Self-diffusion Coefficient Of Methane Research Articles

Molecular insights into supercritical methane sorption and self-diffusion in monospecific and composite nanopores of deep shale

• Montmorillonite, kerogen and MMT-kerogen composite slit nanopores with desirable pore sizes are constructed; • GCMC and EMD simulations are conducted to study the sorption and self-diffusion behaviors of methane in various nanopores; • Pore surface roughness can impede the diffusion of gases, especially in smaller pores. Up to now, a large number of studies have utilized various representative materials to approximate the replacement of shale and investigate the gas adsorption and diffusion behavior in various shapes of nanopores by means of molecular simulations. However, the study of methane sorption and self-diffusion behavior under high temperature and pressure reservoir conditions in deep shale is not clear. In this study, we first established montmorillonite (MMT), kerogen and MMT-kerogen composite slit nanopores using representative shale components of MMT and kerogen. On this basis, we investigated the methane sorption and self-diffusion characteristics employing the grand canonical Monte Carlo (GCMC) and equilibrium molecular dynamics (EMD) simulations. The results show that the differences in the molecular composition and structure of MMT and kerogen surfaces lead to stronger adsorption performance of MMT surface than kerogen in a single nanopore for the same conditions, which results in the inhomogeneity of spatial distribution of methane molecules in the pores. While the sorption capacity of the kerogen matrix is more potent than MMT due to its larger specific surface area (SSA). The smaller pores have stronger adsorption capacity compared to the larger pores. At the same time, the methane density profiles indicate that the adsorption of the MMT and kerogen in smaller pores is less differentiated. The methane sorption energy distribution and isosteric heat of sorption also mutually corroborate the more stable methane sorption at a higher pressure and smaller pores. The self-diffusion coefficient of methane in nanopores gradually decreases with increasing pressure, with a more pronounced variation at lower pressure. Pore surface roughness will hinder the diffusion of gas, and the closer the distance is, the more noticeable the effect will be. This study sheds light on the sorption and self-diffusion phenomena and difference of gas in monospecific and composite nanopores, which provides insights into the reserve evaluation and development of the deep shale gas reservoirs, and is further expected to furnish ideas for exploring the occurrence and transport characteristics of supercritical fluids on other composite nanomaterials.

Study of diffusion coefficients and molecular adsorption laws for the slit-hole coal model under the thermal-gas-liuid coupling effect with hot nitrogen injection

To solve the serious filtering problems of fracturing fluid during active hydraulic fracturing of coalbed methane, which blocks gas migration channels with residual fracturing fluid and results in a rapid decline in coalbed methane production, several preliminary experiment of thermal nitrogen injection was carried out. To explain the process and mechanism of thermal nitrogen injection at the nanoscale, an adsorption and diffusion model was established to study the adsorption and diffusion of methane, water and fracturing fluid during thermal nitrogen injection. The results showed that the self-diffusion coefficient of methane was increased by 23%, 45% and 32%, the self-diffusion coefficient of water molecule was increased by 108%, 185% and 138%, the self-diffusion coefficient of fracturing fluid molecule was increased by 169%, 275% and 181%, and the total number of atoms in the slit hole was decreased by 15%, 25% and 37%, respectively, when hot nitrogen was injected at 2, 4 and 6 Mpa, respectively. This shows that the numbers of methane, water and fracturing fluid molecules in the slit hole were significantly decreased by the thermal and displacement effects of hot nitrogen injection. The self-diffusion coefficient was significantly improved, and the effects of plug removal was remarkable.

Sorption and Diffusion of Methane, Carbon Dioxide, and Their Mixture in Amorphous Polyethylene at High Pressures and Temperatures

Molecular dynamics (MD) simulations are performed to study the sorption and transport properties of CH4 and CO2 in amorphous polyethylene at temperatures from 350 to 600 K and pressures up to 500 bar. The uptake of CH4 and CO2 by polyethylene generally increased with increasing pressure and decreasing temperature. However, at high pressures, for example, the uptake of methane by polyethylene increases with temperature. The self-diffusion coefficients of methane and carbon dioxide generally increase with pressure. These results are, in general, consistent with the swelling behavior of the polymer. Interestingly, for the penetrants, the activation barrier of diffusion decreases with pressure. MD simulations are also carried out for the CH4/CO2 mixture in amorphous polyethylene. Here, the overall sorption and transport properties were similar to those reported for pure CH4 and pure CO2 in polyethylene. The sorption selectivity of CO2/CH4 decreases with increasing pressure and temperature and was mostly independent of the bulk mole fraction of methane. Importantly, at high pressures, the mobility of methane found here is higher than that of the corresponding pure methane in polyethylene and the opposite trend is observed in the case of carbon dioxide. These results might be due to the fact that the swelling of the polymer in the presence of carbon dioxide is significantly higher than that in the presence of methane, especially at high pressures. The diffusion and membrane selectivities of carbon dioxide/methane show a similar trend to the sorption selectivity data. Furthermore, the simulation data were in good agreement with the theoretical calculations based on the PC-SAFT equation of state.

