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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Data-Driven RANS Turbulence Closures for Forced Convection Flow in Reactor Downcomer Geometry

Recent progress in data-driven turbulence modeling has shown its potential to enhance or replace traditional equation-based Reynolds-averaged Navier-Stokes (RANS) turbulence models. Here, this work utilizes invariant neural network (NN) architectures to model Reynolds stresses and turbulent heat fluxes in forced convection flows (when the models can be decoupled). As the considered flow is statistically one dimensional, the invariant NN architecture for the Reynolds stress model reduces to the linear eddy viscosity model. To develop the data-driven models, direct numerical and RANS simulations in vertical planar channel geometry mimicking a part of the reactor downcomer are performed. Different conditions and fluids relevant to advanced reactors (sodium, lead, unitary-Prandtl-number fluid, and molten salt) constitute the training database. The models enabled accurate predictions of velocity and temperature, and compared to the baseline k–τ turbulence model with the simple gradient diffusion hypothesis, do not require tuning of the turbulent Prandtl number. The data-driven framework is implemented in the open-source graphics processing unit–accelerated spectral element solver nekRS and has shown the potential for future developments and consideration of more complex mixed convection flows.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2024

Effects of low-frequency voltage on nonlinear standing wave excitation, plasma uniformity, and ion dynamics in dual-frequency asymmetric capacitive discharges

Abstract It is known that in very-high-frequency (VHF) capacitively coupled plasmas, the higher harmonics generated by nonlinear sheath motion can enhance the standing wave effect (SWE), which can lead to center-peaked plasma density profiles. In this work, an improved nonlinear electromagnetic model incorporating a transmission line model, an electron momentum balance model, a bulk plasma model, a collisionless nonlinear numerical sheath model, and an ion Monte-Carlo collision (MCC) model is developed to study the effects of low-frequency (LF) voltage V L on the nonlinear standing wave excitation, plasma uniformity, and ion energy and angular distribution functions (IEDFs and IADFs) in dual-frequency (DF) asymmetric capacitive argon discharges at relatively low pressure of 3 Pa. The plasma diffusion in the radial direction and ion dynamics within the LF oscillating sheath are self-consistently considered. The LF voltage V L at 2 MHz varies from 0 to 700 V while the HF voltage V H at 60 MHz is fixed at 100 V. Simulation results indicate that without the addition of an LF source (i.e. V L = 0 V), there are a considerable number of high-order harmonics with short wavelengths, leading to significant SWE and central peak in the radial plasma density profile. Nevertheless, the high-order harmonic excitations tend to be weakened and merely occur around the phase of the full LF sheath collapse due to a shorter characteristic damping time of the surface waves as V L increases. This, combined with increased surface wavelengths of both the driving frequency and the higher harmonics at a higher V L , leads to suppressed standing waves and improved plasma uniformity. Meanwhile, the simulations show that both the low and the high energy peaks of IEDF move towards higher energies, and the energy peak separation width ΔEbecomes wider with the increase of V L . The IEDF at the radial center of the powered electrode exhibits a broader ΔEthan that at the edge. For the IADF, an increased V L results in more ions incident on the electrode with a smaller deflection angle. Because of a thinner sheath and a higher sheath voltage at the electrode center, the peak value of IADF at the electrode center is greater than that at the edge.

Physics↗
DOE OSTI2014

Impact of deformation on the atomic structures and dynamics of a Cu-Zr metallic glass: A molecular dynamics study

Despite numerous studies on the atomic structures of Cu-Zr metallic glasses (MGs), their inherent structural ordering, e.g., medium-range order (MRO), remains difficult to describe. Specifically lacking is an understanding of how the MRO responds to deformation and the associated changes in atomic mobility. In this paper, we focus on the impact of deformation on MRO and associated effect on diffusion in a well-relaxed Cu 64.5 Zr 35.5 MG by molecular dynamics simulations. The Cu-Zr MG exhibits a larger elastic limit of 0.035 and a yield stress of 3.5 GPa. The cluster alignment method was employed to characterize the icosahedral short-range order (ISRO) and Bergman-type medium-range order (BMRO) in the models upon loading and unloading. From this analysis, we find the disruption of both ISRO and BMRO occurs as the strain reaches about 0.02, well below the elastic limit. Within the elastic limit, the total fractions of ISRO or BMRO can be fully recovered upon unloading. The diffusivity increases six to eight times in regions undergoing plastic deformation, which is due to the dramatic disruption of the ISRO and BMRO. As a result, by mapping the spatial distributions of the mobile atoms, we demonstrate the increase in atomic mobility is due to the extended regions of disrupted ISRO and more importantly BMRO.

