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Impacts of Pore Network-Scale Wettability Heterogeneity on Immiscible Fluid Displacement: A Micromodel Study
The mixed-wet nature of reservoir formations imposes a wide range of rock wettability from strong resident-fluid wetting to strong invading-fluid wetting. The characteristics of two-phase flow in porous media composed of mixed-wetting surfaces remain poorly understood. In this study, we investigated the displacement of resident ethylene glycol (EG) by hexane in two mixed-wet micromodels of identical 2.5-D geometry heterogeneity, with uniformly or heterogeneously distributed patches strongly wetting to hexane. These patches are mixed among pores with unaltered EG-wetting surfaces. Along with control tests in the originally EG-wet micromodel, here we show the classic fingering and transitions in flow regimes at $logCa$ (capillary number) from -7.2 to -3.9. Moreover, pore-scale distributions of wettability and their spatial correlation influence displacement efficiency. In the two mixed-wet micromodels, we found (a) an increase of steady-state hexane saturation at the end of experiments by up to 0.12 in the capillary fingering regime and a decrease of at most by 0.06 in the viscous fingering regime, compared to the EG-wet micromodel, and (b) dispersed and fragmented hexane distribution after displacement. Brine drainage during supercritical CO 2 (scCO 2 ) injections in these micromodels occurs with lower wettability contrasts, and under similar viscosity ratios and interfacial tensions resulted in higher displacement efficiency relative to displacement of EG by hexane. While mixed-wettability can enhance displacement efficiency compared to uniform wettability, the dynamics of immiscible fluids in strong mixed-wet reservoirs are expected to be less pronounced in contributing to the efficiency of geological CO 2 sequestration, oil recovery, and remediation of hydrocarbon-contaminated aquifers.
Alcove formation in dissolving cliffs driven by density inversion instability
We demonstrate conditions that give rise to cave-like features commonly found in dissolving cliffsides with a minimal two-phase physical model. Alcoves that are wider at the top and tapered at the bottom, with sharp-edged ceilings and sloping floors, are shown to develop on vertical solid surfaces dissolving in aqueous solvents. As evident from descending plumes, sufficiently large indentations evolve into alcoves as a result of the faster dissolution of the ceiling due to a solutal Rayleigh–Bénard density inversion instability. In contrast, defects of size below the boundary layer thickness set by the critical Rayleigh number smooth out, leading to stable planar interfaces. Furthermore, the ceiling recession rate and the alcove opening area evolution are shown to be given to first-order by the critical Rayleigh number. By tracking passive tracers in the fluid phase, we show that the alcoves are shaped by the detachment of the boundary layer flow and the appearance of a pinned vortex at the leading edge of the indentations. The attached boundary layer past the developing alcove is then found to lead to rounding of the other sides and the gradual sloping of the floor.
Insight into pseudo-film-boiling in supercritical water under simplified interfacial conditions
The focus of this paper is the physics of supercritical water film boiling through the simulation of natural convection of supercritical water in a rectangular cavity. It has been widely believed that above a fluid's critical point, only one phase exists. However, recent research has indicated the existence of distinct gas-like and liquid-like regions separated by the Widom line, which is the locus of the maxima of the specific heat. Along the Widom line, density decreases sixfold, viscosity drops by a factor of two, while specific heat spikes by an order of magnitude. These variations, specifically in density and viscosity, produce a thick pseudo-interface and flow dynamics behavior akin to film-boiling, denoted here as pseudo-two-phase flow dynamics. When the cavity is heated from the bottom, a pseudo-film of gas-like fluid is formed at the heated wall, and the flow complexity evolves, characterized by the formation of multiple vortices. Results demonstrate the ability of modern conjugate heat transfer computational fluid dynamics to capture the pseudo two-phase regime, with the formation of a pseudo-film at the heated wall. Further, the boiling curve is studied, showing an increase in heat flux with an increase in the temperature differential between the wall and the pseudo-critical temperature. Furthermore, results also show a previously uncharacterized instability, where the convection cells in the cavity oscillate and can flip directions under certain conditions.
Optimal surface-tension isotropy in the Rothman-Keller color-gradient lattice Boltzmann method for multiphase flow
The Rothman-Keller color-gradient (CG) lattice Boltzmann method is a popular method to simulate two-phase flow because of its ability to deal with fluids with large viscosity contrasts and a wide range of interfacial tensions. Here, two fluids are labeled red and blue, and the gradient in the color difference is used to compute the effect of interfacial tension. It is well known that finite-difference errors in the color-gradient calculation lead to anisotropy of interfacial tension and errors such as spurious currents. Here, we investigate the accuracy of the CG calculation for interfaces between fluids with several radii of curvature and find that the standard CG calculations lead to significant inaccuracy. Specifically, we observe significant anisotropy of the color gradient of order 7% for high curvature of an interface such as when a pinchout occurs. We derive a second order accurate color gradient and find that the diagonal nearest neighbors can be weighted differently than in the usual color-gradient calculation such that anisotropy is minimized to a fraction of a percent. The optimal weights that minimize anisotropy for the smallest radius of curvature interface are found to be w = (0.298, 0.284, 0.275) for diagonal nearest neighbors for the cases of the interface smoothing parameter β = (0.5, 0.7, 0.99), somewhat higher than the w = 0.25 value derived by Leclaire et al. [Leclaire, Reggio, and Trepanier, Computers and Fluids 48, 98 (2011)] based on obtaining isotropic errors to second order. We find that use of these optimal w values yields over a factor of 10 decrease in anisotropy and over a factor of 30 decrease in mean anisotropy relative to using the standard w = 1 value. And we find a factor of about 2 decrease in the anisotropic error and up to factor 15 decrease in mean anisotropic error relative to the choice of w = 0.25 for small radius of curvature interfaces. The improved CG calculations will allow the method to be more reliably applied to studies of phenomenology and pore scale processes such as viscous and capillary fingering, and droplet formation where surface-tension isotropy of narrow fingers and small droplets plays a crucial role in correctly capturing phenomenology. We present an example illustrating how different phenomena can be captured using the improved color-gradient method. Namely, we present simulations of a wetting fluid invading a fluid filled pipe where the viscosity ratio of fluids is unity in which droplets form at the transition to fingering using the improved CG calculations that are not captured using the standard CG calculations. We present an explanation of why this is so which relates to anisotropy of the surface tension, which inhibits the pinchouts needed to form droplets.
