Knudsen Diffusion in the Sequentially Linked Spherical Pore.

1998 ◽  
Vol 31 (4) ◽  
pp. 644-648 ◽  
Author(s):  
Soong-Hyuck Suh ◽  
Nam-Ho Heo ◽  
David Nicholson
Keyword(s):  
Knudsen Diffusion ◽  
Spherical Pore

scholarly journals “Artificial Wood” Lignocellulosic Membranes: Influence of Kraft Lignin on the Properties and Gas Transport in Tunicate-Based Nanocellulose Composites

Membranes ◽  
2021 ◽  
Vol 11 (3) ◽  
pp. 204
Author(s):  
Ievgen Pylypchuk ◽  
Roman Selyanchyn ◽  
Tetyana Budnyak ◽  
Yadong Zhao ◽  
Mikael Lindström ◽  
...  
Keyword(s):  
Knudsen Diffusion ◽  
Cellulose Nanofibers ◽  
Kraft Lignin ◽  
Separation Processes ◽  
New Approach ◽  
Future Studies ◽  
Different Types ◽  
Molecular Sizes ◽  
Fast Transport ◽  
Cellulose Membranes

Nanocellulose membranes based on tunicate-derived cellulose nanofibers, starch, and ~5% wood-derived lignin were investigated using three different types of lignin. The addition of lignin into cellulose membranes increased the specific surface area (from 5 to ~50 m2/g), however the fine porous geometry of the nanocellulose with characteristic pores below 10 nm in diameter remained similar for all membranes. The permeation of H2, CO2, N2, and O2 through the membranes was investigated and a characteristic Knudsen diffusion through the membranes was observed at a rate proportional to the inverse of their molecular sizes. Permeability values, however, varied significantly between samples containing different lignins, ranging from several to thousands of barrers (10−10 cm3 (STP) cm cm−2 s−1 cmHg−1cm), and were related to the observed morphology and lignin distribution inside the membranes. Additionally, the addition of ~5% lignin resulted in a significant increase in tensile strength from 3 GPa to ~6–7 GPa, but did not change thermal properties (glass transition or thermal stability). Overall, the combination of plant-derived lignin as a filler or binder in cellulose–starch composites with a sea-animal derived nanocellulose presents an interesting new approach for the fabrication of membranes from abundant bio-derived materials. Future studies should focus on the optimization of these types of membranes for the selective and fast transport of gases needed for a variety of industrial separation processes.

scholarly journals The effect of Knudsen diffusion and adsorption on shale transport in nanopores

2017 ◽  
Vol 9 (9) ◽  
pp. 168781401772185 ◽  
Author(s):  
Jie Chen ◽  
Jiangyong Hou ◽  
Rui Wang ◽  
Yongchang Hui
Keyword(s):  
Knudsen Diffusion

Microwave-Assisted Synthesis and Permeation Performance of NaA Zeolite Membrane by Secondary Growth Method

2014 ◽  
Vol 1053 ◽  
pp. 389-393
Author(s):  
Zhi Lin Cheng ◽  
Ying Ying Liu
Keyword(s):  
Gas Permeability ◽  
Knudsen Diffusion ◽  
Secondary Growth ◽  
Zeolite Membrane ◽  
Microwave Assisted Synthesis ◽  
Vapor Phase Transport ◽  
Zeolite Membranes ◽  
Synthesis Time ◽  
Naa Zeolite ◽  
Naa Zeolite Membrane

The highly intergrown NaA zeolite membranes on seeded α-Al2O3substrate were synthesized by microwave heating method. The preparation of seeds with the size of ca.120nm employed the vapor phase transport method (VPT). The XRD patterns indicated that the pure NaA zeolite membranes formed on the seeded α-Al2O3substrate for varied synthesis times. However, the peak intensity of NaA zeolite membrane with synthesis time of 50min obviously decreased, suggesting that the NaA membrane could take place the dissolution at that time. The SEM images indicated that the NaA zeolite membranes with synthesis time of 15-30min had a good integrity and consisted of highly intergrown zeolite crystals, but the NaA membrane with synthesis time of 50min appeared some large defects, further verifying the result of XRD pattern. The gas permeability showed that the maximum of H2/N2and H2/C3H8permselectivities attained 4.23 and 8.24, respectively, higher than those of the corresponding Knudsen diffusion. These results suggested that the diffusion of gases, at least in part, are affected by the pore size of zeolite and the function of molecular sieving can be embodied on the synthesized membrane.

