4D microvelocimetry reveals multiphase flow field perturbations in porous media.

Many environmental and industrial processes depend on how fluids displace each other in porous materials. However, the flow dynamics that govern this process are still poorly understood, hampered by the lack of methods to measure flows in optically opaque, microscopic geometries. We introduce a 4D microvelocimetry method based on high-resolution X-ray computed tomography with fast imaging rates (up to 4 Hz). We use this to measure flow fields during unsteady-state drainage, injecting a viscous fluid into rock and filter samples. This provides experimental insight into the nonequilibrium energy dynamics of this process. We show that fluid displacements convert surface energy into kinetic energy. The latter corresponds to velocity perturbations in the pore-scale flow field behind the invading fluid front, reaching local velocities more than 40 times faster than the constant pump rate. The characteristic length scale of these perturbations exceeds the characteristic pore size by more than an order of magnitude. These flow field observations suggest that nonlocal dynamic effects may be long-ranged even at low capillary numbers, impacting the local viscous-capillary force balance and the representative elementary volume. Furthermore, the velocity perturbations can enhance unsaturated dispersive mixing and colloid transport and yet, are not accounted for in current models. Overall, this work shows that 4D X-ray velocimetry opens the way to solve long-standing fundamental questions regarding flow and transport in porous materials, underlying models of, e.g., groundwater pollution remediation and subsurface storage of CO2 and hydrogen.

Pore-scale visualization of hydrogen storage in a sandstone at subsurface pressure and temperature conditions: Trapping, dissolution and wettability.

HYPOTHESIS: Underground hydrogen (H2) storage is a potentially viable solution for large-scale cyclic H2 storage; however, the behavior of H2 at subsurface pressure and temperature conditions is poorly known. This work investigates if the pore-scale displacement processes in H2-brine systems in a porous sandstone can be sufficiently well defined to enable effective and economic storage operations. In particular, this study investigates trapping, dissolution, and wettability of H2-brine systems at the pore-scale, at conditions that are realistic for subsurface H2 storage. EXPERIMENTS: We have performed in situ X-ray imaging during a flow experiment to investigate pore-scale processes during H2 injection and displacement in a brine saturated Bentheimer sandstone sample at temperature and pressure conditions representative of underground reservoirs. Two injection schemes were followed for imbibition: displacement of H2 with H2-equilibrated brine and with non-H2-equilibrated brine. The results from the two cycles were compared with each other. FINDINGS: The sandstone was found to be wetting to the brine and non-wetting to H2 after both displacement cycles, with average contact angles of 54° and 53° for H2-equilibrated and non-H2-equilibrated brine respectively. We also found a higher recovery of H2 (43.1%) when displaced with non-H2-equilibrated brine compared to that of H2-equilibrated brine (31.6%), indicating potential dissolution of H2 in the unequilibrated imbibing brine at reservoir conditions. Our results suggest that underground H2 storage may indeed be a suitable strategy for energy storage, but considerable further research is needed to fully comprehend the pore-scale interactions at reservoir conditions.

Dynamic Effects during the Capillary Rise of Fluids in Cylindrical Tubes.

The mathematical models for the capillary-driven flow of fluids in tubes typically assume a static contact angle at the fluid-air contact line on the tube walls. However, the dynamic evolution of the fluid-air interface is an important feature during capillary rise. Furthermore, inertial effects are relevant at early times and may lead to oscillations. To incorporate and quantify the different effects, a fundamental description of the physical processes within the tube is used to derive an upscaled model of capillary-driven flow in circular cylindrical tubes. The upscaled model extends the classical Lucas-Washburn model by incorporating a dynamic contact angle and slip. It is then further extended to account for inertial effects. Finally, the solutions of the different models are compared to experimental data. In contrast to the Lucas-Washburn model, the models with dynamic contact angle match well the experimental data, both the rise height and the contact angle, even at early times. The models have a free parameter through the dynamic contact angle description, which is fitted using the experimental data. The findings here suggest that this parameter depends only on the properties of the fluid but is independent of geometrical features, such as the tube radius. Therefore, the presented models can predict the capillary-driven flow in tubular systems upon knowledge of the underlying dynamic contact-angle relation.

New type of pore-snap-off and displacement correlations in imbibition.

