Prediction of flow, transport, and deformation in fractured and porous media is critical to improving our scientific understanding of coupled thermal-hydrological-mechanical processes related to subsurface energy storage and recovery, nonproliferation, and nuclear waste storage. Especially, earth rock response to changes in pressure and stress has remained a critically challenging task. In this work, we advance computational capabilities for coupled processes in fractured and porous media using Sandia Sierra Multiphysics software through verification and validation problems such as poro-elasticity, elasto-plasticity and thermo-poroelasticity. We apply Sierra software for geologic carbon storage, fluid injection/extraction, and enhanced geothermal systems. We also significantly improve machine learning approaches through latent space and self-supervised learning. Additionally, we develop new experimental technique for evaluating dynamics of compacted soils at an intermediate scale. Overall, this project will enable us to systematically measure and control the earth system response to changes in stress and pressure due to subsurface energy activities.
Accurate modeling of subsurface flow and transport processes is vital as the prevalence of subsurface activities such as carbon sequestration, geothermal recovery, and nuclear waste disposal increases. Computational modeling of these problems leverages poroelasticity theory, which describes coupled fluid flow and mechanical deformation. Although fully coupled monolithic schemes are accurate for coupled problems, they can demand significant computational resources for large problems. In this work, a fixed stress scheme is implemented into the Sandia Sierra Multiphysics toolkit. Two implementation methods, along with the fully coupled method, are verified with one-dimensional (1D) Terzaghi, 2D Mandel, and 3D Cryer sphere benchmark problems. The impact of a range of material parameters and convergence tolerances on numerical accuracy and efficiency was evaluated. Overall the fixed stress schemes achieved acceptable numerical accuracy and efficiency compared to the fully coupled scheme. However, the accuracy of the fixed stress scheme tends to decrease with low permeable cases, requiring the finer tolerance to achieve a desired numerical accuracy. For the fully coupled scheme, high numerical accuracy was observed in most of cases except a low permeability case where an order of magnitude finer tolerance was required for accurate results. Finally, a two-layer Terzaghi problem and an injection–production well system were used to demonstrate the applicability of findings from the benchmark problems for more realistic conditions over a range of permeability. Simulation results suggest that the fixed stress scheme provides accurate solutions for all cases considered with the proper adjustment of the tolerance. This work clearly demonstrates the robustness of the fixed stress scheme for coupled poroelastic problems, while a cautious selection of numerical tolerance may be required under certain conditions with low permeable materials.
The design, modeling, and integration of high-temperature particle storage bins is a critical component of Gen. 3 concentrated solar power (CSP). Particle storage bins control the temperature and flow rates throughout the particle circulatory system, so having a fundamental understanding of their transient thermal behavior is highly advantageous for the design and multi-level control of future CSP systems. This paper provides contributions to this understanding by presenting a semi-analytic method for modeling the transient thermal behavior of bulk particle bins. The model is verified with experiments and a baseline CFD model and then used to make conclusions about the dominant heat transfer modes in bulk particle bins and the general transient thermal performance of related systems.
Greater utilization of subsurface reservoirs perturbs in-situ chemical-mechanical conditions with wide ranging consequences from decreased performance to project failure. Understanding the chemical precursors to rock deformation is critical to reducing the risks of these activities. To address this need, we investigated the coupled flow-dissolution- precipitation-adsorption reactions involving calcite and environmentally-relevant solid phases. Experimentally, we quantified (1) stable isotope fractionation processes for strontium during calcite nucleation and growth, and during reactive fluid flow; (2) consolidation behavior of calcite assemblages in the common brines. Numerically, we quantified water weakening of calcite using molecular dynamics simulations; and quantified the impact of calcite dissolution rate on macroscopic fracturing using finite element models. With microfluidic experiments and modeling, we show the effect of local flow fields on the dissolution kinetics of calcite. Taken together across a wide range of scales and methods, our studies allow us to separate the effects of reaction, flow, and transport, on calcite fracturing and the evolution of strontium isotopic signatures in the reactive fluids.
