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DOE OSTI2023

A flexible gyro-fluid system of equations

Gyro-fluid equations are velocity space moments of the gyrokinetic equations. Special gyro-Landau-fluid closures have been developed that include the damping due to kinetic resonances by fitting to the collisionless local plasma response functions. This damping allows for accurate linear eigenmodes to be computed with a relatively low number of velocity space moments compared to the number of velocity quadrature points in gyrokinetic codes. However, none of the published gyro-Landau-fluid closure schemes considers the Onsager symmetries of the resulting quasi-linear fluxes as a constraint. Onsager symmetry guarantees that the matrix of diffusivities is positive definite, an important property for the numerical stability of a transport solver. A two-parameter real closure for improving the accuracy of low-resolution gyro-fluid equations, which preserves the Onsager symmetry and allows higher velocity space moments, is presented in this paper. The new linear gyro-fluid system (GFS) is used to extend the TGLF quasi-linear transport model so that it can compute the energy and momentum fluxes due to parallel magnetic fluctuations, completing the transport matrix. The GFS equations do not use a bounce average approximation. The GFS equations are fully electromagnetic with general flux surface magnetic geometry, pitch angle scattering for electron collisions, and subsonic equilibrium toroidal rotation. Using GFS eigenmodes in the quasi-linear TGLF model will be shown to yield a more accurate match to fluxes computed by CGYRO turbulence simulations. In conclusion, prospects for future applications of a quasi-linear theory to new plasma transport regimes and magnetic confinement devices in addition to tokamaks are opened by the flexibility of the GFS eigensolver.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Type-II spacetimes and the double copy for fluids metrics

In our previous paper [Keeler , From Navier-Stokes to Maxwell via Einstein, .] we discussed type-D and type-N fluid-dual spacetimes and provided their associated single copies in the context of the Weyl double copy. In this work we extend our analysis to more general fluids thereby requiring the application of the double-copy picture to type-II spacetimes. By combining our previous type-D and type-N fluids via their associated stream functions we construct an example of a viable type-II double copy. We show that the gravity duals of these fluids perturbatively satisfy Einstein’s equations. We use a near-horizon expansion to identify the type-II double copy for the fluid-dual spacetimes. We show a Maxwell spinor ansatz containing a heterogeneous bispinor component is necessary to provide a viable type-II double copy at the lowest order.

Fluid-gravity correspondence↗

DOE OSTI2017

Phase field model of fluid-driven fracture in elastic media: Immersed-fracture formulation and validation with analytical solutions

Propagation of fluid-driven fractures plays an important role in natural and engineering processes, including transport of magma in the lithosphere, geologic sequestration of carbon dioxide, and oil and gas recovery from low-permeability formations, among many others. The simulation of fracture propagation poses a computational challenge as a result of the complex physics of fracture and the need to capture disparate length scales. Phase field models represent fractures as a diffuse interface and enjoy the advantage that fracture nucleation, propagation, branching, or twisting can be simulated without ad hoc computational strategies like remeshing or local enrichment of the solution space. Here we propose a new quasi-static phase field formulation for modeling fluid-driven fracturing in elastic media at small strains. The approach fully couples the fluid flow in the fracture (described via the Reynolds lubrication approximation) and the deformation of the surrounding medium. The flow is solved on a lower dimensionality mesh immersed in the elastic medium. This approach leads to accurate coupling of both physics. We assessed the performance of the model extensively by comparing results for the evolution of fracture length, aperture, and fracture fluid pressure against analytical solutions under different fracture propagation regimes. Thus, the excellent performance of the numerical model in all regimes builds confidence in the applicability of phase field approaches to simulate fluid-driven fracture.

