Intrinsic Permeability Research Articles

Prediction and Validation of Flow Properties in Porous Lattice Structures

Abstract High-porosity metal foams have been extensively studied as an attractive candidate for efficient and compact heat exchanger design. With the advancements in additive manufacturing, such foams can be manufactured with controlled topology to yield highly tailorable mechanical and transport properties. In this study, a lattice Boltzmann method (LBM)-based pore-scale model is implemented to simulate the fluid flow in additively manufactured (AM) metal foams with unit cell topologies of Cube, Face Diagonal (FD)-Cube, Tetrakaidecahedron (TKD), and Octet lattices. The pressure gradient versus average velocity profiles predicted by the LBM model were validated against in-house measurements on the AM lattice samples with the same unit cell topologies. Based on the simulation results, a novel hybrid model is proposed to accurately predict the volume averaged flow properties (permeability and inertial coefficients) of the four structures. Specifically, the linear LBM (neglecting inertial forces) is first implemented to obtain the intrinsic permeability, and then the standard LBM is applied to obtain the inertial coefficient. Convenient correlations for those flow properties as a function of porosity and fiber diameter are constructed. The effects of the AM print qualities on the flow properties are also discussed. The advantages of the hybrid model compared to the polynomial fitting approach for determining flow properties are discussed and compared quantitatively. The hybrid model and presented results are valuable for flow and thermal transport evaluation when designing new metal foams for specific applications and with different materials and topologies. The presented correlations based on pore-scale simulations can also be conveniently used in volume-averaged models to predict the macroscale flow behavior in such complex structures.

The Anisotropy Permeability Evolution and Deformation Behavior of Raw Coal under Cyclic Loading Conditions

As an anisotropic porous media, coal’s intrinsic permeability is sensitive to stress variably in different directions. Likewise, the degree of damage sustained by the internal solid skeletal structure under external stresses is anisotropic. Four parameters are introduced: permeability stress-based loss rate (PEL) and permeability strain-based loss rate (PSL) highlight the stress sensitivity of the intrinsic permeability and deformation characteristics of coal’s internal structure during the loading process; stress-based irrecoverable permeability coefficient (EIP) and strain-based irrecoverable permeability coefficient (SIP) describe the loss of intrinsic permeability and irreversible deformation features in the whole load cycle. Stress sensitivity of the vertical intrinsic permeability is greater than that of the horizontal, and the ability of the vertical internal structure to resist deformation induced by an external load is weaker. During the cyclic loading process for the same coal sample, the stress sensitivity of the latter loading cycle is significantly less than the former.

Numerical study of the impact of geometrical parameters on the rarefied gas transport in porous media

To understand the transport mechanism of rarefied gas in the shale rock, the geometry of the porous media is generated based on the Voronoi tessellation, and the gas flows in continuum and rarefied flow regimes are simulated by using the Multiple-Relaxation-Time Lattice Boltzmann Method and Linearized Discrete Velocity Method, respectively. Based on explicit topological relations, porous media with diverse geometries are constructed to investigate the effect of pore-to-throat radius ratio, dead pore number and low-tortuosity throat on the rarefied flow in porous media. The relationships of the mass flow rate, apparent permeability and tortuosity versus the Knudsen number are obtained for varying pore-to-throat radius ratios. Results show that the intrinsic and apparent permeabilities of the porous media decrease as the blockage rate increases, while the reduction in intrinsic permeability is more significant than that in apparent permeability. Moreover, the phenomenon of Knudsen minimum reappears after the addition of low-tortuosity throats to porous media, in which the contribution to mass flow rate increases significantly in rarefied regimes relative to continuum regime, and it is supported by the observation that the tortuosity decreases with increasing Knudsen number. The increase in flow rate with increasing rarefaction effect in the low tortuous regions not only reveals the critical impact of fractures created by hydraulic fracturing on exploitation but also can identify the potential causes for the rapid production decay of shale gas reservoirs.

