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Sum-of-Fractions Methodology for Actinides in Water- and Polyethylene-Moderated and -Reflected Systems

Sum-of-fractions is a method intended to make sure a subcritical margin for aqueous solutions and slurries of fissionable isotopes exists. The method indicates that a system is subcritical if the sum of the ratios of the mass of each isotope (in a mixture) to its individual minimum subcritical mass limit is less than or equal to one. Historically, the basis of the sum-of-fractions has been derived from allowances given in the American National Standards Institute (ANSI)/ American Nuclear Society (ANS)-8.15-1981. However, the allowance was removed in ANSI/ANS-8.15-2014 due to a lack of technical basis. A methodology was developed to assess the validity of using the sum-of-fractions for water- or polyethylene-moderated systems for the following nuclides: 232 U, 233 U, 234 U, 235 U, 237 Np, 236 Pu, 238 Pu, 239 Pu, 240 Pu, 241 Pu, 242 Pu, 241 Am, 242 m Am, 243 Am, 242 Cm, 243 Cm, 244 Cm, 245 Cm, 246 Cm, 247 Cm, 249 Cf, and 251 Cf. The methodology uses available benchmark data for mixtures of 233 U, 235 U, and 239 Pu to establish the calculational margin, and a mass limit reduction to establish the margin of subcriticality. Water- or polyethylene-moderated and -reflected mixtures containing the nuclides are evaluated with the code system, SCALE 6.2.4. Including the calculational margin, subcritical mass limits for each nuclide were computed for optimally water- or polyethylene-moderated and fully reflected systems. These masses were used to create nuclide mixtures in which the sum of the mass to subcritical mass limit ratios is one. The various nuclide mixtures were modeled over a range of moderation and demonstrate the keff does not exceed the calculational margin. For additional assurance of subcriticality, a significant mass reduction is applied to each computed minimum critical mass of the nuclides without adequate benchmark data consistent with the method in ANSI/ANS-8.15-2014.

07 ISOTOPE AND RADIATION SOURCES↗

Investigating Similarity Differences for Light-Water-Moderated and Polyethylene-Moderated Systems [Slides]

Validation efforts revealed noticeable differences in c k for light-water and polyethylene moderated systems when compared to experimental systems. Although 1 H-H 2 O and 1 H-poly use some of the same cross section and identical covariance data, the treatment of TSLs in SCALE lead to no contribution to c k between polyethylene application and benchmark experiment. When H 2 O contribution is removed the difference in c k appears to come from 239 Pu chi. Sensitivity profiles and data-induced uncertainty confirm that the polyethylene application more closely resembles the benchmark experiment. Interrogation techniques were used to observe how TSLs and nuclide IDs affect c k . Specific differences between similar systems can be accounted for and examined to help understand differences in similarity (c k ) between systems

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Investigating Similarity Differences for Light-water-Moderated and Polyethylene-Moderated Systems

Oak Ridge National Laboratory has performed validation studies in support of Pacific Northwest National Laboratory’s analysis of the Sum-of-Fractions method. Work in a companion paper examines the validation methods and results for various mixtures of fissile isotopes in various concentrations moderated and reflected by water and polyethylene. Those results indicate a greater coverage of critical experiments for validating water moderated and reflected systems versus those moderated and reflected with polyethylene.

07 ISOTOPE AND RADIATION SOURCES↗

Investigating Similarity Differences for Light-Water-Moderated and Polyethylene-Moderated Systems

Oak Ridge National Laboratory has performed validation studies in support of Pacific Northwest Laboratory’s analysis of the Sum-of-Fractions method. Work in a companion paper examines the validation methods and results for various mixtures of fissile isotopes in various concentrations moderated and reflected by light-water and polyethylene. Those results indicate a greater coverage of critical experiments for validating light water moderated and reflected systems vs. those with polyethylene. The work presented here details the analysis of differences between light-water and polyethylene systems developed from the different concentration mixtures utilized in the Sum-of-Fractions validation study. Differences in actinide contributions are detailed, explaining the differences in ck for the various systems. The available tools and analysis techniques in TSUNAMI are described to illustrate how these types of differences can be understood by practitioners.

