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A gradient‐information‐enhanced image segmentation method using convolutional neural networks is presented, and then combined with contact angle measurement to establish an automated processing workflow. For three‐dimensional X‐ray images, the segmentation accuracy at interfaces and sparsely distributed small objects directly influences the accuracy of the contact angle measurement. Leveraging reliable gradient information to train the neural network, this segmentation method addresses the issue of inaccurate segmentation of interfaces even at low resolution and with small objects present. Furthermore, memory requirements are reduced by performing analysis on orthogonal two‐dimensional planes. The workflow was tested on water‐wet Ketton limestone, as well as on both water‐wet and mixed‐wet sandstone and a reservoir carbonate. The results from both the segmentation and contact angle measurements underscore the effectiveness of the approach. Notably, the workflow shows considerable generalizability and robustness, even with varying wettability and lithology. Plain Language Summary: We use convolutional neural networks enhanced with gradient information to improve the accuracy of segmentation of three‐dimensional images of porous media and the fluids in the pore space, especially at interfaces and for small objects, even when the images have low resolution. We tested the method on several data sets including water‐wet Ketton limestone, both water‐wet and mixed‐wet Bentheimer sandstone, and a reservoir carbonate. The results demonstrated the effectiveness of our approach compared to traditional methods for segmentation. A particular challenge is the determination of contact angle ‐ the local wettability ‐ at the three‐phase contact loop between two fluid phases and the solid. We show that our new method leads to reliable estimates of the distribution of contact angle for the samples studied. This work allows for more accurate image analysis in multiphase flow in porous media with applications in carbon dioxide and hydrogen storage. Key Points: A gradient information enhanced segmentation method is presented to assist automatic contact angle measurementsThe gradient information method reduces the problems associated with low image resolution and manual segmentation [ABSTRACT FROM AUTHOR]

Porous materials, such as carbonate rocks, frequently have pore sizes which span many orders of magnitude. This is a challenge for models that rely on an image of the pore space, since much of the pore space may be unresolved. In this work, sub‐resolution porosity in X‐ray images is characterized using differential imaging which quantifies the difference between a dry scan and 30 wt% potassium iodide brine saturated images. Once characterized, we develop a robust workflow to incorporate the sub‐resolution pore space into a network model using Darcy‐type elements called microlinks. Each grain voxel with sub‐resolution porosity is assigned to the two nearest resolved pores using an automatic dilation algorithm. By including these microlinks with empirical models in flow modeling, we simulate single‐phase and multiphase flow. By fine‐tuning the microlink empirical models, we match permeability, formation factor (the ratio of the resistivity of a rock filled with brine to the resistivity of that brine), and drainage capillary pressure to experimental results. We then show that our model can successfully predict steady‐state relative permeability measurements on a water‐wet Estaillades carbonate sample within the uncertainty of the experiments and modeling. Our approach of incorporating sub‐resolution porosity in two‐phase flow modeling using image‐based multiscale pore network techniques can capture complex pore structures and accurately predict flow behavior in porous materials with a wide range of pore size. Key Points: A dilation‐based algorithm adds sub‐resolution porosity, quantified by differential imaging, as microlinks to an extracted pore networkEmpirical models are used to characterize the flow properties of microlinksThe tuned multiscale network, using permeability, formation factor, and capillary pressure, matches experimental relative permeability [ABSTRACT FROM AUTHOR]

Quasi two‐dimensional approximations of interfacial curvature, present in current network models of multiphase flow in porous media, are extended to three dimensions. The new expressions for threshold capillary pressure are validated and calibrated using high‐resolution direct numerical simulations on synthetic geometries. The effects of pore‐space expansion and sagittal interface curvature on displacement are quantified, and are shown to be a key step in improving the physical accuracy of network models. Finally, the calibrated network model is used to obtain predictions for relative permeability and capillary pressure in a water‐wet Bentheimer sandstone. The predictions are compared to experimental measurements, revealing that the inclusion of three‐dimensional interfacial curvature leads to more accurate predictions. Key Points: Quasi 2D representations of interfacial curvature present in network modeling of multiphase flow are extended to three dimensionsA fully 3D representation of curvature is needed for network models to reproduce the behavior of direct simulations and experimentsCorrect predictions of trapping and relative permeability with network modeling rely on a physically accurate inclusion of curvature [ABSTRACT FROM AUTHOR]

A continuous-time random walk (CTRW) reactive transport model is used to study the impact of physical heterogeneity on the effective reaction rates in porous media in a sample of length 15 cm over timescales up to 10 8 s (3 years). The model has previously been validated using nuclear magnetic resonance (NMR) measurements during dissolution of a limestone. The model assumes first-order reaction. We construct three domains with increasing physical heterogeneity and study dissolution at four Péclet numbers, Pe = 0.0542, 0.542, 5.42 and 54.2. We characterize signatures of physical heterogeneity in the three porous media using velocity distributions and show how these imprint on the signatures of particle displacement, namely particle propagator distributions. In addition, we demonstrate the ability of our CTRW model to capture the impact of physical heterogeneity on the longitudinal dispersion coefficient over several orders of magnitude in space and time. Reactive transport simulations show that the effective reaction rates depend on (i) initial physical heterogeneity and (ii) transport conditions. For all heterogeneities and Pe, the late-time reaction rate exhibits a time dependence t - a with a ≠ 0.5 that indicates the persistence of incomplete mixing. We show that the higher the initial heterogeneity, the lower the late-time reaction rate. A decrease in Pe promotes mixing by diffusion over advection, resulting in higher reaction rates. The post-dissolution propagators indicate an increase in the degree of non-Fickian transport. Overall, we establish a framework to demonstrate and quantify the impact of physical heterogeneity on transport and effective reaction rates in porous media. [ABSTRACT FROM AUTHOR]

