Publications

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Injection of CO2 into formations containing brine is proposed as a long-term sequestration solution. A significant obstacle to sequestration performance is the presence of existing wells providing a transport pathway out of the sequestration formation. To understand how heterogeneity impacts the leakage rate, we employ two dimensional models of the CO2 injection process into a sandstone aquifer with shale inclusions to examine the parameters controlling release through an existing well. This scenario is modeled as a constant-rate injection of super-critical CO2 into the existing formation where buoyancy effects, relative permeabilities, and capillary pressures are employed. Three geologic controls are considered: stratigraphic dip angle, shale inclusion size and shale fraction. In this study, we examine the impact of heterogeneity on the amount and timing of CO2 released through a leaky well. Sensitivity analysis is performed to classify how various geologic controls influence CO2 loss. A 'Design of Experiments' approach is used to identify the most important parameters and combinations of parameters to control CO2 migration while making efficient use of a limited number of computations. Results are used to construct a low-dimensional description of the transport scenario. The goal of this exploration is to develop a small set of parametric descriptors that can be generalized to similar scenarios. Results of this work will allow for estimation of the amount of CO2 that will be lost for a given scenario prior to commencing injection. Additionally, two-dimensional and three-dimensional simulations are compared to quantify the influence that surrounding geologic media has on the CO2 leakage rate.

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This report evaluates the feasibility of high-level radioactive waste disposal in shale within the United States. The U.S. has many possible clay/shale/argillite basins with positive attributes for permanent disposal. Similar geologic formations have been extensively studied by international programs with largely positive results, over significant ranges of the most important material characteristics including permeability, rheology, and sorptive potential. This report is enabled by the advanced work of the international community to establish functional and operational requirements for disposal of a range of waste forms in shale media. We develop scoping performance analyses, based on the applicable features, events, and processes identified by international investigators, to support a generic conclusion regarding post-closure safety. Requisite assumptions for these analyses include waste characteristics, disposal concepts, and important properties of the geologic formation. We then apply lessons learned from Sandia experience on the Waste Isolation Pilot Project and the Yucca Mountain Project to develop a disposal strategy should a shale repository be considered as an alternative disposal pathway in the U.S. Disposal of high-level radioactive waste in suitable shale formations is attractive because the material is essentially impermeable and self-sealing, conditions are chemically reducing, and sorption tends to prevent radionuclide transport. Vertically and laterally extensive shale and clay formations exist in multiple locations in the contiguous 48 states. Thermal-hydrologic-mechanical calculations indicate that temperatures near emplaced waste packages can be maintained below boiling and will decay to within a few degrees of the ambient temperature within a few decades (or longer depending on the waste form). Construction effects, ventilation, and the thermal pulse will lead to clay dehydration and deformation, confined to an excavation disturbed zone within a few meters of the repository, that can be reasonably characterized. Within a few centuries after waste emplacement, overburden pressures will seal fractures, resaturate the dehydrated zones, and provide a repository setting that strongly limits radionuclide movement to diffusive transport. Coupled hydrogeochemical transport calculations indicate maximum extents of radionuclide transport on the order of tens to hundreds of meters, or less, in a million years. Under the conditions modeled, a shale repository could achieve total containment, with no releases to the environment in undisturbed scenarios. The performance analyses described here are based on the assumption that long-term standards for disposal in clay/shale would be identical in the key aspects, to those prescribed for existing repository programs such as Yucca Mountain. This generic repository evaluation for shale is the first developed in the United States. Previous repository considerations have emphasized salt formations and volcanic rock formations. Much of the experience gained from U.S. repository development, such as seal system design, coupled process simulation, and application of performance assessment methodology, is applied here to scoping analyses for a shale repository. A contemporary understanding of clay mineralogy and attendant chemical environments has allowed identification of the appropriate features, events, and processes to be incorporated into the analysis. Advanced multi-physics modeling provides key support for understanding the effects from coupled processes. The results of the assessment show that shale formations provide a technically advanced, scientifically sound disposal option for the U.S.