KNUDSEN DIFFUSION

Soil Science ◽  
1986 ◽  
Vol 141 (4) ◽  
pp. 289-297 ◽  
Author(s):  
STEPHEN M. CLIFFORD ◽  
DANIEL HILLEL
Keyword(s):  
Knudsen Diffusion

scholarly journals Gas Permeation Characteristics across Nano-Porous Inorganic Membranes

1970 ◽  
Vol 5 (2) ◽  
Author(s):  
M.R Othman, H. Mukhtar ◽  
A.L. Ahmad
Keyword(s):  
Pore Size ◽  
Membrane Surface ◽  
Porous Ceramic ◽  
Knudsen Diffusion ◽  
Gas Permeation ◽  
Physical Characteristics ◽  
Inorganic Membrane ◽  
Molecular Characteristics ◽  
Inorganic Membranes ◽  
Operational Parameters

An overview of parameters affecting gas permeation in inorganic membranes is presented. These factors include membrane physical characteristics, operational parameters and gas molecular characteristics. The membrane physical characteristics include membrane materials and surface area, porosity, pore size and pore size distribution and membrane morphology. The operational parameters include feed flow rate and concentration, stage cut, temperature and pressure. The gas molecular characteristics include gas molecular weight, diameter, critical temperature, critical pressure, Lennard-Jones parameters and diffusion volumes. The current techniques of material characterization may require complementary method in describing microscopic heterogeneity of the porous ceramic media. The method to be incorporated in the future will be to apply a stochastic model and/or fractal dimension. Keywords: Inorganic membrane, surface adsorption, Knudsen diffusion, Micro-porous membrane, permeation, gas separation.

Synthesis of Potassium Ionic Sieve Membrane and its Selectivity to Potassium Ion in Seawater

2010 ◽  
Vol 178 ◽  
pp. 300-307 ◽  
Author(s):  
Jun Sheng Yuan ◽  
Fei Li ◽  
Hui Ru Han ◽  
Zhi Yong Ji
Keyword(s):  
Hydrothermal Synthesis ◽  
Gas Permeability ◽  
Knudsen Diffusion ◽  
Potassium Ion ◽  
Zeolite Membranes ◽  
Al2o3 Tube ◽  
Separation Factors ◽  
Α Al2o3 ◽  
High Separation ◽  
The Ideal

Potassium ionic sieve membrane was synthesized on porous α-Al2O3 tube support by the hydrothermal synthesis. The zeolite membranes were characterized by means of XRD and SEM. And the single-gas permeability through the membranes and selectivity to K+, Na+, Ca2+, Mg2+ were measured. The results show that the ideal separation factor is 3.68, which is close to Knudsen diffusion ratio 3.74 for H2/N2; the separation factors of the potassium ionic sieve membrane are , , respectively, indicating its high separation selectivity to potassium ion.

Diffusion-Based Modeling of Gas Transport in Organic-Rich Ultratight Reservoirs

SPE Journal ◽  
2021 ◽  
pp. 1-26
Author(s):  
Zizhong Liu ◽  
Hamid Emami-Meybodi
Keyword(s):  
Diffusion Coefficient ◽  
Adsorption Capacity ◽  
Surface Diffusion ◽  
Diffusion Coefficients ◽  
Gas Transport ◽  
Knudsen Diffusion ◽  
Gas Production ◽  
Hydrocarbon Transport ◽  
The Impact ◽  
And Storage

