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17 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Open library of g-functions for 34,321 configurations

Thermal response functions, known as g-functions, are commonly used in ground heat exchanger design tools and whole building energy simulation programs to simulate the ground heat exchanger performance. Calculation of g-functions can be quite computationally time-consuming, particularly as the number of boreholes gets large. However, once the g-function is computed, the actual simulation time can be quite short, particularly if a hybrid time-step (Cullin and Spitler 2011) approach is used. Because of this, pre-computed g-function libraries are commonly used in design tools and building simulation tools. This paper describes development of a new, publicly available library containing g-functions for 34,321 borehole field configurations; for each configuration, gfunctions are provided for 5 depths to allow interpolation between different borehole-to-height ratios. The available configurations include configurations in standard shapes: lines, rectangles, open rectangles, L-shapes, and U-shapes. It also includes new configurations: C-shapes, lopsided-U-shapes, and zoned rectangles, which are rectangular configurations with different interior and perimeter spacing of the boreholes.

Spitler, Jeffery↗
DOE OSTI2022

Development of New g-function Data for Simulating a Novel Shallow Bore Ground Heat Exchanger

Geothermal heat pump (GHP), which is also referred as ground source heat pump, is the most energy-efficient technology for space heating and cooling. However, the application of GHP is hindered by its high initial cost, of which approximately 30% is for the ground heat exchanger (GHE). In recent years, researchers have developed different types of shallow bore ground heat exchangers (SBGHE) intending to reduce the cost of drilling. The ability to predict the thermal response of an SBGHE is critical for sizing SBGHE. While g-functions have been commonly used for predicting the thermal response of conventional vertical bore ground heat exchangers (VBGHE), they cannot be directly used for predicting the performance of SBGHE because they did not account for the impacts of the seasonal variation of the soil temperature along with the depth of an SBGHE. In addition, an SBGHE has a larger thermal mass within the borehole than the VBGHE due to the larger borehole diameter of SBGHE. This study develops new g-function data pairs for a new design of SBGHE, which is named Underground Thermal Battery (UTB). Impacts of the seasonal variation of soil temperature on the thermal response of UTB were accounted for by superposing a time-dependent soil temperature onto the g-functions calculated with a numerical model that assumes constant undisturbed soil temperature. The TOUGH program was used to predict the thermal response of several configurations involving multiple UTBs. The results indicate that the proposed methodology is appropriate to generate g-functions for the UTB, and the g-function value of UTB is much lower than that of VBGHE in the time range of 15 min to 1 year due to the large thermal mass and convection heat transfer within the UTB.

Shi, Liang↗
DOE OSTI2021

G-Function Library for Modeling Vertical Bore Ground Heat Exchanger

This library contains g-functions (thermal response functions) for standard, regularly spaced vertical borehole ground heat exchangers. In total, it contains 34, 321 configurations. To permit interpolation, each configuration has g-functions for heights of 24, 48, 96, 192, and 384 m. All the g-functions were calculated with burial depths of 2m, and borehole diameters of 15 to 17.5 cm, depending on height. In configurations with uniform spacing, the spacing between the boreholes is set to 5m, though it can be scaled to other horizontal spacings.

15 GEOTHERMAL ENERGY↗
DOE OSTI2026

Optimizing district energy systems by integrating Borehole Thermal Energy Storage Using a Mixed-Integer Linear Programming g-function framework with a Multi-Timescale Rolling Horizon method

Shallow geothermal has gained increasing attention in recent years; however, a reliable framework for its accurate incorporation into large-scale energy system optimization remains lacking. This study proposes a Mixed-Integer Linear Programming (MILP) framework combined with the g-function approach to integrate Borehole Thermal Energy Storage (BTES) technology into energy system optimization. Validation against a Modelica-based reservoir network simulation demonstrates that the proposed framework effectively captures the ground thermal response under varying energy loads and accurately estimates the borefield energy supply. To enhance scalability, a Rolling Horizon with Multi-Timescale (RH-MTS) method is further introduced, reducing computational time by 73 % for the 1-year optimization model with only minor loss of optimality. The framework is demonstrated through the case study of the UC Berkeley campus. Results indicate that BTES is a cost-effective and low-carbon solution: two borefields comprising 382 boreholes can meet 8.0 % and 6.6 % of the total campus heating and cooling demand, respectively, at an average energy rate of 0.70–0.77 USD/kWh and carbon intensity of 0.54 kg-CO2/kWh. Short-term analysis reveals a 35%–65% decline in BTES energy flow after 3–6 months of continuous heating/cooling operation, while long-term simulation shows that annual energy production of BTES can vary by up to 12.0 % after four years before stabilizing. Overall, this study develops a novel optimization framework that couples physics-based g-function method with MILP optimization framework, thereby advancing methodological development for shallow-geothermal integration and providing actionable guidance for BTES deployment in district-energy systems.