Characterization of the Knudsen Number and Gas Transport in Shale Reservoirs: Coupling the Microfracture Network and Capillary Network

An accurate understanding of gas seepage mechanisms in shale reservoirs would have a positive impact on promoting shale gas development. Shale is a complex dual-porosity medium composed of a microfracture network and capillary network. However, most shale dual-porosity permeability models have usually ignored the influence of key mechanisms, such as effective stress and gas adsorption. In addition, the depiction and analysis of the Knudsen number has not been fully discussed in previous studies. In this study, the inner relationship between intrinsic permeability and porosity has been taken to be a bridge, with the fracture width including the pore radius being quantified, leading to a modification of the Knudsen number in the microfracture network and capillary network. Based on the modified Knudsen number, a dual-porosity permeability model has been developed for typical shale reservoirs that considered real gas effect, flow regimes, effective stress, and gas adsorption. The reliability of the new model has been validated by published experimental data under different conditions and through comparisons with the existing theoretical models. Finally, the evolution law relating to gas apparent permeability and the Knudsen number in the microfracture network and capillary network has been discussed, and the effects of different factors concerning apparent permeability and the Knudsen number have been quantified. Based on the results, the relationships between the coupled effects relating to the rock deformation field, the microfracture network seepage field, the capillary network seepage field, and the Knudsen number have been proposed. Moreover, the mechanisms relating to the internal swelling coefficient and gas rarefaction coefficient, including different pore network occupancies on total gas transport capacity, have been presented. The research results will provide a basis for the accurate numerical simulation for shale gas and will be of great significance to the economic development of shale gas in the future.

A bio-hydro-chemical model for gas pressure development in municipal solid waste landfills

Prediction of gas pressure development within municipal solid waste (MSW) landfills is of great importance for the stability analysis and design of gas collection systems. This study presents a fully coupled bio-hydro-chemical model for the gas pressure development in landfills. The reduction of foam on the relative gas permeability and the variation of the intrinsic permeability with degradation degree are considered. The source terms in the governing equations of two-phase flow and solute transport are chosen from the biodegradation process of MSW. Both one-step landfilling and multi-step landfilling are calculated to compare the differences. It is found that the fast hydrolysis of fresh MSW produces most of the volatile fatty acids (VFAs) and leachate within the first 2 months. During multi-step landfilling, the VFA and leachate produced from fresh MSW in the top flow downward to the bottom, leading to high gas production and high leachate saturation in the deep. Meanwhile, the high concentration of VFA reduces the surface tension of the leachate, enabling it to generate foam and further reduce gas permeability. Owing to the high gas production and low gas permeability, the excess gas pressure is easily developed in the deep layer. The maximum gas pressure of multi-step landfilling is about 2·5 times that of one-step landfilling. Case studies of the laboratory column test and in situ borehole test verify the accuracy of the model in predicting the temporal and spatial distribution of gas pressure. For the slope failure induced by high gas pressure, the evolution of shear strength and stability during a 2 year landfilling period is calculated and discussed.

A new analytical method to predict permeability properties of cementitious mortars: The impacts of pore structure evolutions and relative humidity variations

This research develops analytical models in respectively describing the water vapour sorption isotherm and permeability properties based on a probabilistic method for pore size distribution and two transformation models for pore radius of cementitious mortars. By adopting the water vapour sorption model, the water saturation degree in cement-based materials is acquired and the influence of ions on water vapour sorption isotherm is modelled by introducing the water activity in thermodynamic equilibrium relation between liquid and vapour phases. The results reveal that the presence of ions increases the susceptibility of mortars to be water-saturated. Additionally, intrinsic permeability and relative permeability of mortars are predicted and the reliability of the permeability model is investigated. Finally, the permeability model is further extended considering the evolutions of pore structure and variations of relative humidity when cementitious mortars are subjected to precipitation and dissolution, which attempts to give an understanding of interactions between permeability and evolved pore structure that are not yet very commonly mentioned in literature. Modelling results show that both pore size distribution and relative humidity significantly affect permeability properties of mortars, especially when the water saturation degree is large. This research provides a novel insight into quantifying the permeability of mortars undergoing pore structure degradations.

