A thermodynamically consistent characterization of wettability in porous media using high-resolution imaging

Percolation without trapping: How Ostwald ripening during two-phase displacement in porous media alters capillary pressure and relative permeability

Conventional measurements of two-phase flow in porous media often use completely immiscible fluids, or are performed over time scales of days to weeks. If applied to the study of gas storage and recovery, these measurements do not properly account for Ostwald ripening, significantly overestimating the amount of trapping and hysteresis. When there is transport of dissolved species in the aqueous phase, local capillary equilibrium is achieved: this may take weeks to months on the centimeter-sized samples on which measurements are performed. However, in most subsurface applications where the two phases reside for many years, equilibrium can be achieved. We demonstrate that in this case, two-phase displacement in porous media needs to be modeled as percolation without trapping. A pore network model is used to quantify how to convert measurements of trapped saturation, capillary pressure and relative permeability made ignoring Ostwald ripening to account for this effect. We show that conventional measurements overestimate the amount of capillary trapping by 20-25%.

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.

A Molecular Dynamics Investigation on Methane Flow and Water Droplets Sliding in Organic Shale Pores with Nano-structured Roughness

Roughness of surfaces significantly influences how methane and water flow in shale nanopores. We perform molecular dynamics simulations to investigate the influence of surface roughness on pore-scale transport of pure methane as well as of two-phase methane–water systems with the water sliding as droplets over the pore surface. For single-phase methane flow, surface roughness shows a limited influence on bulk methane density, while it significantly reduces the methane flow capacity. In methane–water systems, the mobility of water is a strong function of surface roughness including a clear transition between immobile and mobile water droplets. For cases with mobile water, droplet sliding speeds were correlated with pressure gradient and surface roughness. Sliding water droplets hardly deform, i.e., there is little difference between their advancing and receding contact angle with structured roughness.

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.

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.

Pore-Scale Imaging and Analysis of Wettability Order, Trapping and Displacement in Three-Phase Flow in Porous Media with Various Wettabilities

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.

The growth and shrinkage of water droplets at the oil-solid interface

HYPOTHESIS

The mechanism for the spontaneous formation of water droplets at oil/solid interfaces immersed in water is currently unclear. We hypothesize that growth and shrinkage of droplets are kinetically controlled by diffusion of water through the oil, driven by differences in chemical potential between the solid substrate and the aqueous reservoir.

EXPERIMENTS

The formation, growth and shrinkage of water droplets at an immersed oil/solid interface are investigated theoretically and experimentally with three silicone oils. The surface is hydrophobic and the droplets formed are truncated spheres with radius, a, less than 10 μm. The expansion and contraction of the droplets can be controlled by adjusting the difference in chemical potential. The growth kinetics are modelled in terms of water migration through the oil layer which predicts a²∝t.

FINDINGS

This is the first study of possible mechanisms for the formation of such interfacial droplets. Several possible causes are shown to be unfavourable, negligible, or are eliminated by careful experiments controlling key parameters (such as oil viscosity, substrate chemistry). The rate constant for mass transport is proportional to difference in chemical potential and an estimate shows dissociation of surface groups on the substrate provides a driving chemical potential of the right magnitude.

Determination of contact angles for three-phase flow in porous media using an energy balance

HYPOTHESIS

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.

THEORY

For three phases labelled 1, 2 and 3, and solid, s, using conservation of energy ignoring viscous dissipation (Δa_1scosθ₁₂-Δa₁₂-ϕκ₁₂ΔS₁)σ₁₂=(Δa_3scosθ₂₃+Δa₂₃-ϕκ₂₃ΔS₃)σ₂₃+Δa₁₃σ₁₃, 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, θ₁₃ can be found using the Bartell-Osterhof relationship. The energy balance is also extended to an arbitrary number of phases.

FINDINGS

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 θ₁₂≈48° and θ₁₃≈44°, while θ₂₃=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 θ₁₂=134°±~10°,θ₁₃=119°±~10°, and θ₂₃=66°±~10°.

