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While it is known that changing the salinity of the brine used to displace oil in porous rock can lead to additional recovery, the mechanism by which this occurs at the pore scale is still not fully understood. We investigate whether the emulsification of oil is the process by which recovery is improved, removing oil from the solid surface and rendering the rock more water-wet. High-resolution three-dimensional X-ray imaging was used to visualize the emulsification kinetics during secondary and tertiary low salinity waterflooding in a carbonate reservoir rock. The rock samples were imaged during water flooding, where the salinity of the injected brine was much lower than that of the formation water. An intermediate phase that appeared to be a mixture of oil and brine, and which we hypothesize is an emulsion, was imaged in both tertiary and secondary low salinity waterflooding experiments. The formation of this intermediate phase is observed to be the preliminary step prior to oil mobilization. Gray-level histograms and pore occupancy maps showed a faster displacement of oil in the secondary mode compared to tertiary flooding where the emulsified oil remained in the sample for longer before displacement.

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. 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. 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 A gradient information enhanced segmentation method is presented to assist automatic contact angle measurements The gradient information method reduces the problems associated with low image resolution and manual segmentation

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. 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 A dilation‐based algorithm adds sub‐resolution porosity, quantified by differential imaging, as microlinks to an extracted pore network Empirical models are used to characterize the flow properties of microlinks The tuned multiscale network, using permeability, formation factor, and capillary pressure, matches experimental relative permeability

Drill bit wear reduces drilling efficiency and escalates operational risks. The drill bit tooth wear grading is a measure of lost tooth height. Accurate monitoring of drill bit tooth wear grade is crucial to adjust drilling parameters and plan timely bit replacement, significantly enhancing drilling efficiency and safety. Current real-time monitoring methods for drill bit wear exhibit limitations, particularly in accounting for variations in the geological formation and drilling parameters, resulting in poor model stability. This paper proposes an intelligent modeling approach that utilizes a Domain Adaptation Neural Network (DANN) to establish an ideal drilling rate of penetration (ROP) prediction model. By incorporating measured ROP, wear coefficients are calculated, and a relationship between wear coefficient and tooth wear grade is established, facilitating real-time monitoring of drill bit tooth wear grade. Test results on ten drill bits demonstrate that the DANN ideal ROP prediction model, leveraging data from new drill bits, enhances the model's adaptability to varying working conditions for new drill bits, thereby improving the accuracy of ideal ROP predictions. We establish relationship between calculated wear coefficients and tooth wear grades. The results indicate that the average error in inner wear grade is 0.6 (7.5%) and the average error in outer wear grade is 1.3 (16%) on an 8-point scale which demonstrates the model's effectiveness in monitoring drill bit tooth wear.

We study the impact of physical and chemical heterogeneity on reaction rates in multimineral porous media. We selected two pairs of carbonate samples of different physical heterogeneity in accordance with their initial computed velocity distributions and then injected CO2saturated brine at reservoir conditions at two flow rates. We periodically imaged the samples using X‐ray microtomography. The mineralogical composition was similar (a ratio of dolomite to calcite of 8:1), but the intrinsic reaction rates and mineral spatial distribution were profoundly different. Visualizations of velocity fields and reacted mineral distributions revealed that a dominant flow channel formed in all cases. The more physically homogeneous samples had a narrower velocity distribution and more preexisting fast channels, which promoted dominant channel formation in their proximity. In contrast, the heterogeneous samples exhibit a broader distribution of velocities and fewer fast channels, which accentuated nonuniform calcite distribution and favored calcite dissolution away from the initially fast pathways. We quantify the impact of physical and chemical heterogeneity by computing the proximity of reacted minerals to the fast flow pathways. The average reaction rates were an order of magnitude lower than the intrinsic ones due to mass transfer limitations. The effective reaction rate of calcite decreased by an order of magnitude, in both fast channels and slow regions. After channel formation calcite was shielded by dolomite whose effective rate in slow regions could even increase. Overall, the preferential channeling effect, as opposed to uniform dissolution, was promoted by a higher degree of physical and/or chemical heterogeneity. A screening method was employed to study impact of physical and chemical heterogeneity on reaction rates for multimineral rocksThe proximity of reacted minerals to fast flow pathways is a key determinant of reaction dynamicsThe preferential channeling, as opposed to uniform dissolution, was promoted by a higher degree of physical and/or chemical heterogeneity

