Text

WCAP-18124-NP-A, Revision 0, Fluence Determination with RAPTOR-M3G and Ferret, July 2018
	ML18204A010
Person / Time
Site:	Westinghouse
Issue date:	07/20/2018
From:	; Westinghouse
To:	; Office of Nuclear Reactor Regulation
Shared Package
ML18204A008	List: ML18204A009; ML18204A010;
References
	CAC MF9141, LTR-NRC-18-54 WCAP-18124-NP-A, Rev. 0
	Download: ML18204A010 (138)
	v • d • e

Westinghouse Non-Proprietary Class 3 WCAP-18124-NP-A July 2018 Revision 0 Fluence Determination with RAPTOR-M3G and FERRET

Westinghouse Non-Proprietary Class 3 *Electronically approved records are authenticated in the electronic document management system. Westinghouse Electric Company LLC 1000 Westinghouse Drive Cranberry Township, PA 16066, USA © 2018 Westinghouse Electric Company LLC All Rights Reserved WCAP-18124-NP-A (2).docx-071218 WCAP-18124-NP-A Revision 0 Fluence Determination with RAPTOR-M3G and FERRET Greg A. Fischer* Radiation Engineering & Analysis Jianwei Chen* Radiation Engineering & Analysis July 2018 Technical Reviewer: Eugene T. Hayes* Radiation Engineering & Analysis Licensing Reviewer: James D. Smith* Plant Licensing & Engineering Approved: Laurent P. Houssay*, Manager Radiation Engineering & Analysis Edmond J. Mercier*, Manager Fuels Licensing & Regulatory Support

Westinghouse Non-Proprietary Class 3 ii WCAP-18124-NP-A July 2018 Revision 0 REGULATORY CORRESPONDENCE TABLE OF CONTENTS Section Description A Final Safety Evaluation Letter from Dennis C. Morey (NRC) to James A. Gresham (Westinghouse), "Final Safety Evaluation for Westinghouse Electric Company Topical Report WCAP-18124-NP, Revision 0,

'Fluence Determination with RAPTOR-M3G and FERRET' (CAC No. MF9141)," with attachments "Final Safety Evaluation for Topical Report WCAP-18124-NP, Revision 0, 'Fluence Determination with RAPTOR-M3G and FERRET' Westinghouse Electric Company" and "Resolution of Comments on Draft Safety Evaluation for Topical Report WCAP-18124-NP, Revision 0, 'Fluence Determination with RAPTOR-M3G and FERRET' Westinghouse Electric Company," June 15, 2018 (ADAMS Accession No. ML18155A186). B Submittal of Topical Report Letter from James A. Gresham (Westinghouse) to U. S. NRC, "Submittal of WCAP-18124-NP, Revision 0, 'Fluence Determination with RAPTOR-M3G and FERRET,'" Westinghouse Letter LTR-NRC-17-7, January 25, 2017 (ADAMS Accession No. ML17030A377). C Acceptance for Review Letter from Dennis C. Morey (NRC) to James A. Gresham (Westinghouse), "Acceptance for Review of Westinghouse Electric Company Topical Report WCAP-18124-NP, Revision 0, 'Fluence Determination with RAPTOR-M3G and FERRET' (TAC No. MF9141)," June 27, 2017 (ADAMS Accession No. ML17166A063). D Request for Additional Information Letter from Ekaterina Lenning (NRC) to James A. Gresham (Westinghouse), "Request for Additional Information RE: Westinghouse Electric Company WCAP-18124-NP, Revision 0, 'Fluence Determination with RAPTOR-M3G and FERRET' Topical Report (CAC No. MF9141)," November 21, 2017 (ADAMS Accession No. ML17290A147). E Submittal of Response to Request for Additional Information Letter from James A. Gresham (Westinghouse) to U.S. NRC, "Response to the NRC Request for Additional Information on the RAPTOR-M3G and FERRET Topical Report," Westinghouse Letter LTR-NRC-18-5, January 18, 2018 (ADAMS Accession No. ML18018B347).

Westinghouse Non-Proprietary Class 3 iii WCAP-18124-NP-A July 2018 Revision 0 Section A Final Safety Evaluation Letter (3 Pages) Final Safety Evaluation Attachment (13 Pages) Comment Resolution Attachment (3 Pages)

Westinghouse Non-Proprietary Class 3 WCAP-18124-NP-A July 2018 Revision 0

/RA Serita Sanders for

Westinghouse Non-Proprietary Class 3 WCAP-18124-NP-A July 2018 Revision 0

for Westinghouse Non-Proprietary Class 3 WCAP-18124-NP-A July 2018 Revision 0

Code of Federal Regulations Westinghouse Non-Proprietary Class 3 WCAP-18124-NP-A July 2018 Revision 0

Westinghouse Non-Proprietary Class 3 WCAP-18124-NP-A July 2018 Revision 0

The analytical methods used to determine the RCS pressure and temperature limits shall be those previously reviewed and approved by the NRC, specifically those described in the following documents: ...

Westinghouse Non-Proprietary Class 3 WCAP-18124-NP-A July 2018 Revision 0

Westinghouse Non-Proprietary Class 3 WCAP-18124-NP-A July 2018 Revision 0

Westinghouse Non-Proprietary Class 3 WCAP-18124-NP-A July 2018 Revision 0

Westinghouse Non-Proprietary Class 3 WCAP-18124-NP-A July 2018 Revision 0

Westinghouse Non-Proprietary Class 3 WCAP-18124-NP-A July 2018 Revision 0

license renewal applications

Westinghouse Non-Proprietary Class 3 WCAP-18124-NP-A July 2018 Revision 0

Westinghouse Non-Proprietary Class 3 iv WCAP-18124-NP-A July 2018 Revision 0 Section B Submittal of Topical Report Letter (1 Page)

WCAP-18124-NP-A July 2018 Revision 0 Westinghouse Non-Proprietary Class 3 v WCAP-18124-NP-A July 2018 Revision 0 Section C Acceptance for Review Letter (3 Pages)

June 27, 2017

Mr. James A. Gresham, Manager

Regulatory Compliance and Plant Licensing Westinghouse Electric Company 1000 Westinghouse Drive Cranberry Township, PA 16066

SUBJECT:

ACCEPTANCE FOR REVIEW OF WESTINGHOUSE ELECTRIC COMPANY TOPICAL REPORT WCAP-18124-NP, REVISION 0, "FLUENCE DETERMINATION WITH RAPTOR-M3G AND FERRET" (TAC NO. MF9141)

Dear Mr. Gresham:

By letter dated January 25, 2017 (Agencywide Documents Access and Management System (ADAMS) Accession No. ML17030A377), Westinghouse Electric Company (Westinghouse) submitted for U.S. Nuclear Regulatory Commission (NRC) staff review Topical Report (TR)

WCAP-18124-NP, Revision 0, "Fluence Determination with RAPTOR-M3G and FERRET."

The NRC staff has reviewed submitted information and performed an acceptance review of the TR. We have found that the material presented is sufficient to begin our review. We expect to issue our initial request for additional information by December 15, 2017, and issue a draft safety evaluation by July 31, 2018. This schedule information takes in consideration the NRC's current review priorities and available technical resources and may be subject to change. If

modifications to these dates are deemed necessary, we will provide appropriate updates to this

information.

