Gas Permeability Of Porous Media Research Articles

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.

A Numerical Study on Gas Flow through Anisotropic Sierpinski Carpet with Slippage Effect

A pore-scale model has been developed to study the gas flow through multiscale porous media based on a two-dimensional self-similar Sierpinski carpet. The permeability tensor with slippage effect is proposed, and the effects of complex configurations on gas permeability have been discussed. The present fractal model has been validated by comparison with theoretical models and available experimental data. The numerical results show that the flow field and permeability of the anisotropic Sierpinski model are different from that of the isotropic model, and the anisotropy of porous media can enhance gas permeability. The gas permeability of porous media increases with the increment of porosity, while it decreases with increased pore fractal dimension under fixed porosity. Furthermore, the gas slippage effect strengthens as the pore fractal dimension decreases. However, the relationship between the gas slippage effect and porosity is a nonmonotonic decreasing function because reduced pore size and enhanced flow resistance may be simultaneously involved with decreasing porosity. The proposed pore-scale fractal model can present insights on characterizing complex and multiscale structures of porous media and understanding gas flow mechanisms. The numerical results may provide useful guidelines for the applications of porous materials in oil and gas engineering, hydraulic engineering, chemical engineering, thermal power engineering, food engineering, etc.

GSIS: An efficient and accurate numerical method to obtain the apparent gas permeability of porous media

The apparent gas permeability (AGP) of a porous medium is an important parameter to predict production of unconventional gas. The Klinkenberg correlation, which states that the ratio of the AGP to the intrinsic permeability is approximately a linear function of reciprocal mean gas pressure, is one of the most popular estimations to quantify AGP. However, due to the difficulty in defining the characteristic flow length in complex porous media where the rarefied gas flow is multiscale, the slope in the Klinkenberg correlation varies significantly for different geometries such that a universal expression seems impossible. In this paper, by solving the gas kinetic equation using the general synthetic iterative scheme (GSIS), we compute the AGP in porous media that are represented by Sierpinski fractals and pore body/throat systems. With the abilities of fast convergence to steady-state solution and asymptotic preserving of Navier-Stokes limit, it is shown that GSIS is a promising tool to simulate low-speed rarefied gas flow through complex multiscale geometries. A new definition of the characteristic flow length is proposed as a function of porosity, tortuosity and intrinsic permeability of porous media, which enables to find a unique slope in the Klinkenberg correlation for all the considered geometries. This research also shows that the lattice Boltzmann method using simple wall scaling for the effective shear viscosity is not able to predict the AGP of porous media.

Investigations on gas permeability in porous media

Permeability of gases in porous media is a vital parameter for the design of landfill liners and buffers for nuclear waste repositories, gas extraction from petroleum reservoirs and hydrate bearing sediments, vapor extraction to decontaminate soils, carbon dioxide sequestration, etc. It is well understood that the gas-phase permeability in porous media is predominantly governed by the porosity, pore-characteristics (viz., diameter and distribution), properties of the gas (viz., density, molecular size and weight, sorption capacity, and viscosity) and their state of saturation (Sr). However, the nature of the flow of gas (viz., molecular, viscous and Knudsen), is influenced by the mean free-path, its compressibility and mean diameter of the pores. All these factors and complexities pose a challenge in determining the intrinsic permeability, K, which otherwise is assumed to be a (i) constant and (ii) fingerprint of porous media. In this context, and to facilitate easier determination of the gas-phase permeability, Kg, of porous media, a test setup: Gas Conductivity Measuring device, GasCoM, has been developed. Efforts have also been made to understand the influence of the characteristics of the gas (viz., active, inert, non-polar, monoatomic, diatomic and mixture of several gases) on Kg of different porous media (viz., soils of entirely different physico-chemical-mineralogical characteristics compacted at different densities and saturation, and commercially available alumina discs, referred to as standard porous media, SPM). A critical synthesis of the experimental data reveals that the flow of gas in porous media gets significantly influenced by (a) the hygroscopic moisture content, which also highlights the importance of its mineralogy and (b) its tortuosity. Furthermore, a correlation that can be employed for estimation of the Kg, for various gas-porous media systems, GPMSs, has been proposed and validated by using experimentally obtained results.

Rate dependency of permeability in tight rocks

Matrix permeability of tight rocks is a challenging parameter to measure. The gas permeability measurements of low-permeability rocks are sensitive to pressure, effective stress, temperature, and testing technique. However, the influence of gas flow rate on permeability measurements of tight rocks is unknown.In this work, steady-state gas permeability experiments are conducted on four shale and siltstone samples using methane and nitrogen as flowing fluid. The gas permeability is measured at several flow rates, while mean pressure and mean effective stress are held constant. The measurements are repeated at several mean pressure values. The tests are designed to study the influence of mean pressure as well as flow rate on gas permeability. After the gas permeability measurements, the samples are saturated with water to measure water permeability. Subsequently, the samples are sheared in a triaxial cell and similar gas and water permeability tests are repeated to compare the permeability behavior before and after failure. The results indicate strong rate sensitivity in permeability of tight rocks. Measured permeability is observed to rise as flow rate increases and reaches a constant value at higher rates. Permeability of the failed samples shows a similar behavior, although with higher permeability values. The rate dependency of gas permeability seems to follow a trend, similar to what is reported in the literature as the transition between pre-laminar and laminar flow regimes. Based on the experimental results, a discussion is provided on the rate at which the transition between pre-laminar and laminar flow occurs. Finally, by combining the theories on rate dependent flow regimes and pressure dependent (Knudsen number) flow regimes, a more complete picture of gas permeability in porous media is proposed.