HYPOTHESIS: Imbibition of a fluid into a porous material involves the invasion of a wetting fluid in the pore space through piston-like displacement, film and corner flow, snap-off and pore bypassing. These processes have been studied extensively in two-dimensional (2D) porous systems; however, their relevance to three-dimensional (3D) natural porous media is poorly understood. Here, we investigate these pore-scale processes in a natural rock sample using time-resolved 3D (i.e., four-dimensional or 4D) X-ray imaging. EXPERIMENTS: We performed a capillary-controlled drainage-imbibition experiment on an initially brine-saturated carbonate rock sample. The sample was imaged continuously during imbibition using 4D X-ray imaging to visualize and analyze fluid displacement and snap-off processes at the pore-scale. FINDINGS: We discover a new type of snap-off that occurs in pores, resulting in the entrapment of a small portion of the non-wetting phase in pore corners. This contrasts with previously-observed snap-off in throats which traps the non-wetting phase in pore centers. We relate the new type of pore-snap-off to the pinning of fluid-fluid interfaces at rough surfaces, creating contact angles close to 90°. Subsequently, we provide correlations for displacement events as a function of pore-throat geometry. Our findings indicate that having a small throat does not necessarily favor snap-off: the key criterion is the throat radius in relation to the pore radius involved in a displacement event, captured by the aspect ratio.

Tunable X-ray dark-field imaging for sub-resolution feature size quantification in porous media.

X-ray computed micro-tomography typically involves a trade-off between sample size and resolution, complicating the study at a micrometer scale of representative volumes of materials with broad feature size distributions (e.g. natural stones). X-ray dark-field tomography exploits scattering to probe sub-resolution features, promising to overcome this trade-off. In this work, we present a quantification method for sub-resolution feature sizes using dark-field tomograms obtained by tuning the autocorrelation length of a Talbot grating interferometer. Alumina particles with different nominal pore sizes (50 nm and 150 nm) were mixed and imaged at the TOMCAT beamline of the SLS synchrotron (PSI) at eighteen correlation lengths, covering the pore size range. The different particles cannot be distinguished by traditional absorption µCT due to their very similar density and the pores being unresolved at typical image resolutions. Nevertheless, by exploiting the scattering behavior of the samples, the proposed analysis method allowed to quantify the nominal pore sizes of individual particles. The robustness of this quantification was proven by reproducing the experiment with solid samples of alumina, and alumina particles that were kept separated. Our findings demonstrate the possibility to calibrate dark-field image analysis to quantify sub-resolution feature sizes, allowing multi-scale analyses of heterogeneous materials without subsampling.

Fast micro-computed tomography data of solute transport in porous media with different heterogeneity levels.

Solute transport processes are influenced by pore-scale heterogeneity. To study this, transient micron-scale solute concentration fields were imaged by fast laboratory-based X-ray micro-computed tomography. We performed tracer injection experiments in three types of porous material with increasing levels of heterogeneity (sintered glass, Bentheimer sandstone and Savonnières limestone). Different Peclet numbers were used during the experiments. For each sample and Peclet number, datasets of 40 to 74 3D images were acquired by continuous scanning with a voxel size of 13.4 to 14.6 µm and a temporal resolution of 15 to 12 seconds. To determine the measurement uncertainty on the obtained concentration fields, we performed calibration experiments under similar circumstances (temporal resolution of 12 seconds and voxel size of 13.0 µm). Here, we provide a systematic description of the data acquisition and processing and make all data, a total of 464 tomograms, publicly available. The combined dataset offers new opportunities to study the influence of pore-scale heterogeneity on solute transport, and to validate pore-scale simulations of this process in increasingly complex samples.

Improving image quality in fast, time-resolved micro-CT by weighted back projection.

Time-resolved micro-CT is an increasingly powerful technique for studying dynamic processes in materials and structures. However, it is still difficult to study very fast processes with this technique, since fast scanning is typically associated with high image noise levels. We present weighted back projection, a technique applicable in iterative reconstruction methods using two types of prior knowledge: (1) a virtual starting volume resembling the sample, for example obtained from a scan before the dynamic process was initiated, and (2) knowledge on which regions in the sample are more likely to undergo the dynamic process. Therefore, processes on which this technique is applicable are preferably occurring within a static grid. Weighted back projection has the ability to handle small errors in the prior knowledge, while similar 4D micro-CT techniques require the prior knowledge to be exactly correct. It incorporates the prior knowledge within the reconstruction by using a weight volume, representing for each voxel its probability of undergoing the dynamic process. Qualitative analysis on a sparse subset of projection data from a real micro-CT experiment indicates that this method requires significantly fewer projection angles to converge to a correct volume. This can lead to an improved temporal resolution.

Signature of elastic turbulence of viscoelastic fluid flow in a single pore throat.

