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DOE OSTI2023

FY23 Status Report on MOOSE-Based Approaches to Modeling Core Bowing in Fast Reactors

Under the U.S. Department of Energy Office of Nuclear Energy’s Advanced Modeling and Simulation (NEAMS) Program, an integrated multiphysics approach is being developed to model the core bowing phenomena important to liquid metal-cooled fast reactors. Core bowing is an important passive safety mechanism whereby increased power (which leads to temperature and flux gradients) influences the core to bow into less reactive configurations when the restraint system is properly designed. The phenomenon includes a complex interplay of radiation transport, duct temperature calculations involving fluid flow and heat transfer, and thermo-mechanical responses to the induced temperature and flux gradients. Structural material properties are also important to determining inelastic response to longer term flux gradients which cause irradiation creep and swelling. While core bowing provides a strong negative reactivity feedback when the restraint system is designed properly, it also results in additional forces between assemblies which increase the loads required to extricate them during refueling or control rod movement. Therefore, the restraint system must be designed with these tradeoffs in mind. The first stage of the work, which commenced in FY21 and continues through FY23, assesses thermo-mechanical modeling tools for producing core bowing predictions consistent with conventional tools. The Multiphysics Object Oriented Simulation Environment (MOOSE) Tensor Mechanics and Contact Modules are employed. This status report describes work on additional thermo-mechanical benchmark verification problems with increased complexity from the examples demonstrated in FY21 and FY22. Several benchmark verification examples were selected from the IAEA verification and validation report with increased number of ducts and more complex contact interaction behavior. These examples involve a full symmetric sector with restraint rings at multiple load pad locations to simulate a limited free-bow restraint system concept, as well as irradiation induced swelling and creep effects in a sector. In addition, improvements to the contact module sideset assignment were assessed and compared with previous MOOSE results to verify the contact behavior. The MOOSE-based results were compared to IAEA benchmark participants’ results. In every case, the MOOSE results agreed with other simulations results for estimating bowing behavior, providing additional verification basis of the tools for this particular physics application. Estimation of contact forces were mostly in agreement, with a few outlier results. A plan was suggested for dealing with the discrepancies with estimating contact force values. In addition, a 1-way coupling demonstration was performed using subchannel analysis code Pronghorn-SC and MOOSE on an ABR-1000-design sodium-cooled fast reactor assembly to evaluate coolant and duct wall temperatures.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

Rapid SACR Observations of Convection at Bankhead National Forest (RAPID) Field Campaign Report

Improving our representation of convective cell processes requires better quantification of convective clouds throughout their entire life cycle. This includes gaining a clearer understanding of the controls on key convective cloud properties, such as updraft intensity, particle size distributions, rainfall rates, and hydrometeor species. Our inability to improve convective cloud process modeling stems, in part, from a limited understanding of convective cell properties, particularly given how rapidly these storms evolve. This lack of detailed observations in the most intense and organized convective storms is especially significant, as large errors remain in representing these clouds, which are critical for severe weather prediction and Earth system model performance. Cloud and precipitation radars are essential tools for studying cloud microphysics and dynamics, particularly in deeper convective clouds. The recent U.S. Department of Energy Atmospheric Radiation Measurement (ARM) User Facility’s third Mobile Facility (AMF3) Bankhead National Forest (BNF) deployment provides a unique opportunity to investigate important land–atmosphere interactions, as well as the environmental controls on deep convective cloud processes, in a location favorable for frequent convection. We operate the X/Ka-band Scanning ARM Cloud Radar (X/Ka SACR) using a scan strategy optimized to capture these rapidly evolving clouds and their properties, thereby improving studies of deep convective cloud processes. This effort is strengthened by a complementary and coordinated partnership with ongoing university and multi-agency radar activities collocated in north Alabama—a unique opportunity to examine clouds and precipitation from a lifetime-centric perspective.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

High-Resolution Floating Solar PV Data

This dataset contains over two years of 1-minute resolution data collected from four floating solar sites, as well as data from a land-based PV system co-located with one of the floating sites. The dataset includes highly granular module temperature measurements - five modules per floating site, with three sensors per module, totaling 15 module temperature sensors per floating site. In addition to the module temperature data, meteorological data collected at the floating sites is also included, along with traditional PV system-level parameters. The data is intended for analysis of solar energy production, efficiency, and performance degradation over time. For information about the data file usage see the "README" resource below. See "Metadata File" for information about individual files and other metadata information.

