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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]

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]

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]

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]

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. Plain Language Summary: 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. Key Points: 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 [ABSTRACT FROM AUTHOR]

In the color gradient lattice Boltzmann model (CG-LBM), a fictitious-density wetting boundary condition has been widely used because of its ease of implementation. However, as we show, this may lead to inaccurate results in some cases. In this paper, a new scheme for the wetting boundary condition is proposed which can handle complicated 3D geometries. The validity of our method for static problems is demonstrated by comparing the simulated results to analytical solutions in 2D and 3D geometries with curved boundaries. Then, capillary rise simulations are performed to study dynamic problems where the three-phase contact line moves. The results are compared to experimental results in the literature (Heshmati and Piri, 2014). If a constant contact angle is assumed, the simulations agree with the analytical solution based on the Lucas–Washburn equation. However, to match the experiments, we need to implement a dynamic contact angle that varies with the flow rate. [ABSTRACT FROM AUTHOR]

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, θ=180°, while brine-filled regions remained water-wet), whereas the untreated rock (without doped oil) was weakly water-wet (θ=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. [ABSTRACT FROM AUTHOR]

Highlights: [•] A new method for the extraction of contact angle from micro-CT images is presented. [•] This method is applied to the CO2–brine–water system at 10MPa and 50°C. [•] A distribution of contact angles is seen, ranging from 35° to 55° with a mean of 45°. [•] The range arises from surface roughness variation and contact angle relaxation. [•] Measurement error is analysed and found to be small for this system. [ABSTRACT FROM AUTHOR]

• In this oil-wet carbonate, micro-porosity plays a crucial role in flow connectivity. • The displacement is characterised by a thermodynamic contact angle of 120°. • The flow behaviour is different from a mixed-wet sandstone with angle close to 95°. • The carbonate case has a high brine rel-perm and a large/negative capillary pressure. High-resolution X-ray imaging combined with a steady-state flow experiment is used to demonstrate how pore-scale displacement affects macroscopic properties in an altered-wettability microporous carbonate, where porosity and fluid saturation can be directly obtained from the grey-scale micro-CT images. The resolvable macro pores are largely oil-wet with an average thermodynamic contact angle of 120°. The pore-by-pore analysis shows locally either oil or brine almost fully occupied the macro pores, with some oil displacement in the micro-porosity. We observed a typical oil-wet behaviour consistent with the contact angle measurement. The brine tended to occupy the larger macro pores, leading to a higher brine relative permeability, lower residual oil saturation, than under water-wet conditions and in a mixed-wet sandstone. The capillary pressure was negative and seven times larger in the carbonate than the sandstone, despite having a similar average pore size. These different displacement patterns are principally determined by the difference in wettability. [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]

The development of high-resolution in situ imaging has allowed contact angles to be measured directly inside porous materials. We evaluate the use of concepts in integral geometry to determine contact angle. Specifically, we test the hypothesis that it is possible to determine an average contact angle from measurements of the Gaussian curvature of the fluid/fluid meniscus using the Gauss-Bonnet theorem. We show that it is not possible to unambiguously determine an average contact angle from the Gauss-Bonnet theorem. We instead present an approximate relationship: 2 π n (1 - cos θ) = 4 π - ∫ κ G 12 dS 12 , where n is the number of closed loops of the three-phase contact line where phases 1 and 2 contact the surface, θ is the average contact angle, while κ G 12 is the Gaussian curvature of the fluid meniscus which is integrated over its surface S 12 . We then use the results of pore-scale lattice Boltzmann simulations to assess the accuracy of this approach to determine a representative contact angle for two-phase flow in porous media. We show that in simple cases with a flat solid surface, the approximate expression works well. When applied to simulations on pore space images, the equation provides a robust estimate of contact angle, accurate to within 3 ° , when averaged over many fluid clusters, although individual values can have significant errors because of the approximations used in the calculation. [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]

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]

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]

