Minimal surfaces in porous media: Pore-scale imaging of multiphase flow in an altered-wettability Bentheimer sandstone

Novel fabrication of mixed wettability micromodels for pore-scale studies of fluid-rock interactions

Wettability plays a crucial role in multiphase fluid flow in porous media, impacting various geological applications such as hydrocarbon extraction, aquifer remediation, and carbon dioxide sequestration. Microfluidic methods have attracted interest for their capacity to explore and visualize essential multiphase flow dynamics at the pore level, mimicking actual rock pore structures. However, creating micromodels with representative mixed wettability is currently a challenge. Existing technology is limited to producing micromodels with a singular wettability, either water-wet or oil-wet, leaving a gap in representing mixed-wet scenarios. In this study, we introduce a novel method to fabricate microfluidic devices with controlled spatial distribution of wettability at the micro-scale, mimicking actual configurations of mixed-wet rocks arising from varied mineralogy and pore structures. The proposed method combines the soft lithography process with thin film deposition techniques. The micromodels were designed to mimic the pore network of actual reservoir rocks, and a silicon substrate served as the foundation for the photolithography process optimization and wettability alteration methodology. Perfluorodecyltrichlorosilane coating was applied using molecular vapor deposition technology for surface wettability modification. The coated parts of the microdevice substrate altered the localized wetting state of the silicon towards hydrophobic, while the wettability remained unchanged in the non-coated areas. We utilized surface measurements, including contact angle, X-ray photoelectron spectroscopy, transmission electron microscopy, scanning electron microscopy, and atomic force microscopy, to assess the wettability, composition, thickness, shape, roughness, and overall quality of the coating. Our fabrication process successfully produced a microfluidics device with tailored mixed-wet attributes at the micro-scale, which is, to our best knowledge, the first achievement in the field. This method enables the replication of mixed-wet characteristics commonly seen in various applications, such as carbonates and shales within underground rocks, providing a more accurate examination of fundamental multiphase fluid dynamics and rock interactions at the pore level.

Zeta potential of crude oil in aqueous solution

Despite the broad range of interest and applications, controls on the surface charge of crude oil in aqueous solution remain poorly understood. The primary data source to understand the surface charge on crude oil comprises measurements of zeta potential on individual drops or emulsions obtained using the electrophoretic method (EPM). Here we (i) collate and review previous measurements of zeta potential on crude oil, (ii) compare and contrast the results, and (iii) report new measurements of zeta potential on crude oil wetting films and layers relevant to oil-saturated porous media, obtained using the streaming potential method (SPM). Results show that the zeta potential depends on electrolyte pH and the concentration of divalent ions Ca2+ and Mg2+. Lower pH and higher concentration of these divalent ions yields more positive zeta potential. The isoelectric point (IEP) in simple NaCl electrolytes lies in the pH range 3-5. The IEP in simple CaCl2 and MgCl2 electrolytes can be expressed as pCa or pMg, respectively, and lies in the range 0-1. Close to the IEP, the zeta potential varies linearly with pH, pCa or pMg, suggesting simple Nernstian behaviour of the crude oil surface. The sensitivity of the zeta potential to pH, pCa and pMg decreases with increasing total ionic strength. The impact of pH, pCa and pMg on zeta potential varies significantly across different crude oils and differs from non-polar hydrocarbons. The potential for other multivalent ions to modify crude oil zeta potential has not been tested. Data for crude oil wetting films and layers, obtained using the SPM and strongly oil-wet porous substrates in which the solid surfaces are coated with the crude oil of interest, are comparable to those obtained using emulsions and the EPM, suggesting that the controls on zeta potential on crude oil are the same irrespective of whether the oil forms droplets or wetting layers. The literature data reviewed here, along with new measured data, provide important insight into the effect of pH, and the concentration of divalent ions, on the zeta potential of crude oil in aqueous solution. They demonstrate relationships between ion concentration and zeta potential that are observed irrespective of crude oil composition. They also show that the crude oil composition plays a role, yet no consistent trends are observed between zeta potential and commonly measured bulk oil properties, possibly because bulk properties do not reflect the concentrations of interfacially active species in crude oil that may impact the development of surface charge. Moreover, data are extremely scarce for complex, high ionic strength electrolytes or at elevated temperature. The data reviewed and reported here have broad relevance to many engineering and industrial activities involving crude oil.

