Development of stochastically reconstructed 3D porous media micromodels using additive manufacturing: numerical and experimental validation.

We propose an integrated methodology for the design and fabrication of 3D micromodels that are suitable for the pore-scale study of transport processes in macroporous materials. The micromodels, that bear the pore-scale characteristics of sandstone, such as porosity, mean pore size, etc, are designed following a stochastic reconstruction algorithm that allows for fine-tuning the porosity and the correlation length of the spatial distribution of the solid material. We then construct a series of 3D micromodels at very fine resolution (i.e. 16 µ m) using a state-of-the-art 3D printing infrastructure, specifically a ProJet MJP3600 3D printer, that utilizes the Material Jetting technology. Within the technical constraints of the 3D printer resolution, the fabricated micromodels represent scaled-up replicas of natural sandstones, that are suitable for the study of the scaling between the permeability, the porosity and the mean pore size. The REV- and pore-scale characteristics of the resulting physical micromodels are recovered using a combination of X-ray micro-CT and microfluidic studies. The experimental results are then compared with single-phase flow simulations at pore-scale and geostatistic models in order to determine the effects of the design parameters on the intrinsic permeability and the spatial correlation of the velocity profile. Our numerical and experimental measurements reveal an excellent match between the properties of the designed and fabricated 3D domains, thus demonstrating the robustness of the proposed methodology for the construction of 3D micromodels with fine-tuned and well-controlled pore-scale characteristics. Furthermore, a pore-scale numerical study over a wider range of 3D digital domain realizations reveals a very good match of the measured permeabilities with the predictions of the Kozeny-Carman formulation based on a single control parameter, k 0 , that is found to have a practically constant value for porosities ϕ ≥ 0.2 . This, in turn, enables us to customize the sample size to meet REV constraints, including enlarging pore morphology while considering the Reynolds number. It is also found that at lower porosities there is a significant increase in the fraction of the non-percolating pores, thus leading to different k 0 , as the porosity approaches a numerically determined critical porosity value, ϕ c , where the domain is no longer percolating.

Exploring Carbonate Rock Dissolution Dynamics and the Influence of Rock Mineralogy in CO2 Injection.

Understanding geochemical dissolution in porous materials is crucial, especially in applications such as geological CO2 storage. Accurate estimation of reaction rates enhances predictive modeling in geochemical-flow simulations. Fractured porous media, with distinct transport time scales in fractures and the matrix, raise questions about fracture-matrix interface dissolution rates compared to bulk dissolution rate and the scale-dependency of reaction rate averaging. Our investigation delves into these factors, studying the impact of flow rate and mineralogy on interface dissolution patterns. By injecting carbonated water into carbonate rock samples containing a central channel (mimicking fracture hydrodynamics), our study utilized µCT X-ray imaging at 3.3 µm spatial resolution to estimate the reaction rate and capture the change in pore morphology. Results revealed dissolution rates significantly lower (up to 4 orders of magnitude) than batch experiments. Flow rate notably influenced fracture profiles, causing uneven enlargement at low rates and uniform widening at higher ones. Ankerite presence led to a dissolution-altered layer on the fracture surface, showing high permeability and porosity without greatly affecting the dissolution rate, unlike clay-rich carbonates. This research sheds light on controlling factors influencing dissolution in subsurface environments, critical for accurate modeling in diverse applications.

Visual Analysis of Displacement Processes in Porous Media using Spatio-Temporal Flow Graphs.

We developed a new approach comprised of different visualizations for the comparative spatio-temporal analysis of displacement processes in porous media. We aim to analyze and compare ensemble datasets from experiments to gain insight into the influence of different parameters on fluid flow. To capture the displacement of a defending fluid by an invading fluid, we first condense an input image series to a single time map. From this map, we generate a spatio-temporal flow graph covering the whole process. This graph is further simplified to only reflect topological changes in the movement of the invading fluid. Our interactive tools allow the visual analysis of these processes by visualizing the graph structure and the context of the experimental setup, as well as by providing charts for multiple metrics. We apply our approach to analyze and compare ensemble datasets jointly with domain experts, where we vary either fluid properties or the solid structure of the porous medium. We finally report the generated insights from the domain experts and discuss our contribution's advantages, generality, and limitations.

