ASTM E482-22

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it may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only the current version
of the standard as published by ASTM is to be considered the official document.
Designation: E482 − 16 E482 − 22
Standard Guide for
Application of Neutron Transport Methods for Reactor
Vessel Surveillance
This standard is issued under the fixed designation E482; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope
1.1 Need for Neutronics Calculations—An accurate calculation of the neutron fluence and fluence rate at several locations is
essential for the analysis of integral dosimetry measurements and for predicting irradiation damage exposure parameter values in
the pressure vessel. Exposure parameter values may be obtained directly from calculations or indirectly from calculations that are
adjusted with dosimetry measurements; Guide E944 and Practice E853 define appropriate computational procedures.
1.2 Methodology—Neutronics calculations for application to reactor vessel surveillance encompass three essential areas: (1)
validation of methods by comparison of calculations with dosimetry measurements in a benchmark experiment, (2) determination
of the neutron source distribution in the reactor core, and (3) calculation of neutron fluence rate at the surveillance position and
in the pressure vessel.
1.3 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility
of the user of this standard to establish appropriate safety safety, health, and healthenvironmental practices and determine the
applicability of regulatory requirementslimitations prior to use.
1.4 This international standard was developed in accordance with internationally recognized principles on standardization
established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued
by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
2. Referenced Documents
2.1 ASTM Standards:
E693 Practice for Characterizing Neutron Exposures in Iron and Low Alloy Steels in Terms of Displacements Per Atom (DPA)
E706 Master Matrix for Light-Water Reactor Pressure Vessel Surveillance Standards
E844 Guide for Sensor Set Design and Irradiation for Reactor Surveillance
E853 Practice for Analysis and Interpretation of Light-Water Reactor Surveillance Neutron Exposure Results
E944 Guide for Application of Neutron Spectrum Adjustment Methods in Reactor Surveillance
E1018 Guide for Application of ASTM Evaluated Cross Section Data File
E2006 Guide for Benchmark Testing of Light Water Reactor Calculations
2.2 Nuclear Regulatory Documents:
NUREG/CR-1861 LWR Pressure Vessel Surveillance Dosimetry Improvement Program: PCA Experiments and Blind Test
This guide is under the jurisdiction of ASTM Committee E10 on Nuclear Technology and Applications and is the direct responsibility of Subcommittee E10.05 on Nuclear
Radiation Metrology.
Current edition approved July 1, 2016July 1, 2022. Published August 2016July 2022. Originally approved in 1976. Last previous edition approved in 20112016 as
ɛ1
E482 – 11E482 – 16. . DOI: 10.1520/E0482-16.10.1520/E0482-22.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM Standards
volume information, refer to the standard’s Document Summary page on the ASTM website.
Available from Superintendent of Documents, U.S. Government Printing Office, Washington, DC 20402.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E482 − 22
NUREG/CR-3318 LWR Pressure Vessel Surveillance Dosimetry Improvement Program: PCA Experiments, Blind Test, and
Physics-Dosimetry Support for the PSF Experiments
NUREG/CR-3319 LWR Pressure Vessel Surveillance Dosimetry Improvement Program: LWR Power Reactor Surveillance
Physics-Dosimetry Data Base Compendium
NUREG/CR-5049 Pressure Vessel Fluence Analysis and Neutron Dosimetry
3. Significance and Use
3.1 General:
3.1.1 The methodology recommended in this guide specifies criteria for validating computational methods and outlines procedures
applicable to pressure vessel related neutronics calculations for test and power reactors. The material presented herein is useful for
validating computational methodology and for performing neutronics calculations that accompany reactor vessel surveillance
dosimetry measurements (see Master Matrix E706 and Practice E853). Briefly, the overall methodology involves: (1)
methods-validation calculations based on at least one well-documented benchmark problem, and (2) neutronics calculations for the
facility of interest. The neutronics calculations of the facility of interest and of the benchmark problem should be performed
consistently, with important modeling parameters kept the same or as similar as is feasible. In particular, the same energy group
structure and common broad-group microscopic cross sections should be used for both problems. Further, the benchmark problem
should be characteristically similar to the facility of interest. For example, a power reactor benchmark should be utilized for power
reactor calculations. Non-power reactors may have special features that may affect pressure vessel fluence and require
consideration when developing a benchmark, such as beam tubes, irradiation facilities, and non-core neutron sources. The
neutronics calculations involve two tasks: (1) determination of the neutron source distribution in the reactor core by utilizing
diffusion theory (or transport theory) calculations in conjunction with reactor power distribution measurements, and (2)
performance of a fixed fission rate neutron source (fixed-source) transport theory calculation to determine the neutron fluence rate
distribution in the reactor core, through the internals and in the pressure vessel. Some neutronics modeling details for the
benchmark, test reactor, or the power reactor calculation will differ; therefore, the procedures described herein are general and
apply to each case. (See NUREG/CR–5049, NUREG/CR–1861, NUREG/CR–3318, and NUREG/CR–3319.)NUREG/CR-5049,
NUREG/CR-1861, NUREG/CR-3318, and NUREG/CR-3319.)