36 MATERIALS SCIENCE↗
DOE OSTI2017

Two-Level Convergence Theory for Multigrid Reduction in Time (MGRIT)

Here we develop a two-grid convergence theory for the parallel-in-time scheme known as multigrid reduction in time (MGRIT), as it is implemented in the open-source package [XBraid: Parallel Multigrid in Time, http://llnl.gov/casc/xbraid]. MGRIT is a scalable and multilevel approach to parallel-in-time simulations that nonintrusively uses existing time-stepping schemes, and in a specific two-level setting it is equivalent to the widely known parareal algorithm. The goal of this paper is twofold. First, we present a two-level MGRIT convergence analysis for linear problems where the spatial discretization matrix can be diagonalized, and then apply this analysis to our two basic model problems, the heat equation and the advection equation. One important assumption is that the coarse and fine time-grid propagators can be diagaonalized by the same set of eigenvectors, which is often the case when the same spatial discretization operator is used on the coarse and fine time grids. In many cases, the MGRIT algorithm is guaranteed to converge, and we demonstrate numerically that the theoretically predicted convergence rates are sharp in practice for our model problems. Second, we explore how the convergence of MGRIT compares to the stability of the chosen time-stepping scheme. In particular, we demonstrate that a stable time-stepping scheme does not necessarily imply convergence of MGRIT, although MGRIT with FCF-relaxation always converges for the diffusion dominated problems considered here.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Turbulent nonpremixed cool flames: Experimental measurements, Direct Numerical Simulation, and manifold-based combustion modeling

Turbulence, low-temperature chemistry, and their interactions in the form of turbulent cool flames are critical to understanding and improving advanced engines. Design of such engines requires tractable simulations which in turn necessitate turbulent combustion models that can account for cool flames. While manifold-based turbulent combustion models are an attractive option for hot flames, their applicability to cool flames is not yet fully understood. This is partially due to the lack of turbulent cool flame experiments, which has made model validation difficult. This work addresses these points with a combined experimental and computational investigation of turbulent nonpremixed dimethyl ether cool flames. First, a Co-flow Axisymmetric Reactor-Assisted Turbulent (CARAT) burner is developed and tested. Turbulent cool flames are studied using the formaldehyde planar laser-induced fluorescence (PLIF), acetone PLIF, and planar Rayleigh scattering techniques. The acetone PLIF signals are converted into mixture fraction values, and measurements of time-averaged temperature are derived from the Rayleigh scattering signals by taking advantage of the similarities between cool flames and unburned mixtures. Second, a Direct Numerical Simulation (DNS) of the CARAT burner is conducted. The flame is shown to be sensitive to thermal boundary conditions such that the stabilization method is dependent on a 10 K change in inlet temperature. Comparisons of first- and second-order statistics of temperature, mixture fraction, and formaldehyde between the DNS and experiment show good agreement. The validity of manifold-based turbulent combustion models in turbulent cool flames is then explored by first studying the effective Lewis numbers in the flame using a local differential diffusion parameter analysis. Turbulent cool flames are shown to have effective unity Lewis number transport even at a much lower Reynolds number than typically required for hot flames. Good agreement is shown for temperature and formaldehyde between DNS conditional means and one-dimensional nonpremixed flame solutions. Additionally, the motion of the cool flame in mixture fraction space is shown to be well described by one-dimensional nonpremixed flame solutions. These points indicate that the fundamental physics of turbulent cool flames are analogous to turbulent hot flames, implying that the same reduced-order manifold-based modeling approaches utilized for turbulent hot flames can be utilized for turbulent cool flames.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2017

Numerical study of air ingress transition to natural circulation in a high temperature helium loop

