Pore-scale Information Research Articles

Upscaling and Effective Behavior for Two-Phase Porous-Medium Flow Using a Diffuse Interface Model

We investigate two-phase flow in porous media and derive a two-scale model, which incorporates pore-scale phase distribution and surface tension into the effective behavior at the larger Darcy scale. The free-boundary problem at the pore scale is modeled using a diffuse interface approach in the form of a coupled Allen–Cahn Navier–Stokes system with an additional momentum flux due to surface tension forces. Using periodic homogenization and formal asymptotic expansions, a two-scale model with cell problems for phase evolution and velocity contributions is derived. We investigate the computed effective parameters and their relation to the saturation for different fluid distributions, in comparison to commonly used relative permeability saturation curves. The two-scale model yields non-monotone relations for relative permeability and saturation. The strong dependence on local fluid distribution and effects captured by the cell problems highlights the importance of incorporating pore-scale information into the macro-scale equations.

SVM-based fast 3D pore-scale rock-typing and permeability upscaling for complex rocks using Minkowski functionals

The rapid advancement of digital core analysis has greatly promoted the research progress of flow and transport in porous media. However, complex analytical process with exceeding computational load impedes the application on large data volume. Considering the strong heterogeneity of the underground porous media, the integration of pore-scale information into continuum scale is widely concerned for the future development of digital physical analysis. For hierarchical porous structures, pore-scale rock-typing and upscaling of petrophysical properties is a promising solution towards the issue, and morphological and topological descriptors associating data clustering methods are popularly utilized. However, the size of the regional support through which the parameter fields are generated heavily affects the descriptive capacities of the parameters and the following partitioning process. We propose in this work a robust integrated pore-scale rock-typing and upscaling technology for 3D porous structures which uses Minkowski functionals as the descriptive parameters. A fast-computational method utilising fast Fourier transform has been applied for efficient generation of the parameter fields. A comparative study between the two different classification methods of Support Vector Machine (SVM) and Gaussian Mixture Model (GMM) has been conducted on two complex artificial porous systems and a laminated sandstone through various regional support sizes. Throughout the test, SVM has illustrated obvious advantage of overcoming regional support size effect even with limited labelling information. The Upscaling of permeability on the natural sandstone sample based on the rock type distribution has demonstrated excellent accuracy comparing with full scale direct computation.

Operando Liquid Water Saturation in PEFC Catalyst Layers Determined Via Small Angle X-Ray Scattering

