SEARCH · Search NASA

Results for “boundary value problems”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 469 records · Page 26

All sources NASA NTRS DOE OSTI

DOE OSTI2018

Minimal area surfaces in AdS n+1 and Wilson loops

The AdS/CFT correspondence relates the expectation value of Wilson loops in N = 4 SYM to the area of minimal surfaces in AdS 5 . In this paper we consider minimal area surfaces in generic Euclidean AdS n+1 using the Pohlmeyer reduction in a similar way as we did previously in Euclidean AdS 3 . As in that case, the main obstacle is to find the correct parameterization of the curve in terms of a conformal parameter. Once that is done, the boundary conditions for the Pohlmeyer fields are obtained in terms of conformal invariants of the curve. After solving the Pohlmeyer equations, the area can be expressed as a boundary integral involving a generalization of the conformal arc-length, curvature and torsion of the curve. Furthermore, one can introduce the λ-deformation symmetry of the contours by a simple change in the conformal invariants. This determines the λ-deformed contours in terms of the solution of a boundary linear problem. In fact the condition that all λ deformed contours are periodic can be used as an alternative to solving the Pohlmeyer equations and is equivalent to imposing the vanishing of an infinite set of conserved charges derived from integrability.

't Hooft and Polyakov loops↗

DOE OSTI2022

FROSch Preconditioners for Land Ice Simulations of Greenland and Antarctica

Numerical simulations of Greenland and Antarctic ice sheets involve the solution of large-scale highly nonlinear systems of equations on complex shallow geometries. This work is concerned with the construction of Schwarz preconditioners for the solution of the associated tangent problems, which are challenging for solvers mainly because of the strong anisotropy of the meshes and wildly changing boundary conditions that can lead to poorly constrained problems on large portions of the domain. In this study, two-level generalized Dryja--Smith--Widlund (GDSW)--type Schwarz preconditioners are applied to different land ice problems, i.e., a velocity problem, a temperature problem, as well as the coupling of the former two problems. We employ the message passing interface (MPI)--parallel implementation of multilevel Schwarz preconditioners provided by the package FROSch (fast and robust Schwarz) from the Trilinos library. The strength of the proposed preconditioner is that it yields out-of-the-box scalable and robust preconditioners for the single physics problems. To the best of our knowledge, this is the first time two-level Schwarz preconditioners have been applied to the ice sheet problem and a scalable preconditioner has been used for the coupled problem. The preconditioner for the coupled problem differs from previous monolithic GDSW preconditioners in the sense that decoupled extension operators are used to compute the values in the interior of the subdomains. Additionally, several approaches for improving the performance, such as reuse strategies and shared memory OpenMP parallelization, are explored. In our numerical study we target both uniform meshes of varying resolution for the Antarctic ice sheet as well as nonuniform meshes for the Greenland ice sheet. We present several weak and strong scaling studies confirming the robustness of the approach and the parallel scalability of the FROSch implementation. Among the highlights of the numerical results are a weak scaling study for up to 32,K processor cores (8,K MPI ranks and 4 OpenMP threads) and 566,M degrees of freedom for the velocity problem as well as a strong scaling study for up to 4,K processor cores (and MPI ranks) and 68,M degrees of freedom for the coupled problem.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2014

Adjustable magnetoelectric effect of self-assembled vertical multiferroic nanocomposite films by the in-plane misfit strain and ferromagnetic volume fraction

