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DOE OSTI2015

Monte Carlo Simulations of Coupled Diffusion and Surface Reactions during the Aqueous Corrosion of Borosilicate Glasses

Borosilicate nuclear waste glasses develop complex altered layers as a result of coupled processes such as hydrolysis of network species, condensation of Si species, and diffusion. However, diffusion has often been overlooked in Monte Carlo models of the aqueous corrosion of borosilicate glasses. Therefore, three different models for dissolved Si diffusion in the altered layer were implemented in a Monte Carlo model and evaluated for glasses in the compositional range (75-x) mol% SiO2 (12.5+x/2) mol% B2O3 and (12.5+x/2) mol% Na2O, where 0 ≤ x ≤ 20%, and corroded in static conditions at a surface-to-volume ratio of 1000 m-1. The three models considered instantaneous homogenization (M1), linear concentration gradients (M2), and concentration profiles determined by solving Fick’s 2nd law using a finite difference method (M3). Model M3 revealed that concentration profiles in the altered layer are not linear and show changes in shape and magnitude as corrosion progresses, unlike those assumed in model M2. Furthermore, model M3 showed that, for borosilicate glasses with a high forward dissolution rate compared to the diffusion rate, the gradual polymerization and densification of the altered layer is significantly delayed compared to models M1 and M2. Models M1 and M2 were found to be appropriate models only for glasses with high release rates such as simple borosilicate glasses with low ZrO2 content.

borosilicates↗

DOE OSTI2017

Boundary Conditions for Diffusion-Mediated Processes within Linear Nanopores: Exact Treatment of Coupling to an Equilibrated External Fluid

In this paper, we consider a variety of diffusion-mediated processes occurring within linear nanopores, but which involve coupling to an equilibrated external fluid through adsorption and desorption. By determining adsorption and desorption rates through a set of tailored simulations, and by exploiting a spatial Markov property of the models, we develop a formulation for performing efficient pore-only simulations of these processes. Coupling to the external fluid is described exactly through appropriate nontrivial boundary conditions at the pore openings. This formalism is applied to analyze the following: (i) tracer counter permeation (TCP) where different labeled particles adsorb into opposite ends of the pore and establish a nonequilibrium steady state; (ii) tracer exchange (TE) with exchange of differently labeled particles within and outside the pore; (iii) catalytic conversion reactions where a reactant in the external fluid adsorbs into the pore and converts to a product which may desorb. The TCP analysis also generates a position-dependent generalized tracer diffusion coefficient, the form of which controls behavior in the TE and catalytic conversion processes. We focus on the regime of single-file diffusion within the pore which produces the strongest correlations and largest deviations from mean-field type behavior. Finally, behavior is quantified precisely via kinetic Monte Carlo simulations but is also captured with appropriate analytic treatments.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2015

Understanding the effects of strain on morphological instabilities of a nanoscale island during heteroepitaxial growth

A comprehensive morphological stability analysis of a nanoscale circular island during heteroepitaxial growth is presented based on continuum elasticity theory. The interplay between kinetic and thermodynamic mechanisms is revealed by including strain-related kinetic processes. In the kinetic regime, the Burton-Cabrera-Frank model is adopted to describe the growth front of the island. Together with kinetic boundary conditions, various kinetic processes including deposition flow, adatom diffusion, attachment-detachment kinetics, and the Ehrlich-Schwoebel barrier can be taken into account at the same time. In the thermodynamic regime, line tension, surface energy, and elastic energy are considered. As the strain relief in the early stages of heteroepitaxy is more complicated than commonly suggested by simple consideration of lattice mismatch, we also investigate the effects of external applied strain and elastic response due to perturbations on the island shape evolution. The analytical expressions for elastic fields induced by mismatch strain, external applied strain, and relaxation strain are presented. A systematic approach is developed to solve the system via a perturbation analysis which yields the conditions of film morphological instabilities. Consistent with previous experimental and theoretical work, parametric studies show the kinetic evolution of elastic relaxation, island morphology, and film composition under various conditions. Our present work offers an effective theoretical approach to get a comprehensive understanding of the interplay between different growth mechanisms and how to tailor the growth mode by controlling the nature of the crucial factors.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