Various measurement techniques suitable with the length scale of PEFC components have been explored to address the PEFC water management challenge. For the gas diffusion layer (GDL), technological advances have permitted operando water saturation quantification and elucidation of its mechanism with X-ray tomography with few microns resolution 1-4. Furthermore, sub-voxel information contained in the X-ray tomography data has demonstrated accurate water quantification in the nano-porous microporous layer (MPL)5. However, in the nanoscale regime of the catalyst layer, the quantification of water and the mechanism of the water filling the pores remain nontrivial. Studies involving imaging techniques dedicated to understand the water management in the catalyst layer have been carried out albeit with limited spatial resolution6. Nevertheless, the pore-scale information has remained unresolved.Small angle X-ray scattering (SAXS) technique is proposed as a non-destructive diagnostic tool to investigate the catalyst layer saturation in operating conditions. SAXS is well suited for diagnosing the presence of liquid water during operando experiments because of its sensitivity to electron density contrast, nanoscale observation window, high temporal resolution and adequate spatial resolution to distinguish the components in PEFCs. Herein, SAXS intensity profiles measured at cSAXS, Swiss Light Source, Paul Scherrer Institut, Switzerland, with a recently developed SAXS-compatible operando PEFC (Figure 1 middle and right) are interpreted using representative morphology models and assuming different water filling mechanisms (Figure 1 middle and left). The presentation will provide insights into the wetting phenomena in the catalyst layer of PEFC during operation using a representative morphology modelling approach. This work has been presented in XVIII edition of the International Small-Angle Scattering Conference.(1) Xu, H.; Buhrer, M.; Marone, F.; Schmidt, T. J.; Buchi, F. N.; Eller, J. Effects of Gas Diffusion Layer Substrates on PEFC Water Management: Part I. Operando Liquid Water Saturation and Gas Diffusion Properties. J Electrochem Soc 2021, 168 (7).(2) Eller, J.; Rosen, T.; Marone, F.; Stampanoni, M.; Wokaun, A.; Buchi, F. N. Progress in In Situ X-Ray Tomographic Microscopy of Liquid Water in Gas Diffusion Layers of PEFC. J Electrochem Soc 2011, 158 (8), B963-B970.(3) Mularczyk, A.; Lin, Q. Y.; Niblett, D.; Vasile, A.; Blunt, M. J.; Niasar, V.; Marone, F.; Schmidt, T. J.; Buchi, F. N.; Eller, J. Operando Liquid Pressure Determination in Polymer Electrolyte Fuel Cells. Acs Appl Mater Inter 2021, 13 (29), 34003-34011.(4) Sabharwal, M.; Buchi, F. N.; Nagashima, S.; Marone, F.; Eller, J. Investigation of the transient freeze start behavior of polymer electrolyte fuel cells. J Power Sources 2021, 489.(5) Chen, Y. C.; Berger, A.; De Angelis, S.; Schuler, T.; Bozzetti, M.; Eller, J.; Tileli, V.; Schmidt, T. J.; Buchi, F. N. A Method for Spatial Quantification of Water in Microporous Layers of Polymer Electrolyte Fuel Cells by X-ray Tomographic Microscopy. Acs Appl Mater Inter 2021, 13 (14), 16227-16237.(6) Babu, S. K.; Spernjak, D.; Mukundan, R.; Hussey, D. S.; Jacobson, D. L.; Chung, H. T.; Wu, G.; Steinbach, A. J.; Litster, S.; Borup, R. L.; Zelenay, P. Understanding water management in platinum group metal-free electrodes using neutron imaging. J Power Sources 2020, 472. Figure 1

Pore-Scale Saturation and Liquid Water Pathways in PEFCs: Insights from Correlative 2D and 3D X-Ray Imaging

Improving the efficiency of polymer electrolyte fuel cells (PEFCs) through high power density operation necessitates liquid water management in the cathode gas diffusion layer (GDL), where liquid water saturation inhibits oxygen diffusivity. To this end, there have been numerous efforts aimed at understanding liquid water transport behaviour to guide GDL design improvements. X-ray imaging of representative in-operando miniaturized PEFC samples has been instrumental to much of recent progress [1–4] in understanding liquid water distribution patterns. Radiographic two-dimensional (2D) images have enabled visualization of liquid water dynamics [3] while three-dimensional (3D) computed tomography images have provided pore-scale information of liquid water saturation states in the GDL [2] and of its transport mechanism [4]. However, how liquid water pathways are formed and the likelihood for preferential pathways remain unclear.In this work, we investigate factors that influence liquid water distribution and pathway definition using correlative rapid 2D and long duration 3D operando X-ray datasets which enable a visualization of liquid water breakthrough dynamics and the corresponding pore-scale interactions in the GDL. The correlated images together with GDL pore structure visualization are used to identify three characteristic pore-scale saturation behaviour with sample regions highlighted in Fig. 1. These regions include locations with restricted liquid water breakthrough, locations with apparent large breakthrough porous pathways where breakthrough liquid water is observable at least in the 2D images, and similarly porous regions where no liquid water breakthrough is observed. It is found that the behaviour shown in the identified regions are strongly linked to local pore-scale structural characteristics and capillary pressure distribution in the GDL. Investigating the 3D virtual GDL from around the microporous layer through to the channel interface, it is shown that liquid water pathways get increasingly defined with a decrease in spatial uniformity towards the flow channels. Pore-scale analysis and observed flow mechanisms show that the defined pathways are locally accessible paths of least capillary resistance dictated by pore radius and associated hydrophobicity. These findings highlight the important role that pore scale topology plays in addition to pore size distribution for future GDL design aimed at improving water management. Keywords— operando, fuel cell, water, pore structure, X-ray imaging Acknowledgments Funding for this research was provided by the Natural Sciences and Engineering Research Council of Canada, Ballard Power Systems, Canada Foundation for Innovation, British Columbia Knowledge Development Fund, Western Economic Diversification Canada, and Canada Research Chairs.