The gas effective permeability of porous media with Klinkenberg effect

Gas transport properties in micro and nano-scale porous media are of significance for low-permeability reservoirs. Gas slippage and gas molecular diffusion in micro- and nano-pores take important effect on the gas permeability of porous media. Therefore, gas effective permeability of micro and nano-scale porous media over the entire Knudsen regime is presented by a fractal model. The analytical expression for gas effective permeability with Klinkenberg effect which is a function of structural parameters of porous media (porosity, fractal dimensions and pore diameter) and gas property (mean free path of gas molecule) is derived based on the microflow model and fractal capillary model. In order to further address the local flow field characteristics, numerical simulations are also performed on a fractal Sierpinski carpet. The fractal model is validated by comparison with available experimental results, and the effect of gas slippage on the gas permeability is discussed also. The present results indicate that gas effective permeability with slippage effect increases with the increase of fractal dimension for pore size distribution and decreases as the fractal dimension for tortuosity increases. And the gas slip factor increases with the decrease of pore size, it can be also increased by increased fractal dimension for pore size distribution under fixed maximum pore size and porosity. The current fractal model can characterize the multi-scale microstructures in porous media, and every parameter in the proposed gas effective permeability model has specific physical meaning.

Mesoscopic Simulation of Rarefied Flow in Narrow Channels and Porous Media

Rarefied gas flow in channels and computer-aided reconstructions of porous media is simulated using the direct simulation Monte Carlo (DSMC) method and a modified lattice-Boltzmann (LB) method that can account for rarefaction effects. An increase of two orders of magnitude was noted for the gas permeability as the Knudsen number increased from 0.1 to 10. It was found that incorporation of a Bosanquet expression for the viscosity in the dusty gas flux equations leads to the recovery of the well known Klinkenberg expression for the gas permeability, revealing an explicit relation of the, thus far empirical, permeability correction factor to the fluid and structure properties. The expression for the effective gas viscosity in the transition flow regime is also incorporated in the LB method, which is then validated against the DSMC method by comparing predictions for the velocity profiles in straight channels over the entire transition flow regime. The new LB method offers the additional advantages of simplicity in the code implementation and great savings in computational time and memory compared to the DSMC method. It is shown that the rough adjustment of a single parameter suffices to make the LB method suitable for the reliable prediction of the gas permeability in porous media over the entire transition flow regime.

Knudsen’s Permeability Correction for Tight Porous Media

Various flow regimes including Knudsen, transition, slip and viscous flows (Darcy’s law), as applied to flow of natural gas through porous conventional rocks, tight formations and shale systems, are investigated. Data from the Mesaverde formation in the United States are used to demonstrate that the permeability correction factors range generally between 1 and 10. However, there are instances where the corrections can be between 10 and 100 for gas flow with high Knudsen number in the transition flow regime, and especially in the Knudsen’s flow regime. The results are of practical interest as gas permeability in porous media can be more complex than that of liquid. The gas permeability is influenced by slippage of gas, which is a pressure-dependent parameter, commonly referred to as Klinkenberg’s effect. This phenomenon plays a substantial role in gas flow through porous media, especially in unconventional reservoirs with low permeability, such as tight sands, coal seams, and shale formations. A higher-order permeability correlation for gas flow called Knudsen’s permeability is studied. As opposed to Klinkenberg’s correlation, which is a first-order equation, Knudsen’s correlation is a second-order approximation. Even higher-order equations can be derived based on the concept used in developing this model. A plot of permeability correction factor versus Knudsen number gives a typecurve. This typecurve can be used to generalize the permeability correction in tight porous media. We conclude that Knudsen’s permeability correlation is more accurate than Klinkenberg’s model especially for extremely tight porous media with transition and free molecular flow regimes. The results from this study indicate that Klinkenberg’s model and various extensions developed throughout the past years underestimate the permeability correction especially for the case of fluid flow with the high Knudsen number.

Scaling Analysis of the Effect of Binder Content and Binder Distribution on the Gas Permeability of Porous Green Ceramics

Two models have been developed to describe how variations in binder content and binder distribution influence the specific surface and the gas permeability of porous media. In the Core‐Shell model, a shell of binder surrounds each ceramic particle, and the specific surface increases with decreasing volume fraction of binder. In the Multi‐Sphere model, binder particles occupy the interstices between the ceramic particles, and the specific surface generally decreases with decreasing volume fraction of binder. The variation in the permeability with binder content predicted by each model is different as compared with the case of a constant specific surface.

Pore size of microporous polymer membranes

Pore sizes of microporous polymer membranes were determined by the calculation based on the gas permeability of porous media. The gas permeability coefficient K (given by J = K Δp/l, where J is the steady-state gas flux, Δp is the pressure, difference, and l = the thickness of a membrane) for porous membrane can be given generally by where K0 is the Knudsen permeability coefficient, η is the viscosity of the permeant gas, B0 is the geometric factor of a membrane, and Δp is the mean pressure of the gas on both sides of a membrane. From gas permeability measurements which yield the pressure dependence of gas permeability coefficient (expressed as above equation), the mean pore size of the porous membrane can be estimated as where M is the molecular weight of the permeant gas. The validity of this method was examined with various Millipore filters of which nominal pore sizes are known. It was confirmed that the method provided a simple and reliable means of estimating mean pore size of microporous membranes. The method was applied to investigate the influence of factors involved in preparation of microporous polysulfone membranes by coagulation procedure. It was found that the mean pore size of porous polysulfone membrane increases with (1) increasing with casting thickness, (2) increasing temperature of coagulation bath, and (3) decreasing concentration of polymer in casting solution (DMF as solvent). Water flux and water flux decline due to compaction are also examined as a faction of pore size, porosity, and the thickness of membranes.