Identifying the dominant transport mechanism in single nanoscale pores and 3D nanoporous media.

Gas transport mechanisms can be categorized into viscous flow and mass diffusion, both of which may coexist in a porous media with multiscale pore sizes. To determine the dominant transport mechanism and its contribution to gas transport capacity, the gas viscous flow and mass diffusion processes are analyzed in single nanoscale pores via a theoretical method, and are simulated in 3D nanoporous media via pore-scale lattice Boltzmann methods. The apparent permeability from the viscous flow and apparent diffusivity from the mass diffusion are estimated. A dimensionless parameter, i.e., the diffusion-flow ratio, is proposed to evaluate the dominant transport mechanism, which is a function of the apparent permeability, apparent diffusivity, bulk dynamic viscosity, and working pressure. The results show that the apparent permeability increases by approximately two orders of magnitude when the average Knudsen number (Kn avg) of the nanoporous media or Knudsen number (Kn) of single nanoscale pores increases from 0.1 to 10. Under the same conditions, the increment in the apparent diffusivity is only approximately one order of magnitude. When Kn < 0.01, the apparent permeability has a lower bound (i.e., absolute permeability). When Kn > 10, the apparent diffusivity has an upper bound (i.e., Knudsen diffusivity). The dominant transport mechanism in single nanoscale pores is the viscous flow for 0.01 < Kn < 100, where the maximum diffusion-flow ratio is less than one. In nanoporous media, the dominant transport relies heavily on Kn avg and the structural parameters. For nanoporous media with the pore throat diameter of 3 nm, Kn avg = 0.2 is the critical point, above which the mass diffusion is dominant; otherwise, the viscous flow is dominant. As Kn avg increases to 3.4, the mass diffusion is overwhelming, with the maximum diffusion-flow ratio reaching ∼4.

Sorption Kinetics and Sequential Adsorption Analysis of Volatile Organic Compounds on Mesoporous Silica.

Adsorption-desorption behaviors of polar and nonpolar volatile organic compounds (VOCs), namely, isopropanol and nonane, on mesoporous silica were studied using optical reflectance spectroscopy. Mesoporous silica was fabricated via electrochemical etching of silicon and subsequent thermal oxidation, resulting in an average pore diameter of 11 nm and a surface area of approximately 493 m2/g. The optical thickness of the porous layer, which is proportional to the number of adsorbed molecules, was measured using visible light reflectance interferometry. In situ adsorption and desorption kinetics were obtained for various mesoporous silica temperatures ranging from 10 to 70 °C. Sorption as a function of temperature was acquired for isopropanol and nonane. Sequential adsorption measurements of isopropanol and nonane were performed and showed that, when one VOC is introduced immediately following another, the second VOC displaces the first one regardless of the VOC's polarity and the strength of its interaction with the silica surface.

A Dataset of 3D Structural and Simulated Transport Properties of Complex Porous Media.

Physical processes that occur within porous materials have wide-ranging applications including - but not limited to - carbon sequestration, battery technology, membranes, oil and gas, geothermal energy, nuclear waste disposal, water resource management. The equations that describe these physical processes have been studied extensively; however, approximating them numerically requires immense computational resources due to the complex behavior that arises from the geometrically-intricate solid boundary conditions in porous materials. Here, we introduce a new dataset of unprecedented scale and breadth, DRP-372: a catalog of 3D geometries, simulation results, and structural properties of samples hosted on the Digital Rocks Portal. The dataset includes 1736 flow and electrical simulation results on 217 samples, which required more than 500 core years of computation. This data can be used for many purposes, such as constructing empirical models, validating new simulation codes, and developing machine learning algorithms that closely match the extensive purely-physical simulation. This article offers a detailed description of the contents of the dataset including the data collection, simulation schemes, and data validation.

3D Dataset of binary images: A collection of synthetically created digital rock images of complex media.

Digital rock images are computational representations that capture the geometrical complexity of systems present ubiquitously in nature. In recent years, their use has become widespread due to the increasing availability of repositories, and open-source physics simulators and analysis tools. Here, we present a dataset of 3D binary geometries in a standardized format that represent a wide variety of geological and engineering systems. Our data is freely available at [1].

Comprehensive comparison of pore-scale models for multiphase flow in porous media.

