Knudsen Flow Research Articles

Tri-functional carbon membrane for one-step uptake of low-concentration hydrogen to high purity

The uptake of hydrogen (H2) from natural gas pipelines (CH4) through membrane separation technology is an efficient avenue of obtaining H2 resources. Carbon membranes have the potential to be an attractive option for energy-efficient gas separations in the next generation of membranes due to their precise molecular discrimination ability and easy scalability. Here, we report a carbon membrane composed of a mesoporous substrate, seed layer and sieving layer, achieving a one-step uptake with 55.3 × 10-9 mol·m−2·s−1 Pa−1 permeance and a separation factor for H2/CH4 of 359.1 by feeding hydrogen (20 vol%). As revealed by the kinetic diffusion experiment, H2 is transported in mesoporous substrate via Knudsen flow, differing from the transition flow taken by CH4, thus H2 diffusion rates exceed CH4 by an order of magnitude, which substantially increased H2 purity from 20 vol% to higher purity as gas mixtures passed through the substrate. Then, the H2 passed through the seed layer and sieving layer, resulting in a final H2 purity of ∼ 99 vol%, a sharp increase from the initial low concentration. This carbon membrane integrates three functions of capture, pre-separation and purification into one material and provides a new solution for the uptake of H2 from CH4.

Comparative Study on Flow Characteristics in Deep Marine and Marine-Continental Transitional Shale in the Southeastern Sichuan Basin, China.

Permeability is a significant characteristic of porous media and a crucial parameter for shale gas development. This study focuses on deep marine and marine-continental transitional shale in the southeastern Sichuan area using the gas pulse decay testing method to systematically analyze the gas permeability, stress sensitivity, and gas transport mechanisms of shale under different pressure conditions and directions. The results show that the porosity and gas permeability of the deep marine shale are greater compared to those of the marine-continental transitional shale. The elevated fluid pressure in the deep marine shale offers superior conditions for the preservation of nanopores, while the high quartz content provides advantageous conditions for fluid transport in nanopore channels. The permeability and stress sensitivity of the deep marine shale are greater than those of the marine-continental transitional shale, and the stress sensitivity is greater in the perpendicular bedding direction than in the parallel bedding direction, possibly related to the mineral composition of shale and the compaction it has undergone. The flow mechanism of the deep marine shale is transition flow and Knudsen flow, while that of the marine-continental transitional shale is transition flow. The deep marine shale possesses smaller nanopore sizes and a higher quantity of micropores, which create advantageous conditions for gas transport within nanopores. During the process of extracting shale gas, the extraction of gas causes a decrease in pore pressure and an increase in effective stress, resulting in a reduction in permeability. However, when the pore pressure reaches a specific value, the enhanced slippage effect leads to an increase in permeability, which is advantageous for gas extraction. In the later stage of shale gas well production, intermittent production plans can be developed considering the strength of the slippage effect, leading to a significant improvement in production efficiency.

Modeling of dual-skin asymmetric hollow fiber microporous membranes for predicting the skins parameters separately using gas permeation test

This study presented a comprehensive gas permeation model to predict the skin parameters of a complex system, specifically a hollow fiber membrane with an asymmetric structure consisting of two external and internal skin layers. According to the work of Haefer for n segments of pores connected in series as in hollow fiber membranes, applying the Wakao et al. model, a comprehensive model for the transition regime was derived. The model was examined against the various fabricated PES and PEI hollow fiber membranes. Unlike conventional models, the proposed method predicted the mean pore size and mean pore length independent of surface porosity for each skin layer. The study revealed valuable insights into i) the middle pressure, ii) the difference between the skin parameters of the two membrane skins, and iii) the impact of the feeding direction on gas permeation behavior. It was shown that the dependency of permeation behavior on the feeding direction is linked to the influence of middle pressure on viscous flow, which is closely related to surface porosities of each side. It is evident that even the slightest variations in the fabrication parameters can result in different structures. Furthermore, it is evident that the assumption of neglecting slip flow was reasonable within the experienced Knudsen number range. The model also highlighted that the skin parameters of the two skin layers may not be identical, a distinction not captured by the current models. The traditional approach of setting the middle pressure as the average of the upstream and downstream pressures has been improved by expressing it as a linear function of both pressures. In the feed side, higher pressures led to dominant viscous flow, whilst the permeate side was more influenced by the free molecular regime due to lower pressures. There existed a competition between the Knudsen flow and the viscous flow at a specific Knudsen number for the feeding side pores, whether it was the inner or outer surface. The finding emphasized the significance of porosity values on each side in determining the proximity of middle pressure to feed and permeate side pressures, underscoring the importance of accurate knowledge of surface porosities, mean pore sizes, and pore lengths for both skin layers in understanding processes involving porous dual-skin hollow fiber membranes.

