Micropore Diffusion Coefficients Research Articles

Frequency Response Method for Diffusivity Characterization of Propane in HZSM-5

Transient uptake curves for propane gas in a bed of HZSM-5 using a volumetric frequency response setup (batch system) were obtained. Thereby, a perturbation, such as a change in volume, was applied to the solid/gas system, and the resulting change in pressure was detected. Two cases of mass transfer limitations (bed diffusion control and micropore diffusion control) were compared, and it was concluded that, in the presented case, micropore diffusion is the rate-determining process. The obtained micropore diffusion coefficient for propane in HZSM-5 was, on average, about 1.2 × 10−10 m2 g−1, which is in good agreement with other frequency response studies shown by literature data. The homemade setup and the modeling presented in this work serve as the basis for ongoing numerical simulations.

Quantification of the asynchronous gas diffusivity in macro-/micropores using a Nelder-Mead simplex algorithm and its application on predicting desorption-based indexes

Accurate and intelligent calculation of diffusion coefficient not only helps reduce greenhouse gas emissions, but also conduces to CO2 geological storage and CH4 displacement in coal seams. In this study, a kind of object-oriented software for conveniently and quickly obtaining bidisperse (i.e., macro-pore and micro-pore) diffusion coefficients and grasping main controlling factors of macroscopic desorption curves was designed based on the Nelder-Mead simplex algorithm. Furthermore, the gas desorption characteristics under different pressures were analyzed by performing conventional desorption experiments. The results show that the apparent diffusion coefficient obtained by the bulk technique displays three different trends as the pressure rises, namely a rising, falling and constant diffusion coefficient respectively. The three variation trends mainly result from the difference in deformation caused by adsorption swelling and mechanical compression. As desorption continues, the gas diffusion coefficient values in the macro-pores and micro-pores fluctuate for a short time, but increase in the long term. This is because the early stage corresponds to intense mechanical expansion and a flow boundary effect, while the later stage corresponds to an increasingly intense effect of desorption-induced shrinkage. Moreover, the time-dependent contribution law of macro-pore diffusion and micro-pore diffusion affects the reliability of outburst risk index, making △h2 more stable than K1. The conclusions provide theoretical guidance for the selection of rational gas drainage methods for diffusion-controlled coal seams.

On the development of an innovative adsorber plate heat exchanger for adsorption heat transformation processes; an experimental and numerical study

Abstract An innovative adsorber plate heat exchanger (APHE), which is developed for application in adsorption heat pumps, chillers and thermal energy storage systems, is introduced. A test frame has been constructed as a representative segment of the introduced APHE for applying loose grains of AQSOA-Z02. Adsorption kinetic measurements have been carried out in a volumetric large-temperature-jump setup under typical operating conditions of adsorption processes. A transient 2-D model is developed for the tested sample inside the setup. The measured temporal uptake variations with time have been fed to the model, through which a micro-pore diffusion coefficient at infinite temperature of 2 E−4 [m2s−1] and an activation energy of 42.1 [kJ mol−1] have been estimated. A 3-D model is developed to simulate the combined heat and mass transfer inside the APHE and implemented in a commercial software. Comparing the obtained results with the literature values for an extruded aluminium adsorber heat exchanger coated with a 500 μm layer of the same adsorbent, the differential water uptake obtained after 300 s of adsorption (8.2 g/100 g) implies a sound enhancement of 310%. This result proves the great potential of the introduced APHE to remarkably enhance the performance of adsorption heat transformation appliances.

Experimental study on the effect of inherent moisture on hard coal adsorption–desorption characteristics