Multiphase flows in porous media are important in many natural and industrial processes. Pore-scale models for multiphase flows have seen rapid development in recent years and are becoming increasingly useful as predictive tools in both academic and industrial applications. However, quantitative comparisons between different pore-scale models, and between these models and experimental data, are lacking. Here, we perform an objective comparison of a variety of state-of-the-art pore-scale models, including lattice Boltzmann, stochastic rotation dynamics, volume-of-fluid, level-set, phase-field, and pore-network models. As the basis for this comparison, we use a dataset from recent microfluidic experiments with precisely controlled pore geometry and wettability conditions, which offers an unprecedented benchmarking opportunity. We compare the results of the 14 participating teams both qualitatively and quantitatively using several standard metrics, such as fractal dimension, finger width, and displacement efficiency. We find that no single method excels across all conditions and that thin films and corner flow present substantial modeling and computational challenges.

Replicating carbonaceous vug in synthetic porous media.

This paper presents an alternative method of creating vuggy glass-bead core proxies, which can be used to investigate the effects of pore-scale features on carbonate petrophysical properties. Carbonates are complex rocks having a widespread variation in pore type, size, distribution, and porosity. With this method we can control vug shape, size, and position. Homogeneous glass bead core proxies are sintered using 1.0 mm diameter glass beads in a muffle furnace. Vugs are 3D-printed in plastic and used to make a mold in Play-Doh®; which is cast in gypsum cement and used as a placeholder during the sintering process. The gypsum vug dissolves during acid flood, leaving an empty space inside the glass matrix. Computed tomography (CT) scans are made of the acid washed vug space and compared to the 3D model.

Effect of wettability on two-phase quasi-static displacement: Validation of two pore scale modeling approaches.

Understanding of pore-scale physics for multiphase flow in porous media is essential for accurate description of various flow phenomena. In particular, capillarity and wettability strongly influence capillary pressure-saturation and relative permeability relationships. Wettability is quantified by the contact angle of the fluid-fluid interface at the pore walls. In this work we focus on the non-trivial interface equilibria in presence of non-neutral wetting and complex geometries. We quantify the accuracy of a volume-of-fluid (VOF) formulation, implemented in a popular open-source computational fluid dynamics code, compared with a new formulation of a level set (LS) method, specifically developed for quasi-static capillarity-dominated displacement. The methods are tested in rhomboidal packings of spheres for a range of contact angles and for different rhomboidal configurations and the accuracy is evaluated against the semi-analytical solutions obtained by Mason and Morrow (1994). While the VOF method is implemented in a general purpose code that solves the full Navier-Stokes (NS) dynamics in a finite volume formulation, with additional terms to model surface tension, the LS method is optimized for the quasi-static case and, therefore, less computationally expensive. To overcome the shortcomings of the finite volume NS-VOF system for low capillary number flows, and its computational cost, we introduce an overdamped dynamics and a local time stepping to speed up the convergence to the steady state, for every given imposed pressure gradient (and therefore saturation condition). Despite these modifications, the methods fundamentally differ in the way they capture the interface, as well as in the number of equations solved and in the way the mean curvature (or equivalently capillary pressure) is computed. This study is intended to provide a rigorous validation study and gives important indications on the errors committed by these methods in solving more complex geometry and dynamics, where usually many sources of errors are interplaying.

Percolative core formation in planetesimals enabled by hysteresis in metal connectivity.

The segregation of dense core-forming melts by porous flow is a natural mechanism for core formation in early planetesimals. However, experimental observations show that texturally equilibrated metallic melt does not wet the silicate grain boundaries and tends to reside in isolated pockets that prevent percolation. Here we use pore-scale simulations to determine the minimum melt fraction required to induce porous flow, the percolation threshold. The composition of terrestrial planets suggests that typical planetesimals contain enough metal to overcome this threshold. Nevertheless, it is currently thought that melt segregation is prevented by a pinch-off at melt fractions slightly below the percolation threshold. In contrast to previous work, our simulations on irregular grain geometries reveal that a texturally equilibrated melt network remains connected down to melt fractions of only 1 to 2%. This hysteresis in melt connectivity allows percolative core formation in planetesimals that contain enough metal to exceed the percolation threshold. Evidence for the percolation of metallic melt is provided by X-ray microtomography of primitive achondrite Northwest Africa (NWA) 2993. Microstructural analysis shows that the metal-silicate interface has characteristics expected for a texturally equilibrated pore network with a dihedral angle of ∼85°. The melt network therefore remained close to textural equilibrium despite a complex history. This suggests that the hysteresis in melt connectivity is a viable process for percolative core formation in the parent bodies of primitive achondrites.

High temperature ultralow water content carbon dioxide-in-water foam stabilized with viscoelastic zwitterionic surfactants.

