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Analytical homogenization techniques applied to the Fickian diffusion: Effective diffusivity coefficient

For multiple applications in nuclear energy, the ability to accurately represent material behavior with a simplified model is important to facilitate practical engineering-scale simulations. In this work, we focus on the homogenized thermal response of a medium containing spherical inclusions, similar to a fuel form (compact or pebble) containing TRISO particles. An extensive survey on effective thermal conductivity modeling was performed in our previous study, considering a random distribution of mono-sized spherical inclusions in a continuous matrix. Using the analogy between heat conduction and the simplified Fickian diffusion (or fission product species conservation), we can use the same analytical homogenization methods to obtain ETC as for the effective diffusivity coefficient (EDC). We performed several numerical experiments at varying conditions to assess the validity of our hypothesis for EDC calculations.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Multiscale, mechanistic calculation of the effective silver diffusion coefficient in polycrystalline silicon carbide: application to silver release in AGR-1 TRISO particles

The silicon carbide (SiC) layer in tristructural isotropic (TRISO) fuel particles serves as a barrier to prevent the escape of fission from the fuel kernel. The release of silver (Ag) is a concern due to the long half-life of the 110mAg isotope. In this study, the effective diffusion coefficient of the fission product Ag through the grain boundary (GB) network is calculated using a combination of atomistic and phase-field methods. Atomistic calculations of Ag diffusivity in SiC bulk and GBs are leveraged to develop a mesoscale effective Ag diffusion coefficient (Deff) in SiC. Since GBs serve as pathways for Ag diffusion, Deff is defined as a function of temperature, microstructure variables, and fluence. Deff is implemented in the fuel performance code Bison to predict Ag release from AGR-1 TRISO fuel particles. We hereby quantify the impact of SiC grain size and irradiation on Ag release and improve Bison's predictions.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Assessment and Improvement of Fission Product Transport Predictions of Particle Fuel in BISON

The U.S. Department of Energy’s Nuclear Energy Advanced Modeling and Simulation (NEAMS) program aims to develop predictive capabilities by applying computational methods to the analysis and design of advanced reactor and fuel cycle systems. This program has been providing engineering-scale support for the development of BISON, a high-fidelity and high-resolution fuel performance tool. This study was motivated by the need to incorporate more physics-based models in BISON in order to foster tri-structural isotropic (TRISO) applications. This document details the integration of new modeling capabilities in BISON, including (1) development of pyrolytic carbon (PyC) and silicon carbide (SiC) layer anisotropic thermal and mass transport capabilities, (2) verification of the mass diffusion solution in TRISO modeling, (3) calibration of fission product diffusivity using Advanced Gas Reactor (AGR) experiments, (4) improved fission product release modeling by developing compact diffusion modeling capabilities, and (5) documentation of accelerated failure analysis on the BISON website. Improvements made to the diffusion models and parameters were documented and validated against AGR-1 and -2 experiment data.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Demonstrate Improved Ag Diffusion and Describe the Basis for Pd Penetration Modeling in SiC

In past work, an effective diffusivity coefficient was determined for Ag transport through the silicon carbide layer of a tristructural isotropic fuel particle. The effective diffusivity coefficient accounts for the microstructure of the silicon carbide and includes both bulk diffusion and grain boundary diffusion of Ag. In this report, the model has been improved by accounting for the enhanced concentration of vacancies in the bulk due to irradiation, which substantially influence bulk diffusivity at low temperatures. To improve the BISON model and make it fission rate dependent, effective diffusivity calculations have been performed that incorporate the radiation modified bulk diffusivity. The microstructure and irradiation-dependent effective diffusivity has also been implemented into BISON, and its predictions for Ag release from tristructural isotropic fuel have been successfully compared to AGR-1 post irradiation measurements. Moreover, a new feature has been developed in the Multiphysics Object-Oriented Simulation Environment (MOOSE) to account for different grain boundary types. The Ag diffusivity in 5 (210)/[001] grain boundaries has been computed and was found to be greater than in random high-angle grain boundaries. The presence of the fission product Pd can also have an important effect on the properties of the silicon carbide layer in tristructural isotropic particles. The penetration of Pd into the silicon carbide layer causes a corrosion reaction that can lead to the failure of the silicon carbide layer; however, this corrosion reaction is not well understood. To enable an improved understanding of the mechanism, ab-initio molecular dynamics simulations of Pd interaction with bulk silicon carbide have been performed. The improved understanding of the reaction will form a basis for future improvements to the BISON’s Pd penetration failure model