The strain-mediated magnetoelectric (ME) property of self-assembled vertical multiferroic nanocomposite films epitaxially grown on cubic substrates was calculated by a nonlinear thermodynamic theory combined with the elastic theory. The dependent relations of phase state of ferroelectric films with the in-plane misfit strain, out-of-plane misfit strain, temperature, and volume fraction of ferromagnetic phase were confirmed. The effects of in-plane misfit strain and ferromagnetic volume fraction on the polarization and dielectric constant of ferroelectric films at room temperature were elaborately analyzed for the vertical BaTiO{sub 3}-CoFe{sub 2}O{sub 4} and PbTiO{sub 3}-CoFe{sub 2}O{sub 4} nanocomposite films. Our calculated results confirmed the relationship among ME effect and in-plane misfit strain and ferromagnetic volume fraction in the nanocomposite films. The ME voltage coefficients of vertical BaTiO{sub 3}-CoFe{sub 2}O{sub 4} and PbTiO{sub 3}-CoFe{sub 2}O{sub 4} nanocomposite films displayed various maximums and abrupt points at special phases and phase transition boundaries. The ME voltage coefficients of lead-free BaTiO{sub 3}-CoFe{sub 2}O{sub 4} nanocomposite films epitaxially grown on different substrates could reach a comparative value of ∼2 V·cm{sup −1}·Oe{sup −1} under the controllable in-plane misfit strain induced by substrate clamping. Our results provided an available method for the optimal design of vertical multiferroic nanocomposites with adjustable ME effect by optimizing the ferromagnetic volume fraction and substrate type.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2017

Optical properties of magnetic photonic crystals with an arbitrary magnetization orientation

We have studied the peculiarities of diffraction of light in magnetic photonic crystals at large values of magnetooptical activity parameter and modulation depth. We have considered the case of an arbitrary angle between the directions of the external static magnetic field and the normal to the layer. The problem has been solved by the modified Ambartsumyan layer summation method. It has been shown that the given system is nonreciprocal with respect to not only circular, but linear polarizations also. In this case, a new type of nonreciprocity is observed (namely, the relation R(α) ≠ R(–α) holds, where R is the reflection coefficient and α is the angle of incidence). It has been demonstrated that in the case of oblique incidence, there appears a new photonic forbidden band that is not selective relative to the polarization of incident light. We have detected strong dependences of reflectance, absorbance, transmittance nonreciprocity, and other characteristics on the angle between the direction of the external static magnetic field and the normal to the layer boundary. Such a system can be used as a controllable polarization filter and a mirror, as well as a source of circular (elliptic) polarization, a controllable optical diode, and so on.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Sensitivity analysis of a layered piezoelectric system using ZFEM

The complex variable finite element method (ZFEM) is a numerical technique which aims to find the partial derivatives of the independent variables with respect to variation in dependent parameters declared in the physics. This is done by combining the complex Taylor series expansion within the weak formulation of the governing equation in a coupled system of linear equations forming a complex valued block matrix given by the Cauchy–Riemann matrix representation. In this work, two-dimensional linear first-order elements have been implemented in ZFEM to predict the design derivatives of the mechanical displacement field and the voltage potential field for a layered piezoelectric system in a steady-state study with Dirichlet boundary condition applied at the top and bottom edges of the geometry. This approach allows the standard FEM solution to quantify the sensitivity of the mechanical displacement and voltage potential fields with respect to small variations in the material properties through the information obtained from the computation of the derivatives. The domain is formed by a layered body with PZT-4 and PZT-5 stacked together. For result verification, the numerical solution obtained with ZFEM was compared to results from a commercial FEM package and the solution from the imaginary part was compared to the exact solution of a well-known benchmark problem. In conclusion, comparison of the results showed good agreement for both the real and imaginary parts of the solution and the largest sensitivities were found in PZT-5 specifically in C 13 , C 33 , and ε 33 .

