Pore Space Geometry Research Articles

Lattice Boltzmann Simulation of Flow-Induced Wall Shear Stress in Porous Media

The lattice Boltzmann method is increasingly utilized in the simulation of flow-induced wall shear stress needed in various applications. In image-based flow simulations, the simulation geometry is usually based on a three-dimensional reconstruction of the true structure of the pore space obtained, for example, by X-ray tomography. The geometry is then given in a voxel-based representation, which complicates an accurate determination of the surface-normal vectors that are necessary in the computation of the wall shear stress. To avoid this problem, we introduce here a method for the determination of surface-normal vectors directly from a greyscale image instead of its segmented binary image version. The proposed method is fast and automatic, and it can be used for an arbitrary pore space geometry provided in a greyscale form by any imaging modality. We show that this method can produce accurate surface-normal vectors even for binary images and that their accuracy is further increased when the original greyscale images are used instead. We compute wall shear stresses for generated benchmark geometries and then demonstrate the utility of the method for soil samples with ‘random’ pores imaged by X-ray tomography.

The effect of compaction on complex electrical resistivity of shaly sands

ABSTRACTPore space properties of sedimentary rocks are of fundamental importance with regard to reservoir evaluation and fluid flow modelling or special geotechnical applications such as stability considerations for reservoirs, dams, or embankments. Processes such as compaction due to pressure drawdown in weakly consolidated reservoirs, effects caused by stimulation of reservoirs with decreasing productivity, or the compaction of building ground can be effectively studied by verifying and monitoring changes in porosity. The close connections between electrical resistivity or conductivity and pore space geometry as well as a high sensitivity to even slight changes in pore space characterising parameters are well‐established.Therefore, the results of complex electrical conductivity measurements in the frequency range from 0.05 Hz to 1 kHz on a set of heterogeneous shaly sand samples during increasing compaction are presented in this study. The major objective of these investigations was to quantify the porosity reduction in shaly sands during the step‐wise compaction of the samples in a specially designed measurement cell. Overall, ten unconsolidated shaly sand samples with varying grain size distribution were analysed. In addition, selected shaly sandstone data are presented to enhance the observations made for the sand samples with regard to the potential influence of cementation as expressed by the cementation exponent.With increasing compaction, the measured complex conductivity data of the fully water‐saturated samples show two co‐occurring effects. On the one hand, the real part decreases due to the dominating effect of Archie’s law. On the other hand, the imaginary part increases due to the increasing contribution of interface conductivity. This effect is due to an increase in the internal surface‐area‐to‐porosity ratio. Cementation exponent and the considered porosity range seem to be controlling the magnitude of this effect. These observations may be explained by using a simple complex conductivity model that relates conductivity components to porosity, specific surface area, and cementation exponent. An interpretation algorithm is proposed that allows determining relative porosity variations based on a baseline and a single repeat measurement without prior knowledge of further rock characteristics.To demonstrate the applicability of the algorithm on field measurements, data from spectral induced polarization soundings obtained at a test site for compaction techniques were interpreted. It could be shown that these observations bear further potential for enhancing the prediction of porosity, changes of compaction, and, hence, changes in hydraulic permeability.

Simulation of membrane polarization of porous media with impedance networks

ABSTRACTThe spectral induced polarization method is supposed to have some potential to provide useful information on hydraulic properties of the subsurface. One difficulty for the practical implementation is the simulation of underlying physical processes at the pore scale and their upscaling to hydraulically relevant scales. We extend an existing semi‐analytical membrane polarization model to two‐ and three‐dimensional impedance networks, which are numerically solved to obtain a spectral induced polarization response that can be compared to measured data.The original model consists of two cylinders with different sizes. The model has been shown to be able to reproduce some basic features of spectral induced polarization spectra measured in the laboratory, but it is unable to meet the complexity of macroscopic porous media structures, which can be found within unconsolidated sediments or rocks. To approach realistic pore space geometry, we connect different combinations of cylinders to networks. We treat the smaller of the two cylinders as a pore throat. The pore throat distribution in the network is chosen by matching measured pore throat radii distributions obtained from the mercury injection method. The large cylinder is treated as the (large) pore body, and its radii are associated to the pore throats using existing relationships.We compare the behaviour of the networks with real porous media by using sandstone samples for which both the electrical and petrophysical properties have been measured. We adjust the geometrical parameters of the network, i.e., pore lengths, pore radii, and their relative occurrences, such that they match the measured parameters (specific internal surface area, pore throat distribution, and porosity) of the sandstone samples. The measured spectral induced polarization parameters, like the maximum phase shift and the characteristic relaxation time, are qualitatively consistent with our simulation results.