Coupled fluid-flow and geomechanical analysis of caprock integrity has gained a lot of attention among scientists and researchers investigating the long-term performance of geologic carbon storage systems. Reactivation of pre-existing fractures within the caprock or re-opening of faults can create permeable pathways which can influence the seal integrity. Stability of the caprock during and after injection of super-critical CO2, and the impact of pre-existing fractures in the presence or absence of one or multiple faults have been investigated in this study. The impact of the wellbore orientation and the injection rate are among other key factors in understanding the structural trapping mechanisms within such geological formations. In this study, we numerically investigated the impact of each of these factors. This study revealed the interplay between joints and faults and how different leakage pathways are formed and under which scenario they play a dominant role in terms of CO2 leakage. This study also highlights the role of one versus multiple faults in the domain and the importance of the fault hydrological property in forming leakage pathway.
The National Solar Thermal Test Facility (NSTTF) at Sandia National Laboratories is conducting research on a Generation 3 Particle Pilot Plant (G3P3) that uses falling sand-like particles as the heat transfer medium. The system will include a thermal energy storage (TES) bin with a capacity of 6 MWht¬ requiring ~120,000 kg of flowing particles. Testing and modeling were conducted to develop a validated modeling tool to understand temporal and spatial temperature distributions within the storage bin as it charges and discharges. Flow and energy transport in funnel-flow was modeled using volume averaged conservation equations coupled with level set interface tracking equations that prescribe the dynamic geometry of particle flow within the storage bin. A thin layer of particles on top of the particle bed was allowed to flow toward the center and into the flow channel above the outlet. Model results were validated using particle discharge temperatures taken from thermocouples mounted throughout a small steel bin. The model was then used to predict heat loss during charging, storing, and discharging operational modes at the G3P3 scale. Comparative results from the modeling and testing of the small bin indicate that the model captures many of the salient features of the transient particle outlet temperature over time.
Additive Manufacturing (AM) offers the opportunity to transform design, manufacturing, and qualification with its unique capabilities. AM is a disruptive technology, allowing the capability to simultaneously create part and material while tightly controlling and monitoring the manufacturing process at the voxel level, with the inherent flexibility and agility in printing layer-by-layer. AM enables the possibility of measuring critical material and part parameters during manufacturing, thus changing the way we collect data, assess performance, and accept or qualify parts. It provides an opportunity to shift from the current iterative design-build-test qualification paradigm using traditional manufacturing processes to design-by-predictivity where requirements are addressed concurrently and rapidly. The new qualification paradigm driven by AM provides the opportunity to predict performance probabilistically, to optimally control the manufacturing process, and to implement accelerated cycles of learning. Exploiting these capabilities to realize a new uncertainty quantification-driven qualification that is rapid, flexible, and practical is the focus of this paper.
In this work, we have characterized the calcium carbonate (CaCO3) precipitates over time caused by reaction-driven precipitation and dissolution in a micromodel. Reactive solutions were continuously injected through two separate inlets, resulting in transverse-mixing induced precipitation during the precipitation phase. Subsequently, a dissolution phase was conducted by injecting clean water (pH = 4). The evolution of precipitates was imaged in two and three dimensions (2-, 3-D) at selected times using optical and confocal microscopy. With estimated reactive surface area, effective precipitation and dissolution rates can be quantitatively compared to results in the previous works. Our comparison indicates that we can evaluate the spatial and temporal variations of effective reactive areas more mechanistically in the microfluidic system only with the knowledge of local hydrodynamics, polymorphs, and comprehensive image analysis. Our analysis clearly highlights the feedback mechanisms between reactions and hydrodynamics. Pore-scale modeling results during the dissolution phase were used to account for experimental observations of dissolved CaCO3 plumes with dissolution of the unstable phase of CaCO3. Mineral precipitation and dissolution induce complex dynamic pore structures, thereby impacting pore-scale fluid dynamics. Pore-scale analysis of the evolution of precipitates can reveal the significance of chemical and pore structural controls on reaction and fluid migration.