42 ENGINEERING↗

DOE OSTI2012

Transverse instability of a plane front of fast impact ionization waves

The transverse instability of a plane front of fast impact ionization waves in p{sup +}-n-n{sup +} semiconductor structures with a finite concentration of donors N in the n layer has been theoretically analyzed. It is assumed that the high velocity u of impact ionization waves is ensured owing to the avalanche multiplication of the uniform background of electrons and holes whose concentration {sigma}{sub b} ahead of the front is high enough for the continuum approximation to be applicable. The problem of the calculation of the growth rate s of a small harmonic perturbation with wavenumber k is reduced to the eigenvalue problem for a specific homogeneous Volterra equation of the second kind containing the sum of double and triple integrals of an unknown eigenfunction. This problem has been solved by the method of successive approximations. It has been shown that the function s(k) for small k values increases monotonically in agreement with the analytical theory reported in Thermal Engineering 58 (13), 1119 (2011), reaches a maximum s{sub M} at k = k{sub M}, then decreases, and becomes negative at k > k{sub 01}. This behavior of the function s(k) for short-wavelength perturbations is due to a decrease in the distortion of the field owing to a finite thickness of the space charge region of the front and 'smearing' of perturbation of concentrations owing to the transverse transport of charge carriers. The similarity laws for perturbations with k Greater-Than-Or-Equivalent-To k{sub M} have been established: at fixed {sigma}{sub b} values and the maximum field strength on the front E{sub 0M}, the growth rate s depends only on the ratio k/N and the boundary wavenumber k{sub 01} {proportional_to} N. The parameters s{sub M}, k{sub M}, and k{sub 01}, which determine the perturbation growth dynamics and the upper boundary of the instability region for impact ionization waves, have been presented as functions of E{sub 0M}. These dependences indicate that the model of a plane impact ionization wave is insufficient for describing the operation of avalanche voltage sharpers and that fronts of fast streamers in the continuum approximation should be stable with respect to transverse perturbations in agreement with the previously reported numerical simulation results. The results have been confirmed by the numerical simulation of the evolution of small harmonic perturbations of the steady-state plane impact ionization wave.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2012

Problem Specification for FY12 Modeling of UNF During Extended Storage

The Nuclear Energy Advanced Modeling and Simulation (NEAMS) program of the Advanced Modeling and Simulation Office (AMSO) of the US Department of Energy, Office of Nuclear Energy (DOE/NE) has invested in the initial extension and application of advanced nuclear simulation tools to address relevant needs in evaluating the performance of used nuclear fuel (UNF) during extended periods of dry storage. There are many significant challenges associated with the prediction of the behavior of used fuel during extended periods of dry storage and subsequent transportation. The initial activities are focused on integrating with the Used Fuel Disposition (UFD) Campaign of the DOE/NE and a demonstration that the Advanced Multi-Physics (AMP) Nuclear Fuel Performance code (AMPFuel) for modeling the mechanical state of the cladding after decades of storage. This initial focus will model the long-term storage of the UNF and account for the effect, and generation, of radially and circumferentially oriented hydride precipitates within the cladding and predict the end of storage (EOS) mechanical state (stress, strain) of the cladding. Predicting the EOS state of the cladding is significant because it (1) provides an estimate of the margin to failure of the cladding during nominal storage operation and it (2) establishes the initial state of the fuel for post-storage transportation. Because there are significant uncertainties associated with the storage conditions, hydride precipitate formation, and the beginning of storage (BOS) condition of the UNF, this will also allow for the development of a rigorous capability to evaluate the relative sensitivities of the uncertainties and can help to guide the experimental and analysis efforts of the UFD Campaign. This document is focused on specifying the problem that will be solved with AMPFuel. An associated report, documents the specifics of the constitutive model that will be developed and implemented in AMPFuel to account for the presence and predict the generation of the hydride precipitates. This report satisfies the deliverable for the DOE Office of Nuclear Energy, Advanced Modeling and Simulation Office, milestone M3MS-12OR0605083, 'Definition of Problem Specification,' which defines the problem to be solved that will satisfy milestone M2MS-12OR0605081, 'Demonstration of the Advanced Multi-Physics (AMP) Nuclear Fuel Performance code for modeling UFD.' This document should provide sufficient detail to model a high burnup pressurized water reactor (PWR) fuel rod to provide an estimate of the end of storage (EOS) mechanical state of the cladding. The fuel rod and irradiation history are based on seven cycles of irradiation in the CP and L H.B. Robinson nuclear reactor, which achieved a discharge burnup of 66.682 MWd/kgU. The fuel has been experimentally examined for storage conditions by Argonne National Laboratory for the NRC. In addition, we have compiled a list of key factors that have been shown to strongly influence the EOS state of the fuel and have identified baseline values and ranges of uncertainties that will be considered. The simulations that will be performed have been described in detail and include the modeling assumptions and boundary conditions.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2018

