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Pore-scale images obtained from a synchrotron-based X-ray computed micro-tomography (µCT) imbibition experiment in sandstone rock were used to conduct Navier–Stokes flow simulations on the connected pathways of water and oil phases. The resulting relative permeability was compared with steady-state Darcy-scale imbibition experiments on 5 cm large twin samples from the same outcrop sandstone material. While the relative permeability curves display a large degree of similarity, the endpoint saturations for the µCT data are 10% in saturation units higher than the experimental data. However, the two datasets match well when normalizing to the mobile saturation range. The agreement is particularly good at low water saturations, where the oil is predominantly connected. Apart from different saturation endpoints, in this particular experiment where connected pathway flow dominates, the discrepancies between pore-scale connected pathway flow simulations and Darcy-scale steady-state data are minor overall and have very little impact on fractional flow. The results also indicate that if the pore-scale fluid distributions are available and the amount of disconnected non-wetting phase is low, quasi-static flow simulations may be sufficient to compute relative permeability. When pore-scale fluid distributions are not available, fluid distributions can be obtained from a morphological approach, which approximates capillary-dominated displacement. The relative permeability obtained from the morphological approach compare well to drainage steady state whereas major discrepancies to the imbibition steady-state experimental data are observed. The morphological approach does not represent the imbibition process very well and experimental data for the spatial arrangement of the phases are required. Presumably for modeling imbibition relative permeability an approach is needed that captures moving liquid-liquid interfaces, which requires viscous and capillary forces simultaneously.

Porosity and permeability are the key factors in assessing the hydrocarbon productivity of unconventional (shale) reservoirs, which are complex in nature due to their heterogeneous mineralogy and poorly connected nano- and micro-pore systems. Experimental efforts to measure these petrophysical properties posse many limitations, because they often take weeks to complete and are difficult to reproduce. Alternatively, numerical simulations can be conducted in digital rock 3D models reconstructed from image datasets acquired via e.g., nanoscale-resolution focused ion beam-scanning electron microscopy (FIB-SEM) nano-tomography. In this study, impact of reservoir confinement (stress) on porosity and permeability of shales was investigated using two digital rock 3D models, which represented nanoporous organic/mineral microstructure of the Marcellus Shale. Five stress scenarios were simulated for different depths (2,000-6,000 feet) within the production interval of a typical oil/gas reservoir within the Marcellus Shale play. Porosity and permeability of the pre- and post-compression digital rock 3D models were calculated and compared. A minimal effect of stress on porosity and permeability was observed in both 3D models. These results have direct implications in determining the oil-/gas-in-place and assessing the production potential of a shale reservoir under various stress conditions.

Porosity is frequently specified as only a value to describe the microstructure of a battery electrode. However, porosity is a key parameter for the battery electrode performance and mechanical properties such as adhesion and structural electrode integrity during charge/discharge cycling. This study illustrates the importance of using more than one method to describe the electrode microstructure of LiNi0.6Mn0.2Co0.2O2 (NMC622)-based positive electrodes. A correlative approach, from simple thickness measurements to tomography and segmentation, allowed deciphering the true porous electrode structure and to comprehend the advantages and inaccuracies of each of the analytical techniques. Herein, positive electrodes were calendered from a porosity of 44–18% to cover a wide range of electrode microstructures in state-of-the-art lithium-ion batteries. Especially highly densified electrodes cannot simply be described by a close packing of active and inactive material components, since a considerable amount of active material particles crack due to the intense calendering process. Therefore, a digital 3D model was created based on tomography data and simulation of the inactive material, which allowed the investigation of the complete pore network. For lithium-ion batteries, the results of the mercury intrusion experiments in combination with gas physisorption/pycnometry experiments provide comprehensive insight into the microstructure of positive electrodes.

This open access book provides a thorough review of tortuosity in porous materials and discusses the impact of the microstructure on materials properties