An Improved Model For Determining Salinity Recharge Time for Deep Borehole Disposal - 20405

In a previous publication (K. P. Travis, D. Burley and F. G. F. Gibb, WM2017 Conference, Phoenix Arizona paper no. 17480) we introduced a numerical model to estimate the time it would take for a pressure perturbation to subside following its creation from the construction of a deep geological borehole in water-saturated rock. The model was based on the notion of a point source of momentum - a solution of the time-dependent pressure-diffusion equation. Using the model, we estimated that it would take on the order of 10 k years for physical equilibrium to become re-established following the sinking of a 5 km borehole in granite. The significance of such a model is that it places an upper bound on the lifetime required of a borehole sealing system - a necessary input to a borehole post-closure safety case assessment. No engineered sealing system has ever been devised which is capable of retaining its sealing properties for 10 half-lives of long-lived radioisotopes in spent fuel or high-level waste. One of the key advantages of disposing of nuclear waste via Deep Borehole Disposal (DBD) is the natural sealing provided by density stratified groundwater. Upon sinking of a borehole, and subsequent filling with fresh water, brine or drilling mud, this natural barrier may be temporarily damaged. Over time, fresh brine from the far-field will flow towards or away from the hole (driven by a pressure gradient) and will eventually re-establish the original salinity gradient. It follows that the engineered seals need last only as long as the time required for this salinity gradient to reset itself. One of the limitations of our previous model was the use of a static boundary condition on the borehole wall. The model used a boundary pressure which varied quadratically with depth (arising from differences between the pressure of a column of fresh water in the borehole and that of a column of brine in the host rock). However as brine replaces fresh water in the borehole (driven by a pressure gradient), the boundary function must change with time. We now introduce an improved model which takes this time dependent boundary condition into account. The model also takes into account the time taken for a mixture of brine and fresh water to re-establish chemical equilibrium through the process of diffusion. The paper contains the mathematical details of our new iterative model as well as results showing the time taken to reach steady state, and concentration profiles for the components of the brine-filled borehole as a function of time together with a discussion on the implications of the results for developing a post-closure safety assessment for DBD. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2018

Reactive transport modelling of cement paste leaching in brines

We propose and analyse a unified reactive transport model for leaching of cement paste in brines, with and without CO{sub 2}. We investigate the impact of the boundary conditions on the rate of propagation of the reaction. In agreement with experiments, we observe distinct mechanisms as a function of the pH and the CO{sub 2} concentration of the leaching brine. In particular, clogging is observed at intermediate concentration of CO{sub 2} while higher concentration accelerates the reaction. In addition, we leverage the flexibility of the simulator to explore the impact of different models on the simulations. In particular, aqueous species, phase assemblage and diffusion coefficient model are varied. We demonstrate that in order to be able to obtain quantitative predictions, it is important to accurately capture the feedback between chemical reactions, microstructure and macroscopic transport parameters.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Assessment the leaching characteristics and long-term leaching behavior of some radionuclides from synthesized zeolite cement matrix

