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DOE OSTI2014

Optimization of global model composed of radial basis functions using the term-ranking approach

A term-ranking method is put forward to optimize the global model composed of radial basis functions to improve the predictability of the model. The effectiveness of the proposed method is examined by numerical simulation and experimental data. Numerical simulations indicate that this method can significantly lengthen the prediction time and decrease the Bayesian information criterion of the model. The application to real voice signal shows that the optimized global model can capture more predictable component in chaos-like voice data and simultaneously reduce the predictable component (periodic pitch) in the residual signal.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Deep quantum circuit simulations of low-energy nuclear states

Numerical simulation is an important method for verifying the quantum circuits used to simulate low-energy nuclear states. However, real-world applications of quantum computing for nuclear theory often generate deep quantum circuits that place demanding memory and processing requirements on conventional simulation methods. Here, we present advances in high-performance numerical simulations of deep quantum circuits to efficiently verify the accuracy of low-energy nuclear physics applications. Our approach employs novel methods for accelerating the numerical simulation including management of simulated mid-circuit measurements to verify projection based state preparation circuits. In this study, we test these methods across a variety of high-performance computing systems and our results show that circuits up to 21 qubits and more than 115,000,000 gates can be efficiently simulated.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2017

A suite of benchmark and challenge problems for enhanced geothermal systems

A diverse suite of numerical simulators is currently being applied to predict or understand the performance of enhanced geothermal systems (EGS). To build confidence and identify critical development needs for these analytical tools, the United States Department of Energy, Geothermal Technologies Office sponsored a Code Comparison Study (GTO-CCS), with participants from universities, industry, and national laboratories. A principal objective for the study was to create a community forum for improvement and verification of numerical simulators for EGS modeling. Teams participating in the study were those representing U.S. national laboratories, universities, and industries, and each team brought unique numerical simulation capabilities to bear on the problems. Two classes of problems were developed during the study, benchmark problems and challenge problems. The benchmark problems were structured to test the ability of the collection of numerical simulators to solve various combinations of coupled thermal, hydrologic, geomechanical, and geochemical processes. This class of problems was strictly defined in terms of properties, driving forces, initial conditions, and boundary conditions. The challenge problems were based on the enhanced geothermal systems research conducted at Fenton Hill, near Los Alamos, New Mexico, between 1974 and 1995. The problems involved two phases of research, stimulation, development, and circulation in two separate reservoirs. The challenge problems had specific questions to be answered via numerical simulation in three topical areas: (1) reservoir creation/stimulation, (2) reactive and passive transport, and (3) thermal recovery. Whereas the benchmark class of problems were designed to test capabilities for modeling coupled processes under strictly specified conditions, the stated objective for the challenge class of problems was to demonstrate what new understanding of the Fenton Hill experiments could be realized via the application of modern numerical simulation tools by recognized expert practitioners. Lastly, we present the suite of benchmark and challenge problems developed for the GTO-CCS, providing problem descriptions and sample solutions.