58 GEOSCIENCES↗

DOE OSTI2017

Aseismic Motions Drive a Sparse Seismicity During Fluid Injections Into a Fractured Zone in a Carbonate Reservoir

An increase in fluid pressure in faults can trigger seismicity and large aseismic motions. Understanding how fluid and faults interact is an essential goal for seismic hazard and reservoir monitoring, but this key relation remains unclear. We developed an in situ experiment of fluid injections at a 10 meter scale. Water was injected at high pressure in different geological structures inside a fault damaged zone, in limestone at 280 m depth in the Low Noise Underground Laboratory (France). Induced seismicity, as well as strains, pressure, and flow rate, was continuously monitored during the injections. Although nonreversible deformations related to fracture reactivations were observed for all injections, only a few tests generated seismicity. Events are characterized by a 0.5-to-4 kHz content and a small magnitude (approximately -3.5). They are located within 1.5 m accuracy between 1 and 12 m from the injections. Comparing strain measurements and seismicity shows that more than 96% of the deformation is aseismic. The seismic moment is also small compared to the one expected from the injected volume. Moreover, a dual seismic behavior is observed as (1) the spatiotemporal distribution of some cluster of events is clearly independent from the fluid diffusion (2) while a diffusion-type pattern can be observed for some others clusters. Furthermore, the seismicity might therefore appear as an indirect effect to the fluid pressure, driven by aseismic motion and related stress perturbation transferred through failure.

58 GEOSCIENCES↗

DOE OSTI2021

A coupled fluid-mechanical workflow to simulate the directed energy deposition additive manufacturing process

Simulation of additive manufacturing processes can provide essential insight into material behavior, residual stress, and ultimately, the performance of additively manufactured parts. In this work, we describe a new simulation based workflow utilizing both solid mechanics and fluid mechanics based formulations within the finite element software package SIERRA (Sierra Solid Mechanics Team in Sierra/Solid Mechanics 4.52 User’s Guide SAND2019-2715. Technical report, Sandia National Laboratories, 2011) to enable integrated simulations of directed energy deposition (DED) additive manufacturing processes. In this methodology, a high-fidelity fluid mechanics based model of additive manufacturing is employed as the first step in a simulation workflow. This fluid model uses a level set field to track the location of the boundary between the solid material and background gas and precisely predicts temperatures and material deposition shapes from additive manufacturing process parameters. Next, the resulting deposition shape and temperature field from the fluid model are then mapped into a solid mechanics formulation to provide a more accurate surface topology for radiation and convection boundary conditions and a prescribed temperature field. Solid mechanics simulations are then conducted to predict the evolution of material stresses and microstructure within a part. By combining thermal history and deposition shape from fluid mechanics with residual stress and material property evolutions from solid mechanics, additional fidelity and precision are incorporated into additive manufacturing process simulations providing new insight into complex DED builds.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Predicting Fluid Flow Regime, Permeability, and Diffusivity in Mudrocks from Multiscale Pore Characterisation

In geoenergy applications, mudrocks prevent fluids to leak from temporary (H 2 , CH 4 ) or permanent (CO 2 , radioactive waste) storage/disposal sites and serve as a source and reservoir for unconventional oil and gas. Understanding transport properties integrated with dominant fluid flow mechanisms in mudrocks is essential to better predict the performance of mudrocks within these applications. In this study, small-angle neutron scattering (SANS) experiments were conducted on 71 samples from 13 different sets of mudrocks across the globe to capture the pore structure of nearly the full pore size spectrum (2 nm–5 μm). We develop fractal models to predict transport properties (permeability and diffusivity) based on the SANS-derived pore size distributions. The results indicate that transport phenomena in mudrocks are intrinsically pore size-dependent. Depending on hydrostatic pore pressures, transition flow develops in micropores, slip flow in meso- and macropores, and continuum flow in larger macropores. Fluid flow regimes progress towards larger pore sizes during reservoir depletion or smaller pore sizes during fluid storage, so when pressure is decreased or increased, respectively. Capturing the heterogeneity of mudrocks by considering fractal dimension and tortuosity fractal dimension for defined pore size ranges, fractal models integrate apparent permeability with slip flow, Darcy permeability with continuum flow, and gas diffusivity with diffusion flow in the matrix. This new model of pore size-dependent transport and integrated transport properties using fractal models yields a systematic approach that can also inform multiscale multi-physics models to better understand fluid flow and transport phenomena in mudrocks on the reservoir and basin scale.