Coal is a complex geological body that is composed of organic material, gas, and water. Generally, coal with high hardness is commonly considered to be a non-outburst risk; however, several coal mines with hard coal seams in China have experienced coal and gas outbursts. Coals with different degrees of metamorphism have different inherent moisture ranges, which has a strong influence on gas adsorption and desorption. Currently, inhomogeneous moisture wetting remains an issue in traditional preparation methods for preparing coal samples with different moisture levels. In this paper, we chose three typical hard coals with different degrees of metamorphism and systematically studied their pore structure characteristics, effect of approximate inherent moisture on the gas adsorption–desorption characteristics, and gas diffusion of hard coals. The results show that all of the coal samples have an open pore structure, but each coal sample has different development characteristics of their pore structure. The higher the moisture, the shorter the adsorption equilibrium time required and the lower pressure drop. All of the adsorption isotherm curves fit the Langmuir equation well. The gas adsorption capacity of the same coal sample decreases gradually and the amplitude of the gas adsorption capacity decreases with increasing moisture. This relationship indicates that the existence of moisture occupies a certain space of the pore structure and reduces the gas adsorption sites of coal, reducing the adsorption and desorption amount of the coal samples. Moreover, low and middle rank coal can use the bidisperse model to calculate the diffusion coefficient, while high rank coal can use the unipore model. Increasing moisture causes the macropore diffusion coefficient D a,e and micropore diffusion coefficient D i,e of the YZG and YJ samples to decrease. The effective diffusion coefficient D e of the WLH samples also reduced gradually, which suggests that moisture has an influence on the gas migration and diffusion channels of coal, reducing the gas adsorption equilibrium time, desorption rate, and diffusion rate of coal seam.

Determining the diffusion coefficient of gas diffusion in coal: Development of numerical solution

Determining gas diffusion coefficient from experimental data is a key step of reproducing and predicting the diffusion process in coal. Previously analytical solution, including the unipore diffusion model and the bidisperse diffusion model, has been used extensively to estimate the gas diffusion coefficient(s) in coal. The utilization of analytical solution is convenient, however, there are some defects which may affect the accuracy of the results. For example, it is not suitable for fitting manometric sorption data, and the assumption of linear adsorption isotherm is not true.In this paper, we present a numerical solution to determine the gas diffusion coefficients. Three models were developed based on different assumptions of pore system and diffusion forms, i.e., unipore model assuming one kind of pore and diffusion, bidisperse model I (BM I) assuming independent macropore diffusion and micropore diffusion, bidisperse model II (BM II) assuming dependent macropore diffusion and micropore diffusion. Nitrogen diffusion experiment was conducted and the adsorption isotherm was measured. Sphere geometry was built for numerical simulation and the proposed models were used to fit the experimental data to determine the diffusion coefficients. Results show that neither the analytical unipore model nor the numerical unipore model can describe the diffusion process perfectly. By giving the same diffusion coefficient, the modelled fractional uptake ratio of numerical unipore model is smaller than the result of analytical unipore modeling at early stage while greater at later stage, which is due to the different assumptions of adsorption isotherm. Both BM I and BM II can describe the diffusion process well. The determined macropore diffusion coefficients of the two models are similar, while the micropore diffusion coefficient and the macropore adsorption ratio of BM II are greater than that of BM I. These can be explained by the different roles of the macropore diffusion in the two models. The gas pressure change at the center of the coal sphere was examined, from the modeling result of BM I, the macropore pressure increases sharply and then drops along with the external gas pressure, while the initial increasing rate of macropore pressure of BM II is much smaller and tends to be stable at later stage. No apparent impacts of initial gas pressures on diffusion coefficients can be observed, the change of diffusion coefficients and macropore adsorption ratio are actually small with increasing gas pressure.The numerical solution of determining gas diffusion coefficients can easily relax the assumptions and restrictions of the analytical solution. It can be used to test different kinds of coal samples, investigate different diffusion mechanisms and match all kinds of experimental data. The measured sorption isotherm and coal properties can also be incorporated into the modeling, which makes the determined diffusion coefficients more reliable. This paper is a preliminary attempt and we hope it can bring the researchers some new ideas about studying the gas diffusion characteristics in coal.

Diffusion of CO2 in Large Crystals of Cu-BTC MOF.

Carbon dioxide adsorption in metal-organic frameworks has been widely studied for applications in carbon capture and sequestration. A critical component that has been largely overlooked is the measurement of diffusion rates. This paper describes a new reproducible procedure to synthesize millimeter-scale Cu-BTC single crystals using concentrated reactants and an acetic acid modulator. Microscopic images, X-ray diffraction patterns, Brunauer-Emmett-Teller surface areas, and thermogravimetric analysis results all confirm the high quality of these Cu-BTC single crystals. The large crystal size aids in the accurate measurement of micropore diffusion coefficients. Concentration-swing frequency response performed at varying gas-phase concentrations gives diffusion coefficients that show very little dependence on the loading up to pressures of 0.1 bar. The measured micropore diffusion coefficient for CO2 in Cu-BTC is 1.7 × 10(-9) m(2)/s.