Coupled continuum and network model framework to study catalyst layers of polymer electrolyte fuel cells

The nanostructured thin film (NSTF) catalyst layers which have demonstrated high power densities, mass activities, and exceptional metal and support stability can have limited operational robustness due to their thin thickness and the hydrophilicity of the metal-coated nano whiskers. The dispersed nanostructured thin film (dNSTF) catalyst layers have been developed by dispersing the NSTF Pt whiskers with ionomer and carbon support to increase the thickness and hydrophobicity. Continuum and network models (NM) are coupled through boundary conditions to study the polymer electrolyte fuel cell with a dNSTF cathode catalyst layer. The coupled model combines the computational efficiency of the continuum model with the pore-scale information in the dNSTF cathode catalyst layer of the NM. It captures the special morphology of the partially ionomer/water covered cylindrical whiskers, as well as water percolation through the pore structures and their impact on the cell performance. We observe optimal ionomer coverage on whiskers to be 0.5, ionomer to carbon ratio to be 0.9 and higher whisker to carbon ratios to be desired.

Lattice Boltzmann Simulation of Multicomponent Porous Media Flows With Chemical Reaction

Flows with chemical reactions in porous media are fundamental phenomena encountered in many natural, industrial, and scientific areas. For such flows, most existing studies use continuum assumptions and focus on volume-averaged properties on macroscopic scales. Considering the complex porous structures and fluid–solid interactions in realistic situations, this study develops a sophisticated lattice Boltzmann (LB) model for simulating reactive flows in porous media on the pore scale. In the present model, separate LB equations are built for multicomponent flows and chemical species evolutions, source terms are derived for heat and mass transfer, boundary schemes are formulated for surface reaction, and correction terms are introduced for temperature-dependent density. Thus, the present LB model offers a capability to capture pore-scale information of compressible/incompressible fluid motions, homogeneous reaction between miscible fluids, and heterogeneous reaction at the fluid–solid interface in porous media. Different scenarios of density fingering with homogeneous reaction are investigated, with effects of viscosity contrast being clarified. Furthermore, by introducing thermal flows, the solid coke combustion is modeled in porous media. During coke combustion, fluid viscosity is affected by heat and mass transfer, which results in unstable combustion fronts.

Effects of solution supersaturation on barite precipitation in porous media and consequences on permeability: Experiments and modelling

The understanding of porosity evolution in porous media due to mineral reactions and its impact on the transport of fluids and solutes is important, as this is a key factor in the long-term behaviour of underground engineered systems. The implementation of such coupled processes into numerical codes requires a mechanistic understanding of the relevant precipitation/dissolution processes in porous media and model validation with quantitative experiments. In this context, we conducted a series of flow-through column experiments to investigate the effect of supersaturation on barite precipitation mechanisms (e.g. nucleation) and consequential permeability changes. These experiments were modelled using the reactive transport code OpenGeoSys-GEM. Although the Kozeny-Carman equation is widely applied in numerical models describing porosity and permeability changes due to mineral dissolution and precipitation, it distinctively underestimated the permeability changes observed in the experiments. Instead, a porosity-permeability relationship involving a critical porosity at which the permeability decreases significantly had to be considered in the model. Post-mortem characterization (Scanning Electron Microscopy) highlighted the importance of including pore-scale information on passivation processes in order to get a better match between experimental and simulated results.

