ML19189A111

Final Safety Evaluation for EPRI Topical Reports 3002010613 and 3002010614

ML19189A111
Person / Time
Site:	Nuclear Energy Institute, 99902028
Issue date:	02/07/2019
From:	Dennis Morey NRC/NRR/DLP/PLPB
To:	Mccullum R Nuclear Energy Institute
Drake J, NRR/DLP/PLPB, 415-8378
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ML19168A097	List: ML19189A111 ML19189A112 ML19196A273 ML19196A274 ML19196A275 ML19196A276 ML19196A277 ML19196A302
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3002010613, 3002010614
Download: ML19189A111 (36)

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FINAL SAFETY EVALUATION BY THE OFFICE OF NUCLEAR REACTOR REGULATION TOPICAL REPORT 3002010613, BENCHMARKS FOR QUALIFYING FUEL REACTIVITY DEPLETION UNCERTAINTYREVISION 1 AND TOPICAL REPORT 3002010614, UTILIZATION OF THE EPRI DEPLETION BENCHMARKS FOR BURNUP CREDIT VALIDATIONREVISION 1 PROJECT NO. 689/DOCKET NO. 99902028

1.0 INTRODUCTION

In a letter dated January 3, 2013 (NEI, 2013a), the Director of Used Fuel Programs at the Nuclear Energy Institute (NEI) requested an exemption from the U.S. Nuclear Regulatory Commission (NRC) fees to review NEI 12-16, Guidance for Performing Criticality Analyses of Fuel Storage at Light-Water Reactor Power Plants, Revision 0 (NEI 2013b). The letter states:

NEI 12-16 provides guidance for performing criticality analyses at light water reactor power plants in accordance with 10 CFR [Title 10 to the Code of Federal Regulations] 50.68 and 10 CFR Part 50, Appendix A, GDC 62. As a means to achieve regulatory efficiency and effectiveness, we recommend that the NRC review NEI 12-16 for potential endorsement through a Regulatory Guide. This proposal would fulfill the need for more durable guidance identified in the NRC/NRR Action Plan, On Site Spent Fuel Criticality Analyses, as updated May 19, 2012.

It continues, stating:

The purpose of submitting NEI 12-16 is to assist the NRC in completing the process of updating and stabilizing the regulatory framework governing spent fuel pool criticality analyses through publication of the planned regulatory guide, which meets the requirements for an exemption of fees in 10 CFR 170.11(a)(1)(ii). NEI 12-16 is a guidance document, it is not a topical report, and we believe that the NRC would be the primary beneficiary of its review. This request also meets the requirements of 10 CFR 170.11(a)(1)(iii),

which permits an exemption from fees for exchanging information between industry and the NRC for the specific purpose of supporting NRCs ongoing generic regulatory improvements and development of a Regulatory Guide. In order to facilitate a full review of NEI 12-16, we request that the exemption cover the review of the pre-submittal draft as well as the review of guidance submitted in March 2013 leading to NRC endorsement through a regulatory guide.

The NRC reviewed the request for fee exemption and found that the appropriate requirements for exemption were met (Dyer 2013).

NEI 12-16, Revision 3 (NEI, 2018), contains various references supporting its various subsections. Subsection 4.2.3, PWR Depletion Bias and Uncertainty, references two reports created by the Electric Power Research Institute (EPRI) detailing methods for validating Enclosure

pressurized water reactor (PWR) criticality calculations that credit depleted fuel in spent fuel pool (SFP) storage configurations. One report, Benchmarks for Quantifying Fuel Reactivity Depletion Uncertainty (referred to as EPRI benchmark report for the remainder of this document), details the use of flux map data to infer the uncertainty associated with depletion reactivity calculations using Studsvik Scandpowers CASMO-5 and SIMULATE-3 reactor analysis tools (EPRI 2011; EPRI 2017). The other report, Utilization of the EPRI Depletion Benchmarks for Burnup Credit Validation (referred to as EPRI utilization report for the remainder of this document), relates to the benchmark report by providing eleven calculational PWR depletion benchmarks allowing for determination of an application-specific depletion reactivity bias adjustment (EPRI 2018).

2.0 REGULATORY EVALUATION

As stated in the introduction, criticality safety analyses (CSAs) pertaining to light-water reactor (LWR) power plant SFP storage must meet the applicable regulatory requirements in 10 CFR 50.68 and 10 CFR Part 50, Appendix A, General Design Criterion 62. The regulation at 10 CFR 50.68(b)(4) states:

If no credit for soluble boron is taken, the k-effective of the spent fuel storage racks loaded with fuel of the maximum fuel assembly reactivity must not exceed 0.95, at a 95 percent probability, 95 percent confidence level, if flooded with unborated water. If credit is taken for soluble boron, the k-effective of the spent fuel storage racks loaded with fuel of the maximum fuel assembly reactivity must not exceed 0.95, at a 95 percent probability, 95 percent confidence level, if flooded with borated water, and the k-effective must remain below 1.0 (subcritical), at a 95 percent probability, 95 percent confidence level, if flooded with unborated water.

In order for NRC licensees to fulfill the 10 CFR 50.68(b)(4) requirement, uncertainty evaluations must be performed so that the NRC staff can come to a reasonable assurance determination with respect to satisfying the k-effective acceptance criteria at a 95 percent probability, 95 percent confidence level. One component of a CSA uncertainty evaluation is the depletion uncertainty and pertains to the ability of a set of calculational tools (i.e., depletion and criticality computer codes) to accurately characterize the reactivity associated with depleted fuel in a SFP storage environment. The following section documents the NRC staffs technical evaluation of EPRIs methodology for determining application-specific depletion and criticality code calculational bias and uncertainty as contained in the EPRI benchmark and utilization reports, which are referenced by the NEI 12-16 LWR SFP CSA guidance document.

3.0 TECHNICAL EVALUATION

Summary of Technical Information Provided by EPRI Defining the Scope of Review Initial evaluation of the two EPRI reports resulted in request for additional information (RAI) questions that were issued on September 22, 2014 (Holonich 2014). Responses to the RAI questions, which supplement the original EPRI reports, were received on March 2, 2015 (NEI 2015a). Minor corrections to these responses were made and submitted to the NRC on May 19, 2015 (NEI 2015b). Follow-up RAI questions were also issued and responses were submitted to the NRC on April 13, 2016 (NEI 2016a). On August 25, 2016, the NEI submitted a white paper as a counterpoint to the NRC staffs concern regarding a non-conservative regression fit uncertainty treatment discussed in detail in the Regression Fit and Associated

Uncertainty section below (NEI 2016b). Finally, on January 9, 2017, NEI submitted a supplementary response to address the open item related to the April 13, 2016, follow-up RAI 1 response (NEI 2017). Revised EPRI reports were also submitted incorporating all methodological changes resulting from RAI questions and public meeting discussions (EPRI 2017; EPRI 2018).

Definition of Depletion Uncertainty Previous NRC staff guidance regarding the treatment of depletion uncertainty, discussed in DSS-ISG-2010-01, the current guidance document (NRC 2010), states:

Depletion Analysis: NCS analysis for [spent nuclear fuel] for both boiling-water reactors (BWRs) and pressurized-water reactors (PWRs) typically includes a portion that simulates the use of fuel in a reactor. These depletion simulations are used to create the isotopic number densities used in the criticality analysis.

a. Depletion Uncertainty: The Kopp memorandum (Reference 2) states the following:

A reactivity uncertainty due to uncertainty in the fuel depletion calculations should be developed and combined with other calculational uncertainties. In the absence of any other determination of the depletion uncertainty, an uncertainty equal to 5 percent of the reactivity decrement to the burnup of interest is an acceptable assumption.

The staff should use the Kopp memorandum as follows:

i. Depletion uncertainty as cited in the Kopp memorandum should only be construed as covering the uncertainty in the isotopic number densities generated during the depletion simulations.

ii. The reactivity decrement should be the decrement associated with the keff of a fresh unburned fuel assembly that has no integral burnable neutron absorbers, to the keff of the fuel assembly with the burnup of interest either with or without residual integral burnable neutron absorbers, whichever results in the larger reactivity decrement.

In DSS-ISG-2010-01, it states that the NRC staff should interpret depletion uncertainty as the uncertainty in the isotopic number densities generated during the depletion simulations. The uncertainty in the isotopic number densities can arise from uncertainty associated with the depletion code (i.e., based on chosen models and methods) and the underlying nuclear data used by the depletion code - this also includes how the nuclear data is implemented by the depletion code. Both of these uncertainty components can have a significant impact on the isotopic number densities output by the depletion code. The EPRI depletion benchmarks

attempt to quantify this depletion uncertainty in terms of uncertainty in the reactivity worth of depleted fuel1.

The EPRI approach directly determines the uncertainty in terms of reactivity rather than uncertainty in the number densities of individual isotopes. However, this is a challenging approach because justification for extrapolating from the hot reactor environment to a cold SFP environment must be given. The EPRI approach, rather than trying to quantify the reactivity effect associated with number density uncertainties of individual isotopes, uses isotopic number densities output by a benchmarked depletion code2 directly in a series of criticality calculations. These criticality calculations serve as calculational benchmarks that cover a range of depletion conditions consistent with the benchmarked depletion code. A set of reference reactivity decrements are determined from these benchmarks and form a basis for subsequent comparison with the results of other acceptable criticality codes that are to be used for SFP CSA applications incorporating isotopic number densities from any acceptable depletion code.

Part of the NRC staffs assessment determines whether: (1) the reference reactivity decrements are derived from calculational benchmarks that are sufficient in number and scope to generally validate the simulation of depleted PWR fuel in the SFP environment using an acceptable criticality code incorporating isotopic number densities from an acceptable depletion code, and (2) the process described in the EPRI benchmark and utilization reports is sufficient for NRC licensees to perform application-specific depletion reactivity uncertainty analyses.

To ensure that appropriate biases and uncertainties associated with reference reactivity decrements are accounted for, EPRI-chosen depletion codes (i.e., those used to define the calculational benchmarks) were benchmarked against measured in-core flux map data.

However, this requires the following conditions to be met, which are also assessed by the NRC staff in this report:

1. The reactivity decrement uncertainty inferencing process is appropriate.

2. Identification of and appropriate accounting for all significant contributors to the reactivity decrement uncertainty.