Abstract. Various geoscientific applications require a fast prediction of fracture permeability for an optimal workflow. Hence, the objective of the current study is to introduce and validate a practical method to characterize and approximate single flow in fractures under different stress conditions by using a core-flooding apparatus, in situ X-ray computed tomography (CT) scans and a finite-volume method solving the Navier–Stokes–Brinkman equations. The permeability of the fractured sandstone sample was measured stepwise during a loading–unloading cycle (0.7 to 22.1 MPa and back) to validate the numerical results. Simultaneously, the pressurized core sample was imaged with a medical X-ray CT scanner with a voxel dimension of 0.5 × 0.5 × 1.0 mm3. Fracture geometries were obtained by CT images based on a modification of the simplified missing attenuation (MSMA) approach. Simulation results revealed both qualitative plausibility and a quantitative approximation of the experimentally derived permeabilities. The qualitative results indicate flow channeling along several preferential flow paths with less pronounced tortuosity. Significant changes in permeability can be assigned to temporal and permanent changes within the fracture due to applied stresses. The deviations of the quantitative results appear to be mainly caused by both local underestimation of hydraulic properties due to compositional matrix heterogeneities and the low CT resolution affecting the accurate capturing of sub-grid-scale features. Both affect the proper reproduction of the actual connectivity and therefore also the depiction of the expected permeability hysteresis. Furthermore, the threshold value CTmat (1862.6 HU) depicting the matrix material represents the most sensitive input parameter of the simulations. Small variations of CTmat can cause enormous changes in simulated permeability by up to a factor of 2.6 ± 0.1 and, thus, have to be defined with caution. Nevertheless, comparison with further CT-based flow simulations indicates that the proposed method represents a valuable method to approximate actual permeabilities, particularly for smooth fractures (< 35 µm). However, further systematic investigations concerning the applicability of the method are essential for future studies. Thus, some recommendations are compiled by also including suggestions of comparable studies.

Abstract In recent years, convolutional neural networks (CNNs) have experienced an increasing interest in their ability to perform a fast approximation of effective hydrodynamic parameters in porous media research and applications. This paper presents a novel methodology for permeability prediction from micro-CT scans of geological rock samples. The training data set for CNNs dedicated to permeability prediction consists of permeability labels that are typically generated by classical lattice Boltzmann methods (LBM) that simulate the flow through the pore space of the segmented image data. We instead perform direct numerical simulation (DNS) by solving the stationary Stokes equation in an efficient and distributed-parallel manner. As such, we circumvent the convergence issues of LBM that frequently are observed on complex pore geometries, and therefore, improve the generality and accuracy of our training data set. Using the DNS-computed permeabilities, a physics-informed CNN (PhyCNN) is trained by additionally providing a tailored characteristic quantity of the pore space. More precisely, by exploiting the connection to flow problems on a graph representation of the pore space, additional information about confined structures is provided to the network in terms of the maximum flow value, which is the key innovative component of our workflow. The robustness of this approach is reflected by very high prediction accuracy, which is observed for a variety of sandstone samples from archetypal rock formations.

The hydraulic permeability of sea ice is an important property that influences the role of sea ice in the environment in many ways. As it is difficult to measure, so far not many observations exist, and the quality of deduced empirical relationships between porosity and permeability is unknown. The present work presents a study of the permeability of young sea ice based on the combination of brine extraction in a centrifuge, X-ray micro-tomographic imaging and direct numerical simulations. The approach is new for sea ice. It allows us to relate the permeability and percolation properties explicitly to characteristic properties of the sea ice pore space, in particular to pore size and connectivity metrics. For the young sea ice from the present field study we obtain a brine volume of 2 % to 3 % as a threshold for the vertical permeability (transition to impermeable sea ice). We are able to relate this transition to the necking of brine pores at a critical pore throat diameter of ≈0.07 mm, being consistent with some limited pore analysis from earlier studies. Our optimal estimate of critical brine porosity is half the value of 5 % proposed in earlier work and frequently adopted in sea ice model studies and applications. By placing our results in the broader context of earlier studies, we conclude that the present threshold is more significant in that our centrifuge experiments and high-resolution 3D image analysis enable us to more accurately identify the threshold below which fluid connectivity ceases by examining the brine inclusion microstructure on finer scales than were previously possible. We also find some evidence that the sea ice pore space should be described by directed rather than isotropic percolation. Our revised porosity threshold is valid for the permeability of young columnar sea ice dominated by primary pores. For older sea ice containing wider secondary brine channels, for granular sea ice and for the full-thickness bulk permeability, other thresholds may apply.