The fluid injection into the subsurface perturbs the states of pore pressure and stress on the pre-existing faults, potentially causing earthquakes. In the multiphase flow system, the contrast of fluid and rock properties between different structures produces the changes in pressure gradients and subsequently stress fields. Assuming two-phase fluid flow (gas-water system) and poroelasticity, we simulate the three-layered formation including a basement fault, in which injection-induced pressure encounters the fault directly given injection scenarios. The single-phase poroelasticity model with the same setting is also conducted to evaluate the multiphase flow effects on poroelastic response of the fault to gas injection. Sensitivity tests are performed by varying the fault permeability. The presence of gaseous phase reduces the pressure buildup within the highly gas-saturated region, causing less Coulomb stress changes, whereas capillarity increases the pore pressure within the gas-water mixed region. Even though the gaseous plume does not approach the fault, the poroelastic stressing can affect the fault stability, potentially the earthquake occurrence.
This SAND report fulfills the final report requirement for the Born Qualified Grand Challenge LDRD. Born Qualified was funded from FY16-FY18 with a total budget of ~$13M over the 3 years of funding. Overall 70+ staff, Post Docs, and students supported this project over its lifetime. The driver for Born Qualified was using Additive Manufacturing (AM) to change the qualification paradigm for low volume, high value, high consequence, complex parts that are common in high-risk industries such as ND, defense, energy, aerospace, and medical. AM offers the opportunity to transform design, manufacturing, and qualification with its unique capabilities. AM is a disruptive technology, allowing the capability to simultaneously create part and material while tightly controlling and monitoring the manufacturing process at the voxel level, with the inherent flexibility and agility in printing layer-by-layer. AM enables the possibility of measuring critical material and part parameters during manufacturing, thus changing the way we collect data, assess performance, and accept or qualify parts. It provides an opportunity to shift from the current iterative design-build-test qualification paradigm using traditional manufacturing processes to design-by-predictivity where requirements are addressed concurrently and rapidly. The new qualification paradigm driven by AM provides the opportunity to predict performance probabilistically, to optimally control the manufacturing process, and to implement accelerated cycles of learning. Exploiting these capabilities to realize a new uncertainty quantification-driven qualification that is rapid, flexible, and practical is the focus of this effort.
Injection of large amounts of fluid into the subsurface alters the states of pore pressure and stress in the formation, potentially inducing earthquakes. Increase in the seismicity rate after shut-in is often observed at fluid-injection operation sites, but mechanistic study of the rate surge has not been investigated thoroughly. Considering full poroelastic coupling of pore pressure and stress, the earthquake occurrence after shut-in can be driven by two mechanisms: (1) post shut-in diffusion of pore pressure into distant faults and (2) poroelastic stressing caused by fluid injection. Interactions of these mechanisms can depend on fault geometry, hydraulic and mechanical properties of the formation, and injection operation. In this work, a 2D aerial view of the target reservoir intersected by strike-slip basement faults is used to evaluate the impact of injection-induced pressure buildup on seismicity rate surge. A series of sensitivity tests are performed by considering the variation in (1) permeability of the fault zone, (2) locations and the number of faults with respect to the injector, and (3) well operations with time-dependent injection rates. Lower permeability faults have higher seismicity rates than more permeable faults after shut-in due to delayed diffusion and poroelastic stressing. Hydraulic barriers, depending on their relative location to injection, can either stabilize or weaken a conductive fault via poroelastic stresses. Gradual reduction of the injection rate minimizes the coulomb stress change and the least seismicity rates are predicted due to slower relaxation of coupling-induced compression as well as pore-pressure dissipation.
