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: (1) methods-validation calculations based
on at least one well-documented benchmark problem, and
(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.
3.2Validation—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 Ref 3.2.1Requirements 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,
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
[φ(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-A1, 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 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
(3.2.2.1 For example, model specifications
for discrete-ordinates method on which convergence studies should
be performed include: (1) neutron cross-sections or energy group
structure, (3.2.2.2 Uncertainties that are propagated
from known uncertainties in nuclear data need to be addressed in
the analysis. The uncertainty analysis for discrete ordinates codes
may be performed with sensitivity analysis as discussed in
References 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, and pressure vessel locations, (2) reference case geometry with maximum
and minimum expected deviations in the source distribution, and
(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 (where qi and
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
ε(2) The standard deviation,
S, is less than
ε(3) All absolute values of the
natural logarithmic of the C/E ratios
(q, i = 1 ... (4) ε1, ε2, and ε3 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 3.2.2.8 One acceptable procedure for
performing these comparisons is: (1) obtain group fluence rates at
dosimeter locations from neutronics calculations, (2) collapse the Guide E1018 recommended dosimetry cross section
data to a multigroup set consistent with the neutron energy group
fluence rates or obtain a fine group spectrum (consistent with the
dosimetry cross section data) from the calculated group fluence
rates, (3.3Determination of the Fixed Fission
Source—The power distribution in a typical power 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, 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 Ref 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 Core—The 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 (8)).
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 3.4.1 –3.4.4.
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 power 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 power reactor
dosimetry datum may be discarded if the associated C/E ratios differ substantially from the
average of the applicable C/E ratios and a measurement error can be
suspected. A measurement error can be suspected if the deviation
from the average exceeds the equivalent of three standard
deviations. In addition, the source for power reactor calculations
may be scaled to minimize the bias and variance defined by
Eq 2 and Eq 3 provided that data are not discarded
as a consequence of scaling the source.
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 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.
1.2Methodology—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,
(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 and health practices and determine the
applicability of regulatory requirements prior to use.
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