Adsorption of NO in clinoptilolite-rich zeolitic mineral by concentration pulse chromatography method

The equilibrium and kinetic parameters for NO adsorption in a clinoptilolite-rich natural zeolitic material from Turkey were determined using the concentration pulse chromatography method. Under the experimental conditions (carrier gas velocities and adsorption temperatures) the micropore diffusion resistance was found to be the mass transfer controlling step. Matching the first moment of the response peaks to the mathematical model the Henry’s Law constants and heat of adsorption at zero loading were determined. The axial dispersion, external film, macropore and micropore diffusion coefficients, and activation energy for diffusion of NO in the micropores were calculated from the analysis of the second moments of the response peaks. For successive NO pulses without regeneration between the pulses, the retention times of the response peaks decreased and peak areas increased with the injection number indicating irreversible adsorption. The reversibly adsorbed NO could be desorbed by purging with an inert gas at the adsorption pressure and temperature. Temperature programmed desorption profile obtained by heating the NO saturated adsorbent to 400 °C under inert flow revealed presence of multiple irreversibly adsorbed species in NZ with different thermal stabilities. Desorption of these species was not achieved during the heating up to 400 °C which makes the natural zeolitic materıal suitable for NO storage rather than for cyclic adsorptive separation processes.

Laboratory and Modeling Study on Gas Diffusion with Pore Structures in Different-Rank Chinese Coals

The coalbed methane production rate is mainly controlled by two parameters: diffusivity in the coal matrix and permeability in the cleat system. As one key parameter, diffusion plays an important role in coalbed methane producing process. However, till now there is no systematic study on the relationship of diffusivity, pore size and coal ranks. In this work, three Chinese coal samples which belong to low, middle and high rank, respectively, were studied using experimental and modeling methods. Four gases, H2, N2, CH4 and CO2, are used to study the diffuse characters at four different pressures steps. The experimental results showed that the adsorption balance time varies with different testing gas type and it is closely related with coal rank. Balance time testing with CO2 is the longest, and then is CH4, while He is the slowest. Moreover, high rank coal takes the longest time to reach balance, while low rank coal takes the least. Generally, the sorption balance time for JCC-01 is about 150–350 S 0.5, it is about 250–400 S 0.5 for CZ-1, while it is about 900–1200 S 0.5 for JCC-01. Modeling results showed that for all these three ranked Chinese coals, the bidisperse model can be used to model the diffuse process. The β value, which is the ratio of macropore adsorption/desorption to the total adsorption/desorption, increases with the increasing of pore pressure, except for sample JCC-01 when measured using CO2. There is no regular law for both micropore and macropore diffusion coefficient. In order to study the relationship of diffusivity, pore structure and coal ranks, the experiments of mercury injection test and low-temperature liquid nitrogen experiment were done to analyse the relationship. The results show that, for the low rank coal sample TCG-1, the mesopore takes the majority while the macropore also takes part of the pore distribution, there are few even no micropore. For middle rank sample CZ-1, the mesopore also takes the majority and the macorpore accounts for a small percentage. While for high rank coal sample JCC-01, micropore takes the majority, and mesopore and macropore take small part of the pore structure distribution. The conclusion drawn from these testing results can be used to explain the adsorption and diffusion laws found before.