07 ISOTOPE AND RADIATION SOURCES↗

Sum-of-Fractions Method

Sum-of-fractions is a method intended to make sure a subcritical margin for aqueous solutions and slurries of fissionable isotopes exists. The method indicates that a system is subcritical if the sum of the ratios of the mass of each isotope (in a mixture) to its individual minimum subcritical mass limit is less than or equal to one. Historically, the basis of the sum-of-fractions has been derived from allowances given in the American National Standards Institute (ANSI)/ American Nuclear Society (ANS)-8.15-1981. However, the allowance was removed in ANSI/ANS-8.15-2014 due to a lack of technical basis. A methodology was developed to assess the validity of using the sum-of-fractions for water- or polyethylene-moderated systems for the following nuclides: 232U, 233U, 234U, 235U, 237Np, 236Pu, 238Pu, 239Pu, 240Pu, 241Pu, 242Pu, 241Am, 242mAm, 243Am, 242Cm, 243Cm, 244Cm, 245Cm, 246Cm, 247Cm, 249Cf, and 251Cf. The methodology uses available benchmark data for mixtures of 233U, 235U, and 239Pu to establish the calculational margin, and a mass limit reduction to establish the margin of subcriticality. Water- or polyethylene-moderated and -reflected mixtures containing the nuclides are evaluated with the code system, SCALE 6.2.4. Including the calculational margin, subcritical mass limits for each nuclide were computed for optimally water- or polyethylene-moderated and fully reflected systems. These masses were used to create nuclide mixtures in which the sum of the mass to subcritical mass limit ratios is one. The various nuclide mixtures were modeled over a range of moderation and demonstrate the keff does not exceed the calculational margin. For additional assurance of subcriticality, a significant mass reduction is applied to each computed minimum critical mass of the nuclides without adequate benchmark data consistent with the method in ANSI/ANS-8.15-2014.

criticality safety, Actinide↗

Evaluation of neutron dosimetry capabilities with the MC-15 portable multiplicity counter

This work proposes a preliminary neutron dose rate estimation method for a neutron multiplicity detector through measurement- and simulation-based analyses. Uncharacterized neutron-emitting sources may be encountered in situations such as nuclear emergency response, safeguards, and treaty verification. These circumstances may present irradiation risk to personnel conducting field assay, search, and characterization measurements. It is therefore of interest to provide a field neutron dosimetry capability with the existing neutron multiplicity counting (NMC) capabilities. To date, no commercially-available neutron detection systems are capable of both accurate NMC and real-time neutron dosimetry. This work will focus on estimating dose rate using input from a single fielded NMC called the MC-15. The energy-dependent neutron detection efficiency response of the MC-15 was quantified in monoenergetic neutron simulations and evaluated in response to two neutron-emitting sources and to a polyethylene-moderated source. The results were compared to existing neutron dosimeters and established the proof of concept for further investigation of the MC-15 for dose estimation. Measurement results were also replicated in simulations; additional simulations were then conducted to expand upon the limited empirical data. The initial empirical results provided a conversion factor appropriate for use when measuring 252 Cf neutrons that is independent of polyethylene shielding presence and thickness. The simulated data sets were then used to evaluate a fit equation allowing estimation of the neutron dose rate for less restricted geometric configurations and dependent only on the distance between the source and the detector. Additionally, the energy dependence of the efficiency response indicates that further empirical evaluations could provide energy-dependent conversion factors for broader neutron dosimetry capabilities with a wider range of neutron-emitting sources.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Delayed Critical Highly Enriched Uranium Metal Cylinders with Thin Graphite Top and Bottom Reflectors