Pore-scale modeling of two-phase flow: A comparison of the generalized network model to direct numerical simulation

Despite recent advances in pore-scale modeling of two-phase flow through porous media, the relative strengths and limitations of various modeling approaches have been largely unexplored. In this work, two-phase flow simulations from the generalized network model (GNM) [Phys. Rev. E 96, 013312 (2017)2470-004510.1103/PhysRevE.96.013312; Phys. Rev. E 97, 023308 (2018)2470-004510.1103/PhysRevE.97.023308] are compared with a recently developed lattice-Boltzmann model (LBM) [Adv. Water Resour. 116, 56 (2018)0309-170810.1016/j.advwatres.2018.03.014; J. Colloid Interface Sci. 576, 486 (2020)0021-979710.1016/j.jcis.2020.03.074] for drainage and waterflooding in two samples-a synthetic beadpack and a micro-CT imaged Bentheimer sandstone-under water-wet, mixed-wet, and oil-wet conditions. Macroscopic capillary pressure analysis reveals good agreement between the two models, and with experiments, at intermediate saturations but shows large discrepancy at the end-points. At a resolution of 10 grid blocks per average throat, the LBM is unable to capture the effect of layer flow which manifests as abnormally large initial water and residual oil saturations. Critically, pore-by-pore analysis shows that the absence of layer flow limits displacement to invasion-percolation in mixed-wet systems. The GNM is able to capture the effect of layers, and exhibits predictions closer to experimental observations in water and mixed-wet Bentheimer sandstones. Overall, a workflow for the comparison of pore-network models with direct numerical simulation of multiphase flow is presented. The GNM is shown to be an attractive option for cost and time-effective predictions of two-phase flow, and the importance of small-scale flow features in the accurate representation of pore-scale physics is highlighted.

Wettability effect on oil recovery using rock-structured microfluidics

Surface wettability has a crucial impact on drop splashing, emulsion dynamics, slip flow for drag reduction, fluid-fluid displacement, and various microfluidic applications. Targeting enhanced oil recovery (EOR) applications, we experimentally investigate the effect of matrix wettability on the invasion morphology and sweep efficiency of viscous oil displaced by different aqueous floods using microfluidics, whose porous network mimics a sandstone structure. For comparison, systematic experiments of the same oil-flood pair are done in both hydrophilic and hydrophobic microfluidic chips. The results show that the hydrophilic microfluidic rock has a remarkable increase in oil recovery by a factor of ≈1.44, compared to the hydrophobic case. In addition, we observe a more pronounced lateral growth of the displacing pattern of aqueous flood for the hydrophilic surface. Finally, we quantitatively explain the increasing factor in the recovery rate and finger width for the hydrophilic vs. hydrophobic rock-liked porous networks by incorporating the contact angle into a scaling analysis.

A Closed-Form Equation for Capillary Pressure in Porous Media for All Wettabilities

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 $$P_{{\text{c}}} = A + B\tan \left( {\frac{\pi }{2} - \pi S_{e}^{C} } \right)\,{\text{for}}\,0 \le S_{{\text{e}}} \le 1,$$ P c = A + B tan π 2 - π S e C for 0 ≤ S e ≤ 1 , where $$S_{{\text{e}}}$$ S e is the normalized saturation. A indicates the wettability: $$A>0$$ A > 0 is a water-wet medium, $$A<0$$ 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.

Characterization of Two-Phase Flow from Pore-Scale Imaging Using Fractal Geometry under Water-Wet and Mixed-Wet Conditions