When a viscoelastic fluid, such as an aqueous polymer solution, flows through a porous medium, the fluid undergoes a repetitive expansion and contraction as it passes from one pore to the next. Above a critical flow rate, the interaction between the viscoelastic nature of the polymer and the pore configuration results in spatial and temporal flow instabilities reminiscent of turbulentlike behavior, even though the Reynolds number Re≪1. To investigate whether this is caused by many repeated pore body-pore throat sequences, or simply a consequence of the converging (diverging) nature present in a single pore throat, we performed experiments using anionic hydrolyzed polyacrylamide (HPAM) in a microfluidic flow geometry representing a single pore throat. This allows the viscoelastic fluid to be characterized at increasing flow rates using microparticle image velocimetry in combination with pressure drop measurements. The key finding is that the effect, popularly known as "elastic turbulence," occurs already in a single pore throat geometry. The critical Deborah number at which the transition in rheological flow behavior from pseudoplastic (shear thinning) to dilatant (shear thickening) strongly depends on the ionic strength, the type of cation in the anionic HPAM solution, and the nature of pore configuration. The transition towards the elastic turbulence regime was found to directly correlate with an increase in normal stresses. The topology parameter, Q_{f}, computed from the velocity distribution, suggests that the "shear thickening" regime, where much of the elastic turbulence occurs in a single pore throat, is a consequence of viscoelastic normal stresses that cause a complex flow field. This flow field consists of extensional, shear, and rotational features around the constriction, as well as upstream and downstream of the constriction. Furthermore, this elastic turbulence regime, has high-pressure fluctuations, with a power-law decay exponent of up to |-2.1| which is higher than the Kolmogorov value for turbulence of |-5/3|.

Event-based contact angle measurements inside porous media using time-resolved micro-computed tomography.

HYPOTHESIS: Capillary-dominated multiphase flow in porous materials is strongly affected by the pore walls' wettability. Recent micro-computed tomography (mCT) studies found unexpectedly wide contact angle distributions measured on static fluid distributions inside the pores. We hypothesize that analysis on time-resolved mCT data of fluid invasion events may be more directly relevant to the fluid dynamics. EXPERIMENT: We approximated receding contact angles locally in time and space on time-resolved mCT datasets of drainage in a glass bead pack and a limestone. Whenever a meniscus suddenly entered one or more pores, geometric and thermodynamically consistent contact angles in the surrounding pores were measured in the time step just prior to the displacement event. We introduced a new force-based contact angle, defined to recover the measured capillary pressure in the invaded pore throat prior to interface movement. FINDINGS: Unlike the classical method, the new geometric and force-based contact angles followed plausible, narrower distributions and were mutually consistent. We were unable to obtain credible results with the thermodynamically consistent method, likely because of sensitivity to common imaging artifacts and neglecting dissipation. Time-resolved mCT analysis can yield a more appropriate wettability characterization for pore scale models, despite the need to further reduce image analysis uncertainties.

Mechanisms controlling fluid breakup and reconnection during two-phase flow in porous media.

The use of Darcy's law to describe steady-state multiphase flow in porous media has been justified by the assumption that the fluids flow in continuously connected pathways. However, a range of complex interface dynamics have been observed during macroscopically steady-state flow, including intermittent pathway flow where flow pathways periodically disconnect and reconnect. The physical mechanisms controlling this behavior have remained unclear, leading to uncertainty concerning the occurrence of the different flow regimes. We observe that the fraction of intermittent flow pathways is dependent on the capillary number and viscosity ratio. We propose a phase diagram within this parameter space to quantify the degree of intermittent flow.

Intermittent fluid connectivity during two-phase flow in a heterogeneous carbonate rock.

Subsurface fluid flow is ubiquitous in nature, and understanding the interaction of multiple fluids as they flow within a porous medium is central to many geological, environmental, and industrial processes. It is assumed that the flow pathways of each phase are invariant when modeling subsurface flow using Darcy's law extended to multiphase flow, a condition that is assumed to be valid during steady-state flow. However, it has been observed that intermittent flow pathways exist at steady state even at the low capillary numbers typically encountered in the subsurface. Little is known about the pore structure controls or the impact of intermittency on continuum scale flow properties. Here we investigate the impact of intermittent pathways on the connectivity of the fluids for a carbonate rock. Using laboratory-based micro computed tomography imaging we observe that intermittent pathway flow occurs in intermediate-sized pores due to the competition between both flowing fluids. This competition moves to smaller pores when the flow rate of the nonwetting phase increases. Intermittency occurs in poorly connected pores or in regions where the nonwetting phase itself is poorly connected. Intermittent pathways lead to the interrupted transport of the fluids; this means they are important in determining continuum scale flow properties, such as relative permeability. The impact of intermittency on flow properties is significant because it occurs at key locations, whereby the nonwetting phase is otherwise disconnected.

Validation of model predictions of pore-scale fluid distributions during two-phase flow.