We propose a spatial Markov model to simulate transport in three‐dimensional complex porous media flows. Our methodology is inspired by the concept of training images from geostatistics. Instead of using a training image we use highly resolved training trajectories obtained by high‐resolution particle tracking, from which we sample increments in our random walk model. To reflect higher‐order processes, subsequent increments are correlated. The approach can be split into three steps. First, we subdivide (cut) the training trajectories to form an archive of trajectory segments. Next, we recursively sample segments, where subsequent samples are chosen conditioned to the previous one to ensure continuity and smoothness of velocity (conditional copy). Finally, we merge (paste) consecutive segments together to generate simulated trajectories of arbitrary length. This training trajectory approach aims to overcome three common shortcomings of spatial Markov models: (1) We simulate finite‐Péclet transport in three dimensions without commonly made simplifications (e.g., dimensionality reduction, and neglecting diffusion). (2) We do not parameterize dependence via a high‐dimensional transition matrix. (3) We simulate transport at the resolution of the (highly resolved) training trajectories, which can be important for processes such as mixing and reaction. To validate our methodology, we apply it to simulate transport within a three‐dimensional sandstone sample and compare predictions of a broad range of benchmark metrics against measurements from direct numerical simulations. We demonstrate that the training trajectories approach accurately represents three‐dimensional particle motion, suggesting that this method can capture the governing dependence structure and simulate transport processes in full complexity. We propose a data‐driven spatial Markov model to effectively simulate transport in 3‐D without common simplificationsWe capture process dependence by a systematic rearrangement of highly resolved training trajectoriesWe simulate transport at the resolution of these highly resolved training trajectories

There are a number of challenges associated with the determination of relative permeability and capillary pressure. It is difficult to measure both parameters simultaneously on the same sample using conventional methods. Instead, separate measurements are made on different samples, usually with different flooding protocols. Hence, it is not certain that the pore structure and displacement processes used to determine relative permeability are the same as those when capillary pressure was measured. Moreover, at present, we do not use pore‐scale information from high‐resolution imaging to inform multiphase flow properties directly. We introduce a method using pore‐scale imaging to determine capillary pressure from local interfacial curvature. This, in combination with pressure drop measurements, allows both relative permeabilities and capillary pressure to be determined during steady state coinjection of two phases through the core. A steady state waterflood experiment was performed in a Bentheimer sandstone, where decalin and brine were simultaneously injected through the core at increasing brine fractional flows from 0 to 1. The local saturation and the curvature of the oil‐brine interface were determined. Using the Young‐Laplace law, the curvature was related to a local capillary pressure. There was a detectable gradient in both saturation and capillary pressure along the flow direction. The relative permeability was determined from the experimentally measured pressure drop and average saturation obtained by imaging. An analytical correction to the brine relative permeability could be made using the capillary pressure gradient. The results for both relative permeability and capillary pressure are consistent with previous literature measurements on larger samples. The local capillary pressure was measured and quantified during imbibition using a pore‐scale curvature‐based image analysisThe relative permeability was found from the measured pressure drop with an analytical correction for the capillary pressure gradientThe capillary pressure and relative permeability can be measured directly and simultaneously in the flow experiment