Pore radius distribution and fractal dimension derived from spectral induced polarization

The pore size distribution provides a suitable description of the pore space geometry that can be used to investigate the fractal nature of a pore space or to determine the fractal dimension. The fractal dimension describes the size of the geometric objects as a function of resolution. It can be integrated into the models that are used for permeability prediction. We investigated the fractal dimension of the pore volume of 11 Eocene sandstone samples from China. This study describes an approach to use spectral induced polarisation spectra to estimate the pore size distribution and to determine the fractal dimension of the pore volume. Additionally, the fractal dimension was derived from data of the capillary pressure curves from mercury intrusion and the transversal relaxation time distribution of nuclear magnetic resonance. For samples with an effective pore radius larger than 1 μm, a good agreement exists between the values of the fractal dimension derived from the three different methods, which implies an identification of similar pore structures. Spectral induced polarisation can be a non-invasive laboratory technique for the estimation of the pore size distribution, but the application of the methodology to field measurements remains a challenging problem considering the limited frequency range.

Streaming potential during drainage and imbibition

AbstractThe rock pore space in many subsurface settings is saturated with water and one or more immiscible fluid phases. Examples include nonaqueous phase liquids (NAPLs) in contaminated aquifers, supercritical CO2 during sequestration in deep saline aquifers, the vadose zone, and hydrocarbon reservoirs. Self‐potential (SP) and seismoelectric (SE) methods have been proposed to monitor multiphase flow in such settings. However, to properly interpret and model these data requires an understanding of the saturation dependence of the streaming potential. This paper presents a methodology to determine the saturation dependence of the streaming potential coupling coefficient (C) and streaming current charge density (Qs) in unsteady state drainage and imbibition experiments and applies the method to published experimental data. Unsteady state experiments do not yield representative values of C and Qs (or other transport properties such as relative permeability and electrical conductivity) at partial saturation (Sw) because Sw within the sample is not uniform. An interpretation method is required to determine the saturation dependence of C and Qs within a representative elementary volume with uniform saturation. The proposed method makes no assumptions about the pore space geometry. Application of the method to published experimental data from two natural sandstone samples shows that C exhibits hysteresis between drainage and imbibition, can exhibit significant nonmonotonic variations with saturation, is nonzero at the irreducible water saturation, and can exceed the value observed at Sw = 1. Moreover, Qs increases with decreasing Sw but is not given by 1/Sw as is often assumed. The variation in Qs with Sw is very similar for a given sample and a given drainage or imbibition process, and the difference between samples is less than the difference between drainage and imbibition. The results presented here can be used to help interpret SP and SE measurements obtained in partially saturated subsurface settings.

Effects of Pore-Scale Geometry and Wettability on Two-Phase Relative Permeabilities within Elementary Cells

We study the relative role of the complex pore space geometry and wettability of the solid matrix on the quantification of relative permeabilities of elementary cells of porous media. These constitute a key element upon which upscaling frameworks are typically grounded. In our study we focus on state immiscible two-phase flow taking place at the scale of elementary cells. Pressure-driven two-phase flow following simultaneous co-current injection of water and oil is numerically solved for a suite of regular and stochastically generated two-dimensional explicit elementary cells with fixed porosity and sharing main topological/morphological features. We show that the relative permeabilities of the randomly generated elementary cells are significantly influenced by the formation of preferential percolation paths, called principal pathways, giving rise to a strongly nonuniform distribution of fluid fluxes. These pathways are a result of the spatially variable resistance that the random pore structures exert on the fluid. The overall effect on relative permeabilities of the diverse organization of principal pathways, as driven by a given random realization at the scale of the elementary cell, is significantly larger than that of the wettability of the host rock. In contrast to what can be observed for the random cells analyzed, the relative permeabilities of regular cells display a clear trend with contact angle at the investigated scale.

