Nanoscale Gas Flow Research Articles

Noise and fluctuations in nanoscale gas flow

We theoretically calculate the fundamental noise that is present in gaseous (dilute fluid) flow in channels in the classical and degenerate quantum regime, where the Fermi–Dirac and Bose–Einstein distribution must be considered. Results for both regimes are analogous to their electrical counterparts. The quantum noise is calculated for a two terminal system and is a complicated function of the thermal and shot noise with the thermal noise dominating when 2k B T ρ ≫ mΔP and vice versa. The cumulant generating function for mass flow, which generates all the higher order statistics related to our mass flow distribution, is also derived and is used to find an expression for the third cumulant of flow across a fluidic channel.

Minireview on Lattice Boltzmann Modeling of Gas Flow and Adsorption in Shale Porous Media: Progress and Future Direction

As an important unconventional resource, shale gas reservoirs have unique characteristics different from conventional oil and gas reservoirs. The ultrasmall pore sizes in shale induce the nanopore confinement effect on shale gas flow. In addition, shale rocks are rich in organic matter, which has strong interactions with gas molecules and results in gas adsorption. The lattice Boltzmann method (LBM) for micro- and nanoscale gas flow, which is originally designed for micro-electro-mechanical systems (MEMS), has been modified to simulate gas flow and adsorption in shale rocks. This work reviews four types of lattice Boltzmann models developed recently for shale gas flow/adsorption: (1) the slip-velocity-based LBM, (2) high-order LBM, (3) diffusion-based LBM, and (4) REV-scale LBM. Among these models, the slip-velocity-based LBM is widely used for shale gas modeling, which incorporates the slip boundary condition and Knudsen number (Kn)-determined relaxation time to simulate the nanopore confinement effect. To model the gas adsorption, the fluid–solid interaction force is introduced into the model, and the magnitude of this interaction force is usually obtained from the molecular level simulations. LBMs have been regarded as an efficient numerical tool to estimate the shale gas apparent permeability, to describe the pore-scale flow behaviors, and to address the influence of gas adsorption on shale gas storage and transport. Nevertheless, some challenges exist in current applications of LBMs for shale gas flow and adsorption simulations that are discussed in this minireview as well.

Simulations of Nanoscale Gas Flow with Knudsen Diffusion and Slip Flow

Simulations of Nanoscale Gas Flow with Knudsen Diffusion and Slip Flow

A mean free path approach to the micro/nanochannel gas flows

We investigate the gas flows near to solid surfaces in terms of the local spatial variation in the molecular mean free path (MFP). Molecular dynamics (MD) is the appropriate scientific tool for obtaining molecularly-accurate dynamic information in micro and nano-scale gas flows, and has been used to evaluate the molecular mean free path of gases. In the calibration procedure, the viscosity of a gas in the homogeneous case can be recovered in our MD simulations and reach good agreement with the theoretical prediction and data from NIST. In surface-bounded gas flows, if the collisions between gas molecules and walls are counted, a spatially-varying mean free path is presented, and for the first time we have observed that the distribution of the free paths deviates from the exponential one and spikes appear in their distributions at larger Kn, i.e. in the transition flow regime. Based on elementary kinetic theory, the effective viscosity of the gas derived from the mean free path has been incorporated into the framework of the continuum-fluid dynamics equations, and micro-Couette flows are performed to demonstrate this potential application.

Molecular Dynamics Simulation of Rarefaction Effect on Shear-driven Gas Flow in Nanochannels

The nanoscale gas flow at normal temperature and pressure varies from the slip flow regime to the transition regime, of which the character length changes across several nanometers to several thousand nanometers. The difference in the degree of rarefaction leads to different rules of the flow in nanochannels. In order to study the influence of rare gas effect on the nanoscale gas flow, we use three-dimensional molecular dynamics method to simulate the shear flow confined by two parallel plate under different Knudsen numbers, and then obtain the distribution of flow velocity, density, normal stress and shear stress, thus calculating and analyzing the variation of the tangential momentum accommodation coefficient. Counting the gas molecules according to the velocity with positive and negative values respectively, we find that the gas flow is decomposed into two independent shear flows, which indicates strong non-equilibrium characteristics in the nanochannel.