The NRC staff estimates that the review will require approximately 300 staff hours including project management time. The review schedule milestones and estimated review costs were discussed and agreed upon via email between Jim Smith, Licensing Engineer, Westinghouse, and the NRC staff on June 13, 2017.

Section 170.21 of Title 10 of the Code of Federal Regulations requires that TRs are subject to fees based on the full cost of the review. You did not request a fee waiver; therefore, NRC staff hours will be billed accordingly.

Westinghouse Non-Proprietary Class 3 WCAP-18124-NP-A July 2018 Revision 0

If you have questions regarding this matter, please contact Ekaterina Lenning at (301) 415-3151.

Sincerely, /RA/

Dennis C. Morey, Chief Licensing Processes Branch Division of Policy and Rulemaking Office of Nuclear Reactor Regulation Project No. 700 Westinghouse Non-Proprietary Class 3 WCAP-18124-NP-A July 2018 Revision 0

ML17166A063 *concurred via e-mail NRR-106 OFFICE NRR/DPR/PLPB NRR/DPR/PLPB* NRR/DSS/SNPB NRR/DPR/PLPB NAME ELenning DHarrison RLukes DMorey DATE 06/15/17 06/20/17 06/21/17 06/27/17

Westinghouse Non-Proprietary Class 3 vi WCAP-18124-NP-A July 2018 Revision 0 Section D Request for Additional Information Letter (5 Pages)

November 21, 2017

Mr. James A. Gresham, Manager

Regulatory Compliance and Plant Licensing Westinghouse Electric Company 1000 Westinghouse Drive Cranberry Township, PA 16066

SUBJECT:

REQUEST FOR ADDITIONAL INFORMATION RE: WESTINGHOUSE ELECTRIC COMPANY WCAP-18124-NP, REVISION 0, "FLUENCE DETERMINATION WITH RAPTOR-M3G AND FERRET" TOPICAL REPORT (CAC NO. MF9141)

Dear Mr. Gresham:

By letter dated January 25, 2017 (Agencywide Documents Access and Management System Accession No. ML17030A377), Westinghouse Electric Company (Westinghouse) submitted for U.S. Nuclear Regulatory Commission (NRC) staff review Topical Report (TR)

WCAP-18124-NP, Revision 0, "Fluence Determination with RAPTOR-M3G and FERRET." Upon the review of the TR, the NRC staff has determined that additional information is needed to complete the review.

Enclosed are the NRC staff request for additional information (RAI) questions. During the clarification call on October 17, 2017, Westinghouse informed the NRC staff that Westinghouse will provide the responses to the enclosed NRC staff RAI questions within 60 days after the issuance of the questions.

If you have any questions regarding the enclosed questions, please contact me at 301-415-3151.

Sincerely,

/RA/ Ekaterina Lenning, Project Manager Licensing Processes Branch

Division of Licensing Projects Office of Nuclear Reactor Regulation Project No. 700

Enclosure:

As stated Westinghouse Non-Proprietary Class 3 WCAP-18124-NP-A July 2018 Revision 0

ML17290A147; *via e-mail NRR-106 OFFICE PLPB/PM PLPB/LA* SNPB/BC* PLPB/BC* PLPB/PM NAME ELenning DHarrison RLukes DMorey ELenning DATE 10/17/2017 11/7/2017 11/16/2017 11/17/2017 11/21/2017 Enclosure U. S. NUCLEAR REGULATORY COMMISSION REQUEST FOR ADDITIONAL INFORMATION FOR WCAP-18124-NP, REVISION 0, "FLUENCE DETERMINATION WITH RAPTOR-M3G AND FERRET," TOPICAL REPORT WESTINGHOUSE ELECTRIC COMPANY PROJECT NO. 700 Regulatory Basis Regulatory Guide (RG) 1.190, "Calculational and Dosimetry Methods for Determining Pressure Vessel Neutron Fluence," describes methods and assumptions acceptable to the U.S. Nuclear Regulatory Commission (NRC) staff for determining the reactor pressure vessel (RPV) neutron fluence with respect to the General Design Criteria (GDC) contained in Appendix A of Title 10 of

the Code of Federal Regulations (10 CFR) Part 50. In consideration of the guidance set forth in RG 1.190, GDC 14, 30, and 31 are applicable. GDC 14, "Reactor Coolant Pressure Boundary," requires the design fabrication, erection, and testing of the reactor coolant pressure boundary so as to have an extremely low probability of abnormal leakage, of rapidly propagating failure, and of gross rupture. GDC 30, "Quality of Reactor Coolant Pressure Boundary," requires among other things, that components comprising the reactor coolant pressure boundary be designed, fabricated, erected, and tested to the highest quality standards practical. GDC 31, "Fracture Prevention of Reactor Coolant Pressure Boundary," pertains to the design of the reactor coolant pressure boundary, stating:

The reactor coolant pressure boundary shall be designed with sufficient margin to assure that when stressed under operating, maintenance, testing, and postulated accident conditions, (1) the boundary behaves in a nonbrittle manner and (2) the probability of rapidly propagating fracture is minimized. The design shall reflect consideration of service temperatures and other conditions of the boundary material under operating, maintenance, testing, and postulated accident conditions and the uncertainties in determining (1) materials properties, (2) the effects of irradiation on material properties, (3) residual, steady state and transient stresses, and (4) size of flaws.

RAI 1 Section 2.5, "Discrete Ordinates Transport Calculations with RAPTOR-M3G," of WCAP-18124-NP, Revision 0, Westinghouse Electric Company (Westinghouse) topical report (TR) states: "RAPTOR-M3G calculations are performed with an S 8 (or higher) level-symmetric angular quadrature set." RG 1.190, Section 1.3.1, "Discrete Ordinates Transport Calculation," states: "The adequacy of the spatial mesh and angular quadrature, as well as the convergence criterion, must be demonstrated by tightening the numerics until the resulting changes are negligible (Refernce

32). Westinghouse Non-Proprietary Class 3 WCAP-18124-NP-A July 2018 Revision 0 In discrete ordinates codes, the spatial mesh and the angular quadrature should be refined simultaneously." Regulatory Position 1.3.5, "Cavity Calculations," states: "In discrete ordinates transport calculations, the adequacy of the S 8 angular quadrature used in cavity transport calculations must be demonstrated." Furthermore, Section 1.3.5 of RG 1.190 states: "However, when off-midplane locations are analyzed, the adequacy of the S 8 quadrature to determine the streaming component must be demonstrated with higher-order S n calculations." Based on the above, please explain how the adequacy of the S 8 angular quadrature (and associated spatial mesh) has been demonstrated for the entire spatial domain for which RAPTOR-M3G is applicable. Also, please define the standard method for determining when greater than S 8 angular quadrature is needed.

RAI 2 Please describe how the chi-squared divided by degrees-of-freedom statistic is used to assess the validity of FERRET results. Please define the criteria used and subsequent actions taken for unacceptable chi-squared divided by degrees-of-freedom values.

