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Presentation topics include: Criticality Calculations with MCNP6.2 Results Compared with Experiments and Criticality Accident Alarm System (CAAS) Analysis with MCNP6.2 Results using Hybrid Geometry and Varian Reduction.
In criticality calculations, the effective multiplication factor (k{sub eff}) is an important parameter for reactor analysis. It can be interpreted as the ratio of the neutron production rate to the loss rate in a reactor core. In Monte Carlo (MC) criticality calculations, k{sub eff} is obtained for each active cycle i as: k-i = P{sub i}/L{sub i} for I = 1 to I where P{sub i} and L{sub i} are the production rate and the loss rate at cycle i, respectively, and they are normalized by the nominal source size for cycle. Since all neutron particles in a cycle will be absorbed or leaks out at the end, the loss rate, L{sub i}, can be set as the source rate, which is the unity. Thus, in MCNP5, k{sub i} is simply calculated with P{sub i} by using three conventional estimators; collision, absorption, and track-length estimators. In domain decomposed MC criticality calculations based on the fission and surface source (FSS) iteration method, k{sub i} is calculated by a ratio of P{sub i} and L{sub i}, where both P{sub i} and L{sub i} are random variables, sampled by using the same particle histories. When the numerator and the denominator are correlated, the variance of the ratio can be smaller than that of the numerator. Then, the final estimate of k{sub eff} is provided as the sample mean of k{sub i}, which will be referred as 'simple' ratio estimator in this paper. In Ref., it is shown that this ratio estimator converges faster and fluctuates less than the conventional estimator. A similar ratio estimator is also used in Serpent 2, as an implicit estimate of k{sub eff}. However, this type of 'simple' ratio estimator is biased, which means that the expectation of the ratio is different from the ratio of the expectation of the numerator and that of the denominator. In this paper, an unbiased ratio estimator which was originally derived in the cytometry analysis is introduced to estimate k{sub eff} and is tested on a continuous-energy UO{sub 2} pin-cell problem. In this test problem, it is shown that the variance of the unbiased ratio estimator is smaller than those of the conventional estimators provided by MCNP5, while the simple ratio estimator can be significantly biased when the number of histories per cycle is too small. (authors)
Within the framework of the IAEA Coordinated Research Project on HTGR Uncertainty Analysis in Modeling, criticality calculations of the Very High Temperature Critical Assembly experiment were performed as the validation reference to the prismatic MHTGR-350 lattice calculations. Criticality measurements performed at several temperature points at this Japanese graphite-moderated facility were recently included in the International Handbook of Evaluated Reactor Physics Benchmark Experiments and represent one of the few data sets available for the validation of HTGR lattice physics. Here, this work compares VHTRC criticality simulations utilizing the Monte Carlo codes Serpent and SCALE/KENO-VI. Reasonable agreement was found between Serpent and KENO-VI, but only the use of the latest ENDF cross section library release, namely the ENDF/B-VII.1 library, led to an improved match with the measured data. Furthermore, the fourth beta release of SCALE 6.2/KENO-VI showed significant improvements from the current SCALE 6.1.2 version, compared to the experimental values and Serpent.
This paper examines the prerequisites and boundary conditions for extending burnup credit from pressurized water reactors to boiling water reactors with validated depletion codes by performing uncertainty and sensitivity analyses on a modern boiling water reactor fuel assembly design. We developed a computational chain consisting of an axial boiling water reactor axial irradiation model, followed by a series of depletion calculations and a three-dimensional criticality calculation. The irradiation model puts into relation the profiles of power, burnup and moderator density of the fuel assembly at 24 axial locations. In a simplified fashion it also includes the insertion of control blades. The depletion calculations of the fuel assembly were performed in axial slices with the 2D-depletion code HELIOS 1.12. The criticality calculations were done in 3D-geometry with KENO-Va from the SCALE 6.2.1 package, in which several fuel assemblies are placed into a generic transport cask. For the uncertainty and sensitivity analyses a Monte Carlo sampling based approach is used applying the GRS tool SUnCISTT. We performed several generic investigations testing the capabilities and the limitations of the whole computational chain. The impact of variations of the irradiation model on the resulting reactivity of the fuel assemblies inside a transport cask or storage pool was investigated using an uncertainty and sensitivity analysis on the whole computational chain. Geometrical uncertainties were also included in the evaluation and a parameter study on the use of control blades during irradiation was performed. The goal was to develop the procedures and tools to be able to obtain quantitative uncertainty data which can be used in the future to derive conservative irradiation profiles without unnecessary excess reactivity margins. (authors)