A saturation–capillary pressure relationship is proposed that is applicable for all wettabilities, including mixed-wet and oil-wet or hydrophobic media. This formulation is more flexible than existing correlations that only match water-wet data, while also allowing saturation to be written as a closed-form function of capillary pressure: we can determine capillary pressure explicitly from saturation, and vice versa. We propose P c = A + B tan π 2 - π S e C for 0 ≤ S e ≤ 1 , where S e is the normalized saturation. A indicates the wettability: A > 0 is a water-wet medium, A < 0 is hydrophobic while small A suggests mixed wettability. B represents the average curvature and pore-size distribution which can be much lower in mixed-wet compared to water-wet media with the same pore structure if the menisci are approximately minimal surfaces. C is an exponent that controls the inflection point in the capillary pressure and the asymptotic behaviour near end points. We match the model accurately to 29 datasets in the literature for water-wet, mixed-wet and hydrophobic media, including rocks, soils, bead and sand packs and fibrous materials with over four orders of magnitude difference in permeability and porosities from 20% to nearly 90%. We apply Leverett J-function scaling to make the expression for capillary pressure dimensionless and discuss the behaviour of analytical solutions for spontaneous imbibition. [ABSTRACT FROM AUTHOR]

Multiphase flow in porous materials is conventionally described by an empirical extension to Darcy's law, which assumes that the pressure gradient is proportional to the flow rate. Through a series of two-phase flow experiments, we demonstrate that even when capillary forces are dominant at the pore scale, there is a nonlinear intermittent flow regime with a power-law dependence between pressure gradient and flow rate. Energy balance is used to predict accurately the start of the intermittent regime in hydrophobic porous media. The pore-scale explanation of the behaviour based on the periodic filling of critical flow pathways is confirmed through 3D micron-resolution X-ray imaging. [ABSTRACT FROM AUTHOR]

Three-phase flow in porous media is encountered in many applications including subsurface carbon dioxide storage, enhanced oil recovery, groundwater remediation and the design of microfluidic devices. However, the pore-scale physics that controls three-phase flow under capillary dominated conditions is still not fully understood. Recent advances in three-dimensional pore-scale imaging have provided new insights into three-phase flow. Based on these findings, this paper describes the key pore-scale processes that control flow and trapping in a three-phase system, namely wettability order, spreading and wetting layers, and double/multiple displacement events. We show that in a porous medium containing water, oil and gas, the behaviour is controlled by wettability, which can either be water-wet, weakly oil-wet or strongly oil-wet, and by gas–oil miscibility. We provide evidence that, for the same wettability state, the three-phase pore-scale events are different under near-miscible conditions—where the gas–oil interfacial tension is ≤ 1 mN/m—compared to immiscible conditions. In a water-wet system, at immiscible conditions, water is the most-wetting phase residing in the corners of the pore space, gas is the most non-wetting phase occupying the centres, while oil is the intermediate-wet phase spreading in layers sandwiched between water and gas. This fluid configuration allows for double capillary trapping, which can result in more gas trapping than for two-phase flow. At near-miscible conditions, oil and gas appear to become neutrally wetting to each other, preventing oil from spreading in layers; instead, gas and oil compete to occupy the centre of the larger pores, while water remains connected in wetting layers in the corners. This allows for the rapid production of oil since it is no longer confined to movement in thin layers. In a weakly oil-wet system, at immiscible conditions, the wettability order is oil–water–gas, from most to least wetting, promoting capillary trapping of gas in the pore centres by oil and water during water-alternating-gas injection. This wettability order is altered under near-miscible conditions as gas becomes the intermediate-wet phase, spreading in layers between water in the centres and oil in the corners. This fluid configuration allows for a high oil recovery factor while restricting gas flow in the reservoir. Moreover, we show evidence of the predicted, but hitherto not reported, wettability order in strongly oil-wet systems at immiscible conditions, oil–gas–water, from most to least wetting. At these conditions, gas progresses through the pore space in disconnected clusters by double and multiple displacements; therefore, the injection of large amounts of water to disconnect the gas phase is unnecessary. We place the analysis in a practical context by discussing implications for carbon dioxide storage combined with enhanced oil recovery before suggesting topics for future work. [ABSTRACT FROM AUTHOR]

This study focuses on direct numerical simulation of imbibition, displacement of the non-wetting phase by the wetting phase, through water-wet carbonate rocks. We simulate multiphase flow in a limestone and compare our results with high-resolution synchrotron X-ray images of displacement previously published in the literature by Singh et al. (Sci Rep 7:5192, 2017). We use the results to interpret the observed displacement events that cannot be described using conventional metrics such as pore-to-throat aspect ratio. We show that the complex geometry of porous media can dictate a curvature balance that prevents snap-off from happening in spite of favourable large aspect ratios. We also show that pinned fluid-fluid-solid contact lines can lead to snap-off of small ganglia on pore walls; we propose that this pinning is caused by sub-resolution roughness on scales of less than a micron. Our numerical results show that even in water-wet porous media, we need to allow pinned contacts in place to reproduce experimental results. [ABSTRACT FROM AUTHOR]

We measure the pressure difference during two‐phase flow across a sandstone sample for a range of injection rates and fractional flows of water, the wetting phase, during an imbibition experiment. We quantify the onset of a transition from a linear relationship between flow rate and pressure gradient to a nonlinear power‐law dependence. We show that the transition from linear (Darcy) to nonlinear flow and the exponent in the power‐law is a function of fractional flow. We use energy balance to accurately predict the onset of intermittency for a range of fractional flows, fluid viscosities, and different rock types. Plain Language Summary: Multiphase flow in porous media is described by an empirical extension of Darcy's law where flow rate is proportional to pressure gradient. Darcy's law is used to quantify and design a wide variety of processes including carbon dioxide storage in the subsurface, and air and moisture flows through materials as diverse as soils and surgical masks. However, as flow rate increases, this linear Darcy law breaks down with a transition to a nonlinear intermittent flow regime. Through an extensive set of experimental measurements, we quantify the relationship between flow rate and pressure gradient. A theory based on energy balance accurately predicts the transition to intermittency. Our work quantifies multiphase flow over a wide range of conditions. Key Points: Flow rate and pressure gradient during steady‐state multiphase flow are measured experimentallyThe transition to a non‐Darcy flow regime is quantified and predicted theoreticallyThe theory makes accurate predictions for several rock types, fractional flows, and mobility ratios [ABSTRACT FROM AUTHOR]

