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In order to describe diffusive transport of solutes through a porous material, estimation of effective diffusion coefficients is required. It has been shown theoretically that in the case of uncharged porous materials the effective diffusion coefficient of solutes is a function of the pore morphology of the material and can be described by the tortuosity (tensor) (Bear, 1988 [1]). Given detailed information of the pore geometry at the micro-scale the tortuosity of different materials can be accurately estimated using homogenization procedures. However, many engineering materials (e.g., clays and shales) are characterized by electrical surface charges on particles of the porous material which strongly affect the (diffusive) transport properties of ions. For these type of materials, estimation of effective diffusion coefficients have been mostly based on phenomenological equations with no link to underlying micro-scale properties of these charged materials although a few recent studies have used alternative methods to obtain the diffusion parameters (Jougnot et al., 2009; Pivonka et al., 2009; Revil and Linde, 2006 2, 3 and 4). In this paper we employ a recently proposed up-scaled Poisson–Nernst–Planck type of equation (PNP) and its micro-scale counterpart to estimate effective ion diffusion coefficients in thin charged membranes. We investigate a variety of different pore geometries together with different surface charges on particles. Here, we show that independent of the charges on particles, a (generalized) tortuosity factor can be identified as function of the pore morphology only using the new PNP model. On the other hand, all electro-static interactions of ions and charges on particles can consistently be captured by the ratio of average concentration to effective intrinsic concentration in the macroscopic PNP equations. Using this formulation allows to consistently take into account electrochemical interactions of ions and charges on particles and so excludes any ambiguity generally encountered in phenomenological equations. 相似文献
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Unlike micropores where water moves upward or downward based on hydraulic gradient, in macropores, water flows predominantly downward due to the gravity. Therefore, models based on capillary flow are not capable of simulating macropore flow. There are attempts to model the macropore flow using two domains, one for capillary flow and another one for macropores. These models use Richard’s equation for capillary flow and Poiseuille’s law for macropores in which the macropore is approximated to be cylindrical or planar. This study quantifies the magnitudes of the errors induced by this assumption. Influence of macropore shapes and tortuosity was quantified by using a 3D Lattice Boltzmann model, which is capable of simulating fluid flow in micropores as well as macropores of cracked clays. Artificial macropores of constant sectional area and volume, but different shapes were generated in 3D and the influence of macropore shapes, shape related parameters, and tortuosity were systematically investigated. Macropore flow rate decreases with different shapes compared to cylindrical macropores and increase in aspect ratio of sectional shape leads to decrease in macropore flow rate. The maximum effect of bends/turnings along the tortuous macropore was about 25% on overall decrease of flow rate due to tortuosity. However, more detailed study is required on the influence of bends on macropore flow rate. The macropore flow rate reduces by about 70% for tortuosity of 1.41. A prediction equation is verified to predict the flow rate of different shapes and tortuous macropores based on straight cylindrical macropore using aspect ratio and tortuosity factor. 相似文献
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Caroline Bouvet de Maisonneuve Olivier Bachmann Alain Burgisser 《Bulletin of Volcanology》2009,71(6):643-658
Silicic pumices formed during explosive volcanic eruptions are faithful recorders of the state of the magma in the conduit,
close to or at the fragmentation level. We have characterized four types of pumices from the non-welded rhyolitic Kos Plateau
Tuff, which erupted 161,000 years ago in the East Aegean Arc, Greece. The dominant type of pumice (>90 vol.%) shows highly
elongated tubular vesicles. These tube pumices occur throughout the eruption. Less common pumice types include: (1) “frothy”
pumice (highly porous with large, sub-rounded vesicles), which form 5–10 vol.% of the coarsest pyroclastic flow deposits,
(2) dominantly “microvesicular” and systematically crystal-poor pumices, which are found in early erupted, fine-grained pyroclastic
flow units, and are characterized by many small (<50 μm in diameter) vesicles and few mm-sized, irregular voids, (3) grey
or banded pumices, indicating the interaction between the rhyolite and a more mafic magma, which are found throughout the
eruption sequence and display highly irregular bubble shapes. Except for the grey-banded pumices, all three other types are
compositionally identical and were generated synchronously as they are found in the same pyroclastic units. They, therefore,
record different conditions in the volcanic conduit leading to variable bubble nucleation, growth and coalescence. A total
of 74 pumice samples have been characterized using thin section observation, SEM imagery, porosimetry, and permeametry. We
show that the four pumice types have distinct total and connected porosity, tortuosity and permeability. Grey-banded pumices
show large variations in petrophysical characteristics as a response to mingling of two different magmas. The microvesicular,
crystal-poor, pumices have a bimodal bubble size distribution, interpreted as reflecting an early heterogeneous bubble nucleation
event followed by homogeneous bubble nucleation close to fragmentation. Finally, the significant differences in porosity,
tortuosity and permeability in compositionally identical tube and frothy pumices are the result of variable shear rates in
different parts of the conduit. Differential shear rates may be the result of either: (1) pure shear, inducing a vertical
progression from frothy to tube and implying a relatively thick fragmentation zone to produce both types of pumices at the
same time or (2) localized simple shear, inducing strongly tubular vesicles along the wall and near-spherical bubbles in the
centre of the conduit and not necessarily requiring a thick fragmentation zone. 相似文献
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A new experimental protocol is explored to characterize electrical properties of hydrocarbon-bearing mudrocks at nano/micro scales. Two current flow regimes of peak force - tunneling atomic force microscopy (PF-TUNA) have been used: (1) the vertical out-of-plane current regime with hundred micrometer diameter top electrodes obtains homogenized conductivity quantitatively, (2) the horizontal in-plane current regime was shown powerful to visualize the conductive paths (related to connectivity and tortuosity) for heterogeneous and anisotropic shales. Results show that the approach works well with one to two layers of adsorbed water (25–55% relative humidity) under low frequency (0.5–20 Hz) for shale rocks. Current maps with sub-nanometer resolution emphasize the dominant role of hydrated ions associated with the hydrophilic clay minerals in driving the dielectric response of shales, while conductivity of pyrite and kerogen cannot be neglected for mature organic-rich shale conductive network. The acquired I-V curves at microscale provide a reliable mean to evaluate homogenized conductivity of such multiscale multi-component heterogeneous material under controlled environmental conditions. The procedure discussed herein serves as a complement for fine grained rocks and minerals of ionic-electronic hybrid conductive mechanism under partially water saturation. These results can be used to develop accurate electrical models, specifically for shale rocks with heterogeneous and sophisticated microstructure. The methodology can be also extended to other micro- or meso-porous geomaterials such as cementitious and bituminous nanoporous media. 相似文献
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The characteristic functions relating relative permeabilities and capillary pressures to fluid saturations (kr–S–Pc models) are of great importance for the modelling of sub-surface multi-phase flow and transport. In order to test their performance and to identify their important parameters, four well-known three-phase kr–S–Pc models have been tested against published experimental data on non-aqueous phase liquid (NAPL) migration in the unsaturated zone. Both homogenous systems and systems with embedded heterogeneities have been analysed. 相似文献
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