RAI 3 The text in WCAP-18124-NP, Revision 0, Section 4.4.1, "Core Neutron Source Uncertainties,"

on page 4-17 implies that peripheral pin power for a given node could be effected by each of three independent uncertainties. That is the pin power could be off by as much as 5 percent due to in-core measurement uncertainty for a given assembly, 10 percent due to uncertainty in the relative pin power for a given assembly, and 10 percent based on variation in the axial peaking factor over the course of a fuel cycle. Please explain how the formulations given in Table 4-15, Case Numbers 3, 4, 7, and 8 relate to the assumption of 10 percent uncertainty in

the fuel assembly relative power shapes given that the expectation based on the text descriptions of these formulations imply a direct multiplication of the nodal pin power by a factor of 1 plus or minus the assumed uncertainty.

RAI 4 The text in WCAP-18124-NP, Revision 0, Section 4.4.1, "Core Neutron Source Uncertainties," on page 4-17 regarding the uncertainty due to the burnup of the peripheral fuel assemblies is

ambiguous when considering corresponding information in Table 4-15 (and corresponding footnotes) and Table 4-16, "Source Permutation-to-Nominal Fast Neutron (E > 1.0 MeV) Fluence Rate Difference at Surveillance Capsule Locations." Please provide clarification regarding the reference burnup and perturbed burnup assumed for Cases 5 and 6 of Table 4-15.

RAI 5 Section 4.3.3, "Summary of Operating Reactor and Calculational Benchmark Results," of WCAP-18124-NP, Revision 0, states: "The H. B. Robinson Unit 2 benchmark represents an experimental configuration that is broadly reflective of most operating reactors: data was collected during full-power operation at a commercial light water reactor; the power distribution and power history data supporting the analysis were derived using methods similar to those employed by most operating LWRs; geometric dimensions specified are nominal dimensions, and not necessarily identical to their as-built configuration." Westinghouse Non-Proprietary Class 3 WCAP-18124-NP-A July 2018 Revision 0 In support of WCAP-18124-N, Revision 0, applicability determination for reactor designs other than Westinghouse three-loop pressurized water reactors, provide the reactor designs for the 18nuclear power plants discussed in Section 5.4, "Operating Power Reactor Comparisons," that have been analyzed with RAPTOR-M3G and FERRET.

RAI 6 RG 1.190, Section 1.4.2.1, "Operating Measurements," states: "Well documented fluence dosimetry measurements for operating power reactors may be used for methods and data qualification.... As capsule and cavity measurements become available, they should be incorporated into the operating reactor measurements data base, and the calculational biases and uncertainties should be updated as necessary." From WCAP-18124-NP, Revision 0, Section 5.4, Westinghouse states that "there are 69 in-vessel surveillance capsules with

295 threshold foil measurements from 18 nuclear power plants that have been analyzed with RAPTOR-M3G and FERRET." However, if Westinghouse supports more than 18 plants both domestically and internationally with RAPTOR-M3G/FERRET, please provide a table similar to Tables 5-10, 5-11, and 5-12, including all of the plants supported by Westinghouse both domestically and internationally to confirm the validity of the uncertainties assigned to the results of RAPTOR-M3G/FERRET calculations. Also, please indicate the reactor design for any added data.

Westinghouse Non-Proprietary Class 3 WCAP-18124-NP-A July 2018 Revision 0

Westinghouse Non-Proprietary Class 3 vii WCAP-18124-NP-A July 2018 Revision 0 Section E Submittal of Response to Request for Additional Information Letter (9 Pages)

WCAP-18124-NP-A July 2018 Revision 0 Westinghouse Non-Proprietary Class 3 LTR-REA-18-2, Rev. 0 Attachment 1, Page 1 of 8 January 11, 2018 Attachment 1 Response to the NRC Re quest for Additional Information on the RAPTOR-M3G and FERRET Topical Report

WCAP-18124-NP-A July 2018 Revision 0 Westinghouse Non-Proprietary Class 3 LTR-REA-18-2, Rev. 0 Attachment 1, Page 2 of 8 January 11, 2018 NRC Request #1 Section 2.5, "Discrete Ordinates Transport Calculations with RAPTOR-M3G," of WCAP-18124-NP, Revision 0, Westinghouse Electric Company (Westinghouse) topical report (TR) states: "RAPTOR-M3G calculations are performed with an S 8 (or higher) level-symmetric angular quadrature set."

RG 1.190, Section 1.3.1, "Discrete Ordinates Transport Calculation," states: "The adequacy of the spatial mesh and angular quadrature, as well as the convergence criterion, must be demonstrated by tightening the numerics until the resulting changes are negligible (Reference 32). In discrete ordinates codes, the spatial mesh and the angular quadrature should be refined simultaneously."

Regulatory Position 1.3.5, "Cavity Calculations," states: "In discrete ordinates transport calculations, the adequacy of the S 8 angular quadrature used in cavity transport calculations must be demonstrated." Furthermore, Section 1.3.5 of RG 1.190 states: "However, when off-midplane locations are analyzed, the adequacy of the S 8 quadrature to determine the streaming component must be demonstrated with higher-order S n calculations."

Based on the above, please explain how the adequacy of the S 8 angular quadrature (and associated spatial mesh) has been demonstrated for the entire spatial domain for which RAPTOR-M3G is applicable. Also, please define the standard method for determining when greater than S 8 angular quadrature is needed.

Westinghouse Response to NRC Request #1 RAPTOR-M3G models typically contain 150 to 250 radial intervals, 80 to 150 azimuthal intervals, and 100 to 200 axial intervals. In the case of the 4-loop reactor model used as the basis for the analytic uncertainty analysis, the geometric mesh description consisted of 209 radial intervals, 195 azimuthal intervals, and 179 vertical intervals. The problem was originally evaluated using an S 8 level-symmetric angular quadrature set and a P 3 Legendre expansion of anisotropic scattering matrices.

This problem was re-meshed with the same geometry inputs, but with a 33% reduction in default interval size, to obtain a mesh grid with 311 radial intervals, 288 azimuthal intervals, and 265 vertical intervals. The refined problem geometry was analyzed with a S 12 level-symmetric angular quadrature set and a P 5 Legendre expansion of the anisotropic scattering matrices. Computed values of fast neutron (E > 1.0 MeV) fluence rate were compared to values from the reference case.

The observed difference in the beltline region of the reactor vessel was 0.3%. Observed differences at dosimetry locations in the reactor cavity opposite the top and bottom of the core were 1.6% or less.

The 13% net uncertainty attributed to fluence values at pressure vessel beltline locations in Section 4.5 of WCAP-18124-NP includes a 5% uncertainty component denoted as "Other Factors". Uncertainties that result from discretization choices (spatial and angular) are considered to be encompassed by this category.

The standard method for establishing the adequacy of the spatial mesh, angular discretization, and treatment of anisotropic scattering consists of analyzing the problem with refined parameters until the changes at the locations of interest are negligible. When results produced by the original and refined model differ by less than 2% at the locations of interest, the uncertainty imparted by the discretization choices is encompassed by the 5% "Other Factors" uncertainty component, and the original model is valid with respect to its spatial and angular discretization.

