Determination of the spatial distribution of wetting in the pore networks of rocks.

HYPOTHESIS: The macroscopic movement of subsurface fluids involved in CO2 storage, groundwater, and petroleum engineering applications is controlled by interfacial forces in the pores of rocks. Recent advances in modelling these systems has arisen from approaches simulating flow through a digital representation of the complex pore structure. However, further progress is limited by difficulties in characterising the spatial distribution of the wetting state within the pore structure. In this work, we show how observations of the fluid coverage of mineral surfaces within the pores of rocks can be used as the basis for a quantitative 3D characterisation of heterogeneous wetting states throughout rock pore structures. EXPERIMENTS: We demonstrate the approach with water-oil fluid pairs on rocks with distinct lithologies (sandstone and carbonate) and wetting states (hydrophilic, intermediate wetting, and heterogeneously wetting). FINDINGS: Fluid surface coverage the within rock pores is a robust signal of the wetting state across varying rock types and wetting states. The wetting state can be quantified and the resulting 3D maps can be used as a deterministic input to pore scale models. These may be applied to multiphase flow problems in porous media ranging from soil science to fuel cells.

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.

Thermodynamics of fluctuations based on time-and-space averages.

We develop nonequilibrium theory by using averages in time and space as a generalized way to upscale thermodynamics in nonergodic systems. The approach offers a classical perspective on the energy dynamics in fluctuating systems. The rate of entropy production is shown to be explicitly scale dependent when considered in this context. We show that while any stationary process can be represented as having zero entropy production, second law constraints due to the Clausius theorem are preserved due to the fact that heat and work are related based on conservation of energy. As a demonstration, we consider the energy dynamics for the Carnot cycle and for Maxwell's demon. We then consider nonstationary processes, applying time-and-space averages to characterize nonergodic effects in heterogeneous systems where energy barriers such as compositional gradients are present. We show that the derived theory can be used to understand the origins of anomalous diffusion phenomena in systems where Fick's law applies at small length scales, but not at large length scales. We further characterize fluctuations in capillary-dominated systems, which are nonstationary due to the irreversibility of cooperative events.

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.

Signature of elastic turbulence of viscoelastic fluid flow in a single pore throat.

When a viscoelastic fluid, such as an aqueous polymer solution, flows through a porous medium, the fluid undergoes a repetitive expansion and contraction as it passes from one pore to the next. Above a critical flow rate, the interaction between the viscoelastic nature of the polymer and the pore configuration results in spatial and temporal flow instabilities reminiscent of turbulentlike behavior, even though the Reynolds number Re≪1. To investigate whether this is caused by many repeated pore body-pore throat sequences, or simply a consequence of the converging (diverging) nature present in a single pore throat, we performed experiments using anionic hydrolyzed polyacrylamide (HPAM) in a microfluidic flow geometry representing a single pore throat. This allows the viscoelastic fluid to be characterized at increasing flow rates using microparticle image velocimetry in combination with pressure drop measurements. The key finding is that the effect, popularly known as "elastic turbulence," occurs already in a single pore throat geometry. The critical Deborah number at which the transition in rheological flow behavior from pseudoplastic (shear thinning) to dilatant (shear thickening) strongly depends on the ionic strength, the type of cation in the anionic HPAM solution, and the nature of pore configuration. The transition towards the elastic turbulence regime was found to directly correlate with an increase in normal stresses. The topology parameter, Q_{f}, computed from the velocity distribution, suggests that the "shear thickening" regime, where much of the elastic turbulence occurs in a single pore throat, is a consequence of viscoelastic normal stresses that cause a complex flow field. This flow field consists of extensional, shear, and rotational features around the constriction, as well as upstream and downstream of the constriction. Furthermore, this elastic turbulence regime, has high-pressure fluctuations, with a power-law decay exponent of up to |-2.1| which is higher than the Kolmogorov value for turbulence of |-5/3|.

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.

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.

Surfactant Variations in Porous Media Localize Capillary Instabilities during Haines Jumps.

We use confocal microscopy to measure velocity and interfacial tension between a trapped wetting phase with a surfactant and a flowing, invading nonwetting phase in a porous medium. We relate interfacial tension variations at the fluid-fluid interface to surfactant concentration and show that these variations localize the destabilization of capillary forces and lead to rapid local invasion of the nonwetting fluid, resulting in a Haines jump. These spatial variations in surfactant concentration are caused by velocity variations at the fluid-fluid interfaces and lead to localization of the Haines jumps even in otherwise very uniform pore structure and pressure conditions. Our results provide new insight into the nature of Haines jumps, one of the most ubiquitous and important instabilities in flow in porous media.