Ultralow water content carbon dioxide-in-water (C/W) foams with gas phase volume fractions (ϕ) above 0.95 (that is <0.05 water) tend to be inherently unstable given that the large capillary pressures that cause the lamellar films to thin. Herein, we demonstrate that these C/W foams may be stabilized with viscoelastic aqueous phases formed with a single zwitterionic surfactant at a concentration of only 1% (w/v) in DI water and over a wide range of salinity. Moreover, they are stable with a foam quality ϕ up to 0.98 even for temperatures up to 120°C. The properties of aqueous viscoelastic solutions and foams containing these solutions are examined for a series of zwitterionic amidopropylcarbobetaines, R-ONHC3H6N(CH3)2CH2CO2, where R is varied from C12-14 (coco) to C18 (oleyl) to C22 (erucyl). For the surfactants with long C18 and C22 tails, the relaxation times from complex rheology indicate the presence of viscoelastic wormlike micelles over a wide range in salinity and pH, given the high surfactant packing fraction. The apparent viscosities of these ultralow water content foams reached more than 120cP with stabilities more than 30-fold over those for foams formed with the non-viscoelastic C12-14 surfactant. At 90°C, the foam morphology was composed of ∼35µm diameter bubbles with a polyhedral texture. The apparent foam viscosity typically increased with ϕ and then dropped at ϕ values higher than 0.95-0.98. The Ostwald ripening rate was slower for foams with viscoelastic versus non-viscoelastic lamellae as shown by optical microscopy, as a consequence of slower lamellar drainage rates. The ability to achieve high stabilities for ultralow water content C/W foams over a wide temperature range is of interest in various technologies including polymer and materials science, CO2 enhanced oil recovery, CO2 sequestration (by greater control of the CO2 flow patterns), and possibly even hydraulic fracturing with minimal use of water to reduce the requirements for wastewater disposal.

Viscosity and stability of ultra-high internal phase CO2-in-water foams stabilized with surfactants and nanoparticles with or without polyelectrolytes.

To date, relatively few examples of ultra-high internal phase supercritical CO2-in-water foams (also referred to as macroemulsions) have been observed, despite interest in applications including "waterless" hydraulic fracturing in energy production. The viscosities and stabilities of foams up to 0.98 CO2 volume fraction were investigated in terms of foam bubble size, interfacial tension, and bulk and surface viscosity. The foams were stabilized with laurylamidopropyl betaine (LAPB) surfactant and silica nanoparticles (NPs), with and without partially hydrolyzed polyacrylamide (HPAM). For foams stabilized with mixture of LAPB and NPs, fine ∼70 µm bubbles and high viscosities on the order of 100 cP at>0.90 internal phase fraction were stabilized for hours to days. The surfactant reduces interfacial tension, and thus facilitates bubble generation and decreases the capillary pressure to reduce the drainage rate of the lamella. The LAPB, which is in the cationic protonated form, also attracts anionic NPs (and anionic HPAM in systems containing polymer) to the interface. The adsorbed NPs at the interface are shown to slow down Ostwald ripening (with or without polymer added) and increase foam stability. In systems with added HPAM, the increase in the bulk and surface viscosity of the aqueous phase further decreases the lamella drainage rate and inhibits coalescence of foams. Thus, the added polymer increases the foam viscosity by threefold. Scaling law analysis shows the viscosity of 0.90 volume fraction foams is inversely proportional to the bubble size.

Ultradry Carbon Dioxide-in-Water Foams with Viscoelastic Aqueous Phases.

For foams with ultra low water contents, the capillary pressure is very large and induces rapid drainage that destabilizes the aqueous lamellae between the gas bubbles. However, we show that high-pressure CO2-in-water foams can be stabilized with a viscoelastic aqueous phase composed of entangled wormlike micelles, even for extremely high CO2 volume fractions ϕ of 0.95 to 0.98; the viscosity of these ultradry foams increased by up to 3-4-fold, reaching more than 100 cP relative to foams formed with conventional low viscosity aqueous phases. The foam morphology consisted of fine ∼20 µm polyhedral-shaped CO2 bubbles that were stable for hours. The wormlike micelles were formed by mixing anionic sodium lauryl ether sulfate (SLES) with salt and a protonated cationic surfactant, as shown by cryogenic transmission electron microscopy (cryo-TEM) and large values of the zero-shear viscosity and the dynamic storage and loss moduli. With the highly viscous continuous aqueous phases, the foam lamella drainage rates were low, as corroborated by confocal microscopy. The preservation of viscous thick lamellae resulted in lower rates of Ostwald ripening relative to conventional foams as shown by high-pressure optical microscopy. The ability to stabilize viscous ultra high internal phase foams is expected to find utility in various practical applications, including nearly "waterless" fracturing fluids for recovery of oil and gas in shale, offering the possibility of a massive reduction in the amount of wastewater.