We study the impact of pore space heterogeneity on mixing and reaction in porous media. We simulate the parallel injection of two streams of reactants at different pH in a three‐dimensional microporous consolidated rock whose pore space was resolved by differential micro‐CT imaging. As an exemplar of a heterogeneous medium, we consider the pore structure obtained from a Portland carbonate sample. We use direct numerical simulation to study the coupled impact of flow heterogeneity, characterized by a wide distribution of velocities and chemical reversibility on multispecies reaction. The flow field is found from the Darcy‐Brinkman equation while the advection‐diffusion equation describes transport, which is coupled to a general multispecies geochemical solver for homogeneous reactions; precipitation, and dissolution are ignored. We observe a highly nonuniform spatial distribution of concentration and rates of formation and consumption. For advection‐dominated transport, the heterogeneous flow field leads to significant transverse mixing in macropores at early times, followed by a slower mixing driven by diffusion between macropore and micropore regions. The effective rates of formation and consumption are species‐dependent and distinct in macroporosity and microporosity: while some species reach an asymptotic rate in well‐mixed regions, others still show a transient nonmonotonic behavior as a consequence of incomplete mixing. Our findings have important implications for the understanding of time‐ and space‐dependent reaction rate behavior: the coupled impact of pore space heterogeneity and reversible reactions need to be taken into account as key determinants to describe multispecies reactive transport. Key Points: Reactive behavior is simultaneously influenced by pore space heterogeneity, multispecies reactive transport, and reaction reversibilityThe evolution of rates of formation and consumption is species‐dependent and highly distinct in macroporosity and microporosityWell‐mixed regions result in asymptotic rates; incomplete mixing leads to transient and, for some species, even nonmonotonic behavior [ABSTRACT FROM AUTHOR]

We use synchrotron X-ray micro-tomography to investigate the displacement dynamics during three-phase—oil, water and gas—flow in a hydrophobic porous medium. We observe a distinct gas invasion pattern, where gas progresses through the pore space in the form of disconnected clusters mediated by double and multiple displacement events. Gas advances in a process we name three-phase Haines jumps, during which gas re-arranges its configuration in the pore space, retracting from some regions to enable the rapid filling of multiple pores. The gas retraction leads to a permanent disconnection of gas ganglia, which do not reconnect as gas injection proceeds. We observe, in situ, the direct displacement of oil and water by gas as well as gas–oil–water double displacement. The use of local in situ measurements and an energy balance approach to determine fluid–fluid contact angles alongside the quantification of capillary pressures and pore occupancy indicate that the wettability order is oil–gas–water from most to least wetting. Furthermore, quantifying the evolution of Minkowski functionals implied well-connected oil and water, while the gas connectivity decreased as gas was broken up into discrete clusters during injection. This work can be used to design CO2 storage, improved oil recovery and microfluidic devices. [ABSTRACT FROM AUTHOR]

We use fast synchrotron X-ray microtomography to understand three-phase flow inmixed-wet porous media to design either enhanced permeability or capillary trapping. The dynamics ofthese phenomena are of key importance in subsurface hydrology, carbon dioxide storage, oil recovery, foodand drug manufacturing, and chemical reactors. We study the dynamics of a water-gas-water injectionsequence in a mixed-wet carbonate rock. During the initial waterflooding, water displaced oil from pores ofall size, indicating a mixed-wet system with local contact angles both above and below 90◦. When gas wasinjected, gas displaced oil preferentially with negligible displacement of water. This behavior is explainedin terms of the gas pressure needed for invasion. Overall, gas behaved as the most nonwetting phase withoil as the most wetting phase; however, pores of all size were occupied by oil, water, and gas, as a signatureof mixed-wet media. Thick oil wetting layers were observed, which increased oil connectivity andfacilitated its flow during gas injection. A chase waterflooding resulted in additional oil flow, while gas wastrapped by oil and water. Furthermore, we quantified the evolution of the surface areas and both Gaussianand the total curvature, from which capillary pressure could be estimated. These quantities are related tothe Minkowski functionals which quantify the degree of connectivity and trapping. The combination ofwater and gas injection, under mixed-wet immiscible conditions, leads to both favorable oil flow andsignificant trapping of gas, which is advantageous for storage applications. [ABSTRACT FROM AUTHOR]

We identify a distinct two-phase flow invasion pattern in a mixed-wet porous medium. Time-resolved high-resolution synchrotron X-ray imaging is used to study the invasion of water through a small rock sample filled with oil, characterized by a wide non-uniform distribution of local contact angles both above and below 90°. The water advances in a connected front, but throats are not invaded in decreasing order of size, as predicted by invasion percolation theory for uniformly hydrophobic systems. Instead, we observe pinning of the three-phase contact between the fluids and the solid, manifested as contact angle hysteresis, which prevents snap-off and interface retraction. In the absence of viscous dissipation, we use an energy balance to find an effective, thermodynamic, contact angle for displacement and show that this angle increases during the displacement. Displacement occurs when the local contact angles overcome the advancing contact angles at a pinned interface: it is wettability which controls the filling sequence. The product of the principal interfacial curvatures, the Gaussian curvature, is negative, implying well-connected phases which is consistent with pinning at the contact line while providing a topological explanation for the high displacement efficiencies in mixed-wet media. [ABSTRACT FROM AUTHOR]

At the pore scale, slow invasion of a wetting fluid in porous materials is often modeled with quasi‐static approximations which only consider capillary forces in the form of simple pore‐filling rules. The appropriateness of this approximation, often applied in pore network models, is contested in the literature, reflecting the difficulty of predicting imbibition relative permeability with these models. However, validation by sole comparison to continuum‐scale experiments is prone to induce model overfitting. It has therefore remained unclear whether difficulties generalizing the model performance are caused by errors in the predicted filling sequence or by subsequent calculations. Here, we address this by examining whether such a model can predict the pore‐scale fluid distributions underlying the behavior at the continuum scale. To this end, we compare the fluid arrangement evolution measured in fast synchrotron micro‐CT experiments on two rock types to quasi‐static simulations which implement capillary‐dominated pore filling and snap‐off, including a sophisticated model for cooperative pore filling. The results indicate that such pore network models can, in principle, predict fluid distributions accurately enough to estimate upscaled flow properties of strongly wetted rocks at low capillary numbers. Key Points: A new workflow to compare pore network simulations of two‐phase flow to time‐resolved micro‐CT data is presentedThe evolution of fluid distributions were validated with respect to pore size, connectivity, and flow pathsQuasi‐static pore network models put the fluids in approximately the right pores to predict flow properties [ABSTRACT FROM AUTHOR]