Capillary transport in paper porous materials at low saturation levels: normal, fast or superfast?

The problem of capillary transport in fibrous porous materials at low levels of liquid saturation has been addressed. It has been demonstrated that the process of liquid spreading in this type of porous material at low saturation can be described macroscopically by a similar super-fast, nonlinear diffusion model to that which had been previously identified in experiments and simulations in particulate porous media. The macroscopic diffusion model has been underpinned by simulations using a microscopic network model. The theoretical results have been qualitatively compared with available experimental observations within the witness card technique using persistent liquids. The long-term evolution of the wetting spots was found to be truly universal and fully in line with the mathematical model developed. The result has important repercussions for the witness card technique used in field measurements of the dissemination of various low-volatility agents in imposing severe restrictions on collection and measurement times.

Contact Angles in Two-Phase Flow Images

In this work, we calculate contact angles in X-ray tomography images of two-phase flow in order to investigate the wettability. Triangulated surfaces, generated using the images, are smoothed to calculate the contact angles. As expected, the angles have a spread rather than being a constant value. We attempt to shed light on sources of the spread by addressing the overlooked mesh corrections prior to smoothing, poorly resolved image features, cluster-based analysis, and local variations of contact angles. We verify the smoothing algorithm by analytical examples with known contact angle and curvature. According to the analytical cases, point-wise and average contact angles, average mean curvature and surface area converge to the analytical values with increased voxel grid resolution. Analytical examples show that these parameters can reliably be calculated for fluid–fluid surfaces composed of roughly 3000 vertices or more equivalent to 1000 pixel2. In an experimental image, by looking into individual interfaces and clusters, we show that contact angles are underestimated for wetting fluid clusters where the fluid–fluid surface is resolved with less than roughly 500 vertices. However, for the fluid–fluid surfaces with at least a few thousand vertices, the mean and standard deviation of angles converge to similar values. Further investigation of local variations of angles along three-phase lines for large clusters revealed that a source of angle variations is anomalies in the solid surface. However, in the places least influenced by such noise, we observed that angles tend to be larger when the line is convex and smaller when the line is concave. We believe this pattern may indicate the significance of line energy in the free energy of the two-phase flow systems.

In Situ Wettability Investigation of Aging of Sandstone Surface in Alkane via X-ray Microtomography

Wettability of surfaces remains of paramount importance for understanding various natural and artificial colloidal and interfacial phenomena at various length and time scales. One of the problems discussed in this work is the wettability alteration of a three-phase system comprising high salinity brine as the aqueous phase, Doddington sandstone as porous rock, and decane as the nonaqueous phase liquid. The study utilizes the technique of in situ contact angle measurements of the several 2D projections of the identified 3D oil phase droplets from the 3D images of the saturated sandstone miniature core plugs obtained by X-ray microcomputed tomography (micro-CT). Earlier works that utilize in situ contact angles measurements were carried out for a single plane. The saturated rock samples were scanned at initial saturation conditions and after aging for 21 days. This study at ambient conditions reveals that it is possible to change the initially intermediate water-wet conditions of the sandstone rock surface to a weakly water wetting state on aging by alkanes using induced polarization at the interface. The study adds to the understanding of initial wettability conditions as well as the oil migration process of the paraffinic oil-bearing sandstone reservoirs. Further, it complements the knowledge of the wettability alteration of the rock surface due to chemisorption, usually done by nonrepresentative technique of silanization of rock surface in experimental investigations.

Geometrically derived efficiency of slow immiscible displacement in porous media

The efficiency of a displacement is the fraction of applied work over the change in free energy. This displacement efficiency is essential for linking wettability to applied work during displacement processes. We quantify the efficiency of slow immiscible displacements in porous media from pore space geometry. For this end, we introduce pore-scale definitions for thermodynamically reversible (ison) and irreverisble (rheon) processes. We argue that the efficiency of slow primary displacement is described by the geometry of the pore space for porous media with a sufficient number of pore bodies. This article introduces how to calculate such geometry-based efficiency locally, and integrating this local efficiency over the pore space yields an aggregate efficiency for the primary displacement in the porous medium. Further, we show how the geometrical characterization of the displacement efficiency links the efficiency to the constriction factor from transport processes governed by the Laplace equation. This enables estimation of displacement efficiency from traditional and widely available measurements for porous media. We present a thermodynamically based wettability calculation based on the local efficiency and a method to approximate this thermodynamically based wettability from traditional experiments.