Surface effects on Couette gas flows in nanochannels

A three-dimensional non-equilibrium molecular dynamics method is adopted to investigate the influence of wall force field on the nanoscale gas flow in the transition regime. For the gas flow under nanoscale condition, the dominant effect of the wall force field on the flow field is more obvious, and the flow physical quantity is more sensitive to the change of the wall condition and system temperature. The motion of the wall atoms is governed by the Einstein theory, with using an elastic coefficient <i>k</i> to model the surface stiffness. The results indicate that the surface stiffness has little effect on the physical quantity distribution of the bulk flow region, but a certain influence on that of the near wall region. Increasing the value of the stiffness changes the velocity peak of the gas in the near-wall region and the tangential momentum adaptation coefficient (TMAC) towards lower values, thus demoting the momentum adaptability of the gas molecules to the surface. The wall roughness is simulated by a typical pyramidal model. It is found that the influence of wall roughness on the flow is very obvious, whether it is in the bulk flow region or in the near wall region. For the former case, the increase of roughness leads gas velocity and shear stress to increase, with density and normal stress remaining constant. The linear distribution of physical quantities is also affected to some extent. While for the latter case, as the roughness increases, the velocity of the fluid increases rapidly and approaches to the wall velocity. The peak of density increases, and the adsorption of gas molecules at the surface is obvious. The TMAC approaches to 1, suggesting that the gas and the surface achieve a complete momentum adaptation. Besides, the influence of system temperature on the gas flow in the nanochannel is also studied. The system temperature is controlled by the Nose-Hoover thermostat, making the flow field maintained at the target temperature through the damping coefficient. The results show that the effect of temperature is global in the whole flow region. The increase of temperature causes the flow velocity of the whole flow field to decrease, while the normal stress and shear stress to increase. A higher temperature leads to more frequent collisions between gas molecules, thus increasing the effective viscosity of the gas. At the same time, the degree of gas molecule adsorption in the near-wall region is reduced, contributing to a smaller TMAC value, and consequently a weaker gas-surface interaction.

Determination of rarefaction effects on transport properties of nanoscale gas flows using Green–Kubo molecular dynamic simulation

ABSTRACTThis study aimed to investigate the rarefaction effects on thermal conductivity, viscosity, and density of Argon, Neon and Xenon gas flows in a Platinum nanochannel. Green–Kubo approach with Lenard Jones potential function are used for molecular dynamic simulation. Simulations showed that with decrease in number of atoms, density, viscosity and thermal conductivity decreases, while decrease in nanochannel width in same number of gas atoms leads to increase in viscosity and thermal conductivity.

Scaling law for slip flow of gases in nanoporous media from nanofluidics, rocks, and pore-scale simulations

In unconventional reservoirs, as the effective pore size becomes close to the mean free path of gas molecules, gas transport in porous media begins to deviate from Darcy’s law. The objective of this study is to explore the similarities of gas flows in nanochannels and core samples as well as those simulated by direct simulation BGK (DSBGK), a particle-based method that solves the Bhatnagar-Gross-Krook (BGK) equation.Due to difficulties in fabrication and experimentation, previous study on gas flow experiments in nanochannels is very limited. In this work, steady-state gas flow was measured in reactive-ion etched nanochannels with a controlled channel size on a sillicon wafer. A core-based permeability measurement apparatus was used to perform steady-state gas flow measurements on carbonate and shale samples. Klinkenberg permeability was obtained under varying pore pressures but constant temperature and effective stress. Methane was used in nanofluidic and rock experiments, making them directly comparable. Results from both experiments were then compared to gas flow simulations by DSBGK method carried out on several independently constructed geometry models. DSBGK uses hundreds of millions of simulated molecules to approximate gas flow inside the pore space. The intermolecular collisions are handled by directly integrating the BGK equation along each molecules trajectory, rather than through a sampling scheme like that in the direct simulation Monte-Carlo (DSMC) method. Consequently, the stochastic noise is significantly reduced, and simulation of nano-scale gas flows in complex geometries becomes computationally affordable.The slippage factors obtained from these independent studies varied across three orders of magnitude, yet they all appear to collapse on a single scaling relation where the slippage factor in the slip flow regime is inversely proportional to the square root of intrinsic permeability over porosity. Our correlation could also fit the data in the literature, which were often obtained using nitrogen, after correcting for temperature and gas properties. This study contributes to rock characterization, well testing analysis as well as the understanding of rarefied gas transport in porous media.