Heterogeneous reactivity of soybean/palm biodiesel soot with NO2 and CF3COOH in a Knudsen reactor and DRIFTS/TGA/SEM characterization of the soot

The characteristics and atmospheric reactivity of soot generated from an alternative fuel (soybean/palm biodiesel) have been investigated for the first time using a Knudsen flow reactor with a mass spectrometer as detector for gaseous species. The heterogeneous reactions with nitrogen dioxide (NO2) and trifluoroacetic acid (CF3COOH, TFA) have been investigated. Uptake coefficients calculated for the reaction of NO2 (γ0= (3.85 ± 0.70) ∙10–3) are one order of magnitude higher than the corresponding TFA reactions (γ 0= (6.06 ± 0.24) ∙10–4). NO is the only product observed in the gas phase. Knudsen cell reactor has also been used in the characterization of chemical functions on the surface since NO2 can be used to identify reducing groups, while TFA is used to evaluate basic sites. Compared to other soot samples, biodiesel soot shows higher reactivity with NO2 which has implications in the regeneration process of the diesel particulate filter (DPF). IR bands attributable to polycyclic aromatic compounds have been observed by Diffuse Reflectance Infrared Fourier Transform spectroscopy (DRIFTs). Bands of carbonyl compounds are also clearly observed. Thermogravimetric analysis/ differential scanning calorimetry-mass spectrometry (TGA/DSC-MS) is used to obtain more information about the volatile organic compounds present on the soot surface. Scanning Electron Microscopy/Energy Dispersive Spectroscopy (SEM/EDS) analysis indicates a particle size in the range 14–40 nm and carbon as the major element (92 %). According to the obtained results, a mechanism of processes occurring at the surface has been proposed.

CO2 Leakage Scenarios in Shale Overburden

Potential CO2 leakage from deep geologic reservoirs requires evaluation on a site-specific basis to assess risk and arrange mitigation strategies. In this study, a heterogeneous and realistic numerical model was developed to investigate CO2 migration pathways and uprising time in a shaly overburden, located in the Malaysian off-shore. Fluid flow and reactive transport simulations were performed by TOUGHREACT to evaluate the: (1) seepage through the caprock; (2) CO2-rich brine leakage through a fault connecting the reservoir with seabed. The effect of several factors, which may contribute to CO2 migration, including different rock types and permeability, Fickian and Knudsen diffusion and CO2 adsorption in the shales were investigated. Obtained results show that permeability mainly ruled CO2 uprising velocity and pathways. CO2 migrates upward by buoyancy without any important lateral leakages due to poor-connection of permeable layers and comparable values of vertical and horizontal permeability. Diffusive flux and the Knudsen flow are negligible with respect to the Darcy regime, despite the presence of shales. Main geochemical reactions deal with carbonate and pyrite weathering which easily reach saturation due to low permeability and allowing for re-precipitation as secondary phases. CO2 adsorption on shales together with dissolved CO2 constituted the main trapping mechanisms, although the former represents likely an overestimation due to estimated thermodynamic parameters. Developed models for both scenarios are validated by the good agreement with the pressure profiles recorded in the exploration wells and the seismic data along a fault (the F05 fault), suggesting that they can accurately reproduce the main processes occurring in the system.

