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Progress and investigation on lattice Boltzmann modeling of multiple immiscible fluids or components with variable density and viscosity ratios

Lattice Boltzmann models for simulating multiphase flows are relatively new, and much work remains to be done to demonstrate their ability to solve fundamental test cases before they are considered for engineering problems. From this perspective, a hydrodynamic lattice Boltzmann model for simulating immiscible multiphase flows with high density and high viscosity ratios, up to O(1000) and O(100) respectively, is presented and validated against analytical solutions. The method is based on a two phase flow model with operators extended to handle N immiscible fluids. The current approach is O(N) in computational complexity for the number of different gradient approximations. This is a major improvement, considering the O(N{sup 2}) complexity found in most works. A sequence of systematic and essential tests have been conducted to establish milestones that need to be met by the proposed approach (as well as by other methods). First, the method is validated qualitatively by demonstrating its ability to address the spinodal decomposition of immiscible fluids. Second, the model is quantitatively verified for the case of multilayered planar interfaces. Third, the multiphase Laplace law is studied for the case of three fluids. Fourth, a quality index is developed for the three-phase Laplace–Young’s law, which concerns the position of the interfaces between the fluids resulting from the different surface tensions. The current model is compatible with the analytical solution, and is shown to be first order accurate in terms of this quality index. Finally, the multilayered Couette’s flow is studied. In this study, numerical results can recover the analytical solutions for all the selected test cases, as long as unit density ratios are considered. For high density and high viscosity ratios, the analytical solution is recovered for all tests, except that of the multilayered Couette’s flow. Numerical results and a discussion are presented for this unsuccessful test case. It is believed that other LB models may have the same problem in addressing the simulation of multiphase flows with variable density ratios.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A hybridizable discontinuous Galerkin method for modeling fluid–structure interaction

This study presents a novel application of the hybridizable discontinuous Galerkin (HDG) finite element method to the multi-physics simulation of coupled fluid–structure interaction (FSI) problems. Recent applications of the HDG method have primarily been for single-physics problems including both solids and fluids, which are necessary building blocks for FSI modeling. Utilizing these established models, HDG formulations for linear elastostatics, a nonlinear elastodynamic model, and arbitrary Lagrangian–Eulerian Navier–Stokes are derived. The elasticity formulations are written in a Lagrangian reference frame, with the nonlinear formulation restricted to hyperelastic materials. With these individual solid and fluid formulations, the remaining challenge in FSI modeling is coupling together their disparate mathematics on the fluid–solid interface. This coupling is presented, along with the resultant HDG FSI formulation. Verification of the component models, through the method of manufactured solutions, is performed and each model is shown to converge at the expected rate. The individual components, along with the complete FSI model, are then compared to the benchmark problems proposed by Turek and Hron [1]. The solutions from the HDG formulation presented in this work trend towards the benchmark as the spatial polynomial order and the temporal order of integration are increased.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A blended continuous–discontinuous finite element method for solving the multi-fluid plasma model

The multi-fluid plasma model represents electrons, multiple ion species, and multiple neutral species as separate fluids that interact through short-range collisions and long-range electromagnetic fields. The model spans a large range of temporal and spatial scales, which renders the model stiff and presents numerical challenges. To address the large range of timescales, a blended continuous and discontinuous Galerkin method is proposed, where the massive ion and neutral species are modeled using an explicit discontinuous Galerkin method while the electrons and electromagnetic fields are modeled using an implicit continuous Galerkin method. This approach is able to capture large-gradient ion and neutral physics like shock formation, while resolving high-frequency electron dynamics in a computationally efficient manner. The details of the Blended Finite Element Method (BFEM) are presented. The numerical method is benchmarked for accuracy and tested using two-fluid one-dimensional soliton problem and electromagnetic shock problem. The results are compared to conventional finite volume and finite element methods, and demonstrate that the BFEM is particularly effective in resolving physics in stiff problems involving realistic physical parameters, including realistic electron mass and speed of light. The benefit is illustrated by computing a three-fluid plasma application that demonstrates species separation in multi-component plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

