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DOE OSTI2025

National Modeling of Geothermal District Energy Systems with Ambient-Temperature Loops Using dGeo

Geothermal district energy systems (DES) with ambient-temperature loops, also known as thermal energy networks, are one option for decarbonizing space heating and cooling loads. Geothermal fifth-generation DES include an "ambient" temperature thermal loop that connects heat pumps at each building with thermal balancing sources such as geothermal borehole fields. Heating and cooling are provided via a water-source heat pump at each end-user. This project seeks to analyze the nationwide potential for ambient-temperature loop districts by creating a new module within the Distributed Geothermal Market Demand Model (dGeo). dGeo is an agent-based modeling tool for distributed geothermal resources; it can investigate potential on a nationwide or statewide scale using geospatial data for all 50 states and thermal demands for existing buildings. This process allows for high-level estimates of technical and economic potential for ambient-temperature loop districts across the United States. A lookup table was created using GHEDesigner to size borehole fields for different thermal loads and ground conditions experienced across the country. A cost and financing structure, along with incentives, were applied. Cost estimates include costs for the distribution network, borehole field installation and operation, and circulation pump operation, while savings are calculated based on energy bills for building owners (agents). This newly developed module can be used for assessing which areas of the country have the highest potential for agent benefits from ambient-temperature loop installation and assess the impact of future cost and price scenarios. Initial results for statewide analysis (for Vermont) and nationwide (for United States) are provided. Future work includes expanding the module to consider mixed residential and commercial districts as well as evaluating multiple cost scenarios.

ambient-temperature loop↗

DOE OSTI2024

National Modeling of Geothermal District Energy Systems with Ambient-Temperature Loops Using dGeo: Preprint

Geothermal district energy systems (DES) with ambient-temperature loops, also known as thermal energy networks, are one option for decarbonizing space heating and cooling loads. Geothermal fifth-generation DES include an "ambient" temperature thermal loop that connects heat pumps at each building with thermal balancing sources such as geothermal borehole fields. Heating and cooling are provided via a water-source heat pump at each end-user. This project seeks to analyze the nationwide potential for ambient-temperature loop districts by creating a new module within the Distributed Geothermal Market Demand Model (dGeo). dGeo is an agent-based modeling tool for distributed geothermal resources; it can investigate potential on a nationwide or statewide scale using geospatial data for all 50 states and thermal demands for existing buildings. This process allows for high-level estimates of technical and economic potential for ambient-temperature loop districts across the United States. Using GHEDesigner, a lookup table was created to size borehole fields for different thermal loads and ground conditions experienced across the country. A cost and financing structure, along with incentives, were applied. Cost estimates include costs for the distribution network, borehole field installation and operation, and circulation pump operation, while savings are calculated based on agent energy bills. This newly developed module can be used for assessing which areas of the country have the highest potential for agent benefits from ambient-temperature loop installation and assess the impact of different costing and pricing future scenarios. While the code is still under development and nationwide simulations are ongoing, initial results for two states are provided. Future work includes expanding the module to consider mixed residential and commercial districts and considering multiple costing scenarios.

ambient temperature loop↗

DOE OSTI2021

Optimal Energy Scheduling and Sensitivity Analysis for Integrated Power-Water-Heat Systems

The conventionally independent power, water, and heating networks are becoming more tightly connected, which motivates their joint optimal energy scheduling to improve the overall efficiency of an integrated energy system. However, such a joint optimization is known as a challenging problem with complex network constraints and couplings of electric, hydraulic, and thermal models that are nonlinear and nonconvex. We formulate an optimal power-water-heat flow (OPWHF) problem and develop a computationally efficient heuristic to solve it. The proposed heuristic decomposes OPWHF into subproblems, which are iteratively solved via convex relaxation and convex-concave procedure. Simulation results validate that the proposed framework can improve operational flexibility and social welfare of the integrated system, wherein the water and heating networks respond as virtual energy storage to time-varying energy prices and solar photovoltaic generation. Moreover, we perform sensitivity analysis to compare two modes of heating network control: by flow rate and by temperature. Our results reveal that the latter is more effective for heating networks with a wider space of pipeline parameters.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2023