A novel numerical treatment of the near-wall regions in the k – ω class of RANS models

In this study, we discuss a novel approach to modeling the near-wall region in the class of k – ω to models. The proposed methodology obviates the need for ad hoc boundary conditions of to omega on the wall as typically required in the k – ω model. The primary motivation of this work is to provide a formulation equivalent to the standard k – ω to and k – ω to SST models, but which at the same time overcomes their limitations in the context of their implementation in high-order methods. This is achieved by subtracting the asymptotically known singular behavior of omega at walls. Imposing a grid-dependent value of omega at walls in high-order codes is not straightforward as is demonstrated below and it causes instability as well as accuracy issues. The mathematical formulation of the two novel approaches, termed as the "regularized k – ω model" and the "regularized k – ω OJ SST model", is discussed in detail. A consistency and verification study for these two approaches is performed by proving that the regularized models recover the results of the standard models in various canonical problems, such as turbulent channel and pipe flows, and a systematic investigation of convergence, using both p- (polynomial order) as well as h- (grid) refinement is reported. Furthermore, comparisons highlighting the performance of the proposed methods in more complex configurations such as flow over a backward facing step and the turbulent mixing of fluid streams of different temperatures in a T-junction are also presented.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2017

GeneratorSE: A Sizing Tool for Variable-Speed Wind Turbine Generators

This report documents a set of analytical models employed by the optimization algorithms within the GeneratorSE framework. The initial values and boundary conditions employed for the generation of the various designs and initial estimates for basic design dimensions, masses, and efficiency for the four different models of generators are presented and compared with empirical data collected from previous studies and some existing commercial turbines. These models include designs applicable for variable-speed, high-torque application featuring direct-drive synchronous generators and low-torque application featuring induction generators. In all of the four models presented, the main focus of optimization is electromagnetic design with the exception of permanent-magnet and wire-wound synchronous generators, wherein the structural design is also optimized. Thermal design is accommodated in GeneratorSE as a secondary attribute by limiting the winding current densities to acceptable limits. A preliminary validation of electromagnetic design was carried out by comparing the optimized magnetic loading against those predicted by numerical simulation in FEMM4.2, a finite-element software for analyzing electromagnetic and thermal physics problems for electrical machines. For direct-drive synchronous generators, the analytical models for the structural design are validated by static structural analysis in ANSYS.

17 WIND ENERGY↗

DOE OSTI2015

THE INFLUENCE OF SPATIAL RESOLUTION ON NONLINEAR FORCE-FREE MODELING

The nonlinear force-free field (NLFFF) model is often used to describe the solar coronal magnetic field, however a series of earlier studies revealed difficulties in the numerical solution of the model in application to photospheric boundary data. We investigate the sensitivity of the modeling to the spatial resolution of the boundary data, by applying multiple codes that numerically solve the NLFFF model to a sequence of vector magnetogram data at different resolutions, prepared from a single Hinode/Solar Optical Telescope Spectro-Polarimeter scan of NOAA Active Region 10978 on 2007 December 13. We analyze the resulting energies and relative magnetic helicities, employ a Helmholtz decomposition to characterize divergence errors, and quantify changes made by the codes to the vector magnetogram boundary data in order to be compatible with the force-free model. This study shows that NLFFF modeling results depend quantitatively on the spatial resolution of the input boundary data, and that using more highly resolved boundary data yields more self-consistent results. The free energies of the resulting solutions generally trend higher with increasing resolution, while relative magnetic helicity values vary significantly between resolutions for all methods. All methods require changing the horizontal components, and for some methods also the vertical components, of the vector magnetogram boundary field in excess of nominal uncertainties in the data. The solutions produced by the various methods are significantly different at each resolution level. We continue to recommend verifying agreement between the modeled field lines and corresponding coronal loop images before any NLFFF model is used in a scientific setting.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