IMEX and exact sequence discretization of the multi-fluid plasma model

Multi-fluid plasma models, where an electron fluid is modeled in addition to multiple ion and neutral species as well as the full set of Maxwell's equations, are useful for representing physics beyond the scope of classic MHD. This advantage presents challenges in appropriately dealing with electron dynamics and electromagnetic behavior characterized by the plasma and cyclotron frequencies and the speed of light. For physical systems, such as those near the MHD asymptotic regime, this requirement drastically increases runtimes for explicit time integration even though resolving fast dynamics may not be critical for accuracy. Implicit time integration methods, with efficient solvers, can help to step over fast time-scales that constrain stability, but do not strongly influence accuracy. As an extension, Implicit-explicit (IMEX) schemes provide an additional mechanism to choose which dynamics are evolved using an expensive implicit solve or resolved using a fast explicit solve. In this study, in addition to IMEX methods we also consider a physics compatible exact sequence spatial discretization. Here, this combines nodal bases (H-Grad) for fluid dynamics with a set of vector bases (H-Curl and H-Div) for Maxwell's equations. This discretization allows for multi-fluid plasma modeling without violating Gauss' laws for the electric and magnetic fields. This initial study presents a discussion of the major elements of this formulation and focuses on demonstrating accuracy in the linear wave regime and in the MHD limit for both a visco-resistive and a dispersive ideal MHD problem.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Characterizing mineralization on low carbon steel exposed to aerated and degassed synthetic hydraulic fracture fluids

This study investigates the mineralization occurring at the interface between injected hydraulic fracturing fluids and steel production casing during the shut-in period of unconventional shale wells. Mild steel coupons were reacted with synthetic hydraulic fracturing fluids with varying base fluid and dissolved gas concentrations. Experiments were carried out in an autoclave system set at 50 °C and 2000 PSI for 2 and 14 days. Physical and mineralogical changes to the steel coupons’ surface were characterized using an FEI Quanta 600 field emission gun (FEG) scanning electron microscope (SEM) and a PANalytical XPert Pro diffractometer. Barite precipitation occurred ubiquitously during the first 48 hours in all experimental scenarios. Sulfate radicals created from degradation and reduction of ammonium persulfate breakers facilitate barite formation. Concomitant barite and corrosion related precipitates on the sample surfaces suggest iron hydroxy salts act as nucleation sites for mineral scale growth. These results suggest hydraulic fracturing fluids may have deleterious effects on the wellbore before production of the well begins.

36 MATERIALS SCIENCE↗

Application of parallel distributed Lagrange multiplier technique to simulate coupled Fluid-Granular flows in pipes with varying Cross-Sectional area

Fluid-granular flows are common phenomena in nature and industry. Here, an efficient computational technique based on the distributed Lagrange multiplier method is utilized to simulate complex fluid-granular flows. Each particle is explicitly resolved on an Eulerian grid as a separate domain, using solid volume fractions. The fluid equations are solved through the entire computational domain, however, Lagrange multiplier constrains are applied inside the particle domain such that the fluid within any volume associated with a solid particle moves as an incompressible rigid body. The particle–particle interactions are implemented using explicit force-displacement interactions for frictional inelastic particles similar to the DEM method with some modifications using the volume of an overlapping region as an input to the contact forces. Here, a parallel implementation of the method is based on the SAMRAI (Structured Adaptive Mesh Refinement Application Infrastructure) library.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Surfactants are Ineffective for Reducing Imbibition of Water-Based Fracturing Fluids in Deep Gas Reservoirs