Investigation of the porous structure of cellulosic substrates through confocal laser scanning microscopy

At the most fundamental level, saccharification occurs when cell wall degrading enzymes (CWDEs) diffuse, bind to and react on readily accessible cellulose fibrils. Thus, the study of the diffusive behavior of solutes into and out of cellulosic substrates is important for understanding how biomass pore size distribution affects enzyme transport, binding, and catalysis. In this study, fluorescently labeled dextrans with molecular weights of 20, 70, and 150 kDa were used as probes to assess their diffusion into the porous structure of filter paper. Fluorescence microscopy with high numerical aperture objectives was used to generate high temporal and spatial resolution datasets of probe concentrations versus time. In addition, two diffusion models, including a simple transient diffusion and a pore grouping diffusion models, were developed. These models and the experimental datasets were used to investigate solute diffusion in macro- and micro-pores. Nonlinear least squares fitting of the datasets to the simple transient model yielded diffusion coefficient estimates that were inadequate for describing the initial fast diffusion and the later slow diffusion rates observed; on the other hand, nonlinear least squares fitting of the datasets to the pore grouping diffusion model yielded estimations of the micro-pore diffusion coefficient that described the inherently porous structure of plant-derived cellulose. In addition, modeling results show that on average 75% of the accessible pore volume is available for fast diffusion without any significant pore hindrance. The method developed can be applied to study the porous structure of plant-derived biomass and help assess the diffusion process for enzymes with known sizes.

Mass Transfer and Adsorption Equilibrium for Low Volatility Alkanes in BPL Activated Carbon

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.

Adsorption characteristics of acetone, chloroform and acetonitrile on sludge-derived adsorbent, commercial granular activated carbon and activated carbon fibers

The adsorption characteristics of chloroform, acetone, and acetonitrile on commercial activated carbon (C1), two types of activated carbon fibers (F1 and F2), and sludge adsorbent (S1) was investigated. The chloroform influent concentration ranged from 90 to 7800 ppm and the acetone concentration from 80 to 6900 ppm; the sequence of the adsorption capacity of chloroform and acetone on adsorbents was F2 > F1 ∼ C1 ∼ S1. The adsorption capacity of acetonitrile ranged from 4 to 100 mg/g, corresponding to the influent range from 43 to 2700 ppm for C1, S1, and F1. The acetonitrile adsorption capacity of F2 was ∼20% higher than that of the other adsorbents at temperatures <30 °C. The Freundlich equation fit the data better than the Langmuir and Dubinin–Radushkevich (D–R) equations. The adsorption rate of carbon fibers is higher than that of the other adsorbents due to their smaller fiber diameter and higher surface area. The micropore diffusion coefficient of VOC on activated carbon and sludge adsorbent was ∼10 −4 cm 2 s −1. The diffusion coefficient of VOC on carbon fibers ranged from 10 −8 to 10 −7 cm 2 s −1. The small carbon fiber pore size corresponds to a smaller diffusion coefficient.

Equilibrium and kinetic analysis of CO 2–N 2 adsorption separation by concentration pulse chromatography

CO 2 and N 2 adsorption kinetics and equilibrium behaviours have been studied with silicalite, NaY and 13X by using concentration pulse chromatography for the separation of these gases in the present study. Adsorption Henry's Law constants, the heat of adsorption values, micropore diffusion coefficients and corresponding activation energies are determined experimentally and the three different mass transfer mechanisms are discussed. From the equilibrium data, the corresponding separation factors are obtained for the adsorption separation processes. The heat of adsorption values as well as the Henry's Law adsorption equilibrium constants of CO 2 are much higher than those of N 2 for all the adsorbents studied. 13X, NaY and silicalite all have good separation factors for CO 2/N 2 system based on equilibrium processes. The order of the equilibrium separation factors is 13X (Ceca) > 13X (Zeochem) > NaY (UOP) ≫ silicalite (UOP). Equilibrium selectivity favours CO 2 over N 2. Micropore diffusion resistance is the definite dominant mass transfer mechanism for CO 2 with silicalite and NaY.

Non-isothermal adsorption kinetics of water vapour into a consolidated zeolite layer