The role of water in methane adsorption and diffusion within nanoporous silica investigated by hyperpolarized 129Xe and 1H PFG NMR spectroscopy

Understanding the properties and behavior of water molecules in restricted geometries, such as the nanopores of rocks, is of interest for shale gas exploitation. We present herein ex situ and in situ nuclear magnetic resonance (NMR) studies on the effects of water on the adsorption and diffusion of methane in nanopores. Silica materials with one-dimensional pores of ZSM-22, MCM-41, and SBA-15, with pore sizes ranging from 0.5 to 6 nm, were chosen as models. Hyperpolarized (HP) 129Xe NMR results show that water adsorption does not affect the pore sizes of ZSM-22 and MCM-41 but reduces that of SBA-15. The presence of water suppresses methane adsorption; this suppression effect is stronger in smaller pores. The self-diffusion coefficients of methane within ZSM-22 and MCM-41 are not significantly influenced by the presence of water, as measured by 1H pulsed field gradient (PFG) NMR. However, within SBA-15, which has a pore size of 6 nm, the diffusion coefficient of methane increases as the amount of water adsorption increases, peaks, and then decreases to a constant value with further water adsorption. These experiments reveal the effects of the pore size and the presence of water on methane adsorption and diffusion in constrained spaces, which could have important implications for flow simulations of methane in shales.

Simulation of the effect of coke deposition on the diffusion of methane in zeolite ZSM-5

Coke deposition is one of the main reasons for catalyst deactivation, which is often associated with coverage of the active sites and diffusion restrictions. In this article, the self-diffusion coefficient of methane in ZSM-5 (MFI) with different amounts of coke is studied through molecular dynamics simulation combining hard-sphere and pseudo-particle modeling at a gas loading of 4 molecules per unit cell at 723K. The T12 tetrahedral sites are considered as the possible coke deposition sites at which the pore is blocked. It is shown that the self-diffusion coefficient of methane in ZSM-5 without coke (D0) is approximately 7.0×10−9m2/s. Two coke distribution models are proposed to simulate the actual process of coke formation. At the initial stage of coke deposition, the coke with uniform distribution has little influence on the diffusion process. Once the coke deposits are randomly concentrated on some sites and a few pores are therefore completely blocked, the coke has a significant influence on the self-diffusion coefficient, which decreases to 37.0% of D0 almost linearly with increasing coke amount to 20%. The distribution of coke deposition is the result of the coupling of reaction and diffusion processes. These results may be useful for understanding the reaction–diffusion coupling mechanism of the catalyst deactivation.

Determination of potential energy function of methane via the inversion of reduced viscosity collision integrals at zero pressure

The potential energy function of methane has been determined via the inversion of reduced viscosity collision integrals at zero pressure. A comparison of the potential with the previously determined potentials is included. The viscosity, thermal conductivity, and self-diffusion coefficient of methane at different temperatures and pressures have been calculated and compared with experiment. The interaction potential of methane from the inversion method has been fitted to obtain an analytical potential form.

The importance of various degrees of freedom in the theoretical study of the diffusion of methane in silicalite-1

The self diffusion coefficient of methane in silicalite-1 is influenced by the flexibility of the lattice unlike the self diffusion coefficient of methane in the cation-free zeolite of type A. In the present paper, besides the influence of lattice vibrations on this process, the influence of internal vibrations of the methane molecule and the applicability of several spherical models of this molecule are examined. The method of moments [Chem. Phys. Lett. 198 (1992) 283] is generalized to anisotropic diffusion.