Deep Learning Approaches to Surrogates for Solving the Diffusion Equation for Mechanistic Real-World Simulations

In many mechanistic medical, biological, physical, and engineered spatiotemporal dynamic models the numerical solution of partial differential equations (PDEs), especially for diffusion, fluid flow and mechanical relaxation, can make simulations impractically slow. Biological models of tissues and organs often require the simultaneous calculation of the spatial variation of concentration of dozens of diffusing chemical species. One clinical example where rapid calculation of a diffusing field is of use is the estimation of oxygen gradients in the retina, based on imaging of the retinal vasculature, to guide surgical interventions in diabetic retinopathy. Furthermore, the ability to predict blood perfusion and oxygenation may one day guide clinical interventions in diverse settings, i.e., from stent placement in treating heart disease to BOLD fMRI interpretation in evaluating cognitive function (Xie et al., 2019; Lee et al., 2020). Since the quasi-steady-state solutions required for fast-diffusing chemical species like oxygen are particularly computationally costly, we consider the use of a neural network to provide an approximate solution to the steady-state diffusion equation. Machine learning surrogates, neural networks trained to provide approximate solutions to such complicated numerical problems, can often provide speed-ups of several orders of magnitude compared to direct calculation. Surrogates of PDEs could enable use of larger and more detailed models than are possible with direct calculation and can make including such simulations in real-time or near-real time workflows practical. Creating a surrogate requires running the direct calculation tens of thousands of times to generate training data and then training the neural network, both of which are computationally expensive. Often the practical applications of such models require thousands to millions of replica simulations, for example for parameter identification and uncertainty quantification, each of which gains speed from surrogate use and rapidly recovers the up-front costs of surrogate generation. We use a Convolutional Neural Network to approximate the stationary solution to the diffusion equation in the case of two equal-diameter, circular, constant-value sources located at random positions in a two-dimensional square domain with absorbing boundary conditions. Such a configuration caricatures the chemical concentration field of a fast-diffusing species like oxygen in a tissue with two parallel blood vessels in a cross section perpendicular to the two blood vessels. To improve convergence during training, we apply a training approach that uses roll-back to reject stochastic changes to the network that increase the loss function. The trained neural network approximation is about 1000 times faster than the direct calculation for individual replicas. Because different applications will have different criteria for acceptable approximation accuracy, we discuss a variety of loss functions and accuracy estimators that can help select the best network for a particular application. We briefly discuss some of the issues we encountered with overfitting, mismapping of the field values and the geometrical conditions that lead to large absolute and relative errors in the approximate solution.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2015

Blockage of domain growth by nanoscale heterogeneities in a relaxor ferroelectric Sr{sub 0.61}Ba{sub 0.39}Nb{sub 2}O{sub 6}

The growth of localized subsurface domains in a relaxor ferroelectric Sr{sub 0.61}Ba{sub 0.39}Nb{sub 2}O{sub 6} is studied using the technique of piezoresponse force microscopy (PFM). Ferroelectric domains are created by applying moderate voltages of 10–50 V to the conductive tip of a scanning force microscope brought into contact with a nonpolar face of a Sr{sub 0.61}Ba{sub 0.39}Nb{sub 2}O{sub 6} crystal. PFM images of written domains are acquired and analyzed quantitatively to determine the domain length along the polar axis and its width in the transverse direction. The dependences of domain sizes on the applied voltage, pulse duration, and the time passed after completion of the voltage pulse are reported and analyzed theoretically. It is shown that the observed kinetics of domain growth can be explained by the creep of domain boundaries occurring in the presence of random electric fields inherent in Sr{sub 0.61}Ba{sub 0.39}Nb{sub 2}O{sub 6}. The comparison of measured domain sizes with their equilibrium values calculated with the aid of the thermodynamic theory demonstrates that the growth of subsurface domains in Sr{sub 0.61}Ba{sub 0.39}Nb{sub 2}O{sub 6} is blocked by nanoscale heterogeneities characteristic of this relaxor ferroelectric. These results may have important implications for the development of nonlinear optical devices based on nanoheterogeneous ferroelectrics.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2017