We study the in situ distributions of contact angle and oil/brine interface curvature measured within millimeter‐sized rock samples from a producing hydrocarbon carbonate reservoir imaged after waterflooding using X‐ray microtomography. We analyze their spatial correlation combining automated methods for measuring contact angles and interfacial curvature (AlRatrout et al., 2017, https://doi.org/10.1016/j.advwatres.2017.07.018), with a recently developed method for pore‐network extraction (Raeini et al., 2017, https://doi.org/10.1103/PhysRevE.96.013312). The automated methods allow us to study image volumes of diameter approximately 1.9 mm and 1.2 mm long, obtaining hundreds of thousands of values from a data set with 435 million voxels. We calculate the capillary pressure based on the mode oil/brine interface curvature value and associate this value with a nearby throat in the pore space. We demonstrate the capability of our methods to distinguish different wettability states in the samples studied: water‐wet, weakly oil‐wet, and mixed‐wet. The contact angle and oil/brine interface curvature are spatially correlated over approximately the scale of an average pore. There is a wide distribution of contact angles within a single pore. A range of local oil/brine interface curvature is found with both positive and negative values. There is a correlation between interfacial curvature and contact angle in trapped ganglia, with ganglia in water‐wet patches tending to have a positive curvature and oil‐wet regions seeing negative curvature. We observed a weak correlation between average contact angle and pore size, with the larger pores tending to be more oil‐wet. This research article concerns the pore‐scale characterization of wettability. A novel method has been developed to automatically extract contact angles and fluid/fluid interface curvature from pore‐space images (AlRatrout et al., 2017). The method has been successfully tested on benchmark synthetic images for which the contact angle and curvature are known analytically and has been applied to a real rock data set. Both a water‐wet and a mixed‐wet rock have been analyzed. Further, the method has been utilized to study the spatial correlation of the in situ measured distributions of contact angles and oil/brine interface curvatures within the reservoir rock samples at subsurface conditions used in Alhammadi et al. (2017, https://doi.org/10.1038/s41598-017-10992-w). We relate the measurements of contact angle and interfacial curvature (capillary pressure) to individual trapped ganglia of oil and to the pore sizes extracted by a generalized pore‐network modeling approach (Raeini et al., 2017). Our findings and analysis could potentially have implications for pore‐scale modeling of multiphase flow, in which methods using local curvature measurements could be directly used to calculate capillary pressures for displacement. Analysis of in situ measurements of contact angle and curvature from pore‐space images on rocks at reservoir conditions is performedContact angle and curvature are correlated over approximately a pore sizeContact angle appears uncorrelated with local curvature and throat sizeContact angle and curvature are correlated on a ganlglion‐by‐ganlgion basis

We imaged the steady state flow of brine and decane in Bentheimer sandstone. We devised an experimental method based on differential imaging to examine how flow rate impacts impact the pore‐scale distribution of fluids during coinjection. This allows us to elucidate flow regimes (connected, or breakup of the nonwetting phase pathways) for a range of fractional flows at two capillary numbers, Ca, namely 3.0 × 10−7and 7.5 × 10−6. At the lower Ca, for a fixed fractional flow, the two phases appear to flow in connected unchanging subnetworks of the pore space, consistent with conventional theory. At the higher Ca, we observed that a significant fraction of the pore space contained sometimes oil and sometimes brine during the 1 h scan: this intermittent occupancy, which was interpreted as regions of the pore space that contained both fluid phases for some time, is necessary to explain the flow and dynamic connectivity of the oil phase; pathways of always oil‐filled portions of the void space did not span the core. This phase was segmented from the differential image between the 30 wt % KI brine image and the scans taken at each fractional flow. Using the grey scale histogram distribution of the raw images, the oil proportion in the intermittent phase was calculated. The pressure drops at each fractional flow at low and high flow rates were measured by high‐precision differential pressure sensors. The relative permeabilities and fractional flow obtained by our experiment at the mm‐scale compare well with data from the literature on cm‐scale samples. Differential imaging of fluid configurations during steady state brine/decane fractional flow coinjection at low and high capillary numbersAt low Canumber the two phases flow in their own connected pathways as expected, while an intermittent phase was observed at high CanumberThe relative permeability measured on our mm‐scale core shows a good agreement with conventional experiments on cm‐sized systems

