Straight versus Spongy -- Effect of Tortuosity on Polymer Imbibition into Nanoporous Matrices Assessed by Segmentation-Free Analysis of 3D Sample Reconstructions

We comparatively analyzed imbibition of polystyrene (PS) into two complementary pore models having pore diameters of about 380 nm and hydroxyl-terminated inorganic-oxidic pore walls, controlled porous glass (CPG) and self-ordered porous alumina (AAO), by X-ray computed tomography and EDX spectroscopy. CPG contains continuous spongy-tortuous pore systems. AAO containing arrays of isolated straight cylindrical pores is a reference pore model with a tortuosity close to 1. Comparative evaluation of the spatiotemporal imbibition front evolution yields important information on the pore morphology of a probed tortuous matrix like CPG and on the imbibition mechanism. To this end, pixel brightness dispersions in tomographic 3D reconstructions and 2D EDX maps of infiltrated AAO and CPG samples were condensed into 1D brightness dispersion profiles normal to the membrane surfaces. Their statistical analysis yielded positions and widths of the imbibition fronts without segmentation or determination of pore positions. The retardation of the imbibition front movement with respect to AAO reference samples may be used as a descriptor for the tortuosity of a tested porous matrix. The velocity of the imbibition front movements in CPG equaled two-thirds of the velocity of the imbibition front movements in AAO. Moreover, the dynamics of the imbibition front broadening discloses whether porous matrices are dominated by cylindrical neck-like pore segments or by nodes. Independent single-meniscus movements in cylindrical AAO pores result in faster imbibition front broadening than in CPG, in which a morphology dominated by nodes results in slower cooperative imbibition front movements involving several menisci

Pore Network Modeling of Compressed Fuel Cell Components with OpenPNM

Pore network modeling is used to model water invasion and multiphase transport through compressed PEFC gas diffusion layers. Networks are created using a Delaunay tessellation of randomly placed base-points setting the pore locations and its compliment, the Voronoi diagram, is used to define the location of fibers and resultant pore and throat geometry. The model is validated in comparison to experimental capillary pressure curves obtained on compressed and uncompressed materials. Primary drainage is simulated with an invasion percolation algorithm that sequentially invades pores and throats separately with excellent agreement to experimental data, but required a slight modification to account for the higher aspect ratio of compressed pores. Compression is simulated by scaling the through-plane coordinates in a uniform manner representing a GDL wholly beneath the current-collector land. The relative permeability and diffusivity show some dependence on uniform compression. In-plane porosity variations introduced by land-channel compression are also investigated which have a marked effect on the limiting current. Saturation at breakthrough does not appear to be dependent on compression. However, a more important parameter, namely the peak saturation, is shown to influence the fuel cell performance and is dependent on the percolation inlet conditions

Tracing back the source of contamination

From the time a contaminant is detected in an observation well, the question of where and when the contaminant was introduced in the aquifer needs an answer. Many techniques have been proposed to answer this question, but virtually all of them assume that the aquifer and its dynamics are perfectly known. This work discusses a new approach for the simultaneous identification of the contaminant source location and the spatial variability of hydraulic conductivity in an aquifer which has been validated on synthetic and laboratory experiments and which is in the process of being validated on a real aquifer

Study on the structure formation and transport properties of nanoparticulate, nanoporous media using particle-based stochastic methods