Minimizing loss of injected hydraulic fracturing fluids into shale along fracture-matrix boundaries is desired because imbibed water restricts gas production and wastes valuable water resources. This problem has motivated the addition of surfactants into water-based hydraulic fracturing fluids in order to reduce the capillary driving force for imbibition. Here, we show that reduction in interfacial tension and wettability alteration has negligible ability to reduce imbibition in deep gas reservoirs. The effectiveness of altering capillary forces acting at the wetting front also depends on the injection pressure acting at the fracture-matrix boundary. The pressure at the interface between the fracture and the shale matrix is constrained between the reservoir pore pressure and formation pressure (rock fracture pressure, also known as breakdown pressure of the rock) and increases with depth to magnitudes that greatly exceed that of capillary pressures. Furthermore, the analyses presented here show that even maximum alteration of interfacial properties that result in strongly hydrophobic interactions between the fracturing fluid and reservoir rock is incapable of significantly reducing imbibition in deep reservoirs. Instead of using surfactants, this analysis points to decreases in wellbore shut-in pressures and shut-in times as practical options for reducing imbibition losses of water-based fluids.

03 NATURAL GAS↗

Integrated Experimental and Modeling Study of Geochemical Reactions of Simple Fracturing Fluids with Caney Shale

Interactions between rock minerals and hydraulic fluids directly impact the geochemical and geomechanical properties of shale formations. However, the mechanisms of geochemical reactions in shale unconventional reservoirs remain poorly understood. Here, to investigate the geochemical reactions between shale and hydraulic fracturing fluids, a series of batch reactor experiments were undertaken. Three rock samples with different mineralogical compositions and three fluid samples of different compositions (deionized water, deionized water + 2% potassium chloride (KCl), and deionized water + 0.5% choline chloride (C 5 H 14 ClNO) were used. Experiments were undertaken at reservoir temperature and atmospheric pressure. Elemental compositions of effluents after 1, 3, 7, 14, 28 days were analyzed using Inductively Couple Plasma Mass Spectrometry (ICP-MS). Medical Computed Tomography (CT) scan and X-ray Fluorescence (XRF) were conducted on the entire core run to help upscale results obtained from rock-fluid interaction experiments. Geochemical modeling using a reactive simulator, TOUGHREACT, was undertaken to corroborate experimental results. Results show that lower pH triggered high dissolution rates in the rock samples, especially the carbonate components. As pH increased, the rate of dissolution declined significantly, though for most cases dissolution still continued. Observed dissolved silica concentrations were much higher than the quartz solubility, suggesting that much of the silica originates from more soluble silica polymorphs and possibly desorption from clay mineral exchange sites. Concentration of most elemental species in solution increased but aluminium and magnesium concentrations declined rapidly following initial entry into solution. Geochemical modeling corroborated the conclusions regarding mineral dissolution and precipitation observed from experiments, notably; the dissolution of calcite and oxidation of pyrite in reacted shale samples, the likely presence of silica polymorphs such as opal, chalcedony or amorphous silica in these samples, and the reduction of Al and Mg concentrations in solution by precipitation of secondary aluminosilicate phases. The de-flocculation of clay minerals during reaction implies fines migration after hydraulic fracturing. This is detrimental to reservoir productivity as clay fines are displaces and lodged within the micro and nano-fractures created during fracturing. The immediate consumption of aluminium and magnesium also has implications on blockage of hydrocarbon pathways due to precipitation of new minerals in these locations.

04 OIL SHALES AND TAR SANDS↗

Machine Learning-Based Upscaling of Finite-Size Molecular Dynamics Diffusion Simulations for Binary Fluids

