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Traditionally, steady-state relative permeability is calculated from measurements on small rock samples using Darcy's law and assuming a homogenous saturation profile and constant capillary pressure. However, these assumptions are rarely correct as local inhomogeneities exist; furthermore, the wetting phase tends to be retained at the outlet–the so-called capillary end effect. We have introduced a new method that corrects the relative permeabilities, analytically, for an inhomogeneous saturation profile along the flow direction. The only data required are the measured pressure drops for different fractional flow values, an estimate of capillary pressure, and the saturation profiles. An optimization routine is applied to find the range of relative permeability values consistent with the uncertainty in the measured pressure. Assuming a homogenous saturation profile systematically underestimates the relative permeability and this effect is most marked for media where one of the phases is strongly wetting with a noticeable capillary end effect. Relative permeabilities from seven two-phase flow experiments in centimetre-scale samples with different wettability were corrected while reconciling some hitherto apparently contradictory results. We reproduce relative permeabilities of water-wet Bentheimer sandstone that are closer to other measurements in the literature on larger samples than the original analysis. Furthermore, we find that the water relative permeability during waterflooding a carbonate sample with a wide range of pore sizes can be high, due to good connectivity through the microporosity. For mixed-wet media with lower capillary pressure and less variable saturation profiles, the corrections are less significant. [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]

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]

X-ray micro-tomography combined with a high-pressure high-temperature flow apparatus and advanced image analysis techniques were used to image and study fluid distribution, wetting states and oil recovery during low salinity waterflooding (LSW) in a complex carbonate rock at subsurface conditions. The sample, aged with crude oil, was flooded with low salinity brine with a series of increasing flow rates, eventually recovering 85% of the oil initially in place in the resolved porosity. The pore and throat occupancy analysis revealed a change in fluid distribution in the pore space for different injection rates. Low salinity brine initially invaded large pores, consistent with displacement in an oil-wet rock. However, as more brine was injected, a redistribution of fluids was observed; smaller pores and throats were invaded by brine and the displaced oil moved into larger pore elements. Furthermore, in situ contact angles and curvatures of oil–brine interfaces were measured to characterize wettability changes within the pore space and calculate capillary pressure. Contact angles, mean curvatures and capillary pressures all showed a shift from weakly oil-wet towards a mixed-wet state as more pore volumes of low salinity brine were injected into the sample. Overall, this study establishes a methodology to characterize and quantify wettability changes at the pore scale which appears to be the dominant mechanism for oil recovery by LSW. [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 predict waterflood displacement on a pore-by-pore basis using pore network modelling. The pore structure is captured by a high-resolution image. We then use an energy balance applied to images of the displacement to assign an average contact angle, and then modify the local pore-scale contact angles in the model about this mean to match the observed displacement sequence. Two waterflooding experiments on oil-wet rocks are analysed where the displacement sequence was imaged using time-resolved synchrotron imaging. In both cases the capillary pressure in the model matches the experimentally obtained values derived from the measured interfacial curvature. We then predict relative permeability for the full saturation range. Using the optimised contact angles distributed randomly in space has little effect on the predicted capillary pressures and relative permeabilities, indicating that spatial correlation in wettability is not significant in these oil-wet samples. The calibrated model can be used to predict properties outside the range of conditions considered in the experiment. [ABSTRACT FROM AUTHOR]

Rapid implementation of global scale carbon capture and storage is required to limit temperature rises to 1.5 °C this century. Depleted oilfields provide an immediate option for storage, since injection infrastructure is in place and there is an economic benefit from enhanced oil recovery. To design secure storage, we need to understand how the fluids are configured in the microscopic pore spaces of the reservoir rock. We use high-resolution X-ray imaging to study the flow of oil, water and CO2 in an oil-wet rock at subsurface conditions of high temperature and pressure. We show that contrary to conventional understanding, CO2 does not reside in the largest pores, which would facilitate its escape, but instead occupies smaller pores or is present in layers in the corners of the pore space. The CO2 flow is restricted by a factor of ten, compared to if it occupied the larger pores. This shows that CO2 injection in oilfields provides secure storage with limited recycling of gas; the injection of large amounts of water to capillary trap the CO2 is unnecessary. [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]