Carbonate rocks have multiscale pore systems that are weakly understood. In this study, we use combined experimental, modeling, and pore space generation methods to tackle the impact of microporosity on the flow properties of Estaillades limestone. First, a nano-core from a microporous grain of Estaillades limestone was scanned using nanotomography (nano-XRM). The information from the nano-XRM scan was then used as input into an object-based pore network generator, on which permeability fields were simulated for a range of porosities, creating a synthetic Kozeny–Carman porosity–permeability relationship targeted for the specific microporous system present in Estaillades. We found a good match between the experimental and simulated Mercury Intrusion Capillary Pressure (MICP) range in the imaged geometry and a good match between the imaged and object-generated permeabilities and MICP. A micro-core of Estaillades was then scanned using X-ray microtomography (μCT), the differential pressure was measured during single-phase flow, and the rock was flooded with doped brine. The contrast between the images was used to assign a porosity to each voxel of connected microporosity. The flow through the pore space was solved using the Stokes–Brinkman (S–B) and Stokes-only solvers, and the differences between the measured permeability and computed permeabilities were evaluated. An agreement was seen between the computed permeability of the Stokes and S–B simulation with the measured permeability. However, the velocity fields with the S–B simulation captured stagnant regions of the pore space that were not present in the Stokes simulations. Additionally, we investigated the implications of including microporosity in the estimation of relative permeability. Nitrogen was experimentally co-injected through the core with doped brine at a 50% fractional flow and imaged to capture the two-phase effective permeability and was compared with the simulated numerical permeability. The Stokes simulation was not able to predict relative permeability with this method due to the major flow paths in the macroporosity being impeded by the injected non-wetting phase. The S–B simulations, however, allowed flow in the microporous regions around these blocked flow paths and were able to achieve a relative permeability prediction that was a reasonable match to the experimental measurement.

Abstract Erosion of sand control screens in oil and gas wells can lead to catastrophic completion failures, substantial production losses and damage to downstream facilities. Screen erosion can be caused by a number of completion design and environmental factors. However, the dominant failure mechanism is production of small solids through the screen openings, leading to development of localized high-velocity hot spots in the screen filter media and subsequent failure of the media. The current work discusses a detailed screen erosion study conducted to evaluate screen flow parameters leading to erosion and to provide safe operating guidelines for wells completed using cased hole perforated frac-pack (CHFP) and cased hole perforated gravel-packed (CHGP) completions with premium wire-mesh sand control screens. The erosion study consisted of both experimental work to determine erosion damage in screen samples and computational fluid dynamic (CFD) simulations to help visualize particle flow paths through the metal-mesh sand control media and determine local flow velocities and erosion-induced wear patterns. The experimental erosion tests and CFD modeling were performed on a specific screen configuration used in a number of subsea gas wells subject to high velocity flow conditions and associated high screen erosion potential. An empirical erosion model was then developed to translate short-term, high-velocity laboratory test results into field erosion predictions and well flow guidelines to minimize erosion potential. This paper presents results of the experimental work and associated CFD modeling as well as completion flow guidelines developed for field operation of subsea gas wells.

Abstract The goal of this study was to optimize fibrous filter media by increasing the dust holding capacity (DHC) while maintaining the β ratio and initial pressure drop of the filter media. The key was the use of microstructure models to optimize the filter media. The microstructure of three different variations of a filter media for oil filtration was modeled by using the FiberGeo module of the GeoDict® software package. It was found that by optimizing the fiber volume distribution over the height of the filter media, higher DHC values could be achieved while keeping the pressure drop considerably low. This confirms the hypothesis that the macroscopic properties of the filter element can be improved by modifying the microstructure of the filter media.

Abstract We investigate the feasibility of in-laboratory tomographic X-ray particle tracking velocimetry (TXPTV) and consider creeping flows with nearly density matched flow tracers. Specifically, in these proof-of-concept experiments we examined a Poiseuille flow, flow through porous media and a multiphase flow with a Taylor bubble. For a full 360 $$^\circ$$ ∘ computed tomography (CT) scan we show that the specially selected 60 micron tracer particles could be imaged in less than 3 seconds with a signal-to-noise ratio between the tracers and the fluid of 2.5, sufficient to achieve proper volumetric segmentation at each time step. In the pipe flow, continuous Lagrangian particle trajectories were obtained, after which all the standard techniques used for PTV or PIV (taken at visible wave lengths) could also be employed for TXPTV data. And, with TXPTV we can examine flows inaccessible with visible wave lengths due to opaque media or numerous refractive interfaces. In the case of opaque porous media we were able to observe material accumulation and pore clogging, and for flow with Taylor bubble we can trace the particles and hence obtain velocities in the liquid film between the wall and bubble, with thickness of liquid film itself also simultaneously obtained from the volumetric reconstruction after segmentation. While improvements in scan speed are anticipated due to continuing improvements in CT system components, we show that for the flows examined even the presently available CT systems could yield quantitative flow data with the primary limitation being the quality of available flow tracers. Graphic abstract