Contributions of the Van der Waals Laboratory to the Knowledge of Transport Properties of Fluids

After the presentation of Enskog's theory of the transport phenomena at high densities in 1922, one of the aims of the Van der Waals Laboratory was to check this theory with accurate experimental results. As early as 1931, Michels and Gibson published data on the viscosity of nitrogen taken by means of the Van der Waals vertical-capillary viscometer. In 1952, Michels and Botzen presented thermal-conductivity measurements on nitrogen taken by means of the parallel-plate heat-conductivity apparatus. Finally, in 1968 Trappeniers and Oosting presented data on the self-diffusion coefficient of methane obtained with a nuclear magnetic resonance spin-echo spectrometer. In all of these cases agreement with either the Enskog theory or the modified Enskog theory was not obtained. In 1973 Trappeniers and J. Michels showed that the self-diffusion coefficient of krypton obtained with a tracer method deviates from Enskog theory due to the formation of clusters. Measurements of the thermal conductivity of argon in 1955 motivated a study of transport phenomena of fluids in the critical region. This resulted, in 1962, in the first proof of the existence of a rather strong divergence in the thermal conductivity of carbon dioxide, by Michels, Sengers, and Van der Gulik. In 1978 Offringa showed that the viscosity has only a small critical anomaly, while Oosting showed as early as 1968 that, for selfdiffusion, such an anomaly could not be detected. In 1991 Mostert, and in 1996 Sakonidou, showed that the anomaly in the thermal conductivity is finite in mixtures near the vapor–liquid critical line. In the 1970s a vibrating-wire viscometer suited for measuring the viscosity near the melting line of simple gases was developed to check predictions by computer simulations of the viscosity of hard spheres. From the comparisons, it could be concluded that in the density range from the critical density up to twice this density, a special version of the hard-sphere Enskog theory describes the measurements within the experimental accuracy. With this result it was possible to describe the viscosity in the low-density range, up to the critical density, by a model of a gradual transition from intercluster transport described by the Chapman–Enskog theory to intracluster transport described by the hard-sphere Enskog theory, a model inspired by J. Michels' conclusion that the formation of clusters influences the transport properties.

Use of test particle calculations for the derivation of van der Waals parameters used in force fields

Test particle calculations are employed to derive van der Waals parameters for methane. It is shown that it is possible to derive these parameters completely based on ab initio calculations. The newly derived parameters are tested in molecular dynamics calculations of liquid methane and the results are compared with the results of existing force fields. It is shown that the newly derived parameters perform better in the prediction of the density, the heat of vaporization, and the self-diffusion coefficient of methane. Scaling of the parameters to account for systematic errors in the employed ab initio method does not generally improve the parameters with respect to the properties calculated. © 1997 by John Wiley & Sons, Inc.

Self-Diffusion Coefficients of Methane or Ethane Mixtures with Hydrocarbons at High Pressure by NMR

Self-diffusion coefficients have been measured in homogeneous mixtures of methane + hexane, ethane + hexane, methane + octane, ethane + octan, methane + decane, ethane + decane, and methane + hexane + benzene over the whole concentration range, at 303.2 K and 333.2 K and 30 MPa, 40 MPa, and 50 MPa. The experiments were performed in a glass cell by application of the NMR−PGSE technique. The estimated accuracy of the measurements is ±5%. Experimental self-diffusion coefficients were compared to the Sigmund correlation, which was found not to fit the experimental data.

The self-diffusion coefficient of liquid methane

Self-diffusion coefficients of methane have been calculated over a wide density range using the method of molecular dynamics. Methane intermolecular interactions were modelled using an m-6–8 potential with coefficients determined from viscosity data for the dilute gas. After adding a contribution to the diffusion coefficient due to the long-time behaviour of the velocity autocorrelation function, agreement with experimental data is within the estimated errors given for both the calculated values and the experimental data.

Dense-gas diffusion coefficients in the methane-carbon tetrafluoride system by pulsed nuclear magnetic resonance

Self-diffusion coefficients of methane and carbon tetrafluoride were measured by the pulsed NMR method in three dense-gas mixtures of methane and carbon tetrafluoride having 0.25, 0.50 and 0.75 mole fraction of methane. The measurements were made at temperatures between 0°C and 75°C and pressures between 25 and 500 atmospheres. The data were correlated according to the corresponding-states principle. Mutual-diffusion coefficients were derived from the experimental self-diffusion data and compared with theoretical values calculated on the basis of the Enskog factor. Agreement between the two sets of values ranged from very good to fair.

Intermolecular interactions in methane, carbon tetrafluoride and sulphur hexafluoride

Spherically averaged potential energies of interaction between pairs of methane, carbon tetrafluoride and sulphur hexafluoride molecules have been determined as closely as possible using experimental gaseous viscosity data. Experimental second virial coefficients have then been used to estimate values of the first non zero multipole moment of these molecules. Third virial coefficients calculated with allowance for the triple dipole dispersion interaction agree well with experiment as do calculated self diffusion coefficients for methane.