A multifunctional mechanical testing stage for micro x-ray computed tomography.

An existing open and modular designed micro X-Ray Computed Tomography (µXRCT) system is extended by a test rig in order to combine mechanical and hydro-mechanical experiments with µXRCT characterization. The aim of the system is to cover the complete resolution range of the underlying µXRCT system in combination with a broad load capacity range. A characteristic feature of the developed setup is that it consists mainly of standard components. This makes the shown test rig potentially interesting for other researchers considering extending an existing µXRCT system with an apparatus for mechanical and hydro-mechanical in situ testing. For the load frame, an uniaxial 10 kN universal testing machine with a digital control system was employed, which was extended by two aligned rotational stages. The uniaxial load capacity is ±3.1 kN and can be combined with torque moments of up to ±15 N m both limited by the used rotational stages. The setup is designed in such a way that different x-ray transparent cells (flow cells, oedometer cells, triaxial cells, etc.) can be integrated to generate three-dimensional stress/strain states as required for porous media research. Three applications demonstrate the possible versatile use of the system. As part of these examples, we show how corresponding x-ray transparent cells are designed and implemented. Finally, we discuss the presented approach's technical advantages and disadvantages and suggest improvements.

Machine learning assists in increasing the time resolution of X-ray computed tomography applied to mineral precipitation in porous media.

Many subsurface engineering technologies or natural processes cause porous medium properties, such as porosity or permeability, to evolve in time. Studying and understanding such processes on the pore scale is strongly aided by visualizing the details of geometric and morphological changes in the pores. For realistic 3D porous media, X-Ray Computed Tomography (XRCT) is the method of choice for visualization. However, the necessary high spatial resolution requires either access to limited high-energy synchrotron facilities or data acquisition times which are considerably longer (e.g. hours) than the time scales of the processes causing the pore geometry change (e.g. minutes). Thus, so far, conventional benchtop XRCT technologies are often too slow to allow for studying dynamic processes. Interrupting experiments for performing XRCT scans is also in many instances no viable approach. We propose a novel workflow for investigating dynamic precipitation processes in porous media systems in 3D using a conventional XRCT technology. Our workflow is based on limiting the data acquisition time by reducing the number of projections and enhancing the lower-quality reconstructed images using machine-learning algorithms trained on images reconstructed from high-quality initial- and final-stage scans. We apply the proposed workflow to induced carbonate precipitation within a porous-media sample of sintered glass-beads. So we were able to increase the temporal resolution sufficiently to study the temporal evolution of the precipitate accumulation using an available benchtop XRCT device.

Acoustic waves in saturated porous media with gas bubbles.

The present framework employs various interface characteristics of gas bubbles into a continuum description of acoustics in porous media. It first extends the bubble compressibility in classic models by surface tension and higher-order curvature effects. This modelling extension is significantly relevant to estimate the impact of interface effects, e.g. on emerging nano-scale bubbles or pickering emulsions. The gas bubble dynamics is then homogenized to derive a manageable set of continuum equations. Respective assumptions and limitations are summarized in this process to provide a quick reference when choosing the compromise between a model's complexity and applicability. The acoustic response of a water-saturated sandstone with gas bubbles is finally evaluated with respect to the practical importance at ambient and reservoir conditions. The shape of the bubble-size distribution is represented in the evolution of the inverse quality factor but less distinct in the dispersion of the phase velocity. The presented, rigorous framework thus allows to predict what frequencies and acoustic properties relate to specific gas bubble sizes and whether respective signals may be detected with current apparatus. This article is part of the theme issue 'Wave generation and transmission in multi-scale complex media and structured metamaterials (part 2)'.

Nonuniqueness of hydrodynamic dispersion revealed using fast 4D synchrotron x-ray imaging.

