Diffusion Coefficient Of Methane Research Articles

A nonequilibrium simulation method for calculating tracer diffusion coefficients of small solutes in n-alkane liquids and polymers

The tracer diffusion coefficients of methane in n-alkane liquids of increasing chain length were calculated by measuring the friction from short time nonequilibrium molecular dynamics simulations. The frictional constant was calculated from the exponentially decaying distance between two methane tracer molecules connected by a harmonic spring. The diffusion constants calculated with this method are in good agreement with those obtained from mean square displacement calculations. Unfortunately, both methods required the same computational input even for large values of n. The tracer diffusion coefficient is found to obey an algebraic law D∼n−α for n⩽100, where n is the chain length of the solvent. The value of α=1.1 is in perfect agreement with experimental tracer diffusivities determined with the Taylor dispersion method, the value being mainly determined by the tracer’s size. For larger solvent chain lengths n>100 (tracer diffusion in polymer melts) a second regime of much slower decay is found. The tracer diffusion coefficient converges to a constant value in correspondence with the converging melt density.

Experimental investigation of molecular transport and fluid flow in unfaulted and faulted pelitic rocks

Abstract Laboratory experiments have been performed to investigate the fluid transport properties of fine-grained (pelitic) sedimentary rocks with respect to their hydrocarbon sealing efficiency. The experiments comprised the molecular transport (diffusion) of gases and the pressure-driven volume flow (Darcy flow). Diffusion coefficients of methane and nitrogen in water-saturated rock samples were measured at 90°C from an equimolar mixture of the two gases (10 MPa gas pressure). Methane had lower effective diffusion coefficients but higher steady-state molecular transport rates than nitrogen. Permeability coefficients measured with water on selected unfaulted natural samples, under controlled effective stress up to 47 MPa, ranged between 10 −22 and 10 −19 m 2 . The permeability reduction with increasing stress mostly followed an exponential relationship. Permeabilities of faulted mudstones from compressive fault zones ranged from 2 up to 20 × 10 −21 m 2 . No systematic relationship between permeability and microfault frequency within the samples or distance of samples from microfault planes could be identified. Permeability measurements were also performed on macroscopically homogeneous Carboniferous shales from a compressive tectonic stress field. These samples, which showed distinct sonic velocity anisotropies, had permeability coefficients in the nanodarcy (nDarcy; 10 −21 m 2 ) range. Only in one case was a significant permeability anisotropy associated with the sonic velocity anisotropy.

Experimental characterisation of the hydrocarbon sealing efficiency of cap rocks

Jurassic shales and mudrocks from the Haltenbanken area offshore Norway and red claystones from Carboniferous and Permian intervals of Northern Germany were used in a study of the hydrocarbon sealing efficiency of clastic sediments. The investigations comprised geochemical and mineralogical analysis of the pelitic rocks, petrophysical characterisation by mercury porosimetry and specific surface area measurements, and laboratory experiments to assess the transport properties with respect to both molecular transport (diffusion) and volume flow (Darcy flow). Effective diffusion coefficients of methane in the water-saturated rock samples at 150°C lay between 1.4 × 10 −11 and 4.5 × 10 −10m 2/s and showed a distinct correlation with TOC content. Permeability coefficients, measured by means of a steady-state method, ranged from <1 nDarcy (<10 −21m 2) for Permian (Rotliegend) and Carboniferous red claystones up to 4.3 μDarcy (4.3 × 10 −18m 2) for a bioturbated Jurassic siltstone. The experimental data were used to calculate maximum sustainable gas and petroleum column heights, hydrocarbon leakage rates by pressure-driven volume flow (Darcy flow), and diffusive gas losses for simple, hypothetical scenarios. Computed maximum gas column heights range from 20 m up to >2000 m. Hydrocarbon column heights calculated on the basis of a rich condensate lay between 3 and 340 m. Depending on temperature, pressure, reservoir geometry and seal thickness, diffusive losses can be expected to require tens of millions of years to significantly affect the contents of commercial size natural gas reservoirs.

Small penetrant diffusion in polybutadiene: a molecular dynamics simulation study

Molecular dynamics (MD) simulations have been used to study the diffusion of methane as a small molecule penetrant example in cis-1,4-polybutadiene (PBD). The non-bonded potential for an ‘anisotropic’ united atom (AUA) representation of the CH= group was calibrated by adjusting the constants to fix experimental volume temperature data for the polymer melt. This potential was used along with an already available AUA function for the-CH 2-group. The diffusion coefficient of methane was determined via MD simulation over a wide range of temperature. The results agree well with near room temperature experimental values for N 2 in cis-PBD. The latter gas is similar in diffusion behaviour to methane. The mechanism of diffusion in terms of the nature of the diffusive jump process and its response to temperature is found to be similar to that in atactic polypropylene and polyethylene melts. At low temperatures the penetrant is trapped for relatively long periods in a cage of surrounding polymer and makes occasional large jumps. As temperature increases the size of the jumps increases further. The quiescent trapped periods disappear and a liquid-like scattering regime prevails. This change in mechanism as temperature increases is accompanied by a decrease in activation energy. The diffusion in PBD is faster than in other hydrocarbon polymers studied so far by simulation (polyethylene, polysobutylene and atactic polypropylene). The order of diffusion coefficients correlates with the free volumes available in the polymer hosts.