Array↗

DOE OSTI2020

A Tidal Hydrodynamic Model for Cook Inlet, Alaska, to Support Tidal Energy Resource Characterization

Cook Inlet in Alaska has been identified as a prime site in the U.S. for potential tidal energy development, because of its enormous tidal power potential that accounts for nearly one-third of the national total. As one important step to facilitate tidal energy development, a tidal hydrodynamic model based on the unstructured-grid, finite-volume community ocean model (FVCOM) was developed for Cook Inlet to characterize the tidal stream energy resource. The model has a grid resolution that varies from about 1000 m at the open boundary to 100–300 m inside the Inlet. Extensive model validation was achieved by comparing model predictions with field observations for tidal elevation and velocity at various locations in Cook Inlet. The error statistics confirmed the model performs reasonably well in capturing the tidal dynamics in the system, e.g., R2 > 0.98 for tidal elevation and generally > 0.9 for velocity. Model results suggest that tides in Cook Inlet evolve from progressive waves at the entrance to standing waves at the upper Inlet, and that semi-diurnal tidal constituents are amplified more rapidly than diurnal constituents. The model output was used to identify hotspots that have high energy potential and warrant additional velocity and turbulence measurements such as East Foreland, where averaged power density exceeds 5 kw/m2. Lastly, a tidal energy extraction simulation was conducted for a hypothetical turbine farm configuration at the Forelands cross section to evaluate tidal energy extraction and resulting changes in far-field hydrodynamics.

16 TIDAL AND WAVE POWER↗

DOE OSTI2022

Spatiotemporal Modeling of Real World Backsheets Field Survey Data: Hierarchical (Multilevel) Generalized Additive Models: Preprint

Assessing photovoltaic module backsheet durability is critical to increasing module lifetime. Lab based accelerating testing has recently failed to predict large scale failures of widely adopted polymeric materials. Field surveyed data is critical to assess the performance of component lifetime. Using a documented field survey protocol, 13 field surveys where conducted. Each measurement is encoded with it's spatial location in respect to the other modules. By combining field survey data on degradation predictors with real time satellite weather data, data-driven predictive models of backsheet degradation were trained. LOESS models were constructed to investigate the spatial dependence of measurements. It was found that micro-climatic effects like treelines, ground surface changes, and elevation changes effected the magnitude and variance of the measurements. A GAM model was created to predict the value of degradation based on measured predictors. The model includes variables on the climate of the system and the location of each measurement in the PV mounting structure. The model performed well with an adj:R2 of 0:95 for yellowness index prediction. The model was cross-validated using k-folds.

backsheet↗

DOE OSTI2025

Electric Vehicle Supply Equipment (EVSE) Site Assessment Report for the U.S. Army Corps of Engineers Chena Site Near Fairbanks, Alaska

This report presents an analysis of the requirements for charging station installation and electric vehicle operation at the US Army Corps of Engineers - Chena Site, located in a cold weather climate in the Fairbanks North Star Borough, AK. The report includes findings from a site visit, and a detailed electric vehicle (EV) charging site plan with cost estimates. Cost for three 50-ampere pedestal chargers located on the edge of the existing parking lot is estimated at $\$$53,100, and the cost of three 80-ampere chargers is estimated at $\$$89,400. The authors did not assess the cost of a heated garage. The USACE Chena site reaches extreme cold temperatures of -40 Degrees Celsius (-40 Degrees Fahrenheit) and below in a typical winter, often for days on end. Considerations of operating EVs as well as electrical vehicle supply equipment (EVSE) at this site can be applicable to other cold or extremely cold locations. Interviews with EV users in cold climates and a literature review indicated that EVs operate well but have significantly decreased range compared to 21 Degrees Celsius (70 Degrees Fahrenheit) operations. Some strategies such as prewarming the vehicle while it is plugged in and using heated seats and steering wheel instead of cabin heat, can improve cold weather performance. Storing the EV in a garage would mean the battery and cabin are automatically preheated, the battery would not age as rapidly as when the vehicle is stored outside, and problems with charging the vehicle are less likely. Lowest temperate-rated Electric Vehicle Supply Equipment (EVSE), as electric vehicle chargers are known as, are rated to -40 Degrees Celsius (-40 Degrees Fahrenheit), and sometimes malfunction. No EVSE is rated to the temperatures that USACE Chena site experienced for more than a week in winter 2023-4, of -50 Degrees Celsius (-45 Degrees Fahrenheit) and which are typical for the area. If reliability is a must, entities may want to consider a heated garage to minimize potential problems with charging equipment. There is a companion technical report to this titled "Electric Vehicle and Charging Infrastructure Assessment in Cold-Weather Climates: A Case Study of Fairbanks, Alaska" that examines the data on EV and EVSE cold-weather functionality in more detail. (Esparza, Truffer Moudra, and Hodge 2024).