Here, the generation-IV high temperature gas cooled reactors (HTGRs) are designed with many passive safety features, one of which is the ability to passively remove heat under a loss of coolant accident (LOCA). However, several common reactor designs do not prevent against a large break in the coolant system and may therefore experience a depressurized LOCA. This would lead to air entering into the reactor system via several potential modes of ingress: diffusion, gravity currents, and natural circulation. At the onset of a LOCA, the initial rate of air ingress is expected to be very slow because it is governed by molecular diffusion. However, after several hours, natural circulation would commence, thus, bringing the air into the reactor system at a much higher rate. As a consequence, air ingress would cause the high temperature graphite matrix to oxidize, leading to its thermal degradation and decreased passive heat (decay) removal capability. Therefore, it is essential to understand the transition of air ingress from molecular diffusion to natural circulation in an HTGR system. This paper presents results from a computational fluid dynamics (CFD) model to study the air ingress transition behavior. These results are validated against an h-shaped high temperature helium loop experiment. Details are provided to quantitatively predict the transition time from molecular diffusion to natural circulation.

42 ENGINEERING↗
DOE OSTI2025

Efficient shallow Ritz method for 1D diffusion problems

This paper studies the shallow Ritz method for solving the one-dimensional diffusion problem. It is shown that the shallow Ritz method improves the order of approximation dramatically for non-smooth problems. To realize this optimal or nearly optimal order of the shallow Ritz approximation, we develop a damped block Newton (dBN) method that alternates between updates of the linear and non-linear parameters. Per each iteration, the linear and the non-linear parameters are updated by exact inversion and one step of a modified, damped Newton method applied to a reduced non-linear system, respectively. The computational cost of each dBN iteration is $\mathcal{O}$(n). Starting with the non-linear parameters as a uniform partition of the interval, numerical experiments show that the dBN is capable of efficiently moving mesh points to nearly optimal locations. In conclusion, to improve the efficiency of the dBN further, we propose an adaptive damped block Newton (AdBN) method by combining the dBN with the adaptive neuron enhancement (ANE) method [28].

Diffusion problems↗
DOE OSTI2018

A Weighted Least-Squares Transport Equation Compatible with Source Iteration and Voids

We present that second-order forms of the transport equation allow the use of continuous finite elements (CFEMs). This can be desired in multiphysics calculations where other physics require CFEM discretizations. Second-order transport operators are generally self-adjoint, yielding symmetric positive-definite (SPD) matrices, which allow the use of efficient linear algebra solvers with an enormous advantage in memory usage. Least-squares (LS) forms of the transport equation can circumvent the void problems of other second-order forms but are almost always nonconservative. Additionally, the standard LS form is not compatible with discrete ordinates method (SN) iterative solution techniques such as source iteration. A new form of the LS transport equation has recently been developed that is compatible with voids and standard SN iterative solution techniques. Performing nonlinear diffusion acceleration (NDA) using an independently differenced low-order equation enforces conservation for the whole system and makes this equation suitable for reactor physics calculations. In this context, “independent” means that both the transport and low-order solutions converge to the same scalar flux and current as the spatial mesh is refined, but for a given mesh, the solutions are not necessarily equal. In this paper we show that introducing a weight function into this LS equation improves issues with causality and can render our equation equal to the self-adjoint angular flux (SAAF) equation. Causality is a principle of the transport equation that states that information travels only downstream along characteristics. This principle can be violated numerically. We show how to limit the weight function in voids and demonstrate the effect of this limit on accuracy. Using the C5G7 benchmark, we compare our method to the SAAF formulation with a void treatment (SAAFτ) that is not self-adjoint and has a nonsymmetric coefficient matrix. Finallyl, we show that the weighted LS equation with NDA gives acceptable accuracy relative to the SAAFτ equation while maintaining a SPD system matrix.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Moving beyond the Aerosol Climatology of WRF-Solar: A Case Study over the North China Plain

