# ASTM E482-16

Designation: E482 − 16Standard Guide forApplication of Neutron Transport Methods for ReactorVessel Surveillance1This standard is issued under the fixed designation E482; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon (´) indicates an editorial change since the last revision or reapproval.1. Scope1.1 Need for Neutronics Calculations—An accurate calcu-lation of the neutron fluence and fluence rate at severallocations is essential for the analysis of integral dosimetrymeasurements and for predicting irradiation damage exposureparameter values in the pressure vessel. Exposure parametervalues may be obtained directly from calculations or indirectlyfrom calculations that are adjusted with dosimetry measure-ments; Guide E944 and Practice E853 define appropriatecomputational procedures.1.2 Methodology—Neutronics calculations for applicationto reactor vessel surveillance encompass three essential areas:(1) validation of methods by comparison of calculations withdosimetry measurements in a benchmark experiment, (2)determination of the neutron source distribution in the reactorcore, and (3) calculation of neutron fluence rate at the surveil-lance position and in the pressure vessel.1.3 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibility of the user of this standard to establish appro-priate safety and health practices and determine the applica-bility of regulatory requirements prior to use.2. Referenced Documents2.1 ASTM Standards:2E693 Practice for Characterizing Neutron Exposures in Ironand Low Alloy Steels in Terms of Displacements PerAtom (DPA), E 706(ID)E706 Master Matrix for Light-Water Reactor Pressure VesselSurveillance Standards, E 706(0) (Withdrawn 2011)3E844 Guide for Sensor Set Design and Irradiation forReactor Surveillance, E 706 (IIC)E853 Practice for Analysis and Interpretation of Light-WaterReactor Surveillance ResultsE944 Guide for Application of Neutron Spectrum Adjust-ment Methods in Reactor Surveillance, E 706 (IIA)E1018 Guide for Application of ASTM Evaluated CrossSection Data File, Matrix E706 (IIB)E2006 Guide for Benchmark Testing of Light Water ReactorCalculations2.2 Nuclear Regulatory Documents:4NUREG/CR-1861 LWR Pressure Vessel Surveillance Do-simetry Improvement Program: PCA Experiments andBlind TestNUREG/CR-3318 LWR Pressure Vessel Surveillance Do-simetry Improvement Program: PCA Experiments, BlindTest, and Physics-Dosimetry Support for the PSF Experi-mentsNUREG/CR-3319 LWR Pressure Vessel Surveillance Do-simetry Improvement Program: LWR Power Reactor Sur-veillance Physics-Dosimetry Data Base CompendiumNUREG/CR-5049 Pressure Vessel Fluence Analysis andNeutron Dosimetry3. Significance and Use3.1 General:3.1.1 The methodology recommended in this guide specifiescriteria for validating computational methods and outlinesprocedures applicable to pressure vessel related neutronicscalculations for test and power reactors. The material presentedherein is useful for validating computational methodology andfor performing neutronics calculations that accompany reactorvessel surveillance dosimetry measurements (see Master Ma-trix E706 and Practice E853). Briefly, the overall methodologyinvolves: (1) methods-validation calculations based on at leastone well-documented benchmark problem, and (2) neutronicscalculations for the facility of interest. The neutronics calcula-tions of the facility of interest and of the benchmark problemshould be performed consistently, with important modeling1This guide is under the jurisdiction of ASTM Committee E10 on NuclearTechnology and Applications and is the direct responsibility of SubcommitteeE10.05 on Nuclear Radiation Metrology.Current edition approved July 1, 2016. Published August 2016. Originallyapproved in 1976. Last previous edition approved in 2011 as E482 – 11ɛ1. DOI:10.1520/E0482-16.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at service@astm.org. For Annual Book of ASTMStandards volume information, refer to the standard’s Document Summary page onthe ASTM website.3The last approved version of this historical standard is referenced onwww.astm.org.4Available from Superintendent of Documents, U.S. Government PrintingOffice, Washington, DC 20402.Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States1parameters kept the same or as similar as is feasible. Inparticular, the same energy group structure and commonbroad-group microscopic cross sections should be used forboth problems. Further, the benchmark problem should becharacteristically similar to the facility of interest. Forexample, a power reactor benchmark should be utilized forpower reactor calculations. The neutronics calculations involvetwo tasks: (1) determination of the neutron source distributionin the reactor core by utilizing diffusion theory (or transporttheory) calculations in conjunction with reactor power distri-bution measurements, and (2) performance of a fixed fissionrate neutron source (fixed-source) transport theory calculationto determine the neutron fluence rate distribution in the reactorcore, through the internals and in the pressure vessel. Someneutronics modeling details for the benchmark, test reactor, orthe power reactor calculation will differ; therefore, the proce-dures described herein are general and apply to each case. (SeeNUREG/CR–5049, NUREG/CR–1861, NUREG/CR–3318,and NUREG/CR–3319.)3.1.2 It is expected that transport calculations will beperformed whenever pressure vessel surveillance dosimetrydata become available and that quantitative comparisons willbe performed as prescribed by 3.2.2. All dosimetry dataaccumulated that are applicable to a particular facility shouldbe included in the comparisons.3.2 Validation—Prior to performing transport calculationsfor a particular facility, the computational methods must bevalidated by comparing results with measurements made on abenchmark experiment. Criteria for establishing a benchmarkexperiment for the purpose of validating neutronics methodol-ogy should include those set forth in Guides E944 and E2006as well as those prescribed in 3.2.1.Adiscussion of the limitingaccuracy of benchmark validation discrete ordinate radiationtransport procedures for the LWR surveillance program isgiven in Ref (1). Reference (2) provides details on thebenchmark validation for a Monte Carlo radiation transportcode.3.2.1 Requirements for Benchmarks—In order for a particu-lar experiment to qualify as a calculational benchmark, thefollowing criteria are recommended:3.2.1.1 Sufficient information must be available to accu-rately determine the neutron source distribution in the reactorcore,3.2.1.2 Measurements must be reported in at least twoex-core locations, well separated by steel or coolant,3.2.1.3 Uncertainty estimates should be reported for dosim-etry measurements and calculated fluences including calculatedexposure parameters and calculated dosimetry activities,3.2.1.4 Quantitative criteria, consistent with those specifiedin the methods validation 3.2.2, must be published and dem-onstrated to be achievable,3.2.1.5 Differences between measurements and calculationsshould be consistent with the uncertainty estimates in 3.2.1.3,3.2.1.6 Results for exposure parameter values of neutronfluence greater than 1 MeV and 0.1 MeV [φ(E 1 MeV and 0.1MeV)] and of displacements per atom (dpa) in iron should bereported consistent with Practices E693 and E853.3.2.1.7 Reaction rates (preferably established relative toneutron fluence standards) must be reported for237Np(n,f) or238U(n,f), and58Ni(n,p) or54Fe(n,p); additional reactions thataid in spectral characterization, such as provided by Cu, Ti, andCo-A1, should also be included in the benchmark measure-ments. The237Np(n,f) reaction is particularly important be-cause it is sensitive to the same neutron energy region as theiron dpa. Practices E693 and E853 and Guides E844 and E944discuss this criterion.3.2.2 Methodology Validation—It is essential that the neu-tronics methodology employed for predicting neutron fluencein a reactor pressure vessel be validated by accurately predict-ing appropriate benchmark dosimetry results. In addition, thefollowing documentation should be submitted: (1) convergencestudy results, and (2) estimates of variances and covariancesfor fluence rates and reaction rates arising from uncertainties inboth the source and geometric modeling. For Monte Carlocalculations, the convergence study results should also include(3) an analysis of the figure-of-merit (FOM) as a function ofparticles history, and if applicable, (4) the description of thetechnique utilized to generate the weight window parameters.3.2.2.1 For example, model specifications for discrete-ordinates method on which convergence studies should beperformed include: (1) neutron cross-sections or energy groupstructure, (2) spatial mesh, and (3) angular quadrature. One-dimensional calculations may be performed to check theadequacy of group structure and spatial mesh. Two-dimensional calculations should be employed to check theadequacy of the angular quadrature. A P3cross section expan-sion is recommended along with a S8minimum quadrature.3.2.2.2 Uncertainties that are propagated from known un-certainties in nuclear data need to be addressed in the analysis.The uncertainty analysis for discrete ordinates codes may beperformed with sensitivity analysis as discussed in References(3, 4). In Monte Carlo analysis the uncertainties can be treatedby a perturbation analysis as discussed in Reference (5).Appropriate computer programs and covariance data are avail-able and sensitivity data may be obtained as an intermediatestep in determining uncertainty estimates.53.2.2.3 Effects of known uncertainties in geometry andsource distribution should be evaluated based on the followingtest cases: (1) reference calculation with a time-averagedsource distribution and with best estimates of the core, andpressure vessel locations, (2) reference case geometry withmaximum and minimum expected deviations in the sourcedistribution, and (3) reference case source distribution withmaximum expected spatial perturbations of the core, pressurevessel, and other pertinent locations.3.2.2.4 Measured and calculated integral parameters shouldbe compared for all test cases. It is expected that largeruncertainties are associated with geometry and neutron sourcespecifications than with parameters included in the conver-gence study. Problems associated with space, energy, and anglediscretizations can be identified and corrected. Uncertaintiesassociated with geometry specifications are inherent in the5Much of the nuclear covariance and sensitivity data have been incorporated intoa benchmark database employed with the LEPRICON Code system. See Ref (6).E482 − 162structure tolerances. Calculations based on the expected ex-tremes provide a measure of the sensitivity of integral param-eters to the selected variables. Variations in the proposedconvergence and uncertainty evaluations are appropriate whenthe above procedures are inconsistent with the methodology tobe validated. As-built data could be used to reduce theuncertainty in geometrical dimensions.3.2.2.5 In order to illustrate quantitative criteria based onmeasurements and calculations that should be satisfied, let ψdenote a set of logarithms of calculation (Ci) to measurement(Ei) ratios. Specifically,ψ 5 $qi:qi5 wiln~Ci/Ei!, i 5 1…N% (1)where qiand N are defined implicitly and the wiareweighting factors. Because some reactions provide a greaterresponse over a spectral region of concern than other reactions,weighting factors may be utilized when their selection methodis well documented and adequately defended, such as througha least squares adjustment method as detailed in Guide E944.In the absence of the use of a least squares adjustmentmethodology, the mean of the set q is given byq¯ 51N(i51Nqi(2)and the best estimate of the variance, S2,isS251N 2 1(i51N~ q¯ 2 qi!2(3)3.2.2.6 The neutronics methodology is validated, if (inaddition to qualitative model evaluation) all of the followingcriteria are satisfied:(1) The bias, |q¯|, is less than ε1,(2) The standard deviation, S, is less than ε2,(3) All absolute values of the natural logarithmic of theC/E ratios (|q|, i = 1 . N) are less than ε3, and(4) ε1, ε2, and ε3are defined by the benchmark measure-ment documentation and demonstrated to be attainable for allitems with which calculations are compared.3.2.2.7 Note that a nonzero log-mean of the Ci/Eiratiosindicates that a bias exists. Possible sources of a bias are: (1)source normalization, (2) neutronics data, (3) transverse leak-age corrections (if applicable), (4) geometric modeling, and (5) mathematical approximations. Reaction rates, equivalentfission fluence rates, or exposure parameter values [forexample, φ(E 1 MeV) and dpa] may be used for validatingthe computational methodology if appropriate criteria (that is,as established by 3.2.2.5 and 3.2.2.6) are documented for thebenchmark of interest. Accuracy requirements for reactorvessel surveillance specific benchmark validation proceduresare discussed in Guide E2006. The validation testing for thegeneric discrete ordinates and Monte Carlo transport methodsis discussed in References (1, 2).3.2.2.8 One acceptable procedure for performing these com-parisons is: (1) obtain group fluence rates at dosimeter loca-tions from neutronics calculations, (2) collapse the GuideE1018 recommended dosimetry cross section data to a multi-group set consistent with the neutron energy group fluencerates or obtain a fine group spectrum (consistent with thedosimetry cross section data) from the calculated group fluencerates, (3) fold the energy group fluence rates with the appro-priate cross sections, and (4) compare the calculated andexperimental data according to the specified quantitative crite-ria.3.3 Determination of the Fixed Fission Source—The powerdistribution in a typical power reactor undergoes significantchange during the life of the reactor. A time-averaged powerdistribution is recommended for use in determination of theneutron source distribution utilized for damage predictions. Anadjoint procedure, described in 3.3.2, may be more appropriatefor dosimetry comparisons involving product nuclides withshort half-lives. For multigroup methods, the fixed source maybe determined from the equation:Srg5 xgv¯Pr(4)where:r = a spatial node,g = an energy group,v¯ = average number of neutrons per fission,xg= fraction of the fission spectrum in group g, andPr= fission rate in node r.3.3.1 Note that in addition to the fission rate, v¯ and xgwillvary with fuel burnup, and a proper time average of thesequantities should be used. The ratio between