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Resolving experimental biases in the interpretation of diffusion experiments with a user-friendly numerical reactive transport approach

The reactive transport code CrunchClay was used to derive effective diffusion coefficients (D e ), clay porosities (ε), and adsorption distribution coefficients (K D ) from through-diffusion data while considering accurately the influence of unavoidable experimental biases on the estimation of these diffusion parameters. These effects include the presence of filters holding the solid sample in place, the variations in concentration gradients across the diffusion cell due to sampling events, the impact of tubing/dead volumes on the estimation of diffusive fluxes and sample porosity, and the effects of O-ring-filter setups on the delivery of solutions to the clay packing. Doing so, the direct modeling of the measurements of (radio)tracer concentrations in reservoirs is more accurate than that of data converted directly into diffusive fluxes. While the above-mentioned effects have already been described individually in the literature, a consistent modeling approach addressing all these issues at the same time has never been described nor made easily available to the community. A graphical user interface, CrunchEase, was created, which supports the user by automating the creation of input files, the running of simulations, and the extraction and comparison of data and simulation results. While a classical model considering an effective diffusion coefficient, a porosity and a solid/solution distribution coefficient (D e –ε–K D ) may be implemented in any reactive transport code, the development of CrunchEase makes it easy to apply by experimentalists without a background in reactive transport modeling. CrunchEase makes it also possible to transition more easily from a D e –ε–K D modeling approach to a state-of-the-art process-based understanding modeling approach using the full capabilities of CrunchClay, which include surface complexation modeling and a multi-porosity description of the clay packing with charged diffuse layers.

58 GEOSCIENCES↗

Multi-scale modeling of wastage layer formation in metallic fuel cladding

Fuel-cladding chemical interaction (FCCI) is a major concern for U-Zr metallic fuels' performance, primarily due to the formation of a brittle layer (wastage) in the cladding. This brittle layer, resulting from intermetallic compounds between cladding constituents Fe, Cr, and lanthanide fission products, significantly impacts the cladding's mechanical integrity. Recent efforts focus on developing a mechanistic modeling framework to understand lanthanide production, transport to the fuel-cladding interface, and phase transformation to intermetallic phases. A multi-scale computational approach has been used to calculate lanthanide transport rates, with atomistic calculations determining Nd diffusivities through the solid fuel matrix and along pore surfaces. These diffusivities inform a mesoscale model to determine an effective diffusion coefficient, accounting for porosity and infiltration with bond sodium. This effective diffusivity is used in engineering-scale simulations via the BISON fuel performance code, which has been validated against EBR-II and FFTF reactor experiments.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Impact of oxidation and carbonation on the release rates of iodine, selenium, technetium, and nitrogen from a cementitious waste form

Evaluation of the long-term retention mechanisms and potential release rates for the primary constituents of potential concern (COPCs) (i.e., Tc, I, Se, and nitrate) is necessary to determine if Cast Stone, a radioactive waste form, can meet performance objectives under near-surface disposal scenarios. In this work, a mineral and parameter set accounting for the solubility of I and Se in Cast Stone was developed based on pH-dependent and monolithic diffusion leaching test results, to extend a geochemical speciation model previously developed. The impact of oxidation and carbonation as environmental aging processes on the retention properties of Cast Stone for primary COPCs was systematically estimated. Physically, the effective diffusion coefficients of 4 COPCs in Cast Stone were increased after carbonation and/or oxidation, reflecting an increase in permeability to diffusion. Chemically, i) pH & pe conditions in the original Cast Stone were favorable for the stabilization of Tc, but not for I, Se, and N; ii) oxidation (with/without carbonation) of Cast Stone changed the pe & pH conditions to be detrimental for Tc stabilization; and iii) carbonation (with/without oxidation) of Cast Stone modified the pH & pe conditions to be beneficial for the stabilization of I (in system with Ag added) and Se.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Effective Lanthanide Diffusivity through U-Zr Metallic Fuel

