On the challenges of greyscale-based quantifications using X-ray computed microtomography.

For X-ray computed microtomography (µ-CT) images of porous rocks where the grains and pores are not fully resolved, the greyscale values of each voxel can be used for quantitative calculations. This study addresses the challenges that arise with greyscale-based quantifications by conducting experiments designed to investigate the sources of error/uncertainty. We conduct greyscale-based calculations of porosity, concentration and diffusivity from various µ-CT experiments using a Bentheimer sandstone sample. The dry sandstone is imaged overtime to test the variation of greyscale values over sequential scans due to instrumentation stability. The sandstone is then imaged in a dry and contrast-agent saturated state at low resolution to determine a porosity map, which is compared to a porosity map derived from segmented high-resolution data. Then the linearity of the relationship between the concentration of a contrast agent and its corresponding attenuation coefficient is tested by imaging various solutions of known concentration. Lastly, a diffusion experiment is imaged at low resolution under dynamic conditions to determine local diffusivity values for the sandstone, which is compared to values derived from direct pore-scale simulations using high-resolution data. Overall, we identify the main errors associated with greyscale-based quantification and provide practical suggestions to alleviate these issues. LAY DESCRIPTION: X-ray computed microtomography (CT) imaging has become an important way to study the pore space of a porous medium. Using segmented images, we can build 3D pore space models for porous media and characterize the morphology and/or run simulations on the models. So, image segmentation is a critical image processing step. However, for low resolution images where image segmentation is not possible, grayscales are directly used for quantifications such as porosity and concentration calculations. Although these types of calculations have been widely accepted and used, the uncertainties and errors associated with grayscale-based quantifications are not fully discussed. Here we specifically design experiments with X-ray CT imaging to address the challenges that arise in grayscale-based quantifications. For instance, in order to validate porosity calculation results from low resolution images (with the help of high attenuating tracer), high resolution images are also acquired, which serve as a benchmark. The errors associated with concentration calculation using grayscale values are also discussed. In addition, numerical simulations using grayscale values are performed on a diffusion experiment images with X-ray CT. The problems that arise in dynamic imaging and the subsequent numerical simulations are discussed. The experiments, calculations and discussions provide a more comprehensive understanding on grayscale-based quantifications and aid in designing better X-ray CT experiments.

Pore Scale Dynamics of Microemulsion Formation.

Experiments in various porous media have shown that multiple parameters come into play when an oleic phase is displaced by an aqueous solution of surfactant. In general, the displacement efficiency is improved when the fluids become quasi-miscible. Understanding the phase behavior oil/water/surfactant systems is important because microemulsion has the ability to generate ultralow interfacial tension (<10(-2) mN m(-1)) that is required for miscibility to occur. Many studies focus on microemulsion formation and the resulting properties under equilibrium conditions. However, the majority of applications where microemulsion is present also involve flow, which has received relatively less attention. It is commonly assumed that the characteristics of an oil/water/surfactant system under flowing conditions are identical to the one under equilibrium conditions. Here, we show that this is not necessarily the case. We studied the equilibrium phase behavior of a model system consisting of n-decane and an aqueous solution of olefin sulfonate surfactant, which has practical applications for enhanced oil recovery. The salt content of the aqueous solution was varied to provide a range of different microemulsion compositions and oil-water interfacial tensions. We then performed microfluidic flow experiments to study the dynamic in situ formation of microemulsion by coinjecting bulk fluids of n-decane and surfactant solution into a T-junction capillary geometry. A solvatochromatic fluorescent dye was used to obtain spatially resolved compositional information. In this way, we visualized the microemulsion formation and the flow of it along with the excess phases. A complex interaction between the flow patterns and the microemulsion properties was observed. The formation of microemulsion influenced the flow regimes, and the flow regimes affected the characteristics of the microemulsion formation. In particular, at low flow rates, slug flow was observed, which had profound consequences on the pore scale mixing behavior and resulting microemulsion properties.

Subsecond pore-scale displacement processes and relaxation dynamics in multiphase flow.

With recent advances at X-ray microcomputed tomography (µCT) synchrotron beam lines, it is now possible to study pore-scale flow in porous rock under dynamic flow conditions. The collection of four-dimensional data allows for the direct 3-D visualization of fluid-fluid displacement in porous rock as a function of time. However, even state-of-the-art fast-µCT scans require between one and a few seconds to complete and the much faster fluid movement occurring during that time interval is manifested as imaging artifacts in the reconstructed 3-D volume. We present an approach to analyze the 2-D radiograph data collected during fast-µCT to study the pore-scale displacement dynamics on the time scale of 40 ms which is near the intrinsic time scale of individual Haines jumps. We present a methodology to identify the time intervals at which pore-scale displacement events in the observed field of view occur and hence, how reconstruction intervals can be chosen to avoid fluid-movement-induced reconstruction artifacts. We further quantify the size, order, frequency, and location of fluid-fluid displacement at the millisecond time scale. We observe that after a displacement event, the pore-scale fluid distribution relaxes to (quasi-) equilibrium in cascades of pore-scale fluid rearrangements with an average relaxation time for the whole cascade between 0.5 and 2.0 s. These findings help to identify the flow regimes and intrinsic time and length scales relevant to fractional flow. While the focus of the work is in the context of multiphase flow, the approach could be applied to many different µCT applications where morphological changes occur at a time scale less than that required for collecting a µCT scan.