Numerical weather prediction (NWP), when accessible, is a crucial input to short-term solar power forecasting. WRF-Solar, the first NWP model specifically designed for solar energy applications, has shown promising predictive capability. Nevertheless, few attempts have been made to investigate its performance under high aerosol loading, which attenuates incoming radiation significantly. The North China Plain is a polluted region due to industrialization, which constitutes a proper testbed for such investigation. Here, in this paper, aerosol direct radiative effect (DRE) on three surface shortwave radiation components (i.e., global, beam, and diffuse) during five heavy pollution episodes is studied within the WRF-Solar framework. Results show that WRF-Solar overestimates instantaneous beam radiation up to 795.3 W m -2 when the aerosol DRE is not considered. Although such overestimation can be partially offset by an underestimation of the diffuse radiation of about 194.5 W m -2 , the overestimation of the global radiation still reaches 160.2 W m -2 . This undesirable bias can be reduced when WRF-Solar is powered by Copernicus Atmosphere Monitoring Service (CAMS) aerosol forecasts, which then translates to accuracy improvements in photovoltaic (PV) power forecasts. This work also compares the forecast performance of the CAMS-powered WRF-Solar with that of the European Centre for Medium-Range Weather Forecasts model. Under high aerosol loading conditions, the irradiance forecast accuracy generated by WRF-Solar increased by 53.2% and the PV power forecast accuracy increased by 6.8%.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2015

In situ observations on the coupling between hydraulic diffusivity and displacements during fault reactivation in shales

Key questions in fault reactivation in shales relate to the potential for enhanced fluid transport through previously low-permeability aseismic formations. Here, we explore the behavior of a 20 m long N0-to-170°, 75-to-80°W fault in shales that is critically stressed under a strike-slip regime (σ 1 = 4 ± 2 MPa, horizontal and N162° ± 15°E, σ 2 = 3.8 ± 0.4 MPa and σ 3 = 2.1 ± 1 MPa, respectively 7-8° inclined from vertical and horizontal and N72°). The fault was reactivated by fluid pressurization in a borehole using a straddle packer system isolating a 2.4 m long injection chamber oriented-subnormal to the fault surface at a depth of 250 m. A three-dimensional displacement sensor attached across the fault allowed monitoring fault movements, injection pressure and flow rate. Pressurization induced a hydraulic diffusivity increase from ~2 × 10 -9 to ~10 3 m 2 s -1 associated with a complex three-dimensional fault movement. The shear (x-, z-) and fault-normal (y-) components (U x , U y , and U z ) = (44.0 × 10 -6 m, 10.5 × 10 -6 m, and 20.0 × 10 -6 m) are characterized by much larger shear displacements than the normal opening. Numerical analyses of the experiment show that the fault permeability evolution is controlled by the fault reactivation in shear related to Coulomb failure. The large additional fault hydraulic aperture for fluid flow is not reflected in the total normal displacement that showed a small partly contractile component. This suggests that complex dilatant effects estimated to occur in a plurimeter radius around the injection source affect the flow and slipping patch geometries during fault rupture, controlling the initial slow slip and the strong back slip of the fault following depressurization.

58 GEOSCIENCES↗
DOE OSTI2021

Effective kinetics driven by dynamic concentration gradients under coupled transport and reaction

Biogeochemical reaction kinetics are generally established from batch reactors where concentrations are uniform. In natural systems, many biogeochemical processes are characterized by spatially and temporally variable concentration gradients that often occur at scales which are not resolved by field measurements or biogeochemical and reactive transport models. Yet, it is not clear how these sub-scale chemical gradients affect reaction kinetics compared to batch kinetics. Here we investigate this question by studying the paradigmatic case of localized pulses of solute reacting with a solid or a dissolved species in excess. Additionally, we consider non-linear biogeochemical reactions, representative of mineral dissolution, adsorption and redox reactions, which we quantify using simplified power-law kinetics. The combined effect of diffusion and reaction leads to effective kinetics that differ quantitatively and qualitatively from the batch kinetics. Depending on the nonlinearity (reaction order) of the local kinetics, these effects lead to either enhancement or decrease of the overall reaction rate, and result in a rich variety of reaction dynamics. We derive analytical results for the effective kinetics, which are validated by comparison to direct numerical simulations for a broad range of Damköhler numbers and reaction order. Our findings provide new insights into the interpretation of imperfectly mixed lab experiments, the effective kinetics of field systems characterized by intermittent reactant release and the integration of sub-scale concentration gradients in reactive transport models.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

A numerical simulation study of gallium-phosphide/silicon heterojunction passivated emitter and rear solar cells