LTR-NRC-18-5

WCAP-18124-NP-A July 2018 Revision 0 Westinghouse Non-Proprietary Class 3 LTR-REA-18-2, Rev. 0 Attachment 1, Page 3 of 8 January 11, 2018 NRC Request #2 Please describe how the chi-squared divided by degrees-of-freedom statistic is used to assess the validity of FERRET results. Please define the criteria used and subsequent actions taken for unacceptable chi-squared divided by degrees-of-freedom values.

Westinghouse Response to NRC Request #2 The chi-squared divided by degrees-of-freedom 2/DOF) quantity is frequently used as a means of checking "goodness-of-fit". This quantity is reported in the FERRET code output. It is an indicator of how consistent the best estimate neutron spectrum is with the calculated neutron spectrum, the measurements, and their respective uncertainties.

2/DOF ~= 1.0 are indicative of a good statistical fit of the best estimate neutron spectrum data to the measurements, calculations, 2/DOF < 1.0 indicate the best estimate neutron spectrum deviates from the measurements and calculations less than expected from the assigned uncertainties, perhaps indicating that the assigned uncertainties for the calculated spectrum or measurements may be unnecessarily 2/DOF > 1.0 indicate that the best estimate neutron spectrum deviates from the measurements and calculations more than expected from the assigned uncertainties.

Typical uncertainties for the calculated neutron spectrum input to the FERRET code are provided in Section 3.3 of WCAP-18124-NP. The assigned uncertainty for the "fast" portion of the neutron spectrum is 15%. This value is larger than the stated methodology uncertainty in Section 4.5 of WCAP-18124-NP, and also larger than the uncertainty implied by the comparisons of calculations to measurements in Section 5.4 of WCAP-18124-2/DOF less than 1.0 2/DOF values exceed 1.0 warrant further investigation via re-examination of the calculations and measurements.

2/DOF values exceed 1.0, the first investigative step involves reviewing the calculations. The input data is checked for errors, and the output data is compared to results from similar plants, when available. If no errors are found in the calculations, the next step involves scrutinizing the measurement data. In some cases, there are known problems with the dosimetry. For example, some surveillance capsule designs experience problems wherein cadmium covers partially fuse with the radiometric monitor material during irradiation, resulting in very high uncertainties in the sample mass. In these cases, the agreement between measurements and calculations is poor, and the affected samples are rejected.

In other cases, individual measurements may be inaccurate. Measurement errors may result from incorrect sample mass evaluations, incorrect processing (e.g., cross-contamination, incomplete chemical separation), or abnormalities in the dosimetry itself.

Westinghouse maintains a large database of historical reactor dosimetry measurements. Measurements from similar plants are expected to exhibit consistent reaction rates when appropriately normalized, because the shape of the neutron spectrum should be nearly identical. Normalized reaction rates that deviate widely from the database average are discarded. Westinghouse discards individual measurements 2/DOF quantity to an acceptable level.

LTR-NRC-18-5

WCAP-18124-NP-A July 2018 Revision 0 Westinghouse Non-Proprietary Class 3 LTR-REA-18-2, Rev. 0 Attachment 1, Page 4 of 8 January 11, 2018 NRC Request #3 The text in WCAP-18124-NP, Revision 0, Section 4.4.1, "Core Neutron Source Uncertainties," on page 4-17 implies that peripheral pin power for a given node could be affected by each of three independent uncertainties. That is the pin power could be off by as much as 5% due to in-core measurement uncertainty for a given assembly, 10% due to uncertainty in the relative pin power for a given assembly, and 10% based on variation in the axial peaking factor over the course of a fuel cycle. Please explain how the formulations given in Table 4-15, Case Numbers 3, 4, 7, and 8 relate to the assumption of 10% uncertainty in the fuel assembly relative power shapes given that the expectation based on the text descriptions of these formulations imply a direct multiplication of the nodal pin power by a factor of 1 plus or minus the assumed uncertainty.

Westinghouse Response to NRC Request #3 The formulations given in Table 4-15 are an accurate reflection of the sensitivity studies that were performed with RAPTOR-M3G and the stated results in Section 4.4.

The intent of Cases Numbers 3, 4, 7 and 8 is to capture the effects of uncertainties in the shapes of the radial pin power and axial power distributions. To that end, the total power production from each individual fuel assembly remains unchanged from the reference case; the spatial distribution of power within the assembly is the variable being permuted. The Section 4.4.1 text will be clarified as follows:

Pin-by-pin spatial distributions of neutron source at the core periphery - Core management studies indicate that uncertainties in the spatial distribution of relative pin powers in peripheral fuel assemblies can be on the order of 10%. This parameter is evaluated by holding total assembly power constant while diminishing and intensifying the peripheral pin power gradients.

Axial power distribution - Based on variations in axial peaking factors over the course of a fuel cycle, a 10% uncertainty in the shape of the axial power distribution is considered conservative. This parameter is evaluated by holding total assembly power constant while diminishing and intensifying the axial power gradients.

LTR-NRC-18-5

WCAP-18124-NP-A July 2018 Revision 0 Westinghouse Non-Proprietary Class 3 LTR-REA-18-2, Rev. 0 Attachment 1, Page 5 of 8 January 11, 2018 NRC Request #4 The text in WCAP-18124-NP, Revision 0, Section 4.4.1, "Core Neutron Source Uncertainties," on page 4-17 regarding the uncertainty due to the burnup of the peripheral fuel assemblies is ambiguous when considering corresponding information in Table 4-15 (and corresponding footnotes) and Table 4-16, "Source Permutation-to-Nominal Fast Neutron (E > 1.0 MeV) Fluence Rate Difference at Surveillance Capsule Locations." Please provide clarification regarding the reference burnup and perturbed burnup assumed for Cases 5 and 6 of Table 4-15.

Westinghouse Response to NRC Request #4 The reference case reflects an actual, contemporary power distribution from a Westinghouse 4-Loop plant. While performing the analytic uncertainty analysis, a series of eleven perturbation cases were conducted by holding the assembly power levels fixed to their reference case levels while uniformly modifying the mid-cycle burnup levels for every fuel assembly in the core. This series of perturbations reveals the effect of changes to the neutron spectrum that result only from changes in the assembly burnup level. The perturbation cases were analyzed with mid-cycle burnup levels ranging from 3,000 MWD/MTU to 50,000 MWD/MTU.

The results show a gradual increase in the calculated fast neutron (E > 1.0 MeV) fluence rate from low to high burnup, consistent with a gradual "hardening" of the neutron spectrum as the distribution of fissioning isotopes shifts from being uranium-dominated at lower burnup levels to being plutonium-dominated at higher burnup levels. To reduce the volume of data presented, the two endpoints of the perturbation study were selected as Case Number 5 and Case Number 6 (3,000 MWD/MTU and 50,000 MWD/MTU), which span a burnup range of 47,000 MWD/MTU. The effect of a 5,000 MWD/MTU uncertainty was calculated by scaling the difference between Case 5 and Case 6 by a factor, F = (5,000 / 47,000).