As kidney diseases affect ∼10% of the world population, understanding the underlying mechanisms and developing therapeutic interventions are of high importance. Although animal models have enhanced knowledge of disease mechanisms, human (patho-)physiology may not be adequately represented in animals. Developments in microfluidics and renal cell biology have enabled the development of dynamic models to study renal (patho-)physiology in vitro. Allowing inclusion of human cells and combining different organ models, such as kidney-on-a-chip (KoC) models, enable the refinement and reduction of animal experiments. We systematically reviewed the methodological quality, applicability and effectiveness of kidney-based (multi-)organ-on-a-chip models, and describe the state-of-the-art, strengths and limitations, and opportunities regarding basic research and implementation of these models. We conclude that KoC models have evolved to complex models capable of mimicking systemic (patho-)physiological processes. Commercial chips and human induced pluripotent stem cells and organoids are important for KoC models to study disease mechanisms and assess drug effects, even in a personalized manner. This contributes to the Reduction, Refinement and Replacement of animal models for kidney research. A lack of reporting of intra- and inter-laboratory reproducibility and translational capacity currently hampers implementation of these models.

Abstract Even though current manufacturing methods allow to build precisely‐defined graded depth filter media, it remains unclear which local filtration properties are desirable. We, therefore, introduce a multiscale approach which links pore and continuum scale (PS and CS) to address this question. Based on data from PS simulations, local filtration performance, as described by the filter coefficient, is predicted on the CS by an optimal control solution and the obtained trajectory is translated back to the PS where it is validated. Two case studies are presented: a bidisperse fibrous medium and a granular depth filter composed of bidisperse particles. Both media are optimized to achieve a homogenous deposition of separated impurities along the filter depth. It is found that the presented method allows to reach this goal reasonably well in both cases. We claim that our method forms a good basis for further developments for which promising possibilities are highlighted.

ABSTRACT Rock compressibility is a major control of reservoir compaction, yet only limited core measurements are available to constrain estimates. Improved analytical and computational estimates of rock compressibility of reservoir rock can improve forecasts of reservoir production performance and the geomechanical integrity of compacting reservoirs. The fast-evolving digital rock technology can potentially overcome the need for simplification of pores (e.g., ellipsoids) to estimate rock compressibility as the computations are performed on an actual pore-scale image acquired using 3D microcomputed tomography (micro-CT). However, the computed compressibility using a digital image is impacted by numerous factors, including imaging conditions, image segmentation, constituent properties, choice of numerical simulator, rock field of view, how well the grain contacts are resolved in an image, and the treatment of grain-to-grain contacts. We have analyzed these factors and quantify their relative contribution to the rock moduli computed using micro-CT images of six rocks: a Fontainebleau sandstone sample, two Berea sandstone samples, a Castelgate sandstone sample, a grain pack, and a reservoir rock. We find that image-computed rock moduli are considerably stiffer than those inferred using laboratory-measured ultrasonic velocities. This disagreement cannot be solely explained by any one of the many controls when considered in isolation, but it can be ranked by their relative contribution to the overall rock compressibility. Among these factors, the image resolution generally has the largest impact on the quality of image-derived compressibility. For elasticity simulations, the quality of an image resolution is controlled by the ratio of the contact length and image voxel size. Images of poor resolution overestimate contact lengths, resulting in stiffer simulation results.

Abstract Li-ion batteries are a key technology for both electro-mobility and stationary energy storage systems. In order to be able to represent and improve their service life in these applications, a better understanding of the processes which lead to the degradation of the individual cells is essential. The work presented in this article focuses on the comparative post mortem analysis of type 18650 commercially available cells containing the state of the art active materials (Cathode: LiMn 2 O 4 (LMO) and Li(Ni 1/3 Mn 1/3 Co 1/3 )O 2 (NMC), Anode: Graphite). These cells were subjected to various different ageing procedures. Amongst other effects, the cells investigated revealed signs of crack formation in the LMO- and NMC-particles, a loss in the mechanical integrity of the cathode active mass and plastic deformation of cell structure together with pronounced delamination between the active mass layers, the separator and the current collector.