The performance of passivated emitter and rear (PERC) solar cells made of p-type Si wafers is often limited by recombination in the phosphorus-doped emitter. To overcome this limitation, a realistic PERC solar cell is simulated, whereby the conventional phosphorus-doped emitter is replaced by a thin, crystalline gallium phosphide (GaP) layer. The resulting GaP/Si PERC cell is compared to Si PERC cells, which have (i) a standard POCl{sub 3} diffused emitter, (ii) a solid-state diffused emitter, or (iii) a high efficiency ion-implanted emitter. The maximum efficiencies for these realistic PERC cells are between 20.5% and 21.2% for the phosphorus-doped emitters (i)–(iii), and up to 21.6% for the GaP emitter. The major advantage of this GaP hetero-emitter is a significantly reduced recombination loss, resulting in a higher V{sub oc}. This is so because the high valence band offset between GaP and Si acts as a nearly ideal minority carrier blocker. This effect is comparable to amorphous Si. However, the GaP layer can be contacted with metal fingers like crystalline Si, so no conductive oxide is necessary. Compared to the conventional PERC structure, the GaP/Si PERC cell requires a lower Si base doping density, which reduces the impact of the boron-oxygen complexes. Despite the lower base doping, fewer rear local contacts are necessary. This is so because the GaP emitter shows reduced recombination, leading to a higher minority electron density in the base and, in turn, to a higher base conductivity.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2014

Effect of boron concentration on recombination at the p-Si–Al{sub 2}O{sub 3} interface

We examine the surface passivation properties of Al{sub 2}O{sub 3} deposited on boron-doped planar 〈100〉 crystalline silicon surfaces as a function of the boron concentration. Both uniformly doped and diffused surfaces are studied, with surface boron concentrations ranging from 9.2 × 10{sup 15} to 5.2 × 10{sup 19} cm{sup −3}. Atmospheric pressure chemical vapor deposition and thermal atomic layer deposition are used to deposit the Al{sub 2}O{sub 3} films. The surface recombination rate of each sample is determined from photoconductance measurements together with the measured dopant profiles via numerical simulation, using the latest physical models. These values are compared with calculations based on the interface properties determined from capacitance–voltage and conductance measurements. It is found that the fundamental surface recombination velocity of electrons, S{sub n0}, which describes the chemical passivation of the interface, is independent of the surface boron concentration N{sub s} for N{sub s} ≤ 3 × 10{sup 19} cm{sup −3}, and in excellent agreement with values calculated from the interface state density D{sub it} and capture coefficients c{sub n} and c{sub p} measured on undiffused boron-doped surfaces. We conclude that the physical properties of the Si–Al{sub 2}O{sub 3} interface are independent of the boron dopant concentration over this range.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Response of a charged particle in contact with a chaotic thermostat to an oscillating electric field

A numerical investigation is made of the response of a thermalized charge in contact with a chaotic thermostat to an externally applied, oscillating electric field, with and without a confining magnetic field. This study is based on the recent theoretical development of a chaotic thermostat [G. J. Morales, Phys. Rev. E 99, 062218 (2019)] for which the static properties of a thermalized charge (spatial diffusion and mobilities) were previously established. It is found here that in the unmagnetized case, to extract significant power from the oscillating electric field requires that the oscillatory velocity be larger than the thermal velocity. The spatial diffusion caused by the self-consistent, chaotic fluctuations is shown to be reduced, and even suppressed, by the coherent oscillations. The frequency-dependent mobilities, including cyclotron resonance, are determined, and the nonlinear modifications produced by large electric fields are explored. The value of the mobilities and the modifications to the diffusion coefficient exhibit non-monotonic dependencies on the control parameters.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Development of a tomographic reconstruction method for axisymmetric D α emission profiles in the ITER plasma boundary

A tomographic method for reconstructing the axially symmetric D α emission profile in the ITER scrape-off layer and divertor from D α intensity measurements in the fields of view (FoV) of Vis/IR TV and Divertor Impurity Monitor diagnostics is under development. The method takes into account the strong background signal due to stray light from divertor produced by reflections from the metal wall of the vacuum chamber. The method allows to filter out the reflections in D α signals measured in the main chamber. Here, the accuracy of this method is tested within the framework of a synthetic diagnostic, which uses the Raysect and Cherab numerical codes for ray-tracing simulations. The D α emission profiles, simulated with the SOLPS and OEDGE codes, are used as synthetic experimental data. Uncertainty in light reflection properties of the first wall (FW) is the major factor affecting the accuracy of the D α emission reconstruction. The dependence on the uncertainty in the FW surface roughness and on the ratio of diffusive to specular reflection of the error in recovering useful D α signals (the direct light without reflections) in the FoV of the ITER main chamber H-alpha and Visible Spectroscopy Diagnostic is obtained.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Hydrodynamic theory of scrambling in chaotic long-range interacting systems