High resolution micro-computed tomography images for multiphase flow provide us an effective tool to understand the mechanism of fluid flow in porous media, which is not only fundamental to the understanding of macroscopic measurements but also for providing benchmark datasets to validate pore-scale modeling. In this study, we start from two datasets of pore scale imaging of two-phase flow obtained experimentally under in situ imaging conditions at different water fractional flows under water-wet and mixed-wet conditions. Then, fractal dimension, lacunarity and succolarity are used to quantify the complexity, clustering and flow capacity of water and oil phases. The results show that with the wettability of rock surface altered from water-wet to mixed-wet, the fractal dimension for the water phase increases while for the oil phase, it decreases obviously at low water saturation. Lacunarity largely depends on the degree of wettability alteration. The more uniform wetting surfaces are distributed, the more homogeneous the fluid configuration is, which indicates smaller values for lacunarity. Moreover, succolarity is shown to well characterize the wettability effect on flow capacity. The succolarity of the oil phase in the water-wet case is larger than that in the mixed-wet case while for the water phase, the succolarity value in the water-wet is small compared with that in the mixed-wet, which show a similar trend with relative permeability curves for water-wet and mixed-wet. Our study provides a perspective into the influence that phase geometry has on relative permeability under controlled wettability and the resulting phase fractal changes under different saturations that occur during multiphase flow, which allows a means to understand phase geometric changes that occur during fluid flow.

Operando Liquid Pressure Determination in Polymer Electrolyte Fuel Cells

Extending the operating range of fuel cells to higher current densities is limited by the ability of the cell to remove the water produced by the electrochemical reaction, avoiding flooding of the gas diffusion layers. It is therefore of great interest to understand the complex and dynamic mechanisms of water cluster formation in an operando fuel cell setting as this can elucidate necessary changes to the gas diffusion layer properties with the goal of minimizing the number, size, and instability of the water clusters formed. In this study, we investigate the cluster formation process using X-ray tomographic microscopy at 1 Hz frequency combined with interfacial curvature analysis and volume-of-fluid simulations to assess the pressure evolution in the water phase. This made it possible to observe the increase in capillary pressure when the advancing water front had to overcome a throat between two neighboring pores and the nuanced interactions of volume and pressure evolution during the droplet formation and its feeding path instability. A 2 kPa higher breakthrough pressure compared to static ex situ capillary pressure versus saturation evaluations was observed, which suggests a rethinking of the dynamic liquid water invasion process in polymer electrolyte fuel cell gas diffusion layers.

Pore-scale imaging and analysis of low salinity waterflooding in a heterogeneous carbonate rock at reservoir conditions

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.

Four-dimensional imaging and free-energy analysis of sudden pore-filling events in wicking of yarns

What are the mechanisms at play in the spontaneous imbibition dynamics in polyethylene terephthalate filament yarns at pore scale? Processes at pore scale such as waiting times between the filling of two neighboring pores, as observed in special irregular porous media, like yarns, may overrule the predicted behavior by well-known laws such as Washburn's law. While the imbibition physics are well known, classic models like Washburn's law cannot explain the dynamics observed for yarns. The stepwise dynamics is discussed in terms of the interplay of thermodynamic free energy and viscous dissipation. Time-resolved synchrotron x-ray microtomography documents water filling at pore scale. Spontaneous imbibition in yarns is characterized by a series of fast pore-filling events separated by long periods of low flux. Four-dimensional imaging allows the extraction of interface areas at the boundaries between water, air, and polymer and the calculation of free-energy evolution. It is found that the waiting periods correspond to quasistable water configurations of almost vanishing free-energy gradient. The distributions of pore filling event sizes and waiting times spread over several orders of magnitude, resulting in the pronounced stepwise uptake dynamics.

In-situ capillary pressure and wettability in natural porous media: Multi-scale experimentation and automated characterization using X-ray images

HYPOTHESIS

Geometrical analyses of pore-scale fluid-fluid-rock interfaces have recently been used for in-situ characterization of capillary pressure and wettability in natural porous media. Nevertheless, more robust techniques and multi-scale, well-characterized experimental data are needed to rigorously validate these techniques and enhance their efficacy when applied to saturated porous media.

EXPERIMENTS AND IMAGE ANALYSIS

We present two new techniques for automated measurements of in-situ capillary pressure and contact angle, which offer several advancements over previous methodologies. These approaches are methodically validated using synthetic data and X-ray images of capillary rise experiments, and subsequently, applied on pore-scale fluid occupancy maps of a miniature Berea sandstone sample obtained during steady-state drainage and imbibition flow experiments.