Experimental investigations on the geometry and connectivity of pore space in organic-rich Wufeng and Longmaxi shales

The nano-scale pore systems of organic-rich shale reservoirs were investigated from Upper Ordovician Wufeng and Lower Silurian Longmaxi Formations in southeast Sichuan Basin. These two formations are the most important target plays of shale gas development in China. The purpose of this article is to assess the geometry and connectivity of multi-scale pore systems, and to reveal the nature and complexity of pore structure for these over-mature gas shales. To achieve these objective, total organic carbon, mineralogy, image analyses by focused ion beam-SEM, low pressure nitrogen adsorption, mercury injection capillary pressure (MICP) and spontaneous fluid [deionized (DI) water and n-decane] imbibition were performed.Most of the visible pores from SEM work in Wufeng and Longmaxi shales are within nm- and μm-size regimes and belong to organic matter (OM) pores. The shapes of OM pore in Longmaxi samples are elliptical, bubble-like, irregular or rounded. Wufeng pores are mainly irregular, linear and faveolated, even though two shales have small depth difference, as well as similar thermal maturity, kerogen type and TOC content. Nano-scale pores in Longmaxi are mainly associated with narrow platelike or slitlike pores with pore size of 3–50 nm; while inkbottle pores are dominant in Wufeng samples and over 88% of the pore volume is contributed by pores with diameter <20 nm. Overall, porosity, pore volume and surface area values from Wufeng samples are much higher than those in Longmaxi, which is mainly correlated with the different TOC contents and mineral compositions. MICP tests show that a total of 5 inflection points (indicative of different connected pore networks) are identified in all pressure regions for Longmaxi, while only 2 for Wufeng in high pressure region with the associated permeability at nano-darcy range. Imbibition curves of n-decane are divided into three stages: the initial stage (Stage Ⅰ), linear imbibition stage (Stage Ⅱ) and late imbibition stage (Stage Ⅲ), and the slopes of linear imbibition stage are around 0.5, suggesting well-connected pore spaces for n-decane. In contrast, imbibition curves for DI water are divided in two stages with linear slopes of between 0.25 and 0.5, indicating moderately-connected pore networks for the movement of DI water. This is consistent with the mixed-wet nature of these shales, with observed weak wettability for hydrophilic, while complete wetting for hydrophobic fluids.

Local 3D segmentation of soil pore space based on fractal properties using singularity maps

Over the last decade, major technological advances in X-ray computed tomography (CT) have allowed for the investigation and reconstruction of three-dimensional (3D) natural porous media architectures at very fine scales. Soil scientists can use the internal structure information to develop predictive models for a range of physical, chemical and biological processes in soil. Image segmentation and thresholding are crucial steps when applying these methods to extract complex pore space geometry information from images. Traditional thresholding algorithms face challenges related to the heterogeneity of soil samples, noise and artefacts introduced during the image acquisition process.This study proposes a new segmentation method using local greyscale value (GV) concentration variabilities based on fractal concepts. Singularity maps were created to measure the GV concentration at each point. The C-V method was combined with the singularity map approach (Singularity-CV method) to define thresholds that can be applied to binarize CT images.This study also introduces a new method for creating 3D synthetic soil images based on truncated multifractals that simulate low-contrast and non-bimodal GV histograms. A synthetic soil image was created with the objective to compare traditional segmentation methods (Otsu and maximum entropy) with the Singularity-CV method. We obtained better results in porosity and more amount of pores at all scales than traditional methods, although some small pores were incorrectly identified due to the ability to amplify every anomalous GVs. Misclassification error (ME) was low and similar to Otsu.Two different 3D CT soil images were also used in this analysis, corresponding to samples of the same soil with 1.2 and 1.6gcm−3 bulk densities. After applying the Singularity-CV method to the GV images, the results were compared with the aforementioned traditional segmentation methods. The image comparison was based on the porosity, pore size distribution (PSD) and cumulative pore size distribution (CPSD). The Otsu method achieves a higher porosity than the Singularity-CV method because it defines the largest pores. However, the Singularity-CV method detected more pores at all sizes. The maximum entropy method always yielded the lowest porosity.