Highlights: • Synthesis and characterization of zeolite cement synthesized from fly ash • Leaching tests were used to assess the release rate of {sup 85}Sr and {sup 60}Co radionuclides. • Simple mathematical models were used to detect leaching mechanisms. • Long-term leaching behavior of {sup 85}Sr and {sup 60}Co from cementitious matrix was assessed. The development of cementitious materials remains a vital goal to produce valuable products with good mechanical, physical and chemical properties suitable for the safe disposal of concentrated radionuclides resulted from the treatment of contaminated solutions. In this paper, zeolite cement with good properties was laboratory synthesized from industrial by-products fly ash and characterized using various characterization techniques. The leaching characteristics of strontium and cobalt radionuclides from the synthesized zeolite cement were scrutinized conforming with the standard leaching methodology of International Atomic Energy Authority (IAEA). A mechanical strength assessment was executed to characterize the extent of immobilization process of the solidified matrices. The cumulative leaching fraction (φ) of the two studied radionuclides was found to be less than 5% in all examined conditions, which implies the applicability of the IAEA-recommended methodology for estimating the diffusion coefficient. The experimental leaching data were regressed nonlinearly to various mathematical kinetic models to assess the controlling leaching mechanism and to determine the leaching parameters. The regression results indicated that strontium ({sup 85}Sr) and cobalt ({sup 60}Co) leaching resulted from two succeeding mechanisms: as first order kinetic reaction, and then diffusion. The calculated values of leachability indices signify that the performance of each of the studied matrices is within an acceptable range. A simplified mathematical model, rooted in the first order reaction and diffusion mechanisms, was simulated to predict the radionuclides leaching rates from zeolite cement matrices. By comparing the synthesized zeolite cement with other cementitious materials, it can be concluded that the synthesized material can be classified as an efficient material suitable to immobilize {sup 85}Sr and {sup 60}Co from radioactive wastes. The acquired findings demonstrated that the studied immobilized waste matrices have acceptable mechanical effectiveness.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Model development for flash boiling spray and validations with isooctane, hexane, ethanol and their binary mixtures

The objective of this study is to develop a comprehensive model for spray atomization under the consideration of flash boiling, which includes nucleation, bubble growth, and droplet breakup. Although flash boiling has been previously studied, there is still no well-established analytical and numerical model of their mechanisms, or general guidelines on the implementation of this atomization strategy. In this study, detailed formulations are elaborated for the unified spray atomization model under both non-flash and flash boiling conditions. Next, the model was implemented into CFD software and 3-D simulations were performed for model validations. Two fuel blends are tested: ethanol-isooctane blends and hexane-isooctane blends. Simulation results were compared with the experimental measurements conducted using two methodologies, DBI (Diffuse Backlight Imaging) system for spray images captured by a high-speed camera, and a PDA (Phase Doppler Anemometry) system for droplet size measurement during the spray injection process. It was found that the current flash boiling model can accurately capture the spray characteristics under different environment conditions, such as the spray plume interactions and liquid penetration. The averaged Sauter mean diameter (SMD) calculations match the measurement sufficiently well. The spray structures for both single- and multi-component fuels during the injection process are well represented by current model.

42 ENGINEERING↗

DOE OSTI2024

"Source Term Modeling for Advanced Gas Micro-Reactors"

Maintaining the safety of the public, environment, and operating personnel is the most important factor in designing, operating, maintaining, and decommissioning nuclear reactors. In recent years, there has been a growing interest in the development of micro-reactors employing TRi-structural ISOtropic (TRISO)-coated particle fuel. In gas reactors, TRISO fuel plays an important role in the safety case for high temperature reactors because of the fission product retention properties of the fuel. This ability enables the use of a functional containment strategy for the reactor where multiple barriers are used to prevent fission product release to the environment. Part of the safety analysis of these advanced reactors is the assessment of radionuclide releases under normal and accident conditions through the multiple credited safety barriers. Using conservative assumptions, a mechanistic analysis can be performed to quantify these releases that combines the probabilistic assessment of failure with analytic solutions to radionuclide transport equations. Source term modeling for TRISO fuel has been performed for previous reactor designs; however, these models are outdated, in many cases proprietary, and need updates to be applied to the current state of TRISO fuel technology and alternative gas reactor core configurations [1]. Currently, the only publicly available source term assessment for gas reactors is an expert-based Monte Carlo simulation based on the effectiveness of the fuel kernel, coating layers, and graphite block in a modular high temperature gas reactor [2]. Thus, there is a need to develop a simple, versatile, and mechanistic model of fission product release and transport in gas reactor cores that could be applied to a variety of reactors through user inputs and reactor-specific radionuclide inventories. The release is calculated by the diffusion of the key safety important fission products through the kernel, silicon carbide (SiC), graphite for both intact and defective TRISO particles based on fuel and graphite temperatures in the reactor under normal operation. These releases from the fuel enter the coolant where they can plate-out on cooler surfaces. A clean-up model is included for designs with a coolant purification system to remove fission gases. This initial distribution of fission products in the reactor serves as an initial condition for potential releases under postulated accident conditions. The model then can calculate the fission product release for any transient temperature profile and fission product releases can then be used to assess radiological dose to the workers and the public using conventional dose tools. Data on the diffusion of fission products is based on historic German TRISO experiments and the more current Department of Energy (DOE) Advanced Gas Reactor (AGR) TRISO fuel development program. The model is coded in python with inputs and outputs in excel spreadsheets, as well as python plotting utilities to aid in the interpretation of the results. References: [1] INL, NGNP Mechanistic Source Term White Paper, INL-10-17997, July 2010. [2] David A. Petti, Richard R. Hobbins, Peter Lowry, Hans Gougar, “Representative Source Terms and The Influence of Reactor Attributes on Functional Containment in Modular High Temperature Gas-cooled Reactors,” Nuclear Technology, Vol. 184, p. 181-197, Nov. 2013.