Network construction of non-Abelian chiral spin liquids

We use a network of chiral junctions to construct a family of topological chiral spin liquids in two spatial dimensions. The chiral spin liquid phase harbors SU(2) _k k anyons, which stem from the underlying SU(2) _k k WZW models that describe the constituent spin chains of the network. The network exhibits quantized spin and thermal Hall conductances. We illustrate our construction by inspecting the topological properties of the SU(2) _2 2 model. We find that this model has emergent Ising anyons, with spinons acting as vortex excitations that bind Majorana zero modes. We also show that the ground state of this network is threefold degenerate on the torus, asserting its non-Abelian character. Our results shed new light on the stability of non-Abelian topological phases in artificial quantum materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

A hybrid surrogate modeling framework for the Digital Twin of a Fluoride-salt-cooled High-temperature Reactor (FHR)

While nuclear energy is a non-greenhouse-gas emitting energy source, expensive operational costs due to the high-level of safety requirements decreases their competitiveness in the sustainable energy market. Advanced reactor concepts paired with Digital Twins aim to increase the commercialization gains of nuclear energy by reducing operational costs, increasing reactor reliability and enhancing power generation. To support Digital Twin tasks such as real-time autonomous control, proactive maintenance monitoring or optimizing power demand operations, a fast and accurate virtual representation of the Nuclear Power Plant (NPP) is required. The computational cost of high-fidelity, physics-based models are unsuitable for real-time analysis or scalability. Here, in this work, a hybrid surrogate modeling framework is developed fora Fluoride-salt-cooled High-temperature Reactor (FHR) that leverages physics-inspired models for key reactor components and uses data-driven methods for rapid system state space prediction. The Xenon reactivity feedback model is integrated to inform the surrogate model about the reactor core and the homologous pump theory model is the basis for representing pump degradation. Using a detailed, two dimensional thermal hydraulics model to generate data on the FHR, we train a network of Vectorized Autoregressive Moving-Average with eXogenous input (VARMAX) models to predict the remaining state values. The result is a surrogate model that provides a detailed reactor state representation of 41 system states and a pump degradation analysis. The framework is applied to Load Follows profiles, yielding high accuracy and a speedup that is more than 4000x faster compared to the higher- fidelity thermal hydraulics model, enabling real-time operational intelligence and applications in long horizon predictions. While the surrogate model framework is demonstrated for the particular case of FHR, the hybrid physical/data-driven modeling approach including the network of surrogates and the underlying modularity has the potential to be applied to other physical asset systems.

Digital Twins↗

DOE OSTI2024

Greybox Thermal Parameter Identification of Electric Machine Stators

The parameters of electric machine thermal equivalent circuit networks are difficult to predict due to material and manufacturing uncertainties. In this paper, a Greybox system identification approach is used to identify parameters of electric machine stator lumped parameter thermal networks (LPTNs). LPTNs provide a low order, computationally efficient, dynamic model of temperatures at specific locations. Second and third order LPTN model structures are defined as state space equations with stator thermal parameters to be identified. To test the Greybox electric machine stator thermal system identification, five stator motorette prototypes were constructed with controlled variations in slot fill and slot liner thickness. The variation in the motorette thermal parameters and thermal time constants are detected using the Greybox identification. Special attention is given to the impact of sampling rate and Greybox data record length on parameter estimation accuracy.