Recirculation zones induce non-Fickian transport in three-dimensional periodic porous media.

In this work, the influence of pore space geometry on solute transport in porous media is investigated performing computational fluid dynamics pore-scale simulations of fluid flow and solute transport. The three-dimensional periodic domains are obtained from three different pore structure configurations, namely, face-centered-cubic (fcc), body-centered-cubic (bcc), and sphere-in-cube (sic) arrangements of spherical grains. Although transport simulations are performed with media having the same grain size and the same porosity (in fcc and bcc configurations), the resulting breakthrough curves present noteworthy differences, such as enhanced tailing. The cause of such differences is ascribed to the presence of recirculation zones, even at low Reynolds numbers. Various methods to readily identify recirculation zones and quantify their magnitude using pore-scale data are proposed. The information gained from this analysis is then used to define macroscale models able to provide an appropriate description of the observed anomalous transport. A mass transfer model is applied to estimate relevant macroscale parameters (hydrodynamic dispersion above all) and their spatial variation in the medium; a functional relation describing the spatial variation of such macroscale parameters is then proposed.

Thermal conductivity of partially saturated microstructures

The growing importance of tight reservoirs exacerbates the necessity of pore-scale studies to characterize porous media from the pore-level point of view. Accurate prediction of pore-scale effective thermal and electrical conductivities leads to proper thermophysical and petrophysical characterization of partially saturated media. In this paper, a numerical framework is offered to predict electrical and thermal conductivities of two-phase saturated microstructures. The immiscible displacement scenarios within the microporosities are conducted utilizing a direct pore morphology-based technique; a set of rules to construct the fluid-fluid interfaces under capillary-driven flows. Subsequently effective thermal and electrical conductivity curves are predicted using steady state diffusion equation. Two sets of microstructures are used as the pore space geometries; real and synthetic. The real media under consideration include binary images of oil/water-wet sandstone and carbonate formations and the fluid systems contain steam-oil and water-oil equilibriums. The swelling spheres algorithm is adapted to generate two-dimensional granular synthetic media based on a typical particle size distribution of Alberta's unconsolidated oil sand. The result packages, including thermal diffusivity and conductivity, electrical conductivity, formation factor, and apparent diffusion coefficient are generated and discussed considering rock types and fluid configurations. The thermal and electrical conductance of well-connected consolidated microstructures appear to be weak functions of water saturation and are mainly controlled by porosity and solid phase configuration.

Textural control on the quadrature conductivity of porous media

Induced polarization (IP) has been broadly used for environmental and hydrogeological applications and in civil engineering. The IP response of a porous medium without metallic particles (described by its quadrature conductivity or its normalized chargeability) is controlled by the interfacial electrochemistry of the electrical double layer and the pore-space geometry. We use the specific surface per unit pore volume normalized by the formation factor (i.e., [Formula: see text]) as the controlling textural parameter for the quadrature conductivity. This relationship is obtained by averaging the surface conductance over the pore volume. A database that contains 76 samples (including porous borosilicate glass, sandstones, and clayey sediments) is used to check the new scaling. In addition to these data, we have conducted new IP measurements on 13 samples from the Middle Bakken Formation corresponding to low-porosity clayey materials. Comparison between the experimental data and our model confirms that the ratio [Formula: see text] is the dominant textural parameter describing the quadrature conductivity [Formula: see text] of a broad range of porous media. The database was also used to test whether the quadrature conductivity depended either on [Formula: see text], or the specific surface area [Formula: see text], or the ratio [Formula: see text] ([Formula: see text] being the connected porosity). Although the quadrature conductivity scales with [Formula: see text] and [Formula: see text] for high-porosity sandstones, these relationships are not appropriate for the low-porosity clayey materials presented in this study. However, experimental data support the dependence of the quadrature conductivity on [Formula: see text], a published relationship obtained through the volume averaging approach.