Lithium Depletion in Solar-like Stars: Effect of Overshooting Based on Realistic Multi-dimensional Simulations

We study lithium depletion in low-mass and solar-like stars as a function of time, using a new diffusion coefficient describing extra-mixing taking place at the bottom of a convective envelope. This new form is motivated by multi-dimensional fully compressible, time-implicit hydrodynamic simulations performed with the MUSIC code. Intermittent convective mixing at the convective boundary in a star can be modeled using extreme value theory, a statistical analysis frequently used for finance, meteorology, and environmental science. In this Letter, we implement this statistical diffusion coefficient in a one-dimensional stellar evolution code, using parameters calibrated from multi-dimensional hydrodynamic simulations of a young low-mass star. We propose a new scenario that can explain observations of the surface abundance of lithium in the Sun and in clusters covering a wide range of ages, from ∼50 Myr to ∼4 Gyr. Because it relies on our physical model of convective penetration, this scenario has a limited number of assumptions. It can explain the observed trend between rotation and depletion, based on a single additional assumption, namely, that rotation affects the mixing efficiency at the convective boundary. We suggest the existence of a threshold in stellar rotation rate above which rotation strongly prevents the vertical penetration of plumes and below which rotation has small effects. In addition to providing a possible explanation for the long-standing problem of lithium depletion in pre-main-sequence and main-sequence stars, the strength of our scenario is that its basic assumptions can be tested by future hydrodynamic simulations.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2018

Theoretical Analysis of the Entrainment–Mixing Process at Cloud Boundaries. Part I: Droplet Size Distributions and Humidity within the Interface Zone

Abstract The problem of a complex entrainment–mixing process is analyzed by solving a diffusion–evaporation equation for an open region in the vicinity of the cloud–dry air interface. Upon normalization the problem is reduced to a one-parametric one, the governing parameter being the potential evaporation parameter R proportional to the ratio of saturation deficit in the dry air to the available liquid water content in the cloud air. As distinct from previous multiple studies analyzing mixing within closed adiabatic volumes, we consider a principally nonstationary problem that never leads to a homogeneous equilibrium state. It is shown that at R < −1 the cloud edge shifts toward the cloud; that is, the cloud dissipates due to mixing with dry air, and the cloud volume decreases. If R > −1, the cloud edge shifts outside; that is, the mixing leads to an increase in the cloud volume. The time evolution of droplet size distribution and its moments, as well as the relative humidity within the expanding cloud–dry air interface, are calculated and analyzed. It is shown that the values of the mean volume radii rapidly decrease within the interface zone in the direction away from the cloud, indicating significant changes in the cloud edge microstructure. Scattering diagrams plotted for the cloud edge agree well with high-frequency in situ measurements, corroborating the reliability of the proposed approach. It is shown that the humidity front moves toward dry air faster than the front of liquid water content. As a result, the mixing leads to formation of a humid air shell around the cloud. The widths of the interface zone and humid shell are evaluated.