Molecular diffusion coefficients calculated using molecular dynamics (MD) simulations suffer from finite-size (i.e., finite box size and finite particle number) effects. Results from finite-sized MD simulations can be upscaled to infinite simulation size by applying a correction factor. For self-diffusion of single-component fluids, this correction has been well-studied by many researchers including Yeh and Hummer (YH); for binary fluid mixtures, a modified YH correction was recently proposed for correcting MD-predicted Maxwell–Stephan (MS) diffusion rates. In this study we use both empirical and machine learning methods to identify improvements to the finite-size correction factors for both self-diffusion and MS diffusion of binary Lennard-Jones (LJ) fluid mixtures. Using artificial neural networks (ANNs), the error in the corrected LJ fluid diffusion is reduced by an order of magnitude versus existing YH corrections, and the ANN models perform well for mixtures with large dissimilarities in size and interaction energies where the YH correction proves insufficient.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Thermophysical Properties of Nanoparticle-Enhanced Ionic Liquids (NEILs) Heat-Transfer Fluids

An experimental investigation was completed on nanoparticle enhanced ionic liquid heat transfer fluids as an alternative to conventional organic based heat transfer fluids (HTFs). These nanoparticle-based HTFs have the potential to deliver higher thermal conductivity than the base fluid without a significant increase in viscosity at elevated temperatures. The effect of nanoparticle morphology and chemistry on thermophysical properties was examined. Whisker shaped nanomaterials were found to have the largest thermal conductivity temperature dependence and were also less likely to agglomerate in the base fluid than spherical shaped nanomaterials.

42 ENGINEERING↗

Impact of Pore Fluid Chemistry on Fine-Grained Sediment Fabric and Compressibility

Fines, defined here as grains or particles, less than 75µm in diameter, exist nearly ubiquitously in natural sediment, even those classified as coarse. Macroscopic sediment properties, such as compressibility, which relates applied effective stress to the resulting sediment deformation, depend on the fabric of fines. Unlike coarse grains, fines have sizes and masses small enough to be more strongly influenced by electrical interparticle forces than by gravity. These electrical forces acting through pore fluids are influenced by pore-fluid chemistry changes. Macroscopic property dependence on pore-fluid chemistry must be accounted for in sediment studies involving subsurface flow and sediment stability analyses, as well as in engineered flow situations such as groundwater pollutant remediation, hydrocarbon migration or other energy resource extraction applications. This study demonstrates how the liquid-limit-based electrical sensitivity index can be used to predict sediment compressibility changes due to pore-fluid chemistry changes. Laboratory tests of electrical sensitivity, sedimentation and compressibility illustrate mechanisms linking micro- and macro-scale processes for selected pure, endmember fines. In conclusion, a specific application considered here is methane extraction via depressurization of gas hydrate-bearing sediment, which causes a dramatic pore-water salinity drop concurrent with sediment being compressed by the imposed effective stress increase.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

On equivalence of high temperature series expansion and coupling parameter series expansion in thermodynamic perturbation theory of fluids

The coupling parameter series expansion and the high temperature series expansion in the thermodynamic perturbation theory of fluids are shown to be equivalent if the interaction potential is pairwise additive. As a consequence, for the class of fluids with the potential having a hardcore repulsion, if the hard-sphere fluid is chosen as reference system, the terms of coupling parameter series expansion for radial distribution function, direct correlation function, and Helmholtz free energy follow a scaling law with temperature. The scaling law is confirmed by application to square-well fluids.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Communication: Non-Hadwiger terms in morphological thermodynamics of fluids

We demonstrate that the Hadwiger form of the free energy of a fluid in contact with a wall is insufficient to describe the low-density behavior of a hard-sphere fluid. This implies that morphological thermodynamics of the hard-sphere fluid is an approximate theory if only four geometric measures are included. In order to quantify deviations from the Hadwiger form we extend standard fundamental measure theory of the bulk fluid by introducing additional scaled-particle variables which allow for the description of non-Hadwiger coefficients. The theory is in excellent agreement with recent computer simulations. The fact that the leading non-Hadwiger coefficient is one order of magnitude smaller than the smallest Hadwiger coefficient lends confidence to the numerous results that have been previously obtained within standard morphological thermodynamics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Fluids confined in wedges and by edges: Virial series for the line-thermodynamic properties of hard spheres