Quantitative microporosity evaluation using mercury injection and digital image analysis in tight carbonate rocks: A case study from the Ordovician in the Tazhong Palaeouplift, Tarim Basin, NW China

The heterogeneity of tight carbonate rocks is directly related to the morphology of micropores and the connectivity of the pore network, which have a great influence on the intrinsic microporosity and fluid flow properties of porous media. However, neither can be quantitatively evaluated by conventional techniques. Based on core observation and thin section analysis, combined with high-resolution field emission-scanning electron microscopy (FE-SEM) and mercury injection capillary pressure (MICP) measurements, we can identify carbonate rock types, determine the microporosity and microstructure and calculate the pore structure parameters. Digital image analysis (DIA) and the fractal dimension (FD) method are used to study the relationship between the quantified pore structure parameters, heterogeneity and fluid flow properties. The results indicate that rock types in 12 carbonate samples are dominated by grainstone and packstone, followed by wackestone and dolomitic packstone. The microporosity of rock types has various microstructure characteristics. Crystalline types of microporosity (the small and large intercrystalline pores) increase pore network connectivity whereas micromoldic pores show variations in connectivity of different lithofacies. However, the small intercrystalline pores contribute little to the permeability because of narrow and complex pore networks for fluid flow. MICP data of samples reveal that these samples are relatively tight with low porosity (avg. 3.7%) and permeability (avg. 0.452mD). The pore-throat radius mainly ranges from 0.1 μm to 1.0 μm, which contributes the highest proportion of permeability to the samples. Fractal dimensions calculated from the “J-curve” models vary between 2.0746 and 2.8551 (avg. 2.331), indicating high heterogeneity. Moreover, the fractal dimension is strongly negatively related to the permeability, average pore throat radius and separation coefficient. Additionally, quantified pore geometric parameters from DIA, including dominant pore size (DOMsize), perimeter over area (PoA), pore body-to-throat ratio (BTR) and average roundness (γa), greatly influence the pore structure and fluid flow behavior. The samples with large DOMsize, high γa, low PoA and low BTR show a low fractal dimension and simple pore network but high permeability. Diagenesis can also affect the fractal pore space and self-similarity pore geometries of carbonates across all length scales. This information about the micropore geometry and microstructure of the carbonate rock will further improve the assessment of its reservoir properties.

Biophysical rhizosphere processes affecting root water uptake.

Background Recent advances in imaging techniques now make it possible to visualize the biogeochemical and physical environment around the roots, the rhizosphere. Detailed images of pore space geometry and water content dynamics around roots have demonstrated the heterogeneity of the rhizosphere compared with the soil far from the roots. These findings have inspired new models of root water uptake which aim to describe such small-scale heterogeneity. However, the question remains of how far these image-based findings have really advanced our understanding of how roots extract water from soils. Scope The rhizosphere processes affecting root water uptake are reviewed. Special attention is dedicated to the role of mucilage exuded by roots. Mucilage increases the soil moisture at negative water potentials and it keeps the rhizosphere wet when plants take up water, possibly maintaining the hydraulic connection between roots and soil. However, mucilage becomes viscous and hydrophobic upon severe drying and it limits the water fluxes across the rhizosphere during the rewetting phase. The role of mucilage in maintaining the hydraulic contact between the root surface and the surrounding soil, thereby softening the drops in water potential around the roots in dry soils, remains to be demonstrated. Conclusion Despite detailed images of water content, water fluxes and soil structure in the rhizosphere, a general understanding of how the rhizosphere affects root water uptake is still lacking. The missing elements of the puzzle are the gradient in water potential around roots. Measurements of the xylem water potential at varying soil water potentials and transpiration rates supported by numerical models of root water uptake would allow the estimation of the water potential across the rhizosphere. Such measurements are crucial to comprehend how water enters the roots.