For the past 40 years, it has been known from the theoretical work of Gelbard [1] and Brissenden [2] that the results from Monte Carlo (MC) criticality calculations are biased if the number of neutrons per generation is not sufficiently large. The computed k-effective eigenvalue will be lower than the actual eigenvalue, and the computed eigenfunction will be too low in high-importance regions and too high in low-importance regions. This difficulty is commonly called the undersampling problem for criticality calculations. The biases for undersampling were confirmed for practical, realistic problems with modern MC codes by Brown [3]. The solution to undersampling is simple - use a larger number of neutrons per generation to reduce the biases to levels that are negligible. Over the past few years, the OECD-NEA-WPNCS Expert Group on Advanced Monte Carlo Techniques (EGAMCT) [4,5,6] investigated an extreme form of undersampling called clustering. When the number of neutrons per generation is small, neutrons in successive generations tend to group together (cluster) due to correlations, and the clusters tend to migrate through the problem space. While the problems of undersampling and clustering are well known and well understood theoretically, there were no existing diagnostics for MC codes to determine whether a given calculation is using sufficient neutrons per generation to eliminate these problems. That is, no tools were available to diagnose biases due to undersampling or clustering. The tools described herein resolve this longstanding problem by providing 2 robust methods for detecting undersampling and clustering in MC criticality calculations. The diagnosis of undersampling and clustering is part of a larger effort to thoroughly overhaul the calculational methods for criticality problems, providing for automated sampling of the initial fission distribution, acceleration of the iteration convergence process, automated detection of convergence in the iterations and starting of the active tally cycles, and the diagnosis of undersampling. All of these new methods have been prototyped in a local modified version of mcnp6.2 [7] and tested on a variety of critical systems.
A new version of the CRISTAL criticality calculation package, named CRISTAL V2.0 [1], has been developed by IRSN and CEA, in collaboration with AREVA and EDF. Four calculation routes are now available, using nuclear data issued from the JEFF-3.1.1 evaluation: two multigroup routes based on 281 groups cross-sections (APOLLO2 - MORET 5 or APOLLO2-Sn calculations), a pointwise Monte Carlo route (TRIPOLI-4{sup R}) and a criticality standard calculation route. The CRISTAL V2.0 package, which will be delivered soon to OECD/NEA data bank, benefits from a broad validation database covering almost all areas of criticality-safety applications, from fuel fabrication to reprocessing, including transportation. 3,127 critical experiments, corresponding to 342 series, either issued from the OECD/ICSBEP Handbook or performed in French facilities (confidential data) were selected for the CRISTAL V2.0 validation database. Currently, more than 2,300 experiments are already part of the validation database. This validation work highlights an overall consistency to experimental data and inter-comparisons between the different calculation routes mainly show good agreements on a large set of common experiments. (authors)
SCALE 6.2 provides enhancements for criticality calculations relative to SCALE 6.1, especially with updated nuclear data libraries, resonance self-shielding options for multigroup (MG) calculations, and problem-dependent temperature treatments for continuous-energy (CE) calculations. Benchmark experiments from the International Criticality Safety Benchmark Evaluation Project that are available in the Oak Ridge National Laboratory Verified, Archived, Library of Inputs and Data (VALID) were applied in this validation effort to examine the impact of the SCALE 6.2 enhancements. Over 300 cases are drawn from the VALID library for testing KENO V.a, and a more limited set of approximately 50 configurations is used for validation of KENO-VI. A total of 401 unique critical experiments are used in this validation effort. In some cases, the KENO V.a models were converted to KENO-VI models so that the performance of both codes could be assessed for the same systems. Validation results for the SCALE 6.2 ENDF/B-VII.1 nuclear data libraries are presented, including MG neutron data in 56- and 252-group structures as well as CE data. The performance of all three multipurpose neutron libraries in calculating k{sub eff} is examined with critical experiment models covering a wide range of fuels, moderators, reflectors, absorbers, and neutron spectra. The SCALE 6.2 ENDF/B-VII.1 coupled neutron-photon library, primarily developed for shielding applications with 200 neutron groups and 47 gamma groups, provides additional