In situ characterization of heterogeneous surface wetting in porous materials.

The performance of nano- and micro-porous materials in capturing and releasing fluids, such as during CO2 geo-storage and water/gas removal in fuel cells and electrolyzers, is determined by their wettability in contact with the solid. However, accurately characterizing wettability is challenging due to spatial variations in dynamic forces, chemical heterogeneity, and surface roughness. In situ measurements can potentially measure wettability locally as a contact angle - the angle a denser phase (e.g water) contacts solid in the presence of a second phase (e.g. hydrogen, air, CO2) - but suffer from difficulties in accurately capturing curvatures, contact areas, and contact loops of multiphase fluids. We introduce a novel extended topological method for in situ contact angle measurement and provide a comparative review of current geometric and topological methods, assessing their accuracy on ideal surfaces, porous rocks containing CO2, and water in gas diffusion layers. The new method demonstrates higher accuracy and reliability of in situ measurements for uniformly wetting systems compared to previous topological approaches, while geometric measurements perform best for mixed-wetting domains. This study further provides a comprehensive open-source platform for in situ characterization of wettability in porous materials with implications for gas geo-storage, fuel cells and electrolyzers, filtration, and catalysis.

Positron emission tomography dataset of [11C]carbon dioxide storage in coal for geo-sequestration application.

Positron Emission Tomography (PET) imaging has demonstrated its capability in providing time-lapse fluid flow visualisation for improving the understanding of flow properties of geologic media. To investigate the process of CO2 geo-sequestration using PET imaging technology, [11C]CO2 is the most optimal and direct radiotracer. However, it has not been extensively used due to the short half-life of Carbon-11 (20.4 minutes). In this work, a novel laboratory protocol is developed to use [11C]CO2 as radiolabelled tracer to visualise and quantify in-situ CO2 adsorption, spreading, diffusion, and advection flow in coal. This protocol consists of generation and delivering of [11C]CO2, lab-based PET scanning, subsequent micro-CT scanning, and data processing. The lab-based PET scanning setup integrates in-situ core flooding tests with PET scanning. The real-time PET images are acquired under different storage conditions, including early gas production stage, depleted stage, and late storage stage. These datasets can be used to study across-scale theoretical and experimental study of CO2 flow behaviour in coal with the application to CO2 geo-sequestration.

Large-scale physically accurate modelling of real proton exchange membrane fuel cell with deep learning.

Proton exchange membrane fuel cells, consuming hydrogen and oxygen to generate clean electricity and water, suffer acute liquid water challenges. Accurate liquid water modelling is inherently challenging due to the multi-phase, multi-component, reactive dynamics within multi-scale, multi-layered porous media. In addition, currently inadequate imaging and modelling capabilities are limiting simulations to small areas (<1 mm2) or simplified architectures. Herein, an advancement in water modelling is achieved using X-ray micro-computed tomography, deep learned super-resolution, multi-label segmentation, and direct multi-phase simulation. The resulting image is the most resolved domain (16 mm2 with 700 nm voxel resolution) and the largest direct multi-phase flow simulation of a fuel cell. This generalisable approach unveils multi-scale water clustering and transport mechanisms over large dry and flooded areas in the gas diffusion layer and flow fields, paving the way for next generation proton exchange membrane fuel cells with optimised structures and wettabilities.

Universal description of wetting on multiscale surfaces using integral geometry.

HYPOTHESIS: Emerging energy-related technologies deal with multiscale hierarchical structures, intricate surface morphology, non-axisymmetric interfaces, and complex contact lines where wetting is difficult to quantify with classical methods. We hypothesise that a universal description of wetting on multiscale surfaces can be developed by using integral geometry coupled to thermodynamic laws. The proposed approach separates the different hierarchy levels of physical description from the thermodynamic description, allowing for a universal description of wetting on multiscale surfaces. THEORY AND SIMULATIONS: The theoretical framework is presented followed by application to limiting cases of wetting on multiscale surfaces. Limiting cases include those considered in the Wenzel, Cassie-Baxter, and wicking state models. Wetting characterisation of multiscale surfaces is explored by conducting simulations of a fluid droplet on a structurally rough surface and a chemically heterogeneous surface. FINDINGS: The underlying origin of the classical wetting models is shown to be rooted within the proposed theoretical framework. Integral geometry provides a topological-based wetting metric that is not contingent on any type of wetting state. The wetting metric is demonstrated to account for multiscale features along the common line in a scale consistent way; providing a universal description of wetting for multiscale surfaces.