3. The depletion uncertainty, as determined in the reactor environment, appropriately translates to the SFP environment.3 1

The reactivity of depleted fuel is also referred to as the reactivity decrement, which by the most general definition, is the difference in k-effective between a depleted fuel state of interest and the fresh fuel state.

2 In the context of this discussion, benchmarked depletion code means that the code has a bias and uncertainty associated with it in terms of reactivity over a range of fuel burnup. The benchmarking by inference process is discussed in the following section.

3 This is important since depletion uncertainty is being quantified in terms of in-core reactivity rather than isotopic number density variation. While isotopic number density doesnt change between environments, this is not necessarily true of reactivity.

While the EPRI approach characterizes depletion uncertainty in a new way, the NRC staff believes it is still consistent with the existing definitions from the Kopp memorandum and DSS-ISG-2010-01.

Benchmarks for Quantifying Fuel Reactivity Depletion Uncertainty The introduction to Section 1, Executive Summary, of the EPRI benchmark report explains that:

This report provides experimental quantification of PWR fuel reactivity burnup decrement biases and uncertainties obtained through extensive analysis of in-core flux map data from operating power reactors. Analytical methods, described in this report, are used to systematically determine experimental fuel sub-batch reactivities that best match measured reaction rate distributions and to evaluate biases and uncertainties of computed lattice physics fuel reactivities.

Regarding the reactivity decrement error inferencing methodology, Section 1.1, Analytical Methods, of the EPRI benchmark report explains that:

Forty-four cycles of flux map data from Duke Energys Catawba (Units 1 and 2) and McGuire (Units 1 and 2) plants have been analyzed with Studsvik Scandpowers CASMO [(Rhodes, Smith, and Lee 2006)] and SIMULATE-3

[(DiGiovine and Rhodes III 2005)] reactor analysis codes. By systematically searching for fuel sub-batch reactivities that best match measured reaction rate distributions, biases and uncertainties of computed CASMO reactivity decrements are experimentally determined. These analyses employ more than 8 million SIMULATE-3 nodal core calculations to extract approximately 3000 measured sub-batch reactivities from flux map data. The individual estimates of the reactivity decrement bias (measured minus calculated reactivity decrement) form a large data set...as a function of sub-batch burnup....

The NRC staffs review of the EPRI benchmark report covered:

1. The process by which errors are derived,

2. How the benchmark work performed is generically applicable to PWR operation,

3. How the errors derived in the reactor environment translate to the SFP environment,

4. How the sensitivity/uncertainty analysis was performed.4 4

The NRC staff is concerned with both the reactor and SFP environment analyses; however, reactor environment analyses (e.g., the effects of: reactor operational characteristics, fuel design, sub-batch grouping, data filtering, statistical process, optimization algorithm, etc.) are the subject of the EPRI benchmark report and are therefore of interest in this section.

Reactivity Decrement Error Determination Deduction Process Section 6, Details of Analysis Implementation, describes the algorithm used to deduce reactivity decrement errors as a function of average sub-batch5 burnup. The basic premise is to globally search for the minimum deviation6 in sub-batch reactivity between the calculated reactivity and that inferred from the in-core flux map measurements.7 The basic steps are as follows:

1. Perform the best-estimate simulation.

2. Determine sub-batch k-infinity and the corresponding core k-effective and flux shapes.

3. Change sub-batch burnup to get simulation flux shapes to match simulated flux map measurements as closely as possible.

4. When the best flux shape matches are found for all sub-batches simultaneously, calculate perturbed sub-batch k-infinity.

5. Calculate change in sub-batch k-infinity at the best-estimate calculated average sub-batch burnup.8 A search occurs for each unique sub-batch corresponding to a unique point in time and includes the effects of all other sub-batch searches so that a local minimum deviation between the inferred measurement of sub-batch reactivity and the calculated sub-batch reactivity can be found across all sub-batches simultaneously. That is, more accurate search results are 5

A sub-batch is a group of fuel assemblies that share similar characteristics. As defined by EPRI, this is assembly type, enrichment, burnable absorber (BA) configuration, and burnup batch.

6 The minimum deviation is defined by EPRI as the root-mean-square (RMS) deviation between measured and computed fission detector signals for each fuel sub-batch in the reactor core. EPRI explains in the benchmark report RAI 9 response that the RMS cannot be driven to zero because of:

(1) flux map measurement uncertainty on the order of 0.5 percent and (2) computer code biases and uncertainties aside from those which are caused by fuel depletion. EPRI further explains that errors in core reactivity that are independent of depletion will be addressed as a separate item (normally in the comparisons to cold critical benchmarks) by applicants on a case-specific basis. In other words, SIMULATE-3 is used as a measurement tool through a relative differencing process to infer only reactivity decrement errors resulting from CASMO, therefore quantification of SIMULATE-3 biases and uncertainties is not necessary.

7 The difference in k-infinity between the unadjusted calculation and the burnup-adjusted calculation is the reactivity decrement error described by EPRI.

8 This k-infinity change represents a means to estimate the net effect of all sources of depletion code uncertainty - for example, uncertainty introduced by nuclear data, manufacturing tolerances, thermal hydraulic conditions, etc. - as long as measurement uncertainties are properly accounted for or shown to be insignificant.

obtained for an individual sub-batch by accounting for the influence of all other sub-batch burnup changes. Within a search, each sub-batch nodal burnup is iteratively multiplied by a range of burnup multipliers. The multipliers are appropriately spaced to achieve a resolution fine enough to accurately capture the minimum deviation as seen in Figure 3-2, Change in r.m.s. Fission Rate Error vs. Sub-batch Multiplier, of the EPRI benchmark report.

The global search is performed both on a two-dimensional (2D) axially-integrated-radial basis and a three-dimensional (3D) nodal basis, and it was found that the inferred reactivity decrement is largely insensitive to the global search type. Since the 2D method puts less emphasis on the axial ends versus the 3D method and both are in relative agreement, this indicates that the global search process does not significantly depend on the observed higher calculated-to-measured (C/M) flux differences at the nodes corresponding to the fuel assembly axial ends. The observed higher C/M flux differences at the nodes corresponding to the fuel assembly axial ends are indicative of inaccuracies in SIMULATE-3 models rather than CASMO-5 models since SIMULATE-3 model accuracy begins to degrade closer to the model boundaries where there is increased reliance on simplified reflector models (see the response to RAI 3.a.ii. for additional discussion). If CASMO-5 models were inaccurate, the high C/M values observed at the SIMULATE-3 model axial ends would still persist closer to the axial center of SIMULATE-3 models. However, this is not the case. Therefore, it is concluded that reactivity decrement error data sufficiently represents the accuracy of CASMO-5 models as realized through SIMULATE-3 simulations.9 As further explained in EPRI benchmark report Section 3.4, Flux Map Perturbation Calculations:

The reason for choosing a sub-batch burnup multiplier is that if there are errors in reactivity predictions of the lattice depletion code, the errors would be seen by all assemblies in the sub-batch. For example, if fission rates predicted in all assemblies of a sub-batch were either consistently low or consistently high, this would be a strong indication of lattice code depletion errors (e.g., nuclide concentration errors, cross-section data errors, resonance modeling approximations, approximations in solving neutron transport equations, approximations in solving the nuclide depletion equations, approximations in modeling of boron history, etc.) The data often shows, however, that fission rate differences vary in both sign and magnitude within a sub-batch. This indicates that most of the differences in fission rates are due to factors not directly related to errors in [lattice depletion code] reactivity predictions with burnup.

The relationship shown in Figure 7-1, CASMO-5 Bias in Reactivity, of the EPRI benchmark report quantifies the difference in sub-batch k-infinities between the initial unperturbed states and final minimized-local-error states by minimizing the RMS deviation between measured and 9

CASMO-5 is the code being validated as measured via SIMULATE-3. It should be noted that CASMO-5 is the reference depletion code used to define a subsequent set of 11 calculational benchmarks which are to be used to determine application-specific depletion code biases - this is discussed further in subsequent sections of this report.

computed detector signals corresponding to approximately 3000 flux maps.10 In this figure, each data point represents a unique sub-batch corresponding to a single flux map - this reactivity decrement error relationship to average sub-batch burnup forms the basis for the final reported reactivity decrement error bias and bias uncertainty.

Additional work utilizing the Benchmark for Evaluation And Validation of Reactor Simulations (BEAVRS) flux map data - documented in a report released by EPRI titled, PWR Fuel Reactivity Depletion Verification Using Flux Map Data - has since been performed evaluating reactivity decrement errors as a function of sub-batch average burnup using 2D full-core CASMO-5 calculations directly instead of through SIMULATE-3 (Smith and Gunow 2014). As discussed in the report, this work allows for an assessment of the impact of the following SIMULATE-3 modeling approximations on the calculation of reactivity decrement error bias as a function of burnup:

• Differences in batch spectra vs. CASMO-5 lattice assumption (zero leakage)

• Differences in intra-assembly spatial flux distributions vs. lattice assumption

• Errors in SIMULATE-3 nodal and detector physics models

• Errors in SIMULATE-3 cross-section data fitting models The report utilizing the BEAVRS flux map data explains what was briefly touched on above:

The EPRI/Studsvik study demonstrated that accurate fuel reactivity errors could be determined by minimizing either the 2D (axially-integrated) or [3D] (nodal) r.m.s. differences between measured and calculated 3D SIMULATE-3 fission rates distributions. Hence, it is clear that if 2D calculations can predict the radial fission rate distributions with similar accuracy to 3D calculations, then direct 2D calculations can be used to infer errors in fuel reactivity burnup decrements using the analytical procedure developed in the original [EPRI benchmark report].

The report utilizing the BEAVRS flux map data concludes the following:

It has been successfully demonstrated that the reactivity decrement errors inferred using flux map data and 2D full-core multi-group transport calculations are smaller than those inferred by using 3D nodal diffusion calculations to compute reactor fission rate distributions.

Fuel reactivity errors inferred from 3D SIMULATE-3 and 2D CASMO-5 full-core transport calculations are within 250 [percent millirho (pcm)] of one another for all flux map/batches examined here.[11]

10 Forty-four fuel cycles from 4 PWRs with 12-18 flux maps per cycle and 5-12 sub-batches per cycle.

11 The maximum difference was within 250 pcm and the average was much smaller at 33 pcm +/- 78 pcm at a 1-sigma standard deviation.

