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

In situ characterization of heterogeneous surface wetting in porous materials

The performance of nano- and micro-porous materials in capturing and releasing fluids, such as during CO2 geo-storage and water/gas removal in fuel cells and electrolyzers, is determined by their wettability in contact with the solid. However, accurately characterizing wettability is challenging due to spatial variations in dynamic forces, chemical heterogeneity, and surface roughness. In situ measurements can potentially measure wettability locally as a contact angle - the angle a denser phase (e.g water) contacts solid in the presence of a second phase (e.g. hydrogen, air, CO2) - but suffer from difficulties in accurately capturing curvatures, contact areas, and contact loops of multiphase fluids. We introduce a novel extended topological method for in situ contact angle measurement and provide a comparative review of current geometric and topological methods, assessing their accuracy on ideal surfaces, porous rocks containing CO2, and water in gas diffusion layers. The new method demonstrates higher accuracy and reliability of in situ measurements for uniformly wetting systems compared to previous topological approaches, while geometric measurements perform best for mixed-wetting domains. This study further provides a comprehensive open-source platform for in situ characterization of wettability in porous materials with implications for gas geo-storage, fuel cells and electrolyzers, filtration, and catalysis.

Contact Angle on Rough Curved Surfaces and Its Implications in Porous Media

The equilibrium contact angle depends on both the chemistry of the two fluids and solid base and the microstructure on the solid surface. Actual surface of the pore wall in porous media is typically rough and curved, which has not been well-considered in related applications. This work uses a free interfacial energy minimization approach to theoretically derive the equilibrium contact angle on two specific surface structures on flat surfaces and extends the derivation considering the surface curvatures in porous media. Results reveal that the equilibrium contact angle is not dependent on the curvature of spherical surfaces, and we further prove that this conclusion applies to any point along the apparent common line at solid surfaces with any arbitrary curvature. The fundamental physics is the local mechanical balance of a composite contact among three interfacial tensions. Furthermore, the contacting mode can shift from non-wetting to wetting when the pressure difference between two fluids exceeds the entry pressure of the microstructures, which should be considered in relative dynamic scenarios such as rain droplet impact and fluid displacement in porous media. Note that these conclusions are from pure theoretical analysis based on idealistic assumptions, and real circumstances may deviate from these assumptions.

Capillary imbibition and flow of wetting liquid in irregular capillaries: A 100-year review

Capillary imbibition, such as plant roots taking up water, reservoir rocks absorbing brine and a tissue paper wiping stains, is pervasive occurred in nature, engineering and industrial fields, as well as in our daily life. This phenomenon is earliest modeled through the process that wetting liquid is spontaneously propelled by capillary pressure into regular geometry models. Recent studies have attracted more attention on capillary-driven flow models within more complex geometries of the channel, since a detailed understanding of capillary imbibition dynamics within irregular geometry models necessitates the fundamentals to fluid transport mechanisms in porous media with complex pore topologies. Herein, the fundamentals and concepts of different capillary imbibition models in terms of geometries over the past 100 years are reviewed critically, such as circular and non-circular capillaries, open and closed capillaries with triangular/rectangular cross-sections, and heterogeneous geometries with axial variations. The applications of these models with appropriate conditions are discussed in depth accordingly, with a particular emphasize on the capillary flow pattern as a consequence of capillary geometry. In addition, a universal model is proposed based on the dynamic wetting condition and equivalent cylindrical geometry to describe the capillary imbibition process in terms of various solid topologies. Finally, future research is suggested to focus on analyzing the dynamics during corner flow, the snap-off of wetting fluid, the capillary rise of non-Newtonian fluids and applying accurate physical simulation methods on capillary-driven flow processes. Generally, this review provides a comprehensive understanding of the capillary-driven flow models inside various capillary geometries and affords an overview of potential advanced developments to enhance the current understanding of fluid transport mechanisms in porous media.

Universal description of wetting on multiscale surfaces using integral geometry

HYPOTHESIS

Emerging energy-related technologies deal with multiscale hierarchical structures, intricate surface morphology, non-axisymmetric interfaces, and complex contact lines where wetting is difficult to quantify with classical methods. We hypothesise that a universal description of wetting on multiscale surfaces can be developed by using integral geometry coupled to thermodynamic laws. The proposed approach separates the different hierarchy levels of physical description from the thermodynamic description, allowing for a universal description of wetting on multiscale surfaces.

THEORY AND SIMULATIONS

The theoretical framework is presented followed by application to limiting cases of wetting on multiscale surfaces. Limiting cases include those considered in the Wenzel, Cassie-Baxter, and wicking state models. Wetting characterisation of multiscale surfaces is explored by conducting simulations of a fluid droplet on a structurally rough surface and a chemically heterogeneous surface.

FINDINGS

The underlying origin of the classical wetting models is shown to be rooted within the proposed theoretical framework. Integral geometry provides a topological-based wetting metric that is not contingent on any type of wetting state. The wetting metric is demonstrated to account for multiscale features along the common line in a scale consistent way; providing a universal description of wetting for multiscale surfaces.

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.

Superhydrophobic μ-pillars via simple and scalable SLA 3D-printing: the stair-case effect and their wetting models

In nature, superhydrophobic surfaces (SHSs) exhibit microstructures with several roughness scales. Scalable fabrication and build-up along the X-Y plane represent the promise of 3D printing technology. Herein we report 3D printed microstructures with a dual roughness scale that achieves SHS using a readily available Formlabs stereolithography (SLA) printer. Pillar-like structure (PLS) arrangements with a wide range of geometrical shapes were 3D printed at three resolutions and two printing orientations. We discovered that a tilted printing direction enables a stair-case pattern on the μ-PLS surfaces, conferring them a μ-roughness that reduces the solid-liquid contact area. The programmed resolution governs the number of polymerized layers that give rise to the stepped pattern on the μ-PLS surfaces. However, this is reduced as the printing resolution increases. Also, all samples' experimental contact angles were consistent with theoretical predictions from Cassie-Baxter, Wenzel, and Nagayama wettability models. The underlying mechanisms and governing parameters were also discussed. It is believed that this work will enable scalable and high throughput roughness design in augmenting future 3D printing object applications.

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°.

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.

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.

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.

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.