A critical evaluation of the Miller and Miller similar media theory for application to natural soils

AbstractThe Miller‐Miller similar media theory is widely applied to characterize the spatial variability of soil hydraulic properties. For a group of soils, a distinct scaling factor is commonly assigned to each individual soil to coalesce the soil water characteristic and hydraulic conductivity functions to single curves. It is generally assumed that the Miller‐Miller theory is valid as long as soils are “similar” either with regard to their microscopic pore space geometry or the closely related macroscopic soil hydraulic functions. In this paper, it is illustrated that similarity is not the sole required condition for validity of the Miller‐Miller theory. In addition, the interrelation between the soil water characteristic and the hydraulic conductivity functions considered for scaling need to be comparable. The interrelation is dependent not only on the pore space geometry, but also on solid‐liquid interactions. Hence similar interrelation cannot be concluded from similarity of microscopic pore space geometry. A dimensionless parameter termed the “joint scaling factor” was defined and applied to evaluate the soundness of the interrelation condition for 26 soils from the UNSODA database that were grouped into six classes of similar soils. Obtained results clearly reveal the crucial importance of the interrelation condition for the Miller‐Miller scaling theory, which has been hidden behind the “similarity” requirement, and contradict the general belief that Miller‐Miller scaling is valid as long as soils are “similar.”

X‐ray CT‐Derived Soil Characteristics Explain Varying Air, Water, and Solute Transport Properties across a Loamy Field

Core Ideas We used CT‐derived parameters to explain solute, water, and air transport at field scale. CTmatrix was found to be the best parameter to explain solute transport. Limiting macroporosity gave the highest correlations with water and air transport. Combining macroporosity and CTmatrix improved the relationships of water and air flow. The characterization of soil pore space geometry is important for explaining fluxes of air, water, and solutes through soil and understanding soil hydrogeochemical functions. X‐ray computed tomography (CT) can be applied for this characterization, and in this study CT‐derived parameters were used to explain water, air, and solute transport through soil. Forty‐five soil columns (20 by 20 cm) were collected from an agricultural field in Estrup, Denmark, and subsequently scanned using a medical CT scanner. Nonreactive tracer leaching experiments were performed in the laboratory along with measurements of air permeability (Ka) and saturated hydraulic conductivity (Ksat). The CT number of the matrix (CTmatrix), which represents the moist bulk density of the soil matrix, was obtained from the CT scans as the average CT number of the voxels in the grayscale image excluding macropores and stones. The CTmatrix showed the best relationships with the solute transport characteristics, especially the time by which 5% of the applied mass of tritium was leached, known as the 5% arrival time (t0.05). The CT‐derived macroporosity (pores &gt;1.2 mm) was correlated with Ka and log10(Ksat). The correlation improved when the limiting macroporosity (the minimum macroporosity for every 0.6‐mm layer along the soil column) was used, suggesting that soil layers with the narrowest macropore section restricted the flow through the whole soil column. Water, air, and solute transport were related with the CT‐derived parameters by using a best subsets regression analysis. The regression coefficients improved using CTmatrix, limiting macroporosity, and genus density, while the best model for t0.05 used CTmatrix only. The scanning resolution and the time for soil structure development after mechanical activities could be factors that increased the uncertainty of the relationships. Nevertheless, the results confirmed the potential of X‐ray CT visualization techniques for estimating fluxes through soil at the field scale.

Effect of fluid chemistry on the microstructure of light backfill: An X-ray CT investigation

Bentonite–sand mixtures are widely accepted as the candidate sealing materials of radioactive waste repository due to their high swelling capacity and low hydraulic conductivity. These properties of the material depend largely on its microstructure, particularly, the pore space geometry. The aim of this investigation is to explore the effect of the pore fluid (NaCl and CaCl2) on the microstructure, pore geometry and hydraulic conductivity of a barrier material. Representative samples of light backfill (LBF) prepared with a 50–50 bentonite–sand mixture at a compacted dry density of 1.24Mg/m3 were used. As a first attempt, X-ray computed tomography (X-ray CT) was used to study the LBF under the distilled water (DW) and two other pore fluid conditions. In order to acquire a good quality image with high resolution, X-ray source, detector, and a small LBF specimen (5.5mm in diameter) were placed close together and scanned with Xradia Micro XCT-400. The voxel of the scanned images were (1.15×1.15×1.15) μm3, indicating that the particles with a diameter greater than 2μm could be easily observed. The porosity value estimated at the end of the consolidation test showed significantly higher values compared to the X-ray CT analysis. The interconnected pore components and absolute permeability of distilled water or salt-solution saturated LBF samples were analyzed using Avizo software. This analysis showed that the volume of interconnected pore increased due to the presence of salt solutions and resulted higher hydraulic conductivity. The salt solution increased porosity, pore size, volume of interconnected pore and hydraulic conductivity of the LBF.