33 ADVANCED PROPULSION SYSTEMS↗

DOE OSTI2026

Comparative Analysis of Model Predictive Control and MPC-Informed Rule-Based Control for Thermal Storage Operation in Ultra-Low Temperature 4th Generation District Heating Networks

The integration of thermal storage and heat pumps in district heating networks (DHNs) can significantly enhance operational flexibility and energy efficiency; however, the practical deployment of advanced control strategies is often hindered by forecasting requirements and computational complexity. This study presents a comparative analysis of thermal storage control strategies in an ultra-low-temperature fourth-generation DHN, focusing on the development of a simplified rule-based control (RBC) explicitly informed by Model Predictive Control (MPC) behavior. The proposed methodology systematically analyzes the charging and discharging decisions of an MPC-controlled system under ideal forecasting conditions and extracts recurrent control patterns as a function of key system variables, including outdoor temperature, thermal demand, and electricity price. These patterns are translated into a set of structured time- and condition-based rules, resulting in an MPC-informed RBC that embeds predictive insights while preserving implementation simplicity and operational transparency. The approach is validated on a realistic mixed-use urban district in Denver, Colorado, USA, equipped with a centralized air-source heat pump, distributed water-to-water heat pumps, and a central thermal storage unit. Results show that the tuned RBC attains approximately 96% of ideal MPC economic performance (-27% of costs), preserves values of technical and environmental indicators (reduction only of 2-3%), and substantially reduces complexity. Sensitivity analyses further demonstrate the robustness of the RBC under varying operational conditions (i.e., ambient temperature, electricity price). Overall, the study demonstrates that MPC-informed rule-based control represents an effective trade-off between control performance and real-world applicability, enabling the integration of additional system components while maintaining simplicity, robustness, and ease of implementation.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2024

Stanford Thermal Earth Model for the Conterminous United States

Provided here are various forms of the Stanford Thermal Earth Model, as well as the data and methods used for its creation. The predictions produced by this model were visualized in two-dimensional spatial maps across the modeled depths (0-7 km) for the conterminous United States. The thermal earth model is made available as an application programming interface (API) and as feature layers on ArcGIS, which are both provided via links below. A data-driven spatial interpolation algorithm based on physics-informed graph neural networks was used to develop these national temperature-at-depth maps. The model satisfied the three-dimensional heat conduction law by predicting subsurface temperature, surface heat flow, and rock thermal conductivity. Many physical quantities, including bottomhole temperature, depth, geographic coordinates, elevation, sediment thickness, magnetic anomaly, gravity anomaly, gamma-ray flux of radioactive elements, seismicity, and electric conductivity were used as model inputs. Surface heat flow, temperature, and thermal conductivity predictions were constructed for depths of 0-7 km at an interval of 1 km with spatial resolution of 18 km2 per grid cell. The model showed superior temperature, surface heat flow and thermal conductivity mean absolute errors of 4.8C, 8.1 mW/m2 and 0.07 W/(C-m), respectively..

15 GEOTHERMAL ENERGY↗

DOE OSTI2024

THM: the MOOSE thermal hydraulics module

The MOOSE Thermal Hydraulics Module (THM) is designed to facilitate the development of thermal hydraulic system models. It provides the capability to assemble networks of coupled components such as pipes, junctions, valves, turbomachinery, and heat exchangers. Its library of components supports a single-phase, compressible flow model based on a variable-area formulation of the Euler equations of gas dynamics and discretized using a finite volume scheme. THM offers a flexible system for specifying closures such as friction factors or heat transfer coefficients, allowing the user to choose from built-in correlations or define their own in the input file. A control logic system can be used to control input parameters, necessary for implementing transient scenarios and mirroring real control systems in thermal hydraulic systems. THM can be coupled with other MOOSE-based applications for multiphysics calculations. This talk will give an introduction to the capabilities of THM and provide some examples of its usage and validation.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

MOOSE Thermal-Hydraulics Module - MOOSE workshop

The MOOSE Thermal Hydraulics Module (THM) is designed to facilitate the development of thermal hydraulic system models. It provides the capability to assemble networks of coupled components such as pipes, junctions, valves, turbomachinery, and heat exchangers. Its library of components supports a single-phase, compressible flow model based on a variable-area formulation of the Euler equations of gas dynamics and discretized using a finite volume scheme. THM offers a flexible system for specifying closures such as friction factors or heat transfer coefficients, allowing the user to choose from built-in correlations or define their own in the input file. A control logic system can be used to control input parameters, necessary for implementing transient scenarios and mirroring real control systems in thermal hydraulic systems. THM can be coupled with other MOOSE-based applications for multiphysics calculations. This training will give an introduction to the capabilities of THM and provide some examples of its usage and validation.