Yang, Jiahui↗
DOE OSTI2020

Recent Experiences Calculating g-functions for Use in Simulation of Ground Heat Exchangers

Temperature response functions, known as g-functions, are a computationally efficient method for simulating ground heat exchangers (GHEs), used with ground-source heat pump (GSHP) systems, either as part of a whole-building energy simulation or as part of a dedicated ground heat exchanger design tool. In fact, at present, they are the only feasible way to simulate a ground-source heat pump system in a whole-building energy simulation. This paper summarizes recent developments in the field and recent experience using a new open-source g-function calculation tool known as pygfunction (Cimmino 2018a, 2018b). This experience includes accuracy, computation time, memory requirements and sensitivity to boundary conditions. With larger ground heat exchangers, e.g. in excess of 100 boreholes, the computational time and memory requirements can create challenges.

Spitler, Jeffery↗
DOE OSTI2022

Ground heat exchanger design tool with rowwise placement of boreholes

Simulation-based design tools have been used since the late 1980s for designing ground heat exchangers (GHE) used with ground source heat pump (GSHP) systems. The ground heat exchanger simulations used in these tools rely on thermal response functions known as g-functions. Because of the significant computational burden in computing g-functions for even a single configuration, the design tools have relied on libraries of pre-computed g-functions. These g-functions were available for standard configuration shapes, such as lines, rectangles, open rectangles, L-shapes, and U-shapes. Standard shapes are often sub-optimal. For any building on a site, the available land may preclude use of a standard shape. For large GSHP systems with significantly imbalanced annual heat rejection and extraction loads, large rectangular fields may experience significant heat build-up (or heat draw-down) in the interior of the field. This paper describes a new ground heat exchanger design tool capable of automatically selecting and sizing both standard and irregular configurations. The focus of this paper is a method for creating, selecting and sizing irregular configurations where the available land area and "no-go" zones are described as irregular polygons.

Spitler, Jeffery↗
DOE OSTI2020

Functional equations and separation of variables for exact g -function

The g-function is a measure of degrees of freedom associated to a boundary of two-dimensional quantum field theories. In integrable theories, it can be computed exactly in a form of the Fredholm determinant, but it is often hard to evaluate numerically. In this paper, we derive functional equations — or equivalently integral equations of the thermodynamic Bethe ansatz (TBA) type — which directly compute the g-function in the simplest integrable theory; the sinh-Gordon theory at the self-dual point. The derivation is based on the classic result by Tracy and Widom on the relation between Fredholm determinants and TBA, which was used also in the context of topological string. We demonstrate the efficiency of our formulation through the numerical computation and compare the results in the UV limit with the Liouville CFT. As a side result, we present multiple integrals of Q-functions which we conjecture to describe a universal part of the g-function, and discuss its implication to integrable spin chains.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Lattice realizations of topological defects in the critical (1+1)-d three-state Potts model

Topological/perfectly-transmissive defects play a fundamental role in the analysis of the symmetries of two dimensional conformal field theories (CFTs). In the present work, spin chain regularizations for these defects are proposed and analyzed in the case of the three-state Potts CFT. In particular, lattice versions for all the primitive defects are presented, with the remaining defects obtained from the fusion of the primitive ones. The defects are obtained by introducing modified interactions around two given sites of an otherwise homogeneous spin chain with periodic boundary condition. The various primitive defects are topological on the lattice except for one, which is topological only in the scaling limit. The lattice models are analyzed using a combination of exact diagonalization and density matrix renormalization group techniques. Low-lying energy spectra for different defect Hamiltonians as well as entanglement entropy of blocks located symmetrically around the defects are computed. The latter provides a convenient way to compute the g-function which characterizes various defects. Finally, the eigenvalues of the line operators in the “crossed channel” and fusion of different defect lines are also analyzed. The results are all in agreement with expectations from conformal field theory.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Wormholes with ends of the world

We study classical wormhole solutions in 3D gravity with end-of-the-world (EOW) branes, conical defects, kinks, and punctures. These solutions compute statistical averages of an ensemble of boundary conformal field theories (BCFTs) related to universal asymptotics of OPE data extracted from the 2D conformal bootstrap. Conical defects connect BCFT bulk operators; branes join BCFT boundary intervals with identical boundary conditions; kinks (1D defects along branes) link BCFT boundary operators; and punctures (0D defects) are endpoints where conical defects terminate on branes. We provide evidence for a correspondence between the gravity theory and the ensemble. In particular, the agreement of the g-function dependence results from an underlying topological aspect of the on-shell EOW brane action, from which a BCFT analog of the Schlenker-Witten theorem also follows.