This work is devoted to analyze the relation between the thermodynamic properties of a confined fluid and the shape of its confining vessel. Recently, new insights in this topic were found through the study of cluster integrals for inhomogeneous fluids that revealed the dependence on the vessel shape of the low density behavior of the system. Here, the statistical mechanics and thermodynamics of fluids confined in wedges or by edges is revisited, focusing on their cluster integrals. In particular, the well known hard sphere fluid, which was not studied in this framework so far, is analyzed under confinement and its thermodynamic properties are analytically studied up to order two in the density. Furthermore, the analysis is extended to the confinement produced by a corrugated wall. These results rely on the obtained analytic expression for the second cluster integral of the confined hard sphere system as a function of the opening dihedral angle 0 < β < 2π. It enables a unified approach to both wedges and edges.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Fluids confined in wedges and by edges: From cluster integrals to thermodynamic properties referred to different regions

Recently, new insights into the relation between the geometry of the vessel that confines a fluid and its thermodynamic properties were traced through the study of cluster integrals for inhomogeneous fluids. In this work, I analyze the thermodynamic properties of fluids confined in wedges or by edges, emphasizing on the question of the region to which these properties refer. In this context, the relations between the line-thermodynamic properties referred to different regions are derived as analytic functions of the dihedral angle α, for 0 < α < 2π, which enables a unified approach to both edges and wedges. As a simple application of these results, I analyze the properties of the confined gas in the low-density regime. Finally, using recent analytic results for the second cluster integral of the confined hard sphere fluid, the low density behavior of the line thermodynamic properties is analytically studied up to order two in the density for 0 < α < 2π and by adopting different reference regions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Thermodynamics of Yukawa fluids near the one-component-plasma limit

Thermodynamics of weakly screened (near the one-component-plasma limit) Yukawa fluids in two and three dimensions is analyzed in detail. It is shown that the thermal component of the excess internal energy of these fluids, when expressed in terms of the properly normalized coupling strength, exhibits the scaling pertinent to the corresponding one-component-plasma limit (the scalings differ considerably between the two- and three-dimensional situations). This provides us with a simple and accurate practical tool to estimate thermodynamic properties of weakly screened Yukawa fluids. Particular attention is paid to the two-dimensional fluids, for which several important thermodynamic quantities are calculated to illustrate the application of the approach.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Statistical properties of three-dimensional two-fluid plasma model

The nonlinear dynamics of incompressible non-dissipative two-fluid plasma model is investigated through classical Gibbs ensemble methods. Liouville's theorem of phase space for each wave number is proved, and the absolute equilibrium spectra for Galerkin truncated two-fluid model are calculated. In two-fluid theory, the equilibrium is built on the conservation of three quadratic invariants: the total energy and the self-helicities for ions and electrons fluid, respectively. The implications of statistic equilibrium spectra with arbitrary ratios of conserved invariants are discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

On the relative rotational motion between rigid fibers and fluid in turbulent channel flow

In this study, the rotation of small rigid fibers relative to the surrounding fluid in wall-bounded turbulence is examined by means of direct numerical simulations coupled with Lagrangian tracking. Statistics of the relative (fiber-to-fluid) angular velocity, referred to as slip spin in the present study, are evaluated by modelling fibers as prolate spheroidal particles with Stokes number, St, ranging from 1 to 100 and aspect ratio, λ, ranging from 3 to 50. Results are compared one-to-one with those obtained for spherical particles (λ = 1) to highlight effects due to fiber length. The statistical moments of the slip spin show that differences in the rotation rate of fibers and fluid are influenced by inertia, but depend strongly also on fiber length: Departures from the spherical shape, even when small, are associated with an increase of rotational inertia and prevent fibers from passively following the surrounding fluid. An increase of fiber length, in addition, decouples the rotational dynamics of a fiber from its translational dynamics suggesting that the two motions can be modelled independently only for long enough fibers (e.g., for aspect ratios of order ten or higher in the present simulations)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