Formulating Reduced-Order Models to Include Mesoscale Methods in Full Proton Exchange Membrane Fuel Cell Models

As the scales vary wildly in proton exchange membrane fuel cells (PEMFCs), from the nano and mesoscale in the cathode catalyst layer (CCL) to meter scale for the cell components of the membrane electrode assembly (MEA) themselves, it would not be feasible to run mesoscale models along with any kind of 1D, 1+1D, or 3D model of the entire PEMFC. In some of our previous work, we built a model of liquid and vapor distributions and electrochemical phenomena in a PEMFC electrode through a Lattice-Boltzmann-Method (LBM)-Direct-Numeical-Simulation (DNS) framework. However, as both LBM and DNS are computationally intensive, it would be far too computationally expensive to use these for a full cell model. While advances in computational power has alleviated some of the computing challenges, it does not allow for running computationally impractical experiments. To counter this, we suggest using the reduced-order modeling techniques used in machine learning, such as Bayesian linear regressions or neural networks for cases such as different RH levels, under rib, or different tortuosities and incorporating these into the larger model instead. These methods, especially Bayesian ones, account for the fact that getting accurate tomography data through focused ion beam scanning electron microscopy (FIB-SEM) is quite difficult and still give insight into physics for different microstructures. The idea behind these models would be to collect effective properties from the LBM-DNS framework such as effective diffusivity, conductivity, Dijkstra tortuosity, among others to make accurate predictions without running either LBM or DNS. Doing this allows larger models to incorporate accurate pore-scale information for the CCL while still accounting for global PEMFC issues, such as anode drying, water electro-osmosis, and water back diffusion not modeled by the framework. The ability to build these reduced-order models based off of the real microstructure gives us a major advantage over the field, which currently gloss over microstructure detail. It also allows us to model long-term phenomena, such as carbon corrosion, more effectively because the framework gives more accurate results, but the model allows these results to be accessed much more quickly for new conditions. Since the models utilize information from an actual PEMFC, we can deploy our model predictions to inform practitioners on what type of microstructures they need to build. While it is admittedly difficult to control the individual pore distribution over the whole CCL experimentally, the model predictions can inform what kind of distribution promotes the best performance. While this approach has begun to be adopted in other fields in engineering, it has not been applied to PEMFCs yet – possibly due to the difficulty in obtaining the necessary microstructure data on the CCL. As a proof of concept, this is done on the capillary pressure vs saturation curves – an example parity plot for a GPR (Gaussian Process Regression) and linear regression are shown below in Figure 1 based on the principle components scores from several of the FIB-SEM geometries. One can see that the general shape of the curve is captured with relatively low differences. Figure 1

Numerical investigation of a fully coupled micro-macro model for mineral dissolution and precipitation

Mineral dissolution and precipitation alter a porous medium’s structure and its bulk properties. Due to the medium’s heterogeneity and lack in dynamic pore-scale measurements, there has been an increasing interest in comprehensive models accessing such phenomena on the macroscale without disregarding available pore-scale information. Such micro-macro models may be derived from detailed pore-scale models applying upscaling techniques and comprise several levels of couplings. Our model consists of transport equations at the scale of the porous medium (macroscale) while taking the processes of convection and diffusion into account. They include averaged time- and space-dependent coefficient functions which are in turn explicitly computed by means of auxiliary cell problems (microscale). Structural changes due to dissolution and precipitation reactions result in a time- and space-dependent domain on which cell problems are defined. The interface between the mineral and the fluid, and consequently the explicit geometric structure, is characterized by means of a level set. Here, information from the transport equations’ solutions is taken into account (micro-macroscale). A numerical scheme is introduced which enables evaluating such complex settings. For the level-set equation, an upwind scheme by Rouy and Tourin is applied. An extended finite element method is used for the evaluation of the cell problems while the transport equations are solved applying mixed finite elements. Ultimately, we investigate the potentially degenerating bulk properties of the medium such as porosity and effective diffusion. Moreover, we apply our approach to the dissolution of an array of calcite grains in the micro-macro context and validate our numerical scheme.