Poröse Materialien werden in verschiedenen technischen Anwendungen wie Filtration, Ingenieurwesen, Geowissenschaften, Biologie und Biophysik eingesetzt. Diese Arbeit konzentriert sich auf die Modellierung von Massentransportphänomenen, die im Porennetzwerk und bei der Bildung von nanopartikulären nanoporösen Clustern auftreten, unter Verwendung partikelbasierter stochastischer Methoden. Traditionell werden makroskopische Größen wie Porosität, Tortuosität und Konstriktivität als global gemittelte Parameter in Modellen verwendet, um die Transporteigenschaften poröser Medien abzuschätzen. Diese makroskopischen Ansätze liefern jedoch nicht den Einfluss von strukturellen Heterogenitäten des Mediums auf Massentransportphänomene. Dieser Effekt kann berücksichtigt werden, indem die Rechengebiete auf der Porenskala aufgelöst werden, wie dies bei partikelbasierten Ansätzen geschieht. Einer der Vorteile partikelbasierter Methoden ist ihre effiziente Nutzung auf modernen MehrkernhardwareArchitekturen aufgrund ihrer inhärenten Parallelität. Im Rahmen dieser Arbeit wurde ein Brownscher Dynamik-Solver, der zur Modellierung der Bewegung von Tracern in porösen Medien verwendet wird, in C++ geschrieben und unter Verwendung der OpenMP- und MPI-Bibliotheken für paralleles Rechnen optimiert. Ein weiteres verwendetes partikelbasiertes Modell, die sogenannte Fast lubrication dynamics, ist in der Open-Source-Software LAMMPS implementiert. Mit Hilfe dieser Software wird die Bewegung von kolloidalen Nanopartikeln modelliert. Dazu musste eine angepasste paarweise Wechselwirkung entwickelt werden, die in der Lage ist, abgeschirmte Coulomb-Kräfte zwischen den Partikeln zu modellieren. Zusätzlich werden verschiedene externe Felder (z.B. Geschwindigkeitsfelder, elektrische Felder, Druckfelder, etc.) mit Hilfe von Open-SourceAnwendungen wie Fenics und einem in-house Lattice-Boltzmann-Solver berechnet, um deren Einfluss auf die Bewegung von Nanopartikeln oder Tracern zu evaluieren. In dieser Arbeit werden Massentransportphänomene in porösen Medien behandelt, wobei der Einfluss von Heterogenitäten in der porösen Struktur und der hemmende Effekt von engen Poren auf die Massentransporteigenschaften der genannten Medien untersucht wird. Zu den wichtigsten Erkenntnissen dieser Beiträge gehört die Entwicklung eines partikelbasierten Modells, mit dem die Diffusionsfähigkeit nanoporöser Medien berechnet werden kann. Darüber hinaus werden die Bildungs- und Struktureigenschaften von nanoporösen Clustern untersucht. Einer der Highlights dieser Studie ist ein vorgeschlagener Bildungsmechanismus von nanopartikulären Clustern, die durch Spray-Trocknung hergestellt werden.Porous materials are used in various engineering applications such as filtration, engineering, geoscience, biology and biophysics. This work focuses on modeling mass transport phenomena occurring in the pore network and in the formation of nanoparticulate nanoporous clusters using particle-based stochastic methods. Traditionally, macroscopic quantities such as porosity, tortuosity, and constrictivity are used as globally averaged parameters in models to estimate the transport properties of porous media. However, these macroscopic approaches do not provide the effect of structural heterogeneities of the medium on mass transport phenomena. This effect can be accounted for by resolving the computational domains at the pore scale, as is done in particle-based approaches. One of the advantages of particle-based methods is their efficient use on modern multicore hardware architectures due to their inherent parallelism. In this work, a Brownian dynamics solver used to model the motion of tracers in porous media was written in C++ and optimized for parallel computing using the OpenMP and MPI libraries. Another particle-based model used, called fast lubrication dynamics, is implemented in the open-source LAMMPS software. This software is used to model the motion of colloidal nanoparticles. For this purpose, an adapted pairwise interaction had to be developed, which is able to model screened Coulomb forces between the particles. In addition, various external fields (e.g., velocity fields, electric fields, pressure fields, etc.) are calculated using open-source applications such as Fenics and an in-house Lattice-Boltzmann solver to evaluate their influence on nanoparticle or tracer motion. In this work, mass transport phenomena in porous media are addressed, investigating the influence of heterogeneities in the porous structure and the inhibitory effect of narrow pores on the mass transport properties of said media. Among the main findings of these contributions is the development of a particle-based model that can be used to calculate the diffusivity of nanoporous media. In addition, the formation and structural properties of nanoporous clusters are investigated. One of the highlights of this study is a proposed formation mechanism of nanoparticulate clusters prepared by spray drying

Computational investigation of diffusion, flow, and multi-scale mass transport in disordered and ordered materials using high-performance computing