The most important outcome of this study is that nodal method approximations have now been demonstrated to contribute insignificantly to individual batch reactivity errors. Consequently, nodal methods do not contribute significantly to inferred reactivity decrement biases and uncertainties postulated in the original

[EPRI benchmark report].

Although the BEAVRS work has been done with a different set of flux map data spanning only the first two cycles12 of a 4-loop Westinghouse reactor containing one type of 17x17 fuel assemblies with a maximum enrichment of 3.4 wt% U-235, the insights are nonetheless valuable and provide additional assurance that the SIMULATE-3-derived reactivity decrement errors are consistent with those derived solely from the higher fidelity physics models of a lattice depletion code such as CASMO-5. The results of the report utilizing the BEAVRS flux map data also provides assurance that - as characterized by EPRI - measured biases and uncertainties are not unrealistically low because of some fortuitous cancellation of errors in the numerous approximations made in the 3D nodal diffusion core models that were employed [in the SIMULATE-3 calculations described in the EPRI benchmark report].

Overview of Deduction Process Uncertainties For the given dataset, potentially offsetting reactivity decrement error effects are postulated to be caused from:

1. Use of SIMULATE-3 and its models with CASMO-5 generated cross-sections instead of CASMO-5 models directly,

2. Imprecise knowledge of fuel temperatures when modeling the reactor environment in SIMULATE-3,

3. Uncertainties in the measured fluxes from flux maps input into SIMULATE-3,

4. Uncertainties in the actual geometrical dimensions of components modeled in SIMULATE-3,

5. The algorithm used to arrive at individual sub-batch reactivity decrement errors.

Item (1) was explicitly addressed as explained in the preceding section, (2) has been explicitly addressed by EPRI as discussed further in the Uncertainty Analysis section below, while it is reasonably argued that (3) and (4) have negligible impact on reactivity decrement error bias uncertainty.13 Regarding Item (5), due to the algorithm chosen to derive individual sub-batch reactivity decrement errors, there is substantial uncertainty introduced into the burnup-12 The maximum batch burnup is 23 gigawatt-days per initial metric ton of uranium (GWd/MTU).

13 See RAI 2, 8, and 9 responses as part of responses to RAIs for the EPRI benchmark report for additional discussion. As part of this discussion, EPRI also states that modeling simplifications that create deviations from reality - e.g., deviations in the actual geometrical dimensions of components -

increases the magnitudes of uncertainty attributed to the reactivity decrement errors, which is conservative.

dependent reactivity decrement data of Figure 7-1 of the benchmark report that cannot be separated from the CASMO-5 reactivity decrement error bias uncertainty characterization.

EPRI refers to this uncertainty as arising from sub-batches with low sensitivity meaning that these low sensitivity sub-batches do not change the core flux distribution as significantly as higher sensitivity sub-batches as burnup changes. EPRI argues that these low sensitivity sub-batches are not relevant to the burnup-dependent reactivity decrement error database as they do not complement the implemented deduction technique. In the initial revision of the EPRI benchmark report, EPRI attempted to filter these low sensitivity sub-batches out of the dataset.

However, this is problematic because what the filtering criteria should be is not clear. For example, how would one know which filtering criteria is reasonable and which is unreasonable?

Therefore, these low sensitivity sub-batches cannot be justifiably filtered out and can be viewed as a penalty that must be taken with the chosen reactivity decrement error deduction algorithm.

Even the modest filtering originally proposed by EPRI resulted in large burnup-dependent reactivity decrement errors. This algorithm-associated uncertainty is an integral part of the regression fit uncertainty discussed in the Uncertainty Analysis section below.

Regarding the connection between the burnup-dependent reactivity decrement data to the CASMO-5 lattice physics solver, after accounting for the above, uncertainty associated with use of CASMO-5 to quantify reactivity decrement error for cold in-rack conditions using data from hot in-core conditions must still be accounted for. Of the CASMO-5 inputs, uncertainties associated with temperature-dependent nuclear cross-section data creates additional uncertainty when defining cold versus hot reactivity decrement uncertainties. Table 8-3, [Hot Full Power (HFP)] to Cold Reactivity Uncertainty (2-sigma) as Function of Burnup, of the benchmark report shows uncertainties on the order of approximately 500 pcm from TSUNAMI-3D analyses - this is discussed further in the Uncertainty Analysis section below.

In summary, the major uncertainties that are likely driving the reactivity decrement error data are: (1) temperature-dependent cross-section uncertainties, (2) fuel temperature uncertainties during reactor operation, and (3) the algorithm used to arrive at individual sub-batch reactivity decrement errors.

Method Applicability In-Core Flux Map Benchmarking In the context of the regression analysis performed by EPRI, there is one main issue with EPRIs argument of generic applicability. That is, the population of fuel types in the benchmarking effort is limited to a single Westinghouse 17x17 fuel design with some burnable absorber (BA) variation and a single AREVA 17x17 fuel design with some BA variation.

Similarly, the population is restricted to a subset of fuel enrichments and soluble boron histories.

This makes extrapolation to all PWRs difficult since there is no physical evidence that the variance, using traditional estimation techniques, would not significantly increase due to the variation in the various cycle-specific parameters that has occurred in past PWR operation, does occur in current PWR operation, and will occur in future PWR operation. Given that the benchmark report is intended to be applicable to all PWR fuel (as discussed in the response to RAI 7a), additional study may be warranted for other fuel designs over a range of BA types and loadings.

In EPRI benchmark report RAI 7b, the NRC staff asked EPRI to assess the impact of operational characteristics that might be considered atypical or unexpected (i.e., any operational characteristics that would be considered to be a significant deviation from those forming the

basis of the EPRI benchmark work) on the reactivity decrement error uncertainty. EPRI states that:

The 44 Duke reactor cycles used in this study (approximately 65 reactor-years) are a small percentage (<1%) of the many thousands of PWR reactor-years of operation that have occurred. However, many PWRs have been operated with fuel and operational strategies that are very similar to those of the Duke reactors, and as such, the fuel used in this report is representative of the majority of the discharged fuel in spent fuel pools in the US.

EPRI provides further qualitative discussion regarding why the 44 Duke reactor cycles are appropriate to cover all PWR operations stating that:

While fuel in the Duke reactors was 17x17 fuel, there also exist 14x14, 15x15, and 16x16 fuel in US spent fuel pools. All of these other fuel types are depleted in reactors with very similar fuel-to-coolant ratios, operational power densities, fuel temperatures, and soluble boron concentrations. Thus, we expect that reactivity decrement biases and uncertainties would be very similar for these other fuels.

The NRC staff agrees that reactivity biases and uncertainties are expected to be similar for other fuel types depleted in reactors with similar fuel-to-coolant ratios, operational power densities, fuel temperatures, and soluble boron concentrations; however, the NRC staff would add BAs to this list as CASMO-5 cross-section uncertainties and depletion simulation capability may change as a function of BA.

In EPRI benchmark report RAI 7d, the NRC staff asked for clarification of a statement made regarding a 200 pcm reactivity decrement error sensitivity to soluble boron, fuel enrichment, and BAs. In the response to RAI 7d, EPRI implies that there would be minor sensitivity to reactivity decrement error to various cycle-specific parameters. This is inferred by the observation that the reactivity decrements varied by only 200 pcm (i.e., a small amount) when developing the Kopp 5 percent reactivity decrement curves. In other words, a small percentage of a small amount will be an even smaller amount, therefore EPRI believes it is justified in saying that there would not be any significant sensitivity to soluble boron, fuel enrichment, and BAs.

Based on the discussion above, the NRC staff finds that the 44 cycles of PWR data modeled using CASMO-5 and SIMULATE-3 is sufficient to allow for quantification of the reactivity decrement error and associated uncertainty due to PWR fuel depletion. However, the NRC staff also agrees with the statement in Section 10.3, Range of Fuel Applications, of the initial revision of the EPRI benchmark report:

The results presented in [the EPRI benchmark] report are, strictly speaking, applicable only to those fuel types included in the analysis, namely: 1) 3.5 - 5.0%

enrichment, 2) Westinghouse RFA fuel with [Integral Fuel Burnable Absorber (IFBA)] and [Wet Annular Burnable Absorbers (WABAs)], and 3) AREVA MarkBW fuel with [lumped burnable poison (LBP)] pins. For other fuel types, additional analysis may be needed to demonstrate that results of this study are

[applicable] to those fuel types.

Spent Fuel Storage Applicability Studies Via ck Analysis EPRI proposes to use the bias and uncertainty calculated at hot in-core conditions to cold in-rack SFP conditions. Consequently, the NRC staff asked for a more detailed justification for this extrapolation of bias and uncertainty calculated at hot in-core conditions to cold in-rack SFP conditions. In the EPRI benchmark report RAI 5 response, EPRI explains that possible differences in neutron energy spectrum between SFP geometries and power reactor core geometries are understood by comparison between SCALE Version 6.0 (ORNL 2009)

TSUNAMI-IP correlation coefficients (referred to as ck values) which are given in Table 8-4, Correlation Coefficients, ck, Between Reactor Conditions by Lattice and Burnup, of the EPRI benchmark report.

As explained by EPRI, similarity coefficients were generated using a series of SCALE Version 6.0 TSUNAMI sequences. The TSUNAMI-3D code was used to generate application-specific sensitivity data used as input to the TSUNAMI-IP sequence, which generates the ck values that serve as a measure of similarity between two systems. The similarity is quantified in terms of system k-effective sensitivity to nuclear cross-section data uncertainty. The closer a ck value is to one, the closer two systems are to sharing identical sources of nuclear data uncertainty (Broadhead et al. 2004). In other words, similar reactivity changes can be expected of two systems that correspond to a high ck value when the cross-section data are changed in a systematic way - this strongly implies physical similarity and reactivity sensitivity similarity between the two systems. However, strictly speaking, the only thing that can be said is that the two systems will share similar nuclear data uncertainties (Mennerdahl 2014).