energy resolution for fast systems relative to the MG neutron libraries which were developed to produce low biases for thermal neutron systems. The applicability of this library to criticality calculations for fast neutron spectrum systems is not investigated here but will be addressed in the final SCALE 6.2 validation report. The results of these calculations demonstrate that SCALE 6.2 generally provides lower biases than SCALE 6.1 and that the two versions of KENO provide equivalent results on the same suite of problems. SCALE 6.2 also includes an updated neutron cross-section covariance library based on the ENDF/B-VII.1 covariance data. The effect of these updated covariances on the uncertainty in k{sub eff} due to cross section uncertainties is also presented for some cases. A more thorough investigation of the updated covariance data is presented in a companion paper. (authors)
A new release of the CRISTAL French criticality calculation package, named CRISTAL V2, has been developed and intensively validated by IRSN and CEA, in collaboration with AREVA. This package was designed to cover the needs of criticality practitioners in the fields of nuclear fuel cycle facilities and transportation of fissile materials. Based on an optimized modular architecture in an updated software development environment, the design of CRISTAL package V2 integrates new generation of cross-section libraries, new calculation schemes consistent with new applications, and up-to-date calculation codes capabilities. Four calculation routes are currently available allowing multi-group and continuous energy calculations. The validation database is composed of more than 3000 critical experiments, in order to cover a wide range of configurations. The CRISTAL V2 package also includes customer services covering a large scope of activities like documentations, hotline, maintenance and training courses. A significant promotion and an increased recognition referred both nationally and internationally are foreseen, including the provision of the CRISTAL V2 package to the OECD / NEA Data Bank. (authors)
These slides are used to teach MCNP (Monte Carlo N-Particle) usage to nuclear criticality safety analysts. The following are the lecture topics: course information, introduction, MCNP basics, criticality calculations, advanced geometry, tallies, adjoint-weighted tallies and sensitivities, physics and nuclear data, parameter studies, NCS validation I, NCS validation II, NCS validation III, case study 1 - solution tanks, case study 2 - fuel vault, case study 3 - B&W core, case study 4 - simple TRIGA, case study 5 - fissile mat. vault, criticality accident alarm systems. After completion of this course, you should be able to: Develop an input model for MCNP; Describe how cross section data impact Monte Carlo and deterministic codes; Describe the importance of validation of computer codes and how it is accomplished; Describe the methodology supporting Monte Carlo codes and deterministic codes; Describe pitfalls of Monte Carlo calculations; Discuss the strengths and weaknesses of Monte Carlo and Discrete Ordinants codes; The diffusion theory model is not strictly valid for treating fissile systems in which neutron absorption, voids, and/or material boundaries are present. In the context of these limitations, identify a fissile system for which a diffusion theory solution would be adequate.
There is a very strong need for statistical testing to determine fission source convergence in Monte Carlo criticality calculations. Automation of such tests will greatly streamline and support the work carried out by NCS practitioners. Recent R&D work has shown that no single statistical test for convergence is sufficiently reliable, robust, and “guaranteed.” However, a combination of several standard statistical tests for the similarity of distributions, coupled with a high-fidelity estimate of the fission-matrix source is sufficiently robust, reliable, and repeatable that convergence can be “guaranteed.” During the course of the EG-AMCT studies, a number of statistical metrics and tests were proposed for diagnosing clustering and undersampling. None of these was robust and reliable enough for practical use in production codes. However, the expert group efforts came close. Some recent R&D work stemming from those past efforts has been very successful and promising. This Sub-Group will provide international input and collaboration on the development and implementation of statistical tests for convergence, with the primary goal of having the MC codes automatically detect convergence (or lack thereof). Newly proposed statistical tests to detect undersampling (after convergence) will also be reviewed.
This report describes methods for using statistical tests to automatically determine convergence of Monte Carlo (MC) iterations in criticality calculations. The methods described herein are intended to replace the traditional approach used for the past 60 years: make a trial run; determine convergence based on plots of k-effective and Shannon entropy vs cycle; adjust the input parameters for controlling the iterations; make a final run to obtain results and statistics.