A one-dimensional model for the kinetics of water vapour adsorption into a consolidated zeolite layer is presented. The combined heat and mass transfer problem is modelled and simulated using the software packet gPROMS ® (general PROcess Modelling System). The centered finite difference method approximation is employed in solving the obtained set of partial differential, ordinary differential and algebraic model equations. Mass transfer is described by micro-pore diffusion, while heat transfer is described in terms of conduction. The temperature dependence of the diffusion coefficient is defined by an Arrhenius relationship, whereas the concentration dependence is accounted for by the Darken factor. The validity of the developed model has been checked against an experimental study, in which the kinetics of water vapour adsorption into a consolidated zeolite layer has been investigated in a constant volume-variable pressure test rig. The starting pressure has been changed in the range of 10–30 mbar, while the wall temperature has been adjusted to 35 and 50 °C. The measured characteristic half time for the adsorption kinetics varies between 13 and 21 s, while the required time to reach 90% of the equilibrium water loading lies between 70 and 94 s depending on the adsorption boundary condition. These times are quite short and promise highly compacted adsorption heat pump appliances. Fitting the results of the experimental investigations against the numerical simulation model gives a micro-pore diffusion coefficient ( D ∞) of 1.58 × 10 - 4 (m 2 s −1) and an activation energy of 32.41 (kJ mol −1). Furthermore, a measuring cell wall heat transfer coefficient ( α W) of 230 (W m −2 K −1) has been estimated.

Adsorption separation of N 2, O 2, CO 2 and CH 4 gases by β-zeolite

In the present study, adsorption equilibrium and kinetic separation potential of β-zeolite is investigated for N 2, O 2, CO 2 and CH 4 gases by using concentration pulse chromatography. Adsorption equilibrium and kinetic parameters have been studied. Henry’s Law constants, heat of adsorption values, micro-pore diffusion coefficients and adsorption activation energies are determined experimentally. The three different mass transfer mechanisms, that have to take place for adsorption to occur, are discussed. From the equilibrium and kinetic data, the equilibrium and kinetic selectivities are determined for the separation of the gases studied. With β-zeolite, carbon dioxide has the highest adsorption Henry’s Law constant at all the temperatures studied, followed by methane, nitrogen and oxygen. Carbon dioxide separation from oxygen, nitrogen and methane has good equilibrium separation factors. This factor is not very high for methane/nitrogen and methane/oxygen systems and is the lowest for nitrogen/oxygen system. Micro-pore diffusion is the dominant mass transfer mechanism for all the systems studied, except CH 4, with β-zeolite. The kinetic separation factors are very small at high temperatures for all the systems studied. Nitrogen/carbon dioxide and oxygen/carbon dioxide can be separated in kinetic processes with reasonable separation factors at low temperatures. Both equilibrium and kinetic separation factors decrease as column temperature increases. Considering all the observations from this study, it was concluded that β-zeolite is a good candidate for applications in flue gas separations, as well as natural gas and landfill gas purifications.

DIFFUSION COEFFICIENTS OF CARBON DIOXIDE WITHIN TYPE 13X ZEOLITE PARTICLES

ABSTRACT The self-diffusion processes of CO2 in a single particle of commercial type 13X zeolite have been studied by a new sorption rate method using a constant volume, variable pressure system. Experiments were carried out at 303.2 and 343.2 K. An inverse analysis of experimental uptake curves based on a macropore and micropore series diffusion model was performed to determine effective diffusion coefficients for both macropore and micropore diffusion simultaneously. Knudsen diffusion occurs within the macropore and the micropore diffusion coefficients having values of the order 10−15–10−14 m2/s, which are slightly greater than the previously reported micropore diffusion coefficients of type 5A zeolite crystals.

Permeation of linear and branched alkanes in ZSM-5 supported membranes

Diffusion of methane, n-butane, n-hexane, isobutane and 3-methylpentane in ZSM-5 supported membranes was studied in a wide range of temperatures from ambient to 723 K. The Maxwell–Stefan equations were used for the interpretation of the results. From these, micropore diffusion coefficients and apparent diffusion activation energies were obtained. For the light linear and branched alkanes (C 1 and C 4), the literature data obtained with macroscopic or microscopic techniques or molecular dynamics (MD) simulations are in rather close agreement. In contrast, for n-hexane, the literature data show strong discrepancies. Our diffusivities agree only with the reported macroscopic data. Considering 3-methylpentane molecules, our diffusivities are in close agreement with the macroscopic literature data, but the comparison with the microscopic results is limited.