Many things contribute to the similarity of two systems including neutron energy spectra, spent fuel isotopic concentrations, presence of other non-fuel materials, and the geometric configuration of the two systems. EPRI states that for all lattices of the EPRI study, the correlation coefficients between the in-core conditions and the SFP rack geometry are greater than 0.95, demonstrating that the physical characteristics between the two environments are very similar and justifying the application of nuclear data uncertainties from hot in-core conditions to cold in-rack SFP conditions.

The RAI 5 response focuses on differences in neutron energy spectrum between the two environments referring to the high correlation coefficient similarity. EPRI explains that:

...at hot conditions the neutron spectrum is hardened by the low water density, core soluble boron, and Xenon/Samarium absorbers - just as the SFP neutron spectrum is hardened [by] the presence of absorber panels. Thus, even though the SFP has a much higher water density than the PWR core, the spectral softening of the water is offset by other hardening phenomenon to make the energy spectrum and reactivity sensitivities very similar to those in the reactor core.

In EPRI benchmark report RAI 7a, the NRC staff asked EPRI to formally define the area of applicability as it relates to the benchmarking effort performed. The response provides the burnup range, the U-235 enrichment range, neutron energy spectrum range, and specific power range applicable to a SFP CSA application that would reference the EPRI benchmark work.

However, the area of applicability was also evaluated using TSUNAMI-IP and similarity tests by analyzing ck values which allow for applicability to be defined more generally. In the General Response to the EPRI utilization report RAIs, a high degree of similarity is indicated between a range of 2D lattice models (with varying fuel enrichment, BA type, soluble boron, temperature,

and power) and a range of in-rack SFP models (with varying fuel type, storage rack type, areal density, fuel enrichment, and burnup). EPRI notes that:

Of the 56 spent fuel pool configurations investigated all but 3 had a ck greater than 0.9 for at least one of the benchmark cases. The three that had a maximum ck less than 0.9 were associated with flux trap (Region 1) designs with low burnup ( 20 [gigawatt-days per metric ton uranium (GWd/MTU)] and CE 16x16 fuel (see the bottom of Table GR-1, page 7 of 7). Flux traps add more water to the system than contained in the benchmarks. All of the non-flux trap designs (Region 2) had very good agreement with the minimum of the [maximum] cks being 0.9821 for W 17x17 fuel and 0.9710 for CE 16x16 fuel. Flux trap racks are principally designed to accommodate fresh fuel and therefore do not usually require burnup credit. In fact, two of the three cases which had ck values less than 0.9 were for rack designs which did not need burnup credit. The only spent fuel configuration that is likely to need burnup credit and has a ck less than 0.90 are flux trap designs that do not credit absorber panels. However, these cks are marginally below 0.90.

Consequently, the presented evidence strongly supports the claim in the RAI 7a response that the area of applicability is all current PWR fuel assembly designs for applications with most rack designs and the NRC staff considers the EPRI utilization report calculational benchmarks to be comprehensive. However, a similar limitation to the one mentioned in the previous section regarding in-core flux map benchmarking of PWR fuel types is applied to the utilization report calculational benchmarks. That is, the calculational benchmarks presented in the EPRI utilization report are, strictly speaking, applicable only to the storage of fuel types considered in the EPRI benchmark report stored under SFP storage conditions that are similar to those considered in the similarity analyses supporting the EPRI utilization report.14 For other fuel types, BAs, or other SFP storage conditions, additional analysis may be needed to demonstrate that results of the EPRI benchmark report are applicable to a given application.

Uncertainty Analysis Uncertainty Based on Application of HFP Reactor Benchmarks to Cold SFP Conditions The in-core depletion benchmarks were performed at HFP conditions which creates uncertainty in estimates of reactivity decrement error at cold conditions. This is due to not having precise knowledge of certain fuel properties at HFP conditions. Also, by performing the flux map measurements at HFP conditions rather than cold conditions representative of the SFP, cross-section uncertainties at cold conditions must be considered.

One property that can have an effect on system reactivity is fuel temperature, which cannot be directly measured during HFP operations. The uncertainty treatment is explained in Section 8.2, Fuel Temperature Uncertainties, of the EPRI benchmark report. The driving positive reactivity effect is increasing plutonium content in the fuel as a function of burnup, with 14 Refer to the General Response given in the EPRI utilization report RAI responses for a description of the similarity analyses performed.

more plutonium present when operating at higher fuel temperatures. This positive reactivity effect is masked at HFP in-core conditions by an increasingly negative fuel temperature reactivity feedback effect with increasing burnup, which is also due to higher fuel temperatures.

However, at cold SFP conditions, the fuel temperature feedback effect is not present to offset the positive reactivity effects of increased plutonium at higher temperatures.

Using INTERPIN-4 (Grandi and Hagrman 2007), which provides data for average fuel pin temperatures as a function of burnup and linear heat generation rate for the Studsvik CMS codes, EPRI determines an average fuel pin temperature as a function of burnup to find the minimum and maximum fuel temperatures expected for a given fuel pin. The average fuel pin temperature as a function of burnup used is shown in Figure 8-1, Typical INTERPIN-4 Fuel Temperature Change With Burnup, of the benchmark report. Using these minimum and maximum temperatures, EPRI calculates two separate reactivity effects to bound any potential increase in the reactivity decrement error data due to temperature effects. The first reactivity effect is an instantaneous effect at HFP conditions and the second is a history effect associated with the plutonium build-in as a function of burnup which manifests at cold conditions. Initially, EPRI selected both the maximum instantaneous and history effects over the analyzed burnups,

-150 and 206 pcm respectively, and combined them by the root of the sum of the squares (RSS). However, to obtain a more realistic estimate of the uncertainty, EPRI opted to combine the two fuel temperature uncertainty components by the RSS as a function of burnup in the final revision of the EPRI benchmark report. The NRC staff finds this approach to be appropriate for the intended application of conservatively deriving HFP temperature uncertainties since an appropriately validated fuel performance code was used in a bounding manner to account for all relevant reactivity effects caused by uncertainty in fuel temperatures.

CASMO-5 was used to quantify the reactivity effects due to the difference between minimum and maximum fuel temperatures by performing sensitivity analyses at various fuel burnups - calculations were performed at both hot and cold in-core conditions.15 The maximum reactivity effects are highlighted in Table 8-1, Fuel Temperature Effect on Hot and Cold Lattice Reactivity, of the benchmark report.

Another source of uncertainty caused by performing the depletion benchmarks at HFP conditions comes from the temperature-dependent nuclear data. The goal of the depletion benchmarking effort is to ultimately provide an estimate for reactivity decrement error bias and uncertainty at cold SFP conditions rather than HFP conditions. Therefore, quantification of the nuclear data uncertainty arising from creation of the HFP depletion benchmarks at elevated temperatures instead of at cold SFP conditions is necessary.

TSUNAMI-3D was used to determine the temperature-based nuclear data uncertainty. Upon completion of a TSUNAMI-3D sequence run, an estimate of problem-dependent nuclear data uncertainty is produced in terms of reactivity using problem-specific reactivity sensitivity coefficients and a temperature-specific nuclear data covariance library. EPRI has performed separate TUSNAMI-3D calculations using the appropriate temperature-dependent nuclear cross-section data corresponding to both HFP in-core conditions and cold SFP conditions for a 15 Cold in-core reactivity effects were determined by performing CASMO-5 branch-to-cold calculations over the range of respective hot condition calculations.

range of configurations as detailed in Section 8.5, TSUNAMI Analysis results. The results of these calculations were then adjusted for correlation between hot in-core and cold in-rack states; the results are provided in Table 8-7, HFP to Cold Uncertainty Matrix (2-sigma) at Cold Conditions. Also, the uncertainties associated with fresh fuel nuclear data uncertainties were statistically subtracted by RSS, and the resulting uncertainties are provided in Table 8-9, HFP to Cold Additional Uncertainty Matrix (2-sigma) at Cold Conditions. The NRC staff finds this acceptable because fresh fuel nuclear data uncertainties are treated separately in SFP CSA applications by benchmarking the criticality code with cold fresh fuel critical experiments.

However, in Section 8.6 of the revised EPRI benchmark report, EPRI modified the methodology based on a re-interpretation of the Table 8-9 data, explaining that the additional uncertainty curve does not approach 0.0 for low burnups as one expects from the definition of reactivity decrement, and consequently proposes to use the 0.5 [GWd/MTU] step as the reference for zero burnup, as displayed in the bottom red curve of Figure 8-2. This data adjustment, reflected in Table 8-10, HFP to Cold Additional Uncertainty Matrix (2-sigma) at Cold Conditions, effectively reduces all hot-to-cold additional uncertainties by approximately 50-100 pcm. In the final 95/95 tolerance limits, this reduction in hot-to-cold uncertainties has a pronounced effect only at low burnups. Since the direction of this correction is non-conservative, without a more substantial physical basis for the adjustment, the NRC staff found this to be insufficient to support use of the adjustment.16 Regression Fit and Associated Uncertainty Section 7, Measured HFP Reactivity Bias and Uncertainty, of the EPRI benchmark report, discusses the analysis and interpretation of the reactivity decrement error versus average sub-batch burnup data. This includes an estimate of the regression fit of the reactivity decrement error data and regression fit uncertainty as a function of assembly-average burnup.

In the initial EPRI benchmark report revision, Section 7.5, Burnup Reactivity Decrement Biases and Confidence Intervals, describes why formal statistics cannot strictly be applied to the data in order to determine the regression fit uncertainty based on a 95 percent probability, 95 percent confidence interval consistent with 10 CFR 50.68(b)(4) k-effective determination requirements.

Consequently, Section 7.6, Burnup Reactivity Decrement Biases and Uncertainties, of the original EPRI benchmark report describes a direct method by which the regression fit uncertainty is estimated.

Based on the Section 7.6 demonstration, the NRC staff had concerns with the relatively small estimate of the regression fit uncertainty in light of the relatively large variation in reactivity decrement error versus average sub-batch burnup, especially given that formal statistics was not applied in the determination of the estimate.