AdS-CFT Correspondence↗
DOE OSTI2021

Assessing the predictive impact of factor fixing with an adaptive uncertainty-based approach .

Despite widespread use of factor fixing in environmental modeling, its effect on model predictions has received little attention and is instead commonly presumed to be negligible. We propose a proof-of-concept adaptive method for systematically investigating the impact of factor fixing. The method uses Global Sensitivity Analysis methods to identify groups of sensitive parameters, then quantifies which groups can be safely fixed at nominal values without exceeding a maximum acceptable error, demonstrated using the 21-dimensional Sobol’ G-function. Furthermore, three error measures are considered for quantities of interest, namely Relative Mean Absolute Error, Pearson Product-Moment Correlation and Relative Variance. Results demonstrate that factor fixing may cause large errors in the model results unexpectedly, when preliminary analysis suggests otherwise, and that the default value selected affects the number of factors to fix. To improve the applicability and methodological development of factor fixing, a new research agenda encompassing five opportunities is discussed for further attention.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

Deep Learning enabled spectral energy conversion for in situ exposure measurements

A detector-specific deep learning (DL) approach is presented for spectra-to-exposure conversion using large-format sodium iodide (NaI(Tl)) detectors deployed for in situ environmental radiation measurements in emergency response scenarios. Accurate determination of exposure from NaI spectra is challenging due to poor energy resolution, partial energy absorption, and the strong sensitivity of traditionally deployed analytical conversion methods to calibrated source geometry and pre-deployment assumptions. Here, to address these limitations, a multi-layer perceptron model was trained on a hybrid in situ /Monte Carlo dataset constructed to span a broad range of photon energies, spatial extents, and realistic deployment variability, representative of general in situ emergency response conditions. The DL model was evaluated against commonly fielded analytical approaches under matched simulation conditions, including a single-factor method, a G-function method, and a modeled pressurized ion chamber (PIC) baseline. This study was intentionally computational in scope to enable controlled, like-for-like comparisons between conversion techniques while minimizing confounding real-world variability. Comparison to the modeled PIC provides contextual benchmarking and is not intended as a field inter-comparison with deployed instruments. Across the evaluated 20 keV to 3 MeV energy range, the DL approach consistently exhibited higher accuracy and reduced variance relative to the analytical methods against a deterministically calculated exposure. This may indicate improved robustness to spectral complexity without reliance on source-, geometric-, or spectral region-specific optimization. While results do not represent real-world validation, the presented work demonstrates that deep learning may effectively learn the nonlinear detector response-to-exposure relationship for asymmetric NaI(Tl) detectors and offers a promising pathway for improving in situ exposure estimation using spectroscopic systems already integrated into initial real-time emergency response operations.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2021

Fluid temperature predictions of geothermal borefields using load estimations via state observers

Fluid temperature predictions of geothermal borefields usually involves temporal superposition of its characteristic g-function, using load aggregation schemes to reduce computational times. Assuming that the ground has linear properties, it can be modeled as a linear state space system where the states are the aggregated loads. However, the application and accuracy of these models is compromised when the borefield is already operating and its load history is not registered or there are gaps in the data. This paper assesses the performance of state observers to estimate the borefield load history and obtain accurate fluid predictions. Results show that both Time-Varying Kalman Filter (TVKF) and Moving Horizon Estimator (MHE) provide predictions with average and maximum errors below 0.1 $^\circ C$ and 1 $^\circ C$ respectively. MHE outperforms TVKF in terms of n-step ahead output predictions and load history profile at the expenses of about 5 times more computational time.