Summary The complex pore structure and storage mechanism of organic-rich ultratight reservoirs make the hydrocarbon transport within these reservoirs complicated and significantly different from conventional oil and gas reservoirs. A substantial fraction of pore volume in the ultratight matrix consists of nanopores in which the notion of viscous flow may become irrelevant. Instead, multiple transport and storage mechanisms should be considered to model fluid transport within the shale matrix, including molecular diffusion, Knudsen diffusion, surface diffusion, and sorption. This paper presents a diffusion-based semianalytical model for a single-component gas transport within an infinite-actingorganic-rich ultratight matrix. The model treats free and sorbed gas as two phases coexisting in nanopores. The overall mass conservation equation for both phases is transformed into one governing equation solely on the basis of the concentration (density) of the free phase. As a result, the partial differential equation (PDE) governing the overall mass transport carries two newly defined nonlinear terms; namely, effective diffusion coefficient, De, and capacity factor, Φ. The De term accounts for the molecular, Knudsen, and surface diffusion coefficients, and the Φ term considers the mass exchange between free and sorbed phases under sorption equilibrium condition. Furthermore, the ratio of De/Φ is recognized as an apparent diffusion coefficient Da, which is a function of free phase concentration. The nonlinear PDE is solved by applying a piecewise-constant-coefficient technique that divides the domain under consideration into an arbitrary number of subdomains. Each subdomain is assigned with a constant Da. The diffusion-based model is validated against numerical simulation. The model is then used to investigate the impact of surface and Knudsen diffusion coefficients, porosity, and adsorption capacity on gas transport within the ultratight formation. Further, the model is used to study gas transport and production from the Barnett, Marcellus, and New Albany shales. The results show that surface diffusion significantly contributes to gas production in shales with large values of surface diffusion coefficient and adsorption capacity and small values of Knudsen diffusion coefficient and total porosity. Thus, neglecting surface diffusion in organic-rich shales may result in the underestimation of gas production.

What are the Dominant Flow Regimes During Carbon Dioxide Propagation in Shale Reservoirs’ Matrix, Natural Fractures and Hydraulic Fractures?

2021 ◽  
Author(s):  
Sherif Fakher ◽  
Youssef Elgahawy ◽  
Hesham Abdelaal ◽  
Abdulmohsin Imqam
Keyword(s):  
Carbon Dioxide ◽  
Viscous Flow ◽  
Flow Regime ◽  
Knudsen Diffusion ◽  
Flow Regimes ◽  
Hydraulic Fractures ◽  
Transition Flow ◽  
Pore Sizes ◽  
Thermodynamic Conditions ◽  
Shale Reservoirs

Abstract Carbon dioxide (CO2) injection in low permeability shale reservoirs has recently gained much attention due to the claims that it has a large recovery factor and can also be used in CO2 storage operations. This research investigates the different flow regimes that the CO2 will exhibit during its propagation through the fractures, micropores, and the nanopores in unconventional shale reservoirs to accurately evaluate the mechanism by which CO2 recovers oil from these reservoirs. One of the most widely used tools to distinguish between different flow regimes is the Knudsen Number. Initially, a mathematical analysis of the different flow regimes that can be observed in pore sizes ranging between 0.2 nanometer and more than 2 micrometers was undergone at different pressure and temperature conditions to distinguish between the different flow regimes that the CO2 will exhibit in the different pore sizes. Based on the results, several flow regime maps were conducted for different pore sizes. The pore sizes were grouped together in separate maps based on the flow regimes exhibited at different thermodynamic conditions. Based on the results, it was found that Knudsen diffusion dominated the flow regime in nanopores ranging between 0.2 nanometers, up to 1 nanometer. Pore sizes between 2 and 10 nanometers were dominated by both a transition flow, and slip flow. At 25 nanometer, and up to 100 nanometers, three flow regimes can be observed, including gas slippage flow, transition flow, and viscous flow. When the pore size reached 150 nanometers, Knudsen diffusion and transition flow disappeared, and the slippage and viscous flow regimes were dominant. At pore sizes above one micrometer, the flow was viscous for all thermodynamic conditions. This indicated that in the larger pore sizes the flow will be mainly viscous flow, which is usually modeled using Darcy's law, while in the extremely small pore sizes the dominating flow regime is Knudsen diffusion, which can be modeled using Knudsen's Diffusion law or in cases where surface diffusion is dominant, Fick's law of diffusion can be applied. The mechanism by which the CO2 improves recovery in unconventional shale reservoirs is not fully understood to this date, which is the main reason why this process has proven successful in some shale plays, and failed in others. This research studies the flow behavior of the CO2 in the different features that could be present in the shale reservoir to illustrate the mechanism by which oil recovery can be increased.