FINDINGS

The results show encouraging agreement between the image-based capillary pressure-saturation function and its macroscopic counterpart obtained from a porous membrane experiment. However, unlike the macroscopic behavior, the micro-scale measurements demonstrate a nonmonotonic increase with saturation due to the intermittency of the pore-scale displacement events controlling the overall flow behavior. This is further explained using the pertinent micro-scale mechanisms such as Haines jumps. The new methods also enable one to generate in-situ contact angle distributions and distinguish between the advancing and receding values while automatically excluding invalid measurements.

Improved dynamic imaging of multiphase flow by constrained tomographic reconstruction

Dynamic tomography has become an important technique to study fluid flow processes in porous media. The use of laboratory X-ray tomography instruments is, however, limited by their low X-ray brilliance. The prolonged exposure times, in turn, greatly limit temporal resolution. We have developed a tomographic reconstruction algorithm that maintains high image quality, despite reducing the exposure time and the number of projections significantly. Our approach, based on the Simultaneous Iterative Reconstruction Technique, mitigates the problem of few and noisy exposures by utilising a high-quality scan of the system before the dynamic process is started. We use the high-quality scan to initialise the first time step of the dynamic reconstruction. We further constrain regions of the dynamic reconstruction with a segmentation of the static system. We test the performance of the algorithm by reconstructing the dynamics of fluid separation in a multiphase system. The algorithm is compared quantitatively and qualitatively with several other reconstruction algorithms and we show that it can maintain high image quality using only a fraction of the normally required number of projections and with a substantially larger noise level. By robustly allowing fewer projections and shorter exposure, our algorithm enables the study of faster flow processes using laboratory tomography instrumentation but it can also be used to improve the reconstruction quality of dynamic synchrotron experiments.

Direct Numerical Simulation of Pore-Scale Trapping Events During Capillary-Dominated Two-Phase Flow in Porous Media

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.

Pore-by-Pore Modelling, Validation and Prediction of Waterflooding in Oil-Wet Rocks Using Dynamic Synchrotron Data

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.

Capillary number correlations for two-phase flow in porous media

Relative permeabilities and capillary number correlations are widely used for quantitative estimates of enhanced water flood performance in porous media. They enter as essential parameters into reservoir simulations. Experimental capillary number correlations for seven different reservoir rocks and 21 pairs of wetting and nonwetting fluids are analyzed. The analysis introduces generalized local macroscopic capillary number correlations. It eliminates shortcomings of conventional capillary number correlations. Surprisingly, the use of capillary number correlations on reservoir scales may become inconsistent in the sense that the limits of applicability of the underlying generalized Darcy law are violated. The results show that local macroscopic capillary number correlations can distinguish between rock types. The experimental correlations are ordered systematically using a three-parameter fit function combined with a novel fluid pair based figure of merit.

Review of low salinity waterflooding in carbonate rocks: mechanisms, investigation techniques, and future directions

This review analyses the fundamental thermodynamic theory of the crude oil-brine-rock (COBR) interface and the underlying rock-brine and oil-brine interactions. The available data are then reviewed to outline potential mechanisms responsible for increased oil recovery from low salinity waterflooding (LSWF). We propose an approach to studying LSWF and identify the key missing links that are needed to explain observations at multiple length scales. The synergistic effect of LSWF on other chemical enhanced oil recovery methods such as surfactant, alkaline, nanoparticle and polymer flooding are also outlined. We specifically highlight key uncertainties that must be overcome to fully implement the technique in the field.

Pore-by-pore modeling, analysis, and prediction of two-phase flow in mixed-wet rocks

A pore-network model is an upscaled representation of the pore space and fluid displacement, which is used to simulate two-phase flow through porous media. We use the results of pore-scale imaging experiments to calibrate and validate our simulations, and specifically to find the pore-scale distribution of wettability. We employ energy balance to estimate an average, thermodynamic, contact angle in the model, which is used as the initial estimate of contact angle. We then adjust the contact angle of each pore to match the observed fluid configurations in the experiment as a nonlinear inverse problem. The proposed algorithm is implemented on two sets of steady state micro-computed-tomography experiments for water-wet and mixed-wet Bentheimer sandstone. As a result of the optimization, the pore-by-pore error between the model and experiment is decreased to less than that observed between repeat experiments on the same rock sample. After calibration and matching, the model predictions for capillary pressure and relative permeability are in good agreement with the experiments. The proposed algorithm leads to a distribution of contact angle around the thermodynamic contact angle. We show that the contact angle is spatially correlated over around 4 pore lengths, while larger pores tend to be more oil-wet. Using randomly assigned distributions of contact angle in the model results in poor predictions of relative permeability and capillary pressure, particularly for the mixed-wet case.