Experimental and field studies reported a significant discrepancy between the cleanup and contamination time scales, while its cause is not yet addressed. Using high-resolution fast synchrotron x-ray computed tomography, we characterized the solute transport in a fully saturated sand packing for both contamination and cleanup processes at similar hydrodynamic conditions. The discrepancy in the time scales has been demonstrated by the nonuniqueness of hydrodynamic dispersion coefficient versus injection rate (Péclet number). Observations show that in the mixed advection-diffusion regime, the hydrodynamic dispersion coefficient of cleanup is significantly larger than that of the contamination process. This nonuniqueness has been attributed to the concentration-dependent diffusion coefficient during the cocurrent and countercurrent advection and diffusion, present in contamination and cleanup processes. The new findings enhance our fundamental understanding of transport processes and improve our capability to estimate the transport time scales of chemicals or pollution in geological and engineering systems.

Parameter Identification and Validation of Shape-Memory Polymers within the Framework of Finite Strain Viscoelasticity.

Shape-Memory Polymers (SMPs) can be stretched to large deformations and recover induced strains when exposed to an appropriate stimulus, such as heat. This emerging class of functional polymers has attracted much interest and found applications in medicine and engineering. Nevertheless, prior to any application, their physical and mechanical properties must be thoroughly studied and understood in order to make predictions or to design structures thereof. In this contribution, the viscoelastic behavior of a polyether-based polyurethane (Estane) and its rate- and temperature-dependent behavior have been studied experimentally and by the mean of simulations. The model-inherent material parameters are identified with the assumption of the thermo-rheological complexity. Here, the numerical results of uni-axial stress relaxations were compared with the associated experiments in conjucation with the Levenberg-Marquard optimization method to determine the parameters of the Prony equation. The ability of the model to simulate the thermo-mechanical properties of Estane was evaluated by data-rich experimental observations on tension and torsion in various temperature ranges. Heterogeneous tests are included into the experimental program to cover a broader spectrum of loading scenarios.

From Understanding Mechanical Behavior to Curvature Prediction of Humidity-Triggered Bilayer Actuators.

Nature will always be an endless source of bioinspiration for man-made smart materials and multifunctional devices. Impressively, even cutoff leaves from resurrection plants can autonomously and reproducibly change their shape upon humidity changes, which goes along with total recovery of their mechanical properties after being completely dried. In this work, simple bilayers are presented as autonomously moving, humidity-triggered bending actuators. The bilayers-showing reproducible bending behavior with reversible kinematics and multiway behavior-are studied in terms of their mechanical behavior upon humidity changes. The active layer consists of a highly conducting polymer film based on poly(3,4-ethylenedioxythiophene):poly(styrene sulfonate) (PEDOT:PSS) with poly(dimethylsiloxane) (PDMS) as passive layer. The response to humidity is explored with dynamic mechanical thermal analysis and quartz crystal microbalance measurements. Introduction of a composite beam model allows to predict the curvature of the actuators with input from the rheological measurements. It is clearly demonstrated that volumetric strain and Young's modulus, both heavily influenced by the water uptake, dominate the bending behavior and therefore the curvature of the actuators. This loop of rheological characterization coupled with an analytical model allows to predict curvatures of in principle any complex geometry and material combination for moving parts in soft robotics.

Investigation of the Influence of Moisture Content on Fatigue Behaviour of HPC by Using DMA and XRCT.