Molecular Dynamics Simulation of Nanoscale Channel Flows with Rough Wall Using the Virtual-Wall Model

Molecular dynamics simulation is adopted in the present study to investigate the nanoscale gas flow characteristics in rough channels. The virtual-wall model for the rough wall is proposed and validated. The computational efficiency can be improved greatly by using this model, especially for the low-density gas flow in nanoscale channels. The effect of roughness element geometry on flow behaviors is then studied in detail. The fluid velocity decreases with the increase of roughness element height, while it increases with the increases of element width and spacing.

Molecular dynamics simulations of surface effects on Couette gas flows in nanochannels

Molecular dynamics method is used to investigate gas flows in nanoscale channels. A set of Couette gas flows with the same Knudsen number but different channel heights and densities is simulated to study the dimensional effects on dynamically similar flow conditions. Results show that the gas flow in the channels is divided into two regions:near wall region affected by a wall force field and bulk flow region affected by no wall force field. The flow characteristics in the bulk flow region are in good accordance with the kinetic theory predictions, which are characterized by constant density, normal stress, shear stress and linear velocity distribution while within the near wall region, the velocity, density, normal stress and shear stress distributions exhibit deviations from the kinetic theory predictions. The density and velocity sharply increase, accompanied with a single peak appearing. The normal stress which is dominated by the surface virial is anisotropic and changes drastically. Shear stress value is constant in bulk flow region and part of the near wall region, while the surface virial induces variation at a place about one atom diameter far from the wall. In the near wall region, the normalized density, velocity and stress tensor are constant under different channel heights and densities, which indicates that the gas flow characteristics in this area are determined by the wall force field. Besides, the tangential momentum accommodation coefficient (TMAC) values for different cases can be obtained through the relationship between TAMC and shear stress. It is found that under the same Knudsen number, the TMAC remains constant no matter what the height and density are. Furthermore, another set of Couette gas flows with different gas-surface potential strength ratios but the same channel height and density is simulated to study the gas-surface interaction effects on nanoscale gas flow. The results show that the gas density and velocity in the near wall region increase with increasing potential strength ratio between wall atoms and gas molecules. Large potential strength ratio cases (C 3.0) result in velocity sticking on the surface, which is induced by the gas molecule accumulation and surface adsorption. Using the same approach, the TMAC values for various potential strength ratios are calculated, varying from 0.63 to 0.96 for different cases (C=0.5-4.0), which indicates that the stronger the potential energy acting on the gas molecules, the more easily the gas molecules generate the diffuse reflection on the walls

