1、Designation: E 482 07Standard Guide forApplication of Neutron Transport Methods for ReactorVessel Surveillance, E706 (IID)1This standard is issued under the fixed designation E 482; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, t
2、he year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon (e) 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 severa
3、llocations 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 measur
4、e-ments; Guide E 944 and Practice E 853 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 ex
5、periment, (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 there
6、sponsibility 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:2E 560 Practice for Extrapolating Reactor Vessel Surveil-lance Dosimetry Results, E 706(I
7、C)E 693 Practice for Characterizing Neutron Exposures inIron and Low Alloy Steels in Terms of Displacements PerAtom (DPA), E 706(ID)E 706 Master Matrix for Light-Water Reactor PressureVessel Surveillance Standards, E 706(0)E 844 Guide for Sensor Set Design and Irradiation forReactor Surveillance, E
8、706(IIC)E 853 Practice for Analysis and Interpretation of Light-Water Reactor Surveillance Results, E706(IA)E 944 Guide for Application of Neutron Spectrum Adjust-ment Methods in Reactor Surveillance, E 706 (IIA)E 1018 Guide for Application of ASTM Evaluated CrossSection Data File, Matrix E 706 (IIB
9、)E 2006 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 LWR Pressure Vessel Surveillance Do-simetry Improvement Program: PCA Exp
10、eriments, 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. Signif
11、icance 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 comp
12、utational methodology andfor performing neutronics calculations that accompany reactorvessel surveillance dosimetry measurements (see Master Ma-trix E 706 and Practice E 853). Briefly, the overall methodol-ogy involves: (1) methods-validation calculations based on atleast one well-documented benchma
13、rk problem, and (2) neu-tronics calculations for the facility of interest. The neutronicscalculations on the facility of interest and on the benchmarkproblem should be as nearly the same as is feasible; inparticular, the group structure and common broad-group mi-croscopic cross sections should be pr
14、eserved for both prob-lems. The neutronics calculations involve two tasks: (1)1This 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 June 1, 2007.
15、 Published July 2007. Originally approvedin 1976. Last previous edition approved in 2001 as E 482 01.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual Book of ASTMStandards volume information, refer to the standards D
16、ocument 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.determination of the neutron source distributio
17、n in the reactorcore by utilizing diffusion theory (or transport theory) calcu-lations in conjunction with reactor power distribution measure-ments, and (2) performance of a fixed fission rate neutronsource (fixed-source) transport theory calculation to determinethe neutron fluence rate distribution
18、 in the reactor core, throughthe internals and in the pressure vessel. Some neutronicsmodeling details for the benchmark, test reactor, or the powerreactor calculation will differ; therefore, the procedures de-scribed herein are general and apply to each case. (SeeNUREG/CR5049, NUREG/CR1861, NUREG/C
19、R3318,and NUREG/CR3319.)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
20、facility shouldbe included in the comparisons.3.2 ValidationPrior 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 pu
21、rpose of validating neutronics methodol-ogy should include those set forth in Guides E 944 and E 2006as 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 Reference
22、(1). Reference (2) provides details on thebenchmark validation for a Monte Carlo radiation transportcode.3.2.1 Requirements for BenchmarksIn order for a particu-lar experiment to qualify as a calculational benchmark, thefollowing criteria are recommended:3.2.1.1 Sufficient information must be availa
23、ble 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 ca
24、lculatedexposure 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 u
25、ncertainty 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) and of displacements per atom (dpa) in iron shouldbe reported consistent with Practices E 693 and E 853, and3.2.1.7 Reaction rates (preferably establis
26、hed 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 an import
27、ant reaction since itgives information sensitive to the same energy region as theiron dpa. Practices E 693 and E 853 and Guides E 844 andE 944 discuss this criterion.3.2.2 Methodology ValidationIt is essential that the neu-tronics methodology employed for predicting neutron fluencein a power reactor
28、 pressure vessel be validated by accuratelypredicting appropriate benchmark dosimetry results. In addi-tion, the following documentation should be submitted: (1)convergence study results, and (2) estimates of variances andcovariances for fluences and reaction rates arising from uncer-tainties in bot
29、h the source and geometric modeling. For MonteCarlo calculations, the convergence study results should alsoinclude (3) an analysis of the figure-of-merit (FOM) as afunction of particles history, and if applicable, (4) the techniqueutilized to generate the weight window parameters.3.2.2.1 For example
30、, model specifications for Snmethods onwhich convergence studies should be performed include: (1)group structure, (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 b
31、e employed to check theadequacy of the angular quadrature. A P3cross section expan-sion is recommended along with an 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 ord
32、inate 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, however, and sensitivity data may
33、 be obtained as anintermediate step in determining uncertainty estimates.43.2.2.3 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 c
34、ore, 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
35、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
36、identified and corrected. Uncertaintiesassociated with geometry specifications are inherent in thestructure 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 uncer
37、tainty 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.4Much of the nuclear covariance and sensitivity data have been incorporated intoa benchmark database employ
38、ed with the LEPRICON Code system. See Ref (6).E4820723.2.2.5 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,c5$qi:qi5 wiln Ci/Ei!, i 5 1.N% (1)whe
39、re 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 sq
40、uares adjustment method as detailed in Guide E 944.In the absence of the use of a least squares adjustmentmethodology, 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 (inadditi
41、on to qualitative model evaluation) all of the followingcriteria are satisfied:(1) The bias, | q |, is less than e1,(2) The standard deviation, S, is less than e2,(3) All absolute values of log C/E ratios (| q |, i = 1 . N)are less than e3, and(4) e1, e2, and e3are defined by benchmark measurementdo
42、cumentation and demonstrated to be attainable for all itemswith 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, (4)
43、geometric modeling, and (5) mathematicalapproximations. Reaction rates, equivalent fission fluencerates, or exposure parameter values for example, f(E 1MeV) and dpa may be used for validating the computationalmethodology if appropriate criteria (that is, as established by )are documented for the ben
44、chmark of interest. Accuracyrequirements for reactor vessel surveillance specific bench-mark validation procedures are discussed in Guide E 2006. Thevalidation testing for the generic discrete ordinate and MonteCarlo transport methods is discussed in References (1, 2).3.2.2.8 One acceptable procedur
45、e for performing these com-parisons is: (1) obtain group fluence rates at dosimeter loca-tions from neutronics calculations, (2) collapse the GuideE 1018 recommended dosimetry cross section data to a multi-group set consistent with the neutron energy group fluencerates or obtain a fine group spectru
46、m (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 Fix
47、ed Fission SourceThe 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. Formultigroup methods, the fixed
48、source may be determined fromthe equationSrg5 xgvPr(4)where:r = a spatial node,g = an energy group,v = the average number of neutrons per fission,xg= the fraction of the fission spectrum in group g, andPr= the fission rate in node r.3.3.1 Note that in addition to the fission rate, v and xgwillvary w
49、ith fuel burnup, and a proper time average of thesequantities should be 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