33 ADVANCED PROPULSION SYSTEMS↗

DOE OSTI2026

Comparing ICME simulations with scaled laboratory experiment

In stellar physics and astrophysics, numerical simulations and laboratory experiments are often compared to observational data to support their representation of the real world. However, there is also merit in comparing numerical simulations to properly scaled experiments, especially when the experiment and the simulation are both emulating the solar phenomena. Confirming the credibility of scaled experiments and their scaling with well-validated models is important to expand our knowledge of the associated physical phenomena. This is significant because experiments and simulations can be performed frequently, whereas observations may be limited by location, field of view, and missing data. In this work, we use the Alfvén Wave Solar atmosphere Model, a well-validated magnetohydrodynamic model, to simulate an interplanetary coronal mass ejection (ICME) and compare it to an experiment which provides a scaled analog to a physical ICME. The experiment was performed on the Big Red Ball facility and scaled using dimensionless parameters such as plasma β and magnetosonic Mach number to reproduce the main structure of an ICME. We compare the model-simulated temperature, density, and magnetic field to those from the experiment, as well as the scaling parameters used in the experiment, to those calculated from the simulation. This comparison is performed to further justify the scaling arguments made by the experiment. Additionally, the comparison would lead to the development of stronger scaling arguments for future experiments.

Bryant, K. [University of Michigan, Ann Arbor, MI ↗

DOE OSTI2026

North Slope of Alaska XSAPR b1 Data Processing Report: April 2024-April 2025

The North Slope of Alaska (NSA) atmospheric observatory, operated by the U.S. Department of Energy (DOE)’s Atmospheric Radiation Measurement (ARM) User Facility, is a measurement site in the Arctic that has been collecting crucial atmospheric data for more than 25 years. The central facility located in Utqiaġvik, Alaska (formerly known as Barrow) hosts a suite of instruments that are used to better understand arctic processes, which are often not well represented in earth system models. The NSA site sits only a few kilometers from the Arctic Ocean, which also makes it a prime location to study complex ocean-atmosphere-ice interactions. Arctic cloud and precipitation processes are also of scientific interest, and remote-sensing instruments including radars are a key component of the NSA instrument suite. One of the radars at NSA is the X-band Scanning ARM Precipitation Radar (XSAPR). This report evaluates one year of recent XSAPR data from April 2024 through April 2025 and details the process of generating b1-level data. This analysis marks the first effort by ARM staff to quality-control NSA XSAPR data with the goal of routinely producing b1-level data in the future depending on radar operations.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2020

Characterizing natural fractures and sub-seismic faults for well completion of Marcellus shale in the MSEEL Consortium project, West Virginia, USA