Fuel-cladding chemical interaction (FCCI) is one of the main concerns for the performance of U-Zr metallic fuels. Although FCCI results in complex phase transformations and morphological changes in both the fuel and cladding sides of the interface, the formation of a brittle layer in the cladding side of the interface (sometimes referred to as wastage) has one of the most significant impacts on the cladding mechanical integrity. This brittle layer is associated with the formation of intermetallic compounds between the cladding constituents Fe, Cr and the lanthanide fission product species. The formation of this cladding wastage layer has been the focus of recent efforts to develop a mechanistic modeling framework, including production of lanthanides in the fuel, transport through the fuel to the fuel-cladding interface, and phase transformation to form intermetallic phases. To calculate the rate of transport of lanthanides through the fuel, a multi-scale computational approach has been used. Atomistic calculations have been performed to determine the diffusivities of Nd, the most prevalent lanthanide species, through the solid fuel matrix and along pore surfaces. These diffusivities have been used as input parameters for a mesoscale model to determine an effective diffusion coefficient that accounts for the formation of porosity, its interconnection, and infiltration with bond sodium from the fuel-cladding gap. The effective diffusivity has been used in engineering-scale simulations using the BISON fuel performance code, and BISON simulations have been compared to representative validation cases from the EBR-II reactor.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Conversion Kinetics and Ionic Conductivity in Na-β”-Alumina + YSZ (Naβ”AY) Sodium Solid Electrolyte via Vapor Phase Conversion Process

Sodium ion batteries have been receiving increasing attention and may see potential revival in the near future, particularly in large-scale grid energy storage coupling with wind and solar power generation, due to the abundant sodium resources, low cost, and sufficiently high energy density. Among the known sodium ion conductors, the Na-β”-alumina electrolyte remains highly attractive because of its high ionic conductivity. This study focuses on the vapor phase synthesis of a Na-β”-Alumina + YSZ (Naβ”AY) composite sodium electrolyte, which has higher mechanical strength and stability than conventional single phase β”-Alumina. The objectives are the measurement of conversion kinetics through a newly developed weight-gain based model and the determination of sodium ionic conductivity in the composite electrolyte. Starting samples contained ~70 vol% α-Alumina and ~30 vol% YSZ (3 mol% Y 2 O 3 stabilized Zirconia) with and without a thin alumina surface layer made by sintering in air at 1600 °C. The sintered samples were placed in a powder of Na-β”-alumina and heat-treated at 1250 °C for various periods. Sample dimensions and weight were measured as a function of heat treatment time. The conversion of α-Alumina in the α-Alumina + YSZ composite into Naβ”AY occurred by coupled diffusion of sodium ions through Na-β”-alumina and of oxygen ions through YSZ, effectively diffusing Na2O. From the analysis of the time dependence of sample mass and dimensions, the effective diffusion coefficient of Na 2 O through the sample, D eff , was estimated to be 1.74 x 10 -7 cm2 s -1 , and the effective interface transfer parameter, k eff , was estimated as 2.33 x 10 -6 cm s -1 . By depositing a thin alumina coating layer on top of the bulk composite, the chemical diffusion coefficient of oxygen through single phase Na-β”-alumina was estimated as 4.35 x 10 -10 cm 2 s -1 . An AC impedance measurement was performed on a fully converted Naβ”AY composite, and the conductivity of the composite electrolyte was 1.3 x 10 -1 S cm -1 at 300 °C and 1.6 x 10 -3 S cm -1 at 25 °C, indicating promising applications in solid state or molten salt batteries at low to intermediate temperatures.

36 MATERIALS SCIENCE↗

Sodium diffusion in heterogeneous porous media: Connecting laboratory experiments and simulations

Sodium has been suggested as a tracer for brine in reservoir formations where a significant amount of sodium ion is found mainly in the aqueous phase. Fortunately, the most abundant sodium isotope, 23 Na, is Nuclear Magnetic Resonance (NMR) active, making it possible to study the structure and dynamical properties of both bulk and pore confined fluid systems. We investigated the diffusion of key dissolved sodium species in bulk solution and porous media as a function of composition, ionic strength, and permeability of the carbonate samples using NMR relaxometry and pulsed-field gradient (PFG) NMR techniques. We use Indiana limestone as an example of natural porous media and water as a freely diffusible tracer and carrier. We demonstrate apparent diffusion measurement of sodium based on changes in spin–spin relaxation time (T 2 ) signal in pore confinement. The diffusion rate of sodium decreases with increasing counter-ion size. This effect is greater at higher ionic strengths and lower chemical potentials in porous media. The reactive transport code, CrunchFlow, was used to complement the NMR experiments to simulate diffusion behavior in porous media. Combining these two methods provides a powerful approach to estimating effective diffusion coefficients in heterogeneous matrices. The modeling considers the influence of physical properties (porosity and tortuosity) and chemical properties (geochemical composition and chemical gradients). The results presented in this work highlight the advantage of measuring apparent diffusivity using NMR T 2 relaxometry in conjunction with numerical simulation to derive effective diffusivity and the corresponding matrix properties (i.e., tortuosity) of the system.