EPRI benchmark report RAI 3 covers many NRC staff concerns regarding the approach used to determine the regression fit uncertainty and explains why the approach was unacceptable to the NRC staff. The NRC staff issued EPRI benchmark report RAI 7c to gain an understanding of 16 Note that the values in Table 8-9 are used instead of those in Table 8-10 in the development of the uncertainty values for the NRC-adj case of Appendix C, Table 3, Net SFP CSA Impact in Terms of Percent of Depletion Worth - a confirmatory analysis in this safety evaluation report.

the implications of not meeting certain statistical conditions when performing the regression analysis, such as, for example understanding whether variance estimates might be overestimated or underestimated. EPRI does not provide any practical evaluation of not meeting all strict statistical conditions and the impact on the associated regression fit and its variance, therefore the quantitative implications (e.g., magnitude of overestimation or underestimation) of not meeting the strict statistical conditions when estimating the regression fit and its variance were not clear to the NRC staff. To address concerns described in RAI 3 and RAI 7c, EPRI developed a statistically-based approach to more rigorously quantify the regression fit uncertainty.

The procedure in Attachment 2 of NEIs April 13, 2016, letter (NEI 2016a) modifies the regression confidence interval, at select burnups, by multiplying the Students t-factor by the k-factor divided by the t-factor in Step 8 in the Summary of Analysis Procedure subsection.

Ultimately, this procedure does not allow for the correct statistical inference as it still focuses on the average reactivity decrement as a function of sub-batch average burnup rather than individual reactivity decrements as discussed in a follow-up RAI, RAI 1 (NEI 2016a).

During a June 8, 2016, public meeting, the staff again requested that NEI/EPRI re-align the procedure already developed in Attachment 2 to reflect a 95/95 confidence limit17 to be based on the correct population parameter - the individual reactivity decrement values rather than the mean of these values - for the characterization of the 95/95 uncertainty consistent with the explicit requirements of 10 CFR 50.68(b)(4) (Hsueh 2016a).

On October 14, 2016, a public meeting was held to discuss the proposed closure of the open item related to EPRIs regression fit and associated uncertainty (Hsueh, 2016b). At the meeting, EPRI provided another update of the analysis to address remaining NRC staff concerns and NEI agreed to supplement the previous follow-up RAI 1 response to document this modification to the statistical analysis. Modification of the methodology to support relative bias and uncertainty characterization was also discussed during the meeting and NEI agreed to include the technical basis for this modification as part of the supplemental RAI response and in a subsequent benchmark report revision.

The NRC staff received the supplemental follow-up RAI 1 response submitted on January 9, 2017 (NEI 2017). Upon review of the supplement, it was still not clear why certain assumptions made were appropriate with respect to developing 95/95 regression tolerance intervals (e.g., data collapsing to treat data dependence rather than attempting to model the data dependence without collapsing).

The supplement also described the conversion of absolute values of the bias and uncertainty into relative values in terms of percent reactivity decrement due to fuel depletion. This is desirable because it allows for a scaling of the depletion bias and uncertainty relative to the density of depleted fuel loaded in a given storage configuration. For example, use of an absolute uncertainty would apply the same uncertainty magnitude to a 4-out-of-4 storage array of depleted fuel as would be applied to the same storage array with only 2 of the fuel 17 The NRC staff further clarified that this is also referred to as a one-sided regression tolerance interval in this context.

assemblies present in the array (i.e., 2 empty storage cells checkerboarded with 2 depleted fuel assemblies) resulting in unwarranted additional conservatism. However, this re-formulation requires establishment of an appropriately representative reactivity decrement. In principle, the smaller the reactivity decrement assumed, the higher the relative uncertainty. Therefore, in the supplemental RAI response, EPRI uses the minimum cold out-of-rack reactivity decrement, dependent on burnup, determined from the calculational benchmarks defined in the EPRI utilization report; only the 7 nominal lattices that are depleted, branched to cold conditions, and decayed for 100 hours0.00116 days <br />0.0278 hours <br />1.653439e-4 weeks <br />3.805e-5 months <br /> were considered.18 EPRI also notes that cold depletion reactivities and uncertainties...are smaller in-rack [(i.e., in a SFP storage rack)] than out-of-rack, as reported in the original EPRI [benchmark] report Tables 8-7 and 8-8. Therefore, using out-of-rack reactivities as the basis for the conversion to relative bias and uncertainty is most appropriate (i.e., cold out-of-rack reactivity bias or uncertainty is divided by cold out-of-rack reactivity). EPRI selects the smallest cold out-of-rack reactivity decrement for each increment of burnup across all 7 nominal lattices. Since this has the effect of maximizing the relative bias and uncertainty, this is conservative, and therefore appropriate.

To resolve the open item regarding the regression analysis, as discussed in the revised EPRI depletion benchmark report (EPRI 2017), corresponding RAI responses, and meeting summaries, the NRCs supporting consultants from Pacific Northwest National Laboratory performed a confirmatory analysis to verify the acceptability of the EPRI-determined regression fit and associated uncertainty. As a result of this analysis, the NRC staff determined a regression fit and associated uncertainty based on the results of the confirmatory analysis.19 The NRC staff observed that the main difference arises from determination of the bias from a more appropriate linear regression fit instead of a quadratic fit, which was used by EPRI, because the quadratic fit appears to overfit the data at higher burnups - this is discussed in more detail in Appendix B. The confirmatory analysis also bases the 95/95 regression fit uncertainty on a first-order autoregressive model to account for the correlation structure in the sub-batches of the EPRI-generated reactivity decrement error dataset without questionable collapsing of the sub-batch data within each cycle to remove data correlation.

Since the NRC-derived uncertainties were found to not bound the EPRI-derived uncertainties in the revised EPRI benchmark report, additional NRC staff confirmatory analyses were performed, as documented in Appendix C, to assess whether differences between the NRC staff confirmatory analysis results were significant enough from those in Table 10-2 of the revised EPRI benchmark report such that modification of the EPRI-determined bias and uncertainty would be warranted. As summarized in Appendix C, the NRC staff found that use of a quadratic versus linear regression fit to define the bias results in a significant reactivity effect for burnups greater than 30 GWd/MTU.20 18 See EPRI benchmark report, Table 10-1, Measured Cold Reactivity Decrements (in pcm) for Nominal Benchmark Lattices for the reactivity decrements considered.

19 See Appendices A and B of this report for confirmatory analysis details.

20 Note that the confirmatory analyses in the Appendices contain background information used to support conclusions made in the SER body and are not intended to be used by licensees/applicants.

During a public meeting on December 20, 2018, additional discussion regarding the regression fit used to define the bias associated with the reactivity decrement error dataset led to NEI supplementing the revised EPRI benchmark report to replace the bias determined by quadratic regression with a bias determined by linear regression analysis. NEI developed a burnup-dependent bias adder as shown in Table 1 to be used in licensing applications along with the total uncertainty21. Linear interpolation between the burnup values listed in Table 1 is acceptable to calculate the corresponding uncertainty and additional bias for specific fuel assembly burnups.

Table 1: Bias Adder and Uncertainty (% Reactivity Decrement) Versus Burnup (GWd/MTU) for the EPRI Depletion Reactivity Benchmarks.

Burnup Bias Adder Uncertainty 10 0.00 3.05 20 0.00 2.66 30 0.00 2.33 40 0.15 2.12 50 0.35 1.95 60 0.54 1.81 Finding The [Spent Nuclear Fuel] Rack cases from Table 8-4 of the EPRI benchmark report show that similar reactivity sensitivities to changes in nuclear cross-section data are expected for both the HFP reactor and cold SFP environments. This provides strong indication that the reactivity decrement error bias and uncertainty calculated in the HFP reactor environment is also applicable to the cold SFP environment after appropriately accounting for fuel temperature and temperature-dependent nuclear data uncertainties. This indication is also supported by the observations in the NRC staff confirmatory analysis documented in Appendix C of this report.

Consequently, the NRC staff finds that there is sufficient evidence showing that the benchmarks conducted in the reactor environment are applicable to the SFP environment.

Regarding the reactivity decrement error bias and uncertainty analysis, the NRC staff finds that:

1. Use of the reactivity decrement error bias adder and uncertainty, as quantified in Table 1 of this safety evaluation report is acceptable,

2. Various reactivity decrement uncertainty components were appropriately derived, and

3. Various reactivity decrement uncertainty components were appropriately combined.

21 The total uncertainty shown was determined by combining the regression fit uncertainty with all other uncertainty components as determined by EPRI and is the same as that summarized in Table 10-2 of the revised EPRI benchmark report.

The NRC staff finds that there is sufficient evidence showing that all significant k-effective uncertainties necessary to allow for benchmarking of depletion codes in support of PWR burnup credit in SFP CSA applications have been appropriately accounted for and applied.

Utilization of the EPRI Depletion Benchmarks for Burnup Credit Validation The corresponding depletion code bias and uncertainty to be applied in an NRC licensee CSA application is first taken to be the bias and uncertainty associated with the depletion code used to infer reactivity decrement errors based on in-core flux map data as discussed in the EPRI benchmark report; the bias and uncertainty data is tabulated in Table 10-2 of the EPRI benchmark report with recommended uncertainty usage given in Appendix C of the EPRI benchmark report. As indicated in Section 9.3 of the revised EPRI benchmark report, the CASMO-5 bias data in Table 10-2 has already been applied to produce the reference reactivity decrement tables in Appendix C, therefore an end user only has to account for the bias adder in Table 1 of this safety evaluation report in their CSA application.

EPRI has defined 11 reference calculational benchmarks,22 which have been modeled using CASMO the same reactor analysis code used to infer reactivity decrement errors from in-core flux map data as discussed in the EPRI benchmark report and the corresponding section above. These calculational benchmarks are designed to represent a broad range of depletion conditions typical of fuel stored in PWR SFPs and analyzed in PWR SFP CSA applications. To provide an example of how a NRC licensee might use these 11 calculational benchmarks, EPRI models the benchmarks using the SCALE, Version 6.1.2, TRITON T5-DEPL sequence (ORNL 2013), for depletion calculations, and the SCALE, Version 6.1.2, CSAS5 sequence (using the KENO-V.a criticality code) for criticality calculations, as explained in Section 3, Comparison of Measured Versus Predicted Reactivity Decrements Using SCALE, of the revised EPRI utilization report (EPRI 2018).23 Next, a process is described by which additional depletion code bias is determined by comparison of reference calculational benchmark reactivity decrement values to the reactivity decrement values derived from the example computer codes; the reference values are also tabulated in Appendix C of the EPRI benchmark report. Comparisons are made between reference depletion reactivity decrements and a NRC licensees or applicants depletion and criticality code determined reactivity decrements, and any observed differences are accounted for as additional bias attributable to use of a users specific set of depletion and criticality codes used to simulate depleted fuel, as part of the CSA application.