15 GEOTHERMAL ENERGY↗
DOE OSTI2021

Integrated Heat Exchanger-Phase Change Material Thermal Energy Storage System

The purpose of this study is to experimentally investigate the thermal performance of an innovative thermal energy storage (TES) system that combines the advantages of the phase-change material (PCM)/graphite foam latent heat TES medium developed at Argonne National Laboratory (Argonne) and the internally supported plate-fin (ISPE) cell architecture heat transfer fluid (HTF) flow channels developed at Brayton Energy (Brayton). Several essential tasks were accomplished: (1) Thermal property characterization. Thermal properties of the graphite foam were characterized, providing necessary data for experimental result analysis and numerical simulation. (2) Design and optimization of lab-scale test module. Based on Brayton’s full-scale heat exchanger (HX)-TES system, the experimental test module was designed, optimized, and fabricated. (3) Thermal performance testing and data analysis. Five cycle tests were successfully conducted—including one with approximately 3.5 psig of pressure applied to the diaphragms—to investigate the thermal performance of the experimental test module for charging and discharging. Temperature profiles were generated for each charging test and discharging test as a function of time. The temperature profiles clearly show three TES stages: sensible heat (temperature increase), latent heat (melting), and sensible heat (temperature increase) for the charging process. Similarly, the temperature profiles clearly show three thermal energy release stages: sensible heat (temperature decrease), latent heat (solidification), and sensible heat (temperature decrease). Melting and solidification of the PCM generally occurred in relatively narrow temperature ranges, indicated by the flattened temperature regions in the temperature profiles. These phase changes ranged approximately 3°C for melting and 3.5°C for solidification. The charging and discharging temperature profiles were similar for similar experimental parameter tests whether or not pressure was applied to the diaphragm to eliminate the gap between the HX surface and the TES subsystem. This indicates that the effect of a small gap between the HX surface and the TES subsystem is insignificant for charging and discharging. (4) Comparison of experimental data and simulation results. We compared the experimental data to the numerical simulation results. Numerical simulations were conducted by using the ANSYS FLUENT 2019 R3 commercial computational fluid dynamics software. The predicted phase-change times agreed reasonably well with those from the experimental data. In most cases, the estimated time differences between the relative phase changes were within 16%. The predicted start and end times for the charging process agreed well with those from the experimental data. However, the simulation results showed earlier start and end times than the experimental data for the discharging process. Overall, the experimental data and its comparison with the simulation predictions verified the technical viability of the integrated ISPF HX-PCM/graphite foam latent-heat TES system.

25 ENERGY STORAGE↗
DOE OSTI2014

Comparison of analytic models of instability of rarefied gas flow in a channel

Numerical and analytical results are compared concerning the limit properties of the trajectories, attractors and bifurcations of rarefied gas flows in channels. The cascade of bifurcations obtained in our previous analytical and numerical investigations is simulated numerically for different scattering functions V generalizing the ray-diffuse reflection of gas particles from the surface. The main purpose of numerical simulation by Monte Carlo method is the investigation of the properties of different analytic nonlinear dynamic systems corresponding to rarefied gas flow in a channel. The results are compared as well for the models suggested originally by R. N. Miroshin, as for the approximations considered for the first time or for studied in our subsequent papers. Analytical solutions we obtained earlier for the ray reflection which means only one determined velocity of scattered from the walls gas atoms, generally different from the specular reflection. The nonlinear iterative equation describing a rarefied gas flow in a long channel becomes unstable in some regions of corresponding parameters of V (it means the sensitivity to boundary conditions). The values of the parameters are found from analytical approximations in these regions. Numerical results show that the chaotic behavior of the nonlinear dynamic system corresponds to strange attractors and distinguishes clearly from Maxwellian distribution and from the equilibrium on the whole. In the regions of instability (as the dimension of the attractor increases) the search for a corresponding state requires a lot more computation time and a lot of data (the amount of data required increases exponentially with embedding dimension). Therefore the main complication in the computation is reducing as well the computing time as the amount of data to find a suitably close solution. To reduce the computing time our analytical results are applied. Flow conditions satisfying the requirements to the experiment are indicated where the instability of considered type can be detected. The advantages and the drawbacks of considered approximations are detected and the features of obtained solutions are indicated. The recommendations are given for applying the results in practical applications and in numerical calculations of rarefied gas flows.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Toward predictive and computationally affordable Lagrangian–Eulerian modeling of spray–wall interaction

