavior of the hydrocarbons can be considered relative to pore sizes. The cross-sectional dimensions of n-decane are 4.85 × 4.15 Å2,35 and the C−C bond length is 1.53 Å.36 The pore size distribution for BPL activated carbon covers a full range of 5−25 Å, as shown in the inset of Figure 3. Thus, these alkanes can diffuse easily in most micropores in the activated carbon with the molecule oriented lengthwise along the pore. However, the total length of the alkanes increases with carbon number from about 8 Å for n-hexane to 14 Å for n-decane. Thus, depending on the orientation of the alkanes in the micropores, longitudinally or perpendicularly, there can be limitations on the diffusion of the molecules. We observe an obvious trend for normal alkanes in BPL activated carbon, with the longer chain molecules having a lower diffusivity. This pattern is similar to that of the vapor pressure, which decreases with an increasing number of carbon atoms and gives normal boiling points for n-hexane, n-octane, and n-decane of 69, 126, and 174 °C, respectively.
Figure 12. Frequency response plot for adsorption of 2,7dimethyloctane in BPL activated carbon at 406 and 753 ppmv.
2,7-dimethyloctane, as shown in Figure 12. These experimental conditions were chosen to have either a similar concentration or a similar relative saturation P/Ps as compared to data for ndecane. Data for both systems can be described well with the miD model. For dimethyloctane at the lower concentration of 406 ppmv, the combined resistance model with an external mass transfer resistance gives a marginally better description. It is noteworthy that the external mass transfer resistance is not important for cyclodecane at 63 ppmv. The model description was not improved by adding the secondary external mass transfer resistance, which is not shown in the figure, whereas the external mass transfer resistance was important for n-decane at 61 ppmv. 2942
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presented in Figure 13. For loadings below approximately 1 mol/ kg at the sample collection conditions, the resolution of the gas
The diffusion time constants of the C10 hydrocarbons in BPL activated carbon are compared in relation to partial pressure P and relative pressure P/Ps in Figure 10. Decane has a slightly larger micropore diffusivity compared to cyclodecane at similar relative pressures and absolute pressures, which helps to reveal the external mass transfer resistance for decane. Decane and 2,7dimethyloctane have similar diffusivities at similar absolute and relative pressures. There is no clear evidence for the diffusivities to change appreciably solely on the basis of molecular geometry for the C10 alkanes. Although the overall molecular volumes are similar for these hydrocarbons, the dimensions are quite different in terms of length and cross-sectional area. Decane is the longest but has the smallest cross section, cyclodecane has the shortest length but largest cross section, and 2,7-dimethyloctane is in between. Because BPL activated carbon has micropores mostly greater than 7 Å and larger in size, these alkanes can all diffuse with similar rates. Figure 10a shows an important trend for all of the alkanes considered. When viewed in their entirety, the data for the group of alkanes show a generally increasing trend of micropore diffusivity with partial pressure. This observation is based on the experimental results; in theory, the diffusivities of the various alkanes at a given pressure would not be expected to agree exactly, as a shorter chain n-alkane would be expected to diffuse faster than a longer chain n-alkane. When the micropore diffusion parameter is plotted versus relative saturation, as shown in Figure 10b, trends are less apparent. Given that micropore diffusion depends on adsorbate−adsorbent thermodynamic properties, the lower excluded molecular area37 of hexane is consistent with its larger micropore diffusion coefficient. In this research, we have considered micropore diffusion and not macropore diffusion to be the controlling mass transfer mechanism within particles. This is based