The NRC staffs review of the EPRI utilization report covered:

1. How the 11 proposed benchmarks are generally representative of the PWR SFP environment, 22 There are six burnups and three cooling times per benchmark.

23 In this demonstration, both Version V of Evaluated Nuclear Data File/Brookhaven (ENDF/B-V) and ENDF/B-VII libraries are used.

2. The validity and applicability of the sensitivity/uncertainty analysis performed,24 and

3. How biases and uncertainties will be calculated and applied by NRC licensees and applicants in their SFP CSA applications.

Determination of Application-Specific Bias In EPRI utilization report RAI 2a, the NRC staff asked how the 11 calculational benchmarks are sufficient to produce an application-specific depletion reactivity decrement bias - defined as the bias associated with a users chosen depletion and criticality codes25 - that is consistent with the 10 CFR 50.68(b)(4) requirements. In the RAI 2a response, EPRI explains that the worst bias of the 66 benchmark cases (11 benchmarks at 6 different burnups) is used for the bias, which is a bounding approach that is conservative with respect to the development of a statistically based confidence interval provided that the 11 benchmarks are sufficiently applicable to the population of all possible SFP storage configurations. The details of the General Response provided in the EPRI utilization report (discussed above in the Benchmarks for Quantifying Fuel Reactivity Depletion Uncertainty subsection titled Applicability Studies Via Ck Analysis) demonstrates that the area of applicability is all current PWR fuel assembly designs for applications with most rack designs since it is indicated that all cases from the General Response exhibit similar reactivity sensitivities to nuclear data uncertainties.

It should also be noted that the confirmatory analysis in Appendix C produced uncertainties for 14x14 fuel in SFP geometry that are close to the uncertainties derived in the EPRI benchmark report. The observation that 14x14 fuel SFP uncertainties are similar is expected because sensitivity coefficients (e.g., ck values) have been shown to be greater than 0.9 for a broad range of fuel enrichments, assembly geometries, BA types, and storage rack geometries. This high degree of similarity supports application of the EPRI depletion benchmark uncertainties to a wide range of PWR fuel types and SFP geometries.

24 The NRC staff is concerned with both the reactor and SFP environment analyses; however, SFP environment analyses (e.g., sensitivity of the 11 calculation benchmark biases and uncertainties described in the utilization report to the entire population of actual SFP configurations) are the subject of the EPRI utilization report and are therefore of interest in this section.

25 This bias term is to be determined through the criticality code to be validated as part of the NRC licensee or applicant SFP CSA application.

As EPRI states in the EPRI utilization report RAI 7 response:

The General Response to [the EPRI utilization report] RAIs provides a similarity analysis to a range of rack and fuel designs and shows excellent agreement with non-flux trap racks designs and good agreement with flux trap designs with low burnup fuel. The criticality safety analyst can rely on the similarity analysis given in the general response and only needs to do further analysis if the rack or fuel is significantly different than current racks and fuel. If there is a new rack or fuel design significantly different [than] the current generation racks or fuels then the analyst should confirm similarity or use alternate methods to establish a bias and uncertainty for burned fuel in the spent fuel rack.

Finding The NRC staff agrees that if a new rack or fuel design is significantly different from those analyzed in the EPRI utilization report, then the analyst should confirm similarity or use alternate methods to establish a bias and uncertainty for depleted fuel storage in the SFP.

Given the above discussion, the NRC staff finds that:

1. The 11 calculational benchmarks are sufficient in number and diversity to be representative of the population of current SFP storage configurations, and

2. The use of a bounding approach for determination of the application-specific reactivity decrement bias is consistent with the intent of 10 CFR 50.68(b)(4).

Expected NRC Licensee Application of the EPRI Utilization Report Process Section 9.4, End-Users Application of Experimental Reactivity Decrements, of the EPRI benchmark report summarizes the general process, based on the EPRI benchmarking activities discussed in the EPRI benchmark and utilization reports, that EPRI believes end-users should use to validate their application-specific depletion and criticality codes for the purposes of crediting the reduced reactivity of depleted fuel in a SFP environment. The NRC staff, in general, finds this process to be acceptable, which is outlined in more detail in the EPRI utilization report. End-users should also take note of the reactivity decrement determination process described in Appendix C of the EPRI benchmark report.

Additional implementation guidance is given in the EPRI utilization report RAI 8 response regarding conservative treatment of reactivity decrement bias:

The most limiting bias is not merely the largest of the calculated biases but could include perturbations off of case 3 when a number of these perturbations simultaneously exist in the application. For example, the application could be 5 wt% enriched fuel run at 150% power. For this example, the application bias would be the case 3 bias (4.25% U-235, 100% power) plus the difference between case 3 and case 2 (5 wt% U-235, 100% power) plus the difference between case 3 and case 11 (4.25 wt% U-235, 150% power). If any of the differences were negative (i.e., non-conservative), then that difference would be set to zero. This example was chosen to provide a clear explanation; however, for the actual implementation, it is recommended to start with case 3 and then

conservatively add all the biases from all the deltas off of case 3 to determine a single bounding bias for the range of benchmarks.

Some applications may have enrichment less than 3.25 wt% U-235 from first core fuel, so extrapolation of the bias may be necessary. No general method for extrapolation is provided. It is expected that the applicant will use a conservative extrapolation consistent with their available margin. The extrapolation will be reviewed by the NRC and can be used to judge the acceptability of the extrapolation in the totality of the margin to criticality. In the Utilization report, analysis of the trend with [increasing] enrichment produced higher biases with

[increasing] enrichment. Therefore, the bias from the highest enrichment would be sufficient to cover enrichments below 3.25 wt% U-235.

Since application margin is part of the decision on the extrapolation method and the amount of conservatism to add, no generic approach is proposed.

When applying reactivity differences between cases, it would be conservative to consider any positive bias calculated, regardless of the Monte Carlo uncertainty. Not doing this would require some evidence that reactivity differences are not statistically significant, which would require consideration of the Monte Carlo uncertainty in support of this argument.

4.0 LIMITATIONS AND CONDITIONS

1. While the EPRI benchmark report utilized reactor measurements for cores containing two specific vendor fuel types with enrichments between 3.5% and 5.0%, EPRI also provided a similarity analysis between those fuel types contained in the benchmark and many other PWR fuel types to support the derived depletion reactivity benchmarks and associated uncertainties. Therefore, the derived depletion reactivity benchmarks and associated uncertainties are generally applicable to all PWR fuel types, with the exception of reactors using operational strategies and fuel designs that differ significantly from those of the EPRI benchmark report. For any such fuel designs, additional analysis may be required when applying the EPRI benchmarks for SFP burnup credit. For example, the applicability to fuel designs that credit residual gadolinia as a burnable absorber may require additional analysis and/or justification.

2. When using the EPRI benchmark and utilization report methodologies, the bias adder in Table 1 of this safety evaluation report must be included as a bias term when determining k-effective in SFP CSA applications.

5.0 CONCLUSION

The NRC staff has reviewed the EPRI benchmark and utilization reports, including supplemental information, and the NRC staff finds that the reports provide a sufficient technical basis for the determination of depletion code bias and uncertainty as part of a SFP CSA application.

6.0 REFERENCES

1. Broadhead, B. L., Rearden, B. T., Hopper, C. M., Wagschal, J. J., and Parks, C. V., 2004, Sensitivity-and Uncertainty-Based Criticality Safety Validation Techniques, Nuclear Science and Engineering 146, American Nuclear Society: 340-66.

2. DiGiovine, A.S., and Rhodes III, J.D., 2005, SIMULATE-3, Advanced Three-Dimensional Two-Group Reactor Analysis Code, Studsvik Scandpower SSP-95/15 Rev. 3.

3. Dyer, J. E., 2013, Letter to Nuclear Energy Institute Regarding Fee Waiver Under Part 170, Agencywide Documents Access and Management System (ADAMS) Accession No. ML13261A080.

4. EPRI, 2011, Benchmarks for Quantifying Fuel Reactivity Depletion Uncertainty, EPRI, Palo Alto, CA: 2011,1022909, ADAMS Accession No. ML12165A457.

5. EPRI, 2017, Benchmarks for Quantifying Fuel Reactivity Depletion UncertaintyRevision 1, EPRI, Palo Alto, CA: 2017, 3002010613, ADAMS Accession No. ML18088B397.

6. EPRI, 2018, Utilization of the EPRI Depletion Benchmarks for Burnup Credit Validation Revision 1, EPRI, Palo Alto, CA: 2018, 3002010614, ADAMS Accession No. ML18088B395.

7. Grandi, G. M., and Hagrman, D., 2007, Improvements to the INTERPIN Code for High Burnup and MOX Fuel, Transactions-American Nuclear Society 97, American Nuclear Society: 614-15.

8. Holonich, J., 2014, Request for Additional Information Related to Benchmarks for Quantifying Fuel Reactivity Depletion Uncertainty and Utilization of the EPRI Benchmarks for Burnup Credit Validation, ADAMS Accession No. ML14238A517.

9. Hsueh, K., 2016a, Summary of June 8, 2016, Meeting with the Nuclear Energy Institute to Discuss the Electric Power Research Institute Depletion Code Validation Approach, ADAMS Accession No. ML16175A323.

10. Hsueh, K., 2016b, Summary of October 14, 2016, Meeting with the Nuclear Energy Institute to Discuss EPRI Depletion Code Validation Approach, ADAMS Accession No. ML16335A107.

11. Mennerdahl, D., 2014, Correlations of Error Sources and Associated Reactivity Influences, Transactions-American Nuclear Society 110, American Nuclear Society: 292-94.

12. NEI, 2013a, Request for Exemption from NRC Fees to Review NEI 12-16, Guidance for Performing Criticality Analyses of Fuel Storage at Light-Water Reactor Power Plants, and Solicitation of Feedback on Pre-Submittal Draft, Dated January 2013, ADAMS Accession No. ML13004A392.