High-performance concrete (HPC) is a topic of current research and construction projects, due to its outstanding compressive strength and durability. In particular, its behaviour under high-cycle fatigue loading is the focus of current investigations, to further pave the way to highly challenging long-lasting constructions; e.g., bridges or offshore buildings. In order to investigate the behaviour of HPC with different moisture contents in more detail, a mixture of silica sand and basalt aggregate with a maximum grain size of 8 mm was investigated with three different moisture contents. For this purpose, cyclic compressive fatigue tests at a loading frequency of 10 Hz and different maximum stress levels were performed. The main focus was the moisture influence on the number of cycles to failure and the development of concrete temperature and strain. In a further step, only the mortar matrix was investigated. For this purpose, the mixture was produced without basalt, and the moisture influence was investigated on smaller-sized test specimens using dynamic mechanical analysis (DMA) and X-ray computed tomography (XRCT). It was shown that the moisture content of HPC had a significant influence on the fatigue damage behaviour due to the number of cycles to failure decreasing significantly with increased moisture. In addition, there was also an influence on the temperature development, as well as on the strain development. It was shown that increasing moisture content was associated with an increase in strain development. XRCT scans, in the course of the damage phases, showed an increase in internal cracks, and made their size visible. With the help of DMA as a new research method in the field of concrete research, we were also able to measure damage development related to a decrease in sample stiffness. Both methods, XRCT and DMA, can be listed as nondestructive methods, and thus can complement the known destructive test methods, such as light microscopy.

Elastic waves in particulate glass-rubber mixtures.

We investigate the propagation of waves in dense static granular packings made of soft and stiff particles subjected to hydrostatic stress. Physical experiments in a triaxial cell equipped with broadband piezoelectric wave transducers have been performed at ultrasound frequencies. The time of flight is measured in order to study the combined effect of applied stress and rubber content on the elastic properties of the mixtures. The bulk stiffness deduced from the wave speed is nonlinear and non-monotonic with the increasing percentage of rubber with a more prominent effect at higher pressures. Moreover, in the frequency domain, a spectral analysis gives insights on the transition from a glass- to a rubber-dominated regime and the influence of rubber particles on the energy dissipation. Mixtures with rubber content below 30% show enhanced damping properties, associated with slightly higher stiffness and lighter weight.

An open, modular, and flexible micro X-ray computed tomography system for research.

In this paper, a modular and open micro X-ray Computed Tomography (µXRCT) system is presented, which was set up during the last years at the Institute of Applied Mechanics (CE) of the University of Stuttgart and earlier at the Institute of Computational Engineering of Ruhr-University Bochum. The system is characterized by its intrinsic flexibility resulting from the modular and open design on each level and the opportunity to implement advanced experimental in situ setups. On the one hand, the presented work is intended to support researchers interested in setting up an experimental XRCT system for the microstructural characterization of materials. On the other hand, it aims to support scientists confronted with the decision to set up a system on their own or to buy a commercial scanner. In addition to the presentation of the various hardware components and the applied modular software concept, the technical opportunities of the open and modular hard- and software design are demonstrated by implementing a simple and reliable method for the compensation of bad detector pixels to enhance the raw data quality of the projections. A detailed investigation of the performance of the presented system with regard to the achievable spatial resolution is presented. XRCT datasets of three different applications are finally shown and discussed, demonstrating the wide scope of options of the presented system.

Direct characterization of solute transport in unsaturated porous media using fast X-ray synchrotron microtomography.

Solute transport in unsaturated porous materials is a complex process, which exhibits some distinct features differentiating it from transport under saturated conditions. These features emerge mostly due to the different transport time scales at different regions of the flow network, which can be classified into flowing and stagnant regions, predominantly controlled by advection and diffusion, respectively. Under unsaturated conditions, the solute breakthrough curves show early arrivals and very long tails, and this type of transport is usually referred to as non-Fickian. This study directly characterizes transport through an unsaturated porous medium in three spatial dimensions at the resolution of 3.25 µm and the time resolution of 6 s. Using advanced high-speed, high-spatial resolution, synchrotron-based X-ray computed microtomography (sCT) we obtained detailed information on solute transport through a glass bead packing at different saturations. A large experimental dataset (>50 TB) was produced, while imaging the evolution of the solute concentration with time at any given point within the field of view. We show that the fluids' topology has a critical signature on the non-Fickian transport, which yet needs to be included in the Darcy-scale solute transport models. The three-dimensional (3D) results show that the fully mixing assumption at the pore scale is not valid, and even after injection of several pore volumes the concentration field at the pore scale is not uniform. Additionally, results demonstrate that dispersivity is changing with saturation, being twofold larger at the saturation of 0.52 compared to that at the fully saturated domain.