Numerical Study of Gas Flow in Super Nanoporous Materials Using the Direct Simulation Monte-Carlo Method.

The direct simulation Monte Carlo (DSMC) method, which is a probabilistic particle-based gas kinetic simulation approach, is employed in the present work to describe the physics of rarefied gas flow in super nanoporous materials (also known as mesoporous). The simulations are performed for different material porosities (0.5≤ϕ≤0.9), Knudsen numbers (0.05≤Kn≤1.0), and thermal boundary conditions (constant wall temperature and constant wall heat flux) at an inlet-to-outlet pressure ratio of 2. The present computational model captures the structure of heat and fluid flow in porous materials with various pore morphologies under rarefied gas flow regime and is applied to evaluate hydraulic tortuosity, permeability, and skin friction factor of gas (argon) flow in super nanoporous materials. The skin friction factors and permeabilities obtained from the present DSMC simulations are compared with the theoretical and numerical models available in the literature. The results show that the ratio of apparent to intrinsic permeability, hydraulic tortuosity, and skin friction factor increase with decreasing the material porosity. The hydraulic tortuosity and skin friction factor decrease with increasing the Knudsen number, leading to an increase in the apparent permeability. The results also show that the skin friction factor and apparent permeability increase with increasing the wall heat flux at a specific Knudsen number.

Analysis of the Permeability Change Resulting from Active Mineral Precipitation in Pores of Rocks by 3D-DEM

Carbon dioxide capture and storage (CCS) is a promising technique for reducing the concentration of CO2 in the atmosphere, and several million tons of CO2 are sequestered every year. The most important problem in CCS is ensuring aquifer safety. However, there is still room for improvement in the flow characteristics of aquifers to prevent CO2 leakage. To decrease the permeability of porous rocks, in this study, a method called ‘active mineral deposition’ was developed. In this method, some minerals are actively precipitated in aquifers, and the pores in the rock mass are closed by precipitated minerals. Because the pores are closed and stacked by minerals, the permeability of the rock mass is expected to decrease. For the precipitated minerals, CaCO3 is a promising mineral, and CaCO3 is precipitated in the pores of rocks. From microscopic observation, the approximate size of the precipitated mineral was estimated to be 10 μm in the rock pores. To verify the effect of the method, the permeability of the porous rocks was simulated using the three-dimensional discrete-element method (3D-DEM). Here, the rock minerals and pores were simulated using DEM elements, and the initial permeability of the models was estimated. Then, the small minerals, which represent precipitated minerals, were generated in the pore space, and changes in the intrinsic permeability, flow path, and pressure distributions in the rocks were estimated. The value of intrinsic permeability decreased to one tenth of the initial condition when 1% of the pore spaces were occupied by the precipitated minerals. A small amount of precipitation could change the permeability of the porous materials.

Recent advances in permeable polymersomes: fabrication, responsiveness, and applications.

Polymersomes are vesicular nanostructures enclosed by a bilayer-membrane self-assembled from amphiphilic block copolymers, which exhibit higher stability compared with their biological analogues (e.g. liposomes). Due to their versatility, polymersomes have found various applications in different research fields such as drug delivery, nanomedicine, biological nanoreactors, and artificial cells. However, polymersomes prepared with high molecular weight components typically display low permeability to molecules and ions. It hence remains a major challenge to balance the opposing features of robustness and permeability of polymersomes. In this review, we focus on the design and strategies for fabricating permeable polymersomes, including polymersomes with intrinsic permeability, the formation of nanopores in the membrane bilayers by protein insertion, and the construction of stimuli-responsive polymersomes. Then, we highlight the applications of permeable polymersomes in the fields of biomimetic nanoreactors, artificial cells and organelles, and nanomedicine, to underline the challenges in the development of polymersomes as soft matter with biomedical utilities.