Diffusion of gases in polymer blends near the lower critical solution temperature

AbstractGas diffusion through miscible blends of polystyrene (PS) with poly(vinyl methyl ether) (PVME) and poly(styrene‐stat‐acrylonitrile) (PSAN) with poly(methyl methacrylate) (PMMA) is studied from temperatures below the corresponding lower critical solution temperature (LCST) to temperatures above. The Arrhenius equation describes the temperature dependence of diffusion coefficients of pure components. Diffusion coefficients of methane in the 20/80 PS/PVME blend also follow the Arrhenius equation in the temperature ranges above and below their corresponding LCST; however, discontinuity is observed in the LCST region. In contrast to the PS/PVME blend, discontinuity in the LCST region is not obvious for nitrogen and methane in the 50/50 PSAN/PMMA blend. These phenomena are discussed in terms of free volume and morphology changes in the LCST region.

Coverage dependent surface diffusion of noble gases and methane on Pt(111)

The surface diffusion of krypton, xenon, and methane on the Pt(111) surface was studied using laser induced thermal desorption (LITD) techniques. The surface diffusion coefficient of krypton on Pt(111) at 45 K decreased dramatically with coverage from D = 1.4 × 10 −7 cm 2 s at θ = 0.05θ s to approximately D ≈ 1 × 10 −9 cm 2 s at θ = θ s Similarly, the surface diffusion coefficient of xenon on Pt(111) at 80 K decreased from D = 8 × 10 −7 cm 2 s at θ = 0.05θ s to D> = 2 × 10 −8 cm 2 s at θ = θ s . The coverage-dependent surface diffusion coefficients for the noble gases on Pt(111) were consistent with attractive interactions between the adsorbed atoms and a multiple site diffusion mechanism. In contrast, the surface diffusion coefficient of methane on Pt(111) at 45 K was independent of surface coverage at D = 1 × 10 −6 cm 2 s . This coverage independence indicated that latera interactions between the adsorbed methane molecules did not influence the surface diffusion process. Thermal desorption kinetics for krypton, xenon, and methane on Pt(111) were determined using temperature programmed desorption (TPD) experiments. Using the variation of heating rates method, the desorption energies were E des = 3.7 ± 0.1 kcal mol for Kr/Pt(111), E des = 6. kcal mol for Xe/Pt(111), and E des = 3.6 ± 0.15 kcal/ mol for CH 4/Pt(111). The TPD peaks for krypton and xenon on Pt(111) shifted to higher temperature versus initial coverage, consistent with attractive interactions between the adsorbed atoms. In contrast, the coverage-independent TPD peak temperature for methane on Pt(111) provided further evidence for the absence of interactions between the adsorbed methane molecules.

Transport of gases in miscible polymer blends above and below the glass transition region

AbstractThe study of diffusion and permeation of methane, nitrogen, and helium in miscible blends of poly(styrene‐stat‐acrylonitrile) (PSAN) and poly (methyl methacrylate) (PMMA) at 35–140°C shows that permeation coefficients (P) of helium followed the linear logarithmic mixing rule. Positive deviations from the linear logarithmic mixing rule were observed for permeation and diffusion coefficients (D) of methane and nitrogen below the glass transition temperature (Tg). The deviations decreased with increasing temperature and disappeared above Tg. The experimental results were analyzed by free volume and activated state theories. The Arrnenius plots of log D or log P vs. the reciprocal of temperature exhibited discontinuities in the glass transition region for all gases and blend compositions. The discontinuities are caused by large thermal expansion coefficient differences between the rubbery and glassy states of PSAN and PMMA. The sorption of methane in 50/50 PSAN/PMMA has dual‐mode characteristics below Tg.