Modes of multi-mechanistic gas diffusion in shale matrix at varied effective stresses: Observations and analysis

Gas diffusion in the shale matrix has a dominant effect on late-stage production from shale gas reservoirs. However, adequate research on the mechanisms and contributions of gas diffusion for varied pore size populations in shale matrix under recreated in situ stress is lacking. We report gas-diffusion measurements under constant in situ stress but variable gas pressures for contrasting non-adsorbent (helium (He)) and adsorbed (methane (CH4)) gases to investigate the impact of effective stress on the evolution of dominant mechanisms of diffusion. An intact sample replicates true pore-network topology and diffusion paths. An integrated diffusion model is proposed that combines the effects of slip flow, Knudsen flow, and surface diffusion to constrain the evolution of these flow regimes and their respective contributions to the observational data. Finally, a probability density function (PDF) is employed to separate the gas content distributions of macropores and micropores from the total gas content and to investigate gas contributions in various pores. The results reveal that the diffusion coefficients of both He and CH4 in macropores and micropores increase with gas pressure but decrease with increasing effective stress. The diffusion coefficients of He and CH4 are different in macropores but remain nearly the same in micropores. The diffusion coefficients of slip flow and surface diffusion increase with decreasing effective stress except for CH4 diffusion in the micropores, while the evolution of Knudsen diffusion shows the opposite trend. Slip flow plays a dominant role in He and CH4 diffusion within macropores (pore size 45 nm). Knudsen diffusion gradually becomes significant for He diffusion in the micropores (pore size 4 nm), conversely, for CH4 diffusion in the micropores, surface diffusion becomes significant. Related to gas production from reservoirs, the contributions of the micropores will increase gradually with the duration of gas recovery, indicating the significant role of gas diffusion in micropores to steady supply during late-stage production.

Characterization of H2O vapor transport through lunar mare and lunar highland simulants at low pressures for in-situ resource utilization

H2O(v) transport through packed beds of lunar mare and lunar highland simulants was examined for relevant in-situ resource utilization conditions to inform volatile H2O extraction from the lunar surface. Experiments were conducted with different packed beds at average bed pressures of 105 and 3,960 Pa at ∼ 350 K for different flow regimes in the range of 0.47 <Kn¯ < 20.7. A piecewise model was used to describe the transition between the advective flow regime and the Knudsen flow regime. Non-linear regression was used to determine a tortuosity shape factor of 2.6175 ± 0.0092 and 0.0937 ± 0.0008, a transition Knudsen number of 1.5984 and 4.0995, and a viscous flow permeability of 0.8238 ± 0.0010 × 10-12 m2 and 5.4805 ± 0.0061 × 10-12 m2 for the lunar mare and lunar highland simulants, respectively. The resulting Knudsen diffusivities were 6.6530 ± 0.0018 cm2·s−1 and 18.9008 ± 0.0100 cm2·s−1, respectively. These results are necessary for informing the development of in-situ resource utilization technologies for the thermal extraction of H2O.

GAS PERMEABILITY IN POROUS MEDIA WITH ROUGH SURFACES BY FRACTAL-MONTE CARLO SIMULATIONS

Gas permeability is an important parameter for gas transport in microporous and nanoporous media. A probability model of gas permeability of fractal porous media with rough surfaces is proposed and numerically simulated by the Monte Carlo technique. This model consists of two gas flow mechanisms: the Poiseuille flow and the Knudsen flow, and can be expressed by structural parameters, such as the pore fractal dimension, the tortuosity fractal dimension, the relative roughness and porosity. The validity of the proposed model is investigated through the available experimental data, and a good agreement is obtained. The predicted results indicate that gas permeability of microporous and nanoporous media with rough surfaces decreases with the increase of the relative roughness and the tortuosity fractal dimension, and increases with the increase of porosity and the pore fractal dimension. Our gas permeability model could reveal the physical mechanisms of gas transport in porous media with rough surfaces.

The Kinetics of Adsorption and Desorption of Selected Semivolatile Hydrocarbons and H2O Vapor on Two Mineral Dust Materials: A Molecular View.