The work presented in this article focuses on improving the understanding of spray–wall interaction phenomena and the predictivity of computational models for modern internal combustion engine–like conditions. Previous work from the authors highlighted some of the limitations of the currently available spray–wall interaction sub-models, especially those based on experimental observations carried out on single droplet impingement of non-hydrocarbon fluids. Previous experimental observations and direct numerical simulations provided unique qualitative and quantitative details that were leveraged to improve Lagrangian–Eulerian simulations of spray–wall interaction. In this work, Yarin and Weiss’ theory for droplet train impingements, as interpreted by Stanton and Rutland, was implemented in the CONVERGE software. A novel and mathematically rigorous calculation of the impingement frequency for Lagrangian parcels was proposed to replace the zero-droplet-spacing assumption present in the original model and improve the prediction of droplet splash. Preliminary testing and validation of the new formulation against experiments carried out in a constant volume vessel showed encouraging results. The feedback loop between experiments, Lagrangian–Eulerian simulations, and direct numerical simulations also motivated the investigation of the surface roughness model available in the Lagrangian–Eulerian framework. This part of the study pointed out the importance of correctly predicting the interaction between liquid and surrounding gas in the near-wall region. Overall, the results shown indicate that correctly capturing the pre-impingement physics and liquid–gas interaction, together with improving splash predictions, was key for improving the accuracy of Lagrangian–Eulerian computational fluid dynamics simulations of spray–wall impingement.

Torelli, Roberto↗
DOE OSTI2012

Advanced Horizontal Well Recirculation Systems for Geothermal Energy Recovery in Sedimentary Formations

There is increased recognition that geothermal energy resources are more widespread than previously thought, with potential for providing a significant amount of sustainable clean energy worldwide. Recent advances in drilling, completion, and production technology from the oil and gas industry can now be applied to unlock vast new geothermal resources, with some estimates for potential electricity generation from geothermal energy now on the order of 2 million megawatts. Terralog USA, in collaboration with the University of California, Irvine (UCI), are currently investigating advanced design concepts for paired horizontal well recirculation systems, optimally configured for geothermal energy recovery in permeable sedimentary and crystalline formations of varying structure and material properties. This two-year research project, funded by the US Department of Energy, includes combined efforts for: 1) Resource characterization; 2) Small and large scale laboratory investigations; 3) Numerical simulation at both the laboratory and field scale; and 4) Engineering feasibility studies and economic evaluations. The research project is currently in its early stages. This paper summarizes our technical approach and preliminary findings related to potential resources, small-scale laboratory simulation, and supporting numerical simulation efforts.

15 GEOTHERMAL ENERGY↗
DOE OSTI2023

DNS of a Simplified Gas Turbine Premixer: Auto-Ignition and Flame Stabilization

With the increasing need for fuel-flexibility, an understanding of auto-ignition inside gas turbine premixers is crucial. Direct numerical simulation (DNS) is a great tool to reveal the fine grain details of physics inside the premixer and guide the choice of the models to use for less expensive simulations. We present numerical simulations of a simplified and downscaled premixer, with multiple air jets in rich fuel crossflow. The simulations show intense fuel-air mixing and flame-turbulence interaction. We examine flow acceleration by the incoming jets, and the combustion within the device. We observe low-temperature and high-temperature combustion signatures, and compute the flame index to quantify local stabilization modes.

combustion↗
DOE OSTI2019

A Leray regularized ensemble-proper orthogonal decomposition method for parameterized convection-dominated flows

Abstract Partial differential equations (PDEs) are often dependent on input quantities that are uncertain. To quantify this uncertainty PDEs must be solved over a large ensemble of parameters. Even for a single realization this can be a computationally intensive process. In the case of flows governed by the Navier–Stokes equations, an efficient method has been devised for computing an ensemble of solutions. To further reduce the computational cost of this method, an ensemble-proper orthogonal decomposition (POD) method was recently proposed. The main contribution of this work is the introduction of POD spatial filtering for ensemble-POD methods. The POD spatial filter makes possible the construction of the Leray ensemble-POD model, which is a regularized-reduced order model for the numerical simulation of convection-dominated flows of moderate Reynolds number. The Leray ensemble-POD model employs the POD spatial filter to smooth (regularize) the convection term in the Navier–Stokes equations, and diminishes the numerical inaccuracies produced by the ensemble-POD method in the numerical simulation of convection-dominated flows. Specifically, for the numerical simulation of a convection-dominated two-dimensional flow between two offset cylinders, we show that the Leray ensemble-POD method better reflects the dynamics of the benchmark results than the ensemble-POD scheme. The second contribution of this work is a new numerical discretization of the variable viscosity ensemble algorithm in which the average viscosity is replaced with the maximum viscosity. It is shown that this new numerical discretization is significantly more stable than those in current use. Furthermore, error estimates for the novel Leray ensemble-POD algorithm with this new numerical discretization are also proven.