The fluid injection into deep geological formations altar the states of pore pressure and stress on the faults, potentially causing earthquakes. In the multiphase flow system, the interaction between fluid flow and mechanical deformation in porous media is critical to determine the spatio-temporal distribution of pore pressure and stress. The contrast of fluid and rock properties between different structures produces the changes in pressure gradients and subsequently stress fields. Assuming two-phase fluid flow (gas-water system), we simulate the two-dimensional reservoir including a basement fault, in which injection-induced pressure encounters the fault directly given injection scenarios. The single-phase flow model with the same setting is also conducted to evaluate the multiphase flow effects on mechanical response of the fault to gas injection. A series of sensitivity tests are performed by varying the fault permeability. The presence of gaseous phase reduces the pressure buildup within the gas-saturated region, causing less Coulomb stress change. The low-permeability fault prevent diffusion initially as observed in the single-phase flow system. Once gaseous phase approaches, the fault acts as a capillary barrier that causes increases in pressure within the fault zone, potentially inducing earthquakes even without direct diffusion.
The migration and trapping of supercritical CO2 (scCO2) in geologic carbon storage is strongly dependent on the geometry and wettability of the pore network in the reservoir rock. During displacement, resident fluids may become trapped in the pits of a rough pore surface forming an immiscible two-phase fluid interface with the invading fluid, allowing apparent slip flow at this interface. We present a two-phase fluid dynamics model, including interfacial tension, to characterize the impact of mineral surface roughness on this slip flow. We show that the slip flow can be cast in more familiar terms as a contact-angle (wettability)-dependent effective permeability to the invading fluid, a nondimensional measurement which relates the interfacial slip to the pore geometry. The analysis shows the surface roughness-induced slip flow can effectively increase or decrease this effective permeability, depending on the wettability and roughness of the mineral surfaces. Configurations of the pore geometry where interfacial slip has a tangible influence on permeability have been identified. The results suggest that for large roughness features, permeability to CO2 may be enhanced by approximately 30% during drainage, while the permeability to brine during reimbibition may be enhanced or diminished by 60%, depending on the contact angle with the mineral surfaces and degrees of roughness. For smaller roughness features, the changes in permeability through interfacial slip are small. A much larger range of effective permeabilities are suggested for general fluid pairs and contact angles, including occlusion of the pore by the trapped phase.
Economic feasibility of geologic carbon storage demands sustaining large storage rates without damaging caprock seals. Reactivation of pre-existing or newly formed fractures may provide a leakage pathway across caprock layers. In this study, we apply an equivalent continuum approach within a finite element framework to model the fluid-pressure-induced reactivation of pre-existing fractures within the caprock, during high-rate injection of super-critical CO2 into a brine-saturated reservoir in a hypothetical system, using realistic geomechanical and fluid properties. We investigate the impact of reservoir to caprock layer thickness, wellbore orientation, and injection rate on overall performance of the system with respect to caprock failure and leakage. We find that vertical wells result in locally higher reservoir pressures relative to horizontal injection wells for the same injection rate, with high pressure inducing caprock leakage along reactivated opening-mode fractures in the caprock. After prolonged injection, leakage along reactivated fractures in the caprock is always higher for vertical than horizontal injection wells. Furthermore, we find that low ratios of reservoir to caprock thickness favor high excess pressure and thus fracture reactivation in the caprock. Injection into thick reservoir units thus lowers the risk associated with CO2 leakage.
An enriched finite element method is described for capillary hydrodynamics including dynamic wetting. The method is enriched via the Conformal Decomposition Finite Element Method (CDFEM). Two formulations are described, one with first-order accuracy and one with second-order accuracy in time. Both formulations utilize a semi-implicit form for the surface tension that is shown to effectively circumvent the explicit capillary time step limit. Sharp interface boundary conditions are developed for capturing the dynamic contact angle as the fluid interface moves along the wall. By virtue of the CDFEM, the contact line is free to move without risk of mesh tangling, but is sharply captured. Multiple problems are used to demonstrate the effectiveness of the methods.
Coupled reservoir and geomechanical simulations are significantly important to understand the long-term behavior of geologic carbon storage (GCS) systems. In this study, we performed coupled fluid flow and geomechanical modeling of CO2 storage using available field data to (1) validate our existing numerical model and (2) perform parameter estimation via inverse modeling to identify the impact of key geomechanical (Young's modulus and Biot's coefficient) and hydrogeological (permeability and anisotropy ratio) properties on surface uplift and the pore pressure buildup at In Salah in Algeria. Furthermore, two sets of surface uplift data featuring low and high uplifts above two injection wells and the maximum change in the pore pressure due to CO2 injection were used to constrain the inverse model.