Pinsky, Mark↗

DOE OSTI2012

Chord length sampling method for analyzing VHTR unit cells in continuous energy simulations

The chord length sampling method (CLS) is studied in the continuous energy simulations by applying it to analyzing two types of Very High Temperature Gas-cooled Reactor (VHTR) unit cells: the fuel compact cell in the prismatic type VHTR and the fuel pebble cell in the pebble-bed type VHTR. Infinite multiplication factors of the unit cells are calculated by the CLS and compared to the benchmark simulations at different volume packing fractions from 5% to 30%. It is shown that the accuracy of the CLS is affected by the boundary effect, which is induced by the CLS procedure itself and results in a reduction in the total volume packing fraction of the fuel particles. To mitigate the boundary effect, three correction schemes based on the research of 1) Murata et al. 2) Ji and Martin 3) Griesheimer et al. are used to improve the accuracy by applying a corrected value of the volume packing fraction to the CLS. These corrected values are calculated based on 1) a simple linear relationship, 2) an iterative self-consistent simulation correction method, and 3) a theoretically derived non-linear relationship, respectively. The CLS simulation using the corrected volume packing fraction shows excellent improvements in the infinite multiplication factors for the VHTR unit cells. Ji and Martin's self-consistent correction method shows the best improvement. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2015

Simplified predictive models for CO 2 sequestration performance assessment

CO2 sequestration in deep saline formations is increasingly being considered as a viable strategy for the mitigation of greenhouse gas emissions from anthropogenic sources. In this context, detailed numerical simulation based models are routinely used to understand key processes and parameters affecting pressure propagation and buoyant plume migration following CO2 injection into the subsurface. As these models are data and computation intensive, the development of computationally-efficient alternatives to conventional numerical simulators has become an active area of research. Such simplified models can be valuable assets during preliminary CO2 injection project screening, serve as a key element of probabilistic system assessment modeling tools, and assist regulators in quickly evaluating geological storage projects. We present three strategies for the development and validation of simplified modeling approaches for CO2 sequestration in deep saline formations: (1) simplified physics-based modeling, (2) statisticallearning based modeling, and (3) reduced-order method based modeling. In the first category, a set of full-physics compositional simulations is used to develop correlations for dimensionless injectivity as a function of the slope of the CO2 fractional-flow curve, variance of layer permeability values, and the nature of vertical permeability arrangement. The same variables, along with a modified gravity number, can be used to develop a correlation for the total storage efficiency within the CO2 plume footprint. Furthermore, the dimensionless average pressure buildup after the onset of boundary effects can be correlated to dimensionless time, CO2 plume footprint, and storativity contrast between the reservoir and caprock. In the second category, statistical “proxy models” are developed using the simulation domain described previously with two approaches: (a) classical Box-Behnken experimental design with a quadratic response surface, and (b) maximin Latin Hypercube sampling (LHS) based design with a multidimensional kriging metamodel fit. For roughly the same number of simulations, the LHS-based metamodel yields a more robust predictive model, as verified by a k-fold cross-validation approach (with data split into training and test sets) as well by validation with an independent dataset. In the third category, a reduced-order modeling procedure is utilized that combines proper orthogonal decomposition (POD) for reducing problem dimensionality with trajectory-piecewise linearization (TPWL) in order to represent system response at new control settings from a limited number of training runs. Significant savings in computational time are observed with reasonable accuracy from the PODTPWL reduced-order model for both vertical and horizontal well problems – which could be important in the context of history matching, uncertainty quantification and optimization problems. The simplified physics and statistical learning based models are also validated using an uncertainty analysis framework. Reference cumulative distribution functions of key model outcomes (i.e., plume radius and reservoir pressure buildup) generated using a 97-run full-physics simulation are successfully validated against the CDF from 10,000 sample probabilistic simulations using the simplified models. The main contribution of this research project is the development and validation of a portfolio of simplified modeling approaches that will enable rapid feasibility and risk assessment for CO2 sequestration in deep saline formations.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2011