We demonstrate how to use numerical simulation models directly on micro-CT images to understand the impact of several enhanced oil recovery (EOR) methods on microscopic displacement efficiency. To describe the physics with high-fidelity, we calibrate the model to match a water-flooding experiment conducted on the same rock sample (Akai et al. in Transp Porous Media 127(2):393–414, 2019. 10.1007/s11242-018-1198-8). First we show comparisons of water-flooding processes between the experiment and simulation, focusing on the characteristics of remaining oil after water-flooding in a mixed-wet state. In both the experiment and simulation, oil is mainly present as thin oil layers confined to pore walls. Then, taking this calibrated simulation model as a base case, we examine the application of three EOR processes: low salinity water-flooding, surfactant flooding and polymer flooding. In low salinity water-flooding, the increase in oil recovery was caused by displacement of oil from the centers of pores without leaving oil layers behind. Surfactant flooding gave the best improvement in the recovery factor of 16% by reducing the amount of oil trapped by capillary forces. Polymer flooding indicated improvement in microscopic sweep efficiency at a higher capillary number, while it did not show an improvement at a low capillary number. Overall, this work quantifies the impact of different EOR processes on local displacement efficiency and establishes a workflow based on combining experiment and modeling to design optimal recovery processes. [ABSTRACT FROM AUTHOR]

A reliable prediction of two-phase flow through porous media requires the development and validation of models for flow across multiple length scales. The generalized network model is a step towards efficient and accurate upscaling of flow from the pore to the core scale. This paper presents a validation of the generalized network model using micro-CT images of two-phase flow experiments on a pore-by-pore basis. Three experimental secondary imbibition datasets are studied for both sandstone and carbonate rock samples. We first present a quantification of uncertainties in the experimental measurements. Then, we show that the model can reproduce the experimental fluid occupancies and saturations with a good accuracy, which in some cases is comparable with the similarity between repeat experiments. However, high-resolution images need to be acquired to characterize the pore geometry for modelling, while the results are sensitive to the initial condition at the end of primary drainage. The results provide a methodology for improving our physical models using large experimental datasets which, at the pore scale, can be generated using micro-CT imaging of multiphase flow. [ABSTRACT FROM AUTHOR]

A quantitative in situ characterization of the impact of surface roughness on wettability in porous media is currently lacking. We use reservoir condition micrometer-resolution X-ray tomography combined with automated methods for the measurement of contact angle, interfacial curvature, and surface roughness to examine fluid/fluid and fluid/solid interfaces inside a porous material. We study oil and water in the pore space of limestone from a giant producing oilfield, acquiring millions of measurements of curvature and contact angle on three millimeter-sized samples. We identify a distinct wetting state with a broad distribution of contact angle at the submillimeter scale with a mix of water-wet and water-repellent regions. Importantly, this state allows both fluid phases to flow simultaneously over a wide range of saturation. We establish that, in media that are largely water wet, the interfacial curvature does not depend on solid surface roughness, quantified as the local deviation from a plane. However, where there has been a significant wettability alteration, rougher surfaces are associated with lower contact angles and higher interfacial curvature. The variation of both contact angle and interfacial curvature increases with the local degree of roughness. We hypothesize that this mixed wettability may also be seen in biological systems to facilitate the simultaneous flow of water and gases; furthermore, wettability-altering agents could be used in both geological systems and material science to design a mixed-wetting state with optimal process performance. [ABSTRACT FROM AUTHOR]

We present an experimental and numerical study of transport in carbonates during dissolution and its upscaling from the pore (∼μm) to core (∼cm) scale. For the experimental part, we use nuclear magnetic resonance (NMR) to probe molecular displacements (propagators) of an aqueous hydrochloric acid (HCl) solution through a Ketton limestone core. A series of propagator profiles are obtained at a large number of spatial points along the core at multiple time-steps during dissolution. For the numerical part, first, the transport model—a particle-tracking method based on Continuous Time Random Walks (CTRW) by Rhodes et al. (2008)—is validated at the pore scale by matching to the NMR-measured propagators in a beadpack, Bentheimer sandstone, and Portland carbonate (Scheven et al., 2005). It was found that the emerging distribution of particle transit times in these samples can be approximated satisfactorily using the power law function ψ ( t ) ∼ t −1 − β , where 0 < β < 2. Next, the evolution of the propagators during reaction is modelled: at the pore scale, the experimental data is used to calibrate the CTRW parameters; then the shape of the propagators is predicted at later observation times. Finally, a numerical upscaling technique is employed to obtain CTRW parameters for the core. From the NMR-measured propagators, an increasing frequency of displacements in stagnant regions was apparent as the reaction progressed. The present model predicts that non-Fickian behaviour exhibited at the pore scale persists on the centimetre scale. [ABSTRACT FROM AUTHOR]

Transport of passive, dissolved compounds in fully-saturated complex porous media frequently exhibits non-Fickian characteristics. One of the most interesting questions is to ascertain the time scales at which it is possible to describe transport as a statistically independent process. Therefore, we study the mechanisms for evolution and then the decrease of non-Fickianity as a function of increasing time. Adopting the Lagrangian perspective, we provide a nonlinear copula analysis of advective-diffusive processes by analyzing particle trajectories in a real porous media, as provided by direct numerical simulations on the three-dimensional image of Doddington sandstone. First, we analyze the memory effects between time-consecutive particle position increments and cross dependence between longitudinal and transversal particle position increments as a function of given time increments and time lags between consecutive time increments. Second, we investigate the influence of the Péclet regime on the temporal evolution of dependence. Our main findings are: (a) Cross dependence between longitudinal and transversal particle position increments is persistent over the investigated range of time increments, even though this aspect has been neglected up to date. (b) Lower Péclet numbers lead to a weaker dependence that is, however, more persistent over time than in higher-Péclet transport regimes. We confirm that non-Fickianity comes from spatial coherence associated with heterogeneities of the velocity field that introduce cross dependence and memory into the transport process. Overall, we show that memory and cross dependence are persistent in and among all directions, that the dependence is highly-nonlinear, occurs at different temporal scales, and is dependent on the Péclet number. [ABSTRACT FROM AUTHOR]