Remobilization of residually trapped CO2can occur under pressure depletion, caused by any sort of leakage, brine extraction for pressure maintenance purposes, or simply by near wellbore pressure dissipation once CO2injection has ceased. This phenomenon affects the long‐term stability of CO2residual trapping and should therefore be considered for an accurate assessment of CO2storage security. In this study, pore‐network modeling is performed to understand the relevant physics of remobilization. Gas remobilization occurs at a higher gas saturation than the residual saturation, the so‐called critical saturation; the difference is called the mobilization saturation, a parameter that is a function of the network properties and the mechanisms involved. Regardless of the network type and properties, Ostwald ripening tends to slightly increase the mobilization saturation, thereby enhancing the security of residual trapping. Moreover, significant hysteresis and reduction in gas relative permeability is observed, implying slow reconnection of the trapped gas clusters. These observations are safety enhancing features, due to which the remobilization of residual CO2is delayed. The results, consistent with our previous analysis of the field‐scale Heletz experiments, have important implications for underground gas and CO2storage. In the context of CO2storage, they provide important insights into the fate of residual trapping in both the short and long term. Remobilization of residually trapped gas occurs at a higher saturation than residual saturation, called the critical gas saturationOstwald ripening tends to slightly increase the mobilization saturationThe relative permeability of remobilized gas is significantly reduced, which adds to the security of residual trapping Remobilization of residually trapped gas occurs at a higher saturation than residual saturation, called the critical gas saturation Ostwald ripening tends to slightly increase the mobilization saturation The relative permeability of remobilized gas is significantly reduced, which adds to the security of residual trapping

The experimental determination of capillary pressure drainage curves at the pore scale is of vital importance for the mapping of reservoir fluid distribution. To fully characterize capillary drainage in a complex pore space, we design a differential imaging‐based porous plate (DIPP) method using X‐ray microtomography. For an exemplar mm‐scale laminated sandstone microcore with a porous plate, we quantify the displacement from resolvable macropores and subresolution micropores. Nitrogen (N2) was injected as the nonwetting phase at a constant pressure while the porous plate prevented its escape. The measured porosity and capillary pressure at the imaged saturations agree well with helium measurements and experiments on larger core samples, while providing a pore‐scale explanation of the fluid distribution. We observed that the majority of the brine was displaced by N2in macropores at low capillary pressures, followed by a further brine displacement in micropores when capillary pressure increases. Furthermore, we were able to discern that brine predominantly remained within the subresolution micropores, such as regions of fine lamination. The capillary pressure curve for pressures ranging from 0 to 1151 kPa is provided from the image analysis compares well with the conventional porous plate method for a cm‐scale core but was conducted over a period of 10 days rather than up to few months with the conventional porous plate method. Overall, we demonstrate the capability of our method to provide quantitative information on two‐phase saturation in heterogeneous core samples for a wide range of capillary pressures even at scales smaller than the micro‐CT resolution. A differential imaging‐based porous plate method is devised to visualize brine distribution during capillary drainage with micro‐CTThe sequence of capillary‐controlled pore filling in a laminated sandstone is determined with a pore‐scale interpretation of displacementThe capillary pressure measurements agree with porous plate experiments on a larger core but with much shorter experimental time

Rock heterogeneity plays an important role in solute spreading and mixing in hydrogeologic systems. Few observations, however, have been made that can spatially resolve these processes in 3‐D, in consolidated rocks. We make observations of the spatially resolved steady state concentration of a sodium iodide solute while flowing brine through cylindrical rock cores using X‐ray CT imaging. Three rocks with an increasing level of heterogeneity are chosen: a Berea sandstone, a Ketton carbonate, and an Indiana carbonate. The impact of heterogeneity on solute transport is analyzed by: (1) quantifying spreading and mixing using metrics such as the transverse dispersion coefficient, the dilution index, the reactor ratio, and the scalar dissipation rate and (2) visualizing and analyzing flow structures such as meandering, flow‐focusing, and flow‐splitting using isoconcentration contour maps. The transverse dispersion coefficient, Dt, and the variation in Dtthroughout the rock core, increases with Peclét number (Pe) and rock heterogeneity. The reactor ratio indicates that mixing is Fickian for the Berea sandstone and Ketton carbonate, but diverges for the Indiana carbonate. The temporal evolution of the scalar dissipation rate, a measure of the mixing rate, remains close to that of Fickian mixing for the Berea and Ketton rocks but not for the Indiana. Heterogeneous rock features are observed to cause meandering, focusing, or splitting of the plume depending on Pe. We have imaged transverse spreading and mixing in 3‐D in heterogeneous rock cores using X‐ray CTSpatially resolved observations of solute in 3‐D rock samples show an increase of Dtwith Pe and rock heterogeneityReactor ratio and scalar dissipation rate show either Fickian or non‐Fickian behavior depending on heterogeneity