Simulation of boiling water reactor (BWR) fuel depletion poses a challenge for nuclide inventory validation and nuclear criticality safety analyses. This challenge is due to the complex operating conditions and assembly design heterogeneities that characterize these nuclear systems. Fuel depletion simulations and in-cask criticality calculations are affected by (1) completeness of design information, (2) variability of operating conditions needed for modeling purposes, and (3) possible modeling choices. These effects must be identified, quantified, and ranked according to their significance. This paper presents an investigation of BWR fuel depletion using a complete set of actual design specifications and detailed operational data available for five operating cycles of the Swedish BWR Forsmark 3 reactor. The data includes detailed axial profiles of power, burnup, and void fraction in a very fine temporal mesh for a GE14 (10x10) fuel assembly. The specifications of this case can be used to assess the impacts of different modeling choices on inventory prediction and in-cask criticality, specifically regarding the key parameters that drive inventory and reactivity throughout fuel burnup. This study focused on the effects of the fidelity with which power history and void fraction distributions are modeled. The corresponding sensitivity of the reactivity in storage configurations is assessed, and the impacts of modeling choices on decay heat and inventory are addressed. (authors)
A 3D model of the Missouri S and T Research Reactor (MSTR) was developed using SCALE-6.2.2 in this study. The criticality calculation of MSTR was modeled with the CSAS6/KENO-VI sequence within the SCALE-6.2.2 package. The critical control rods height was predicted, and the criticality was achieved when the control rod withdrawn 22.25 in with the k{sub eff} value of 1.0001±0.00083. Then, the neutron source distribution of the critical core was used as a mesh source for the shielding analysis. The shielding analysis was performed using a flexible MAVRIC/FW-CADIS model of the MSTR that could perform and analyze deep penetration shielding problems. (authors)
The increasing integration of renewable energy sources in modern power systems has led to a decline in system inertia, raising concerns about frequency stability following large disturbances. Determining critical inertia is essential to prevent excessive frequency decline and ensure grid stability. This paper evaluates four different methods for calculating critical inertia, using the Electric Reliability Council of Texas (ERCOT) system as a test case. The results highlight the importance of employing multiple methodologies to capture the full spectrum of inertia requirements.
Criticality studies need several calculations with small variations in a number of parameters. Therefore, a calculation package written at VTT in order to facilitate sensitivity studies in criticality calculations was used. This package is based on MCNP5 [1], and consists of a data transfer and analysis program written in Perl, and a set of pseudo inputs for the transport and storage systems including the fuel assembly. The pseudo inputs contain key words that are replaced by a given value for the specific parameter. In this paper, the package is described in more detail including the new modifications needed for this study. The usability will be demonstrated with a study of the fuel pool in the case of steam gathered under the support plates of the pool. In the new pool model the steam layer was added as a water layer with a very low density. The density of this layer, i.e. the steam density, could be varied as well as the thickness of the layer. This package was then used to study the reactivity effect of the moderator density, the steam density and the thickness of the steam layer. As can be expected the strongest effect was obtained with the moderator density. However, the steam density seemed not to affect the reactivity while the thickness of the layer had a small effect. (author)
The US Nuclear Regulatory Commission (NRC) Division of Spent Fuel Storage and Transportation issued Interim Staff Guidance (ISG) 8, Revision 3 in September 2012. This ISG provides guidance for NRC staff members' review of burnup credit (BUC) analyses supporting transport and dry storage of pressurized water reactor spent nuclear fuel (SNF) in casks. The ISG includes guidance for addressing validation of criticality (k{sub eff}) calculations crediting the presence of a limited set of fission products and minor actinides (FP and MAs). Based on previous work documented in NRC Regulatory Guide (NUREG) Contractor Report (CR)-7109, the ISG recommends that NRC staff members accept the use of either 1.5 or 3% of the FP and MA worth - in addition to bias and bias uncertainty resulting from validation of k{sub eff} calculations for the major actinides in SNF - to conservatively account for the bias and bias uncertainty associated with the specified unvalidated FP and MAs. The ISG recommends (1) use of 1.5% of the FP and MA worth if a modern version of SCALE and its nuclear data are used and (2) 3% of the FP and MA worth for well qualified, industry standard code systems other than SCALE with the Evaluated Nuclear Data Files, Part B (ENDF/B),-V, ENDF/B-VI, or ENDF/B-VII cross sections libraries. The work presented in this paper provides a basis for extending the use of the 1.5% of the FP and MA worth bias to BUC criticality calculations performed using the Monte Carlo N-Particle (MCNP) code. The extended use of the 1.5% FP and MA worth bias is shown to be acceptable by comparison of FP and MA worths calculated using SCALE and MCNP with ENDF/B-V, -VI, and -VII-based nuclear data. The comparison supports use of the 1.5% FP and MA worth bias when the MCNP code is used for criticality calculations, provided that the cask design is similar to the hypothetical generic BUC-32 cask model and that the credited FP and MA worth is no more than 0.1 Δk{sub eff} (ISG-8, Rev. 3, Recommendation 4). (authors)
This report provides an MCNP ® input file for a k-eigenvalue (kcode) calculation of the Oak Ridge National Laboratory (ORNL) Pool Critical Assembly (PCA). That is, this report provides the input file used for the first of the calculations described to produce a fission source term for the ORNL PCA.
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