36 MATERIALS SCIENCE↗

DOE OSTI2024

The MOOSE fluid properties module

The Fluid Properties module within the Multiphysics Object-Oriented Simulation Environment (MOOSE) is used to compute fluid properties for numerous applications, ranging from nuclear reactor thermal hydraulics to geothermal energy. Those applications drove the development of the module to enable numerous different fluid equations of states, property lookups with primitive and conserved flow variable to cater to pressure and density-driven solvers, and an object-oriented design facilitating expansion and maintenance. Each fluid property is implemented in its own class but inherits capabilities such as automatic differentiation, automated out-of-bounds handling or variable conversion capabilities. Here, this paper presents the module, its design, its user and developer interface, its content in terms of fluids and properties, and several of its applications showing its major role in the MOOSE simulation ecosystem.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

NdPO 4 solubility and aqueous Neodymium speciation in supercritical fluids: An experimental study at 500–700 °C and 1.7 kbar

A key aspect in the formation of rare earth elements (REE) deposits is the role of REE transport as aqueous REE complexes in supercritical hydrothermal solutions, where the nature of the aqueous complex is controlled by solution composition, temperature and pressure. Despite chloride being considered as one of the most abundant transporting ligands in magmatic-hydrothermal fluids, experimental investigations on the stability of aqueous REE chloride complexes are scarce above 300 °C. In this study, synthetic NdPO 4 crystals were reacted with non-saline and saline (0, 0.05 and 0.5 mNaCl), acidic (0.01 mHCl) aqueous solutions in a series of solubility experiments conducted at 500–700 °C and 1.7 kbar, where the solubilities were determined using a stable Nd isotope ( 145 Nd isotope spike) dilution technique. NdPO 4 solubility ranges between 28 ppm and 10,858 ppm, where solubility increases with both temperature and salinity. At 500 °C, log mNdPO 4 increases from –3.93 to –1.60 and there is a strong correlation between NdPO 4 solubility and NaCl concentrations (slope of 1.2 ± 0.3), indicating stabilization of the Nd chloride aqueous complexes with a stoichiometry corresponding to NdCl 2+ . At 600 °C, this correlation is weaker (slope of 0.4, log mNdPO 4 increases from –2.63 to –1.88) indicating the stabilization of both Nd chloride and hydroxyl species controlling solubility. At 700 °C, NdPO 4 solubility is largely independent of NaCl concentration indicating that solubility is controlled by Nd hydroxyl complexes, where stoichiometry suggests the neutral Nd(OH) 3 0 species is dominant. The solubility product (Ksp) of NdPO4 is derived from experimental data with the relation: log K sp = -41.81 – 0.057T – 20987/T, with T temperature in Kelvin. Comparison of the measured Nd phosphate solubility to thermodynamic predictions using the available Helgeson-Kirkham-Flowers equation of state parameters for aqueous Nd complexes indicate that predictions are up to three orders of magnitude lower compared to experimental observations. This discrepancy is most pronounced in saline solutions, suggesting that thermodynamic properties of the REE chloride species in supercritical fluids require revision. Numerical simulations of fluid-rock interaction between acidic, saline fluids and a Strange Lake felsic mineral assemblage demonstrates that NdPO 4 solubility predictions from models are four to six orders of magnitude lower than those calculated based on empirical fits from experiments, which suggests that acidic, saline fluids may play an important role in mobilizing large amounts of light REE from 450 to 700 °C.