This report summarizes the results of a computer model that describes the behavior of pulsating heat pipes (PHP). The purpose of the project was to develop a highly efficient (as compared to the heat transfer capability of solid copper) thermal groundplane (TGP) using silicon carbide (SiC) as the substrate material and water as the working fluid. The objective of this project is to develop a multi-physics model for this complex phenomenon to assist with an understanding of how PHPs operate and to be able to understand how various parameters (geometry, fill ratio, materials, working fluid, etc.) affect its performance. The physical processes describing a PHP are highly coupled. Understanding its operation is further complicated by the non-equilibrium nature of the interplay between evaporation/condensation, bubble growth and collapse or coalescence, and the coupled response of the multiphase fluid dynamics among the different channels. A comprehensive theory of operation and design tools for PHPs is still an unrealized task. In the following we first analyze, in some detail, a simple model that has been proposed to describe PHP behavior. Although it includes fundamental features of a PHP, it also makes some assumptions to keep the model tractable. In an effort to improve on current modeling practice, we constructed a model for a PHP using some unique features available in FLOW-3D, version 9.2-3 (Flow Science, 2007). We believe that this flow modeling software retains more of the salient features of a PHP and thus, provides a closer representation of its behavior.

This document summarizes research and planning for the development of a numerical simulation capability for nonisothermal multiphase, multicomponent transport in heterogeneous deformable porous materials. Particular attention is given to describing a mathematical formulation for flow in deformable media and for numerical techniques for dealing with phase transitions. A development plan is formulated to provide a computational capability motivated by current and future needs in geosystems management for energy security.

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This report documents the results for the FY07 ASC Integrated Codes Level 2 Milestone number 2354. The description for this milestone is, 'Demonstrate level set free surface tracking capabilities in ARIA to simulate the dynamics of the formation and time evolution of a weld pool in laser welding applications for neutron generator production'. The specialized boundary conditions and material properties for the laser welding application were implemented and verified by comparison with existing, two-dimensional applications. Analyses of stationary spot welds and traveling line welds were performed and the accuracy of the three-dimensional (3D) level set algorithm is assessed by comparison with 3D moving mesh calculations.

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Analytical and numerical solutions are presented for steady evaporating flow in open microchannels having a rectangular cross section and a uniform depth. The flow, driven by the axial gradient of capillary pressure, generally consists of an entry region where the meniscus is attached to the top corners of the channel followed by a jump-like transition to a corner-flow region in which the meniscus progressively recedes into the bottom corners of the channel. Illustrative numerical solutions are used to guide the derivation of an easily applied analytical approximation for the maximum sustainable heat flux or capillary limit. © 2005 Elsevier Ltd. All rights reserved.

The control volume finite element method (CVFEM) was developed to combine the local numerical conservation property of control volume methods with the unstructured grid and generality of finite element methods (FEMs). Most implementations of CVFEM include mass-lumping and upwinding techniques typical of control volume schemes. In this work we compare, via numerical error analysis, CVFEM and FEM utilizing consistent and lumped mass implementations, and stabilized Petrov-Galerkin streamline upwind schemes in the context of advection-diffusion processes. For this type of problem, we find no apparent advantage to the local numerical conservation aspect of CVFEM as compared to FEM. The stabilized schemes improve accuracy and degree of positivity on coarse grids, and also reduce iteration counts for advection-dominated problems.

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The derivation and justification for various low-speed approximations to the fully compressible, Navier-Stokes equations are presented. A numerical formulation based on the finite element method is developed and implemented as an extension to the standard Boussinesq equations. Example steady and transient flow problems are simulated to examine the performance of the numerical algorithm and the solution differences with the more commonly studied Boussinesq approximation. © 2004 Elsevier B.V. All rights reserved.