Nine 7, 11, and 15 in. diam highly enriched uranium (HEU, 93.15 wt % 235 U) metal cylinders were assembled on the vertical assembly machine in the Oak Ridge Critical Experiments Facility (ORCEF) and had 1, 2, or 3 in. thick HLM graphite reflectors on the top and bottom. The experiments, which were performed between April 3, 1970, and February 18, 1971, used 23 operational days at ORCEF. Before those experiments were carried out, unreflected and unmoderated, graphite- and polyethylene-reflected, and polyethylene-moderated HEU metal cylinders had been assembled to obtain delayed criticality at ORCEF in the 1960s and reported by the International Criticality Safety Benchmark Evaluation Project (ICSBEP) at the Nuclear Energy Agency (NEA)*. The data from the nine critical experiments are acceptable for use as criticality safety benchmark experiments for the NEA’s ICSBEP once the uncertainty analysis is completed. Based on previous ICSBEP benchmarks with HEU metal at ORCEF, the uncertainties in k eff are expected to be as low as ±0.0004.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

TEX-Hf Assemblies: Highly Enriched Uranium Plates with Hafnium Using Polyethylene Moderator and Polyethylene Reflector

This report documents the integral experiment evaluation and publication for IER-532 (TEX-Hf), Thermal/Epithermal eXperiments (TEX) with highly enriched uranium (HEU) fuel and hafnium (Hf), moderated and reflected by polyethylene. The design of TEX-Hf is a variation of IER-297 (TEX-HEU), with the inclusion of hafnium as a diluent material. The experiment and evaluation include seven configurations, all of which were acceptable as benchmark cases. These benchmark cases provide validation for hafnium in the thermal, intermediate, and fast neutron energy regimes by maximizing the sensitivity in k eff to the hafnium cross sections. The evaluation was reviewed and accepted by the International Criticality Safety Benchmark Evaluation Project (ICSBEP) Technical Review Group on April 17, 2024, and was submitted to the ICSBEP in August 2024 following subgroup approval.

42 ENGINEERING↗

TEX-Chlorine: Highly Enriched Uranium with Chloride Absorbers to Provide Validation Benchmarks for Y-12 Electrorefining Facility

This report documents the final benchmark of the TEX-Chlorine (IER-499) Thermal Epithermal eXperiments (TEX) with highly enriched uranium with chlorine absorbers and high-density polyethylene reflectors and moderators. TEX-Chlorine is a variation of the TEX-HEU baseline assembly with the addition of sodium chloride absorber plates. This evaluation contains three experimental configurations that were performed on Comet at NCERC between July and August 2024. The three configurations, which were acceptable as benchmark cases, spanned from thermal (first two configurations) to fast (third configuration). All three cases were reviewed and accepted by the ICSBEP TRG in April 2025 and was submitted to the ICSBEP in August 2025 after receiving subgroup approval.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

TEX-Chlorine Assemblies: Highly Enriched Uranium Plates with Sodium Chloride Absorbers Using Polyethylene Moderator and Polyethylene Reflector

This evaluation documents highly enriched uranium (HEU) experimental critical configurations with polyethylene moderators and sodium chloride absorbers conducted as part of the United States Nuclear Criticality Safety Program’s Thermal/Epithermal eXperiments (TEX) program. HEU-MET-MIXED-021 provides the benchmark evaluation of five TEX experiments designed to establish baseline configurations with HEU Jemima plates moderated by high density polyethylene (HDPE). The TEX-HEU experiments were designed to cover five different fission energy regimes by varying the thickness of the interstitial HDPE moderator, with varying fractions of thermal, intermediate, and fast fissions, and to be easily modified to accommodate test materials of interest. HEU-MET-INTER-013 documents the first TEX-HEU variation, incorporating hafnium in seven different experimental configurations. This evaluation covers an additional variant that incorporates absorber plates of compacted high-purity sodium chloride salt. These experiments were motivated by a criticality safety need for validation data for uranium purification by means of electrorefining with chloride salts, especially thermal and intermediate energy configurations resulting from moderator upset conditions, and their design was optimized by matching sensitivity profiles from application cases. All three experimental configurations are judged to be acceptable as benchmark cases. The main parameter varied between the configurations is the thickness of the polyethylene moderators and the sodium chloride absorbers between the HEU plates. Varying the thickness of the polyethylene tunes the neutron energy spectrum between majority thermal (Case 1 and 2) and intermediate (Case 3). The fission fractions, presented in Table 1, are determined calculationally. Case 3 is cross listed as HEU-MET-INTER-014.

42 ENGINEERING↗