Figueroa, Iago C.↗
DOE OSTI2022

Coupling Subsurface and Above-Surface Models for Optimizing the Design of Borefields and District Heating and Cooling Systems

Accurate dynamic energy simulation is important for the design and sizing of district heating and cooling systems with geothermal heat exchange for seasonal energy storage. Current modeling approaches in building and district energy simulation tools typically consider heat conduction through the ground between boreholes without flowing groundwater. While detailed simulation tools for subsurface heat and mass transfer exist, these fall short in simulating above-surface energy systems. To support the design and operation of such systems, the study developed a coupled model including a software package for building and district energy simulation, and software for detailed heat and mass transfer in the subsurface. For the first, it uses the open-source Modelica Buildings Library, which includes dynamic simulation models for building and district energy and control systems. For the heat and mass transfer in the soil, it uses the TOUGH simulator. The TOUGH family of codes can model heat and multi-phase, multi-component mass transport for a variety of fluid systems, as well as chemical reactions, in fractured porous media. The study validated the coupled modeling approach by comparing the simulation results with one from the g-function based ground response model. It then looked into effects when the water table and the regional groundwater flow are considered in the ground, from the perspective of heat exchange between borehole and ground, and the electrical consumption of the district heating and cooling systems. To access the simulation models, please find the links in the submission: -- For coupled approach validation: see model Buildings.Fluid.Geothermal.Borefields.Examples.BorefieldsWithTough and Buildings.Examples.DistrictReservoirNetworks.Examples.Reservoir3Variable_TOUGH from the "Modelica Building Library" resource, branch issue1495_tough_interface, commit a2667c0. -- For the study of the effect of water table: see model Buildings.Examples.DistrictReservoirNetworks.Examples.Reservoir3Variable_TOUGH from he "Modelica Building Library" resource, branch issue1495_tough_interface_moreIO, commit 760de49. -- For the study of the effect of regional groundwater flow: see Buildings.Examples.DistrictReservoirNetworks.Examples.Reservoir3Variable_TOUGH from he "Modelica Building Library" resource, branch issue1495_tough_interface_moreIO_3D, commit c2a2d2a. The coupling interface script "GrounResponse.py" can be found from the above links in the folder Buildings/Resources/Python-Sources. Also, the needed files for TOUGH simulation are in the folder Buildings/Resources/Python-Sources/ToughFiles that can be accessed through the above links. A brief description of these files is given below; detailed specifications for the first three files may be found in the TOUGH3 Users Guide (Jung et al., 2018) https://tough.lbl.gov/documentation/tough-manuals/. (1) INCON - initial conditions for each grid block (2) INFILE - main input file with material properties and control parameters (3) MESH - description of the computational grid (4) readsave - Modelica/TOUGH interface program: read the final output of TOUGH simulation after TOUGH time step and prepare for transfer to Modelica for next Modelica time step (5) readsave.inp - input parameters for program readsave (6) writeincon - Modelica/TOUGH interface program: write the output of Modelica after Modelica time step and prepare for transfer to TOUGH as initial conditions for the next TOUGH step (7) writeincon.inp - input parameters for program writeincon

15 GEOTHERMAL ENERGY↗
DOE OSTI2024

Ground Source Heat Pump Screening Tool and Related Resources

This archive contains both a link to Oak Ridge National Laboratory's Ground Source Heat Pump (GSHP) Screening Tool and related resources documenting its development, technical features, and applications. The web-based screening tool is a techno-economic analysis resource designed to evaluate the feasibility, costs, and benefits of implementing GSHP systems in buildings across various U.S. climate zones. It is intended for use by building owners, HVAC system designers, and installers to support decision-making in residential and commercial applications, incorporating advanced modeling capabilities such as ground heat exchanger design. The included resources detail the tool's creation and use, covering topics such as innovative ground heat exchanger design methodologies, the development of an open library of g-functions for borehole configurations, and studies on GSHP performance and economic viability in retrofitting single-family homes.

15 GEOTHERMAL ENERGY↗
DOE OSTI2023

High Fidelity Modeling of WELL58-32 DFITS

Between 2017 and 2019, a series of injection tests were performed at pilot vertical well 58-32 at the Utah FORGE site. These injection activities were conducted in three distinct zones, isolated with packers and bridge plugs during the tests. Zone 1 consists of an open-hole section at the toe of the well, whereas Zones 2 and 3 are three-meter long cased and perforated sections. Several injection cycles were conducted in each zone. A detailed description of the geology of the FORGE site, of well 58-32 and of all injection cycles can be found in (Xing et al., 2020). The injection cycles included Diagnostic Fracture Injection Tests (DFITs). DFITs comprise two primary stages: an injection (pump-in) phase, where controlled fluid injection is employed to create a small hydraulic fracture in the surrounding rock, followed by a shut-in phase, where injection ceases, allowing observation of the formation’s pressure response. Utilizing methodologies such as the G-function analysis, DFITs provide valuable insights, including fracture closure pressure and the Instantaneous Shut-in Pressure (ISIP) and can be employed to estimate the minimum horizontal stress.