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This report presents a detailed multi-methods comparison of the spatial errors associated with finite difference, finite element and finite volume semi-discretizations of the scalar advection-diffusion equation. The errors are reported in terms of non-dimensional phase and group speeds, discrete diffusivity, artificial diffusivity, and grid-induced anisotropy. It is demonstrated that Fourier analysis (aka von Neumann analysis) provides an automatic process for separating the spectral behavior of the discrete advective operator into its symmetric dissipative and skew-symmetric advective components. Further it is demonstrated that streamline upwind Petrov-Galerkin and its control-volume finite element analogue, streamline upwind control-volume, produce both an artificial diffusivity and an artificial phase speed in addition to the usual semi-discrete artifacts observed in the discrete phase speed, group speed and diffusivity. For each of the numerical methods considered, asymptotic truncation error and resolution estimates are presented for the limiting cases of pure advection and pure diffusion. The Galerkin finite element method and its streamline upwind derivatives are shown to exhibit super-convergent behavior in terms of phase and group speed when a consistent mass matrix is used in the formulation. In contrast, the CVFEM method and its streamline upwind derivatives yield strictly second-order behavior. While this work can only be considered a first step in a comprehensive multi-methods analysis and comparison, it serves to identify some of the relative strengths and weaknesses of multiple numerical methods in a common mathematical framework.

This report describes the use of PorSalsa, a parallel-processing, finite-element-based, unstructured-grid code for the simulation of subsurface nonisothermal two-phase, two component flow through heterogeneous porous materials. PorSalsa can also model the advective-dispersive transport of any number of species. General source term and transport coefficient implementation greatly expands possible applications. Spatially heterogeneous flow and transport data are accommodated via a flexible interface. Discretization methods include both Galerkin and control volume finite element methods, with various options for weighting of nonlinear coefficients. Time integration includes both first and second-order predictor/corrector methods with automatic time step selection. Parallel processing is accomplished by domain decomposition and message passing, using MPI, enabling seamless execution on single computers, networked clusters, and massively parallel computers.

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Many research activities in subsurface transport require the numerical simulation of multiphase flow in porous media. This capability is critical to research in environmental remediation (e.g. contaminations with dense, non-aqueous-phase liquids), nuclear waste management, reservoir engineering, and to the assessment of the future availability of groundwater in many parts of the world. This paper presents an unstructured grid numerical algorithm for subsurface transport in heterogeneous porous media implemented for use on massively parallel (MP) computers. The mathematical model considers nonisothermal two-phase (liquid/gas) flow, including capillary pressure effects, binary diffusion in the gas phase, conductive, latent, and sensible heat transport. The Galerkin finite element method is used for spatial discretization, and temporal integration is accomplished via a predictor/corrector scheme. Message-passing and domain decomposition techniques are used for implementing a scalable algorithm for distributed memory parallel computers. Illustrative applications are shown to demonstrate capabilities and performance, one of which is modeling hydrothermal transport at the Yucca Mountain site for a radioactive waste facility.

This document reports on the accomplishments of a laboratory-directed research and development (LDRD) project whose objective was to initiate a research program for developing a fundamental understanding of multiphase multicomponent subsurface transport in heterogeneous porous media and to develop parallel processing computational tools for numerical simulation of such problems. The main achievement of this project was the successful development of a general-purpose, unstructured grid, multiphase thermal simulator for subsurface transport in heterogeneous porous media implemented for use on massively parallel (MP) computers via message-passing and domain decomposition techniques. The numerical platform provides an excellent base for new and continuing project development in areas of current interest to SNL and the DOE complex including, subsurface nuclear waste disposal and cleanup, groundwater availability and contamination studies, fuel-spill transport for accident analysis, and DNAPL transport and remediation.

We present a numerical method for nonisothermal, multiphase subsurface transport in heterogeneous porous media. The mathematical model considers nonisothermal two-phase (liquid/gas) flow, including capillary pressure effects, binary diffusion in the gas phase, conductive, latent, and sensible heat transport. The Galerkin finite element method is used for spatial discretization, and temporal integration is accomplished via a predictor/corrector scheme. Message-passing and domain decomposition techniques are used for implementing a scalable algorithm for distributed memory parallel computers. An illustrative application is shown to demonstrate capabilities and performance.

A mathematical formulation is presented for describing the transport of air, water, NAPL, and energy through porous media. The development follows a continuum mechanics approach. The theory assumes the existence of various average macroscopic variables which describe the state of the system. Balance equations for mass and energy are formulated in terms of these macroscopic variables. The system is supplemented with constitutive equations relating fluxes to the state variables, and with transport property specifications. Specification of phase equilibrium criteria, various mixing rules and thermodynamic relations completes the system of equations. A numerical simulation scheme based on finite-differences is described.