Diffusion coefficients of sulfate and methane in marine sediments: Influence of porosity

Tracer diffusion coefficients of sulfate and methane were determined in seawater ( D o ) and in sediments ( D s ). The diffusion coefficients in seawater (20‰ S) at 4°C were 0.56 ± 0.04 ∗ 10 −5 cm 2 s −1 for sulfate and 0.87 ±0.10 ∗ 10 −5 cm 2 s −1 for methane. The sediment diffusion coefficients can be related to the diffusion coefficient in free solution by D s = D o θ 2 , where θ is the tortuosity of the sediment. The sediment tortuosity calculated from this equation showed a linear relationship with sediment porosity (φ) over the porosity range of 0.4–0.9. From our data, it was possible to deduce the empirical equation θ 2 = 1 + n(1 − θ), which was used to calculate D s from D o:D s = D o 1 + n(1−φ) , using n = 3 for claysilt sediments and n = 2 for sandy sediments.

Measurement and modelling of diffusion, porosity and other pore level characteristics of sandstones

The diffusion coefficients of methane, iso-butane and n-butane through dry and water-saturated sandstones and their dependence on relative molar mass are discussed. The diffusion of iso-butane is anomalously fast in dry sandstones and that of methane is anomalously low in water-saturated sandstones. A three-dimensional computer model of the pores and throats in the sandstone has been developed. Simulations have been made of the sandstone's porosity, surface area, pore and throat size distribution, tortuosity, mercury porosimetry primary drainage curve, average pore connectivity and diffusion coefficient for mixed gaseous alkanes.

Chemical modification of polysulphone: 2. Gas and liquid permeability of polysulphone/polydimethylsiloxane graft copolymer membranes

The gas and liquid permeabilities of polysulphone/polydimethylsiloxane (PSF/PDMS) graft copolymer membranes have been investigated. The permeability coefficients to nitrogen, oxygen, hydrogen, methane and carbon dioxide were evaluated. The gas permeability coefficients of the graft copolymer membranes were influenced by the PDMS content of the graft copolymer. In the region of >60wt% PDMS content, the oxygen permeability coefficient of PSF/PDMS graft copolymer membrane was (1−3) × 10 −8 cm 3 cm cm −2 s −1 cmHg −1. In addition, the permeability to methane and carbon dioxide was remarkably enhanced in comparison with PSF membrane. The introduction of PDMS chains greatly increased the diffusion coefficients of methane and carbon dioxide. In the case of pervaporation of aqueous ethanol solution, the preferential permeation of ethanol was observed through the graft copolymer membrane for which the PDMS content was >50wt%.

Translational‐rotational coupling parameters for mutual diffusion in N‐octane

AbstractThe infinite dilution diffusion coefficients of methane, ethane, n‐propane, n‐pentane, n‐heptane, n‐decane, n‐dodecane, and n‐tetradecane have been measured in n‐octane using the Taylor dispersion technique in the temperature range 304–435 K at 1.72 × 106 N/m2. Using the framework of the rough hard sphere theory, the values of the translation‐rotational coupling parameter have been determined for each solute‐solvent pair at each temperature. The coupling parameter was found to be independent of temperature over the entire temperature range of the experiments performed and it has the same value for solutes ranging from n‐pentane to n‐tetradecane. A calculation scheme is presented for accurate determination of infinite dilution diffusion coefficients for a wide range of solutes in n‐octane at a wide temperature range.

Stochastic model for calculation of diffusion coefficients of adsorbed species in zeolites

1. A stochastic method was developed for the calculation of the diffusion coefficients of an adsorbed substance taking into account the arbitrary number of states of the diffusing species. 2. The method was used to calculate the diffusion coefficient of methane adsorbed by zeolite 5A. The calculation results do not contradict the experimental data.

Spectroscopic diffusion coefficient of methane at 3.39 micron wavelength by a laser study

A novel differential re-analysis of Hubbert's (1976) laser study data of the 3.39 μm absorption (Dicke-narrowed) of methane shows that the spectroscopic diffusion coefficient is 10% different from the calculated self-diffusion coefficient. More accurate studies above 10 torr pressure are needed.

Determination of the intracrystalline diffusion coefficient of methane in A zeolites by means of neutron spin-echo experiments

The intracrystalline motion of methane molecules adsorbed on CaNaA (5A) and NaA (4A) zeolites have been studied by means of spin-echo neutron scattering spectroscopy over distances from 15 to 30 A within the time-scale from 10–10 to 10–8 s. In CaNaA zeolite we were able to measure a mean lifetime of 4 × 10–10 s for the molecule in one cavity. In NaA this lifetime is > 10–8 s. The increase in residence time on going from CaNaA to NaA shows the influence of the cations located in the eight-membered oxygen windows. The interpretation of the results in terms of a diffusion-jump model involving discrete sites on a cubic lattice leads to a value of the intracrystalline diffusion coefficient in agreement with that obtained from n.m.r. pulse field-gradient measurement. This shows the influence of crystallinity on the diffusivity.