99/00239 Catalytic hydrogenation of aromatic hydrocarbons in a trickle bed reactor

Determining gas diffusion coefficient from experimental data is a key step of reproducing and predicting the diffusion process in coal. Previously analytical solution, including the unipore diffusion model and the bidisperse diffusion model, has been used extensively to estimate the gas diffusion coefficient(s) in coal. The utilization of analytical solution is convenient, however, there are some defects which may affect the accuracy of the results. For example, it is not suitable for fitting manometric sorption data, and the assumption of linear adsorption isotherm is not true.In this paper, we present a numerical solution to determine the gas diffusion coefficients. Three models were developed based on different assumptions of pore system and diffusion forms, i.e., unipore model assuming one kind of pore and diffusion, bidisperse model I (BM I) assuming independent macropore diffusion and micropore diffusion, bidisperse model II (BM II) assuming dependent macropore diffusion and micropore diffusion. Nitrogen diffusion experiment was conducted and the adsorption isotherm was measured. Sphere geometry was built for numerical simulation and the proposed models were used to fit the experimental data to determine the diffusion coefficients. Results show that neither the analytical unipore model nor the numerical unipore model can describe the diffusion process perfectly. By giving the same diffusion coefficient, the modelled fractional uptake ratio of numerical unipore model is smaller than the result of analytical unipore modeling at early stage while greater at later stage, which is due to the different assumptions of adsorption isotherm. Both BM I and BM II can describe the diffusion process well. The determined macropore diffusion coefficients of the two models are similar, while the micropore diffusion coefficient and the macropore adsorption ratio of BM II are greater than that of BM I. These can be explained by the different roles of the macropore diffusion in the two models. The gas pressure change at the center of the coal sphere was examined, from the modeling result of BM I, the macropore pressure increases sharply and then drops along with the external gas pressure, while the initial increasing rate of macropore pressure of BM II is much smaller and tends to be stable at later stage. No apparent impacts of initial gas pressures on diffusion coefficients can be observed, the change of diffusion coefficients and macropore adsorption ratio are actually small with increasing gas pressure.The numerical solution of determining gas diffusion coefficients can easily relax the assumptions and restrictions of the analytical solution. It can be used to test different kinds of coal samples, investigate different diffusion mechanisms and match all kinds of experimental data. The measured sorption isotherm and coal properties can also be incorporated into the modeling, which makes the determined diffusion coefficients more reliable. This paper is a preliminary attempt and we hope it can bring the researchers some new ideas about studying the gas diffusion characteristics in coal.

Analysis of the temperature frequency response for diffusion in crystals and biporous pellets

The frequency response behaviour of the adsorbent temperature is analysed in detail for both diffusion in crystals and in biporous pellets. In the case of crystals, it is shown that the temperature frequency response may exhibit very different behaviour under effects of intracrystalline diffusion or surface barrier, making it easier to discriminate between the diffusion and surface barrier processes. For biporous pellets, the frequency response of the surface temperature proves to be very sensitive to the competition between micropore diffusion and macropore diffusion, due to finite-rate heat conduction inside pellets. This high sensitivity can lead to a much better estimation of the micropore diffusion coefficient in the presence of macropore diffusion than the estimation obtained with the gas pressure frequency response. Finally, it is shown that, in the case of high-pressure experiments, the effect of heating by gas compression may be significant if the gaseous adsorbate has a large specific heat ratio and a large heat capacity, and if the heat exchange at the chamber wall is slow enough. The effect of gas compression heating on the temperature frequency response is confirmed experimentally for diffusion of xenon in zeolite 5A crystals. The present paper shows, however, the effect of gas compression heating on the gas pressure can be efficiently eliminated using the frequency response data corrected with respect to blank experiments, as proposed by Yasuda.

Diffusion of light alkanes in silicalite studied by the zero length column method

Micropore diffusion coefficients for propane, n-butane, and isobutane in three samples of silicalite crystals were measured by the zero length column (ZLC) method. Experiments were analyzed by the traditional long-time approach and by a new short-time method. For isobutane, micropore diffusion coefficients obtained from all three samples by both analysis methods agreed well with previously reported chromatographic and membrane measurements. For the linear alkanes, the rate of micropore diffusion, even in the largest crystals (350×100 μm), was too fast for reliable measurement and the form of the ZLC response curves was consistent with equilibrium control. Taken as a lower limit, the apparent diffusion coefficients obtained for propane and n-butane are consistent with the results of microscopic experiments and recent chromatographic and frequency response studies