• We provided new multiphase flow measurements in a carbonate limestone with complex geometry and wettability. • We discussed its unique features related to contact angle, pore occupancy, curvature, capillary pressure and relative permeability. • The relative permeability values were corrected by considering the measured saturation profile along the sample length to correct for the so-called capillary end effect. • Greyscale based differential imaging was used and demonstrated for accurately determining the porosity and saturation without segmentation. • We demonstrated that not only wettability but also pore size distribution and microporosity have significant impact on displacement processes. Pore-scale X-ray imaging combined with a steady-state flow experiment was used to study the displacement processes during waterflooding in an altered-wettability carbonate, Ketton limestone, with more than two orders of magnitude difference in pore size between macropores and microporosity. We simultaneously characterized macroscopic and local multiphase flow parameters, including relative permeability, capillary pressure, wettability, and fluid occupancy in pores and throats. An accurate method was applied for porosity and fluid saturation measurements using greyscale based differential imaging without image segmentation. The relative permeability values were corrected by considering the measured saturation profile along the sample length to account for the so-called capillary end effect. The behaviour of relative permeability and capillary pressure was compared to other measurements in the literature to demonstrate the combined effects of wettability and pore structure. Typical oil-wet behaviour in resolvable macropores was measured from contact angle, fluid occupancy and curvature. The capillary pressure was negative while the oil relative permeability dropped quickly as oil was drained to low saturation and flowed through connected oil layers. Brine initially largely flowed through water-wet microporosity, and then filled the centre of large oil-wet pore bodies. Thus, the brine relative permeability remained exceptionally low until brine formed a connected flow path in the macropores leading to a substantial increase in relative permeability. Overall, this work demonstrates that not only wettability but also pore size distribution and microporosity have significant impact on displacement processes. [ABSTRACT FROM AUTHOR]

We use a generalized pore network model in combination with image-based experiments to understand the parameters that control upscaled flow properties. The study is focued on water-flooding through a reservoir sandstone under water-wet and mixed-wet conditions. A set of sensitivity studies is presented to quantify the role of wettability, pore geometry, initial and boundary conditions as well as a selection of model parameters used in the computation of fluid volumes, curvatures and flow and electrical conductivities. We quantify the uncertainty in the model predictions, which match the measured relative permeability and capillary pressure within the uncertainty of the experiments. Our results show that contact angle, initial saturation, image quality and image processing algorithm are amongst the parameters which introduce the largest variance in the predictions of upscaled flow properties for both mixed-wet and water-wet conditions. • Quantification of saturation and its uncertainty using differential imaging. • A new clustering algorithm for studying the effect of image segmentation. • Validation of the generalized network model against experimental data. • Sensitivity study on characterisation of wettability and pore geometry. • Sensitivity study on initial and boundary conditions as well as model parameters. [ABSTRACT FROM AUTHOR]

• Micro-CT imaging is applied to measure relative permeability and capillary pressure on one reservoir sandstone both under water-wet and mixed-wet condition. • We show that filling sequence is dependant on wettability. • The oil-water interfacial area had a larger maximum in the mixed-wet case than that of the water-wet case on the same rock. • We showed a better connectivity of the oil phase and the lower residual oil saturation in the mixed-wet case than that of the water-wet case on the same rock. Using micro-CT imaging and differential pressure measurements, we design a comparative study in which we simultaneously measure relative permeability and capillary pressure on the same reservoir sandstone sample under water-wet and mixed-wet conditions during steady-state waterflooding experiments. This allows us to isolate the impact of wettability on a pore-by-pore basis and its effect on the macroscopic parameters, capillary pressure and relative permeability, while keeping the pore-space geometry unchanged. First, oil and brine were injected through a water-wet reservoir sandstone sample at a fixed total flow rate, but in a sequence of increasing brine fractional flows with micro-CT scans of the fluid phases taken in each step. Then the sample was brought back to initial water saturation and the surface wettability of the sample was altered after prolonged contact with crude oil and the same measurement procedure was repeated on the altered-wettability sample which we call mixed-wet. Geometric contact angles were measured, which discriminated the water-wet and mixed-wet cases with average values of 75° and 89° respectively. Additionally, an energy balance was used to determine the effective contact angles for displacement which indicated that a higher advancing contact angle of 116° was needed to displace oil in the mixed-wet case. For the water-wet experiment the filling sequence was pore-size dependent, with a strong correlation between pore size and oil occupancy. However, in the mixed-wet experiment the principal determinant of the filling sequence was the wettability rather than the pore size, and there was no correlation between pore size and the residual oil occupancy. The oil-water interfacial area had a larger maximum in the mixed-wet case which was supported by the observation of sheet or saddle-like menisci shapes present throughout the sample volume that impede the flow. These shapes were quantified by much larger negative Gaussian curvature which indicated better connectivity of the phases, consistent with the lower residual oil saturation. Mean curvature and associated capillary pressure were positive for the water-wet case but decreased to a negative value for the mixed-wet case pointing to forced displacement from oil-wet pores. This analysis explained why the relative permeabilities for the mixed-wet case were lower than for the water-wet case for the same fractional flow. [ABSTRACT FROM AUTHOR]