Characterization of wetting using topological principles

HYPOTHESIS

Understanding wetting behavior is of great importance for natural systems and technological applications. The traditional concept of contact angle, a purely geometrical measure related to curvature, is often used for characterizing the wetting state of a system. It can be determined from Young's equation by applying equilibrium thermodynamics. However, whether contact angle is a representative measure of wetting for systems with significant complexity is unclear. Herein, we hypothesize that topological principles based on the Gauss-Bonnet theorem could yield a robust measure to characterize wetting.

THEORY AND EXPERIMENTS

We introduce a macroscopic contact angle based on the deficit curvature of the fluid interfaces that are imposed by contacts with other immiscible phases. We perform sessile droplet simulations followed by multiphase experiments for porous sintered glass and Bentheimer sandstone to assess the sensitivity and robustness of the topological approach and compare the results to other traditional approaches.

FINDINGS

We show that the presented topological principle is consistent with thermodynamics under the simplest conditions through a variational analysis. Furthermore, we elucidate that at sufficiently high image resolution the proposed topological approach and local contact angle measurements are comparable. While at lower resolutions, the proposed approach provides more accurate results being robust to resolution-based effects. Overall, the presented concepts open new pathways to characterize the wetting state of complex systems and theoretical developments to study multiphase systems.

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.

Pore-scale numerical simulation of low salinity water flooding using the lattice Boltzmann method

HYPOTHESIS

The change of wettability toward more water-wet by the injection of low salinity water can improve oil recovery from porous rocks, which is known as low salinity water flooding. To simulate this process at the pore-scale, we propose that the alteration in surface wettability mediated by thin water films which are below the resolution of simulation grid blocks has to be considered, as observed in experiments. This is modeled by a wettability alteration model based on rate-limited adsorption of ions onto the rock surface.

SIMULATIONS

The wettability alteration model is developed and incorporated into a lattice Boltzmann simulator which solves both the Navier-Stokes equation for oil/water two-phase flow and the advection-diffusion equation for ion transport. The model is validated against two experiments in the literature, then applied to 3D micro-CT images of a rock.

FINDINGS

Our model correctly simulated the experimental observations caused by the slow wettability alteration driven by the development of water films. In the simulations on the 3D rock pore structure, a distinct difference in the mixing of high and low salinity water is observed between secondary and tertiary low salinity flooding, resulting in different oil recoveries.

Linking continuum-scale state of wetting to pore-scale contact angles in porous media

HYPOTHESIS

Wetting phenomena play a key role in flows through porous media. Relative permeability and capillary pressure-saturation functions show a high sensitivity to wettability, which has different definitions at the continuum- and pore-scale. We hypothesize that the wetting state of a porous medium can be described in terms of topological arguments that constrain the morphological state of immiscible fluids, which provides a direct link between the continuum-scale metrics of wettability and pore-scale contact angles.

EXPERIMENTS

We perform primary drainage and imbibition experiments on Bentheimer sandstone using air and brine. Topological properties, such as Euler characteristic and interfacial curvature are measured utilizing X-ray micro-computed tomography at irreducible air saturation. We also present measurements for the United States Bureau of Mines (USBM) index, capillary pressure and pore-scale contact angles. Additional studies are performed using two-phase Lattice Boltzmann simulations to test a wider range of wetting conditions.

FINDINGS

We demonstrate that contact angle distributions for a porous multiphase system can be predicted within a few percent difference of directly measured pore-scale contact angles using the presented method. This provides a general framework on how continuum-scale data can be used to describe the geometrical state of fluids within porous 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.

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

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.