A FRACTAL PERMEABILITY MODEL FOR REAL GAS IN SHALE RESERVOIRS COUPLED WITH KNUDSEN DIFFUSION AND SURFACE DIFFUSION EFFECTS

Fractals ◽  
2020 ◽  
Vol 28 (01) ◽  
pp. 2050017 ◽  
Author(s):  
TAO WU ◽  
SHIFANG WANG
Keyword(s):  
Fractal Dimension ◽  
Surface Diffusion ◽  
Shale Gas ◽  
Gas Transport ◽  
Fractal Theory ◽  
Knudsen Diffusion ◽  
Apparent Permeability ◽  
Permeability Model ◽  
Real Gas ◽  
Shale Reservoirs

A better comprehension of the behavior of shale gas transport in shale gas reservoirs will aid in predicting shale gas production rates. In this paper, an analytical apparent permeability expression for real gas is derived on the basis of the fractal theory and Fick’s law, with adequate consideration of the effects of Knudsen diffusion, surface diffusion and flexible pore shape. The gas apparent permeability model is found to be a function of microstructural parameters of shale reservoirs, gas property, Langmuir pressure, shale reservoir temperature and pressure. The results show that the apparent permeability increases with the increase of pore area fractal dimension and the maximum effective pore radius and decreases with an increase of the tortuosity fractal dimension; the effects of Knudsen diffusion and surface diffusion on the total apparent permeability cannot be ignored under high-temperature and low-pressure circumstances. These findings can contribute to a better understanding of the mechanism of gas transport in shale reservoirs.

scholarly journals Transport Simulations on Scanning Transmission Electron Microscope Images of Nanoporous Shale

Energies ◽  
2020 ◽  
Vol 13 (24) ◽  
pp. 6665
Author(s):  
Laura Frouté ◽  
Yuhang Wang ◽  
Jesse McKinzie ◽  
Saman Aryana ◽  
Anthony Kovscek
Keyword(s):  
Gas Permeability ◽  
Pore Space ◽  
Knudsen Diffusion ◽  
Transport Processes ◽  
Pore Scale ◽  
Pore Networks ◽  
Scanning Transmission Electron ◽  
Transmission Electron ◽  
Scanning Transmission ◽  
Stem Tomography

Digital rock physics is an often-mentioned approach to better understand and model transport processes occurring in tight nanoporous media including the organic and inorganic matrix of shale. Workflows integrating nanometer-scale image data and pore-scale simulations are relatively undeveloped, however. In this paper, a workflow is demonstrated progressing from sample acquisition and preparation, to image acquisition by Scanning Transmission Electron Microscopy (STEM) tomography, to volumetric reconstruction to pore-space discretization to numerical simulation of pore-scale transport. Key aspects of the workflow include (i) STEM tomography in high angle annular dark field (HAADF) mode to image three-dimensional pore networks in µm-sized samples with nanometer resolution and (ii) lattice Boltzmann method (LBM) simulations to describe gas flow in slip, transitional, and Knudsen diffusion regimes. It is shown that STEM tomography with nanoscale resolution yields excellent representation of the size and connectivity of organic nanopore networks. In turn, pore-scale simulation on such networks contributes to understanding of transport and storage properties of nanoporous shale. Interestingly, flow occurs primarily along pore networks with pore dimensions on the order of tens of nanometers. Smaller pores do not form percolating pathways in the sample volume imaged. Apparent gas permeability in the range of 10−19 to 10−16 m2 is computed.

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