Dynamics of Viscous Entrapped Saturated Zones in Partially Wetted Porous Media

As a typical multiphase fluid flow process, drainage in porous media is of fundamental interest in nature and industrial applications. During drainage processes in unsaturated soils and porous media in general, saturated clusters, in which a liquid phase fully occupies the pore space between solid grains, affect the relative permeability and effective stress of the system. In this study, we experimentally studied drainage processes in unsaturated granular media as a model porous system. The distribution of saturated clusters is analysed by an optical imaging method under different drainage conditions, in which pore-scale information from Voronoi and Delaunay tessellation was used to characterise the topology of saturated cluster distributions. By employing statistical analyses, the observed spatial and temporal information of multiphase flow and fluid entrapment in porous media are described. The results indicate that the distributions of both the crystallised cell size and pore size are positively correlated to the spatial and temporal distribution of saturated cluster sizes. The saturated cluster size is found to follow a lognormal distribution, in which the generalised Bond number correlates negatively to the scale parameter and positively to the shape parameter. These findings can be used to connect pore-scale behaviour with overall hydro-mechanical characteristics in partially saturated porous media, using both the degree of saturation and generalised Bond number.

A binomial modeling approach for upscaling colloid transport under unfavorable attachment conditions: Emergent prediction of non-monotonic retention profiles.

We used a recently developed simple mathematical network model to upscale pore-scale colloid transport information determined under unfavorable attachment conditions. Classical log-linear and non-monotonic retention profiles, both well-reported under favorable and unfavorable attachment conditions, respectively, emerged from our upscaling. The primary attribute of the network is colloid transfer between bulk pore fluid, the near surface fluid domain (NSFD), and attachment (treated as irreversible). The network model accounts for colloid transfer to the NSFD of down-gradient grains and for reentrainment to bulk pore fluid via diffusion or via expulsion at rear flow stagnation zones (RFSZs). The model describes colloid transport by a sequence of random trials in a 1D network of Happel cells, which contain a grain and a pore. Using combinatorial analysis that capitalizes on the binomial coefficient, we derived from the pore-scale information the theoretical residence time distribution of colloids in the network. The transition from log-linear to non-monotonic retention profiles occurs when the conditions underlying classical filtration theory are not fulfilled, i.e., when a NSFD colloid population is maintained. Then, nonmonotonic retention profiles result, potentially both for attached and NSFD colloids. The concentration maxima shift downgradient depending on specific parameter choice. The concentration maxima were also shown to shift downgradient temporally (with continued elution) under conditions where attachment is negligible, explaining experimentally-observed down-gradient transport of retained concentration maxima of adhesion-deficient bacteria. For the case of zero reentrainment, we develop closed form, analytical expressions for the shape and the maximum of the colloid retention profile.

Effects of Pore and Grain Size on Water and Polymer Flooding in Micromodels

We have conducted a comprehensive series of experiments to evaluate the effects of pore size distribution of porous media on the dynamics of shear-thinning fluid flow and oil displacement efficiency. To do so, we have conducted microfluidic experiments, using micromodels fabricated from X-ray computed tomography images of sand-packs with varying grain sizes to create a realistic pore network. Three micromodels with well-defined particle size distribution were fabricated and used in our experiments. The use of micromodels to assess the effectiveness of polymer flooding is often superior to methods such as core flooding because of the detailed pore-scale information obtained during the experiments. The micromodels were initially saturated by oil, and the displacing fluids were prepared as aqueous solutions with dissolved xanthan gum. The dynamics and patterns of the interface displacement as well as the size distribution of the trapped oil ganglia were visualized using an optical microscope. The main findin...

