1、Designation: E482 11Standard Guide forApplication of Neutron Transport Methods for ReactorVessel Surveillance, E706 (IID)1This 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
2、 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 CalculationsAn accurate calcu-lation of the neutron fluence and fluence rate at severallo
3、cations 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-m
4、ents; Guide E944 and Practice E853 define appropriatecomputational procedures.1.2 MethodologyNeutronics calculations for applicationto reactor vessel surveillance encompass three essential areas:(1) validation of methods by comparison of calculations withdosimetry measurements in a benchmark experim
5、ent, (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 therespons
6、ibility 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:2E706 Master Matrix for Light-Water Reactor Pressure Ves-sel Surveillance Standards, E 706(0)E
7、844 Guide for Sensor Set Design and Irradiation forReactor Surveillance, E 706(IIC)E853 Practice for Analysis and Interpretation of Light-Water Reactor Surveillance Results, E706(IA)E944 Guide for Application of Neutron Spectrum Adjust-ment Methods in Reactor Surveillance, E 706 (IIA)E1018 Guide for
8、 Application of ASTM Evaluated CrossSection Data File, Matrix E706 (IIB)E2006 Guide for Benchmark Testing of Light Water Reac-tor Calculations2.2 Nuclear Regulatory Documents:3NUREG/CR-1861 LWR Pressure Vessel Surveillance Do-simetry Improvement Program: PCA Experiments andBlind TestNUREG/CR-3318 LW
9、R 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/
10、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 powe
11、r 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-va
12、lidation 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 modelingparameters kept the
13、 same or as similar as is feasible. Inparticular, the same energy group structure and commonbroad-group microscopic cross sections should be used forboth problems. The neutronics calculations involve two tasks:(1) determination of the neutron source distribution in thereactor core by utilizing diffu
14、sion theory (or transport theory)calculations in conjunction with reactor power distribution1This 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
15、 June 1, 2011. Published June 2011. Originallyapproved in 1976. Last previous edition approved in 2007 as E482 07 DOI:10.1520/E0482-11.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual Book of ASTMStandards volume inf
16、ormation, refer to the standards Document Summary page onthe ASTM website.3Available from Superintendent of Documents, U.S. Government PrintingOffice, Washington, DC 20402.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.measurements,
17、 and (2) performance of a fixed fission rateneutron source (fixed-source) transport theory calculation todetermine 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
18、reactor calculation will differ; therefore, the proce-dures described herein are general and apply to each case. (SeeNUREG/CR5049, NUREG/CR1861, NUREG/CR3318,and NUREG/CR3319.)3.1.2 It is expected that transport calculations will beperformed whenever pressure vessel surveillance dosimetrydata become
19、 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 ValidationPrior to performing transport calculationsfor a particular facility, the computational m
20、ethods 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
21、of the limitingaccuracy of benchmark validation discrete ordinate radiationtransport procedures for the LWR surveillance program isgiven in Reference (1). Reference (2) provides details on thebenchmark validation for a Monte Carlo radiation transportcode.3.2.1 Requirements for BenchmarksIn order for
22、 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
23、, 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 validatio
24、n 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 f(E 1 MeV and0.1 MeV) a
25、nd of displacements per atom (dpa) in iron shouldbe reported consistent with Practices 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 characte
26、rization, 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 and E853 and Guides E844 and E944discuss this criterion.3.2.2
27、Methodology ValidationIt 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
28、 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 o
29、fparticles 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 groupstru
30、cture, (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 alo
31、ng 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 ana
32、lysis 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.43.2.2.3 Effects of known uncertainties in
33、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 so
34、urcedistribution, 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 ass
35、ociated 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 thestructure toleranc
36、es. 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
37、-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 cdenote a set of logarithms of calculation (Ci) to measurement(Ei) ratios. Specifically,4Much of the n
38、uclear covariance and sensitivity data have been incorporated intoa benchmark database employed with the LEPRICON Code system. See Ref (6).E482 112c5$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
39、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 adjustmentmethodolog
40、y, the mean of the set q is given byq 51N(i 5 1Nqi(2)and the best estimate of the variance, S2,isS251N21(i 5 1N 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 1,(2)
41、 The standard deviation, S, is less than 2,(3) All absolute values of the natural logarithmic of theC/E ratios (|q|, i = 1 . N) are less than 3, and(4) 1, 2, and 3are defined by the benchmark measure-ment documentation and demonstrated to be attainable for allitems with which calculations are compar
42、ed.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, equiv
43、alent fis-sion fluence rates, or exposure parameter values for example,f(E 1 MeV) and dpa may be used for validating thecomputational methodology if appropriate criteria (that is, asestablished by 3.2.2.5 and 3.2.2.6) are documented for thebenchmark of interest. Accuracy requirements for reactorvess
44、el 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 fl
45、uence 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
46、 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 SourceThe powerdistribution in a typical power re
47、actor 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. Formultigroup methods, the fixed source may be determined fromthe equationSrg5 xgvPr(4)where:
48、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
49、used. The ratio between fission rate andpower (that is, fission/s per watt) will also vary with burnup.3.3.2 An adjoint procedure may be used as suggested inNUREG/CR-5049 instead of calculation with a time-averagedsource calculation. The influence of changing source distribu-tion is discussed in Reference (7)3.4 Calculation of the Neutron Fluence Rate Based on aFixed Source in the Reactor CoreThe discussion in thissection relates to methods validation calculations and to routinesurveillance calculations. In either case, neutron transportcalculations must