LTR-NRC-18-5

WCAP-18124-NP-A July 2018 Revision 0 Westinghouse Non-Proprietary Class 3 LTR-REA-18-2, Rev. 0 Attachment 1, Page 6 of 8 January 11, 2018 NRC Request #5 Section 4.3.3, "Summary of Operating Reactor and Calculational Benchmark Results," of WCAP-18124-NP, Revision 0, states: "The H. B. Robinson Unit 2 benchmark represents an experimental configuration that is broadly reflective of most operating reactors: data was collected during full-power operation at a commercial LWR; the power distribution and power history data supporting the analysis were derived using methods similar to those employed by most operating LWRs; geometric dimensions specified are nominal dimensions, and not necessarily identical to their as-built configuration."

In support of WCAP-18124-NP, Revision 0, applicability determination for reactor designs other than Westinghouse three-loop PWRs, provide the reactor designs for the 18 nuclear power plants discussed in Section 5.4, "Operating Power Reactor Comparisons," that have been analyzed with RAPTOR-M3G and FERRET.' Westinghouse Response to NRC Request #5 Table 1 provides the reactor designs associated with each of the plants listed in Section 5.4 of WCAP-18124-NP.

Table 1 Reactor Designs Reported in Section 5.4 of WCAP-18124-NP Plant Number Reactor Design Domestic Plant #1 Westinghouse 4-Loop Domestic Plant #2 Westinghouse 4-Loop International Plant #1 Westinghouse 3-Loop International Plant #2 Westinghouse 3-Loop International Plant #3 Combustion Engineering International Plant #4 Westinghouse 3-Loop International Plant #5 Westinghouse 2-Loop International Plant #6 Westinghouse 3-Loop International Plant #7 Westinghouse 3-Loop Domestic Plant #3 Westinghouse 4-Loop Domestic Plant #4 Westinghouse 4-Loop Domestic Plant #5 Westinghouse 4-Loop International Plant #8 Westinghouse 3-Loop International Plant #9 Westinghouse 3-Loop Domestic Plant #6 Westinghouse 3-Loop Domestic Plant #7 Combustion Engineering Domestic Plant #8 Combustion Engineering Domestic Plant #9 Westinghouse 4-Loop LTR-NRC-18-5

WCAP-18124-NP-A July 2018 Revision 0 Westinghouse Non-Proprietary Class 3 LTR-REA-18-2, Rev. 0 Attachment 1, Page 7 of 8 January 11, 2018 NRC Request #6 RG 1.190, Section 1.4.2.1, "Operating Measurements," states: "Well documented fluence dosimetry measurements for operating power reactors may be used for methods and data qualification... As capsule and cavity measurements become available, they should be incorporated into the operating reactor measurements data base, and the calculational biases and uncertainties should be updated as necessary." From WCAP-18124-NP, Revision 0, Section 5.4, Westinghouse states that "there are 69 in-vessel surveillance capsules with 295 threshold foil measurements from 18 nuclear power plants that have been analyzed with RAPTOR-M3G and FERRET." However, if Westinghouse supports more than 18 plants both domestically and internationally with RAPTOR-M3G/FERRET, please provide a table similar to Tables 5-10, 5-11, and 5-12, including all of the plants supported by Westinghouse both domestically and internationally to confirm the validity of the uncertainties assigned to the results of RAPTOR-M3G/FERRET calculations. Also, please indicate the reactor design for any added data.

Westinghouse Response to NRC Request #6 The database presented in Section 5.4 of WCAP-18124-NP represents the state of the database at the time the document was written. The current database of reactor dosimetry comparisons performed with RAPTOR-M3G includes comparisons from 77 in-vessel capsules containing 332 threshold foils and 164 ex-vessel dosimetry capsules containing 824 threshold foils that have been removed from 23 nuclear power plants worldwide.

The database is updated periodically in a formal capacity, typically every two or three years, depending on the volume of new comparisons that are available.

Relative to the database that was presented in Section 5.4 of WCAP-18124-NP, comparisons of calculations and measurements applicable to the following reactor types have been added to the database in the intervening time period:

Westinghouse 3-Loop PWR Framatome PWR Combustion Engineering PWR ABB-Atom BWR OKB Gidropress PWR A high-level summary of the most recent database of RAPTOR-M3G comparisons appears in Table 2. The detailed database can be made available for review by NRC staff at a Westinghouse office.

LTR-NRC-18-5

WCAP-18124-NP-A July 2018 Revision 0 Westinghouse Non-Proprietary Class 3 LTR-REA-18-2, Rev. 0 Attachment 1, Page 8 of 8 January 11, 2018 Table 2 Summary of the 2017 RAPTOR-M3G Dosimetry Comparison Database Plant-Averaged Threshold Sensor Reaction Rate Comparisons In-Vessel M/C Ex-Vessel Midplane M/C Average 1.03 0.92 Std. Dev. 5% 9% Number of Plants 19 19 Plant-Averaged In-Vessel Surveillance Capsule BE/C Ratios BE/C Fluence (E>1.0 MeV) BE/C DPA Average 0.99 1.00 Std. Dev. 6% 5% Number of Plants 19 19 Plant-Averaged Ex-Vessel Midplane Capsule BE/C Ratios BE/C Fluence (E>1.0 MeV) BE/C DPA Average 0.93 0.94 Std. Dev. 9% 9% Number of Plants 19 19 LTR-NRC-18-5

WCAP-18124-NP-A July 2018 Revision 0 Westinghouse Non-Proprietary Class 3 viii WCAP-18124-NP-A July 2018 Revision 0 RECORD OF REVISIONS Revision Description Completed 0 Original issue (WCAP-18124-NP) January 2017 0 U.S. NRC-approved version (WCAP-18124-NP-A). Per the Westinghouse response to U.S. NRC Request for Additional Information (RAI) #3, clarification has been added to Subsection 4.4.1. July 2018

Westinghouse Non-Proprietary Class 3 ix WCAP-18124-NP-A July 2018 Revision 0 TOPICAL REPORT TABLE OF CONTENTS LIST OF TABLES ................................................................................................................

....................... xi LIST OF FIGURES ................................................................................................................................... xiii 1 INTRODUCTION ........................................................................................................................ 1-1

1.1 BACKGROUND

............................................................................................................. 1-1

1.2 CURRENT

WESTINGHOUSE FLUENCE DETERMINATION METHODOLOGY .......................................................................................................... 1-1 1.3 NEED FOR ENHANCEMENTS TO THE FLUENCE DETERMINATION METHODOLOGY .......................................................................................................... 1-2 1.4

SUMMARY

OF THIS REPORT ..................................................................................... 1-3 2 FLUENCE CALCULATIONS WITH RAPTOR-M3G ................................................................ 2-1

2.1 BACKGROUND

............................................................................................................. 2-1

2.2 GEOMETRIC

MODELING ............................................................................................ 2-2

2.3 CROSS

SECTIONS AND MATERIALS ........................................................................ 2-3 2.4 CORE SOURCE DEFINITION ...................................................................................... 2-4

2.5 DISCRETE

ORDINATES TRANSPORT CALCULATIONS WITH RAPTOR-M3G ................................................................................................................ 2-5 2.5.1 The Linear Boltzmann Transport Equation ..................................................... 2-5

2.5.2 Weighted

Difference Methods ......................................................................... 2-7