Geologic carbon storage in deep saline aquifers is a promising technology for reducing anthropogenic emissions into the atmosphere. Dissolution of injected CO2 into resident brines is one of the primary trapping mechanisms generally considered necessary to provide long-term storage security. Given that diffusion of CO2 in brine is woefully slow, convective dissolution, driven by a small increase in brine density with CO2 saturation, is considered to be the primary mechanism of dissolution trapping. Previous studies of convective dissolution have typically only considered the convective process in the single-phase region below the capillary transition zone and have either ignored the overlying two-phase region where dissolution actually takes place or replaced it with a virtual region with reduced or enhanced constant permeability. Our objective is to improve estimates of the long-term dissolution flux of CO2 into brine by including the capillary transition zone in two-phase model simulations. In the fully two-phase model, there is a capillary transition zone above the brine-saturated region over which the brine saturation decreases with increasing elevation. Our two-phase simulations show that the dissolution flux obtained by assuming a brine-saturated, single-phase porous region with a closed upper boundary is recovered in the limit of vanishing entry pressure and capillary transition zone. For typical finite entry pressures and capillary transition zone, however, convection currents penetrate into the two-phase region. This removes the mass transfer limitation of the diffusive boundary layer and enhances the convective dissolution flux of CO2 more than 3 times above the rate assuming single-phase conditions.
Fracture and fragmentation are extremely nonlinear multiscale processes in which microscale damage mechanisms emerge at the macroscale as new fracture surfaces. Numerous numerical methods have been developed for simulating fracture initiation, propagation, and coalescence. Here, we present a computational approach for modeling pervasive fracture in quasi-brittle materials based on random close-packed Voronoi tessellations. Each Voronoi cell is formulated as a polyhedral finite element containing an arbitrary number of vertices and faces. Fracture surfaces are allowed to nucleate only at the intercell faces. Cohesive softening tractions are applied to new fracture surfaces in order to model the energy dissipated during fracture growth. The randomly seeded Voronoi cells provide a regularized discrete random network for representing fracture surfaces. The potential crack paths within the random network are viewed as instances of realizable crack paths within the continuum material. Mesh convergence of fracture simulations is viewed in a weak, or distributional, sense. The explicit facet representation of fractures within this approach is advantageous for modeling contact on new fracture surfaces and fluid flow within the evolving fracture network. Applications of interest include fracture and fragmentation in quasi-brittle materials and geomechanical applications such as hydraulic fracturing, engineered geothermal systems, compressed-air energy storage, and carbon sequestration.
We develop a capability to simulate reduction-oxidation (redox) flow batteries in the Sierra Multi-Mechanics code base. Specifically, we focus on all-vanadium redox flow batteries; however, the capability is general in implementation and could be adopted to other chemistries. The electrochemical and porous flow models follow those developed in the recent publication by [28]. We review the model implemented in this work and its assumptions, and we show several verification cases including a binary electrolyte, and a battery half-cell. Then, we compare our model implementation with the experimental results shown in [28], with good agreement seen. Next, a sensitivity study is conducted for the major model parameters, which is beneficial in targeting specific features of the redox flow cell for improvement. Lastly, we simulate a three-dimensional version of the flow cell to determine the impact of plenum channels on the performance of the cell. Such channels are frequently seen in experimental designs where the current collector plates are borrowed from fuel cell designs. These designs use a serpentine channel etched into a solid collector plate.