The Middle Devonian Marcellus shale play has emerged as a major world-class hydrocarbon accumulation and represents one of the largest and most prolific shale plays in the world. According to many outcrop studies in the region, natural fractures are well developed in the Marcellus Shale. However, evaluating fractures in the subsurface is often a significant challenge due to a lack of sufficient data. Therefore, in the Marcellus Shale Energy and Environment Laboratory (MSEEL) consortium project, significant efforts have been made to acquire high-quality image logs in the Marcellus laterals. The project provided tremendous opportunities to characterize the natural fractures and sub-seismic faults and to evaluate their impact on well stimulation. In this study, about 70,000 ft of acquired high-resolution logging while drilling (LWD) acoustic images from five long laterals located in Monongalia County, West Virginia, were processed and interpreted. In addition, the study used high-quality micro-resistivity images from a pilot well, allowing the evaluation of natural fractures in the entire Marcellus vertical sequence. Based on the available acoustic images, the natural fractures were classified into three basic categories: high-amplitude fractures, low-amplitude fractures, and faults. Further, larger open fractures can also be determined when a low-amplitude fracture is evident on caliper images. The fractures in the Marcellus usually have a medium to high angle dip; however, multiple fracture sets in terms of strike orientation were clearly observed in all the laterals. The fracture set with a strike at NE-SW (or 60-240 deg) seems to be the predominant one in all the wells. A few other sets, including those with N-S, NWW-SEE, and E-W strikes, were also observed. Several sub-seismic faults, with mostly a low dip angle and a NE-SW strike, have also been seen in two of the laterals. The fracture density is variable across all the laterals, ranging from very low (or none) to very high (up to 5 fractures per ft). The average fracture density for all the laterals is about 1 fracture per 10 ft. In the vertical sequence, the natural fracture development showed a clear preference for shale or shaly facies over carbonate-rich or thin limestone layers. The interpreted fracture and fault data were used as input data for the stimulation design with the purpose of better understanding the fractures’ impact on well stimulation. Production data from the laterals were also used to evaluate the natural fractures’ influence on well performance. The quality image database and the consistent interpretation results for the entire project enabled a systematic approach to characterizing fractures and, more importantly, to evaluating the impact of fractures on well stimulation and production.

03 NATURAL GAS↗

DOE OSTI2021

Framework for optimization of long-term, multi-period investment planning of integrated urban energy systems

In order to achieve stringent greenhouse gas emission reductions, a transition of our entire energy system from fossil to renewable resources needs to be designed. Such an energy transition brings two main challenges: most renewables generate variable electric energy, yet most demand is currently not electric (carrier mismatch) and does not always manifest at the same time as supply (temporal mismatch). Integrating multiple energy infrastructures can address both challenges by using the synergy between different energy carriers; building on existing infrastructure, while allowing a robust and flexible integration of the new. This paper proposes an optimization framework for long-term, multi-period investment planning of urban energy systems in an integrated manner. We formulate it as a mixed-integer linear program, combining a capacitated facility location with a multi-dimensional, capacitated network design problem. It includes generation and network expansion planning as well as interconnections between networks and storage infrastructure for each energy system. It can incorporate pathway effects like techno-economic developments, policy measures, and weather variations. The intended use is to support urban decision makers with long-term investment planning, though it can be tailored to fit other geographical or temporal scales. We demonstrate the model using two cases based on an average city in The Netherlands, which wants to reduce its CO 2 -emissions with 95% by 2050. In the first case, we include explicit carbon-emission constraints to study the effects of the carrier mismatch. In the second case, we implement interannual weather variations to analyze the temporal mismatch. The results give valuable insights into the energy transition design strategy for urban decision makers. They also show the future potential, as well as the computational challenges of the optimization framework.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2021

Methane Plume Emissions Associated With Puget Sound Faults in the Cascadia Forearc

Methane gas plumes have been discovered to issue from the seafloor in the Puget Sound estuary. These gas emission sites are co-located over traces of three major fault zones that fracture the entire forearc crust of the Cascadia Subduction Zone. Multibeam and single-beam sonar data from cruises conducted in 2011, 2018, 2019, 2020 and 2021 identified the acoustic signature of over 330 bubble plumes. Dissolved gas from the plumes combines to elevate seawater methane concentrations of the entire Puget Sound estuary. Fluid samples from adjacent terrestrial hot springs and deep-water wells surrounding the estuary contain a helium-3 isotope signature, indicating a deep fluid source located near the underlying Cascadia Subduction Zone. However, Puget Sound seawater emission sites lack chemical isotope signatures and elevated thermal anomalies expected from association with a deep plate-interface reservoir. The existence of vigorous marine methane plumes located in areas of thin sediment cover and above the traces of deeply-penetrating forearc fault zones – but still presenting no thermal or chemical anomalies that are found in many other similar forearc environments and remain an unresolved paradox.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

A new synthetic correlation electron cyclotron emission diagnostic for validating nonlinear gyrokinetic simulations of electron temperature turbulence