We use high‐resolution three‐dimensional X‐ray imaging to study hydrogen injection and withdrawal in the pore space of Bentheimer sandstone. The results are compared with a replicate experiment using nitrogen. We observe less trapping with hydrogen because the initial saturation after drainage is lower due to channeling. Remarkably we observe that after imbibition, if the sample is imaged again after 12 hr, there is a significant rearrangement of the trapped hydrogen. Many smaller ganglia disappear while the larger ganglia swell, with no detectable change in overall gas volume. For nitrogen, the fluid configuration is largely unchanged. This rearrangement is facilitated by concentration gradients of dissolved gas in the aqueous phase—Ostwald ripening, We estimate the time‐scales for this effect to be significant, consistent with the experimental observations. The swelling of larger ganglia potentially increases the gas connectivity, leading to less hysteresis and more efficient withdrawal. The supply of energy by hydrogen is a key component of a zero‐carbon economy; an essential part of global hydrogen use is underground storage at the gigatonne scale in porous rocks. However, the behavior of hydrogen in the subsurface is not well understood. Using high‐resolution three‐dimensional X‐ray imaging, we observe that in the pore‐space, there is a significant rearrangement of hydrogen trapped by water. Many smaller trapped bubbles disappear while the larger ones grow. The process is driven by differences in the amount of gas dissolved in the aqueous phase: this is called Ostwald ripening. We estimate the time‐scales effect as being important, which are consistent with the experimental observations. The work implies that there is less trapping for hydrogen injection and withdrawal compared to equivalent hydrocarbon systems, which makes the process efficient. Hydrogen trapping and rearrangement in porous rock have been observed in situOstwald ripening is observed over timescales consistent with theoretical predictionsThe results imply less trapping and hysteresis than with completely insoluble gas Hydrogen trapping and rearrangement in porous rock have been observed in situ Ostwald ripening is observed over timescales consistent with theoretical predictions The results imply less trapping and hysteresis than with completely insoluble gas

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. 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 Quasi 2D representations of interfacial curvature present in network modeling of multiphase flow are extended to three dimensions A fully 3D representation of curvature is needed for network models to reproduce the behavior of direct simulations and experiments Correct predictions of trapping and relative permeability with network modeling rely on a physically accurate inclusion of curvature

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. The root of non-Fickianity is preferential flow at the small-scale and stagnant zones at larger-scaleCross-directional dependence is highly nonlinear and persistent over time although it is usually neglectedDependence is weaker but the memory shows stronger temporal persistence under higher-Péclet conditions

The structure and connectivity of the pore space during the pyrolysis of oil shales determines hydrocarbon flow behavior and ultimate recovery. We image the time evolution of the pore and microfracture networks during oil shale pyrolysis using synchrotron X‐ray microtomography. Immature Green River (Mahogany Zone) shale samples were thermally matured under vacuum conditions at temperatures up to 500°C while being periodically imaged with a 2 µm voxel size. The structural transformation of both organic‐rich and organic‐lean layers within the shale was quantified. The images reveal a dramatic change in porosity accompanying pyrolysis between 390 and 400°C with the formation of micron‐scale heterogeneous pores. With a further increase in temperature, the pores steadily expand resulting in connected microfracture networks that predominantly develop along the kerogen‐rich laminations. Dynamic oil shale imaging under pyrolysis conditions is performed using synchrotron X‐ray microtomography3‐D visualization and quantification of the pore space is performed as a function of temperature and time in organic‐rich and organic‐lean regionsMicroscale disconnected pores are first observed at 390 degrees Celsius; the porosity increases dramatically between 390 and 400 degrees Celsius and becomes connected

We have investigated the effect of wettability of carbonate rocks on the morphologies of remaining oil after sequential oil and brine injection in a capillary-dominated flow regime at elevated pressure. The wettability of Ketton limestone was altered in situ using an oil phase doped with fatty acid which produced mixed-wet conditions (the contact angle where oil contacted the solid surface, measured directly from the images, ?=180°, while brine-filled regions remained water-wet), whereas the untreated rock (without doped oil) was weakly water-wet (?=47?±?9°). Using X-ray micro-tomography, we show that the brine displaces oil in larger pores during brine injection in the mixed-wet system, leaving oil layers in the pore corners or sandwiched between two brine interfaces. These oil layers, with an average thickness of 47?±?17 µm, may provide a conductive flow path for slow oil drainage. In contrast, the oil fragments into isolated oil clusters/ganglia during brine injection under water-wet conditions. Although the remaining oil saturation in a water-wet system is about a factor of two larger than that obtained in the mixed-wet rock, the measured brine-oil interfacial area of the disconnected ganglia is a factor of three smaller than that of oil layers. Mixed-wet conditions were obtained by chemical treatment of the carbonate rockX-ray micro-tomography was used to resolve oil layers in oil-wet pores and throatsIn situ contact angle, brine-oil curvatures and local capillary pressure were measured