An SPH Approach for Non-Spherical Particles Immersed in Newtonian Fluids.

Solid particles immersed in a fluid can be found in many engineering, environmental or medical fields. Applications are suspensions, sedimentation processes or procedural processes in the production of medication, food or construction materials. While homogenized behavior of these applications is well understood, contributions in the field of pore-scale fully resolved numerical simulations with non-spherical particles are rare. Using Smoothed Particle Hydrodynamics (SPH) as a simulation framework, we therefore present a modeling approach for Direct Numerical Simulations (DNS) of single-phase fluid containing non-spherically formed solid aggregates. Notable and discussed model specifications are the surface-coupled fluid-solid interaction forces as well as the contact forces between solid aggregates. The focus of this contribution is the numerical modeling approach and its implementation in SPH. Since SPH presents a fully resolved approach, the construction of arbitrary shaped particles is conveniently realizable. After validating our model for single non-spherical particles, we therefore investigate the motion of solid bodies in a Newtonian fluid and their interaction with the surrounding fluid and with other solid bodies by analyzing velocity fields of shear flow with respect to hydromechanical and contact forces. Results show a dependency of the motion and interaction of solid particles on their form and orientation. While spherical particles move to the centerline region, ellipsoidal particles move and rotate due to vortex formation in the fluid flow in between.

Digital rock physics and laboratory considerations on a high-porosity volcanic rock.

Digital rock physics combines microtomographic imaging with advanced numerical simulations of effective material properties. It is used to complement laboratory investigations with the aim to gain a deeper understanding of relevant physical processes related to transport and effective mechanical properties. We apply digital rock physics to reticulite, a natural mineral with a strong analogy to synthetic open-cell foams. We consider reticulite an end-member for high-porosity materials with a high stiffness and brittleness. For this specific material, hydro-mechanical experiments are very difficult to perform. Reticulite is a pyroclastic rock formed during intense Hawaiian fountaining events. The honeycombed network of bubbles is supported by glassy threads and forms a structure with a porosity of more than 80%. Comparing experimental with numerical results and theoretical estimates, we demonstrate the high potential of in situ characterization with respect to the investigation of effective material properties. We show that a digital rock physics workflow, so far applied to conventional rocks, yields reasonable results for high-porosity rocks and can be adopted for fabricated foam-like materials with similar properties. Numerically determined porosities, effective elastic properties, thermal conductivities and permeabilities of reticulite show a fair agreement to experimental results that required exeptionally high experimental efforts.

Visualization of Bubble Formation in Porous Media.

We present a visualization approach for the analysis of CO2 bubble-induced attenuation in porous rock formations. As a basis for this, we introduce customized techniques to extract CO2 bubbles and their surrounding porous structure from X-ray computed tomography data (XCT) measurements. To understand how the structure of porous media influences the occurrence and the shape of formed bubbles, we automatically classify and relate them in terms of morphology and geometric features, and further directly support searching for promising porous structures. To allow for the meaningful direct visual comparison of bubbles and their structures, we propose a customized registration technique considering the bubble shape as well as its points of contact with the porous media surface. With our quantitative extraction of geometric bubble features, we further support the analysis as well as the creation of a physical model. We demonstrate that our approach was successfully used to answer several research questions in the domain, and discuss its high practical relevance to identify critical seismic characteristics of fluid-saturated rock that govern its capability to store CO2.

Demonstrating the Influence of Physical Aging on the Functional Properties of Shape-Memory Polymers.