3.1.2 It is expected that transport calculations will be performed whenever pressure vessel surveillance dosimetry data become
available and that quantitative comparisons will be performed as prescribed by 3.2.2. All dosimetry data accumulated that are
applicable to a particular facility should be included in the comparisons.
3.2 Validation—Prior to performing transport calculations for a particular facility, the computational methods must be validated
by comparing results with measurements made on a benchmark experiment. Criteria for establishing a benchmark experiment for
the purpose of validating neutronics methodology should include those set forth in Guides E944 and E2006 as well as those
prescribed in 3.2.1. A discussion of the limiting accuracy of benchmark validation discrete ordinate radiation transport procedures
for the LWR surveillance program is given in RefReference (1). Reference (2) provides details on the benchmark validation for
a Monte Carlo radiation transport code.
3.2.1 Requirements for Benchmarks—In order for a particular experiment to qualify as a calculational benchmark, the following
criteria are recommended:
3.2.1.1 Sufficient information must be available to accurately determine the neutron source distribution in the reactor core,core.
3.2.1.2 Measurements must be reported in at least two ex-core locations, well separated by steel or coolant,coolant.
3.2.1.3 Uncertainty estimates should be reported for dosimetry measurements and calculated fluences including calculated
exposure parameters and calculated dosimetry activities,activities.
3.2.1.4 Quantitative criteria, consistent with those specified in the methods validation 3.2.2, must be published and demonstrated
to be achievable,achievable.
3.2.1.5 Differences between measurements and calculations should be consistent with the uncertainty estimates in 3.2.1.3,.
The boldface numbers in parentheses refer to a list of references at the end of this standard.
E482 − 22
3.2.1.6 Results for exposure parameter values of neutron fluence greater than 1 MeV and 0.1 MeV [φ(E > 1 MeV and 0.1 MeV)]
and of displacements per atom (dpa) in iron should be reported consistent with Practices E693 and E853.
237 238
3.2.1.7 Reaction rates (preferably established relative to neutron fluence standards) must be reported for Np(n,f) or U(n,f),
58 54
and Ni(n,p) or Fe(n,p); additional reactions that aid in spectral characterization, such as provided by Cu, Ti, and Co-A1,Co-Al,
should also be included in the benchmark measurements. The Np(n,f) reaction is particularly important because it is sensitive
to the same neutron energy region as the iron dpa. Practices E693 and E853 and Guides E844 and E944 discuss this criterion.
3.2.2 Methodology Validation—It is essential that the neutronics methodology employed for predicting neutron fluence in a reactor
pressure vessel be validated by accurately predicting appropriate benchmark dosimetry results. In addition, the following
documentation should be submitted: (1) convergence study results, and (2) estimates of variances and covariances for fluence rates
and reaction rates arising from uncertainties in both the source and geometric modeling. For Monte Carlo calculations, the
convergence study results should also include (3) an analysis of the figure-of-merit (FOM) as a function of particles history, and
if applicable, (4) the description of the technique utilized to generate the weight window parameters.