Influence of permeability on rainfall infiltration based on water gas two phase flow

The permeability function is one of the key properties in unsaturated soil mechanics and variation of parameters in soil water characteristic curve can easily affect matric suction as well as infiltration. The purpose of this research is to explore the significant effect of parameters in SWCC on rainfall infiltration. A water gas two phase flow analysis method was conducted to investigate the influence of parameters in SWCC on stable infiltration intensity. Result showed that when saturation was low, stable intensity of infiltration was greatly affected by matric suction because the modified parameters were related to pore size distribution such as air entry value ρ0 and parameter m. When saturation was close to 1, the influence of soil infiltration intensity was almost not affected by matric suction. The minimum value of stable infiltration of intensity was mainly determined by the intrinsic permeability, while saturation of this value was mainly affected by soil water characteristic curve, intrinsic permeability coefficient of soil as well as water relative permeability coefficient.

Groundwater flow through fractured rocks and seepage control in geotechnical engineering: Theories and practices

Groundwater flow through fractured rocks has been recognized as an important issue in many geotechnical engineering practices. Several key aspects of fundamental mechanisms, numerical modeling and engineering applications of flow in fractured rocks are discussed. First, the microscopic mechanisms of fluid flow in fractured rocks, especially under the complex conditions of non-Darcian flow, multiphase flow, rock dissolution, and particle transport, have been revealed through a combined effort of visualized experiments and theoretical analysis. Then, laboratory and field methods of characterizing hydraulic properties (e.g. intrinsic permeability, inertial permeability, and unsaturated flow parameters) of fractured rocks in different flow regimes have been proposed. Subsequently, high-performance numerical simulation approaches for large-scale modeling of groundwater flow in fractured rocks and aquifers have been developed. Numerical procedures for optimization design of seepage control systems in various settings have also been proposed. Mechanisms of coupled hydro-mechanical processes and control of flow-induced deformation have been discussed. Finally, three case studies are presented to illustrate the applications of the improved theoretical understanding, characterization methods, modeling approaches, and seepage and deformation control strategies to geotechnical engineering projects.

Transport Characteristics of Aquaporins.

Aquaporins (AQP) are a class of the integral membrane proteins. The main physiological function of AQPs is to facilitate the water transport across plasma membrane of cells. However, the transport of various kinds of small molecules by AQPs is an interesting topic. Studies using in vitro cell models have found that AQPs mediated transport of small molecules, including glycerol, urea, carbamides, polyols, purines, pyrimidines and monocarboxylates, and gases such as CO2, NO, NH3, H2O2 and O2, although the high intrinsic membrane permeabilities for these gases make aquaporin-facilitated transport not dominant in physiological mechanism. AQPs are also considered to transport silicon, antimonite, arsenite and some ions; however, most data about transport characteristics of AQPs are derived from in vitro experiments. The physiological significance of AQPs that are permeable to various small molecules is necessary to be determined by in vivo experiments. This chapter will provide information about the transport characteristics of AQPs.

Asymptotic homogenization in the determination of effective intrinsic magnetic properties of composites

We present a computational framework for two-scale asymptotic homogenization to determine the intrinsic magnetic permeability of composites. To this end, considering linear magnetostatics, both vector and scalar potential formulations are used. Our homogenization algorithm for solving the cell problem is based on the displacement method presented in Lukkassen et al. 1995, Composites Engineering, 5(5), 519-531. We propose the use of the meridional eccentricity of the permeability tensor ellipsoid as an anisotropy index quantifying the degree of directionality in the linear magnetic response. As application problems, 2D regular and random microstructures with overlapping and nonoverlapping monodisperse disks, all of which are periodic, are considered. We show that, for the vanishing corrector function, the derived effective magnetic permeability tensor gives the (lower) Reuss and (upper) Voigt bounds with the vector and scalar potential formulations, respectively. Our results with periodic boundary conditions show an excellent agreement with analytical solutions for regular composites, whereas, for random heterogeneous materials, their convergence with volume element size is fast. Predictions for material systems with monodisperse overlapping disks for a given inclusion volume fraction provide the highest magnetic permeability with the most increased inclusion interaction. In contrast, the disk arrangements in regular square lattices result in the lowest magnetic permeability and inadequate inclusion interaction. Such differences are beyond the reach of the isotropic effective medium theories, which use only the phase volume fraction and shape as mere statistical microstructural descriptors.