Dynamics of water injection in an oil-wet reservoir rock at subsurface conditions: Invasion patterns and pore-filling events

We use fast synchrotron x-ray microtomography to investigate the pore-scale dynamics of water injection in an oil-wet carbonate reservoir rock at subsurface conditions. We measure, in situ, the geometric contact angles to confirm the oil-wet nature of the rock and define the displacement contact angles using an energy-balance-based approach. We observe that the displacement of oil by water is a drainagelike process, where water advances as a connected front displacing oil in the center of the pores, confining the oil to wetting layers. The displacement is an invasion percolation process, where throats, the restrictions between pores, fill in order of size, with the largest available throats filled first. In our heterogeneous carbonate rock, the displacement is predominantly size controlled; wettability has a smaller effect, due to the wide range of pore and throat sizes, as well as largely oil-wet surfaces. Wettability only has an impact early in the displacement, where the less oil-wet pores fill by water first. We observe drainage associated pore-filling dynamics including Haines jumps and snap-off events. Haines jumps occur on single- and/or multiple-pore levels accompanied by the rearrangement of water in the pore space to allow the rapid filling. Snap-off events are observed both locally and distally and the capillary pressure of the trapped water ganglia is shown to reach a new capillary equilibrium state. We measure the curvature of the oil-water interface. We find that the total curvature, the sum of the curvatures in orthogonal directions, is negative, giving a negative capillary pressure, consistent with oil-wet conditions, where displacement occurs as the water pressure exceeds that of the oil. However, the product of the principal curvatures, the Gaussian curvature, is generally negative, meaning that water bulges into oil in one direction, while oil bulges into water in the other. A negative Gaussian curvature provides a topological quantification of the good connectivity of the phases throughout the displacement.

Using energy balance to determine pore-scale wettability

HYPOTHESIS

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.

SIMULATIONS

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.

FINDINGS

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.

Evaluation of methods using topology and integral geometry to assess wettability

HYPOTHESIS

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.

THEORY AND SIMULATION

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: 2πn(1-cosθ)=4π-∫κ_G12dS₁₂, 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_G12 is the Gaussian curvature of the fluid meniscus which is integrated over its surface S₁₂. 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.

FINDINGS

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.

Dynamics of fluid displacement in mixed-wet porous media

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.

Quantification of Uncertainty and Best Practice in Computing Interfacial Curvature from Complex Pore Space Images

Recent advances in high-resolution three-dimensional X-ray CT imaging have made it possible to visualize fluid configurations during multiphase displacement at the pore-scale. However, there is an inherited difficulty in image-based curvature measurements: the use of voxelized image data may introduce significant error, which has not-to date-been quantified. To find the best method to compute curvature from micro-CT images and quantify the likely error, we performed drainage and imbibition direct numerical simulations for an oil/water system on a bead pack and a Bentheimer sandstone. From the simulations, local fluid configurations and fluid pressures were obtained. We then investigated methods to compute curvature on the oil/water interface. The interface was defined in two ways; in one case the simulated interface with a sub-resolution smoothness was used, while the other was a smoothed interface extracted from synthetic segmented data based on the simulated phase distribution. The curvature computed on these surfaces was compared with that obtained from the simulated capillary pressure, which does not depend on the explicit consideration of the shape of the interface. As distinguished from previous studies which compared an average or peak curvature with the value derived from the measured macroscopic capillary pressure, our approach can also be used to study the pore-by-pore variation. This paper suggests the best method to compute curvature on images with a quantification of likely errors: local capillary pressures for each pore can be estimated to within 30% if the average radius of curvature is more than 6 times the image resolution, while the average capillary pressure can also be estimated to within 11% if the average radius of curvature is more than 10 times the image resolution.