To examine the need to incorporate in situ wettability measurements in direct numerical simulations, we compare waterflooding experiments in a mixed-wet carbonate from a producing reservoir and results of direct multiphase numerical simulations using the color-gradient lattice Boltzmann method. We study the experiments of Alhammadi et al. (Sci Rep 7(1):10753, 2017. 10.1038/s41598-017-10992-w) where the pore-scale distribution of remaining oil was imaged using micro-CT scanning. In the experiment, in situ contact angles were measured using an automated algorithm (AlRatrout et al. in Adv Water Resour 109:158-169, 2017. 10.1016/j.advwatres.2017.07.018), which indicated a mixed-wet state with spatially non-uniform angles. In our simulations, the pore structure was obtained from segmented images of the sample used in the experiment. Furthermore, in situ measured angles were also incorporated into our simulations using our previously developed wetting boundary condition (Akai et al. in Adv Water Resour 116(March):56-66, 2018. 10.1016/j.advwatres.2018.03.014). We designed six simulations with different contact angle assignments based on experimentally measured values. Both a constant contact angle based on the average value of the measured values and non-uniform contact angles informed by the measured values gave a good agreement for fluid pore occupancy between the simulation and the experiment. However, the constant contact angle assignment predicted 54% higher water effective permeability after waterflooding than that estimated for the experimental result, whereas the non-uniform contact angle assignment gave less than 1% relative error. This means that to correctly predict fluid conductivity in mixed-wet rocks, a spatially heterogeneous wettability state needs to be taken into account. The novelty of this work is to provide a direct pore-scale comparison between experiments and simulations employing experimentally measured contact angles, and to demonstrate how to use measured contact angle data to improve the predictability of direct numerical simulation, highlighting the difference between the contact angle required for the simulation of dynamic displacement process and the contact angle measured at equilibrium after waterflooding. [ABSTRACT FROM AUTHOR]

Fast synchrotron-based X-ray microtomography was used to image the injection of super-critical $$\hbox {CO}_{2}$$ under subsurface conditions into a brine-saturated carbonate sample at the pore-scale with a voxel size of $$3.64\,\upmu \hbox {m}$$ and a temporal resolution of 45 s. Capillary pressure was measured from the images by finding the curvature of terminal menisci of both connected and disconnected $$\hbox {CO}_{2}$$ clusters. We provide an analysis of three individual dynamic drainage events at elevated temperatures and pressures on the tens of seconds timescale, showing non-local interface recession due to capillary pressure change, and both local and distal (non-local) snap-off. The measured capillary pressure change is not sufficient to explain snap-off in this system, as the disconnected $$\hbox {CO}_{2}$$ has a much lower capillary pressure than the connected $$\hbox {CO}_{2}$$ both before and after the event. Disconnected regions instead preserve extremely low dynamic capillary pressures generated during the event. Snap-off due to these dynamic effects is not only controlled by the pore topography and throat radius, but also by the local fluid arrangement. Whereas disconnected fluid configurations produced by local snap-off were rapidly reconnected with the connected $$\hbox {CO}_{2}$$ region, distal snap-off produced much more long-lasting fluid configurations, showing that dynamic forces can have a persistent impact on the pattern and sequence of drainage events. [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 apply an accurate numerical scheme to solve for Stokes flow directly on binarized three-dimensional rock images, such as those obtained by micro-CT imaging. The method imposes no-flow conditions exactly at the solid boundaries and employs an algebraic multigrid method to solve for the resultant set of linear equations. We compute the permeability of a range of consolidated and unconsolidated porous rocks; the results are comparable with those obtained using the lattice Boltzmann method and agree with experimental measurements on larger core samples. We show that the Kozeny-Carman equation can over-estimate permeability by a factor of 10 or more, particularly for the more heterogeneous systems studied. We study the existence and size of the representative elementary volume (REV) at lamina scale. We demonstrate that the REV for permeability is larger than for static properties-porosity and specific surface area-since it needs to account for the tortuosity and connectedness of the flow paths. For the carbonate samples, the REV appeared to be larger than the image size. We also study the anisotropy of permeability at the pore scale. We show that the permeability of sandpacks varies by less than 10 % in different directions. For sandstones, permeability changes by 25 % on average. However, the anisotropy of permeability in carbonates can be up to 50 %, indicating the existence of connected pores in one direction which are not connected in another. [ABSTRACT FROM AUTHOR]