07 ISOTOPE AND RADIATION SOURCES↗

DOE OSTI2013

A diffuse interface model with immiscibility preservation

A new, simple, and computationally efficient interface capturing scheme based on a diffuse interface approach is presented for simulation of compressible multiphase flows. Multi-fluid interfaces are represented using field variables (interface functions) with associated transport equations that are augmented, with respect to an established formulation, to enforce a selected interface thickness. The resulting interface region can be set just thick enough to be resolved by the underlying mesh and numerical method, yet thin enough to provide an efficient model for dynamics of well-resolved scales. A key advance in the present method is that the interface regularization is asymptotically compatible with the thermodynamic mixture laws of the mixture model upon which it is constructed. It incorporates first-order pressure and velocity non-equilibrium effects while preserving interface conditions for equilibrium flows, even within the thin diffused mixture region. We first quantify the improved convergence of this formulation in some widely used one-dimensional configurations, then show that it enables fundamentally better simulations of bubble dynamics. Demonstrations include both a spherical-bubble collapse, which is shown to maintain excellent symmetry despite the Cartesian mesh, and a jetting bubble collapse adjacent a wall. Comparisons show that without the new formulation the jet is suppressed by numerical diffusion leading to qualitatively incorrect results.

42 ENGINEERING↗

DOE OSTI2023

Reduced Sediment Settling in Turbulent Flows Due To Basset History and Virtual Mass Effects

The behavior of suspended particles in turbulent flows is a recalcitrant problem spanning wide-ranging fields including geomorphology, hydrology, and dispersion of particulate matter in the atmosphere. One key mechanism underlying particle suspension is the difference between particle settling velocity (w s ) in turbulence and its still water counterpart (w so ). This difference is explored here for a range of particle-to-fluid densities (1 – 10) and particle diameter to Kolmogorov micro-eddy sizes (0.1 – 10). Conventional models of particle fluxes that equate w s to w so result in eddy diffusivities and turbulent Schmidt numbers contradictory to laboratory experiments. Incorporating virtual mass and Basset history forces resolves these inconsistencies, providing clarity as to why w s /w so is sub-unity for the aforementioned conditions. The proposed formulation can be imminently used to model particle settling in turbulence, especially when sediment distribution outcomes over extended time scales far surpassing turbulence time scales are sought.