Modern system of multiphase flow in porous media and its development trend

Fluid flow in porous media is the key scientific problem in the development of oil and gas reservoirs. The traditional mechanics of fluid flow in porous media which based on the continuum hypothesis and Darcy′s law plays an important role in developing conventional oil and gas resources. In recent years, unconventional reservoirs are drawing more and more attention all over the world, therefore the development theory and technology, especially the corresponding flow mechanisms have become the hot research issues. The unconventional reservoirs exhibit distinct multiscale characteristics, even with six orders of magnitude difference. In addition, the application of massive multi-stage hydraulic fracturing can induce strong stress interactions. Therefore, the traditional theory of fluid flow in porous media cannot accurately describe the flow characteristics in unconventional reservoirs. In essence, the development of unconventional oil and gas resources involves multiphase fluids (e.g. oil, water and gas) flow in multi-scale porous media with multi-field coupling and various flow patterns. Therefore, the concept of modern system of multiphase flow in porous media is proposed, which means multiphase fluids flowing in multi-scale porous media with multi-field coupling and various flow patterns. The research status and development tendency are reviewed from the aspects of: (1) micro- and nanoscale oil and gas flow simulation; (2) upscaling for reservoir simulation, (3) macroscale flow simulation of unconventional oil and gas reservoirs; (4) simulation of flow in large scale fractured and vuggy carbonate reservoirs and (5) physical simulation of hydrocarbon transport in porous media. More specifically, in nanoscale the density functional theory and molecular simulation method can be used to study the interfacial phenomena to understand the hydrocarbon transport behavior in nanopores and provide key parameters for mesoscale flow simulation. The current study of nanoscale simulation mainly focuses on developing more realistic molecular structure model to represent the heterogeneous shale samples. Microscale simulation methods involve pore network model, lattice Boltzmann method, direct simulation of Navies-Stokes equation, level-set method and smoothed particle hydrodynamics, etc. Digital core and pore network model are the fundamental research platforms. Various methods can be used to reconstruct digital cores with multiscale pore structures and mineral compositions. The complex physicochemical phenomena namely adsorption/desorption, wettability change and boundary effect should be considered in the microscale flow simulations and extensive works have been done in microscale gas flow simulations. The future work on microscale simulation should focus on the multiphase flow mechanisms with multi-field coupling. The multiscale characteristics of unconventional reservoirs indicate the necessity of upscaling process to introduce the microscale flow mechanisms to macroscale. Homogenization theory and volume averaging method are the main upscaling approaches. Current upscaling methods are mostly based on the periodic boundary condition and are unreliable to be used in complex oil and gas reservoirs, which needs further study. In addition, more research needs to be conducted on the upscaling from molecular scale to mesoscale. In macroscale simulations of unconventional oil and gas reservoirs, the fluid-structure interaction should be considered and high efficiency numerical algorithm needs to be established. For large scale fractured and vuggy carbonate reservoirs, the non-Darcy flow characteristics and different flow regimes in vugs and fractures should be taken into account during flow simulation. Physical simulations of hydrocarbon transport in porous media are conducted at two scales: macroscale, nano- and microscale. Macroscale physical simulations aim at monitoring the dynamic saturation and pressure fields change under the realistic reservoir conditions. Nano- and microscale physical simulations are mainly applied to study the fluid transport mechanisms in single pore or throat. In summary, the proposed theory of multiphase fluids flowing in multi-scale porous media with multi-field coupling and various flow patterns can be applied to study the fluid flow problems in unconventional oil and gas industries.

The slip effect of micro-droplets in Rankine vortex

The method of moments with interphase slip is simplified to numerically study the interaction between nanoscale droplets and gas flow in a Rankine vortex. In the method, the flow of gas phase and the moments of the droplets size distribution are calculated respectively and the transfers of momentum and heat between the gas and the droplets which are expressed by the moments are introduced into the governing equations as the source terms. In this way, the velocity slip between the gas phase and the droplet phase is captured by the present method. Then, the method is used to simulate the flow of Rankine vortex where the water droplets with constant radius are injected into the vortex core. The results show that the vortex is disturbed and the droplets move outward due to the effect of the velocity slip between the phases. The larger the droplet radius, the stronger the velocity slip effect. When the radius of the injected droplets is small, the vortex keeps stable and the droplets aggregate as a ring outside the core of the vortex. When the droplets radii are large enough, the vortex is not stable any more due to the strong slip effect and negative vorticity is induced in the core of the vortex. The droplets form a swing arm and spiral out of the vortex. At last, the effects of the growth of droplets on the vortex evolution and interphase slip are also investigated. The grown droplets spiral out and the position of maximum mean radius also moves outward with time. In the vortex core, condensation stops after a short time because no more vapor is supplied. With the growing process, more momentum is transferred from the gas phase to the droplets and the slip velocity between droplets and gas vanishes more quickly.