97 - MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Temporal Forecasting of Distributed Temperature Sensing in a Thermal Hydraulic System With Machine Learning and Statistical Models

We benchmark performance of long-short term memory (LSTM) network machine learning model and autoregressive integrated moving average (ARIMA) statistical model in temporal forecasting of distributed temperature sensing (DTS). Data in this study consists of fluid temperature transient measured with two co-located Rayleigh scattering fiber optic sensors (FOS) in a forced convection mixing zone of a thermal tee. We treat each gauge of a FOS as an independent temperature sensor. We first study prediction of DTS time series using Vanilla LSTM and ARIMA models trained on prior history of the same FOS that is used for testing. The results yield maximum absolute percentage error (MaxAPE) and root mean squared percentage error (RMSPE) of 1.58% and 0.06% for ARIMA, and 3.14% and 0.44% for LSTM, respectively. Next, we investigate zero-shot forecasting (ZSF) with LSTM and ARIMA trained on history of the co-located FOS only, which is advantageous when limited training data is available. The ZSF MaxAPE and RMSPE values for ARIMA are comparable to those of the Vanilla use case, while the error values for LSTM increase. We show that in ZSF, performance of LSTM network can be improved by training on most correlated gauges between the two FOS, which are identified by calculating the Pearson correlation coefficient. The improved ZSF MaxAPE and RMSPE for LSTM are 4.4% and 0.33%, respectively. Performance of ZSF LSTM can be further enhanced through transfer learning (TL), where LSTM is re-trained on a subset of the FOS that is the target of forecasting. We show that LSTM pre-trained on correlated dataset and re-trained on 30% of testing target dataset achieves MaxAPE and RMSPE values of 2.32% and 0.28%, respectively.

ARIMA↗

DOE OSTI2026

Seamlessly joining length scales: From atomistic thermal graphs to anisotropic continuum conductivity

Thermal transport in complex solids is governed by local structure, defects, and anisotropy, yet most continuum models still rely on oversimplified and homogenized conductivities. Here, we bridge atomistic and continuum descriptions by building finite element (FE) models directly from the site-projected thermal conductivity (SPTC), an atomic-level decomposition of the Green–Kubo thermal conductivity. We introduce a toolkit, the “Simulator Collection for Atomic-to-Continuum Scales (SCACS)”, which uses a graph neural network to predict SPTC on large atomic structures, coarse-grains these fields into anisotropic conductivity tensors, and embeds them into the heat-flow FE equation with a customized, anisotropy-aware adaptive mesh refinement scheme. Applied to silicon nanostructures, the resulting FE models act as representative volume elements, reproduce bulk conductivities, and capture interfacial and defect-driven anisotropy while maintaining thermodynamic consistency. Additionally, SCACS predicts experimental conductance trends and fields. This work demonstrates a general route for transferring atomistic transport information into device-scale thermal simulations with physics-based approximations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

Transient Coupled Chemical-Thermal-Fluid Field Simulation for Sealed Aluminum-clad Spent Nuclear Fuel Storage Canister

As the first step toward developing three-dimensional (3D) multi-physics computational fluid dynamics (CFD) model for unsealed and vented canister storage system, a 3D CFD model coupled with bulk gas radiolysis reactions was developed first for sealed DOE standard canisters filled with inert gas and trace amount of air and water. The workflow for constructing canister-scale 3D CFD models and coupling with gas phase radiolysis reactions were established, which can be readily extended to unsealed, vented canister storage system. This interim milestone report documents the theory of the model, workflow to establish radiolysis reaction network, and initial simulations of the evolutions of thermal fields and hydrogen gas concentrations within sealed DOE standard canisters over long period of time. In addition, a mesh refinement test was done to show that increasing the models mesh refinement had negligible impact upon the temperature profiles.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2022