58 GEOSCIENCES↗

DOE OSTI2021

Field-scale fault reactivation experiments by fluid injection highlight aseismic leakage in caprock analogs: Implications for CO 2 sequestration

Observations on tens-of-meter scale experiments of fault activation by fluid injection conducted in shales allow exploring how aseismic and seismic events may jeopardize the integrity of a sealing caprock overlying a CO 2 sequestration reservoir. We contrast the behavior of shale faults with another set of experiments conducted in carbonates. Significant fluid leakage occurs along the initially low-permeability shale faults when rupture is activated. Most of the leakage pathway closes when fluid injection ceases and fluid pressure drops. Dilatant slip on the fault plane alone does not explain the observed leakage behavior, which is also caused by fault opening favored by the softness of the shale, and by the structure of the fault zone that prevents fluids from diffusing into the adjacent damage zone. Experiments show a large amount of aseismic deformation. Small-magnitude seismicity (M w < -2.5) is observed outside the pressurized leakage patch. Stress transferred from this aseismic deformation patch can build up to stress-criticality and favor seismicity. Thus, in terms of fault activation in caprocks, aseismic fault slip leading to increased permeability and a loss of seal integrity is of great concern.

58 GEOSCIENCES↗

DOE OSTI2018

Exergy of air, CO 2 , and H 2 O for use as geothermal fluids

Geothermal energy refers to the thermal energy naturally stored in the hot rock formation buried deep beneath the Earth’s surface. To harvest this source of energy, a fluid is pumped down in a set of injection wells, circulates through the hot rock and then is collected via a set of production wells for heating or other purposes. Furthermore, the selection of this fluid is an important component of a geothermal system. In this work, we review, evaluate, and develop the fundamental equations that can reliably predict the thermodynamic and the transport properties of air, CO 2 , and H 2 O. Using these equations, we characterize and compare the heat extraction and exergy carried by these fluids as they circulate through a hot rock reservoir to determine which fluid offers better functionality for geothermal heat harvesting applications. The results indicate that, in terms of heat extraction and exergy, air is a better fluid compared to CO 2 and water.

15 GEOTHERMAL ENERGY↗

DOE OSTI2022

Design and performance of a variable gap system for thermal conductivity measurements of high temperature, corrosive, and reactive fluids

We report high-temperature fluids such as molten salts, liquid metals, and gasses are being proposed for many advanced energy systems including thermal energy storage devices, concentrating solar plants, and advanced nuclear reactor designs. However, the chemical behavior and thermophysical properties of many of these fluids have not been well characterized, which hinders the design, modeling, safety analysis, and deployment of these systems. Thermal conductivity is a property that is especially limited by existing measurement capabilities, which are subject to errors caused by convection, material interaction, radiative heat transfer, and instrument degradation. Therefore, there is a lack of standard, systematic measurement techniques for high-temperature, reactive, and corrosive fluids. In this work, the development of a variable gap thermal conductivity measurement system is detailed. The system is designed to measure the thermal conductivity of highly corrosive and reactive fluids, and survive operation between 100 °C and 800 °C. The effects of convection are minimized by limiting the thickness of the specimen to thin sizes (<0.3 mm). Corrections for radiative heat transfer were included in the working equations to consider specimens with varying optical properties. The design, construction, instrumentation, operating principles, and data analysis techniques are discussed in detail. The system was tested up to 500 °C using helium gas and molten KNO 3 -NaNO 3 to verify the measurement technique and determine the sources of error. At 300 and 400 °C KNO 3 -NaNO 3 , results showed maximum relative error of 6% when compared to results in the literature. The helium results were within 13% of those in the literature at 300 and 400 °C. Higher errors were observed at 500 °C for both fluids, and the sources of these errors are discussed.

42 ENGINEERING↗

DOE OSTI2016

Effects of shear-thinning fluids on residual oil formation in microfluidic pore networks

Two-phase immiscible displacement in porous media is controlled by capillary and viscous forces when gravitational effects are negligible. The relative importance of these forces is quantified through the dimensionless capillary number Ca and the viscosity ratio M between fluid phases. When the displacing fluid is Newtonian, the effects of Ca and M on the displacement patterns can be evaluated independently. However, when the injecting fluids exhibit shear-thinning viscosity behaviour the values of M and Ca are interdependent. Under these conditions, the effects on phase entrapment and the general displacement dynamics cannot be dissociated. In the particular case of shear-thinning aqueous polymer solutions, the degree of interdependence between M and Ca is determined by the polymer concentration. In this work, two-phase immiscible displacement experiments were performed in micromodels, using shear-thinning aqueous polymer solutions as displacing fluids, to investigate the effect of polymer concentration on the relationship between Ca and M, the recovery efficiency, and the size distribution of the trapped non-wetting fluid. Our results show that the differences in terms of magnitude and distribution of the trapped phase are related to the polymer concentration which influences the values of Ca and M.