Local effective viscosity of gas in nano-scale channels

The non-equilibrium molecular dynamics method is used in the present study to investigate the local effective viscosity in nano-scale shear-driven gas flows. The profiles of gas velocity and shear stress across the channel are sampled and the Newton law of viscosity is applied to obtain the local effective viscosity. By using this method, the profile of local effective viscosity across the channel is obtained. In the bulk region of the channel, the local effective viscosity agrees well with the experimental value. However, in the near wall region, the local effective viscosity deviates from experimental value. The wall influence depth decreases with the increase of gas density, and this depth is independent of channel height, temperature and shear velocity in the shear driven Couette flow. The wall influence depth is approximately twice of the mean free path.

Diffusion characteristics of nanoscale gas flow in shale matrix from Haenam basin, Korea

To develop a shale gas reservoir, the gas flow in shale matrix essentially needs to be analyzed. The shale matrix consists of fractures and nanopores that have separate flow mechanisms. The purpose of this study is to investigate the gas diffusion in the nanopores of a shale matrix from the Haenam basin, Korea. To examine gas diffusion, an apparatus was developed to measure shale properties at the nanopore-scale. Subsequently, the measured properties were used to describe gas diffusion based on the Knudsen and Fick diffusion models. During the investigations, the pressure condition ranged from 0.69 to 41.37 MPa, setting temperature condition of 298.15 K. From the results, it was revealed that Knudsen diffusion was controlled by the pore sizes and pressure, while the Fick diffusion was governed by gas molecular radius and temperature. Therefore, shale gas diffusion should be evaluated by considering the parameters such as pore size, pressure, temperature, and gas molecular radius.

Porous silver nanosheets: a novel sensing material for nanoscale and microscale airflow sensors

Fabrication of nanoscale and microscale machines and devices is one of the goals of nanotechnology. For this purpose, different materials, methods, and devices should be developed. Among them, various types of miniaturized sensors are required to build the nanoscale and microscale systems. In this research, we introduce a new nanoscale sensing material, silver nanosheets, for applications such as nanoscale and microscale gas flow sensors. The silver nanosheets were synthesized through the reduction of silver ions by ascorbic acid in the presence of poly(methacrylic acid) as a capping agent, followed by the growth of silver in the shape of hexagonal and triangular nanoplates, and self-assembly and nanojoining of these structural blocks. At the end of this process, the synthesized nanosheets were floated on the solution. Then, their electrical and thermal stability was demonstrated at 120 °C, and their atmospheric corrosion resistance was clarified at the same temperature range by thermogravimetric analysis. We employed the silver nanosheets in fabricating airflow sensors by scooping out the nanosheets by means of a sensor substrate, drying them at room temperature, and then annealing them at 300 °C for one hour. The fabricated sensors were tested for their ability to measure airflow in the range of 1 to 5 ml min−1, which resulted in a linear response to the airflow with a response and recovery time around 2 s. Moreover, continuous dynamic testing demonstrated that the response of the sensors was stable and hence the sensors can be used for a long time without detectable drift in their response.