2.5.3 Source

Term Calculations .............................................................................. 2-10

2.5.4 Domain

Decomposition for Parallel-Processing ........................................... 2-12

2.5.5 Solution

Process ............................................................................................ 2-15 3 LEAST SQUARES ADJUSTMENT WITH FERRET ................................................................. 3-1

3.1 BACKGROUND

............................................................................................................. 3-1

3.2 APPLICATION

OF THE MET HODOLOGY ................................................................. 3-3 3.3 INPUT SPECTRUM UNCERTAINTY ........................................................................... 3-4

3.4 MEASUREMENT

UNCERTAINTY .............................................................................. 3-6

3.5 DOSIMETRY

CROSS-SECTIONS AND UNCERTAINTY ........................................ 3-13 4 FLUENCE CALCULATION METHODOLOGY QUALIFICATION ........................................ 4-1

4.1 OVERVIEW

.................................................................................................................... 4

-1 4.2 SIMULATOR BENCHMARK CALCULATIONS ......................................................... 4-2 4.2.1 PCA ................................................................................................................. 4-2 4.2.2 VENUS-1 Benchmark ..................................................................................... 4-4

4.2.3 Summary

of Simulator Benchmark Results .................................................... 4-7

4.3 OPERATING

REACTOR AND CALCULATIONAL BENCHMARKS........................ 4-9 4.3.1 H.B. Robinson Unit 2 Benchmark ................................................................... 4-9 4.3.2 NRC Fluence Calculation Benchmark .......................................................... 4-13

4.3.3 Summary

of Operating Reactor and Calculational Benchmark Results ........ 4-16

4.4 ANALYTIC

UNCERTAINTY ANALYSIS ................................................................... 4-17 4.4.1 Core Neutron Source Uncertainties ............................................................... 4-17

4.4.2 Geometric

and Temperature Uncertainties .................................................... 4-22

4.4.3 Summary

of Analytic Uncertainty Analysis .................................................. 4-27

4.5 ESTIMATE

OF BIAS AND UNCERTAINTY .............................................................. 4-30

Westinghouse Non-Proprietary Class 3 x WCAP-18124-NP-A July 2018 Revision 0 5 VALIDATION OF LEAST SQUARES ADJUSTMENT PROCEDURES .................................. 5-1

5.1 OVERVIEW

.................................................................................................................... 5

-1 5.2 DATA COMPARISONS IN THE NIST U-235 FISSION FIELD ................................... 5-2

5.3 FERRET

SENSITIVITY STUDIES ................................................................................ 5-7

5.3.1 Composition

of the Multiple Foil Sensor Set .................................................. 5-7

5.3.2 Input

Uncertainties .......................................................................................... 5-8

5.4 OPERATING

POWER REACTOR COMPARISONS .................................................. 5-14 6

SUMMARY

, CONCLUSIONS, AND CONDITIONS ................................................................. 6-1 7 REFERENCES ............................................................................................................................. 7-1

Westinghouse Non-Proprietary Class 3 xi WCAP-18124-NP-A July 2018 Revision 0 LIST OF TABLES Table 4-1: PCA Experimental Measurement Locations ............................................................................. 4-2 Table 4-2: M/C Comparisons for the PCA 12/13 Blind Test Experiment (TW Differencing) ................... 4-3 Table 4-3: M/C Comparisons for the PCA 12/13 Blind Test Experiment (DTW Differencing) ................ 4-3 Table 4-4: VENUS-1 Measurement Locations .......................................................................................... 4-4 Table 4-5: M/C Reaction Rate Comparisons for the VENUS-1 Experiment (TW Differencing) .............. 4-5 Table 4-6: M/C Reaction Rate Comparisons for the VENUS-1 Experiment (DTW Differencing) ........... 4-6 Table 4-7: Summary of Simulator Benchmark M/C Reaction Rate Comparisons (TW Differencing) .................................................................................................................... 4-8 Table 4-8: Summary of Simulator Benchmark M/C Reaction Rate Comparisons (DTW Differencing) .................................................................................................................... 4-8 Table 4-9: FERRET Results for the H. B. Robinson Unit 2 Cycle 9 Dosimetry Benchmark Experiment (TW Differencing) ...................................................................................... 4-10 Table 4-10: FERRET Results for the H. B. Robinson Unit 2 Cycle 9 Dosimetry Benchmark Experiment (DTW Differencing) ................................................................................... 4-11 Table 4-11: Summary of Least Squares Adjustment Results for the H. B. Robinson Unit 2 Benchmark (TW Differencing) ...................................................................................... 4-12 Table 4-12: Summary of Least Squares Adjustment Results for the H. B. Robinson Unit 2 Benchmark (DTW Differencing) ................................................................................... 4-12 Table 4-13: NRC Fluence Benchmark Comparisons with RAPTOR-M3G PWR Problem with Standard Core Loading Pressure Vessel Inner-Wall Lower Weld Location (R=219.393 cm, Z=67.1048 cm) ................................................................................... 4-14 Table 4-14: NRC Fluence Benchmark Comparisons with RAPTOR-M3G BWR Problem Pressure Vessel Inner-Wall (R=321.786 cm, Z=239.93 cm) .......................................... 4-15 Table 4-15: Summary of Core Neutron Source Sensitivity Study ........................................................... 4-19 Table 4-16: Source Permutation-to-Nominal Fast Neutron (E > 1.0 MeV) Fluence Rate Difference at Surveillance Capsule Locations ................................................................................. 4-19 Table 4-17: Source Permutation-to-Nominal Fast Neutron (E > 1.0 MeV) Fluence Rate Difference at Pressure Vessel Inner Radius Locations ..................................................................... 4-20 Table 4-18: Source Permutation-to-Nominal Fast Neutron (E > 1.0 MeV) Fluence Rate Difference at Reactor Cavity Locations ........................................................................................... 4-20 Table 4-19: Summary of Neutron Fluence Rate Uncertainties at Surveillance Capsule Locations Resulting from Core Neutron Source Uncertainties ...................................................... 4-21 Table 4-20: Summary of Neutron Fluence Rate Uncertainties at Pressure Vessel Inner Radius Locations Resulting from Core Neutron Source Uncertainties...................................... 4-21