We study the nature of non‐Fickian particle transport in 3‐D porous media by simulating fluid flow in the intricate pore space of real rock. We solve the full Navier‐Stokes equations at the same resolution as the 3‐D micro‐CT (computed tomography) image of the rock sample and simulate particle transport along the streamlines of the velocity field. We find that transport at the pore scale is markedly anomalous: longitudinal spreading is superdiffusive, while transverse spreading is subdiffusive. We demonstrate that this anomalous behavior originates from the intermittent structure of the velocity field at the pore scale, which in turn emanates from the interplay between velocity heterogeneity and velocity correlation. Finally, we propose a continuous time random walk model that honors this intermittent structure at the pore scale and captures the anomalous 3‐D transport behavior at the macroscale. We study flow and transport in 3‐D porous media at the pore scaleLongitudinal spreading is superdiffusive; transverse spreading is subdiffusiveAnomalous behavior originates from the intermittent structure of the velocity

Transport computed through micro‐CT images of six carbonate rocks is anomalousHighly anomalous transport is explained by the wide local velocity distributionThe effect of pore structure and Peclet number is quantified We study and explain the origin of early breakthrough and long tailing plume behavior by simulating solute transport through 3‐D X‐ray images of six different carbonate rock samples, representing geological media with a high degree of pore‐scale complexity. A Stokes solver is employed to compute the flow field, and the particles are then transported along streamlines to represent advection, while the random walk method is used to model diffusion. We compute the propagators (concentration versus displacement) for a range of Peclet numbers (Pe) and relate it to the velocity distribution obtained directly on the images. There is a very wide distribution of velocity that quantifies the impact of pore structure on transport. In samples with a relatively narrow spread of velocities, transport is characterized by a small immobile concentration peak, representing essentially stagnant portions of the pore space, and a dominant secondary peak of mobile solute moving at approximately the average flow speed. On the other hand, in carbonates with a wider velocity distribution, there is a significant immobile peak concentration and an elongated tail of moving fluid. An increase in Pe, decreasing the relative impact of diffusion, leads to the faster formation of secondary mobile peak(s). This behavior indicates highly anomalous transport. The implications for modeling field‐scale transport are discussed.

We use high‐resolution three‐dimensional X‐ray microtomography to investigate fluid displacement during steady‐state three‐phase flow in a cm‐sized water‐wet sandstone rock sample. The pressure differential across the sample is measured which enables the determination of relative permeability; capillary pressure is also estimated from the interfacial curvature. Though the measured relative permeabilities are consistent, to within experimental uncertainty, with values obtained without imaging on larger samples, we discover a unique flow dynamics. The most non‐wetting phase (gas) is disconnected across the system: gas flows by periodically opening critical flow pathways in intermediate‐sized pores. While this phenomenon has been observed in two‐phase flow, here it is significant at low flow rates, where capillary forces dominate at the pore‐scale. Gas movement proceeds in a series of double and multiple displacement events. Implications for the design of three‐phase flow processes and current empirical models are discussed: the traditional conceptualization of three‐phase dynamics based on analogies to two‐phase flow vastly over‐estimates the connectivity and flow potential of the gas phase. Gas flow is disconnected at steady‐state conditions, explaining the low gas relative permeability seen in this water‐wet three‐phase systemIntermittent gas‐oil flow is observed in intermediate‐sized pores despite flowing at low flowrates, where capillary forces are dominantThe traditional use of two‐phase data to predict three‐phase flow vastly over‐estimates the connectivity and mobility of the gas phase Gas flow is disconnected at steady‐state conditions, explaining the low gas relative permeability seen in this water‐wet three‐phase system Intermittent gas‐oil flow is observed in intermediate‐sized pores despite flowing at low flowrates, where capillary forces are dominant The traditional use of two‐phase data to predict three‐phase flow vastly over‐estimates the connectivity and mobility of the gas phase