High-flux CO2 separation using thin-film composite polyether block amide membranes fabricated by transient-filler treatment

An energy-efficient and eco-friendly membrane-based CO2 separation process is required to address global concerns pertaining to energy and environment. In this context, polymer materials such as polyimides, polyvinyl alcohol, and polyether block amide (PEBA) have been intensively explored, and a high CO2 selectivity has been attained; however, these membranes exhibit a low permeance, thereby hindering process efficiency. Gas permeance depends mainly on the thickness and morphology of the selective layer; but it is difficult to overcome the limitation of the intrinsic permeability of the polymer material by controlling the thickness of the selective layer. Herein, we report a method for manufacturing thin-film composite (TFC) membranes with a defect-free, ultrathin, and highly permeable selective layer through transient-filler (TF) treatment consisting of blending a TF/polymer matrix and then removing the TF. Polyethylene glycol (PEG), used as the TF, was homogeneously blended through hydrogen bonding with the polymer matrix, PEBA. The blended membrane, PEG/PEBA, possessed a less crystalline structure than that of PEBA and a large free volume, thereby exhibiting a high gas permeance. After the removal of the TF from PEG/PEBA, the resultant PEBA (r-PEBA) retained the less crystalline structure, and the thickness of the selective layer decreased substantially. The permeance of the r-PEBA TFC membrane, 2371 GPU, was substantially higher than that of neat PEBA, 1350 GPU, owing to the aforementioned synergistic effects.

Thermo-mechanical effect on the anisotropic permeability of a mudstone

Tamusu mudstone is a candidate geological medium for high-level radioactive waste disposal in China. This paper investigates its anisotropic hydraulic properties. Permeability measurements were conducted on two kinds of samples, i.e., along the directions perpendicular and parallel to the beddings, under different stress conditions with heating-cooling cycles (20 → 40→60 → 80→60 → 40→20 °C). The results confirmed the hydraulic anisotropy of Tamusu mudstone. Increasing lithostatic pressure decreases the intrinsic permeability k and hydraulic conductivity K and decreases the hydraulic anisotropy of Tamusu mudstone. The temperature significantly affects the hydraulic properties: the k values exhibit a negative correlation with temperature. A notable variation in parallel hydraulic properties upon temperature elevation indicates that the thermal effect is more crucial in the direction parallel at low lithostatic pressure. A notable effect of thermal paths on the hydraulic properties of Tamusu mudstone was exhibited through the different K or k at the same temperatures before and after heating-cooling cycles.

Microstructural changes of young cement paste due to moisture transfer at low air pressures

It has been long recognized that low air pressure (AP) affects the moisture transfer in concrete, and thus its microstructure and bulk property, but less is known about the thermodynamic mechanism. This research investigated the microstructure evolution of young white Portland cement paste during wetting or drying at different APs (i.e. 101 kPa, 60 kPa, 20 kPa), the experimental and numerical analyses reveal the moisture transfer changes at low APs, which matters for the microstructural features of hardened cement paste. It was found that low APs increase the water vapor diffusion and convective mass transfer coefficients, and the intrinsic permeability of cement paste sample, which results in higher water contents within cement paste during wetting at 98 % RH but more rapid water losses during drying at 43 % RH. Owing to the distinct moisture transfer behaviors, the C-S-H structures were linked with water contents within confined pores.