Environmental Molecular Sciences Laboratory↗

DOE OSTI2022

Computing Thermodynamic Properties of Fluids Augmented by Nanoconfinement: Application to Pressurized Methane

Nanoconfined fluids exhibit remarkably different thermodynamic behavior compared to the bulk phase. These confinement effects render predictions of thermodynamic quantities of nanoconfined fluids challenging. In particular, confinement creates a spatially varying density profile near the wall that is primarily responsible for adsorption and capillary condensation behavior. Significant fluctuations in thermodynamic quantities, inherent in such nanoscale systems, coupled to strong fluid–wall interactions give rise to this near-wall density profile. Empirical models have been proposed to explain and model these effects, yet no first-principles based formulation has been developed. We present a statistical mechanics framework that embeds such a coupling to describe the effect of the fluid–wall interaction in amplifying the near-wall density behavior for compressible gases at elevated pressures such as pressurized methane in confinement. We show that the proposed theory predicts accurately the adsorbed layer thickness as obtained with small-angle neutron scattering measurements. Furthermore, the predictions of density under confinement from the proposed theory are shown to be in excellent agreement with available experimental and atomistic simulations data for a range of temperatures for nanoconfined methane. While the framework is presented for evaluating the near-wall density, owing to its rigorous foundation in statistical mechanics, the proposed theory can also be generalized for predicting phase-transition and nonequilibrium transport of nanoconfined fluids.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Effect of Confinement on the Density and Diffusivity of Organic Molecules in Single-Digit Nanopores Relative to Bulk Fluid Behavior

Prediction of fluid properties in microporous and mesoporous confinement is non-trivial due to distinct influences from pore surface functionality and shape and fluid molecular characteristics. The vast majority of literature focuses nearly exclusively on a small number of components that are generally low molecular weight gases and vapors. Missing are studies that utilize a relatively large number of compounds that are liquid at ambient conditions to probe the impact of molecular shape and size on confined fluid properties. Such materials are of great interest in the extraction of oil and gas from shale reservoirs or for the design of selective adsorbents for chemical separation. In this work, we reveal non-intuitive relationships that emerge when comparing bulk fluid properties to those when confined in amorphous silica single-digit nanopores (approx. 5 nm SBA-15), specifically the confined density and self-diffusivity. A counterintuitive result was obtained where larger molecules had relatively faster self-diffusivities; however, this behavior was revealed to be caused by these larger compounds exhibiting a relatively low density when confined. As the prediction of confined fluid properties impacts a diversity of disciplines, the results highlight the need for additional investigations where consistent and large-scale experimental procedures are employed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2019

Mineral-Filled Fractures as Indicators of Multigenerational Fluid Flow in the Pahrump Hills Member of the Murray Formation, Gale Crater, Mars

Mineral-filled fractures (veins) are valuable indicators of deformation and fluid flow within a sedimentary package. Information obtained from vein morphology, texture, and chemistry may elucidate the sequence and nature of postdepositional fluid events. Additional information from vein patterns and interactions between veins and host rock provides insight into fracture formation mechanism(s). The widespread occurrence of veins and other diagenetic features in the sedimentary rock record preserved in Gale crater, Mars, indicates that postdepositional fluids were regionally active considerably later in time than the primary fluviolacustrine environments responsible for the deposition of Mount Sharp strata. Here we report a suite of veins within the Murray formation at the Pahrump Hills locality that were investigated using the scientific payload of the Mars Science Laboratory Curiosity rover. Based on an analysis of vein color, morphology, and texture, and corroborated by vein chemistry, we interpret three distinct vein types at Pahrump Hills: gray veins, white veins, and dark-toned veins. These veins represent distinct, separate episodes of postdepositional fluid flow, suggesting a protracted history of fluid stability in Gale crater. Additionally, we utilize vein patterns across multiple lithologies at the Pahrump Hills field site to suggest hydrofracture as the primary mechanism of fracture formation.