To validate nonlinear gyrokinetic simulations of electron temperature turbulence, the experimental correlation electron cyclotron emission (CECE) measurements are to be compared using a synthetic CECE diagnostic, which generates modeled CECE measurement quantities by implementing realistic measurement parameters (e.g., spatial and wavenumber resolutions, radial location, etc.) to nonlinear gyrokinetic simulations. In this work, we calculate the radial and vertical spatial and wavenumber transfer functions, which are defined by the electron cyclotron emission emissivity radial profile and vertical probing antenna pattern, respectively. These transfer functions are applied to nonlinear gyrokinetic simulations of electron temperature turbulence using the continuum gyrokinetic code. A simultaneous comparison of the experimental electron temperature turbulence power spectrum and root-mean-square (RMS) level, as well as the radial correlation length with the new synthetic CECE diagnostic at a core location ρ ∼ 0.75 in an L-mode DIII-D tokamak plasma, is presented. Here, the preliminary result shows that the synthetic CECE output underestimates the RMS level by ∼42% and overestimates the radial correlation length by ∼40%.

Cyclotron radiation↗

DOE OSTI2020

Distributed Acoustic Sensing (DAS) Seismic Monitoring of CO 2 Injected for Enhanced Oil Recovery in Northern Michigan (Volume II.C)

The Midwest Regional Carbon Sequestration Partnership (MRCSP) was founded in 2003 as part of the U.S. Department of Energy’s (DOE’s) Regional Carbon Sequestration Partnership initiative. Since its founding, MRCSP has made significant strides toward making CCUS a viable option for states in the region. The public/private consortium, funded through the DOE Regional Carbon Sequestration Initiative, brings together nearly 40 industry partners and 10 states. Battelle, as the project lead, oversees research, development and operations and coordinates activities among the partners. The incremental, phased approach has built a valuable knowledge base for the industry and paved the way for commercial-scale adoption of CCUS technologies. From 2008 to 2020, MRCSP Phase III focused on the development of large-scale injection projects. This report is part of a series of reports prepared under the Midwestern Regional Carbon Sequestration Partnership (MRCSP) Phase III (Development Phase). These reports summarize and detail the findings of the work conducted under the Phase III project. This report describes the monitoring study conducted to assess the effectiveness of DAS (Distributed Acoustic Sensing) -based VSP (Vertical Seismic Profiling) technology for delineating CO 2 injected into the Silurian-age pinnacle reefs in northern Michigan, the host rocks for the MRCSP Phase III demonstration project. The DAS VSP study was conducted in the Chester 16 reef, one of several reefs in Otsego County Michigan that is operated by Core Energy, LLC of Traverse City, Michigan. Time-lapse DAS VSP was implemented at the Chester 16 reef to attempt to detect approximately 85,000 tonnes of CO 2 injected into the A-1 Carbonate and Brown Niagaran Formations. A baseline survey was conducted in February 2017 prior to injecting CO 2 and a repeat survey was conducted in August 2018. During the interim period between the baseline and repeat surveys, CO 2 was injected into the Chester 16 reef via the 6-16 injection well without production (withdrawal) of fluids from the reef. A grid of 181 source positions consisting of 44 vibrator positions, plus 137 dynamite shot locations, was used to give approximately continuous spatial coverage of the injection zone (A-1 Carbonate and upper Brown Niagaran) in the area between the two wells.

01 COAL, LIGNITE, AND PEAT↗

DOE OSTI2022

Inference of bipolar neutrino flavor oscillations near a core-collapse supernova based on multiple measurements at Earth

Neutrinos in compact-object environments, such as core-collapse supernovae, can experience various kinds of collective effects in flavor space, engendered by neutrino-neutrino interactions. These include “bipolar” collective oscillations, which are exhibited by neutrino ensembles where different flavors dominate at different energies. Considering the importance of neutrinos in the dynamics and nucleosynthesis in these environments, it is desirable to ascertain whether an Earth-based detection could contain signatures of bipolar oscillations that occurred within a supernova envelope. To that end, we, in this study, continue examining a cost-function formulation of statistical data assimilation (SDA) to infer solutions to a small-scale model of neutrino flavor transformation. SDA is an inference paradigm designed to optimize a model with sparse data. Our model consists of two monoenergetic neutrino beams with different energies emanating from a source and coherently interacting with each other and with a matter background, with radially varying interaction strengths. We attempt to infer flavor transformation histories of these beams using simulated measurements of the flavor content at locations “in vacuum” (that is, far from the source), which could in principle correspond to Earth-based detectors. Within the scope of this small-scale model, we found that: (i) based on such measurements, the SDA procedure is able to infer whether bipolar oscillations had occurred within the protoneutron star envelope, and (ii) if the measurements sample the full amplitude of the neutrino oscillations in vacuum, then the amplitude of the prior bipolar oscillations is well predicted. This result intimates that the inference paradigm can well complement numerical integration codes, via its ability to infer flavor evolution at physically inaccessible locations.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