3.2.2.1 For example, model specifications for discrete-ordinates method on which convergence studies should be performed
include: (1) neutron cross-sections cross sections or energy group structure, (2) spatial mesh, and (3) angular quadrature.
One-dimensionalReference (3) evaluates the effects of many discrete-ordinates parameters individually and in combination and
may help guide the analysis. For regions adjacent to the reactor core, one-dimensional calculations may be performed to check the
adequacy of group structure and spatial mesh. Two-dimensional calculations should be employed to check the adequacy of the
angular quadrature. A P cross section expansion is recommended along with a S minimum quadrature. For regions that are not
3 8
adjacent to the reactor core, convergence studies for spatial mesh and angular quadrature should apply three-dimensional
calculations.
3.2.2.2 Uncertainties that are propagated from known uncertainties in nuclear data need to should be addressedconsidered in the
analysis. The uncertainty analysis for discrete ordinates codes may be performed with sensitivity analysis as discussed in
References (34, 45). In Monte Carlo analysis the uncertainties can be treated by a perturbation analysis as discussed in Reference
(56). Appropriate computer programs and covariance data are available and sensitivity data may be obtained as an intermediate
step in determining uncertainty estimates.
3.2.2.3 Effects of known uncertainties in geometry and source distribution should be evaluated based on the following test cases:
(1) reference calculation with a time-averaged source distribution and with best estimates of the core,core and pressure vessel
locations, (2) reference case geometry with maximum and minimum expected deviations in the source distribution, and (3)
reference case source distribution with maximum expected spatial perturbations of the core, pressure vessel, and other pertinent
locations.
3.2.2.4 Measured and calculated integral parameters should be compared for all test cases. It is expected that larger uncertainties
are associated with geometry and neutron source specifications than with parameters included in the convergence study. Problems
associated with space, energy, and angle discretizations can be identified and corrected. Uncertainties associated with geometry
specifications are inherent in the structure tolerances. Calculations based on the expected extremes provide a measure of the
sensitivity of integral parameters to the selected variables. Variations in the proposed convergence and uncertainty evaluations are
appropriate when the above procedures are inconsistent with the methodology to be validated. As-built data could be used to reduce
the uncertainty in geometrical dimensions.
3.2.2.5 In order to illustrate quantitative criteria based on measurements and calculations that should be satisfied, let ψ denote a
set of logarithms of calculation (C ) to measurement (E ) ratios. Specifically,
ii ii
ψ5 q :q 5 w ln C /E , i 5 1…N (1)
$ ~ ! %
i i i i i
where q and N are defined implicitly and the w are weighting factors. Because some reactions provide a greater response over
ii ii
a spectral region of concern than other reactions, weighting factors may be utilized when their selection method is well documented
and adequately defended, such as through a least squares least-squares adjustment method as detailed in Guide E944. In the
absence of the use of a least squares least-squares adjustment methodology, the mean of the set q is given by
N
q¯ 5 q (2)
( i
N
i51
Much of the nuclear covariance and sensitivity data have been incorporated into a benchmark database employed with the LEPRICON Code system. See RefReference
(67).
E482 − 22
and the best estimate of the variance, S , is
N
2 2
S 5 ~ q¯ 2 q ! (3)
( i
N 2 1
i51
3.2.2.6 The neutronics methodology is validated,validated if (in addition to qualitative model evaluation) all of the following
criteria are satisfied:
(1) TheThe bias, |q¯|, is less than ε ,
(2) TheThe standard deviation, S, is less than ε ,
(3) AllAll absolute values of the natural logarithmic of the C/E ratios (|q|, i = 1 . N) are less than ε , and
(4) εε , ε , and ε are defined by the benchmark measurement documentation and demonstrated to be attainable for all items
1 2 3
with which calculations are compared.
3.2.2.7 Note that a nonzero log-mean of the C /E ratios indicates that a bias exists. Possible sources of a bias are: (1) sou
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