Flow and mass transport processes through porous materials are ubiquitous in nature and industry. In order to study these phenomena, we developed a computational framework for massively parallel supercomputers based on lattice-Boltzmann and random-walk particle tracking methods. Using this framework, we simulated the flow and mass transport (advection-diffusion problem) in several types of ordered and disordered porous materials. The pore network of the materials was either generated algorithmically (using Jodrey-Tory method) or reconstructed using confocal laser scanning microscopy or scanning electron microscopy. The simulated flow velocity field and dynamics of the random-walk tracer ensemble were used to study the transient and asymptotic behavior of macroscopic transport parameters: permeability, effective diffusion, and hydrodynamic dispersion coefficients. This work has three distinct topics developed and analyzed in four chapters. Each chapter has been published as a separate study. The date of publication and corresponding journal name are denoted at the beginning of each chapter. The first part of this work (Chapter 1) is addressing a timely question of high-performance liquid chromatography on whether particle size distribution of the modern packing materials gives any advantage in terms of separation efficiency. The second part (Chapters 2 and 3) is focused on the effects of dimensionality and geometry of the channels on the transport inside different types of chromatographic supports (particulate packings, monoliths, and pillar arrays). In order to analyze these effects, we recorded transient values of the longitudinal and transverse hydrodynamic dispersion coefficients in unconfined, partially, and fully confined structures and analyzed the time and length scales of the transport phenomena within. In the last part of this work (Chapter 4) we investigated the influence of the shell thickness and diffusivity on separation efficiency of the core--shell packings. Based on the simulation results, we extended the Giddings theory of coupled eddy dispersion and confirmed the validity of the Kaczmarski-Guiochon model of interparticle mass-transfer. Overall, this study extends the understanding of the connection of geometry and morphology of the porous materials with their macroscopic transport parameters

A review on reactive transport model and porosity evolution in the porous media

This work comprehensively reviews the equations governing multicomponent flow and reactive transport in porous media on the pore-scale, mesoscale and continuum scale. For each of these approaches, the different numerical schemes for solving the coupled advection–diffusion-reactions equations are presented. The parameters influenced by coupled biological and chemical reactions in evolving porous media are emphasised and defined from a pore-scale perspective. Recent pore-scale studies, which have enhanced the basic understanding of processes that affect and control porous media parameters, are discussed. Subsequently, a summary of the common methods used to describe the transport process, fluid flow, reactive surface area and reaction parameters such as porosity, permeability and tortuosity are reviewed

Machine Learning Methods and Computationally Efficient Techniques in Digital Rock Analysis

Digital Rock Analysis involves (1) 3D X-ray CT imaging and processing, (2) identifying and segmenting the minerals, and (3) performing flow simulation to obtain upscalable petrophysical parameters. Limitations exist at each step, primarily: (1) the resolution and Field of View (FOV), (2) bias and accuracy of identification and segmentation, and (3) the accuracy and computational intensity of direct simulation. These limitations are surpassed with machine learning and efficient simulation techniques. Super Resolution Convolutional Neural Networks (SRCNNs) and Enhanced Deep Generative Adversarial Networks (EDSRGANs) are shown in 2D and 3D to compensate for resolution-FOV limitations. SRCNNs boost resolution and recover edge sharpness, while EDSRGANs also recover texture. The noise reduction of SRCNNs precondition for image segmentation. Physical accuracy measured by phase topology and permeability achieves the closest match with EDSRGAN. Generalisation with augmentation shows high adaptability to noise and blur. Regenerated under-resolution features and comparison with SEM images shows consistency with underlying geometry. A custom formulated Deep CNN, U-ResNet and other networks are trained to perform 3D multi-mineral segmentation to eliminate user-bias, manual tuning, and algorithmic limitations inherent in traditional methods. U-ResNet performs most accurately and reliably, achieving the highest voxelwise accuracy and most consistent physical accuracy measured by calculating the topology of segmented mineral phases and comparing single and multi-phase direct flow simulations. Several techniques are proposed for efficient single and multi-phase flow at steady-state conditions. Single-phase flow in large images can be estimated using a Dual Grid Domain Decomposition (DGDD) that significantly reduces memory computational requirements, allowing workstations to solve supercomputer size problems. Multi-phase flow can be accelerated with a Morphologically Coupled Multi-phase Lattice Boltzmann Method (MorphLBM), rapidly computing capillary dominated flows, typically 5x faster using a Shell Aggregation morphing method. A U-net CNN can also rapidly estimate steady-state velocity fields, used as-is or as preconditioner in direct LBM simulation (ML-LBM). Similarly, the same acceleration procedure can also be coupled to Pore Network Models and Semi-Analytical Solvers to form accelerated direct simulation techniques. At each step of the Digital Rock workflow, machine learning methods and efficient techniques enhance results past physical limits and/or boost performance of traditional techniques