We applied three‐dimensional X‐ray microtomography to image a capillary drainage process (0–1,000 kPa) in a cm‐scale heterogeneous laminated sandstone containing three distinct regions with different pore sizes to study the capillary pressure. We used differential imaging to distinguish solid, macropore, and five levels of subresolution pore phases associated with each region. The brine saturation distribution was computed based on average CT values. The nonwetting phase displaced the wetting phase in order of pore size and connectivity. The drainage capillary pressure in the highly heterogeneous rock was dependent on the capillary pressures in the individual regions as well as distance to the boundary between regions. The complex capillary pressure distribution has important implications for accurate water saturation estimation, gas and/or oil migration and the capillary rise of water in heterogeneous aquifers. Carbon‐dioxide storage, hydrocarbon migration, and the capillary rise of water in heterogeneous aquifers and reservoirs are all controlled by capillary pressure. The capillary pressure varies dependent on the pore‐space heterogeneity. We used X‐ray microtomography to image capillary drainage in a laminated sandstone as an exemplar of a highly heterogeneous rock. The distribution of capillary pressure and pore‐scale configuration of fluid during displacement were measured and related to distinct heterogeneities in the rock. Differential imaging is used to characterize the larger macropores and subresolution porosity. We show that fluid displacement is controlled by pore size, connectivity, and proximity to the boundaries between regions with different pore‐space characteristics. Our study demonstrates how to characterize the complex capillary pressure distribution and fluid displacement in highly heterogeneous porous media. The pore space, including subresolution pores, was divided into three regions with different heterogeneity for a laminated sandstoneThe capillary pressure distribution, influenced by pore size and connectivity, had distinct displacement behavior in different regionsThe trends in capillary pressure and displacement were measured across the boundaries between regions The pore space, including subresolution pores, was divided into three regions with different heterogeneity for a laminated sandstone The capillary pressure distribution, influenced by pore size and connectivity, had distinct displacement behavior in different regions The trends in capillary pressure and displacement were measured across the boundaries between regions

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. 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. 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 Flow rate and pressure gradient during steady‐state multiphase flow are measured experimentally The transition to a non‐Darcy flow regime is quantified and predicted theoretically The theory makes accurate predictions for several rock types, fractional flows, and mobility ratios

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. 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

We use fast synchrotron X‐ray microtomography to understand three‐phase flow in mixed‐wet porous media to design either enhanced permeability or capillary trapping. The dynamics of these phenomena are of key importance in subsurface hydrology, carbon dioxide storage, oil recovery, food and drug manufacturing, and chemical reactors. We study the dynamics of a water‐gas‐water injection sequence in a mixed‐wet carbonate rock. During the initial waterflooding, water displaced oil from pores of all size, indicating a mixed‐wet system with local contact angles both above and below 90°. When gas was injected, gas displaced oil preferentially with negligible displacement of water. This behavior is explained in terms of the gas pressure needed for invasion. Overall, gas behaved as the most nonwetting phase with oil as the most wetting phase; however, pores of all size were occupied by oil, water, and gas, as a signature of mixed‐wet media. Thick oil wetting layers were observed, which increased oil connectivity and facilitated its flow during gas injection. A chase waterflooding resulted in additional oil flow, while gas was trapped by oil and water. Furthermore, we quantified the evolution of the surface areas and both Gaussian and the total curvature, from which capillary pressure could be estimated. These quantities are related to the Minkowski functionals which quantify the degree of connectivity and trapping. The combination of water and gas injection, under mixed‐wet immiscible conditions, leads to both favorable oil flow and significant trapping of gas, which is advantageous for storage applications. We use synchrotron X‐ray microtomography to quantify dynamics of three‐phase flow and trapping in porous mediaThe wettability order for immiscible three‐phase flow in a mixed‐wet rock was oil‐water‐gas from the most to the least wetting phaseOil flow and gas trapping were measured using topological descriptors and were found to be both favored by the wettability alteration

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. 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