Capillary flows across layers and textural interfaces – Pathways and colloid transport considerations in unsaturated layered porous media

Soils and other geologic porous media often display layering and associated textural contrasts that may alter unsaturated flow and transport pathways. Such natural interfaces are usually represented empirically in continuum flow models with limited mechanistic account of the effect of adjusted pathways across layers on colloid transport and on the nature of unsaturated flow. In this study we present the soil foam drainage equation (SFDE) as alternative framework to simulate unsaturated flow in layered porous media. HypothesisIn contrast to standard continuum flow models, the SFDE explicitly accounts for capillary flow pathways and their adjustment across textural interfaces that in turn define flow geometry for colloidal transport not predicted by continuum models. ExperimentsPore scale water distribution in a layered sand sample was measured using X-ray tomography to quantify capillary flow pathways. Literature values of measured saturation and capillary pressure profiles in layered porous columns were used to evaluate solutions based on the SFDE framework and to deduce velocity profiles and their effects for colloid transport. FindingsThe SFDE framework provides new insights into capillary architecture in unsaturated layered media and opens a new way for using pore scale information (from imaging) to provide the necessary SFDE parameters and potentially improve on the standard continuum representation of capillary flows in layered media.

Multiscale imaging, modeling, and principal component analysis of gas transport in shale reservoirs

Characterization and upscaling of gas transport in shales is challenging because of the multiple spatial scales. Rock characterization using high-resolution imaging (e.g., X-ray computed tomography [CT] and scanning electron microscope [SEM]) captures fundamental geometrical and transport properties, but the obtained information is usually highly localized and contains significant uncertainties. An effective upscaling method is thus needed to propagate the pore-scale information across multiple spatial scales. A modified dual-porosity model was proposed to study multiscale gas transport in shales. The model consists of two domains, a kerogen domain, and an inorganic matrix. Within kerogen, gas transport is dominated by molecular diffusion and nonlinear adsorption and desorption. Within inorganic matrix, gas transport is dominated by viscous flow driven by a pressure gradient. A mass-exchange-rate coefficient is used to describe gas transport between kerogen and inorganic matrix. The modified dual-porosity model was used to perform history matching of a pressure-pulse-decay experiment in the laboratory. The long tail of the pressure decline curve was well-captured by the model, suggesting that it accounted for both fast and slow transport mechanisms. Sensitivity analysis was conducted to study the impact of input variation on model output. We found that the impact of the transport processes within the slower domain (kerogen) depends primarily on the transport rate within the faster domain (inorganic matrix). The principal component analysis (PCA) method was applied to study the continuous movement of the upstream pressure decline curve resulting from input parameter variation. This study is the first to apply the PCA method in analysis of pressure decline curve in reservoir engineering. We found that increased convective transport rate within inorganic matrix expedited upstream pressure decline; conversely, increased mass-exchange rate and desorption-rate coefficients slowed down upstream pressure decline in the short term, but expedited it in the long term, when convective transport within inorganic matrix was fast. We also conducted primary recovery simulations to study the impacts of adsorbed gas ratio and Klinkenberg effect on upstream pressure decline, recovery factor, and recovery rate. We found that a higher adsorbed gas ratio led to a longer recovery rate curve. This confirms that a higher adsorbed gas ratio increases the longevity of a gas-producing well. Furthermore, Klinkenberg effect significantly enhanced initial recovery rate while lowering recovery rate at later times. Therefore, it is critical to accurately evaluate adsorbed gas ratio because it determines the shape and longevity of production curves; when reservoir pressure is relatively low, Klinkenberg effect might affect both early- and later-time production and thus cannot be simply ignored.

Quantifying background magnetic-field inhomogeneity for improved interpretation of free induction decay measurements