13. NEI, 2013b, Guidance for Performing Criticality Analyses of Fuel Storage at Light-Water Reactor Power Plants, Revision 0, Nuclear Energy Institute, ADAMS Accession No. ML130840163.

14. NEI, 2015a, Responses to Requests for Additional Information for EPRI Reports 1022909 and 1022503 Referenced in NEI 12-16, ADAMS Accession No. ML15061A351.

15. NEI, 2015b, Updated Responses to Requests for Additional Information for EPRI Report 1022503 Referenced in NEI 12-16, ADAMS Accession No. ML15139A074.

16. NEI, 2016a, Response to Request for Additional Information (RAI) Questions Regarding EPRI Report 1025203, Utilization of the EPRI Depletion Benchmarks for Burnup Credit Validation, and EPRI Report 1022909, Benchmarks for Quantifying Fuel Reactivity Depletion Uncertainty, ADAMS Accession No. ML16104A332.

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ANS Topical Meeting on Reactor Physics (PHYSOR-2006), American Nuclear Society.

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ProductAbstract.aspx?ProductId=000000003002001948.

Principal Contributor: Amrit Patel, NRR/DSS/SNPB Date: February 7, 2019

APPENDIX A: HETEROSCEDASTIC REGRESSION POINT-WISE TOLERANCE INTERVALS Introduction This appendix provides the details behind the derivation of tolerance interval K-factors for use with linear regressions when the error structure is heteroscedastic. The heteroscedastic errors require that a weighted least squares be used for the parameter estimation. The derivation of the one-sided point-wise tolerance intervals involve the cumulative distribution function of the non-central t distribution. The derivations of the one-sided and two-sided K-factors are more complicated than for the standard tolerance intervals applied to a simple random sample. The tolerance intervals considered here are point-wise for given values of the independent variable and do not provide joint confidence. The derivation given below uses a quadratic regression model to illustrate the analysis. Extensions to other polynomial and nonlinear regression models are also possible. A similar problem and approach is considered in Myhre et al., 200926.

Weighted Least Squares Suppose the data ( , ) may be modeled with a quadratic reqression:

= + + + (1) for = 1,2, , , where , , and are unknown parameters and the Normally distributed random errors are independent with zero mean and variances equal to ( ) for a known function () and an unknown parameter . Some common examples are ( ) = and

( )= .

Let the vector contain the values . Let the matrix have three columns: the first a column of ones, the second containing the values , and the third containing the values . Let be a diagonal matrix containing ( ) as the diagonal elements. The weighted least squares estimates are:

=( )

where the primes indicate the matrix transpose. The estimated covariance matrix associated with the weighted least squares estimates is:

= ( )

where, 26 Myhre, Janet, Daniel R. Jeske, Michael Rennie, and Yingtao Bi, (2009). Tolerance intervals in a heteroscedastic linear regression context with applications to aerospace equipment surveillance, International Journal of Quality, Statistics, and Reliability, 2009:1-8. doi:10.1155/2009/126283.

= + +

and,

= ( ) .

Aspects of the Predictive Distribution Consider the distribution of values for a future fixed value of assuming the model in Equation 1. The distribution is assumed to be Normal with mean = + + and variance = ( ). The mean is estimated as = + + and the variance is estimated as = ( ). The variance of is which is estimated as the quadratic form

= , where the vector = (1, , ). The degrees of freedom associated with is 3.

One-Sided Tolerance Intervals A general upper one-sided tolerance interval on the distribution of the previous section has confidence x 100% of containing the lower x 100% of the distribution. The upper one-sided tolerance limit takes the form:

+ ( )

The notation indicates that the one-sided K-factor depends on the value of (as well as on , ,

and ). Because the mean estimator is normally distributed and the variance estimator is distributed as / times a Chi-squared random variable with = 3 degrees of freedom, it may demonstrated that the K-factor ( ) is:

1

( )=  ; 3, where (; , ) is the cumulative distribution function of the non-central t distribution with degrees of freedom and non-centrality parameter and is the x 100% quantile of the standard Normal distribution. The value of the factor is / which reduces to:

/

( )

=

( )

a function of the data and , but not the data.

The same K-factor is used for a lower one-sided tolerance interval. Also, the K-factor ( ) is not constant nor is it linear in .

Two-Sided Tolerance Intervals The limits of the two-sided tolerance interval take the form:

+/- ( )

The computation of the exact two-sided K-factor is complicated. However, a simpler approximation usually suffices:

/

1 1+

( )

( )

where = (1 + )/2, , is the critical value of the Chi-Squared distribution with degrees of freedom = 3 that is exceeded with probability , and ( ) is the effective for :

( )=

The interpretation of ( ) is that we can treat as if it were the average from a simple random sample of size ( ).

If the variance is reduced by an estimate of the ground truth variance, that is = ( )

, then it is necessary to modify the factor:

/

( )

=

and the degrees of freedom (using Satterthwaites formula) accordingly.

APPENDIX B: TOLERANCE INTERVAL CONFIRMATORY ANALYSIS RESULTS The NRCs consultant, Pacific Northwest National Laboratory, analyzed the burnup/decrement bias data, provided by EPRI, using a heteroskedastic/generalized least squares approach to independently confirm the validity of EPRIs data analysis as described in Section 7 of the revised EPRI benchmark report. The focus was on producing reasonable one-sided 95/95 tolerance intervals on the decrement bias as a function of burnup.

The data within each sub-batch was assumed to be correlated. These correlations required a modification of the tolerance interval calculations described in detail in Appendix A.

The first attempt at modeling the correlation structure in the sub-batches involved a simple random effects model (following Nichols and Schaffer, 200727). Examination of the data suggested that this model was inappropriate. The second attempt at modeling the correlation structure in the sub-batches involved a first-order autoregressive model, written as AR(1), which was found to provide a better fit to the data.

The results of the analysis assuming a linear function for the average decrement bias as a function of burnup are shown in Figure 1. The correlated heteroskedastic error structure within each sub-batch was assumed to be an AR(1) (with scaling parameter of 0.83 and a single stationary variance for all sub-batches) multiplied by the burnups.

Figure 1. Results of the Linear Model Fitting.

27 Nichols, Austin and Schaffer, Mark, (2007), Clustered standard errors in Stata, United Kingdom Stata Users Group Meetings 2007, Stata Users Group, http://EconPapers.repec.org/RePEc:boc:usug07:07.

The estimate of the stationary standard deviation was 14.15. So, the estimate of the standard deviation of the decrement biases for a burnup of is 14.15 . The resulting tolerance intervals are nearly linear. The one-sided upper 95/95 tolerance interval fails to include 155 of the 2856 data points (5.427 percent). The one-sided lower 95/95 tolerance interval fails to include 89 of the 2856 data points (3.116 percent). These are reasonable values as the intervals are constructed to contain 95 percent of the decrement biases with 95 percent confidence.

The results of the analysis assuming a quadratic function for the average decrement bias as a function of burnup are shown in Figure 2. The estimate of the stationary standard deviation was 14.14. So, the estimate of the standard deviation of the decrement biases for a burnup of is 14.14 . The one-sided upper 95/95 tolerance interval fails to include 146 of the 2856 data points (5.112 percent). The one-sided lower 95/95 tolerance interval fails to include 85 of the 2856 data points (2.976 percent). The estimate of the quadratic term is not very statistically significant (the t-value is only -1.66), so the linear model analysis is preferred.

Figure 2. Results of the Quadratic Model Fitting.

Figure 3 supports the assumed heteroskedastic error structure because dividing the decrement biases by the burnups produces a substantially more homoscedastic looking data plot. Some obvious structure in the data is not accounted for in the modeling. The lines of data are not explained by the sub-batching of the data. This type of structure is likely caused by the use of discrete burnup multipliers in the error deduction algorithm described in Section 6.4, Iteration Implementation, of the EPRI benchmark report.

The tolerance intervals may be viewed as being conservative as no attempt was made to remove measurement error from the decrement bias errors.

Figure 3. Plot of the Decrement Bias divided by Burnup.

APPENDIX C: CONFIRMATION OF MEASURED COLD REACTIVITY BIAS AND UNCERTAINTY Introduction The nature of the in-core measurement benchmarks (i.e., at hot in-core conditions instead of cold in-rack conditions) led EPRI to develop a methodology to translate the depletion reactivity worth uncertainty at hot in-core conditions to an effective worth at cold in-rack conditions representative of a SFP environment. EPRI benchmark report28 Section 7, Measured HFP Reactivity Bias and Uncertainty, is devoted to use of statistical analysis requiring many assumptions to deduce the depletion worth bias and uncertainty as a function of burnup at hot in-core conditions. Additionally, EPRI benchmark report Section 8, Measured Cold Reactivity Bias and Uncertainty, is devoted to quantifying the effect of fuel temperature uncertainty during fuel depletion and how this might propagate to cold in-rack conditions while also translating cross-section uncertainties at cold in-rack conditions to those at hot in-core conditions again requiring several assumptions to be made.

As a simple confirmatory check against the numerous assumptions in Sections 7 and 8 of the EPRI benchmark report to translate the hot in-core depletion worth uncertainty to cold in-rack depletion worth uncertainty applicable to SFP CSAs, two hypothetical SFP configurations were created to compare CASMO-5 quantified hot in-core depletion worth uncertainty to an effective cold in-rack depletion worth uncertainty directly without use of statistical analysis or fuel temperature and cross-section uncertainty analysis.

Confirmatory Method The idea is to transfer EPRI-generated nuclide concentrations from one axial node of a SIMULATE-3 calculation to a potential SFP storage configuration. However, the EPRI-generated nuclide concentrations for all axial nodes from all SIMULATE calculations are unavailable. Instead, EPRI has provided the burnup multipliers that serve to correct the calculated sub-batch average burnups to a measured sub-batch average burnup. Therefore, this analysis uses the effective measured sub-batch average burnup from SIMULATE to derive a corresponding lattice depletion code model to determine representative measured sub-batch average nuclide concentrations. Since CASMO-5 was unavailable for use to determine measured sub-batch average nuclide concentrations, the NRC confirmatory SCALE/TRITON29 depletion code was used instead. Note that EPRI has shown in Table 3-1, Difference Between Calculated and Measured Reactivity Decrements for EPRI Benchmarks with 100-Hour Cooling Using ENDF/B-VII Cross Section Library, from the EPRI utilization report30 that using 28 ADAMS Accession No. ML18088B397.