Because of the recent advancements in hardware and reconstruction algorithms, multiphase flow modeling in porous media is experiencing a shift toward using advanced imaging techniques such as X-ray computed tomography in conjunction with direct numerical simulations. This approach captures heterogeneities in soil samples utilized in laboratory testing and results in quick and less tedious predictions compared to the existing methods. In this paper, an experimental setup is developed specifically to validate numerical predictions of the soil water retention curve (SWRC) for two types of sands with identical size but distinct grain morphology of round (Ottawa sand) and angular particle shape (Q-Rok). The complex 3D pore network is captured noninvasively using high-resolution attenuation-based X-ray computed tomography. The numerical predictions are carried out by solving a Young-Laplace equation using the pore morphology method. The experimental results and numerical predictions match well, including the effect of hysteresis in SWRC measurements. The spatial distribution of pore water and pore air corresponding to different capillary suctions is obtained from numerical predictions, providing greater insights into the hydromechanical behavior of partially saturated soils. The sensitivity of the voxel size on simulations is quantified by predicting the pore size distribution of Ottawa sand at three different tomography resolutions.

Abstract Aerosols represent a health risk since small droplets may enter the respiratory system and cause lung cancer, allergies, or diseases like COVID‐19. In this work, an Eulerian‐Lagrangian computational fluid dynamics model is used based on a voxel‐based (GeoDict) and a mesh‐based (StarCCM+) code. For evaluating accuracy and computational time of both models, fractional filtration efficiency and pressure drop are compared to an empirical solution for a single fiber and to experimental results for a complex 3D fibrous filter material. Simulation results of both methods are in good agreement with empirical and measurement results although the complex geometry of the fibers is captured more accurately by the unstructured mesh using the same resolution. Computing times are much faster using the voxel‐based code.

A workflow for the stochastic microstructure modeling of solid oxide cell electrodes is presented. Based on a few real microstructures, the design space can be virtually explored, allowing for a subsequent optimization of microstructure properties.

, largely because there are no known hand bones that can be definitively attributed to this genus. Here we report fossil hand and foot bones unambiguously associated with craniodental material of P. boisei. KNM-ER 101000 demonstrates that P. boisei shared key manipulative and bipedal adaptations with the genus Homo. Moreover, the hand morphology of KNM-ER 101000 converges on that of gorillas in ways that are consistent with manual food processing and would have facilitated powerful grasping, such as that used in climbing. These fossils suggest that P. boisei was capable of tool making and use in some capacity while also supporting the proposed dichotomy of distinct dietary adaptations between Paranthropus and Homo. In addition to offering insights into the poorly known postcranial functional anatomy of Paranthropus, this discovery illuminates broader patterns of hominin hand evolution and tool use.

Abstract It is generally assumed that transport resistance in porous media, which can also be expressed as tortuosity, correlates somehow with the pore volume fraction. Hence, mathematical expressions such as the Bruggeman relation (i.e., τ2 = ε−1/2) are often used to describe tortuosity (τ)—porosity (ε) relationships in porous materials. In this chapter, the validity of such mathematical expressions is critically evaluated based on empirical data from literature. More than 2200 datapoints (i.e., τ – ε couples) are collected from 69 studies on porous media transport. When the empirical data is analysed separately for different material types (e.g., for battery electrodes, SOFC electrodes, sandstones, packed spheres etc.), the resulting τ versus ε—plots do not show clear trend lines, that could be expressed with a mathematical expression. Instead, the datapoints for different materials show strongly scattered distributions in rather ill-defined ‘characteristic’ fields. Overall, those characteristic fields are strongly overlapping, which means that the τ – ε characteristics of different materials cannot be separated clearly. When the empirical data is analysed for different tortuosity types, a much more consistent pattern becomes apparent. Hence, the observed τ − ε pattern indicates that the measured tortuosity values strongly depend on the involved type of tortuosity. A relative order of measured tortuosity values then becomes apparent. For example, the values observed for direct geometric and mixed tortuosities are concentrated in a relatively narrow band close to the Bruggeman trend line, with values that are typically < 2. In contrast, indirect tortuosities show higher values, and they scatter over a much larger range. Based on the analysis of empirical data, a detailed pattern with a very consistent relative order among the different tortuosity types can be established. The main conclusion from this chapter is thus that the tortuosity value that is measured for a specific material, is much more dependent on the type of tortuosity than it is dependent on the material and its microstructure. The empirical data also illustrates that tortuosity is not strictly bound to porosity. As the pore volume decreases, the more scattering of tortuosity values can be observed. Consequently, any mathematical expression that aims to provide a generalized description of τ − ε relationships in porous media must be questioned. A short section is thus provided with a discussion of the limitations of such mathematical expressions for τ − ε relationships. This discussion also includes a description of the rare and special cases, for which the use of such mathematical expressions can be justified.