Deformation-assisted fluid percolation in rock salt.

Deep geological storage sites for nuclear waste are commonly located in rock salt to ensure hydrological isolation from groundwater. The low permeability of static rock salt is due to a percolation threshold. However, deformation may be able to overcome this threshold and allow fluid flow. We confirm the percolation threshold in static experiments on synthetic salt samples with x-ray microtomography. We then analyze wells penetrating salt deposits in the Gulf of Mexico. The observed hydrocarbon distributions in rock salt require that percolation occurred at porosities considerably below the static threshold due to deformation-assisted percolation. Therefore, the design of nuclear waste repositories in salt should guard against deformation-driven fluid percolation. In general, static percolation thresholds may not always limit fluid flow in deforming environments.

Percolation and grain boundary wetting in anisotropic texturally equilibrated pore networks.

In texturally equilibrated porous media the pore geometry evolves to minimize the energy of the liquid-solid interfaces, while maintaining the dihedral angle θ at solid-solid-liquid contact lines. We present computations of three-dimensional texturally equilibrated pore networks using a level-set method. Our results show that the grain boundaries with the smallest area can be fully wetted by the pore fluid even for θ > 0. This was previously not thought to be possible at textural equilibrium and reconciles the theory with experimental observations. Even small anisotropy in the fabric of the porous medium allows the wetting of these faces at very low porosities, ϕ<3%. Percolation and orientation of the wetted faces relative to the anisotropy of the fabric are controlled by θ. The wetted grain boundaries are perpendicular to the direction of stretching for θ > 60° and the pores do not percolate for any investigated ϕ. For θ < 60°, in contrast, the grain boundaries parallel to the direction of stretching are wetted and a percolating pore network forms for all ϕ investigated. At low θ even small anisotropy in the fabric induces large anisotropy in the permeability, due to the concentration of liquid on the grain boundaries and faces.

Contact line extraction and length measurements in model sediments and sedimentary rocks.

The mechanisms that govern the transport of colloids in the unsaturated zone of soils are still poorly understood, because of the complexity of processes that occur at pore scale. These mechanisms are of specific interest in quantifying water quality with respect to pathogen transport (e.g. Escherichia coli, Cryptosporidium) between the source (e.g. farms) and human users. Besides straining in pore throats and constrictions of smaller or equivalent size, the colloids can be retained at the interfaces between air, water, and grains. Theories competing to explain this mechanism claim that retention can be caused by adhesion at the air-water-interface (AWI) between sediment grains or by straining at the air-water-solid (AWS) contact line. Currently, there are no established methods for the estimation of pathogen retention in unsaturated media because of the intricate influence of AWI and AWS on transport and retention. What is known is that the geometric configuration and connectivity of the aqueous phase is an important factor in unsaturated transport. In this work we develop a computational method based on level set functions to identify and quantify the AWS contact line (in general the non-wetting-wetting-solid contact line) in any porous material. This is the first comprehensive report on contact line measurement for fluid configurations from both level-set method based fluid displacement simulation and imaged experiments. The method is applicable to any type of porous system, as long as the detailed pore scale geometry is available. We calculated the contact line length in model sediments (packs of spheres) as well as in real porous media, whose geometry is taken from high-resolution images of glass bead packs and sedimentary rocks. We observed a strong dependence of contact line length on the geometry of the sediment grains and the arrangement of the air and water phases. These measurements can help determine the relative contribution of the AWS line to pathogen retention.

A level set method for determining critical curvatures for drainage and imbibition.

An accurate description of the mechanics of pore level displacement of immiscible fluids could significantly improve the predictions from pore network models of capillary pressure-saturation curves, interfacial areas and relative permeability in real porous media. If we assume quasi-static displacement, at constant pressure and surface tension, pore scale interfaces are modeled as constant mean curvature surfaces, which are not easy to calculate. Moreover, the extremely irregular geometry of natural porous media makes it difficult to evaluate surface curvature values and corresponding geometric configurations of two fluids. Finally, accounting for the topological changes of the interface, such as splitting or merging, is nontrivial. We apply the level set method for tracking and propagating interfaces in order to robustly handle topological changes and to obtain geometrically correct interfaces. We describe a simple but robust model for determining critical curvatures for throat drainage and pore imbibition. The model is set up for quasi-static displacements but it nevertheless captures both reversible and irreversible behavior (Haines jump, pore body imbibition). The pore scale grain boundary conditions are extracted from model porous media and from imaged geometries in real rocks. The method gives quantitative agreement with measurements and with other theories and computational approaches.