Scale-invariant machine-learning model accelerates the discovery of quaternary chalcogenides with ultralow lattice thermal conductivity

We design an advanced machine-learning (ML) model based on crystal graph convolutional neural network that is insensitive to volumes (i.e., scale) of the input crystal structures to discover novel quaternary chalcogenides, AMM'Q 3 (A/M/M' = alkali, alkaline earth, post-transition metals, lanthanides, and Q = chalcogens). These compounds are shown to possess ultralow lattice thermal conductivity (κ l ), a desired requirement for thermal-barrier coatings and thermoelectrics. Upon screening the thermodynamic stability of ~1 million compounds using the ML model iteratively and performing density-functional theory (DFT) calculations for a small fraction of compounds, we discover 99 compounds that are validated to be stable in DFT. Taking several DFT-stable compounds, we calculate their κ l using Peierls–Boltzmann transport equation, which reveals ultralow κ l (<2 Wm -1 K -1 at room temperature) due to their soft elasticity and strong phonon anharmonicity. Our work demonstrates the high efficiency of scale-invariant ML model in predicting novel compounds and presents experimental-research opportunities with these new compounds.

36 MATERIALS SCIENCE↗

DOE OSTI2023

A thermodynamic model of integrated liquid-to-liquid thermoelectric heat pump systems

Thermoelectric (TE) heat pumps (TEHPs) are advantageous for heating and cooling in various applications because of their modularity and simple design. A TEHP system includes the TE modules with p- and n-type materials bonded to substrates, plus heat exchangers, thermal interfaces to the heat exchangers, and heat transfer fluids. Although modeling an individual TE module has been extensively studied, limited studies have reported performance at the larger system-level. Furthermore, no prior study has addressed the impact of temperature-dependent TE material properties (e.g., electric resistivity, thermal conductivity, and Seebeck coefficient) on overall heat-pump-system-level performance. Here, this work presents a mathematical model for TEHP system performance based on Goldsmid's approach for TE material performance, “effective” TE material properties, Gnielinski's correlation for convective heat transfer, and thermal balance theory for a heat exchange network. This combined approach provides an accurate model of the liquid-to-liquid TEHP system. Three different approaches—one empirical, one based on the manufacturer's specifications, and one drawn from the literature—were then used to determine values for TE material properties. The first two methods treated properties as constants, while the last approach treated properties as surface-temperature-based functions. Finally, experimental TEHP data was used to validate the models, all with relative absolute deviations of approximately 10% when predicting heating capacity and 10%–25% when forecasting cooling capacity up to a 30 K surface temperature lift. The results demonstrated that, at the TEHP system level, the TE material properties could be treated as constants, avoiding solver iterations and reducing the performance uncertainty by up to 95%.

42 ENGINEERING↗

DOE OSTI2024

An Efficient Annual-Performance Model of a Geothermal Network for Improved System Design, Operation, and Control: Preprint