A flowing gas experiment using a Knudsen flow reactor was performed on a series of seven semivolatile probe gases interacting with two often used mineral dust materials, namely, coarse Arizona test dust (ATD-C) and kaolinite. The semivolatile probe gases used were applinate (acetate ester), pipol (ethyl ester of 2-methylvaleric acid), benzylacetate (acetate ester of benzylalcohol), menthol (alcohol), toluene, limonene, and γ-terpinene (terpene hydrocarbon). Uptake experiments under molecular flow conditions resulted in absolute coverages and initial uptake coefficients γ0 based on the geometric sample surface. Integration of a simple Langmuir adsorption model afforded an analytical solution of the desorption kinetics of the semivolatile hydrocarbon upon spontaneous desorption from the solid mineral dust substrate at ambient temperature. Numerical fitting of the desorption rate resulted in adsorption (ka) and desorption (kd) rate constants, where 1/kd represented the surface residence time of the adsorbed semivolatile. The major conclusions are as follows: (a) Desorption at short ("prompt") and long time scales reveal stronger binding to ATD compared to kaolinite for all tested organic probe gases. (b) No difference in the desorption yields and kinetics was observed for H2O vapor on either substrate. (c) Prompt desorption at ambient temperature starts with the immediate detection of probe gases adsorbed on the vessel walls of the sample compartment, followed by the slower growth and decay of semivolatiles adsorbed on the substrate, leading to ka and kd. (d) Surface residence times at ambient temperatures for semivolatile organics vary from 50 to 40 000 s for toluene/ATD and menthol/ATD, respectively. For H2O vapor, 3000 s was measured on both kaolinite and ATD. (e) Large initial uptake coefficients γ0 in the range of 0.25-0.77 were measured for all semivolatiles except toluene, whose values were lower by roughly one order of magnitude. Rapid saturation was observed in all cases except for limonene, which appeared to undergo chemical reactions on both mineral substrates.

Shale gas mass transfer characteristics in hydration-induced fracture networks

The hydration-induced fractures significantly enhance shale gas production after well shut-in, which reveals considerable gas mass transfer characteristics. However, few studies focus on multiple flow mechanisms coupling the fracture distribution and morphological properties. Therefore, a novel apparent permeability (AP) model, in which poromechanics and desorption-induced aperture evolution are captured, has been derived to precisely define gas mass transfer through fracture networks. In this study, the fracture distributions are derived by fractal law, and the morphologies are solved using the orthogonal decomposition method (ODM) and shape coefficient correction. Viscosity changes in confined channels are also considered, further upscaling volume flux, Knudsen and surface diffusion through fractal theory by discrete integrals and derivation of the AP model combined with Darcy's law. The proposed model is verified well by experiments and the literature. The results show that the viscous flow contribution ratio decreases with decreasing aperture, while the Knudsen flow ratio slightly increases, and gas desorption significantly increases permeability when pp < pL. Therefore, the viscous flow is the dominant flow regime at high pp, and Knudsen and desorption diffusion gradually dominate the transmission at low pp. The larger bmax/bmin obviously enhances AP, the more confined apertures, and the AP decreases obviously as pp decreases. The stronger desorption and diffusion capability represent that gas will be transported sufficiently, higher co and δ indicate that the aperture is close more effectively, causing the AP reduction to be fast, and hydration further lowers E and v denotes higher AP due to the aperture shrinkage being replaced by matrix parts. The real gas effect on AP reduction cannot be ignored. This study identifies the gas transport characteristics in hydration fracture networks, with the research method also being applicable to other structures.

Flowing Gas Experiments Reveal Mechanistic Details of Interfacial Reactions on a Molecular Level at Knudsen Flow Conditions