Mathematics↗
DOE OSTI2018

Outcomes from a Collaborative Approach to a Code Comparison Study for Enhanced Geothermal Systems

A code comparison study, supported by the U.S. Department of Energy, Geothermal Technologies Office, has recently been completed whose stated purpose was to test, diagnose differences, and demonstrate the state of modeling capabilities developed at national laboratories and academic institutes within the United States for modeling enhanced geothermal systems. This three-year study comprised two sets of problems; those classified as benchmark problems and those classified as challenge problems. The benchmark problems were structured to test the ability of the collection of numerical simulators to solve various combinations of coupled thermal, hydrologic, geomechanical, and geochemical processes. This class of problems was strictly defined in terms of properties, driving forces, initial conditions, and boundary conditions. Study participants submitted solutions to problems for which their simulation tools were deemed capable or nearly capable. Some participating codes were originally developed for EGS applications whereas some others were designed for different applications but can simulate processes similar to those in EGS. Solution submissions from both were encouraged. In some cases participants made small incremental changes to their numerical simulation codes to address specific elements of the problem, and in other cases participants submitted solutions with existing simulation tools, acknowledging the limitations of the code. The challenge problems were based on the enhanced geothermal systems research conducted in hot dry rock at Fenton Hill, near Los Alamos, New Mexico, between 1974 and 1995, covering two research stimulation, development and circulation phases in two separate reservoirs. Both challenge problems have specific questions to be answered via numerical simulation in three topical areas: 1) reservoir creation/stimulation, 2) reactive and passive transport, and 3) thermal recovery. Whereas the benchmark class of problems were designed to test capabilities for modeling coupled processes under strictly specified conditions, the stated objective for the challenge class of problems was to demonstrate what new understanding of the Fenton Hill experiments could be realized via the application of modern numerical simulation tools by recognized expert practitioners. Critical observations and data from the Fenton Hill experiments were varied and scattered among a number of individual experiments, and numerical simulation solutions were sought that satisfied as many observations at possible. Achieving agreement in multiple experimental observations from Fenton Hill often required participants to critically think about stimulation mechanisms involving natural and hydraulic fractures and re-evaluate their conceptual models and numerical solution approaches. This process has yielded new insights to Fenton Hill reservoirs and direction for future EGS research. The keys to the success of this study were the high quality numerical simulation tools available, the expertise of the developers and practitioners, and the collaborative approach to reporting preliminary results among the study participants. This paper describes results submitted to the challenge problems and the outcomes of a collaborative approach to conducting a code comparison study.

Enhanced Geothermal Systems, numerical simulation,↗
DOE OSTI2017

Regression-based reduced-order models to predict transient thermal output for enhanced geothermal systems