The Fisher-Kolmogorov-Petrovsky-Piskunov (FKPP) equation provides a mean-field theory of out-of-time-ordered commutators in locally interacting quantum chaotic systems at high energy density. In systems with power-law interactions, the corresponding fractional-derivative FKPP equation provides an analogous mean-field theory. However, the fractional FKPP description is potentially subject to strong quantum fluctuation effects, so it is not clear a priori if it provides a suitable effective description for generic chaotic systems with power-law interactions. Here, in this work, we study this problem using a model of coupled quantum dots with interactions decaying as 1/r α , where each dot hosts N degrees of freedom. The large-N limit corresponds to the mean-field description, while quantum fluctuations contributing to the OTOC can be modeled by 1/N corrections consisting of a cutoff function and noise. Within this framework, we show that the parameters of the effective theory can be chosen to reproduce the butterfly light cone scalings previously found for N=1 and generic finite N. In order to reproduce these scalings, the fractional index μ in the FKPP equation needs to be shifted from the naïve value of μ=2⁢α–1 to a renormalized value μ=2⁢α–2. We provide supporting analytic evidence for the cutoff model and numerical confirmation for the full fractional FKPP equation with cutoff and noise.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

The Paschen Jump as a Diagnostic of the Diffuse Nebular Continuum Emission in Active Galactic Nuclei*

Photoionization modeling of active galactic nuclei (AGN) predicts that diffuse continuum (DC) emission from the broad-line region makes a substantial contribution to the total continuum emission from ultraviolet through near-infrared wavelengths. Evidence for this DC component is present in the strong Balmer jump feature in AGN spectra, and possibly from reverberation measurements that find longer lags than expected from disk emission alone. However, the Balmer jump region contains numerous blended emission features, making it difficult to isolate the DC emission strength. In contrast, the Paschen jump region near 8200 Å is relatively uncontaminated by other strong emission features. Here, we examine whether the Paschen jump can aid in constraining the DC contribution, using Hubble Space Telescope Space Telescope Imaging Spectrograph spectra of six nearby Seyfert 1 nuclei. The spectra appear smooth across the Paschen edge, and we find no evidence of a Paschen spectral break or jump in total flux. We fit multicomponent spectral models over the range 6800–9700 Å and find that the spectra can still be compatible with a significant DC contribution if the DC Paschen jump is offset by an opposite spectral break resulting from blended high-order Paschen emission lines. The fits imply DC contributions ranging from ~10% to 50% at 8000 Å, but the fitting results are highly dependent on assumptions made about other model components. These degeneracies can potentially be alleviated by carrying out fits over a broader wavelength range, provided that models can accurately represent the disk continuum shape, Fe ii emission, high-order Balmer line emission, and other components.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

A numerical study of the relationship between NMR relaxation and permeability in sands and gravels

The accuracy of NMR-derived permeability estimates in sands and gravels were examined through simulations on numerical grain packs composed of uniform spherical grains. The packs consisted of randomly packed grains, with grain sizes set to represent a range corresponding to sands and gravels. The material properties for each pack were quantified through numerical analysis and the NMR response was simulated for a range of surface relaxivity values. The agreement between the numerically-derived permeability estimates and the permeability estimates derived using the Schlumberger Doll Research (SDR) and Seevers equations was evaluated. Use of the SDR equation assumes that the relaxation of the bulk pore fluid can be neglected. The NMR-derived permeability estimates were calculated using each equation for the cases where relaxation was assumed to occur in one of the two major diffusion regimes. We found that permeability is most accurately estimated in all packs through use of the Seevers equation with the empirical constant n set equal to 1. We showed that the contribution of bulk fluid relaxation should be accounted for in materials with grain radii greater than 1.2e-4m (fine sand) and surface relaxivity values less than 1.0e-3 m s -1 20 . In practice, this range of surface relaxivity values and grain sizes corresponds to situations where the measured relaxation time T 2 is greater than approximately one-third the value of the bulk fluid relaxation time T 2B .

Dlubac, Katherine↗