Nuclear magnetic resonance measurements provide useful insight into pore-scale properties of porous media. One influence affecting the measurement is inhomogeneity in the static background magnetic field ([Formula: see text]). This inhomogeneity can significantly alter the relaxation signal and potentially obscure pore-scale information. To improve the understanding of this effect on the free-induction decay (FID), a measurement still commonly used in practice, a novel methodology is developed to estimate the statistical distribution of [Formula: see text]. A suite of preparatory pulse sequences is developed to encode information about the [Formula: see text] field in the initial amplitude and phase of the FID following each sequence and an inversion is employed to predict the statistical distribution of [Formula: see text]. Knowledge of the [Formula: see text] distribution is then used to correct for the impact of [Formula: see text] inhomogeneity on the FID measurement; this is essential for improving the usefulness of FID measurements for the estimation of pore-scale properties. Results are presented for both numerical and laboratory studies verifying the feasibility of the developed methodology in a controlled laboratory environment, and demonstrating that knowledge of the statistical distribution of [Formula: see text] is sufficient to estimate the impact of [Formula: see text] inhomogeneity on the FID in cases where [Formula: see text] inhomogeneity causes less than an order of magnitude decrease in the relaxation times governing the FID.

Escherichia coli transport through intact gypsiferous and calcareous soils during saturated and unsaturated flows

Agricultural manures are the source of several pathogenic microorganisms in surface and groundwater that could cause diseases and adversely affect human health. Some strains of E. coli, an indicator microorganism, when transported over and/or through the soils reaching the water resources, cause urinary tract infections, diarrheal diseases, and contribute to infant mortality, fatal renal or neurological complications. To the best of the authors' knowledge, there is no information about the bacterial transport through natural/intact calcareous and gypsiferous soils. In this study, we selected four soil types to investigate the influence of lime and gypsum content on transport and filtration of E. coli released from cow manure during saturated and unsaturated flows. Intact soil columns from Hamadan and Isfahan provinces in Iran were transported to the laboratory. Cow manure was applied to the surface of each column at a rate of 10Mgha−1 dry basis. Soil columns were leached up to four pore volumes (PVs) at 20°C. E. coli influent (Co) and effluent (C) concentrations were measured by the plate-count method and Co/C values were drawn vs. PV as breakthrough curves (BTCs). Filtration coefficient (λf), relative adsorption index (SR), and maximum depth of potential contamination (Zmax) were calculated as indices of filtration and transport processes. Our results illustrated that contamination of water is possible where flooding irrigation systems occur in the low-lime soil due to low ionic strength and salinity, and greater structural stability. The BTCs showed that preferential pathways are greater in the low-lime soils than in the other studied soils. The presence of the natural lime and gypsum affected solution chemistry, macro and microporosity of the studied soils, which resulted in more bacterial filtration. The soils high in lime and gypsum also had maximum values for λf and SR, respectively. Minimum Zmax was observed in the high-lime soil and its mean was significantly lower than in the three other soils. The Zmax was greater in saturated flow conditions than in unsaturated flow conditions. Overall, when a source of E. coli (e.g. cow manure) is applied on a low-lime or gypsum soil, subsurface water contamination would be expected while high-lime and gypsum soils could filter more bacteria. This study showed the effect of natural lime and gypsum on bacterial transportation through intact soils. It is suggested to use techniques such as scanning electron microscope (SEM) and image analysis to present pore-scale information for bacterial movement through calcareous and gypsiferous soils.

PoreFlow: A complex pore-network model for simulation of reactive transport in variably saturated porous media

This study introduces PoreFlow, a pore-network modeling tool capable of simulating fluid flow and multi-component reactive and adsorptive transport under saturated and variably saturated conditions. PoreFlow includes a variety of modules, such as: pore network generator, drainage simulator, calculation of pressure and velocity distributions, and modeling of reactive solute transport accounting for advection and diffusion. The pore space is represented using a multi-directional pore-network capable of capturing the random structure of a given porous media with user-defined directional connectivities for anisotropic pore structures. The chemical reactions can occur within the liquid phase, as well as between the liquid and solid phases which may result in an evolution of porosity and permeability. Under variably saturated conditions the area of interfaces changes with degree of the fluid saturation.PoreFlow uses complex formulations for more accurate modeling of transport problems in presence of the nonwetting phase. This is done by refining the discretization within drained pores. An implicit numerical scheme is used to solve the governing equations, and an efficient substitution method is applied to considerably minimize computational times. Several examples are provided, under saturated and variably saturated conditions, to demonstrate the model applicability in hydrogeology problems and petroleum fields. We show that PoreFlow is a powerful tool for upscaling of flow and transport in porous media, utilizing different pore scale information such as various interfaces, phase distributions and local fluxes and concentrations to determine macro scale properties such as average saturation, relative permeability, solute dispersivity, adsorption coefficients, effective diffusion and tortuosity. Such information can be used as constitutive relations within continuum scale governing equations to model physical and chemical processes more accurately at the larger scales.