Gas-Solid Chromatography of Methane-Helium Mixtures: Transmission of a Step Increase in the Concentration of Methane through an Activated Carbon Adsorber Bed at 25°C

Abstract Time-dependent transmission or “breakthrough” curves of methane in helium flowing through an activated carbon adsorber bed were measured for methane concentrations between 34 and 105 ppm, and for mixture flow rates between 0.69 and 6.64 cm/s. The transmission is the ratio of the outlet concentration to the inlet concentration. The experimental transmission curves for a step-function increase in the methane concentration are compared with the predictions from a model which assumes a linear adsorption isotherm and equilibrium between the gas and solid phases. These two basic assumptions are discussed in detail. The data show that the two assumptions hold within the concentration and flow rate regions of this study. Effective diffusion coefficients of methane were calculated from the transmission data and found to increase with increasing flow rates.

The Diffusion of Gases at High Pressures. V. The Diffusion of CTH3 in the CO2–Ar System

Abstract The diffusion coefficients of radioactive methane (CTH3) in argon and in mixtures of carbon dioxide with argon(0.719, 0.497, and 0.245 mol fractions of aigon) were measured at the temperatures of 25, 50, and 75°C in the 15∼250 atm pressure range. The measurements were made through a plug of porous bronze in the diffusion cell by using the radioactive tracer technique. The diffusion coefficient-density products, Dρ, for the CTH3–argon system increased slightly with the density in the region below 5 mol/1, and decreased slightly in the region above 5 mol/1. The Dρ for the CTH3–mixture systems decreased slightly with the density over the whole range studied here. The density dependence of Dρ-values at high densities could not be predicted by Enskog-Thorne’s theory.

The Diffusion of Gases at High Pressures. IV. The Diffusion of CTH3 in the CH4-CO2 System

Abstract The diffusion coefficients of radioactive methane (CTH3) in normal methane, in carbon dioxide, and in a mixture of normal methane with carbon dioxide (0.522 mol fraction of methane) were measured at the temperatures of 25, 50, and 75°C in the 15–250 atm pressure range. The measurements were made through a plug of porous bronze in the diffusion cell, using the radioactive tracer technique. The diffusion coefficient-density products, Dρ, for the CTH3–normal methane system and the CTH3- the binary mixture system increased slightly with an increase in the density in the lower-density region at 25 and 50°C, but they were nearly constant at 75°C. The Dρ for the CTH3–carbon dioxide system decreased with an increase in the density at each temperature. The Dρ-values at 1 atm, obtained by extrapolation, agreed fairly well with those reported in the literature. The density dependence of the Dρ values at high densities could not be predicted by Enskog-Thorne’s theory.

Diffusion coefficients of water and organic volatiles in carbohydrate‐water systems

Summary. The diffusion coefficients of water, Dw, and acetone, Da, in aqueous solutions of malto‐dextrin have been determined over a range of moisture contents of the malto‐dextrin above 10%. At a few selected moisture contents, the diffusion coefficients of ethyl acetate, benzene, carbon tetrachloride, camphor and methane have also been determined. Diffusion coefficients were derived from measurements of sorption and desorption by a malto‐dextrin layer.The diffusion coefficient was found to be dependent on both the moisture contents and the size of the diffusing molecule. Over the range of moisture contents investigated, log Dw was found to be proportional to Cw‐1 and log Da proportional to Cw‐1/2, where Cw is the concentration of water (kg/m3) in the malto‐dextrin. For the compounds studied, the logarithm of the diffusion coefficient measured at a moisture content of 20.1% was found to be approximately proportional to the molecular ‘diameter’ of the diffusant.This knowledge helps to explain the phenomenon of flavour retention during the drying of liquid foods.

Controlling ventilation currents to prevent layered methane accumulations in mines

1. The authors have studied the shaping effect of grids on the velocity field and turbulent characteristics of air streams in mine workings. 2. The dependence of the diffusion coefficient of methane in an air stream on the distance to the grid in the case of complete coverage of the roadway cross section has been established. The degree of the effect of the increase of the diffusion coefficient in the area immediately beneath the roof, with partial coverage of the roadway cross section by a grid, has been determined. 3. The effectiveness of reducing the concentration of layered methane accumulations by shaping the air steam parameters by grids has been determined in mines. It has been established that the use of a single grid with a mesh size of 0.5–1 mm enables us to reduce greatly the methane concentration beneath the roof at a distance of up to 20–25 roadway diameters.

Corrections to the Kinetic Theory of Fluid Diffusion

The measured diffusion coefficients of methane along the liquid branch of the liquid-vapor coexistence curve at temperatures from the critical down to near the normal boiling temperature can be quantitatively predicted on the basis of hard-sphere diffusion theory. This constitutes an experimental verification of the van der Waals theory of transport, and furthermore, it shows the practical importance of the contribution of correlated events to hard sphere diffusion, recently observed in computer experiments.