Geology↗

DOE OSTI2022

Monte Carlo event generator for initial conditions of conserved charges in nuclear geometry

At top collider energies where baryon stopping is negligible, the initial state of heavy-ion collisions is overall charge neutral and predominantly composed of gluons. Nevertheless, there can also be significant local fluctuations of the baryon number, strangeness, and electric charge densities about zero, perturbatively corresponding to the production of quark/antiquark pairs. These previously ignored local charge fluctuations can permit the study of charge diffusion in the quark-gluon plasma (QGP), even at top collider energies. In this paper we present a new model denoted ICCING (initial conserved charges in nuclear geometry) which can reconstruct the initial conditions of conserved charges in the QGP by sampling a (g→q¯q) splitting probability over the initial energy density. We find that the new charge distributions generally differ from the bulk energy density; in particular, the strangeness distribution is significantly more eccentric than standard bulk observables and appears to be associated with the geometry of hot spots in the initial state. The new information provided by these conserved charges opens the door to studying a wealth of new charge- and flavor-dependent correlations in the initial state and ultimately the charge transport parameters of the QGP.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2014

Modeling results for the ITER cryogenic fore pump

The cryogenic fore pump (CFP) is designed for ITER to collect and compress hydrogen isotopes during the regeneration process of torus cryopumps. Different from common cryopumps, the ITER-CFP works in the viscous flow regime. As a result, both adsorption boundary conditions and transport phenomena contribute unique features to the pump performance. In this report, the physical mechanisms of cryopumping are studied, especially the diffusion-adsorption process and these are coupled with standard equations of species, momentum and energy balance, as well as the equation of state. Numerical models are developed, which include highly coupled non-linear conservation equations of species, momentum and energy and equation of state. Thermal and kinetic properties are treated as functions of temperature, pressure, and composition. To solve such a set of equations, a novel numerical technique, identified as the Group-Member numerical technique is proposed. It is presented here a 1D numerical model. The results include comparison with the experimental data of pure hydrogen flow and a prediction for hydrogen flow with trace helium. An advanced 2D model and detailed explanation of the Group-Member technique are to be presented in following papers.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2026

Modeling glass degradation and release of radionuclides from vitrified waste for performance assessment simulations

The release of radionuclides initially encapsulated in a slowly degrading solid waste form and contained in an eventually corroding canister defines the source term for numerical simulations for the assessment of a geologic repository for high-level radioactive waste. While the details of waste degradation, canister corrosion, and dissolution and mobilization of the radionuclides in pore water include complex chemical reaction and transport processes that are coupled to the thermal, hydrological, microbiological, and mechanical conditions in the repository, the source-term model suitable for use in a numerical performance assessment model should be a defensible abstraction of these mechanisms. We developed a radiological source-term model and implemented it into a non-isothermal flow and transport simulator. While the proposed source-term model is applicable to various waste forms, canister systems, and disposal concepts, we specifically considered radionuclide releases from vitrified high-level waste placed in a cylindrical canister disposed in a deep vertical borehole repository. In this model, waste degradation is a function of temperature, and it can be adjusted to evaluate the influence of and propagate uncertainties in pH, passivation reactions, and chemical conditions as well as geometrical factors. The time-dependent, congruent release of safety-relevant radionuclides present in the decaying inventory is then calculated. Finally, the radionuclides are mobilized by diffusive and advective transport according to the thermo-hydraulic conditions prevailing in the near field of the repository, from where they migrate through the geosphere to the accessible environment. We examine the influence of the source-term model’s parameters on performance assessment calculations through sensitivity and uncertainty propagation analyses, identifying influential factors and confirming the upper bound of their impact. These considerations align with the overarching goal of repository design, which is to demonstrate that engineered and natural barriers can collectively delay radionuclide migration for timescales far exceeding human planning, thereby providing multiple, redundant barriers against environmental contamination.

iTOUGH2↗

DOE OSTI2016

Two-fluid and finite Larmor radius effects on helicity evolution in a plasma pinch

The evolution of magnetic energy, helicity, and hybrid helicity during nonlinear relaxation of a driven-damped plasma pinch is compared in visco-resistive magnetohydrodynamics and two-fluid models with and without the ion gyroviscous stress tensor. Magnetic energy and helicity are supplied via a boundary electric field which initially balances the resistive dissipation, and the plasma undergoes multiple relaxation events during the nonlinear evolution. The magnetic helicity is well conserved relative to the magnetic energy over each event, which is short compared with the global resistive diffusion time. The magnetic energy decreases by roughly 1.5% of its initial value over a relaxation event, while the magnetic helicity changes by at most 0.2% of the initial value. The hybrid helicity is dominated by magnetic helicity in low-β pinch conditions and is also well conserved. Differences of less than 1% between magnetic helicity and hybrid helicity are observed with two-fluid modeling and result from cross helicity evolution. The cross helicity is found to change appreciably due to the first-order finite Larmor radius effects which have not been included in contemporary relaxation theories. The plasma current evolves towards the flat parallel current state predicted by Taylor relaxation theory but does not achieve it. Plasma flow develops significant structure for two-fluid models, and the flow perpendicular to the magnetic field is much more substantial than the flow along it.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