58 GEOSCIENCES↗

Hydrogen Diffusion Coefficient Measures on Thin Film Uranium Oxide

Thin films of uranium oxides, putatively UO 2 and U 3 O 8 , were deposited on palladium/silver (75/25) foil discs (10 μm thick, 10 mm diameter). Methodology for sealing these foils, applying a hydrogen pressure (~ 1 atm) to the oxide side, and measuring the pressure on the permeate side (opposite side of foil) is reported. The experimental apparatus is held at 100 °C to speed diffusion, aided by the pressure differential across the foil (~1 atm (750 torr) on oxide side, initially low vacuum on permeate side, ~1x 10 -4 torr). Early results indicate an effective diffusion coefficient of roughly 7.66 x 10 -17 +/- 2.22 x 10 -17 cm 2 /sec for UO 2 . These values are in line with expectations and prior measures relative to large lag times for system baseline (substrate only). Evaluation of the technique for U 3 O 8 thin films suggests further development will be needed to extend the technique to more oxidized films (U 3 O 8 , UO 3 ). Characterization of the foils (thickness and speciation) post diffusion experiments will be carried out by SIGMA (Eric Tegtmeier and Andy Richards) in FY24 which will sharpen the uncertainty quantification for UO 2 diffusion coefficients, aiding the nucleation model for DRACO.

36 MATERIALS SCIENCE↗

Preferential adsorption of noble gases in zeolitic tuff with variable saturation: A modeling study of counter-intuitive diffusive-adsorptive behavior

Noble gas transport through geologic media has important applications in the prediction and characterization of measured gas signatures related to underground nuclear explosions (UNEs). Retarding processes such as adsorption can cause significant species fractionation of radionuclide gases, which has implications for measured and predicted signatures used to distinguish radioxenon originating from civilian nuclear facilities or from UNEs. Accounting for the effects of variable water saturation in geologic media on tracer transport is one of the most challenging aspects of modeling gas transport because there is no unifying relationship for the associated tortuosity changes between different rock types, and reactive transport processes such as adsorption that are affected by the presence of water likewise behave differently between gas species. In this study, we perform numerical diffusive-adsorptive transport simulations to estimate gas transport parameters associated with bench-scale laboratory diffusion cell experiments measuring breakthrough in zeolitic and non-zeolitic rocks for a gaseous mixture of xenon, krypton, and SF 6 at varying degrees of water saturation (S w ). Counter-intuitive transport behavior was observed in the zeolitic rock experiments whereby breakthrough concentrations were significantly higher when the core was partially saturated (S w = 17 %) than under dry (S w = 0 %) conditions. Breakthrough of xenon was especially retarded in the dry core – likely due to comparatively high affinity of xenon for zeolitic adsorption sites – and estimated effective diffusion coefficients for all gases were approximately an order of magnitude lower than what is predicted by porosity-tortuosity models. We propose the counter-intuitive behavior observed is because water infiltration of zeolite nanopores reduces both the adsorptive capacity of the rock and the tortuosity of connected flow paths. We developed a two-site competitive kinetic Langmuir adsorption reaction for the porous media transport simulator in order to constrain transport parameters within zeolitic tuff, where differential adsorption to zeolite and non-zeolite pores was observed. We determined that liquid saturation-dependent diffusive-adsorptive transport is affected by subtle and at times competing processes that are specific to different gases, which have a significant overall influence on effective transport parameters.