Beyond Darcy's law: The role of phase topology and ganglion dynamics for two-fluid flow.

In multiphase flow in porous media the consistent pore to Darcy scale description of two-fluid flow processes has been a long-standing challenge. Immiscible displacement processes occur at the scale of individual pores. However, the larger scale behavior is described by phenomenological relationships such as relative permeability, which typically uses only fluid saturation as a state variable. As a consequence pore scale properties such as contact angle cannot be directly related to Darcy scale flow parameters. Advanced imaging and computational technologies are closing the gap between the pore and Darcy scale, supporting the development of new theory. We utilize fast x-ray microtomography to observe pore-scale two-fluid configurations during immiscible flow and initialize lattice Boltzmann simulations that demonstrate that the mobilization of disconnected nonwetting phase clusters can account for a significant fraction of the total flux. We show that fluid topology can undergo substantial changes during flow at constant saturation, which is one of the underlying causes of hysteretic behavior. Traditional assumptions about fluid configurations are therefore an oversimplification. Our results suggest that the role of fluid connectivity cannot be ignored for multiphase flow. On the Darcy scale, fluid topology and phase connectivity are accounted for by interfacial area and Euler characteristic as parameters that are missing from our current models.

Improved syntheses of ß-octabromo-meso-triarylcorrole derivatives.

In spite of significant applications as starting materials for a variety of metallocorrole derivatives, free-base ß-octabromo-meso-triarylcorroles continue to be viewed as inaccessible. The reasons range from the need for tedious column-chromatographic purification to limitations of the reductive demetallation protocol for selected systems. Here we report that column chromatography may be entirely avoided for a number of ß-octabromo-meso-tris(p-X-phenyl)corrole derivatives, where X=CF3, NO2, F, H, CH3, and OCH3; instead, analytically pure products may be obtained by recrystallization from chloroform/methanol. In addition, we have presented an optimized synthesis of the heretofore inaccessible, sterically hindered ligand ß-octabromo-meso-tris(2,6-dichlorophenyl)corrole, H3[Br8TDCPC], via reductive demetallation of the corresponding Mn(III) complex. With our earlier report of ß-octabromo-meso-tris(pentafluorophenyl)corrole, H3[Br8TPFPC], a comprehensive set of optimized synthetic protocols are thus in place for a good number of ß-octabromo-meso-triarylcorrole ligands. Furthermore, we have illustrated the use of these ligands by synthesizing the iron complexes Fe[Br8TDCPC]Cl and Fe[Br8TDCPC](py)2, of which the latter lent itself to single-crystal X-ray structure determination.

Subsecond pore-scale displacement processes and relaxation dynamics in multiphase flow.

With recent advances at X-ray microcomputed tomography (µCT) synchrotron beam lines, it is now possible to study pore-scale flow in porous rock under dynamic flow conditions. The collection of four-dimensional data allows for the direct 3-D visualization of fluid-fluid displacement in porous rock as a function of time. However, even state-of-the-art fast-µCT scans require between one and a few seconds to complete and the much faster fluid movement occurring during that time interval is manifested as imaging artifacts in the reconstructed 3-D volume. We present an approach to analyze the 2-D radiograph data collected during fast-µCT to study the pore-scale displacement dynamics on the time scale of 40 ms which is near the intrinsic time scale of individual Haines jumps. We present a methodology to identify the time intervals at which pore-scale displacement events in the observed field of view occur and hence, how reconstruction intervals can be chosen to avoid fluid-movement-induced reconstruction artifacts. We further quantify the size, order, frequency, and location of fluid-fluid displacement at the millisecond time scale. We observe that after a displacement event, the pore-scale fluid distribution relaxes to (quasi-) equilibrium in cascades of pore-scale fluid rearrangements with an average relaxation time for the whole cascade between 0.5 and 2.0 s. These findings help to identify the flow regimes and intrinsic time and length scales relevant to fractional flow. While the focus of the work is in the context of multiphase flow, the approach could be applied to many different µCT applications where morphological changes occur at a time scale less than that required for collecting a µCT scan.

Interfacial velocities and capillary pressure gradients during Haines jumps.