We study capillary trapping in porous media using direct pore-scale simulation of two-phase flow on micro-CT images of a Berea sandstone and a sandpack. The trapped non-wetting phase saturations are predicted by solving the full Navier–Stokes equations using a volume-of-fluid based finite-volume framework to simulate primary drainage followed by water injection. Using these simulations, we analyse the effects of initial non-wetting-phase saturation, capillary number and flow direction on the residual saturation. The predictions from our numerical method are in agreement with published experimental measurements of capillary trapping curves. This shows that our direct simulation method can be used to elucidate the effect of pore structure and flow pattern of capillary trapping and provides a platform to study the physics of multiphase flow at the pore scale. [ABSTRACT FROM AUTHOR]

The trapped saturations of oil and gas are measured as functions of initial oil and gas saturation in water-wet sand packs. Analogue fluids-water, octane and air-are used at ambient conditions. Starting with a sand-pack column which has been saturated with brine, oil (octane) is injected with the column horizontal until irreducible water saturation is reached. The column is then positioned vertically and air is allowed to enter from the top of the column, while oil is allowed to drain under gravity for varying lengths of time. At this point, the column may be sliced and the fluids analyzed by gas chromatography to obtain the initial saturations. Alternatively, brine is injected through the bottom of the vertical column to trap oil and gas, before slicing the columns and measuring the trapped or residual saturations by gas chromatography and mass balance. The experiments show that in three-phase flow, the total trapped saturations of oil and gas are considerably higher than the trapped saturations reported in the literature for two-phase systems. It is found that the residual saturation of oil and gas combined could be as high as 23 %, as opposed to a maximum two-phase residual of only 14 %. For very high initial gas saturations, the residual gas saturation, up to 17 %, was also higher than for two-phase displacement. These observations are explained in terms of the competition between piston-like displacement and snap-off. It is also observed that less oil is always trapped in three-phase flow than in two-phase displacement, and the difference depends on the amount of gas present. For low and intermediate initial gas saturations, the trapped gas saturation rises linearly with initial saturation, followed by a constant residual, as seen in two-phase displacements. However, at very high initial gas saturations, the residual saturation rises again. [ABSTRACT FROM AUTHOR]

We use a new volume-of-fluid based finite-volume method to model two-phase flow through simple pore geometries and study the mechanisms controlling two-phase flow at the pore scale. The numerical model is used to study layer flow and snap-off, and investigate the effect of geometry and flow rate on trapping and mobilization of the disconnected ganglia. Furthermore, a new variable, the capillary field, is introduced to characterize the capillary force under dynamic situations, and a force-balance concept is presented to relate flow rates to pore-scale forces-dynamic pressure gradient and the capillary field. This description of the flow has the potential to be used in pore-network models to study the effect of pore-scale structures on the flow at larger scales. As an illustration of the applicability of this concept, we use the relations obtained from the numerical simulations to predict the threshold capillary number for blob mobilization during imbibition and show that this information can be used to reproduce the direct numerical simulation results accurately. [ABSTRACT FROM AUTHOR]

We present predictions of transport through micro-CT images of porous media that include the analysis of correlation structure, velocity, and the dynamics of the evolving plume. We simulate solute transport through millimeter-sized three-dimensional images of a beadpack, a sandstone, and a carbonate, representing porous media with an increasing degree of pore-scale complexity. The Navier-Stokes equations are solved to compute the flow field and a streamline simulation approach is used to move particles by advection, while the random walk method is employed to represent diffusion. We show how the computed propagators (concentration as a function of displacement) for the beadpack, sandstone, and carbonate depend on the width of the velocity distribution. A narrow velocity distribution in the beadpack leads to the least anomalous behavior, where the propagators rapidly become Gaussian in shape; the wider velocity distribution in the sandstone gives rise to a small immobile concentration peak, and a large secondary mobile peak moving at approximately the average flow speed; in the carbonate with the widest velocity distribution, the stagnant concentration peak is persistent, with a slower emergence of a smaller secondary mobile peak, characteristic of highly anomalous behavior. This defines different types of transport in the three media and quantifies the effect of pore structure on transport. The propagators obtained by the model are in excellent agreement with those measured on similar cores in nuclear magnetic resonance experiments by Scheven, Verganelakis, Harris, Johns, and Gladden, Phys. Fluids 17, 117107 (2005). [ABSTRACT FROM AUTHOR]

Abstract: Tracer tailing in breakthrough curves in porous media with two distinct porosities is analyzed in terms of the dynamic responses of experimental fixed bed columns filled either with solid or porous beads. The flow is fast in the column interstitial space between beads (for both solid and porous beads) but slow within the porous beads that act as controlled ‘traps’ constituting an immobile zone. The transport is quantified using a Continuous Time Random Walk (CTRW) framework, which accounts for domains with controlled structural and flow heterogeneity associated with two distinct spatial and time spectra. We first demonstrate that breakthrough curves for a column containing solid glass beads exhibit non-Fickian transport, quantifiable both in fitting and validation mode by a CTRW based on a power law transition time distribution. We then examine breakthrough curves in the porous bead case, obtaining fits with a two-scale CTRW model that accounts explicitly for the two time spectra. Because the porous beads are uniform, tracer trapping within them is described by a simple first-order approximation trap model, with relatively weak capture and relatively faster release rates. The extent of tailing apparent in the porous bead breakthrough curves, due to the traps, can be quantitatively distinguished from the contribution to tailing due to mobile zone non-Fickian transport. A parameter study of the two-scale CTRW adds further insight into the dynamics of the process, showing the interaction between the advective non-Fickian transport and the mass exchange to immobile regions. [ABSTRACT FROM AUTHOR]

