Keywords: discrete ordinates, dosimetry, exposure parameter, Monte Carlo, neutron fluence, pressure vessel, radiation transport,, ICS Number Code 27.120.20 (Nuclear power plants. Safety)
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Significance and Use
3.1General:
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: (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.
3.2ValidationPrior 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 Reference 3.2.1Requirements for BenchmarksIn
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.
3.2.1.2
Measurements must be reported in at least two ex-core locations,
well separated by steel or coolant.
3.2.1.3
Uncertainty estimates should be reported for dosimetry measurements
and calculated fluences including calculated exposure parameters
and calculated dosimetry 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.
3.2.1.5
Differences between measurements and calculations should be
consistent with the uncertainty estimates in 3.2.1.3.
3.2.1.6
Results for exposure parameter values of neutron fluence greater
than 1 MeV and 0.1 MeV [?(E > 1 MeV and 0.1 MeV)] and of
displacements per atom (dpa) in iron should be reported consistent
with Practices E693 and
E853.
3.2.1.7
Reaction rates (preferably established relative to neutron fluence
standards) must be reported for 237Np(n,f) or
238U(n,f), and 58Ni(n,p) or
54Fe(n,p); additional reactions that aid in spectral
characterization, such as provided by Cu, Ti, and Co-Al, should
also be included in the benchmark measurements. The
237Np(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.
3.2.2Methodology ValidationIt 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:
(3.2.2.1
For example, model specifications for discrete-ordinates method on
which convergence studies should be performed include:
(3.2.2.2
Uncertainties that are propagated from known uncertainties in
nuclear data should be considered in the analysis. The uncertainty
analysis for discrete ordinates codes may be performed with
sensitivity analysis as discussed in References (4, 5). In Monte Carlo analysis the
uncertainties can be treated by a perturbation analysis as
discussed in Reference 3.2.2.3
Effects of known uncertainties in geometry and source distribution
should be evaluated based on the following test cases:
(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 ? denote a set of
logarithms of calculation (Ci) to measurement
(where qi and N are defined implicitly and the
and the best estimate of the variance,
3.2.2.6
The neutronics methodology is validated if (in addition to
qualitative model evaluation) all of the following criteria are
satisfied:
(1) The bias, (q), is less than
?(2) The standard deviation,
S, is less than
?(3) All absolute values of the
natural logarithmic of the C/E ratios
(q), i = 1 ...
N) are less than
?(4) ?1, ?2, and ?3 are defined by the benchmark
measurement documentation and demonstrated to be attainable for all
items with which calculations are compared.
3.2.2.7
Note that a nonzero log-mean of the Ci/Ei ratios indicates that a
bias exists. Possible sources of a bias are: (1) source normalization, (2) neutronics data, (3) transverse leakage corrections (if
applicable), (3.2.2.8
One acceptable procedure for performing these comparisons is:
(3.3Determination of the Fixed Fission
SourceThe power distribution in a typical reactor undergoes
significant change during the life of the reactor. A time-averaged
power distribution is recommended for use in determination of the
neutron source distribution utilized for damage predictions. An
adjoint procedure, described in 3.3.2, may be more appropriate for
dosimetry comparisons involving product nuclides with short
half-lives. For multigroup methods, the fixed source may be
determined from the equation:
3.3.1
Note that in addition to the fission rate, v and xg will vary with fuel burnup,
and a proper time average of these quantities should be used. The
ratio between fission rate and power (that is, fission/s per watt)
will also vary with burnup for any given spatial node.
3.3.2 An
adjoint procedure may be used as suggested in NUREG/CR-5049 instead
of calculation with a time-averaged source calculation.
3.3.2.1
The influence of changing source distribution is discussed in
Reference 3.3.2.2
Care should be exercised to ensure that adjoint calculations
adequately address cycle-to-cycle variations in coolant densities
and any changes to the geometric configuration of the reactor.
3.4Calculation of the Neutron Fluence
Rate Based on a Fixed Source in the Reactor CoreThe
discussion in this section relates to methods validation
calculations and to routine surveillance calculations. In either
case, neutron transport calculations must estimate the neutron
fluence rate in the core, through the internals, in the reactor
pressure vessel, and outside the vessel, if for example, ex-vessel
dosimetry is used. Procedures for methods validation differ very
little from procedures for predicting neutron fluence rate in the
pressure vessel or test facility; consequently, the following
procedure is recommended:
3.4.1
Obtain detailed geometric and composition descriptions of the
material configurations involved in the transport calculation.
Uncertainty in the data should also be estimated.
3.4.2
Obtain applicable cross section sets from appropriate data bases
such as:
3.4.2.1
The evaluated nuclear data file (ENDF/B or its equivalent), or
3.4.2.2
A fine group library obtained by processing the above file (for
example, see Reference 3.4.3
Perform a one-dimensional, fixed-source, fine-group calculation in
order to collapse the fine-group cross sections to a broad-group
set for multidimensional calculations. At least two broad-group
sets are recommended for performing the one-dimensional group
structure convergence evaluation. The broad-group structure should
emphasize the high-energy range and should take cross section
minima of important materials (for example, iron) into
consideration.
3.4.4
Perform the convergence studies outlined in 3.2.2.
3.4.5
Perform two- or three-dimensional fixed-source transport
calculations based on the model established in 3.4.13.4.4.
3.4.6
Compare appropriate dosimetry results with neutronics results from
3.4.5 according to the
procedure given in 3.2.2. It
is recommended that all valid lifetime-accumulated reactor
dosimetry data be included in this comparison each time new data
become available except when dosimeter-specific comparisons are
made.
3.4.7
Repeat appropriate steps if validation criteria are not satisfied.
Note that a reactor dosimetry datum may be discarded if the
associated 3.4.8
Results from neutronics calculations may be used in a variety of
ways:
3.4.8.1
Determine a single normalization constant that minimizes bias in
the calculated values relative to the measurements in order to
scale the group fluences. This is a simple and frequently used
alternative to adjustment procedures. However, the magnitude of
this constant should be critically examined in terms of estimated
source uncertainties.
3.4.8.2
Use a spectrum adjustment procedure as recommended in Guide
E944 using calculated group
fluences and dosimetry data with uncertainty estimates to obtain an
adjustment to the calculated group fluences and exposure
parameters. Predicted pressure vessel fluences could then
incorporate the spectral and normalization data obtained from the
adjusted fluences.
3.4.8.3
Use the calculated fluence spectrum with Practice E693 for damage exposure predictions.
3.4.8.4
It is expected that in some cases the procedure recommended above
will be inconsistent with some methodologies to be validated. In
these cases procedural variations are appropriate but should be
well documented.
1. Scope
1.1Need for Neutronics
CalculationsAn 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.
1.2MethodologyNeutronics
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,
(1.3This 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,
health, and environmental practices and determine the applicability
of regulatory limitations prior to use.
1.4This 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.
Standard Practice for Characterizing
Neutron Exposures in Iron and Low Alloy Steels in Terms of
Displacements Per Atom (DPA)
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