Symmetric Mass Generation with Four SU(2) Doublet Fermions
We study a single exactly massless staggered fermion in the fundamental representation of an SU(2) gauge group. We utilize an nHYP-smeared fermion action supplemented with additional heavy Pauli-Villars fields that serve to decrease lattice artifacts. The phase diagram exhibits a clear two-phase structure with a conformal phase at weak coupling and a novel new phase, the symmetric mass generation (SMG) phase, appearing at strong coupling. The SMG phase is confining with all states gapped and chiral symmetry unbroken. Our finite size scaling analysis provides strong evidence that the phase transition between these two phases is continuous, which would allow for the existence of a continuum SMG phase. Furthermore, the renormalization group flows are consistent with a 𝛽 function that vanishes quadratically at the new fixed point, suggesting that the 𝑁 𝑓 = 4 flavor SU(2) gauge theory lies at the opening of the conformal window.
Evaluating the Feasibility of Measuring and Analyzing Strain Caused by Changes in Barometric Pressure in the Vadose Zone
Changes in barometric pressure propagate into the subsurface where they can affect water level measurements in wells and cause vertical strain. Previous strain sensors were developed to measure vertical strain, but they were limited to measurements at a single depth, making it difficult to evaluate strains from a migrating pressure wave. Technology known as Coherence-length-gated Microwave Photonics Interferometry (CMPI) uses optical fiber sensors to measure strain at multiple locations. It has the potential to detect strain caused by variations in barometric pressure at multiple depths in the subsurface. The goal of this study is to evaluate the feasibility of using this technology to record the changes in vertical strain in the vadose zone from small fluctuations in air pressure. Propagation of these air pressure fluctuations is affected by hydrogeological properties such as water content and permeability. A second goal of this study is to evaluate how these properties affect the air pressure distribution, strain, and gas-phase diffusivity with a long-term goal of using strain to monitor the vadose zone. The focus of this study is on a suite of laboratory experiments that used a sand-filled column with an open head space. The CMPI fiber was packaged and embedded along the axis of the column to measure the strain at multiple locations while air pressure transducers were installed through the wall of the column. Small periodic fluctuations in air pressure, similar to barometric pressure fluctuations, were created in the head space of the column using an audio driven speaker driven at 4 Hz using a sinusoidal signal created by a function generator. Then, the fluctuations propagated along the column where they were measured by the transducers and recorded as functions of time. Initial tests were conducted using dry sand, but then additional tests were conducted after injecting water into the column, which changed the hydrologic and mechanical properties. Another experiment was conducted after creating a thin barrier to air flow, which was designed to simulate a thin layer of saturated ground during rainfall. A final experiment was conducted by changing the grain size of the material to create a heterogeneity in the upper half of the column. The suite of six experiments was conducted to highlight effects of variations in water content and heterogeneities on air pressure and vertical strain. Numerical simulations were also created to evaluate the laboratory data and to provide a baseline analysis for the results. The numerical simulations used the governing equations to linear poroelasticity and two-phase flow with boundary conditions representing the experiments. The conceptual model for strain caused by barometric pressure recognizes that a fluctuating barometric pressure causes fluctuations in the air pore pressure that decrease in amplitude and lag in time with increase depth. The pressure distribution results in two different loads that cause strain: 1.) a mechanical load as the barometric pressure acts on the ground surface; and 2.) pressure loading in the pore space. The results show that the total vertical strain is a contribution of both of these loads, and this is the strain that was observed in the laboratory. The lab experiments show that both air pressure and strain vary as sinusoids that propagate with depth. The amplitude of the air pressure and strain decrease as a function of depth in all the conditions that were evaluate. For example, in the dry sand, the amplitude of the air pressure decreases from 25 Pa at the head space to 5 Pa at a depth of 70 cm, whereas the amplitude of the strain decreases from 0.15 to 0.06 µε over the same depth interval. In many cases the amplitudes decrease is approximately negative exponential functions of depth. When water was injected into the sand and the saturation increased, the amplitude of the air pressure increased in the partially saturated sand but decreased sharply to zero where the soil was saturated. The strain decreased with depth, but the transition from partially to fully saturated conditions had little effect on the strain profile, even though it had a major effect on the air pressure. This apparently is because strain is caused by variations in both water and air pressure. The fluctuating air pressure caused the water pressure to fluctuate, which caused strain throughout the column. Phase delay of the air pressure and the strain both increase as linear to bi-linear functions of depth. The phase delays indicate that pressure propagates at a velocity of 7 to 8 m/s in dry or partially saturated sand, but it drops by more than an order of magnitude in the vicinity of the capillary fringe. The phase delays indicate the strain propagates faster than the pressure. The data indicate that the strain propagates from 1.2 to more than 4x faster than the pressure. Switching from sand to silt in the column caused the velocity of the pressure to drop by roughly half for both pressures, but curiously, it had little effect on the velocity of the strain.