Progress on a New Integrated 3-D UCG Simulator and its Initial Application

A comprehensive simulator is being developed for underground coal gasification (UCG), with the capability to support site selection, design, hazard analyses, operations, and monitoring (Nitao et al., 2010). UCG is computationally challenging because it involves tightly-coupled multi-physical/chemical processes, with vastly different timescales. This new capability will predict cavity growth, product gas composition and rate, and the interaction with the host environment, accounting for site characteristics, injection gas composition and rate, and associated water-well extraction rates. Progress on the new simulator includes completion and system integration of a wall model, a rock spalling model, a cavity boundary tracking model, a one-dimensional cavity gas reactive transport model, a rudimentary rubble heat, mass, and reaction model, and coupling with a pre-existing hydrology simulator. An existing geomechanical simulator was enhanced to model cavity collapse and overburden subsidence. A commercial computational fluid dynamics (CFD) code is being evaluated to model cavity gas flow and combustion in two and three dimensions. Although the simulator is midway in its development, it was applied to modeling the Hoe Creek III field test (Stephens, 1981) conducted in the 1970s, in order to evaluate and demonstrate the simulator's basic capabilities, gain experience, and guide future development. Furthermore, it is consistent with our philosophy of incremental, spiral software development, which helps in identifying and resolving potential problems early in the process. The simulation accounts for two coal seams, two injection points, and air and oxygen phases. Approximate extent and shape of cavity growth showed reasonable agreement with interpreted field data. Product gas composition and carbon consumed could not be simultaneously matched for a given set of parameter values due to the rudimentary rubble model currently used, although they can be matched using separate parameter sets. This result is not surprising and confirms plans for a more sophisticated rubble model as our next step, as well as adding geomechanical collapse modeling and higher accuracy cavity gas reactive transport models. The results are very encouraging and demonstrate that our approach is sound.

01 COAL, LIGNITE, AND PEAT↗

DOE OSTI2013

DIRECT NUMERICAL SIMULATIONS OF REFLECTION-DRIVEN, REDUCED MAGNETOHYDRODYNAMIC TURBULENCE FROM THE SUN TO THE ALFVÉN CRITICAL POINT

We present direct numerical simulations of inhomogeneous reduced magnetohydrodynamic (RMHD) turbulence between the Sun and the Alfvén critical point. These are the first such simulations that take into account the solar-wind outflow velocity and the radial inhomogeneity of the background solar wind without approximating the nonlinear terms in the governing equations. RMHD turbulence is driven by outward-propagating Alfvén waves (z {sup +} fluctuations) launched from the Sun, which undergo partial non-WKB reflection to produce sunward-propagating Alfvén waves (z {sup –} fluctuations). We present 10 simulations with different values of the correlation time τ{sub c{sub sun}{sup +}} and perpendicular correlation length L{sub ☉} of outward-propagating Alfvén waves at the coronal base. We find that between 15% and 33% of the z {sup +} energy launched into the corona dissipates between the coronal base and Alfvén critical point. Between 33% and 40% of this input energy goes into work on the solar-wind outflow, and between 22% and 36% escapes as z {sup +} fluctuations through the simulation boundary at r = r{sub A}. The z {sup ±} power spectra scale like k{sub perpendicular}{sup -α{sup ±}}, where k is the wavenumber in the plane perpendicular to B{sub 0}. In our simulation with the smallest value of τ{sub c{sub sun}{sup +}} (∼2 minutes) and largest value of L{sub ☉} (2 × 10{sup 4} km), we find that α{sup +} decreases approximately linearly with increasing ln (r), reaching a value of 1.3 at r = 11.1 R{sub ☉}. Our simulations with larger values of τ{sub c{sub sun}{sup +}} exhibit alignment between the contours of constant φ{sup +}, φ{sup –}, Ω{sub 0}{sup +}, and Ω{sub 0}{sup -}, where φ{sup ±} are the Elsässer potentials and Ω{sub 0}{sup ±} are the outer-scale parallel Elsässer vorticities.

79 ASTRONOMY AND ASTROPHYSICS↗