29 SCALE Version 6.2 (April 2016) was used for all confirmatory calculations. The specific TRITON depletion sequence used was the T-DEPL sequence with the 252 group ENDF/B-VII nuclear data library collapsed to 56 groups. The specific KENO-VI criticality sequence used was the CSAS6 sequence with the 252 group ENDF/B-VII nuclear data library.

30 ADAMS Accession No. ML18088B395.

SCALE/TRITON with ENDF/B-VII cross-section data produces excellent agreement with CASMO-5 over the range of relevant fuel burnups. Consequently, no correction has been applied to account for code-to-code differences for the confirmatory analyses performed; however, it is expected that this be done when applying EPRIs method in SFP CSA licensing applications.

The SFP storage configuration chosen was arbitrary, but it is noted that a fuel design different from those that form the basis of the data in the EPRI benchmark report is used.

The basic steps used to carry out the analyses are as follows:

1. Choose a data point from those presented in EPRI benchmark report Figure 7-1, CASMO-5 Bias in Reactivity.

2. Specify the enrichment and SIMULATE-calculated average sub-batch burnup corresponding to Step 1 in a SCALE/TRITON depletion input file.

3. Using the input file in Step 2, add the following specifications:

a. Borated (natural) water at 1500 ppm; the value is an arbitrarily chosen simplification instead of using a letdown curve but it is valid.

b. Fuel temperature at 922 K; the value was chosen to approximate the burnup averaged fuel temperature of the data given in Figure 8-1, Typical INTERPIN-4 Fuel Temperature Change With Burnup.

c. Moderator density at 0.654 grams per cubic centimeter and 598 K; the values were arbitrarily chosen but are valid.

d. Westinghouse 14x14 fuel assembly design with 119 IFBA; this is an arbitrarily chosen fuel design but it is valid.

4. Run the hot in-core depletion case; at completion, run a decay case for five days to minimize the short-lived fission products and maximize SFP reactivity.

5. Transfer the fuel nuclide concentrations to a SCALE/KENO-VI SFP criticality input file, which models:

a. A semi-infinite representative 2x2 stainless steel storage cell array without fixed neutron absorber panels (i.e., modeled with periodic boundary conditions on the x- and y- coordinate faces and vacuum boundary conditions on the z-faces).

b. Three out of four storage cells filled with depleted fuel using the transferred fuel nuclide concentrations.

6. Run the cold in-rack criticality case modeled in Step 5.

7. Repeat Steps 2-6 but specify the average sub-batch burnup in Step 2 to be equal to the calculated average sub-batch burnup multiplied by the burnup multiplier31 determined by applying the methodology in Section 6.4, Iteration Implementation, of the EPRI benchmark report. This is effectively the inferred measured average sub-batch burnup.

8. Using the same criticality model from Step 5, replace depleted fuel with fresh fuel with IFBA removed and run the case.

9. Calculate the reactivity difference between Step 6 and Step 7. This is an estimate of the depletion worth uncertainty.

10. Calculate the reactivity difference between Step 6 and Step 8. This is an estimate of the depletion worth.

11. Divide the result of Step 9 by the result of Step 10. This is an estimate of the depletion worth uncertainty as a percentage of the depletion worth.

If the assumptions of Sections 7 and 8 of the EPRI benchmark report are valid, the estimate of the uncertainty calculated in Step 11 is expected to be similar (ideally it would be bounded) to that specified by EPRI in Table 10-2, Measured CASMO-5 Cold Reactivity Decrement Biases and Tolerance Limits Expressed as Percentage of Absolute Value of Depletion Reactivity Decrement. This is verified as discussed in the Observations section below.

Additionally, it is expected that the hot in-core depletion worth uncertainty without temperature and cross-section uncertainty correction for the two sub-batches analyzed will be approximately the same as the nodal cold in-rack depletion worth uncertainty in order to substantiate EPRIs claim of similarity between hot in-core conditions and cold in-rack conditions. This is also verified and discussed in the Observations section below.

Cases The confirmatory method described above was applied to two cases taken from the EPRI depletion benchmark data - one at a relatively low burnup and one at a relatively high burnup:

1. Calculated average sub-batch burnup equal to 15.913 GWd/MTU with an initial enrichment of 3.86 wt% UO2 and a burnup multiplier equal to 0.95. For this case, the EPRI-determined reactivity decrement bias is equal to 474 pcm. That is, in EPRI benchmark report Figure 7-1, this represents a single data point at a burnup of 15.913 GWd/MTU and reactivity decrement bias of 474 pcm.

2. Calculated average sub-batch burnup equal to 42.625 GWd/MTU with an initial enrichment of 3.81 wt% UO2 and a burnup multiplier equal to 0.96. For this case, the EPRI-determined reactivity decrement bias is equal to 977 pcm.

31 Burnup multipliers and corresponding reactivity decrement biases for the various sub-batches were provided in Attachment 2 to a letter dated January 9, 2017 (ADAMS Accession No. ML18018A852).

Results The table below contains the results of applying the confirmatory method described above to the two cases described above. The values in columns Step6 through Step8 are the calculated k-effective values from the SCALE/KENO-VI runs, those in columns Step9 and Step10 are in units of k, and Step11 is the depletion code uncertainty in units of percent reactivity decrement.

Table 1: Confirmatory Analysis Results Case Step6 Step7 Step8 Step9 Step10 Step11 1 1.02132 1.02596 1.13006 -0.00464 -0.10874 4.267059 2 0.86958 0.87857 1.13006 -0.00899 -0.26048 3.451321 In the EPRI utilization report, EPRI defines burnup dependent uncertainty data in terms of percent reactivity decrement in Table 4-1, Measured Reactivity Decrement Biases and Tolerance Limits Expressed as Percentage of Depletion Reactivity Decrement, which is based on Table 10-2 in the EPRI benchmark report. The bias and uncertainty data is reproduced in Table 2 below. EPRI notes that the bias term in Table 10-2 of the EPRI benchmark report has been added to the measured reactivity decrement values tabulated in Tables C-3 to C-5 of the EPRI benchmark report, which are used to determine application-specific bias, therefore an end-user of the EPRI utilization report does not need to consider this bias term separately.

However, it is included in Table 2 below to allow for appropriate comparisons in this analysis.

Table 2: EPRI-Defined Bias and Uncertainty Burnup Bias Uncertainty 10 0.58 3.05 20 0.50 2.66 30 0.38 2.33 40 0.23 2.12 50 0.05 1.95 60 -0.13 1.81 Finally, the results of applying four methods per case are presented:

1. The EPRI-defined percent reactivity decrement values (labeled EPRI),

2. The NRC-adjusted EPRI-defined percent reactivity decrement values based on the linear fit confirmatory analysis described in Appendix B (labeled NRC-adj),

3. The NRC confirmatory analysis result produced using the confirmatory method outlined in this appendix (labeled NRC-conf), and

4. The historical Kopp 5 percent method.

In order to compare methods (1) and (2) to (3) and (4), the percent reactivity decrements must be put in terms of a net reactivity effect applied to a typical SFP CSA. All methods have an uncertainty component that would be added, typically by RSS, to establish a net uncertainty term. Therefore, to simulate addition by RSS, the uncertainty values are divided by a factor to estimate the bottom-line reactivity impact in the SFP CSA. Based on experience in past

licensing applications, the depletion code uncertainty contributes approximately a tenth of the net uncertainty at low burnup and about a fourth at higher burnup. Therefore, Case 1 uncertainties are reduced by a factor of 10 and Case 2 uncertainties are reduced by a factor of 4; the respective terms are then added directly to the corresponding bias components since bias components have a direct effect on the bottom-line reactivity impact (this is the value in the RelImpact column of Table 3). The AbsImpact column is the RelImpact column multiplied by the depletion worth from Table 1.

Table 3: Net SFP CSA Impact in Terms of Percent of Depletion Worth Case Method Bias Uncertainty RelImpact AbsImpact 1 EPRI 0.53 2.82 0.89 88 1 NRC-adj 0.17 3.53 0.52 57 1 NRC-conf 0.00 4.27 0.43 46 1 Kopp 5% 0.00 5.00 0.50 54 2 EPRI 0.18 2.08 0.70 182 2 NRC-adj 0.54 3.03 1.30 338 2 NRC-conf 0.00 3.45 0.86 225 2 Kopp 5% 0.00 5.00 1.25 326 Observations The main observations to highlight are:

1. The hot in-core depletion worth uncertainty without temperature and cross-section uncertainty correction for the two sub-batches analyzed was seen to be approximately the same as the nodal cold in-rack depletion worth uncertainty, which support verification of the assumptions in Sections 7 and 8 of the EPRI benchmark report.32

2. The net SFP CSA bias plus uncertainty determined from the confirmatory method described in this appendix is either bounded by EPRIs method or is comparable.

3. All four methods give approximately the same net SFP CSA bias plus uncertainty at lower burnups, but not at higher burnups; refer to the AbsImpact column of Table 3 which is the absolute magnitude of the impact on the SFP CSA bias plus total uncertainty.

These observations support EPRIs recommended burnup-dependent bias and uncertainty values as provided in Table 4-1 of the revised EPRI utilization report at lower burnups, but not at higher burnups. The higher burnup case used in the Case 2 methods described in this appendix is 42.625 GWd/MTU. A maximum difference of 156 pcm is observed at this burnup between bottom-line reactivity impacts among EPRI and NRC uncertainty results. This means that the difference will only increase up to 60 GWd/MTU since EPRIs bias and uncertainty 32 The hot in-core depletion worth uncertainty for Case 1 and 2, calculated by EPRI using SIMULATE-3, is 474 pcm and 977 pcm, respectively. The cold in-rack depletion worth uncertainty for Case 1 and 2, taken from Table 1 in column Step9, is 464 pcm and 899 pcm, respectively.

terms decrease with increasing burnup. Further inspection of the confirmatory results indicate that differences are minimal for burnups less than or equal to 30 GWd/MTU.