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 (Δa1scosθ12-Δa12-ϕκ12ΔS1)σ12=(Δa3scosθ23+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°.

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 mechanisms of CO2 storage in oilfields.

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

Three-phase flow displacement dynamics and Haines jumps in a hydrophobic porous medium.

We use synchrotron X-ray micro-tomography to investigate the displacement dynamics during three-phase-oil, water and gas-flow in a hydrophobic porous medium. We observe a distinct gas invasion pattern, where gas progresses through the pore space in the form of disconnected clusters mediated by double and multiple displacement events. Gas advances in a process we name three-phase Haines jumps, during which gas re-arranges its configuration in the pore space, retracting from some regions to enable the rapid filling of multiple pores. The gas retraction leads to a permanent disconnection of gas ganglia, which do not reconnect as gas injection proceeds. We observe, in situ, the direct displacement of oil and water by gas as well as gas-oil-water double displacement. The use of local in situ measurements and an energy balance approach to determine fluid-fluid contact angles alongside the quantification of capillary pressures and pore occupancy indicate that the wettability order is oil-gas-water from most to least wetting. Furthermore, quantifying the evolution of Minkowski functionals implied well-connected oil and water, while the gas connectivity decreased as gas was broken up into discrete clusters during injection. This work can be used to design CO2 storage, improved oil recovery and microfluidic devices.

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.

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.

Laser inscription of pseudorandom structures for microphotonic diffuser applications.

Optical diffusers provide a solution for a variety of applications requiring a Gaussian intensity distribution including imaging systems, biomedical optics, and aerospace. Advances in laser ablation processes have allowed the rapid production of efficient optical diffusers. Here, we demonstrate a novel technique to fabricate high-quality glass optical diffusers with cost-efficiency using a continuous CO2 laser. Surface relief pseudorandom microstructures were patterned on both sides of the glass substrates. A numerical simulation of the temperature distribution showed that the CO2 laser drills a 137 µm hole in the glass for every 2 ms of processing time. FFT simulation was utilized to design predictable optical diffusers. The pseudorandom microstructures were characterized by optical microscopy, Raman spectroscopy, and angle-resolved spectroscopy to assess their chemical properties, optical scattering, transmittance, and polarization response. Increasing laser exposure and the number of diffusing surfaces enhanced the diffusion and homogenized the incident light. The recorded speckle pattern showed high contrast with sharp bright spot free diffusion in the far field view range (250 mm). A model of glass surface peeling was also developed to prevent its occurrence during the fabrication process. The demonstrated method provides an economical approach in fabricating optical glass diffusers in a controlled and predictable manner. The produced optical diffusers have application in fibre optics, LED systems, and spotlights.