Westinghouse Non-Proprietary Class 3 xii WCAP-18124-NP-A July 2018 Revision 0 Table 4-21: Summary of Neutron Fluence Rate Uncertainties at Reactor Cavity Locations Resulting from Core Neutron Source Uncertainties ...................................................... 4-21 Table 4-22: Summary of Geometry and Temperature Sensitivity Study ................................................. 4-23 Table 4-23: Geometry and Temperature Permutation-to-Nominal Fast Neutron (E > 1.0 MeV) Fluence Rate Difference at Surveillance Capsule Locations ......................................... 4-23 Table 4-24: Geometry and Temperature Permutation-to-Nominal Fast Neutron (E > 1.0 MeV) Fluence Rate Difference at Pressure Vessel Inner Radius Locations ............................. 4-24 Table 4-25: Geometry and Temperature Permutation-to-Nominal Fast Neutron (E > 1.0 MeV) Fluence Rate Difference at Reactor Cavity Locations ................................................... 4-25 Table 4-26: Summary of Neutron Fluence Rate Uncertainties at Surveillance Capsule Locations Resulting from Geometry and Temperature Uncertainties ............................................ 4-25 Table 4-27: Summary of Neutron Fluence Rate Uncertainties at Pressure Vessel Inner Radius Locations Resulting from Geometry and Temperature Uncertainties ........................... 4-26 Table 4-28: Summary of Neutron Fluence Rate Uncertainties at Reactor Cavity Locations Resulting from Geometry and Temperature Uncertainties ............................................ 4-26 Table 4-29: Summary of Neutron Fluence Rate Uncertainties at Surveillance Capsule Locations ......... 4-27 Table 4-30: Summary of Neutron Fluence Rate Uncertainties at Pressure Vessel Inner Radius Locations ........................................................................................................................ 4-28 Table 4-31: Summary of Neutron Fluence Rate Uncertainties at Reactor Cavity Locations................... 4-29 Table 5-1: U-235 Fission Spectrum Averaged Cross-Sections from ASTM E261 .................................... 5-4 Table 5-2: Cf-252 Fission Spectrum Averaged Cross-Sections from ASTM E261 ................................... 5-5 Table 5-3: Comparison of Calculated U-235 Fission Spectrum Averaged Cross-Sections........................ 5-6 Table 5-4: Dosimeter Foil Composition Sensitivity Study Case Descriptions (with Fission Monitors) ......................................................................................................................... 5-9 Table 5-5: Dosimeter Foil Composition Sensitivity Study Results (with Fission Monitors) ..................... 5-9 Table 5-6: Dosimeter Foil Composition Sensitivity Study Case Descriptions (with Niobium) .............. 5-10 Table 5-7: Dosimeter Foil Composition Sensitivity Study Results (with Niobium) ................................ 5-10 Table 5-8: Least Squares Adjustment Input Uncertainty Sensitivity Study ............................................. 5-11 Table 5-9: Input Uncertainty Sensitivity Study Results - Adjusted (E > 1.0 MeV) and % Standard Deviation ........................................................................................................ 5-1 1 Table 5-10: In-Vessel and Ex-Vessel Capsules Threshold Reactions M/C Reaction Rate Ratios ............ 5-15 Table 5-11: In-Vessel Surveillance Capsules BE/C Reaction Rate Ratios ............................................... 5-16 Table 5-12: EVND Core Midplane BE/C Reaction Rate Ratios .............................................................. 5-17

Westinghouse Non-Proprietary Class 3 xiii WCAP-18124-NP-A July 2018 Revision 0 LIST OF FIGURES Figure 2-1: Symmetric S 8 Quadrature Set ................................................................................................ 2-13 Figure 2-2: Numbering of Octants in Cartesian Geometry ...................................................................... 2-14 Figure 2-3: Distribution of Angles Solved with Two Angle Domains ..................................................... 2-14 Figure 2-4: Conceptual Depiction of Four Space Domains ..................................................................... 2-15 Figure 5-1: Cumulative Sensor Response as a Function of Neutron Energy at In-Vessel Surveillance Capsule Locations ..................................................................................... 5-12 Figure 5-2: Cumulative Sensor Response as a Function of Neutron Energy at Ex-Vessel Dosimetry Locations ...................................................................................................... 5-13

Westinghouse Non-Proprietary Class 3 1-1 WCAP-18124-NP-A July 2018 Revision 0 1 INTRODUCTION

1.1 BACKGROUND

To assess embrittlement of Light Water Reactor (LWR) pressure vessels, accurately evaluating the neutron exposure of the materials comprising the beltline region of the vessel is required. This exposure evaluation must, in general, include assessments not only at locations of maximum exposure at the inner diameter of the vessel, but also as a function of axial, azimuthal, and radial location throughout the vessel wall. To satisfy the requirements of 10CFR50, Appendices G and H (Reference 1) for calculating pressure/temperature limit curves for normal reactor coolant system heatup and cooldown, fast neutron exposure levels must be defined at depths within the vessel wall equal to 25% and 75% of the wall thickness for each of the materials comprising the beltline region. These locations are commonly referred to as the 1/4T and 3/4T positions in the vessel wall. The 1/4T exposure levels are also used in the determination of upper shelf fracture toughness as specified in 10CFR50, Appendix G. To determine the pressurized thermal shock reference temperature (RT PTS) for comparison with the applicable screening criteria as defined in 10CFR50.61 (Reference 2), licensees are required to determine the maximum neutron exposure levels experienced by each of the reactor vessel materials. These maximum levels typically occur at the vessel inner radius, but maximum levels may occur at the vessel outer radius for reactor vessel materials that are more distant from the active fuel. Furthermore, if performing a probabilistic fracture mechanics analysis of the pressure vessel, a complete neutron exposure profile is required for the entire pressure vessel beltline volume. Methods acceptable to the Nuclear Regulatory Commission (NRC) staff for determining the neutron exposure of LWR pressure vessels are described in Regulatory Guide 1.190, "Calculational and Dosimetry Methods for Determining Pressure Vessel Neutron Fluence" (Reference 3). This Regulatory Guide requires the exposure projections to be completed with a calculation. It also requires that measurements be used to qualify the calculational methodology, to identify biases in the calculations, and to provide reliable estimates of the uncertainties in the exposure projections. The guide also states that, in the determination of potential biases and uncertainties, measurement to calculation (M/C) comparisons should include a suitably weighted average of individual M/C values that accounts for the spectral coverage of the sensor set and the uncertainties in the measurements, the dosimetry cross-sections, and the neutron energy spectrum.