on several factors. First, the adsorbates considered are of low volatility and are partitioned strongly into the adsorbed phase in comparison to the gas phase. The gas-phase gradients for macropore diffusion are much weaker than adsorbed-phase gradients for micropore diffusion. For macropore and micropore resistances in parallel, the macropore gradients will be of little significance. Second, in the analysis of data, we find that the external mass transfer resistance becomes more important at lower concentrations and that the magnitude of the external mass transfer coefficient agrees with the value predicted by correlations. If mass transfer were to be dominated by the macropore resistance, the magnitude of this residence would scale with the magnitude of the external mass transfer resistance, because both are based on gas-phase gradients. We would not expect to see a change in the relative importance of the two resistances as concentration changes. In other words, at low partial pressures of decane, we would not expect to find the appearance of a secondary resistance. Third, in attempting to describe the data using a macropore resistance instead of a micropore resistance, results were inconsistent, with no patterns apparent, and the macropore diffusion coefficients extracted from the frequency response experiments were generally larger than gas-phase binary diffusion coefficients, which is unreasonable. Fourth, in considering the possibility of micropore and macropore resistances in series, we found that the macropore diffusion parameter (Dpore/r2s ) was roughly constant and not dependent on particle size. Thus, we do not consider macropore diffusion to be a controlling mass transfer resistance in this study of low volatility alkanes. Adsorption Equilibria. Data for adsorption equilibria of ndecane, 2,7-dimethyloctane, and cyclodecane at 25 °C are
Figure 13. Isotherms for n-decane, 2,7-dimethyloctane, and cyclodecane on BPL carbon at 25 °C. Data measured using VC method except as noted. Solid curves are plots of the modified DR equation.
chromatograph was reached. At low loadings, the volume adsorbed is similar for each of the C10 alkanes. However, at higher loadings the volume adsorbed increases at a given relative pressure, with cyclodecane showing the highest loadings. This suggests that in larger pores there is increased packing efficiency for cyclodecane, which is preferentially adsorbed compared to 2,7-dimethyloctane and n-decane. Given the experimental difficulties in measuring isotherms for low volatility compounds, predictive methods are especially useful in providing a comparative basis. A method based on a modified form of the Dubinin−Radushkevich (DR) equation has been developed using a large data set to predict adsorption isotherms for organic compounds adsorbed on BPL activated carbon based on the physical properties of the adsorbate. The model equations from which n(P) or P(n) can be easily estimated are given by38 ⎛ nkvVb ⎞ ⎛ ϵ ⎞2 ln⎜ ⎟ = −⎜ ⎟ ⎝ V0 ⎠ ⎝ βE 0 ⎠
(7)
ϵ = RT ln(Ps/P)
(8)
β = (Vb/Vb , ref )0.69
(9)
kv = 1 + 0.049[(Vb/Vb , ref )−2.62 − 1]
(10)
where Vb is the molar volume of the adsorbate as liquid at its normal boiling point. The reference compound is n-hexane. Values of micropore volume, characteristic energy of the reference, and molar volume of the reference at its normal boiling point are V0 = 473.2 cm3/kg, E0 = 23.880 J/mol, and Vb,ref = Vb, hex = 139.9 cm3/mol. Isotherm slopes can also be extracted from the CSFR experimental mass transfer rate data for comparison. The isotherm slopes are local information which are linearized around the small perturbation at the particular experiment 2943
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conditions as given by eq 4. The extracted isotherm slopes are compared with the values from the modified DR predictions and isotherm measurements in Figure 14. Extracted values for
Figure 15. Plot of micropore diffusivity for hydrocarbons vs thermodynamic factor.
decane and the other C10 isomers, which indicates that corrected diffusivity has a strong relationship with carbon number.