Polymers that allow the adjustment of Shape-Memory properties by the variation of physical parameters during programming are advantageous compared with their counterparts requiring synthesis of new material. Here, we explored the influence of hydrolytic (physical) aging on the Shape-Memory properties of the polyetherurethane system Estane, programmed in repeated thermomechanical cycles under torsional load. We were able to demonstrate that physical aging occurred through water adsorption influencing the existing free volume of the samples as well as the functional properties of Estane. Dynamic Mechanical Thermal Analysis determined the glass transition temperatures of dry and hydrolytically aged samples. According to our results, Estane takes up to 3 wt % water for two weeks (at an ambient temperature of θ = 20 °C). The glass transition temperatures of dry samples decreased within this period from 55 to 48 °C as a consequence of a plasticization effect. Next, for both samples, six subsequent thermomechanical cycles under torsional loading conditions were performed. We were able to confirm that hydrolytically aged samples showed higher shape recovery ratios of Rr ≥ 97%, although dry samples revealed better shape fixity values of about 98%. Moreover, it was observed that the shape fixity ratio of both dry and hydrolytically (physically) aged samples remained almost unchanged even after six successive cycles. Besides this, the shape recovery ratio values of the aged samples were nearly unaltered, although the shape recovery values of the dry samples increased from Rr = 81% in the first cycle to 96% at the end of six repeated cycles. Further, the evolution of the free volume as a function of temperature was studied using Positron Annihilation Lifetime Spectroscopy. It was shown that the uptake of two other organic solvents (acetone and ethanol) resulted in much higher specific free volume inside the samples and, consequently, a softening effect was observed. We anticipate that the presented approach will assist in defining design criteria for self-sufficiently moving scaffolds within a knowledge-based development process.

Oscillatory fluid flow in deformable tubes: Implications for pore-scale hydromechanics from comparing experimental observations with theoretical predictions.

Oscillatory flow of four fluids (air, water, two aqueous sodium-tungstate solutions) was excited at frequencies up to 250 Hz in tubes of two materials (steel, silicone) covering a wide range in length, diameter, and thickness. The hydrodynamical response was characterized by phase shift and amplitude ratio between pressures in an upstream (pressure excitation) and a downstream reservoir connected by the tubes. The resulting standing flow waves reflect viscosity-controlled diffusive behavior and inertia-controlled wave behavior for oscillation frequencies relatively low and high compared to Biot's critical frequency, respectively. Rigid-tube theories correspond well with the experimental results for steel tubes filled with air or water. The wave modes observed for silicone tubes filled with the rather incompressible liquids or air, however, require accounting for the solid's shear and bulk modulus to correctly predict speed of pressure propagation and deformation mode. The shear mode may be responsible for significant macroscopic attenuation in porous materials with effective frame-shear moduli lower than the bulk modulus of the pore fluid. Despite notable effects of the ratio of densities and of acoustic and shear velocity of fluid and solid, Biot's frequency remains an approximate indicator of the transition from the viscosity to the inertia controlled regime.

A low-cost X-ray-transparent experimental cell for synchrotron-based X-ray microtomography studies under geological reservoir conditions.

A new modular X-ray-transparent experimental cell enables tomographic investigations of fluid rock interaction under natural reservoir conditions (confining pressure up to 20 MPa, pore fluid pressure up to 15 MPa, temperature ranging from 296 to 473 K). The portable cell can be used at synchrotron radiation sources that deliver a minimum X-ray flux density of 10(9) photons mm(-2) s(-1) in the energy range 30-100 keV to acquire tomographic datasets in less than 60 s. It has been successfully used in three experiments at the bending-magnet beamline 2BM at the Advanced Photon Source. The cell can be easily machined and assembled from off-the-shelf components at relatively low costs, and its modular design allows it to be adapted to a wide range of experiments and lower-energy X-ray sources.

About the transition frequency in Biot's theory.

Biot's theory of wave propagation in porous media includes a characteristic frequency which is used to distinguish the low-frequency from the high-frequency range. Its determination is based on an investigation of fluid flow through different pore geometries on a smaller scale and a subsequent upscaling process. This idea is limited due to the assumptions made on the smaller scale. It can be enhanced for a general two-phase system by three properties: Inertia of the solid, elasticity of the solid, and frequency dependent corrections of the momentum exchange. They become important for highly porous media with liquids.