A mathematical formulation is presented for describing the transport of air, water and energy through porous media. The development follows a continuum mechanics approach. The theory assumes the existence of various average macroscopic variables which describe the state of the system. Balance equations for mass and energy are formulated in terms of these macroscopic variables. The system is supplemented with constitutive equations relating fluxes to the state variables, and with transport property specifications. Specification of various mixing rules and thermodynamic relations completes the system of equations. A numerical simulation scheme, employing the method of lines, is described for one-dimensional flow. The numerical method is demonstrated on sample problems involving nonisothermal flow of air and water. The implementation is verified by comparison with existing numerical solutions.

In this report, we reconsider the various approximations made to the full equations of motion and energy transport for treating low-speed flows with significant temperature induced property variations. This entails assessment of the development of so-called anelastic for low-Mach number flows outside the range of validity of the Boussinesq equations. An integral part of this assessment is the development of a finite element-based numerical scheme for obtaining approximate numerical solutions to this class of problems. Several formulations were attempted and are compared.

A boundary integral equation method for steady unsaturated flow in nonhomogeneous porous media is presented. Steady unsaturated flow in porous media is described by the steady form of the so-called Richards equation, a highly nonlinear Fokker-Planck equation. By applying a Kirchhoff transformation and employing an exponential model for the relation between capillary pressure and hydraulic conductivity, the flow equation is rendered linear in each subdomain of a piece-wise homogeneous material. Unfortunately, the transformation results in nonlinear conditions along material interfaces, giving rise to a jump in the potential along these boundaries. An algorithm developed to solve the nonhomogeneous flow problem is described and verified by comparison to analytical and numerical solutions. The code is applied to examine the moisture distribution in a layered porous medium due to infiltration from a strip source, a model for infiltration from shallow ponds and washes in arid regions.

The governing equation for steady flow in a partially saturated, porous medium can be written in a linear form if one adopts a hydraulic conductivity function that is exponential in the capillary-pressure head. The resulting linear field equation is well suited to numerical solution by the boundary integral equation method (BIEM). The exponential conductivity function is compared to a more complex form often assumed for tuffs, and is found to be a reasonable approximation over limited ranges of pressure head. A computer code based on the BIEM is described and tested. The BIEM is found to exhibit quadratic convergence with element size reduction on smooth solutions and on singular problems, if mesh grading is used. Agreement between results from the BIEM code an a finite-element code that solves the fully nonlinear problem is excellent, and is achieved at a substantial advantage in computer processing time. 26 refs., 23 figs., 8 tabs.

The distribution of moisture beneath a two-dimensional strip source is analyzed by applying the quasi-linear approximation. The source is described by specifying either the moisture content or the infiltration rate. A water table is specified at some depth, D, below the surface, the depth varying from shallow to semi-infinite. Numerical solutions are determined, via the boundary integral equation method, as a function of material sorptivity, α, the width of the strip source, 2L, and the depth to the water table. The moisture introduced at the source is broadly spread below the surface when αL $\ll$ 1, for which absorption by capillary forces is dominant over gravity-induced flow. Conversely, the distribution becomes finger-like along the vertical when αL $\gg$ 1, where gravity is dominant over absorption. For a source described by specifying the moisture content, the presence of a water table at finite depth influences the infiltration through the source when αD is less than about 4; infiltration rates obtained when the water table depth is semi-infinite are of sufficient accuracy for greater values of αD. When the source is described by a specified infiltration flux, the maximum allowable value of this flux for which the material beneath the source remains unsaturated is determined as a function of nondimensional sorptivity and depth to the water table.

The ignition of reactive powders by a semiconductor bridge (SCB) is analyzed by applying a multiphase flow model based upon the theory of mixtures. The hot plasma produced by the SCB permeates the cold granular explosive, deposits its latent heat upon fusing to the grains, therby heating the explosive granular surfaces to energy states required for self-sustained reaction. This mechanism is predicted to heat the granular explosive in a region local to the SCB to temperatures well above those required for thermal ignition. The analysis demonstates that this mechanism explains the prompt ignition of explosives using SCB's as opposed to the conductively controlled heating of conventional bridgewires. 16 refs., 14 figs., 1 tab.