Thermodynamics of fluctuations based on time-and-space averages.

We develop nonequilibrium theory by using averages in time and space as a generalized way to upscale thermodynamics in nonergodic systems. The approach offers a classical perspective on the energy dynamics in fluctuating systems. The rate of entropy production is shown to be explicitly scale dependent when considered in this context. We show that while any stationary process can be represented as having zero entropy production, second law constraints due to the Clausius theorem are preserved due to the fact that heat and work are related based on conservation of energy. As a demonstration, we consider the energy dynamics for the Carnot cycle and for Maxwell's demon. We then consider nonstationary processes, applying time-and-space averages to characterize nonergodic effects in heterogeneous systems where energy barriers such as compositional gradients are present. We show that the derived theory can be used to understand the origins of anomalous diffusion phenomena in systems where Fick's law applies at small length scales, but not at large length scales. We further characterize fluctuations in capillary-dominated systems, which are nonstationary due to the irreversibility of cooperative events.

Characterization of wetting using topological principles.

HYPOTHESIS: Understanding wetting behavior is of great importance for natural systems and technological applications. The traditional concept of contact angle, a purely geometrical measure related to curvature, is often used for characterizing the wetting state of a system. It can be determined from Young's equation by applying equilibrium thermodynamics. However, whether contact angle is a representative measure of wetting for systems with significant complexity is unclear. Herein, we hypothesize that topological principles based on the Gauss-Bonnet theorem could yield a robust measure to characterize wetting. THEORY AND EXPERIMENTS: We introduce a macroscopic contact angle based on the deficit curvature of the fluid interfaces that are imposed by contacts with other immiscible phases. We perform sessile droplet simulations followed by multiphase experiments for porous sintered glass and Bentheimer sandstone to assess the sensitivity and robustness of the topological approach and compare the results to other traditional approaches. FINDINGS: We show that the presented topological principle is consistent with thermodynamics under the simplest conditions through a variational analysis. Furthermore, we elucidate that at sufficiently high image resolution the proposed topological approach and local contact angle measurements are comparable. While at lower resolutions, the proposed approach provides more accurate results being robust to resolution-based effects. Overall, the presented concepts open new pathways to characterize the wetting state of complex systems and theoretical developments to study multiphase systems.

Linking continuum-scale state of wetting to pore-scale contact angles in porous media.

HYPOTHESIS: Wetting phenomena play a key role in flows through porous media. Relative permeability and capillary pressure-saturation functions show a high sensitivity to wettability, which has different definitions at the continuum- and pore-scale. We hypothesize that the wetting state of a porous medium can be described in terms of topological arguments that constrain the morphological state of immiscible fluids, which provides a direct link between the continuum-scale metrics of wettability and pore-scale contact angles. EXPERIMENTS: We perform primary drainage and imbibition experiments on Bentheimer sandstone using air and brine. Topological properties, such as Euler characteristic and interfacial curvature are measured utilizing X-ray micro-computed tomography at irreducible air saturation. We also present measurements for the United States Bureau of Mines (USBM) index, capillary pressure and pore-scale contact angles. Additional studies are performed using two-phase Lattice Boltzmann simulations to test a wider range of wetting conditions. FINDINGS: We demonstrate that contact angle distributions for a porous multiphase system can be predicted within a few percent difference of directly measured pore-scale contact angles using the presented method. This provides a general framework on how continuum-scale data can be used to describe the geometrical state of fluids within porous media.

Oil mobilization and solubilization in porous media by in situ emulsification.