From noise to information: The transfer function formalism for uncertainty quantification in reconstructing the nuclear density

The neutron distribution of neutron-rich nuclei provides critical information on the structure of finite nuclei and neutron stars. Parity violating experiments—such as PREX and CREX—provide a clean and largely model-independent determination of neutron densities. Such experiments, however, are challenging and expensive, which is why sound statistical arguments are required to maximize the information gained. We introduce a new framework, the “transfer function formalism,” aimed at uncertainty quantification, model selection, and experimental design in the context of neutron densities. The transfer functions (TFs) are built analytically by expressing the linear response of the objective function (e.g., χ2) to small perturbations of the data. Using the TF formalism, we are able to analyze the expected overall uncertainty—quantified in terms of bias and variance—of the mean square radius and interior density of 48 Ca and 208 Pb. Using relativistic mean field models as a proxy for the weak-charge density—and assuming that a total of five measurements could be performed on the weak form factor of 48 Ca and 208 Pb—we identify the optimal models and experimental locations that minimize the uncertainty in the extraction of the radius and interior density. We also explore the use of the TF formalism to understand the influence of prior distributions for the model parameters, as well as the optimization of model hyperparameters not constrained by the data. Here,we establish how the choice of experimental locations and the model that is used can have a significant impact on the final uncertainties of the extracted quantities of interest. For challenging experiments such as CREX and PREX, a proper quantification of such uncertainties is critical. We have demonstrated how the TF formalism provides several advantages for this type of analysis.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2022

Extreme variation in fatigue: Fatigue life prediction and dependence on build volume location in laser powder bed fusion of 17-4 stainless steel

Laser powder bed fusion (LPBF), a metal additive manufacturing technology, is well-suited for design optimization but fatigue life is limited by manufacturing defects. In this work, 17-4 stainless steel components were manufactured in densely populated build volumes, simulating at-scale LPBF production. Tests revealed extreme variability in fatigue life data, analyzed via rigorous statistical tools. The El-Haddad model, modified for finite-life, enabled defect-based life prediction. Specimen location within the build volume correlated to life, which was heteroscedastic. Investigating defect concentration over the build volume explained typical life and scatter. Finally, these findings argue for qualification approaches which acknowledge high material lot variability.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Local Control After Proton Therapy for Pediatric Chordoma

Due to the location and high dose required for disease control, pediatric chordomas are theoretically well-suited for treatment with proton therapy, but their low incidence limits the clinical outcome data available in the literature. We sought to report the efficacy and toxicity of proton therapy among a single-institution cohort.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

DOE OSTI2023

Multiscale spatial analysis of fracture nodes in two dimensions

Spatial arrangement of fractures as a function of scale is an important component of fracture quantification for inferential and predictive modeling. Available methods that analyze fracture spatial arrangement are based on one-dimensional spacing data; therefore, they are limited to semi-parallel fractures. Such methods cannot be applied to fracture networks in higher dimensions, particularly when fractures have different orientations. Here to characterize fracture arrangements in two dimensions, we propose using Ripley’s K-function, as a method of point pattern analysis, to quantify spatial arrangement of fracture nodes. Fracture nodes, such as barycenters, intersection points, and tips, are point-based representations of fracture locations and connectivity within the fracture network. We introduce formulations for isotropic as well as directional analyses of spatial arrangement. In addition, we derive formulations for edge correction in circular and rectangular study domains. Finally, we demonstrate applications of Ripley’s K-function on two natural fracture datasets. Our proposed method supports quantification and characterization of fracture spatial arrangements that allow practitioners to build representative models of fractures in the subsurface.

02 PETROLEUM↗