Reduced-order modeling is a promising approach, as many phenomena can be described by a few parameters/mechanisms. An advantage and attractive aspect of a reduced-order model is that it is computational inexpensive to evaluate when compared to running a high-fidelity numerical simulation. A reduced-order model takes couple of seconds to run on a laptop while a high-fidelity simulation may take couple of hours to run on a high-performance computing cluster. The goal of this paper is to assess the utility of regression-based reduced-order models (ROMs) developed from high-fidelity numerical simulations for predicting transient thermal power output for an enhanced geothermal reservoir while explicitly accounting for uncertainties in the subsurface system and site-specific details. Numerical simulations are performed based on equally spaced values in the specified range of model parameters. Key sensitive parameters are then identified from these simulations, which are fracture zone permeability, well/skin factor, bottom hole pressure, and injection flow rate. We found the fracture zone permeability to be the most sensitive parameter. The fracture zone permeability along with time, are used to build regression-based ROMs for the thermal power output. The ROMs are trained and validated using detailed physics-based numerical simulations. Finally, predictions from the ROMs are then compared with field data. We propose three different ROMs with different levels of model parsimony, each describing key and essential features of the power production curves. The coefficients in the proposed regression-based ROMs are developed by minimizing a non-linear least-squares misfit function using the Levenberg–Marquardt algorithm. The misfit function is based on the difference between numerical simulation data and reduced-order model. ROM-1 is constructed based on polynomials up to fourth order. ROM-1 is able to accurately reproduce the power output of numerical simulations for low values of permeabilities and certain features of the field-scale data. ROM-2 is a model with more analytical functions consisting of polynomials up to order eight, exponential functions and smooth approximations of Heaviside functions, and accurately describes the field-data. At higher permeabilities, ROM-2 reproduces numerical results better than ROM-1, however, there is a considerable deviation from numerical results at low fracture zone permeabilities. ROM-3 consists of polynomials up to order ten, and is developed by taking the best aspects of ROM-1 and ROM-2. ROM-1 is relatively parsimonious than ROM-2 and ROM-3, while ROM-2 overfits the data. ROM-3 on the other hand, provides a middle ground for model parsimony. Based on R 2 -values for training, validation, and prediction data sets we found that ROM-3 is better model than ROM-2 and ROM-1. For predicting thermal drawdown in EGS applications, where high fracture zone permeabilities (typically greater than 10 –15 m 2 ) are desired, ROM-2 and ROM-3 outperform ROM-1. As per computational time, all the ROMs are 10 4 times faster when compared to running a high-fidelity numerical simulation. In conclusion, this makes the proposed regression-based ROMs attractive for real-time EGS applications because they are fast and provide reasonably good predictions for thermal power output.

58 GEOSCIENCES↗
DOE OSTI2016

Benchmark Problems of the Geothermal Technologies Office Code Comparison Study

A diverse suite of numerical simulators is currently being applied to predict or understand the performance of enhanced geothermal systems (EGS). To build confidence and identify critical development needs for these analytical tools, the United States Department of Energy, Geothermal Technologies Office has sponsored a Code Comparison Study (GTO-CCS), with participants from universities, industry, and national laboratories. A principal objective for the study was to create a community forum for improvement and verification of numerical simulators for EGS modeling. Teams participating in the study were those representing U.S. national laboratories, universities, and industries, and each team brought unique numerical simulation capabilities to bear on the problems. Two classes of problems were developed during the study, benchmark problems and challenge problems. The benchmark problems were structured to test the ability of the collection of numerical simulators to solve various combinations of coupled thermal, hydrologic, geomechanical, and geochemical processes. This class of problems was strictly defined in terms of properties, driving forces, initial conditions, and boundary conditions. Study participants submitted solutions to problems for which their simulation tools were deemed capable or nearly capable. Some participating codes were originally developed for EGS applications whereas some others were designed for different applications but can simulate processes similar to those in EGS. Solution submissions from both were encouraged. In some cases, participants made small incremental changes to their numerical simulation codes to address specific elements of the problem, and in other cases participants submitted solutions with existing simulation tools, acknowledging the limitations of the code. The challenge problems were based on the enhanced geothermal systems research conducted at Fenton Hill, near Los Alamos, New Mexico, between 1974 and 1995. The problems involved two phases of research, stimulation, development, and circulation in two separate reservoirs. The challenge problems had specific questions to be answered via numerical simulation in three topical areas: 1) reservoir creation/stimulation, 2) reactive and passive transport, and 3) thermal recovery. Whereas the benchmark class of problems were designed to test capabilities for modeling coupled processes under strictly specified conditions, the stated objective for the challenge class of problems was to demonstrate what new understanding of the Fenton Hill experiments could be realized via the application of modern numerical simulation tools by recognized expert practitioners.