58 GEOSCIENCES↗

Evaluation of Nuclear Spent Fuel Disposal in Clay-Bearing Rock - Process Model Development and Experimental Studies

This report represents the milestone deliverable M2SF-23SN010301072 “Evaluation of Nuclear Spent Fuel Disposal in Clay-Bearing Rock - Process Model Development and Experimental Studies” The report provides a status update of FY23 activities for the work package Argillite Disposal work packages for the DOE-NE Spent Fuel Waste Form Science and Technology (SFWST) Program. Clay-rich geological media (often referred as shale or argillite) are among the most abundant type of sedimentary rock near the Earth’s surface. Argillaceous rock formations have the following advantageous attributes for deep geological nuclear waste disposal: widespread geologic occurrence, found in stable geologic settings, low permeability, self-sealing properties, low effective diffusion coefficient, high sorption capacity, and have the appropriate depth and thickness to host nuclear waste repository concepts. The DOE R&D program under the Spent Fuel Waste Science Technology (SFWST) campaign has made key progress (through experiment, modeling, and testing) in the study of chemical and physical phenomena that could impact the long-term safety assessment of heat-generating nuclear waste disposition in clay/shale/argillaceous rock. International collaboration activities comprising field-scale heater tests, field data monitoring, and laboratory-scale experiments provide key information on changes to the engineered barrier system (EBS) material exposed high thermal loads. Moreover, consideration of direct disposal of large capacity dual-purpose canisters (DPCs) as part of the back-end SNF waste disposition strategy has generated interest in improving our understanding of the effects of elevated temperatures on the engineered barrier system (EBS) design concepts. Chemical and structural analyses of sampled bentonite material from laboratory tests at elevated temperatures are key to the characterization of thermal effects affecting bentonite clay barrier performance. The knowledge provided by these experiments is crucial to constrain the extent of sacrificial zones in the EBS design during the thermal period. Thermal, hydrologic, mechanical, and chemical (THMC) data collected from heater tests and laboratory experiments have been used in the development, validation, and calibration of THMC simulators to model near-field coupled processes. This information leads to the development of simulation approaches to assess issues on coupled processes involving porous media flow, transport, geomechanical phenomena, chemical interactions with barrier/geologic materials, and the development of EBS concepts. These lines of knowledge are central to the design of deep geological backfilled repository concepts where temperature plays a key role in the EBS behavior, potential interactions with host rock, and long-term performance in the safety assessment.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

HTO and selenate diffusion through compacted Na-, Na–Ca-, and Ca-montmorillonite

Radionuclide transport in smectite clay barrier systems used for nuclear waste disposal is controlled by diffusion, with adsorption significantly retarding transport rates. While a relatively minor component of spent nuclear fuel, 79 Se is a major driver of the safety case for spent fuel disposal due to its long half-life (3.3×10 5 yr) and its low adsorption to clay (K D < 10 L/kg), thus a thorough understanding of Se diffusion through clay is critical for understanding the long-term safety of spent fuel disposal systems. Through-diffusion experiments with tritiated water (HTO, conservative tracer) and Se(VI) were conducted with a well-characterized, purified montmorillonite source clay (SWy-2) under a constant ionic strength (0.1 M) and three different electrolyte compositions: Na + , Ca 2+ , and a Na + -Ca 2+ mixture at pH 6.5 in order to probe the effects of electrolyte composition and interlayer cation composition on clay microstructure, Se(VI) aqueous speciation, and ultimately diffusion. Further, the results were modeled using a reactive transport modeling approach to determine values of porosity (ε), D e (effective diffusion coefficient), and K D (distribution coefficient for adsorption). HTO diffusive flux was higher in Ca-montmorillonite (D e =1.68×10 -10 m 2 s -1 ) compared to Na-montmorillonite (De=7.83×10 -11 m 2 s -1 ). This increase in flux is likely due to a greater degree of clay layer stacking in the presence of Ca 2+ compared to Na + , which leads to larger inter-particle pores. Overall, the Se(VI) flux was much lower than the HTO flux due to anion exclusion, with Se(VI) flux following the order Ca (D e = 1.03×10 -11 m 2 s -1 ) > Na–Ca (D e = 2.12×10 -12 m 2 s -1 ) > Na (D e = 1.28×10 -12 m 2 s -1 ). These differences in Se(VI) flux are due to a combination of factors, including (1) larger accessible porosity in Ca-montmorillonite due to clay layer stacking and smaller electrostatic effects compared to Na-montmorillonite, (2) larger accessible porosity for neutral-charge CaSeO4 species which makes up 32% of aqueous Se(VI) in the pure Ca system, and (3) possibly higher Se(VI) adsorption for Ca-montmorillonite. Through a combination of experimental and modeling work, this study highlights the compounding effects that electrolyte and counterion compositions can have on radionuclide transport through clay. Diffusion models that neglect these effects are not transferable from laboratory experimental conditions to in situ repository conditions.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