Geothermal district energy systems (DES), and specifically geothermal networks, provide a viable solution for decarbonizing residential and commercial heating and cooling loads. District energy systems of all kinds enable a thermal resource with a relatively high capital cost (such as a geothermal borehole field) to be shared among a large number of users. While district heating and cooling has been studied for many years, geothermal networks, fifth generation DES that utilize water-source heat pumps and an ambient temperature loop to meet heating and cooling loads, have not been implemented extensively and thus require additional technical and economic optimization to obtain maximum benefits. This paper presents a newly developed reduced-order model that captures the flow of energy within the network, including the commercial and residential users' electrical usage, at an hourly rate over a year. The model includes building loads, heat pumps, borehole fields, and auxiliary heat/cool input, all connected with an ambient-temperature thermal loop model. In the model, operational control is possible for the borehole fields, circulation pump, and auxiliary system. For a given system, the model can output the complete state parameters for each component, the thermal loop, and the collective system, such as flow rate over time, average thermal loop temperature over time, and total electricity usage. The model can also be used to optimize the system control for maximizing system efficiency or minimizing system operational cost. For example, one initial assessment of the borehole controller for an example system showed that a controller with on/off operation of the borehole field reduces annual electrical usage by 33%, compared with continuous operation mode. Hence, the model can assist in optimizing a given system's operation to get the most value out of a geothermal network installation. Future work will consider the model's application to a demonstration project, including the model validation against operational data and system operation optimization.

ambient-temperature loop↗

DOE OSTI2022

Machine Learning-Assisted High-Temperature Reservoir Thermal Energy Storage Optimization: Numerical Modeling and Machine Learning Input and Output Files

This data set includes the numerical modeling input files and output files used to synthesize data, and the reduced-order machine learning models trained from the synthesized data for reservoir thermal energy storage site identification. In this study, a machine-learning-assisted computational framework is presented to identify High-Temperature Reservoir Thermal Energy Storage (HT-RTES) site with optimal performance metrics by combining physics-based simulation with stochastic hydrogeologic formation and thermal energy storage operation parameters, artificial neural network regression of the simulation data, and genetic algorithm-enabled multi-objective optimization. A doublet well configuration with a layered (aquitard-aquifer-aquitard) generic reservoir is simulated for cases of continuous operation and seasonal-cycle operation scenarios. Neural network-based surrogate models are developed for the two scenarios and applied to generate the Pareto fronts of the HT-RTES performance for four potential HT-RTES sites. The developed Pareto optimal solutions indicate the performance of HT-RTES is operation-scenario (i.e., fluid cycle) and reservoir-site dependent, and the performance metrics have competing effects for a given site and a given fluid cycle. The developed neural network models can be applied to identify suitable sites for HT-RTES, and the proposed framework sheds light on the design of resilient HT-RTES systems. All the simulations and the neural network model were done by Idaho National Laboratory. A detailed description of the work was reported in publication linked below.

15 GEOTHERMAL ENERGY↗

DOE OSTI2026

Coalition for Community-Supported Affordable Geothermal Energy Systems (C2SAGES)

The C2SAGES project evaluated the feasibility of a community geothermal system for the planned Windy Ridge affordable housing development in Hinesburg, Vermont. Led by GTI Energy with Vermont Gas Systems, LN Consulting, NREL, and Frontier Energy, the work assessed technical design, energy performance, costs, business models, community engagement, maintenance, workforce development, and permitting. The proposed system was designed to serve 100% of the development’s heating, cooling, and domestic hot water loads. Compared with a baseline using air-source heat pumps and natural gas water heating, the geothermal system was estimated to reduce HVAC and domestic hot water energy use by about 45% to 48%, lower operating and maintenance costs, and reduce 30-year life-cycle costs by 37% for Phase 1 and 10% for Phase 2. Technical testing and modeling indicated that the Windy Ridge site is suitable for a community-scale geothermal system. The project also developed borehole field layouts, piping concepts, pump house designs, controls, maintenance plans, and supporting engineering drawings. The business model analysis found that first cost, ownership structure, and customer affordability remain major deployment challenges. Utility-led maintenance and operation were viewed favorably, but traditional utility cost-recovery models may require subsidy or revised financing structures to be practical for affordable housing. Community engagement highlighted the need for clear public education, transparent financing, reliable long-term maintenance, trained technicians, and the potential to pair geothermal systems with weatherization. Overall, the report concludes that community geothermal is technically feasible and offers meaningful energy, emissions, and life-cycle cost benefits, but broader deployment will depend on workable financing models and workforce readiness.

15 GEOTHERMAL ENERGY↗