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CONCLUSIONS Rate behavior for adsorption of C6 to C10 alkanes in BPL activated carbon has been studied using a concentration-swing frequency response apparatus. The method is sensitive to various mass transfer mechanisms and can show changes in mechanism with operating conditions. We also measured the pore size distribution of the adsorbent, vapor pressures of one of the alkanes, and adsorption isotherms. The hydrocarbons were considered in two groupings: three n-alkanes (n-hexane, noctane, and n-decane) and three C10 alkanes with different structures (n-decane, 2,7-dimethyloctane, and cyclodecane). The rate controlling mass transfer mechanism was found to be primarily micropore diffusion. Uptake was faster for small particles, which showed quantitatively that the characteristic length for diffusion of low volatility alkanes in BPL activated carbon is particle size rather than the size of smaller microporous subdomains. At low concentrations, n-decane showed a secondary external mass transfer resistance. The diffusivity of the hydrocarbons increased with concentration and decreased with an increase in carbon number. The n-alkanes have the same cross-sectional dimension, which is smaller than the predominant pore sizes in BPL activated carbon. No clear steric effect was observed for the C10 hydrocarbons with different geometries, as BPL activated carbon has a wide pore size distribution and does not provide a molecular sieving effect for molecules of the sizes considered. Adsorption equilibrium, measured different ways, was compared with isotherm information extracted from the CSFR measurements as well as a predictive model, and reasonably good agreement was obtained.
Figure 14. Comparison of isotherm slopes determined by direct isotherm measurements, CSFR experiments, and DR model predictions.
isotherm slopes tend to vary much more than isotherm loadings, as they are derivative properties. Examination of the cyclodecane isotherms shows that there is a large difference in the local isotherm slopes, even though the isotherm loadings at 63 ppmv only change by 1% for a 5% concentration change. Also, different isotherm models applied to the same data will give a range of values for a predicted loading and an even wider range of values for the isotherm slope. It has been previously shown that CSFR can be used to obtain accurate isotherm slopes for chloroethane adsorbed on BPL activated carbon.21 The isotherm slopes in this work are also in reasonably good agreement based on the three methods used. The Darken relation can be applied to the mass transfer rate data in an attempt to describe theoretically and quantitatively the concentration dependences of the measured micropore diffusion coefficients. This relation is of the form D = D0 Γ, where D0 is the corrected diffusivity and Γ = d ln P/d ln n is the thermodynamic factor. The result is shown in Figure 15, where Γ was calculated using the modified DR equation. The data points can be extended to give D0, the corrected diffusivity, when Γ approaches unity. It is clear that D0 for hexane is much larger than D0 for
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AUTHOR INFORMATION
Corresponding Author
*Full address: Vanderbilt University, VU Station B 351604, Nashville, TN 37235, USA. Tel.: (615) 343-1672. Fax: (615) 343-7951. E-mail:
[email protected]. 2944
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Notes