Predicting Permeability and Capillary Pressure in Low-Resolution Micro-CT Images of Heterogeneous Laminated Sandstones

Subsurface oil and gas reservoirs and fresh water aquifer systems are defined by fundamental geological characteristics such as mineral assemblage, grain and pore texture (size and shape), and porosity, and a range of petrophysical properties such as permeability, tortuosity, and capillary pressure, all of which contribute to fluid flow behaviour during extraction, injection, and storage. Computer-based models of reservoir and aquifer systems use these fundamental rock characteristics and petrophysical properties for large-scale fluid flow simulations. Designing and testing accurate static models is essential for reliable flow predictions. A wide range of analytical techniques has been developed over many years to expand the range and quality of formation modelling data. The most commonly used techniques include down-hole logging systems and laboratory-based core analysis. Down-hole logging tools measure the geophysical properties of formations, for example: gamma radiation and electrical resistivity, and typically collect data at the scale of tens of centimetres to metres, though image logs from micro-resistivity tools can collect millimetre to centimetre scale data. Commonly used laboratory-based analytical techniques involve the use of drill core, core plugs, and drill cuttings, for routine and special core/cuttings analysis to determine reservoir and seal rock properties. Modern X-ray micro-Computed Tomography (µCT) core imaging, in combination with petrophysical simulation software, often referred to as Digital Rock Physics, is fast becoming a standard tool for augmenting formation characterisation and modelling. Due to the nature of high-resolution µCT imaging and the associated analytical equipment, sample size is limited and governs the attainable resolution. It follows that metre-scale whole core samples cannot be imaged at the same high resolution as centimetre- and millimetre-scale core plugs. High-resolution images are critical to achieve reliable results from simulations of transport properties such as permeability and threshold injection pressure, which relies on all significant pathways in the pore space being correctly represented in the image. With current technology a µCT image of a 25mm diameter x 100mm tall sample, imaged using a detector with 2000 pixels per row, will have a minimum voxel size of ~13 µm, which implies that rock bands with grain and pore textures smaller than ~50 µm (i.e. 4 voxels across) cannot be represented with enough detail to reliably simulate petrophysical properties. The main research objective is to investigate the relationships between geological characteristics and petrophysical properties of heterogeneous laminated sandstone with the aim of estimating fluid flow properties for low-resolution images of larger rock volumes where fluid flow cannot be computed directly because of insufficient image resolution. This thesis presents an imaging and computation workflow for predicting absolute permeability, threshold pressure, lambda (a parameter in the Brooks-Corey equation describing the shape of drainage capillary pressure curves), and residual non-wetting phase saturation for sample volumes that are too large to allow direct computation of these properties or where traditional correlation methods fail. The workflow involves computing the above-mentioned petrophysical properties from high-resolution µCT images, along with a series of rock characteristics from spatially registered low-resolution images. Multiple linear regression models correlating the petrophysical properties to rock characteristics provide a means of predicting and mapping those property variations in larger scale low-resolution images. Two core samples of 25 mm diameter 80 mm tall of heterogeneous sandstone, for which 5 µm/voxel resolution is required to compute permeability and capillary pressure directly, were investigated in this study. Results show good agreement between statistical predictions of petrophysical properties made from intermediate-resolution images at 16 µm/voxel and low-resolution images at 64 and 61 µm/voxel for samples 1 and 2 respectively. The statistical models to predict permeability from low-resolution images at 64 and 61 µm/voxel (similar to typical whole core image resolutions) include open pore fraction and formation factor as predictor characteristics. Although binarized images at this resolution do not completely capture the pore system, I infer that these characteristics implicitly contain information about the critical fluid flow pathways, which control permeability. Capillary pressure simulations were performed using both pore-morphology and network model-based methods. A prediction model of threshold pressure containing open pore fraction, formation factor, and, in this case, clay fraction is similar to the model of permeability from the low-resolution image of sample 1. My conclusion, which is similar to that of the permeability model results, is that formation factor and clay fraction, because their computation takes into account the image gray scale values, inherently capture information about the pore system length scale that controls threshold pressure. A surprising yet important result is that of sample 2, where the set of predictor characteristics are unable to accurately predict threshold pressure. I conclude that this is because of image processing difficulties arising from a low signal to noise ratio in the high-resolution image, which complicates the segmentation of pore space from grain volume. The result suggests that image quality is critically important, which potentially eliminates the use of data collected using imaging techniques like ‘region of interest’ scans. Statistical models of lambda using characteristics from pore morphology-based simulations describe 62% of the parameter variance. The predictor characteristics included in the model using low-resolution characteristics are open pore fraction, surface area, and mean curvature. Correlations between lambda computed from network model-simulations and low-resolution predictors are more encouraging with formation factor and clay fraction describing 93% of the variance in lambda. Predicting residual non-wetting phase saturation poses a significant challenge and was not successfully addressed in this project. Neither the morphology-based nor the network model simulations produced data that correlate well with predictor characteristics. In the case of the network model-derived data it is possible that a larger dataset may improve residual non-wetting phase predictions