The modeling work described herein represents Sandia National Laboratories (SNL) portion of a collaborative three-year project with Northrop Grumman Electronic Systems (NGES) and the University of Missouri to develop an advanced, thermal ground-plane (TGP), which is a device, of planar configuration, that delivers heat from a source to an ambient environment with high efficiency. Work at all three institutions was funded by DARPA/MTO; Sandia was funded under DARPA/MTO project number 015070924. This is the final report on this project for SNL. This report presents a numerical model of a pulsating heat pipe, a device employing a two phase (liquid and its vapor) working fluid confined in a closed loop channel etched/milled into a serpentine configuration in a solid metal plate. The device delivers heat from an evaporator (hot zone) to a condenser (cold zone). This new model includes key physical processes important to the operation of flat plate pulsating heat pipes (e.g. dynamic bubble nucleation, evaporation and condensation), together with conjugate heat transfer with the solid portion of the device. The model qualitatively and quantitatively predicts performance characteristics and metrics, which was demonstrated by favorable comparisons with experimental results on similar configurations. Application of the model also corroborated many previous performance observations with respect to key parameters such as heat load, fill ratio and orientation.
This document summarizes research performed under the SNL LDRD entitled - Computational Mechanics for Geosystems Management to Support the Energy and Natural Resources Mission. The main accomplishment was development of a foundational SNL capability for computational thermal, chemical, fluid, and solid mechanics analysis of geosystems. The code was developed within the SNL Sierra software system. This report summarizes the capabilities of the simulation code and the supporting research and development conducted under this LDRD. The main goal of this project was the development of a foundational capability for coupled thermal, hydrological, mechanical, chemical (THMC) simulation of heterogeneous geosystems utilizing massively parallel processing. To solve these complex issues, this project integrated research in numerical mathematics and algorithms for chemically reactive multiphase systems with computer science research in adaptive coupled solution control and framework architecture. This report summarizes and demonstrates the capabilities that were developed together with the supporting research underlying the models. Key accomplishments are: (1) General capability for modeling nonisothermal, multiphase, multicomponent flow in heterogeneous porous geologic materials; (2) General capability to model multiphase reactive transport of species in heterogeneous porous media; (3) Constitutive models for describing real, general geomaterials under multiphase conditions utilizing laboratory data; (4) General capability to couple nonisothermal reactive flow with geomechanics (THMC); (5) Phase behavior thermodynamics for the CO2-H2O-NaCl system. General implementation enables modeling of other fluid mixtures. Adaptive look-up tables enable thermodynamic capability to other simulators; (6) Capability for statistical modeling of heterogeneity in geologic materials; and (7) Simulator utilizes unstructured grids on parallel processing computers.
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.
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.
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.
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.
This paper 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 speed, discrete diffusivity, artificial diffusivity, and grid-induced anisotropy, it is demonstrated that Fourier analysis provides an automatic process for separating the discrete advective operator into its symmetric and skew-symmetric components and characterizing the spectral behaviour of each operator. 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. It is demonstrated that streamline upwind Petrov-Galerkin and its control-volume finite element analogue, the streamline upwind control-volume method, produce both an artificial diffusivity and a concomitant phase speed adjustment in addition to the usual semi-discrete artifacts observed in the phase speed, group speed and diffusivity. The Galerkin finite element method and its streamline upwind derivatives are shown to exhibit super-convergent behaviour 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 behaviour. In Part II of this paper, we consider two-dimensional semi-discretizations of the advection-diffusion equation and also assess the affects of grid-induced anisotropy observed in the non-dimensional phase speed, and the discrete and artificial diffusivities. Although 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 analysis framework.
Part I of this work presents a detailed multi-methods comparison of the spatial errors associated with the one-dimensional finite difference, finite element and finite volume semi-discretizations of the scalar advection-diffusion equation. In Part II we extend the analysis to two-dimensional domains and also consider the effects of wave propagation direction and grid aspect ratio on the phase speed, and the discrete and artificial diffusivities. The observed dependence of dispersive and diffusive behaviour on propagation direction makes comparison of methods more difficult relative to the one-dimensional results. For this reason, integrated (over propagation direction and wave number) error and anisotropy metrics are introduced to facilitate comparison among the various methods. With respect to these metrics, the consistent mass Galerkin and consistent mass control-volume finite element methods, and their streamline upwind derivatives, exhibit comparable accuracy, and generally out-perform their lumped mass counterparts and finite-difference based schemes. 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.
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.
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.