Slow flow of an incompressible Newtonian fluid across a fibrous porous medium bounded by a free-flow region of variable width was studied experimentally by magnetic resonance imaging velocimetry. The fibrous porous medium (fibre lattice) comprised of aligned rows of cylindrical rods, which were macroscopically arranged in a semi-circular fashion in a Hele-Shaw cell. The local aspects of the flow in the interior of and exterior to the fibre lattices were studied for (i) three individual semi-circular fibre lattices of different porosity and/or cylinder size, with each lattice bounded by an open channel and (ii) an assembly of five fibre lattices with the interstitial space between them forming a free-flow region. The symmetry (in a practical sense) of slow flow over symmetrical lattice–channel arrangements is demonstrated. The subtle characteristics of the flow within the lattices are seen as considerable local velocity enhancements (LVE) transverse to and in the direction of superficial flow. These LVE within the lattices strongly depend on the interface configuration of the lattice–channel arrangement, the gap size between the cylinders and the lattice porosity. The penetration depth of the LVE may even extend to the lattice centre. When a fibre lattice is a part of an assembly, the surface irregularities of neighbouring lattices create more complex tortuous flow pathways in the free-flow region. These pathways produce recurrent LVE within the fibre lattice. The implications that the above findings have for the flow, heat transfer and mass transfer in conceptually similar heterogeneous porous media used in, for example, liquid composite moulding processes and filtration processes are discussed. [Copyright &y& Elsevier]

• A reactive transport model is developed using CTRW and validated with NMR experiment. • Both model and experiment effective reaction rates are 3 orders of magnitude lower than batch rates. • Model and experimental molecular propagators describe flow and porosity evolution. We develop a reactive transport model for dissolution of porous materials using a Continuous Time Random Walk (CTRW) formulation with first-order kinetics. Our model is validated with a dataset for a Ketton carbonate rock sample undergoing dissolution on injection of an acid, monitored using Nuclear Magnetic Resonance (NMR). The experimental data includes the 3D porosity distribution at the beginning and end of the experiment, 1D porosity profiles along the direction of flow during dissolution, as well as the molecular fluid displacement probability distributions (propagators). With the calibration of only a single parameter, we successfully predict the porosity changes and the propagators as a signature of flow heterogeneity evolution in the dissolution experiment. We also demonstrate that heterogeneity in the flow field leads to an effective reaction rate, limited by transport of reactants, that is almost three orders of magnitude lower than measured under batch reaction conditions. The effective reaction rate predicted by the model is in good agreement with the experimentally measured rate. Furthermore, as dissolution proceeds, the formation of channels in the rock focused the flow in a few fast-flowing regions. The predicted dissolution patterns are similar to those observed experimentally. This study establishes a workflow to calibrate and validate the CTRW reactive transport model with NMR experiments. [ABSTRACT FROM AUTHOR]

High-resolution x-ray imaging was used in combination with differential pressure measurements to measure relative permeability and capillary pressure simultaneously during a steady-state waterflood experiment on a sample of Bentheimer sandstone 51.6 mm long and 6.1 mm in diameter. After prolonged contact with crude oil to alter the surface wettability, a refined oil and formation brine were injected through the sample at a fixed total flow rate but in a sequence of increasing brine fractional flows. When the pressure across the system stabilized, x-ray tomographic images were taken. The images were used to compute saturation, interfacial area, curvature, and contact angle. From this information relative permeability and capillary pressure were determined as functions of saturation. We compare our results with a previously published experiment under water-wet conditions. The oil relative permeability was lower than in the water-wet case, although a smaller residual oil saturation, of approximately 0.11, was obtained, since the oil remained connected in layers in the altered wettability rock. The capillary pressure was slightly negative and 10 times smaller in magnitude than for the water-wet rock, and approximately constant over a wide range of intermediate saturation. The oil-brine interfacial area was also largely constant in this saturation range. The measured static contact angles had an average of 80° with a standard deviation of 17°. We observed that the oil-brine interfaces were not flat, as may be expected for a very low mean curvature, but had two approximately equal, but opposite, curvatures in orthogonal directions. These interfaces were approximately minimal surfaces, which implies well-connected phases. Saddle-shaped menisci swept through the pore space at a constant capillary pressure and with an almost fixed area, removing most of the oil. [ABSTRACT FROM AUTHOR]

We present a generalized network model for simulating capillary-dominated two-phase flow through porous media at the pore scale. Three-dimensional images of the pore space are discretized using a generalized network--described in a companion paper [A. Q. Raeini, B. Bijeljic, and M. J. Blunt, Phys. Rev. E 96, 013312 (2017)]--which comprises pores that are divided into smaller elements called half-throats and subsequently into corners. Half-throats define the connectivity of the network at the coarsest level, connecting each pore to half-throats of its neighboring pores from their narrower ends, while corners define the connectivity of pore crevices. The corners are discretized at different levels for accurate calculation of entry pressures, fluid volumes, and flow conductivities that are obtained using direct simulation of flow on the underlying image. This paper discusses the two-phase flow model that is used to compute the averaged flow properties of the generalized network, including relative permeability and capillary pressure. We validate the model using direct finite-volume two-phase flow simulations on synthetic geometries, and then present a comparison of the model predictions with a conventional pore-network model and experimental measurements of relative permeability in the literature. [ABSTRACT FROM AUTHOR]

Based on energy balance during two-phase displacement in porous media, it has recently been shown that a thermodynamically consistent contact angle can be determined from micro-tomography images. However, the impact of viscous dissipation on the energy balance has not been fully understood. Furthermore, it is of great importance to determine the spatial distribution of wettability. We use direct numerical simulation to validate the determination of the thermodynamic contact angle both in an entire domain and on a pore-by-pore basis. Two-phase direct numerical simulations are performed on complex 3D porous media with three wettability states: uniformly water-wet, uniformly oil-wet, and non-uniform mixed-wet. Using the simulated fluid configurations, the thermodynamic contact angle is computed, then compared with the input contact angles. The impact of viscous dissipation on the energy balance is quantified; it is insignificant for water flooding in water-wet and mixed-wet media, resulting in an accurate estimation of a representative contact angle for the entire domain even if viscous effects are ignored. An increasing trend in the computed thermodynamic contact angle during water injection is shown to be a manifestation of the displacement sequence. Furthermore, the spatial distribution of wettability can be represented by the thermodynamic contact angle computed on a pore-by-pore basis. [ABSTRACT FROM AUTHOR]