Pore-scale two-phase flow modeling is an important technology to study a rock's relative permeability behavior. To investigate if these models are predictive, the calculated pore-scale fluid distributions which determine the relative permeability need to be validated. In this work, we introduce a methodology to quantitatively compare models to experimental fluid distributions in flow experiments visualized with microcomputed tomography. First, we analyzed five repeated drainage-imbibition experiments on a single sample. In these experiments, the exact fluid distributions were not fully repeatable on a pore-by-pore basis, while the global properties of the fluid distribution were. Then two fractional flow experiments were used to validate a quasistatic pore network model. The model correctly predicted the fluid present in more than 75% of pores and throats in drainage and imbibition. To quantify what this means for the relevant global properties of the fluid distribution, we compare the main flow paths and the connectivity across the different pore sizes in the modeled and experimental fluid distributions. These essential topology characteristics matched well for drainage simulations, but not for imbibition. This suggests that the pore-filling rules in the network model we used need to be improved to make reliable predictions of imbibition. The presented analysis illustrates the potential of our methodology to systematically and robustly test two-phase flow models to aid in model development and calibration.

Petrographic characterization to build an accurate rock model using micro-CT: Case study on low-permeable to tight turbidite sandstone from Eocene Shahejie Formation.

Pore scale flow simulations heavily depend on petrographic characterizing and modeling of reservoir rocks. Mineral phase segmentation and pore network modeling are crucial stages in micro-CT based rock modeling. The success of the pore network model (PNM) to predict petrophysical properties relies on image segmentation, image resolution and most importantly nature of rock (homogenous, complex or microporous). The pore network modeling has experienced extensive research and development during last decade, however the application of these models to a variety of naturally heterogenous reservoir rock is still a challenge. In this paper, four samples from a low permeable to tight sandstone reservoir were used to characterize their petrographic and petrophysical properties using high-resolution micro-CT imaging. The phase segmentation analysis from micro-CT images shows that 5-6% microporous regions are present in kaolinite rich sandstone (E3 and E4), while 1.7-1.8% are present in illite rich sandstone (E1 and E2). The pore system percolates without micropores in E1 and E2 while it does not percolate without micropores in E3 and E4. In E1 and E2, total MICP porosity is equal to the volume percent of macrospores determined from micro-CT images, which indicate that the macropores are well connected and microspores do not play any role in non-wetting fluid (mercury) displacement process. Whereas in E3 and E4 sandstones, the volume percent of micropores is far less (almost 50%) than the total MICP porosity which means that almost half of the pore space was not detected by the micro-CT scan. PNM behaved well in E1 and E2 where better agreement exists in PNM and MICP measurements. While E3 and E4 exhibit multiscale pore space which cannot be addressed with single scale PNM method, a multiscale approach is needed to characterize such complex rocks. This study provides helpful insights towards the application of existing micro-CT based petrographic characterization methodology to naturally complex petroleum reservoir rocks.

In Situ Triaxial Testing To Determine Fracture Permeability and Aperture Distribution for CO2 Sequestration in Svalbard, Norway.

On Svalbard, Arctic Norway, an unconventional siliciclastic reservoir, relying on (micro)fractures for enhanced fluid flow in a low-permeable system, is investigated as a potential CO2 sequestration site. The fractures' properties at depth are, however, poorly understood. High resolution X-ray computed tomography (micro-CT) imaging allows one to visualize such geomaterials at reservoir conditions. We investigated reservoir samples from the De Geerdalen Formation on Svalbard to understand the influence of fracture closure on the reservoir fluid flow behavior. Small rock plugs were brought to reservoir conditions, while permeability was measured through them during micro-CT imaging. Local fracture apertures were quantified down to a few micrometers wide. The permeability measurements were complemented with fracture permeability simulations based on the obtained micro-CT images. The relationship between fracture permeability and the imposed confining pressure was determined and linked to the fracture apertures. The investigated fractures closed due to the increased confining pressure, with apertures reducing to approximately 40% of their original size as the confining pressure increased from 1 to 10 MPa. This coincides with a permeability drop of more than 90%. Despite their closure, fluid flow is still controlled by the fractures at pressure conditions similar to those at the proposed storage depth of 800-1000 m.

Comparison between traditional laboratory tests, permeability measurements and CT-based fluid flow modelling for cultural heritage applications.

In this paper, we examine the possibility to use on-site permeability measurements for cultural heritage applications as an alternative for traditional laboratory tests such as determination of the capillary absorption coefficient. These on-site measurements, performed with a portable air permeameter, were correlated with the pore network properties of eight sandstones and one granular limestone that are discussed in this paper. The network properties of the 9 materials tested in this study were obtained from micro-computed tomography (µCT) and compared to measurements and calculations of permeability and the capillary absorption rate of the stones under investigation, in order to find the correlation between pore network characteristics and fluid management characteristics of these sandstones. Results show a good correlation between capillary absorption, permeability and network properties, opening the possibility of using on-site permeability measurements as a standard method in cultural heritage applications.