Knudsen flow experiments and its interpretation in terms of adsorption/desorption kinetics as well as quantitative uptake on substrates of interest is presented together with the description of critical design parameters of the Knudsen Flow Reactor (KFR). Hitherto focused almost exclusively on the uptake phase exposing a virgin substrate to interacting gases, we now extend the experiment and its interpretation to the desorption phase at ambient temperature. We present analytical expressions for different experimental situations in terms of adsorption (ka), desorption (kd) and effusion (ke) rate constants. The measurement of kd leads to surface residence times (1/kd) obtained under the same experimental conditions as the uptake (ka) that results in the determination of the Langmuir equilibrium constant KL = ka/kd. We emphasize the interaction of semivolatile organic probe gases and small polar molecules with amorphous carbon and mineral dust materials at ambient temperatures. The latter leads to a molecular characterization scheme based on the use of up to ten different reactive probe gases. After saturation of the uptake of each probe gas this results in a reactivity map of the interface. Several examples are used to underline the broad applicability of the technique such as the silver/air (Ag) interface and the reactivity of TiO2 materials towards uptake of CO2 and CH3OH. Following characterization of several types of amorphous carbon a model incorporating several structural elements in agreement with the reactive gas titration is proposed. For instance, an interface that is at the same time weakly basic and strongly reducing is composed of pyrones and hydroquinones whose simultaneous occurrence leads to stable free radicals that may play a role in atmospheric chemistry (EPFR). The question is raised what makes an interface hydrophobic in terms of surface functional groups when interacting with small polar molecules such as H2O(D2O), HCl, NO2 and NH2OH. Multidiagnostic studies of heterogeneous reactions are enabled using stirred-flow reactors (SRF) that are a logical extension of the KFR approach thus relaxing the Knudsen flow requirements. Previous work using SRF on low-temperature substrates such as H2O ices is highlighted that may be of interest to the exoplanetary and space sciences community.

Computational fluid dynamics based numerical simulations of heat transfer, fluid flow and mass transfer in vacuum membrane distillation process

Abstract In this study, we developed a comprehensive two-dimensional computational fluid dynamics (CFD) model using COMSOL™ Multiphysics to describe and simulate heat transfer, mass transfer and fluid flow in the flat sheet vacuum membrane distillation (VMD) under laminar flow conditions. A combination of Knudsen and Poiseuille flow was applied to study mass transfer across the membrane. The effect of variation of Reynolds number, inlet feed temperature and degree of vacuum on different parameters (mass flux, temperature polarization coefficient- TPC, concentration polarisation, heat transfer coefficient) was studied. There was a positive impact of the Reynolds number (50–200) on mass flux (13.15%), heat transfer coefficient (2.64%) and TPC (1.42%), while CPC decreased by 56.63%. The increment in the heat transfer coefficient was due to fluid mixing on the feed side, while the increment in the TPC was due to a higher temperature gradient across the membrane surfaces. The increment in the feed temperature (323–343 K) resulted in an increase in mass flux by 132.9%, while TPC decreased from 0.98 to 0.90. The degree of vacuum (640–750 mm Hg) increased mass flux and heat transfer coefficient by 72.52 and 425.83%, respectively, while the TPC decreased by 8.81%. The feed temperature was the most sensitive parameter with respect to mass flux. The developed CFD model was validated with in-house experimental results with reasonable accuracy.

Investigation of Shale Permeability Evolution considering Bivalued Effective Stress Coefficients for CO2 Injection

Because of the existence of multiscale pores from nano- to macroscale, a multimechanistic shale gas flow process involving the Darcy and Knudsen flows occurs during gas shale well depletion. The respective contribution of the Darcy and Knudsen flows to the permeability is constantly changing with pressure evolution. In this study, laboratory measurements of shale permeability with CO2 injections were carried out under hydrostatic conditions, using the transient pulse-decay method. The “U”-shape permeability curve resulted in both positive and negative effective stress coefficients (Biot’s coefficient) χ . A permeability turning point was thus created to partition permeability curves into the Darcy and Knudsen sections. The Knudsen effect was proven to be significant at low pressure/late time in the laboratory. Effective stress and sorption-induced deformation have been found to govern the Darcy permeability evolution under the tested experimental conditions. Thus, negative effective stress coefficients, together with the positive ones, should be applied to a nonmonotonic pressure-permeability evolution to explain the concurrent effect of the Darcy flow and Knudsen flow at different pore pressures.