Drainage is typically understood as a process where the pore space is invaded by a nonwetting phase pore-by-pore, the controlling parameters of which are represented by capillary number and mobility ratio. However, what is less understood and where experimental data are lacking is direct knowledge of the dynamics of pore drainage and the associated intrinsic time scales since the rate dependencies often observed with displacement processes are potentially dependent on these time scales. Herein, we study pore drainage events with a high speed camera in a micromodel system and analyze the dependency of interfacial velocity on bulk flow rate and spatial fluid configurations. We find that pore drainage events are cooperative, meaning that capillary pressure differences which extend over multiple pores directly affect fluid topology and menisci dynamics. Results suggest that not only viscous forces but also capillarity acts in a nonlocal way. Lastly, the existence of a pore morphological parameter where pore drainage transitions from capillary to inertial and/or viscous dominated is discussed followed by a discussion on capillary dispersion and time scale dependencies. We show that the displacement front is disperse when volumetric flow rate is less than the intrinsic time scale for a pore drainage event and becomes sharp when the flow rate is greater than the intrinsic time scale (i.e., overruns the pore drainage event), which clearly shows how pore-scale parameters influence macroscale flow behavior.

Real-time 3D imaging of Haines jumps in porous media flow.

Newly developed high-speed, synchrotron-based X-ray computed microtomography enabled us to directly image pore-scale displacement events in porous rock in real time. Common approaches to modeling macroscopic fluid behavior are phenomenological, have many shortcomings, and lack consistent links to elementary pore-scale displacement processes, such as Haines jumps and snap-off. Unlike the common singular pore jump paradigm based on observations of restricted artificial capillaries, we found that Haines jumps typically cascade through 10-20 geometrically defined pores per event, accounting for 64% of the energy dissipation. Real-time imaging provided a more detailed fundamental understanding of the elementary processes in porous media, such as hysteresis, snap-off, and nonwetting phase entrapment, and it opens the way for a rigorous process for upscaling based on thermodynamic models.

Undecaphenylcorroles.

A first major study of undecaphenylcorrole (UPC) derivatives is presented. Three different Cu-UPC derivatives with different para substituents X (X = CF(3), H, CH(3)) on the ß-aryl groups were synthesized via Suzuki-Miyaura coupling of Cu[Br(8)TPC] and the appropriate arylboronic acid. A single-crystal X-ray structure of the X = CF(3) complex revealed a distinctly saddled macrocycle conformation with adjacent pyrrole rings tilted by ~60-66° relative to one another (within the dipyrromethane units), which is somewhat higher than that observed for ß-unsubstituted Cu-TPC derivatives but slightly lower than that observed for Cu[Br(8)TPC] (~70°) derivatives. Electrochemical and electronic absorption measurements afforded some of the first comparative insights into meso versus ß substituent effects on the copper corrole core. The Soret maxima of the Cu-UPC complexes (~440-445 nm), however, are comparable to those of Cu[Br(8)TPC] derivatives and are considerably red-shifted relative to Cu-TPC derivatives. Para substituents on the ß-phenyl groups were found to tune the redox potentials of copper corroles more effectively than those on meso-phenyl substituents, a somewhat surprising observation given that neither the HOMO nor LUMO has significant amplitudes at the ß-pyrrolic positions.

Experimental study of entrainment and drainage flows in microscale soap films.

The thickness of freely suspended surfactant films during vertical withdrawal and drainage is investigated using laser reflectivity. The withdrawal process conducted at capillary numbers below 10(-3) generates initial film thicknesses in the micrometer range; subsequent thinning is predominantly impelled by capillary and not gravitational forces. Under these conditions, our results show that film thinning above and below the critical micelle concentration (cmc) is well approximated by a power law function in time whose exponents, which range from -0.9 to -1.8, are inconsistent with current descriptions of capillary-viscous drainage in inextensible films which predict exponents close to -0.5. Correlations between the experimental fitting parameters illustrate important differences in film behavior across the cmc. In addition, normalization of the drainage data yields a collapse to a single functional form over 3 decades in time for a wide range of initial withdrawal rates. We demonstrate that modification of the interface boundary condition in current models to account for Marangoni stresses through an effective slip parameter yields values of the exponents and other key parameters in excellent agreement with experiment. This modification also successfully describes the withdrawal thickness below the cmc.

High-frequency measurements of interfacial friction using quartz crystal resonators integrated into a surface forces apparatus.

A quartz crystal resonator covered with a thin sheet of mica was integrated into a surface forces apparatus. The shifts in resonance frequency and bandwidth were monitored as the mica surface came into contact with a spherical lens approached from above. We compare experiments where the lens was either coated with a second mica sheet or just had a silver layer evaporated onto its surface. For the contact with the silver surface, strong maxima in bandwidth occurred during the formation and the disruption of the contact. No such maxima were seen when approaching and separating two mica surfaces. We attribute this increased dissipation to sliding and rolling friction, involving plastic deformation of the metal surface under oscillatory load.