Vertical dynamic response of pipe pile embedded in unsaturated soil based on fractional‐order standard linear solid model and Rayleigh‐Love rod model

AbstractConsidering the flow‐independent viscosity of soil skeleton and the lateral inertia effect of pipe pile, the vertical dynamic behavior of a pipe pile embedded in unsaturated soil is investigated in this work when the pipe pile is subjected to the vertical dynamic loading. In order to model this problem, the fractional‐order standard linear solid (FSLS) model is introduced to characterize the flow‐independent viscosity of the soil skeleton, the Rayleigh‐Love rod model is employed to specify the lateral inertia effect of pipe pile, while both vertical and radial soil displacement are entirely considered. The analytical solution of the pipe pile complex impedance is obtained through the rigorous theoretical derivation. Numerical results with known analytical solution are finally presented to discuss the influence of the model parameters for the FSLS model, lateral inertia effect and geometrical characteristic for the pipe pile, and saturation degree and intrinsic permeability for the unsaturated soil on the vertical complex impedance of the pipe pile. The main results indicate that enlarging the fractional‐order index, raising the strain relaxation time, or shortening the stress relaxation time will reduce the oscillation amplitude and natural frequency for the dynamic stiffness and damping of the pipe pile but will improve their mean value. The lateral inertia effect of pipe pile has effect on its complex impedance only in the high‐frequency region. The outer and inner radii of pipe pile, pile length, soil saturation degree, and soil intrinsic permeability are highly correlated with the pipe pile complex impedance.

Modified random hierarchical bundle model for predicting gas permeability of cement-based materials

Permeability is a fundamental property indicating the durability of cement-based materials, predicted according to the material’s pore size distribution (PSD). The random hierarchical bundle model is a promising approach based on a random hierarchical assembly of capillary segments to estimate the permeability of porous media. However, the original model neglected the slippage effect during gas penetration—a common occurrence in cement-based materials and other low-permeability porous media. Thus, we considered this effect in a modified model proposed herein, and the permeability of cement-based materials can be directly predicted using the PSD obtained via mercury intrusion porosimetry. Compared with data from experiments and literatures for various mortars and concretes with permeabilities ranging over 3 orders of magnitude, the results revealed that this modified model can accurately predict the intrinsic permeability and Klinkenberg constant. Moreover, this model can predict the intrinsic permeability and apparent permeability of various gases and porous media.

An improved apparent permeability model considering full pore pressure range, variable intrinsic permeability and slippage coefficient

An improved apparent permeability model considering full pore pressure range, variable intrinsic permeability and slippage coefficient

Evaluation of the effectiveness of poly (phenyl sulfone) / nanoclay mixed matrix membranes for carbon dioxide/methane separation

Poly (phenyl sulfone) (PPSU) is a recently introduced poly (aryl sulfone) polymer that has attracted much attention for membrane fabrication. PPSU could fabricate both porous and non-porous membranes. Intrinsic gas permeability of pure PPSU is low, but it has good selectivity for CO2/CH4 separation. Therefore, this study aimed to investigate the effect of adding a layered nanoclay material to PPSU on CO2 permeability and CO2/CH4 selectivity. The fabricated membranes were characterized by FTIR, FESEM, XRD, DSC, EDS, Contact angle, gas solubility, and gas permeability. The permeability of each gas was measured by the constant volume-variable pressure method, and ideal selectivity was determined. The effect of nanoclay loading (1-3 wt.%) and feed pressure (2-8 bar) on the gases' permeability and CO2/CH4 selectivity was investigated at a constant temperature of 27 ± 2°C. The results showed that the addition of the nanoclay to PPSU has a considerable effect on CO2 permeability (up to 52% increase) while CO2/CH4 selectivity remains nearly unchanged or slightly decreases (down to 6%). Solubility measurement results revealed that adding the nanoclay to the PPSU polymer increases the solubility selectivity by 22%, while the diffusivity selectivity is decreased by 23%, revealing the formation of an intercalated morphology, confirmed by XRD analysis.