Quantification of Grain, Pore, and Fluid Microstructure of Unsaturated Sand from X-Ray Computed Tomography Images

Abstract A comprehensive series of three-dimensional x-ray computed tomography (XCT) imaging experiments was conducted to quantitatively assess the multiphase particle- and pore-scale properties of fine Ottawa (F-75) sand. The specimens were prepared to saturations ranging from approximately 5 % to 80 %. Specimens were doped with 10 % CsCl pore fluid solution and imaged using a monochromatic synchrotron x-ray source at energies below and above the Cs x-ray absorption k-edge to allow for high contrast between the solid, liquid, and air phases. Multiphase properties quantified from the XCT images included individual particle sizes and areas, as well as grain size distribution, pore shape and size distribution, water menisci distribution, solid, liquid, and gas surface areas, and particle contact coordination number. At low saturations, pore water is distributed primarily in the form of pendular rings and liquid bridges located between individual grains and in the smallest pore throats and bodies. A highly discontinuous water phase is evident as a large number of separately identifiable water units having very small volume. As the water saturation increases, the number of individual water units decreases; as expected, the average volume of these units increases significantly as the pore water coalesces into larger and larger units. Results obtained using SEM imaging and conventional geotechnical testing methods for particle-size distribution and soil–water retention were compared with those derived from analysis of the XCT images. Results compare very well in each case, typically within a few %. It is shown that the XCT is a reliable and non-destructive method to quantify pore-scale information vital to advance understanding of the hydrologic and mechanical behavior of unsaturated soils at the macroscale.

Coupling between finite volume method and lattice Boltzmann method and its application to fluid flow and mass transport in proton exchange membrane fuel cell

In this paper, a concentration distribution function reconstruction operator is derived to lift macroscopic parameter concentration to concentration distribution function in lattice Boltzmann method (LBM). Combined with a density–velocity distribution function reconstruction operator previously derived by the author’s group, the coupled finite volume method and LBM scheme (CFVLBM), previously proposed by the authors’ group is extended to simulate both fluid flow and mass transport processes. The accuracy of concentration distribution function reconstruction operator and the feasibility of CFVLBM are validated by two numerical examples, diffusion–convection–reaction problem and natural convection in a square cavity induced by concentration gradient. Finally, the CFVLBM is further adopted to simulate fluid flow and mass transport in the gas channel (GC) and gas diffusion layer (GDL) of a proton exchange membrane fuel cell (PEMFC). It is found that the CFVLBM can capture the pore-scale information of fluid flow and species transport in porous GDL and can save the computational resources.

Pore structure of the packing of fine particles

This paper presents a numerical study of the pore structure of fine particles. By means of granular dynamics simulation, packings of mono-sized particles ranging from 1 to 1000 μm are constructed. Our results show that packing density varies with particle size due to the effect of the cohesive van der Waals force. Pores and their connectivity are then analysed in terms of Delaunay tessellation. The geometries of the pores are represented by the size and shape of Delaunay cells and quantified as a function of packing density or particle size. It shows that the cell size decreases and the cell shape becomes more spherical with increasing packing density. A general correlation exists between the size and shape of cells: the larger the cell size relative to particle size, the more spherical the cell shape. This correlation, however, becomes weaker as packing density decreases. The connectivity between pores is represented by throat size and channel length. With decreasing packing density, the throat size increases and the channel length decreases. The pore scale information would be useful to understand and model the transport and mechanical properties of porous media.