Coexistence of reactive functional groups at the interface of a powdered activated amorphous carbon: a molecular view

Titration experiments using ten reactive probe gases interacting with a Powdered Activated Carbon (PAC) sample have been performed in a two-chamber Knudsen flow reactor equipped with molecular-beam modulated mass spectrometric detection. The goal of these uptake and desorption experiments performed at ambient temperature was to establish a map of reactive sites at the PAC interface of 1580 m2/g BET surface area. The extent of the net uptake of the probe gases in molecule cm−2 was in the order O3 >> NO2 > TFA (trifluoroacetic acid, CF3COOH) >HA (hydroxylamine, NH2OH) > C4H4S (thiophene) > TMA (trimethylamine) > HCl > H2O > H2S > SO2. PAC may, therefore, be characterised as a reduced and weakly basic type of amorphous carbon. The sum of individual coverages amounts to 62.5% and corresponds to a highly decorated PAC interface. Six out of ten probe gases (H2O, NO2, HCl, TMA, TFA and thiophene (C4H4S)) spontaneously desorb to variable extents at ambient temperature under flow reactor conditions from a previously saturated PAC interface. The adsorption/desorption rate coefficients were fitted to the experimental desorption rates using an analytical solution. For HCl, NO2 and H2O a rather large discrepancy of a factor of 7.3, 12.7 and 71.4, respectively, between the initial uptake rate constant k 0 on a virgin non-polar PAC surface and a gas-saturated PAC surface upon readsorption occurring in spontaneous desorption experiments (ka ) has been detected.

Viscous and Knudsen gas flow through dry porous cometary analogue material

ABSTRACTAccording to current theories of the formation of stellar systems, comets belong to the oldest and most pristine class of bodies to be found around a star. When approaching the Sun, the nucleus shows increasing activity and a pressure increase inside the material causes sublimated and trapped gas molecules to stream away from their regions of origin towards the surface. The present work studies two essential mechanisms of gas transport through a porous layer, namely the Darcy and the Knudsen flow. Gas flow measurements are performed in the laboratory with several analogue materials, which are mimicking dry cometary surface properties. In this first series of measurements, the aim was to separate gas transport properties from internal sources like local sublimation or release of trapped gases. Therefore, only dry granular materials were used and maintaining a low temperature environment was unnecessary. The gas permeability and the Knudsen diffusion coefficient of the sample materials are obtained, thereby representing the relative importance of the respective flow mechanism. The experiments performed with air at a stable room temperature show that the grain size distribution and the packing density of the sample play a major role for the permeability of the sample. The larger the grains, the bigger the permeability and the Knudsen diffusion coefficient. From the latter, we estimated effective pore diameters. Finally, we explain how these parameters can be adapted to obtain the gas flow properties of the investigated analogue materials under the conditions to be expected on the comet.

Impact of Evaporation and Precipitation on Estuarine Mixing

AbstractRecent studies could link the quantities of estuarine exchange flows to the volume-integrated mixing inside an estuary, where mixing is defined as the destruction of salinity variance. The existing mixing relations quantify mixing inside an estuary by the net boundary fluxes of volume, salinity, and salinity variance, which are quantified as Knudsen or total exchange flow bulk values. So far, river runoff is the only freshwater flux included, and the freshwater exchange due to precipitation and evaporation is neglected. Yet, the latter is the driving force of inverse estuaries, which could not be described by the existing relations. To close this gap, this study considers evaporation and precipitation to complete the existing mixing relations by including cross-surface salinity variance transport. This allows decomposing the mixing into a riverine and a surface transport contribution. The improved relations are tested against idealized two-dimensional numerical simulations of different combinations of freshwater forcing. The mixing diagnosed from the model results agrees exactly with the derived mixing relation. An annual hindcast simulation of the Persian Gulf is then used to test the mixing relations, both exact and approximated, e.g., long-term averaged, for a realistic inverse estuary. The results show that the annual mean mixing contributions of river discharge and evaporation are almost equal, although the freshwater transport due to evaporation is about one order of magnitude larger than the river runoff.

Petrophysical Characterizations of Shale Gas Reservoirs of the Ranikot Formation in the Lower Indus Basin, Pakistan

The complex pore structure with nano-pores of shale gas reservoirs has an impact on the hydrocarbon storage and transport systems. We examined the pore structure of the shales of the Ranikot Formation in the Lower Indus Basin, Pakistan to investigate the full scaled pore size distributions by using a combination of techniques, mercury injection capillary pressure analysis and low pressure gas adsorption methods using N2 and CO2. Isotherm curves obtained N2 and CO2 adsorptions were interpreted using density functional theory analysis for describing the nano-scaled pore size distributions. The pore geometry of the shales was estimated to be slit-type from the isotherm hysteresis loop shape. The pore size distributions determined the density functional theory showed the dominant pore size of below around 10 nm. The Micro-scale effects such as slippage and adsorption/desorption also significantly influence the gas flow in nano-pore structure. The gas flow regimes in shales are classified into four types Darcy flow, slip flow, transition flow, Knudsen flow based on the value of the Knudsen number. Applying the specific reservoir conditions in Ranikot shale and pore size distribution to the Knudsen number, the gas flow regimes of the Ranikot shales were estimated mostly within the transition and slip flow.