A generalized network extraction workflow is developed for parameterizing three-dimensional (3D) images of porous media. The aim of this workflow is to reduce the uncertainties in conventional network modeling predictions introduced due to the oversimplification of complex pore geometries encountered in natural porous media. The generalized network serves as a coarse discretization of the surface generated from a medial-axis transformation of the 3D image. This discretization divides the void space into individual pores and then subdivides each pore into sub-elements called half-throat connections. Each half-throat connection is further segmented into corners by analyzing the medial axis curves of its axial plane. The parameters approximating each corner--corner angle, volume, and conductivity--are extracted at different discretization levels, corresponding to different wetting layer thickness and local capillary pressures during multiphase flow simulations. Conductivities are calculated using direct single-phase flow simulation so that the network can reproduce the single-phase flow permeability of the underlying image exactly. We first validate the algorithm by using it to discretize synthetic angular pore geometries and show that the network model reproduces the corner angles accurately. We then extract network models from micro-CT images of porous rocks and show that the network extraction preserves macroscopic properties, the permeability and formation factor, and the statistics of the micro-CT images. [ABSTRACT FROM AUTHOR]

We devise an efficient methodology to provide a universal statistical description of advection-dominated dispersion (Péclet→∞) in natural porous media including carbonates. First, we investigate the dispersion of tracer particles by direct numerical simulation (DNS). The transverse dispersion is found to be essentially determined by the tortuosity and it approaches a Fickian limit within a dozen characteristic scales. Longitudinal dispersion was found to be Fickian in the limit for bead packs and superdiffusive for all other natural media inspected. We demonstrate that the Lagrangian velocity correlation length is a quantity that characterizes the spatial variability for transport. Finally, a statistical transport model is presented that sheds light on the connection between pore-scale characteristics and the resulting macroscopic transport behavior. Our computationally efficient model accurately reproduces the transport behavior in longitudinal direction and approaches the Fickian limit in transverse direction. [ABSTRACT FROM AUTHOR]

Pore-scale forces have a significant effect on the macroscopic behaviour of multiphase flow through porous media. This paper studies the effect of these forces using a new volume-of-fluid based finite volume method developed for simulating two-phase flow directly on micro-CT images of porous media. An analytical analysis of the relationship between the pore-scale forces and the Darcy-scale pressure drops is presented. We use this analysis to propose unambiguous definitions of Darcy-scale viscous pressure drops as the rate of energy dissipation per unit flow rate of each phase, and then use them to obtain the relative permeability curves. We show that this definition is consistent with conventional laboratory/field measurements by comparing our predictions with experimental relative permeability. We present single and two-phase flow simulations for primary oil injection followed by water injection on a sandpack and a Berea sandstone. The two-phase flow simulations are presented at different capillary numbers which cover the transition from capillary fingering at low capillary numbers to a more viscous fingering displacement pattern at higher capillary numbers, and the effect of capillary number on the relative permeability curves is investigated. Overall, this paper presents a new finite volume-based methodology for the detailed analysis of two-phase flow directly on micro-CT images of porous media and upscaling of the results to the Darcy scale. [ABSTRACT FROM AUTHOR]

Abstract: We present a stable numerical scheme for modelling multiphase flow in porous media, where the characteristic size of the flow domain is of the order of microns to millimetres. The numerical method is developed for efficient modelling of multiphase flow in porous media with complex interface motion and irregular solid boundaries. The Navier–Stokes equations are discretised using a finite volume approach, while the volume-of-fluid method is used to capture the location of interfaces. Capillary forces are computed using a semi-sharp surface force model, in which the transition area for capillary pressure is effectively limited to one grid block. This new formulation along with two new filtering methods, developed for correcting capillary forces, permits simulations at very low capillary numbers and avoids non-physical velocities. Capillary forces are implemented using a semi-implicit formulation, which allows larger time step sizes at low capillary numbers. We verify the accuracy and stability of the numerical method on several test cases, which indicate the potential of the method to predict multiphase flow processes. [Copyright &y& Elsevier]

We define contact angles, θ , during displacement of three fluid phases in a porous medium using energy balance, extending previous work on two-phase flow. We test if this theory can be applied to quantify the three contact angles and wettability order in pore-scale images of three-phase displacement. For three phases labelled 1, 2 and 3, and solid, s , using conservation of energy ignoring viscous dissipation (Δ a 1 s cos θ 12 - Δ a 12 - ϕ κ 12 Δ S 1) σ 12 = (Δ a 3 s cos θ 23 + Δ a 23 - ϕ κ 23 Δ S 3) σ 23 + Δ a 13 σ 13 , where ϕ is the porosity, σ is the interfacial tension, a is the specific interfacial area, S is the saturation, and κ is the fluid–fluid interfacial curvature. Δ represents the change during a displacement. The third contact angle, θ 13 can be found using the Bartell-Osterhof relationship. The energy balance is also extended to an arbitrary number of phases. X-ray imaging of porous media and the fluids within them, at pore-scale resolution, allows the difference terms in the energy balance equation to be measured. This enables wettability, the contact angles, to be determined for complex displacements, to characterize the behaviour, and for input into pore-scale models. Two synchrotron imaging datasets are used to illustrate the approach, comparing the flow of oil, water and gas in a water-wet and an altered-wettability limestone rock sample. We show that in the water-wet case, as expected, water (phase 1) is the most wetting phase, oil (phase 2) is intermediate wet, while gas (phase 3) is most non-wetting with effective contact angles of θ 12 ≈ 48 ° and θ 13 ≈ 44 ° , while θ 23 = 0 since oil is always present in spreading layers. In contrast, for the altered-wettability case, oil is most wetting, gas is intermediate-wet, while water is most non-wetting with contact angles of θ 12 = 134 ° ± ~ 10 ° , θ 13 = 119 ° ± ~ 10 ° , and θ 23 = 66 ° ± ~ 10 °. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Conservation of energy is used to derive a thermodynamically-consistent contact angle, θ t , when fluid phase 1 displaces phase 2 in a porous medium. Assuming no change in Helmholtz free energy between two local equilibrium states we find that Δ a 1 s cos θ t = κ ϕ Δ S 1 + Δ a 12 , where a is the interfacial area per unit volume, ϕ is the porosity, S is the saturation and κ the curvature of the fluid-fluid interface. The subscript s denotes the solid, and we consider changes, Δ , in saturation and area. With the advent of high-resolution time-resolved three-dimensional X-ray imaging, all the terms in this expression can be measured directly. We analyse imaging datasets for displacement of oil by water in a water-wet and a mixed-wet sandstone. For the water-wet sample, the curvature is positive and oil bulges into the brine with almost spherical interfaces. In the mixed-wet case, larger interfacial areas are found, as the oil resides in layers. The mean curvature is close to zero, but the interface tends to bulge into brine in one direction, while brine bulges into oil in the other. We compare θ t with the values measured geometrically in situ on the pore-scale images, θ g . The thermodynamic angle θ t provides a robust and consistent characterization of wettability. For the water-wet case the calculated value of θ t gives an accurate prediction of multiphase flow properties using pore-scale modelling. [ABSTRACT FROM AUTHOR]