42 ENGINEERING↗
DOE OSTI2024

Quarterly Research Performance Progress Report (Q8)

As part of Task 1, we have started by testing our modeling capabilities by reproducing isothermal DFIT simulations presented in the literature. Once satisfied with the results we have started by targeting the modeling of the DFITs at conducted at well 58-32. We have a identified a specific test (cycle 4 in zone 2) as the most interesting to be model with GEOS hydraulic fracturing module. Thus, we have first produced results with an isothermal model and adjusted model parameters to get a satisfying match with field pressure data. The, we have added thermal effects and compared the modeling results with and without thermal effects to estimate how thermal effects may influence test interpretation. Models seem to suggest that, for small volumes of fluid, thermal effects are moderate. In Task 2, we have adapted GEOS phase-field formulation to be able to simulate near-wellbore hydraulic fracture nucleation and propagation. We have devised a novel formulation that, compared to other existing ones, incorporates rock strengths. We have submitted a journal publication about our work. We are currently employing this phase-field formulation to model the experiments taking place at U Pitt and help us understand the effect of various parameters. In Task 3, we have built a model of the region surround well 16A and have started modeling stage 3 stimulation because of its simpler planar geometry. After calibrating simulation parameters using known analytical solutions, we have simulated the stage 3 stimulation using our isothermal hydraulic fracturing module, varying the permeability field, the stress conditions including different physics to get a better understanding of the numerical challenges and of the effects of varying these parameters on the simulation results. In Task 4 laboratory experimentation, a set of specialized drilling and injection tools has been customized and constructed to accommodate an inclined well with an orientation of up to 30 degrees relative to material anisotropy or principal stress axes. These inclined samples have also undergone thermal stress and hydraulic fracturing at a temperature of 190 degrees Celsius. Furthermore, both vertical and deviated sampling testing setups enable an extended analysis of post-peak pressure behaviors, facilitating post-test pressure analyses such as the G-function, step rate, and fracture reopening measurements. Thus, the key components of in-situ stress estimation can be extracted and validated through our experiment, providing a solid foundation for validating existing in-situ stress estimation theories or proposing new ones. Simultaneously, we are integrating computer vision techniques with traditional experimental fracture observation methods such as multi-overcore/slicing and water-penetration fracture observation. This combination will prove beneficial in populating the hydraulic fracture patterns database, generated under challenging EGS conditions. This approach aims to deepen our understanding of the complexities in EGS reservoirs and pave the way for future data-driven investigations. Additionally, PITT has also equipped the ELE International compression machine, which is now prepared for conducting indirect tensile and fracture toughness tests. These tests will aid in characterizing how rock fabrics influence the resulting fracture patterns. Additionally, we have completed the required personnel training and gained access to Scanning Electron Microscopy (SEM) and Energy Dispersive Spectroscopy (EDS) for conducting more detailed characterization and analysis of rock fabrics, as well as the examination of thermal and hydraulically induced fracture patterns. Thus, the PITT team has effectively demonstrated the capabilities of our experimental apparatuses in exploring the thermal effects, well deviation angles, material anisotropy, and operational choices (such as circulation rate, injection fluid viscosity, and injection rate) and their impact on pressure responses and fracture trajectories under the Utah FORGE conditions.

15 GEOTHERMAL ENERGY↗
DOE OSTI2022

Development of a web-based screening tool for ground source heat pump applications

Ground source heat pump (GSHP) technology has great potential to help the nation meet its energy and decarbonization goals, but several barriers hinder the wide application of GSHP. Important barriers include the lack of a coherent toolset for analyzing the technical feasibility and economic viability of the GSHP application. The current design and analysis methods are ineffective and require significant expertise to apply. Although building energy modeling is increasingly important in designing buildings, the tools for GSHP modeling and simulation are lacking. A web-based free-to-use tool is being developed for quick techno-economic analysis of GSHP applications in nearly any building in the United States. This tool is enabled by improvements in the calculation methodology to allow rapid sizing of borehole configurations that provide significant cost savings. The screening tool currently uses US Department of Energy (DOE) prototype building models and an extended g-function library to size ground heat exchangers and simulate the performance of GSHP systems. The team is integrating with DOE's Oak Ridge National Laboratory's AutoBEM program to automatically create a building model based on user inputs. This paper introduces the structure, components, features, and results of the web-based screening tool for GSHP applications. Future directions for further developing the tool are also discussed.

Liu, Xiaobing↗