Permeation of CO 2 and N 2 through glassy poly(dimethyl phenylene) oxide under steady- and presteady-state conditions

Glassy polymers are often used for gas separations because of their high selectivity. Although the dual-mode permeation model correctly fits their sorption and permeation isotherms, its physical interpretation is disputed, and it does not describe permeation far from steady state, a condition expected when separations involve intermittent renewable energy sources. To develop a more comprehensive permeation model, we combine experiment, molecular dynamics, and multiscale reaction–diffusion modeling to characterize the time-dependent permeation of N 2 and CO 2 through a glassy poly(dimethyl phenylene oxide) membrane, a model system. Simulations of experimental time-dependent permeation data for both gases in the presteady-state and steady-state regimes show that both single- and dual-mode reaction–diffusion models reproduce the experimental observations, and that sorbed gas concentrations lag the external pressure rise. The results point to environment-sensitive diffusion coefficients as a vital characteristic of transport in glassy polymers.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2018

Emergent supersymmetry in local equilibrium systems

Many physical processes we observe in nature involve variations of macroscopic quantities over spatial and temporal scales much larger than microscopic molecular collision scales and can be considered as in local thermal equilibrium. In this paper we show that any classical statistical system in local thermal equilibrium has an emergent supersymmetry at low energies. We use the framework of non-equilibrium effective field theory for quantum many-body systems defined on a closed time path contour and consider its classical limit. Unitarity of time evolution requires introducing anti-commuting degrees of freedom and BRST symmetry which survive in the classical limit. The local equilibrium is realized through a Z2 dynamical KMS symmetry. We show that supersymmetry is equivalent to the combination of BRST and a specific consequence of the dynamical KMS symmetry, to which we refer as the special dynamical KMS condition. In particular, we prove a theorem stating that a system satisfying the special dynamical KMS condition is always supersymmetrizable. Here, we discuss a number of examples explicitly, including model A for dynamical critical phenomena, a hydrodynamic theory of nonlinear diffusion, and fluctuating hydrodynamics for relativistic charged fluids.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2016

Smoothed Particle Hydrodynamics and its applications for multiphase flow and reactive transport in porous media

Smoothed Particle Hydrodynamics (SPH) is a Lagrangian method based on a meshless discretization of partial differential equations. In this review, we present SPH discretization of the Navier-Stokes and Advection-Diffusion-Reaction equations, implementation of various boundary conditions, and time integration of the SPH equations, and we discuss applications of the SPH method for modeling pore-scale multiphase flows and reactive transport in porous and fractured media.

Tartakovsky, Alexandre M.↗

DOE OSTI2015

A hybrid molecular dynamics/fluctuating hydrodynamics method for modelling liquids at multiple scales in space and time

A new 3D implementation of a hybrid model based on the analogy with two-phase hydrodynamics has been developed for the simulation of liquids at microscale. The idea of the method is to smoothly combine the atomistic description in the molecular dynamics zone with the Landau-Lifshitz fluctuating hydrodynamics representation in the rest of the system in the framework of macroscopic conservation laws through the use of a single “zoom-in” user-defined function s that has the meaning of a partial concentration in the two-phase analogy model. In comparison with our previous works, the implementation has been extended to full 3D simulations for a range of atomistic models in GROMACS from argon to water in equilibrium conditions with a constant or a spatially variable function s. Preliminary results of simulating the diffusion of a small peptide in water are also reported.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