An electrochemical mesoscale tool for modeling the corrosion of structural alloys by molten salt

Understanding the impact of microstructure on corrosion rates can aid the development of corrosion-resistant alloys for molten salt reactors. Here in this work, we develop an electrochemical phase-field model for capturing the microstructure-dependent corrosion of structural alloys by molten salts. As a demonstration problem, we apply this model to capture the selective depletion of Cr from Ni-Cr grain boundaries during corrosion in molten FLiBe salt. We perform sensitivity analysis and model verification on 1D simulations to confirm that the model predicts diffusion-limited kinetics. The model is validated using 1D, 2D, and 3D simulations against experimental data for Ni-5Cr and Ni-20Cr corrosion in molten FLiBe. The 1D simulations predict the corrosion behavior with reasonable accuracy when using an effective diffusion coefficient that accurately represents the grain boundary diffusion. 2D simulations that represent the grain structure underpredict the corrosion. 3D simulations that represent the grain structure predict the corrosion with reasonable accuracy. The corrosion rate predicted by the 3D simulations is proportional to the average grain size at the alloy/salt interface.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Hydrogen and deuterium permeation in Hastelloy N

Hastelloy N was chosen as the fluoride salt-contacting structural material for the Molten Salt Reactor Experiment due to its excellent compatibility with the fuel salt FLiBe. FLiBe is currently investigated for several advanced fusion and fission reactor concepts where tritium generation in the FLiBe is anticipated. Knowledge of hydrogen transport properties through Hastelloy N is important to understand how tritium would permeate through this material and result in an unintentional release. In this study, the hydrogen and deuterium permeability, diffusivity, and solubility were measured from 500 to 700 °C at a primary-side pressure of 10 kPa in a well-characterized sample of Hastelloy N. The prepared polycrystalline Hastelloy N had C and O impurities present on the surface. These impurities were investigated using Auger Emission Spectroscopy and Ar depth profiling. Here, the adventitious C was removed upon the first Ar sputter cycle whereas O persisted deeper into the sample. For permeation experiments, applied deuterium pressures ranged from 13 Pa to 100 kPa and deuterium transport remained in the diffusion-limited regime (J ∝ P 0.5 ) throughout the pressure range examined. Two methods are employed to measure the effective hydrogen and deuterium diffusivity: rise and decline. The decline method produced improved statistical model fits for calculating the effective diffusion coefficient compared to the rise method. The resultant transport properties compared well to published values for other nickel alloys.

08 HYDROGEN↗

Experimental Characterization of Hydrogen Diffusion in Shale Rocks for Geologic Storage Applications

As global energy systems undergo a transition to cleaner alternatives, geologic hydrogen storage has emerged as a promising solution for large-scale energy storage. A critical factor in determining the feasibility of this approach is the effectiveness of caprock formations, such as shale, in preventing hydrogen migration. This study investigates the diffusion behavior of hydrogen through shale to assess its suitability as a caprock for geologic hydrogen storage. Using a novel double-seal core holder design and a through-diffusion apparatus, hydrogen diffusion was measured through shale rock from the Eagle Ford and Wolfcamp Formations under dry conditions. These measurements were complemented by microstructural and mineralogical analyses using low-pressure nitrogen adsorption and X-ray diffraction. The effective diffusion coefficient of hydrogen in these shale caprocks ranged from 2.51 × 10 –8 to 9.85 × 10 –8 m 2 /s. Notably, we observed that the diffusion behavior was more related to the pore network structure and could not be attributed to differences in the total pore volume between shale types alone. Here, to further understand the role of pore network complexity, a fractal pore model was developed to correlate tortuosity with the fractal dimension of the pore structure (a measure of pore network complexity). The proposed model closely matched tortuosity values obtained from diffusion experiments, outperforming existing theoretical tortuosity–porosity correlations. These findings provide key quantitative parameters needed to assess the feasibility of geologic hydrogen storage as well as insights that can be applied to hydrogen storage in a range of geologic formations.

08 HYDROGEN↗

Resistive drift wave turbulence and anomalous transport of multi-species plasma

Anomalous transport of multi-species plasma is considered with the generalized Hasegawa–Wakatani model. It is shown that the transport of all plasma species is described by fractional diffusion equations with the same effective diffusion coefficient. Strongly enhanced perturbations of heavy impurity density are found in long-living plasma flow vortices.

Physics↗