58 GEOSCIENCES↗

DOE OSTI2022

Self-mixing in microtubule-kinesin active fluid from nonuniform to uniform distribution of activity

Active fluids have applications in micromixing, but little is known about the mixing kinematics of systems with spatiotemporally-varying activity. To investigate, UV-activated caged ATP is used to activate controlled regions of microtubule-kinesin active fluid and the mixing process is observed with fluorescent tracers and molecular dyes. At low Péclet numbers (diffusive transport), the active-inactive interface progresses toward the inactive area in a diffusion-like manner that is described by a simple model combining diffusion with Michaelis-Menten kinetics. At high Péclet numbers (convective transport), the active-inactive interface progresses in a superdiffusion-like manner that is qualitatively captured by an active-fluid hydrodynamic model coupled to ATP transport. Results show that active fluid mixing involves complex coupling between distribution of active stress and active transport of ATP and reduces mixing time for suspended components with decreased impact of initial component distribution. This work will inform application of active fluids to promote micromixing in microfluidic devices.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2020

Imaging viscous flow of the Dirac fluid in graphene

The electron–hole plasma in charge-neutral graphene is predicted to realize a quantum critical system in which electrical transport features a universal hydrodynamic description, even at room temperature. This quantum critical ‘Dirac fluid’ is expected to have a shear viscosity close to a minimum bound, with an interparticle scattering rate saturating1 at the Planckian time, the shortest possible timescale for particles to relax. Although electrical transport measurements at finite carrier density are consistent with hydrodynamic electron flow in graphene a clear demonstration of viscous flow at the charge-neutrality point remains elusive. In this work, we directly image viscous Dirac fluid flow in graphene at room temperature by measuring the associated stray magnetic field. Nanoscale magnetic imaging is performed using quantum spin magnetometers realized with nitrogen vacancy centres in diamond. Scanning single-spin and wide-field magnetometry reveal a parabolic Poiseuille profile for electron flow in a high-mobility graphene channel near the charge-neutrality point, establishing the viscous transport of the Dirac fluid. This measurement is in contrast to the conventional uniform flow profile imaged in a metallic conductor and also in a low-mobility graphene channel. Furthermore, via combined imaging and transport measurements, we obtain viscosity and scattering rates, and observe that these quantities are comparable to the universal values expected at quantum criticality. This finding establishes a nearly ideal electron fluid in charge-neutral, high-mobility graphene at room temperature4. Our results will enable the study of hydrodynamic transport in quantum critical fluids relevant to strongly correlated electrons in high-temperature superconductors9. This work also highlights the capability of quantum spin magnetometers to probe correlated electronic phenomena at the nanoscale.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

DOE OSTI2013

Experimental evidence of ion acoustic soliton chain formation and validation of nonlinear fluid theory

We perform one-dimensional fluid simulation of ion acoustic (IA) solitons propagating parallel to the magnetic field in electron-ion plasmas by assuming a large system length. To model the initial density perturbations (IDP), we employ a KdV soliton type solution. Our simulation demonstrates that the generation mechanism of IA solitons depends on the wavelength of the IDP. The short wavelength IDP evolve into two oppositely propagating identical IA solitons, whereas the long wavelength IDP develop into two indistinguishable chains of multiple IA solitons through a wave breaking process. The wave breaking occurs close to the time when electrostatic energy exceeds half of the kinetic energy of the electron fluid. The wave breaking amplitude and time of its initiation are found to be dependent on characteristics of the IDP. The strength of the IDP controls the number of IA solitons in the solitary chains. The speed, width, and amplitude of IA solitons estimated during their stable propagation in the simulation are in good agreement with the nonlinear fluid theory. This fluid simulation is the first to confirm the validity of the general nonlinear fluid theory, which is widely used in the study of solitary waves in laboratory and space plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