Comparative assessment of continuum-scale models of bimolecular reactive transport in porous media under pre-asymptotic conditions

We compare the ability of various continuum-scale models to reproduce the key features of a transport setting associated with a bimolecular reaction taking place in the fluid phase and numerically simulated at the pore-scale level in a disordered porous medium. We start by considering a continuum-scale formulation which results from formal upscaling of this reactive transport process by means of volume averaging. The resulting (upscaled) continuum-scale system of equations includes nonlocal integro-differential terms and the effective parameters embedded in the model are quantified directly through computed pore-scale fluid velocity and pore space geometry attributes. The results obtained through this predictive model formulation are then compared against those provided by available effective continuum models which require calibration through parameter estimation. Our analysis considers two models recently proposed in the literature which are designed to embed incomplete mixing arising from the presence of fast reactions under advection-dominated transport conditions. We show that best estimates of the parameters of these two models heavily depend on the type of data employed for model calibration. Our upscaled nonlocal formulation enables us to reproduce most of the critical features observed through pore-scale simulation without any model calibration. As such, our results clearly show that embedding into a continuum-scale model the information content associated with pore-scale geometrical features and fluid velocity yields improved interpretation of typically available continuum-scale transport observations.

Mesopore‐Promoted Transport in Microporous Materials

AbstractIn addition to the respective pore space geometries, transport enhancement in hierarchical nanoporous materials may most decisively depend on the nature of the probe molecule under consideration. As a function of these two influences, mass transfer in hierarchical materials may follow quite different scenarios. Considering mass transfer enhancement by a network of mesopores within a microporous continuum, this work presents an approach to assess these influences quantitatively. The validity of this approach is tested by dynamic Monte Carlo simulations and by comparison with the results of diffusion measurements.

Continuum‐scale characterization of solute transport based on pore‐scale velocity distributions

AbstractWe present a methodology to characterize a continuum‐scale model of transport in porous media on the basis of pore‐scale distributions of velocities computed in three‐dimensional pore‐space images. The methodology is tested against pore‐scale simulations of flow and transport for a bead pack and a sandstone sample. We employ a double‐continuum approach to describe transport in mobile and immobile regions. Model parameters are characterized through inputs resulting from the micron‐scale reconstruction of the pore space geometry and the related velocity field. We employ the outputs of pore‐scale analysis to (i) quantify the proportion of mobile and immobile fluid regions and (ii) assign the velocity distribution in an effective representation of the medium internal structure. Our results (1) show that this simple conceptual model reproduces the spatial profiles of solute concentration rendered by pore‐scale simulation without resorting to model calibration and (2) highlight the critical role of pore‐scale velocities in the characterization of the model parameters.

Diffusion and Molecular Exchange in Hollow Core-Shell Silica Nanoparticles.

The diffusion behavior of small molecules in hollow core-shell nanocapsules was studied using pulsed field gradient NMR. By purposefully selecting the liquid saturating the hollow core and the porous shell and the solvent between the nanocapsules, two different situations corresponding to the excluded and admitted molecular exchange between the intra- and intercapsule liquids at the external boundary of the nanoparticles were covered. In the former case, corresponding to the reflective boundary condition for the molecules approaching the nanocapsule boundary, restricted diffusion in the complex pore space formed by the hollow core and the mesoporous shell was observed. The time-dependent diffusivities measured in the experiment were inter-related with the geometry of the intraparticle pore space. The thus assessed structural information was found to be in a good agreement with that provided by electron microscopy. In the case of the molecular exchange occurring between the two pools of molecules in the nanocapsules and between them, the diffusive dynamics of only the molecules remaining in the nanocapsules during the entire observation times was studied.