A new form of the second-order temperature jump boundary condition for the low-speed nanoscale and hypersonic rarefied gas flow simulations

The accuracy of numerical simulations of rarefied gas flows, in particular the Navier-Stokes-Fourier (N–S–F) equations, depends on the employed surface boundary conditions. In the literature, the combination of the second-order slip/jump conditions has primarily been used for either the Burnett or the BGK Burnett equations for hypersonic gas flows. In this work, we suggest the second-order temperature jump condition in a new form. The second-order slip/jump conditions are implemented in the framework of OpenFOAM to employ with the N–S–F equations for low-speed nanoscale and hypersonic rarefied gas flows. We investigate both the first and second-order slip/jump boundary conditions for low speed rarefied gas flow in the pressure-driven backward facing step nanochannel as well as hypersonic gas flows over the flat plate and past a circular cylinder in cross-flow. Simulation results show that the combination of the second-order slip/jump (in new form) conditions predicts better surface properties than those of the first-order slip/jump conditions for all cases studied by comparing the Burnett and DSMC data. Especially, the N–S–F simulation results of the second-order slip/jump (in new form) conditions of the cylinder case can capture the Burnett data at Kn = 0.1, while those of the first-order conditions do not.

Experimental investigation on the characteristics of gas diffusion in shale gas reservoir using porosity and permeability of nanopore scale

Abstract The aim of this study is to investigate the diffusion characteristics of nanoscale gas flow in a shale gas reservoir. An experimental apparatus was designed and set up to measure porosity and permeability at the nanopore scale. The measured properties have been used to determine a diffusion coefficient by classification standard of gas flow regime. To investigate the impact of pressure and pore size, the analysis of diffusion flow was conducted using Knudsen and Fick diffusion coefficients. From the results, it was revealed that Knudsen diffusion coefficient gradually increased with the growth of pressure and pore radius and Fick diffusion coefficient was dependent on the gas molecular diameter and temperature. It was also found that Knudsen diffusion coefficient was equal to Fick diffusion coefficient if pore radius is too small. The study implied that the characteristics of gas diffusion should be implemented by using the diffusion coefficient theory based on gas flow regime in shale gas reservoirs.

Investigation of Gas Local Effective Viscosity in Nano-scale Channels

The non-equilibrium molecular dynamics method is used in this paper to simulate the nano-scale shear-driven gas flows. The velocity gradients and shear stress profiles across the channel are first sampled according to molecular positions and thermal velocities. The Newton viscosity law is then adopted to obtain the local effective viscosity. By using this method, the distribution of effective viscosity across the channel is achieved for the first time. The effective viscosity in the bulk region of the channel agrees very well with the experimental data at different gas density and wall velocity. However, the local effective viscosity decreases when the fluid approaches the wall, because of the interactions between wall and gas molecules. The wall influence depth is independent of the wall velocity in Couette flow. However, this depth decreases with the increase of gas density due to more inter-molecule collisions.

J0540202 多孔質体内ナノスケール気体流れの流動特性に関する研究

J0540202 多孔質体内ナノスケール気体流れの流動特性に関する研究

Molecular free paths in nanoscale gas flows

Average distance traveled by gas molecules between intermolecular collisions, known as the mean free path (MFP), is a key parameter for characterizing gas flows in the entire Knudsen regime. Recent literature presents variations in MFP as a function of the surface confinement, which is in disagreement with the kinetic theory and leads to wrong physical interpretations of nanoscale gas flows. This controversy occurs due to erroneous definition and calculation practices, such as consideration of gas wall collisions, using local bins smaller than a MFP, and utilizing time frames shorter than a mean collision time in the MFP calculations. This study reports proper molecular MFP calculations in nanoscale confinements by using realistic molecular surfaces. We utilize molecular dynamics (MD) simulations to calculate gas MFP in three-dimensional periodic systems of various sizes and for force-driven gas flows confined in nano-channels. Studies performed in the transition flow regime in various size nano-channels and under a range of gas–surface interaction strengths have shown isotropic mean travelled distance and MFP values in agreement with the kinetic theory regardless of the surface forces and surface adsorption effects. Comparison of the velocity profiles obtained in MD simulations with the linearized Boltzmann solutions at predicted Knudsen values shows good agreement in the bulk of the channels, while deviations in the near wall region due to the influence of surface forces are reported.