15 GEOTHERMAL ENERGY↗
DOE OSTI2012

Study of the core-corona structure formed during the explosion of an aluminum wire in vacuum

The time evolution of the matter parameters and current distribution in the discharge channel formed during a nanosecond explosion of a 25-{mu}m-diameter 12-mm-long aluminum wire was studied in a series of experiments with the following parameters: the discharge voltage was U{sub 0} = 20 kV, the current amplitude was I{sub max} {approx} 8 kA, and the current rise rate was dI/dt {approx} 40 A/ns. Optical shadow and schlieren images of the discharge channel were obtained using the second harmonic of a YAG: Nd{sup +3} laser, and UV images of the discharge channel self-radiation were recorded using a four-frame camera with a microchannel plate. The process of aluminum wire explosion was simulated numerically (including simulations performed from the 'cold start'). The numerical results were compared with the experimental data.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Estimation of the Water Table Position in Unconfined Aquifers with MODFLOW 6

Abstract The numerical estimation of the position of the water table in unconfined aquifers is important for many practical applications. Its determination through observations or analytical methods is restricted to a few cases. Therefore, it is often estimated through numerical simulations, which may be affected by numerical artifacts and/or poor stability. We use MODFLOW to estimate the position of the water table for a seemingly simple example problem and demonstrate difficulties that can be faced when performing this kind of numerical simulation. We explain the causes for the numerical challenges that originate from the properties of the mathematical equations that must be solved. Based on the results of more than 600 steady‐state simulations, we show how the stability of the numerical solution can be affected by the values of physical parameters that define the problem (e.g., recharge rate, anisotropy ratio, and other parameters that control the numerical algorithm such as settings of the linear and nonlinear solution methods). Finally, we comment on some best practices to apply numerical simulations to estimate the water table position.

Geology↗
DOE OSTI2013

Tail-ion transport and Knudsen layer formation in the presence of magnetic fields

Knudsen layer losses of tail fuel ions could reduce significantly the fusion reactivity of highly compressed cylindrical and spherical targets in inertial confinement fusion (ICF). With the class of magnetized ICF targets in mind, the effect of embedded magnetic fields on Knudsen layer formation is investigated for the first time. The modified energy scaling of ion diffusivity in magnetized hot spots is found to suppress the preferential losses of tail-ions perpendicular to the magnetic field lines to a degree that the tail distribution can be at least partially, if not fully, restored. Two simple threshold conditions are identified leading to the restoration of fusion reactivity in magnetized hot spots. A kinetic equation for tail-ion transport in the presence of a magnetic field is derived, and solutions to the equation are obtained numerically in simulations. Numerical results confirm the validity of the threshold conditions for restored reactivity and identify two different asymptotic regimes of the fusion fuel. While Knudsen layer formation is shown to be suppressed entirely in strongly magnetized cylindrical hot spot cavities, uniformly magnetized spherical cavities demonstrate remnant, albeit reduced, levels of tail-ion depletion.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2014

Theoretical and numerical predictions of hypervelocity impact-generated plasma

The hypervelocity impact generated plasmas (HVIGP) in thermodynamic non-equilibrium state were theoretically analyzed, and a physical model was presented to explore the relationship between plasma ionization degree and internal energy of the system by a group of equations including a chemical reaction equilibrium equation, a chemical reaction rate equation, and an energy conservation equation. A series of AUTODYN 3D (a widely used software in dynamic numerical simulations and developed by Century Dynamic Inc.) numerical simulations of the impacts of hypervelocity Al projectile on its targets at different incident angles were performed. The internal energy and the material density obtained from the numerical simulations were then used to calculate the ionization degree and the electron temperature. Based on a self-developed 2D smooth particle hydrodynamic (SPH) code and the theoretical model, the plasmas generated by 6 hypervelocity impacts were directly simulated and their total charges were calculated. The numerical results are in good agreements with the experimental results as well as the empirical formulas, demonstrating that the theoretical model is justified by the AUTODYN 3D and self-developed 2D SPH simulations and applicable to predict HVIGPs. The study is of significance for astrophysical and cosmonautic researches and safety.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Application of an Embedded Fracture and Borehole Modeling Approach to the Understanding of EGS Collab Experiment 1