(GB) on Activated Carbon at Ultralow Relative Pressures. Langmuir 1999, 15, 6343−6345. (20) Glover, T. G.; Wang, Y.; LeVan, M. D. Diffusion of Condensable Vapors in Single Adsorbent Particles Measured via ConcentrationSwing Frequency Response. Langmuir 2009, 24, 13406−13413. (21) Wang, Y.; LeVan, M. D. Nanopore Diffusion Rates for Adsorption Determined by Pressure-Swing and Concentration-Swing Frequency Response and Comparison with Darken’s Equation. Ind. Eng. Chem. Res. 2008, 47, 3121−3128. (22) Wang, Y.; LeVan, M. D. Mixture Diffusion in Nanoporous Adsorbents: Development of Fickian Flux Relationship and Concentration-Swing Frequency Response Method. Ind. Eng. Chem. Res. 2007, 46, 2141−2154. (23) Karger, J.; Ruthven, D. M. Diffusion in Zeolites and Other Microporous Solids; Wiley and Sons: New York, 1992. (24) Wang, Y.; LeVan, M. D. Master Curves for Mass Transfer in Bidisperse Adsorbents for Pressure-Swing and Volume-Swing Frequency Response Methods. AIChE J. 2011, 57, 2054−2065. (25) Carruthl, G. F.; Kobayashi, R. Vapor Pressure of Normal Paraffins Ethane through n-Decane from their Triple Points to about 10 mm Hg. J. Chem. Eng. Data 1973, 18, 115−126. (26) Buchanan, J. H.; Buettner, L. C.; Tevault, D. E. The Vapor Pressure of Solid Bis(2-Chloroethyl) Sulfide. J. Chem. Eng. Data 2006, 51, 1331−1334. (27) Yang, H.-C.; Yaws, C. L. To Estimate Vapor Pressure Easily. Hydrocarbon Processing 1989, 68, 65−68. (28) McCabe, W. L. Manufacture of Activated Charcoal. In Summary Technical Report of Division 10; National Defense Research Committee: Washington, DC, 1946; Vol. 1, Chapter 3, pp 27−28. (29) Daguerre, E.; Guillot, A.; Py, X. Microporosity of Activated Carbons Produced from Heat-Treated and Fractionated Pitches. Carbon 2000, 38, 59−64. (30) Do, D. D. A Model for Surface Diffusion of Ethane and Propane in Activated Carbon. Chem. Eng. Sci. 1996, 51, 4145−4158. (31) Wakao, N.; Funazkri, T. Effect of Fluid Dispersion Coefficients on Particle-to-Fluid Mass Transfer Coefficients in Packed Beds. Chem. Eng. Sci. 1978, 33, 1375−1384. (32) Carberry, J. J. A Boundary-Layer Model of Fluid-Particle Mass Transfer in Fixed Beds. AIChE J. 1960, 6, 460−463. (33) Tereck, C. D.; Kovach, D. S.; LeVan, M. D. Constant-Pattern Behavior for Adsorption on the Wall of a Cylindrical Channel. Ind. Eng. Chem. Res. 1987, 26, 1222−1227. (34) Glover, T. G.; LeVan, M. D. Sensitivity Analysis of Adsorption Bed Behavior: Examination of Pulse Inputs and Layered-Bed Optimization. Chem. Eng. Sci. 2008, 63, 2086−2098. (35) Pazzona, F. G.; Borah, B. J.; Demontis, P.; Suffritti, G. B.; Yashonath, S. A Comparative Molecular Dynamics Study of Diffusion of n-Decane and 3-Methyl Pentane in Y Zeolite. J. Chem. Sci. 2009, 121, 921−927. (36) van Buuren, A. R.; Marrink, S.-J.; Berendsen, H. J. C. A Molecular Dynamics Study of the Decane/Water Interface. J. Phys. Chem. 1993, 97, 9206−9212. (37) Webster, C. E.; Drago, R. S.; Zerner, M. C. Molecular Dimensions of Adsorptives. J. Am. Chem. Soc. 1998, 120, 5509−5516. (38) Ye, X.; Qi, N.; Ding, Y.; LeVan, M. D. Prediction of Adsorption Equilibrium Using a Modified D-R Equation: Pure Organic Compounds on BPL Carbon. Carbon 2003, 41, 681−686.
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We are grateful to the U.S. Army ECBC and the Defense Threat Reduction Agency (DTRA) for the support of this research. REFERENCES