Effect of coating steps on uniformity and gas permeability of mesoporous layers in ceramic membranes

Abstract Porous silica, silica-cobalt, silica-zirconia and zirconia membranes were synthesized by the sol-gel method. Multi-step coating (two, six, and ten steps) was used to reduce the defectiveness of the mesoporous layer. Scanning electron microscopy (SEM) images indicated that an increase in the number of coating steps improved the mesoporous layer quality. The results obtained from gas permeability tests with nitrogen and argon, however, indicated a reduction in the gas permeability with increasing coating steps. The reduction in gas permeability from two to six coating steps was more pronounced than from sixto ten- coating steps. It was found that six-step coating was economically justified in obtaining a uniform mesoporous layer. The results of pore radius calculations by Knudsen flow mechanism revealed that the pores in the silica, silica-cobalt, and zirconia membranes were in the mesoporous range. The sols with a mean particle size more than 100 nm are not recommended for synthesis of mesoporous layer free of defects. Furthermore, the type of acid used as a catalyst is also important in obtaining a layer without defectiveness.

Shale gas transport mechanisms in inorganic and organic pores based on lattice Boltzmann simulation

A better understanding on the mechanism and difference of shale gas transport through inorganic and organic pores is critical to accurately predicting shale gas recovery. Due to the complicated gas flow dynamics in such narrow pores, traditional experimental methods or simulation methods is difficult to accurately describe these processes. Here, a regularized lattice Boltzmann (LB) model coupled with the slippage boundary condition and gas adsorption effect is employed to simulate shale gas transport in the inorganic and organic pore. The adsorption parameters of shale gas in the LB model are obtained from the molecular dynamics (MD) simulations. Effects of the adsorption effect, pore size, pore wall roughness and gas rarefaction effect on the shale gas transport are studied. The simulation results show that the shale gas transport mechanism heavily depends on the pore size. Basically, in the nano-scale pore, the gas slippage and Knudsen flow are the dominated transport mechanism, but the gas transport is dominated by the surface diffusion in the organic pore width with less than 5 nm owing to the gas adsorption effect. The surface roughness effect plays an important role in the gas transport, and this effect significantly increases with the decreasing of the Knudsen number. At the same time, the gas adsorption effect can also cause a significant increase of the friction factor and a slight decrease of the mass flow rate, which indicates that the gas adsorption effect must be considered in the organic roughness pores.

Apparent Permeability Prediction of Coal Matrix with Generalized Lattice Boltzmann Model considering Non-Darcy Effect

Methane flow in coal is associated with the content of both organic matter (OM) and inorganic matter (IOM). Coal matrix contains nanopores ranging in size from a few to hundreds of nanometers, which leads to a non-Darcy effect where the measured permeability of a gas (apparent permeability) is higher than that of a liquid (intrinsic permeability). In this study, a generalized Lattice Boltzmann model (GLBM) is employed for gas flow through the reconstructed coal matrix consisting of OM, IOM, and fractures. The apparent permeability model is proposed to calculate the total flow flux accounting for multiple transport mechanisms including viscous flow, slip flow, transitional flow, and the Knudsen diffusion. The impact of effective pore radius and gas surface diffusion on permeability in the gas adsorption-desorption process is also considered in the model. What’s more, the weighting factors are adopted to adjust the contribution of the viscous flow and the Knudsen flow. The effect of total organic/inorganic content and the development of fractures on the apparent permeability of the reconstructed coal matrix is also studied. It is found that the apparent permeability is extremely low when a fracture is nonexistent, and varies almost linearly with the total organic/inorganic content. A fracture plays a significant role in determining apparent permeability and the velocity distribution of the coal matrix.