EGS Collab is a series of meso-scale experiments and associated numerical simulation activities being funded by the United States Department of Energy, Geothermal Technologies Office (GTO) to investigate enhanced geothermal system processes under in-situ stress and slightly elevated temperature conditions. This project is designed to provide scientists and engineers with immediate access to impermeable rock at scales larger than possible in the laboratory, but generally smaller than those for commercial production. Immediate access to rock is provided via the existing drifts of the former Homestake Gold Mine, now operated as the Sanford Underground Research Facility in Lead, South Dakota. The objectives of the EGS Collab project are to develop well controlled fracture networks between injector and producer boreholes using normal and shear stimulation for permeability enhancement. The first experimental site was located off the West Access drift on the 4850 Level (4850 feet below ground surface) in phyllite of the Precambrian Poorman formation, and involved the creation of a fracture network comprising a combination of hydraulic and natural fractures. A second experimental site is now being considered near the battery alcove on the 4100 Level in amphibolite and rhyolite of the Yates Unit. Data generated during these experiments will be compared against predictions of a suite of computer codes specifically designed to solve problems involving coupled thermal, hydrological, geomechanical, and geochemical processes. Comparisons between experimental and numerical simulation results will provide code developers with direction for improvements and verification of process models, build confidence in the suite of available numerical tools, and ultimately identify critical future development needs for the geothermal modeling community. Moreover, conducting thorough comparisons of models, modelling approaches, measurement approaches and measured data, via the EGS Collab project, will serve to identify techniques that are most likely to succeed at the Frontier Observatory for Research in Geothermal Energy (FORGE), the GTO’s flagship EGS research effort. Experiment 1 has comprised a series of successful tests, including a long-term chilled-water circulation test, but the testbed has two atypical EGS elements. Active ventilation in the adjacent drift over a 50-year period cooled the testbed rock mass and hydraulic fracturing intersected monitoring boreholes making them conduits for fluid flow. Numerical simulations executed in support of the design of the EGS Collab Experiment 1, computed a radial temperature distribution and stress gradient orthogonal to the drift axis, resulting in the forecast of an oblong hydraulic fracture geometry, extended in the direction of the drift from the stimulation borehole. This paper describes the numerical simulation of long-term chilled-water circulation test with an embedded fracture and borehole modeling approach. The principal objective of the simulation work is show agreement between experimental observations in terms of production fluid temperatures, monitoring borehole temperatures, injection and production pressures, and tracer recoveries using a single conceptual model for the fracture network, using characterization and monitoring data generally available for EGS. A secondary objective is to improve the numerical simulation result comparisons with additional data available from the broader monitoring equipment within the testbed versus deeper, hotter, and more remote EGS. One complicating factor for comparisons between the numerical simulation results and experimental observations, is the Joule-Thomson heating associated with large pressure drops across the fracture network.

numerical simulation, embedded fractures and boreh↗
DOE OSTI2019

DiaMonD: An Integrated Multifaceted Approach to Mathematics at the Interfaces of Data, Models, and Decisions

The major goal of the project was to invent, analyze, implement, and apply new algorithms to speed up the computational simulation of complex systems in settings in which multiple simulations are needed. The main efforts we undertook are as follows: 1. Develop novel reduced order methods to reduce the costs of simulations, especially in settings (e.g., UQ, inference, optimization and control) for which numerous simulation are needed and also for nonlocal problems (e.g., fractional derivative, anomalous diffusion, nonlocal mechanics) for which lack of sparsity results in more expensive full-order simulation than encountered in partial differential equations settings; rigorous analyses as well as computational tests were carried out, 2. Develop multifidelity methods based on the usage of a variety of models having different fidelities and different costs to accelerate simulations again in settings where numerous simulations are needed or are especially expensive; rigorous analyses as well as computational tests were carried out, 3. Develop ensemble methods to reduced the costs of simulations again in settings where numerous simulations are needed or are especially expensive; rigorous analyses as well as computational tests were carried out, and 4. Analyze a model for Richardson pair dispersion in turbulent flows and develop discretization methods for the efficient and accurate approximations of the solution of the model; rigorous analyses as well as computational tests were carried out.

97 MATHEMATICS AND COMPUTING↗