Soil structure exploration and measurement of its macroscopic behavior for a better understanding of the soil hydropedodynamic functionalities

Air permeability and water conductivity are fundamental physical properties when it comes to the soil functions across the environment. The water conductivity and the air permeability as functions of the soil’s degree of saturation (K(θ) and ka(ɛ), respectively) are only discretely measurable, and the use of models is necessary to obtain continuous expressions of these functions. Most models however consider the soil pore network structure as a fitting parameter although it is public knowledge that K(θ) and ka(ɛ) depend mostly on the soil microstructure, which is, none the less, unique between samples with homogeneous texture. New ways of studying K(θ) and ka(ɛ) are needed. The direct soil pore space visualization is a promising avenue to lead us to objectifying soil physics. The X-ray microtomographic technique (X-ray µCT) is now widely used by soil scientists and delivers 3D grayscale images of objects composed by materials of different densities. When dealing with a porous medium such as the natural soil, the X-ray µCT images need to be cautiously and expertly processed to obtain realistic feature quantification. A parallel, but however perquisite, objective of this dissertation is to statistically compare the effects of various image processing on the final X-ray µCT image features quantification. We simulated grayscale images to be processed to conclude about the image processing methodology we applied in our research. The overall objective of this dissertation is to explore the relationships between one microscopic soil structure (the volume of the smallest visible pore is 0.0004 mm³) and its macroscopic functionalities, such as its water conductivity and air permeability. More specifically, we confirmed that the use of 3D X-ray µCT data enables a better estimation of the soil water retention curve near saturation through the identification of the largest soil pores. These are indeed often by-passed with pressure plate’s laboratory measurements because of various artefacts. We also identified microscopic pore space morphological parameters that explained the soil saturated hydraulic conductivity, and microscopic porosity distribution measures that explained the soil air permeability. The final X-ray µCT image features quantification depends on the applied image processing, as stated, but also, clearly, on the image resolution. We concluded that working with a higher resolution would not necessarily lead to a higher degree of knowledge because resolution is sample-size dependent, and one pore size distribution could moreover be sufficiently visible at low resolution. We however observed that the pore network morphological and topological connectivity increases with resolution. Finally, we highlighted the imperfections of the capillary theory applied to soil through scanning the same soil samples at various water contents. As hypothesized, the pore network connectivity seems to play an important role in the pore accessibility to draining. After having studied the effects of the soil pore network structure on the soil hydrodynamic properties, we turned the question around and evaluated the effects of the chemical soil composition (organic carbon and free forms of iron) on the very same soil pore network structure. This dissertation therefore discusses the advantages and limitations of the use of X-ray microtomography to study soils for a more realistic understanding of the soil hydropedodynamic processes