HYPOTHESIS: For a wide range of subsurface engineering processes, such as geological carbon sequestration and enhanced oil recovery, it is critical to understand multiphase flow at a fundamental level. To this end, geomaterial microfluidic devices provide visual data that can be quantified to explain the physics of multiphase flow at the length scale of individual pores in realistic rock structures. For surfactant enhanced oil recovery, it is the underlying geometrical states of the capillary trapped oil that dictates the recovery process and the degree to which oil is recovered through either mobilization or solubilization during in situ emulsification. EXPERIMENTS: A novel geomaterial microfluidic device is fabricated and its integrity is checked using light microscopy and X-ray micro-computed tomography (µ-CT) imaging. Subsequently, alkaline surfactant (AS) flooding of an oil saturated device is studied for enhanced recovery. The recovery process is analyzed by collecting 2D radiographic projections of the device during water flooding and in situ emulsification. 3D µ-CT images are also collected to quantify the geometrical states of the fluids after each flooding sequence. FINDINGS: Our study reveals the processes of oil cluster mobilization and solubilization in porous media. After water flooding there are numerous oil clusters that are relatively large, extending over multiple pores, forming various loop-like structures. These clusters are mobile under AS flooding accounting for 75% of the recovered oil. The less mobile smaller clusters, isolated to single pores, forming no loop-like structures are immobile. These clusters are solubilized during AS flooding accounting for 25% of the recovered oil. The mobilized clusters coalesce forming an oil bank prior to total solubilization. The remaining oil clusters after AS flooding are highly non-wetting, as indicated by contact angle measurements and would only be recoverable after further solubilization.

Functionalisation of Polydimethylsiloxane (PDMS)- Microfluidic Devices coated with Rock Minerals.

Fluid flow in porous rocks is commonly capillary driven and thus, dependent on the surface characteristics of rock grains and in particular the connectivity of corners and crevices in which fluids reside. Traditional microfluidic fabrication techniques do not provide a connected pathway of crevices that are essential to mimic multiphase flow in rocks. Here, geo-material microfluidic devices with connected pathways of corners and crevices were created by functionalising Polydimethylsiloxane (PDMS) with rock minerals. A novel fabrication process that provides attachment of rock minerals onto PDMS was demonstrated. The geo-material microfluidic devices were compared to carbonate and sandstone rocks by using energy dispersive X-ray spectroscopy, scanning electron microscopy (SEM), contact angle measurements, and a surface profilometer. Based on SEM coupled with energy-dispersive X-ray spectrometry (SEM-EDS) analyses, roughness measurements, contact angle, wettability, and roughness were comparable to real rocks. In addition, semivariograms showed that mineral deposition across the different geo-material devices was nearly isotropic. Lastly, important multiphase flow phenomena, such as snap-off and corner flow mechanisms, equivalent to those occurring in reservoir rocks have been visualised. The presented approach can be used to visualise rock-fluid interactions that are relevant to subsurface engineering applications, such as hydrocarbon recovery and CO2 sequestration.

Beyond Darcy's law: The role of phase topology and ganglion dynamics for two-fluid flow.

In multiphase flow in porous media the consistent pore to Darcy scale description of two-fluid flow processes has been a long-standing challenge. Immiscible displacement processes occur at the scale of individual pores. However, the larger scale behavior is described by phenomenological relationships such as relative permeability, which typically uses only fluid saturation as a state variable. As a consequence pore scale properties such as contact angle cannot be directly related to Darcy scale flow parameters. Advanced imaging and computational technologies are closing the gap between the pore and Darcy scale, supporting the development of new theory. We utilize fast x-ray microtomography to observe pore-scale two-fluid configurations during immiscible flow and initialize lattice Boltzmann simulations that demonstrate that the mobilization of disconnected nonwetting phase clusters can account for a significant fraction of the total flux. We show that fluid topology can undergo substantial changes during flow at constant saturation, which is one of the underlying causes of hysteretic behavior. Traditional assumptions about fluid configurations are therefore an oversimplification. Our results suggest that the role of fluid connectivity cannot be ignored for multiphase flow. On the Darcy scale, fluid topology and phase connectivity are accounted for by interfacial area and Euler characteristic as parameters that are missing from our current models.

Interfacial velocities and capillary pressure gradients during Haines jumps.

Drainage is typically understood as a process where the pore space is invaded by a nonwetting phase pore-by-pore, the controlling parameters of which are represented by capillary number and mobility ratio. However, what is less understood and where experimental data are lacking is direct knowledge of the dynamics of pore drainage and the associated intrinsic time scales since the rate dependencies often observed with displacement processes are potentially dependent on these time scales. Herein, we study pore drainage events with a high speed camera in a micromodel system and analyze the dependency of interfacial velocity on bulk flow rate and spatial fluid configurations. We find that pore drainage events are cooperative, meaning that capillary pressure differences which extend over multiple pores directly affect fluid topology and menisci dynamics. Results suggest that not only viscous forces but also capillarity acts in a nonlocal way. Lastly, the existence of a pore morphological parameter where pore drainage transitions from capillary to inertial and/or viscous dominated is discussed followed by a discussion on capillary dispersion and time scale dependencies. We show that the displacement front is disperse when volumetric flow rate is less than the intrinsic time scale for a pore drainage event and becomes sharp when the flow rate is greater than the intrinsic time scale (i.e., overruns the pore drainage event), which clearly shows how pore-scale parameters influence macroscale flow behavior.