Wettability design is of crucial importance for the optimization of multiphase flow behaviour in gas diffusion layers (GDLs) in fuel cells. The accumulation of electrochemically-generated water in the GDLs will impact fuel cell performance. Hence, it is necessary to understand multiphase displacement to design optimal pore structures and wettability to allow the rapid flow of gases and water in GDLs over a wide saturation range. This work uses high-resolution in situ three-dimensional X-ray imaging combined with a pore network model to investigate the breakthrough capillary pressure and water saturation in GDLs manufactured with different mass fractions of polytetrafluoroethylene coating: 5, 20, 40, and 60%, making them more hydrophobic. We first demonstrate that the pore network extraction method provides representative networks for the fibrous porous media examined. Then, using a pore-network flow model we simulate water invasion into initially gas-filled fibrous media, and analyze the effect of wettability on breakthrough capillary pressure and water saturation. With an appropriate pore-scale characterization of wettability, a pore network model can match experimental results and predict displacement behaviour. • Pore network modelling is extended to study fibrous materials. • The model estimates water breakthrough pressure accurately. • The model is extended to study primary imbibition and drainage in mixed-wet media. • A representative wettability can be determined to match experiment. [ABSTRACT FROM AUTHOR]

Highlights • We obtained micro scale three-dimensional images of three-phase flow in situ at high temperature and pressure in a water-wet carbonate rock. • Pore occupancy is quantified: brine, oil and gas occupy the centre of respectively small, intermediate and large pores. • Double drainage and double imbibition are visualized in three-dimensions. • Spreading oil layers and water wetting layers are observed and their thickness allows for effective flow. • Wettability and the formation of oil layers favour trapping of gas over oil when the three phases are simultaneously present in the pore space. Abstract X-ray micro-tomography is used to image the pore-scale configurations of fluid in a rock saturated with three phases - brine, oil and gas - mimicking a subsurface reservoir, at high pressure and temperature. We determine pore occupancy during a displacement sequence that involves waterflooding, gas injection and water re-injection. In the water-wet sample considered, brine occupied the smallest pores, gas the biggest, while oil occupied pores of intermediate size and is displaced by both water and gas. Double displacement events have been observed, where gas displaces oil that displaces water or vice versa. The thickness of water and oil layers have been quantified, as have the contact angles between gas and oil, and oil and water. These results are used to explain the nature of trapping in three-phase flow, specifically how oil preferentially traps gas in the presence of water. [ABSTRACT FROM AUTHOR]

This study presents a simple and robust numerical scheme to model two-phase flow in porous media where capillary forces dominate over viscous effects. The volume-of-fluid method is employed to capture the fluid-fluid interface whose dynamics is explicitly described based on a finite volume discretization of the Navier–Stokes equations. Interfacial forces are calculated directly on reconstructed interface elements such that the total curvature is preserved. The computed interfacial forces are explicitly added to the Navier–Stokes equations using a sharp formulation which effectively eliminates spurious currents. The stability and accuracy of the implemented scheme is validated on several two- and three-dimensional test cases, which indicate the capability of the method to model two-phase flow processes at the micro-scale. In particular we show how the co-current flow of two viscous fluids leads to greatly enhanced flow conductance for the wetting phase in corners of the pore space, compared to a case where the non-wetting phase is an inviscid gas. [ABSTRACT FROM AUTHOR]

• Gas flows in disconnected ganglia in mixed-wet steady-state conditions. • Intermittent gas-oil and oil-water flow is observed at low flow rates. • Gas-oil and oil-water intermittency occur in intermediate-sized pores. • No gas is trapped when water and oil are only injected at SS conditions. • Low gas relative permeability is attributed to low gas connectivity. We use three-dimensional X-ray imaging to investigate steady-state three-phase flow in a mixed-wet reservoir rock, while measuring both relative permeability and capillary pressure. Oil occupied the smallest pores, gas the biggest, while water occupied medium-sized pores. We report a distinct flow pattern, where gas flows in the form of disconnected ganglia by periodically opening critical flow pathways. Despite having capillary-controlled displacements, a significant fraction of the pore space was intermittently occupied by gas-oil and oil-water phases. Both types of intermittency occurred in intermediate-sized pores. Gas mainly displaces oil, and oil displaces water as the gas flow rate is increased, while oil displaces gas, and water displaces oil as gas flow is decreased. At the resolution of the images, no detectable gas was trapped in the rock due to its mixed-wettability which prevents either oil or water completely surrounding gas, suppressing snap-off and capillary trapping, which has significant implications for the design of gas storage in three-phase systems. [ABSTRACT FROM AUTHOR]

The effect of pore-scale heterogeneity on non-Darcy flow behaviour is investigated by means of direct flow simulations on 3-D images of a beadpack, Bentheimer sandstone and Estaillades carbonate. The critical Reynolds number indicating the cessation of the creeping Darcy flow regime in Estaillades carbonate is two orders of magnitude smaller than in Bentheimer sandstone, and is three orders of magnitude smaller than in the beadpack. It is inferred from the examination of flow field features that the emergence of steady eddies in pore space of Estaillades at elevated fluid velocities accounts for the early transition away from the Darcy flow regime. The non-Darcy coefficient β , the onset of non-Darcy flow, and the Darcy permeability for all samples are obtained and compared to available experimental data demonstrating the predictive capability of our approach. X-ray imaging along with direct pore-scale simulation of flow provides a viable alternative to experiments and empirical correlations for predicting non-Darcy flow parameters such as the β factor, and the onset of non-Darcy flow. [ABSTRACT FROM AUTHOR]