(1) Denayer, J. F.; Souverijns, W.; Jacobs, P. A.; Martens, J. A.; Baron, G. V. High-Temperature Low-Pressure Adsorption of Branched C5-C8 Alkanes on Zeolite Beta, ZSM-5, ZSM-22, Zeolite Y, and Mordenite. J. Phys. Chem. B. 1998, 102, 4588−4597. (2) Huddersman, K.; Klimczyk, M. Separation of Hexane Isomers on Zeolites Mordenite and Beta. J. Chem. Soc., Faraday Trans. 1996, 92, 143−147. (3) Huddersman, K.; Klimczyk, M. Separation of Branched Hexane Isomers using Zeolite Molecular Sieves. AIChE J. 1996, 42, 405−408. (4) Cavalcante, C. L.; Ruthven, D. M. Adsorption of Branched and Cyclic Paraffins in Silicalite. 2. Kinetics. Ind. Eng. Chem. Res. 1995, 34, 185−191. (5) Yonli, A.; Bouillault, N.; Batonneau, I. G.; Mignard, S. Separation of Monobranched and Dibranched Isomers of n-Hexane on Zeolitic Molecular Sieves: A Thermodynamic Study. J. Phys. Chem. B 2010, 114, 4465−4470. (6) Anson, A.; Lin, C. C. H.; Kuznick, T. M.; Kuznicki, S. M. Separation of Ethylene/Ethane Mixtures by Adsorption on Small-Pored Titanosilicate Molecular Sieves. Chem. Eng. Sci. 2010, 65, 807−811. (7) Suda, H.; Haraya, K. Alkene/Alkane Permselectivities of a Carbon Molecular Sieve Membrane. Chem. Commun. 1997, 1997, 93−94. (8) Gorring, R. L. Diffusion of Normal Paraffins in Zeolite T: Occurrence of Window Effect. J. Catal. 1973, 31, 13−26. (9) Ruthven, D. M. The Window Effect in Zeolitic Diffusion. Microporous Mesoporous Mater. 2006, 96, 262−269. (10) Cavalcante, C. L.; Eic, M.; Ruthven, D. M.; Occelli, M. L. Diffusion of n-Paraffins in Offretite-Erionite Type Zeolites. Zeolites 1995, 15, 293−307. (11) Barrie, P. J.; Lee, C. K.; Gladden, L. F. Adsorption and Desorption Kinetics of Hydrocarbons in FCC Catalysts Studied Using a Tapered Element Oscillating Microbalance (TEOM). Part 2: Numerical Simulations. Chem. Eng. Sci. 2004, 59, 1139−1151. (12) Jobic, H.; Karger, J.; Krause, C.; Brandani, S.; Gunadi, A.; Methivier, A.; Ehlers, G.; Farago, B.; Haeussler, W.; Ruthven, D. M.; Occelli, M. L. Diffusivities of n-Alkanes in 5A Zeolite Measured by Neutron Spin Echo, Pulsed-Field Gradient NMR, and Zero Length Column Techniques. Adsorption 2005, 11, 403−407. (13) Laredo, G. C.; Meneses, E.; Castillo, J.; Marroquin, J. O.; JimenezCruz, F. Adsorption Equilibrium and Kinetics of Branched Octane Isomers on a Polyvinylidene Chloride-Based Carbon Molecular Sieve. Energy Fuels 2008, 22, 2641−2648. (14) Silva, J. A. C.; Rodrigues, A. E. Sorption and Diffusion of nPentane in Pellets of 5A Zeolite. Ind. Eng. Chem. Res. 1997, 36, 493−500. (15) Barcia, P. S.; Silva, J. A. C.; Rodrigues, A. E. Adsorption Equilibrium and Kinetics of Branched Hexane Isomers in Pellets of BETA Zeolite. Microporous Mesoporous Mater. 2005, 79, 145−163. (16) Jolimaitre, E.; Tayakout-Fayolle, M.; Jallut, C.; Ragil, K. Determination of Mass Transfer and Thermodynamic Properties of Branched Paraffins in Silicalite by Inverse Chromatography Technique. Ind. Eng. Chem. Res. 2001, 40, 914−926. (17) Onyestyak, G.; Shen, D. M.; Rees, L. V. C. Frequency-response Study of Micro- and Macro-pore Diffusion in Manufactured Zeolite Pellets. J. Chem. Soc., Faraday Trans. 1995, 91, 1399−1405. (18) Onyestyak, G.; Valyon, J.; Rees, L. V. C. The Sorption Dynamics for N2 and O2 in Zeolite Particles. In Molecular Sieves: From Basic Research to Industrial Applications; Cejka, J., Zilkova, N., Nachtigall, Eds.; Studies in Surface Science and Catalysis Vol. 158; Elsevier, B. V.: 2005; pp 1019−1026. (19) Karwacki, C. J.; Tevault, D. E.; Mahle, J. J.; Buchanan, J. H.; Buettner, L. C. Adsorption Equilibria of Isopropyl Methylphosphonate 2945
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