1.2 CURRENT

WESTINGHOUSE FLUENCE DETERMINATION METHODOLOGY The current Westinghouse methodology to determine neutron fluence is described WCAP-16083-NP-A, Rev. 0, Benchmark Testing of the FERRET Code for Least Squares Evaluation of Light Water Reactor Dosimetry (Reference 4). The neutron transport methodology described in Reference 4 is identical to the NRC-approved neutron transport methodology described in WCAP-14040-A, Rev. 4, Methodology Used to Develop Cold Overpressure Mitigation System Setpoints and RCS Heatup and Cooldown Limit Curves (Reference 5). The WCAP-16083-NP-A methodology is based on applying benchmarked, plant-specific neutron transport calculations providing neutron exposure maps throughout the reactor geometry including the Westinghouse Non-Proprietary Class 3 1-2 WCAP-18124-NP-A July 2018 Revision 0 pressure vessel wall, all in-vessel, and/or ex-vessel measurement locations. Neutron transport calculations are performed with codes from the industry standard DOORS package (Reference 6), including the DORT code for 2D calculations, and the TORT code for 3D Calculations. The cross-section data is obtained from the BUGLE-96 library (Reference 7), and core neutron source is computed as a function of space and energy using the assembly burnup and enrichment data applicable to the irradiation conditions under consideration. This methodology was found by the NRC staff to adhere to the guidance in Regulatory Guide 1.190. Evaluating the dosimetry from the in-vessel and/or ex-vessel irradiations is subsequently accomplished with a least squares analysis. A least squares adjustment method to perform dosimetry evaluations represents a rigorous approach to weighting the spectral coverage of individual sensor measurements and to combining the uncertainties associated with the transport calculations, measured reaction rates, and dosimetry cross-sections. Further, the results of the least squares evaluations provide comparisons of the best estimates of exposure parameters of interest (Fluence [E > 1.0 MeV] and iron atom displacements [dpa]) with the corresponding calculated results before adjustment. It is these damage exposure parameters and their uncertainties rather than individual sensor reaction rates that are inputs to material embrittlement evaluations. WCAP-16083-NP-A describes the use of the FERRET code (References 8 and 9) to combine multiple foil sensor measurements and plant-specific calculated neutron spectra to determine best estimate exposure parameters at in-vessel and ex-vessel measurement locations. This approach allows for appropriate spectral weighting of the measurements obtained from the multiple foil sensor sets. It also provides a rigorous treatment of the various measurement and calculational uncertainties associated with the process. Thus, the application of the least squares procedure allows the validation of the transport calculations to be based on comparisons of the exposure parameters of interest such as (E > 1.0 MeV) rather than on some combination of individual sensor reaction rate M/C ratios. The FERRET code is used solely to determine the best estimate exposure at locations where calculations and measurements coincide. The relationship between the best estimate exposure at the measurement locations and that at the pressure vessel wall, where no measurements exist, is not addressed internal to the FERRET code. Rather, the results of the plant-specific neutron transport calculations are relied on to relate the neutron exposure at the pressure vessel wall to that at the various measurement locations within the reactor downcomer and/or the ex-vessel cavity. This is analogous to an approach where one might use spatial calculations throughout the reactor core in addition to measurements at the center of selected fuel assemblies to generate detailed core power distribution maps that include locations removed from the measurement positions.

1.3 NEED FOR ENHANCEMENTS TO THE FLUENCE DETERMINATION METHODOLOGY Performing neutron exposure calculations using the discrete ordinates method requires extensive computational resources for large 3D models due to the concurrent discretization of the angular, spatial, and energy domains. The discretization of the phase-space of the transport equation imposes large memory and processing requirements which can easily overwhelm the capabilities of single processor workstations. Using the previous generation of discrete ordinates neutron transport codes, such as DORT Westinghouse Non-Proprietary Class 3 1-3 WCAP-18124-NP-A July 2018 Revision 0 and TORT, analysts frequently encounter limitations in the amount of detail they can represent in their models. This often necessitates overly-conservative simplifying assumptions. Additionally, as plants enter into periods of extended operation, there has been increased interest in accurately quantifying neutron exposure levels outside of the traditional beltline region of the reactor vessel. Areas of interest include the "extended beltline" of the reactor vessel, comprising portions of the reactor vessel located above and below the elevation of the reactor core; and reactor internals components and materials, particularly those located above and below the elevation of the reactor core. Two-dimensional transport methods have shown limitations in their ability to accurately determine neutron exposure quantities in these regions. As a result, there is a need to move to efficient 3D techniques for neutron fluence determination. Recent years have seen the widespread application of parallel-processing techniques to solve problems in almost every area of scientific computing. This shift has been driven by the commoditization of powerful computer hardware and the development of high-speed, low-latency networking technologies. Parallel-processing techniques allow a given problem to be solved more quickly, and they allow a large problem to be distributed across the memory of multiple computers. This enables the solution of significantly larger problems, and provides results on a timescale conducive to production engineering applications. To take advantage of these benefits, Westinghouse developed RAPTOR-M3G, a 3D parallel discrete ordinates radiation transport code. The methodology employed by RAPTOR-M3G is essentially the same as the methodology employed by the TORT code, with a number of evolutionary solution enhancements resulting from the last two decades of research. RAPTOR-M3G has been designed from its inception as a parallel-processing code, and adheres to modern best practices of software development. It has been rigorously tested against the TORT code and benchmarked on an extensive set of academic and real-world problems. Westinghouse seeks to deploy the enhanced capabilities of RAPTOR-M3G to the commercial nuclear power industry. However, commercial or other practical considerations may dictate the continued use of 2D fluence calculation techniques (i.e. the DORT code) in some situations. Therefore, this report is not intended to supersede WCAP-16083-NP-A.

1.4

SUMMARY

OF THIS REPORT This report describes the application of the RAPTOR-M3G code to perform calculations of neutron exposure for LWRs, and the subsequent application of the FERRET code to perform least squares analysis of LWR dosimetry. The methodology follows the guidance provided in Regulatory Guide 1.190.

Relative to the NRC-reviewed and approved methodology in WCAP-16083-NP-A, the methodology described in this report is largely the same, and contains the following notable differences: RAPTOR-M3G is used as the radiation transport code instead of the DORT/TORT codes. The geometric modeling practices, cross-section data, and core neutron source preparation techniques are the same as those previously described in WCAP-16083-NP-A. The use of Nb-93 as a neutron sensor is described. Nb-93 is increasingly used as a neutron sensor due to the availability and transportation challenges surrounding the use of fission monitors, such Westinghouse Non-Proprietary Class 3 1-4 WCAP-18124-NP-A July 2018 Revision 0 as U-238 and Np-237. There are no changes to the underlying least squares adjustment software or processes. This report focuses on the use of RAPTOR-M3G to calculate beltline reactor vessel neutron exposure. The neutron exposure calculational methodology is qualified against the requirements of Regulatory Guide 1.190, and estimates of the uncertainty and bias are provided. The methodology is qualified in both benchmark and power reactor neutron fields. The results provided in this report validate the application of the RAPTOR-M3G and FERRET codes for use in the analysis of LWR neutron exposure and dosimetry.

Westinghouse Non-Proprietary Class 3 2-1 WCAP-18124-NP-A July 2018 Revision 0 2 FLUENCE CALCULATIONS WITH RAPTOR-M3G In this section, the methodology employed by Westinghouse to perform neutron and gamma ray transport calculations for LWR applications is described in detail. The methodology used to provide neutron exposure evaluations for the reactor pressure vessel (RPV) follows the guidance provided in Regulatory Guide 1.190. The material in this section addresses Regulatory Positions 1.1 through 1.3 of Regulatory Guide 1.190.

2.1 BACKGROUND

Reactor vessel neutron fluence has traditionally been quantified using discrete ordinates (S N) radiation transport calculations. Codes used to perform early calculations include TWOTRAN (Reference 10) and DOT (Reference 11). With the limitations on computing power at the time, both TWOTRAN and DOT were only capable of analyzing one-dimensional (1D) and two-dimensional (2D) models. In the 1980s, Oak Ridge National Laboratory developed the DORT (2D) and TORT (3D) codes, and these codes remain in widespread use today. The methodology described in this document uses the RAPTOR-M3G code to perform plant-specific neutron transport calculations. RAPTOR-M3G is a Westinghouse-developed 3D parallel-processing discrete ordinates radiation transport code. The methodology employed is essentially the same as the widely-used TORT code. The parallel-processing feature of RAPTOR-M3G allows large, 3D radiation transport calculations to be performed that would otherwise be prohibitively time consuming or impossible with TORT.

Westinghouse Non-Proprietary Class 3 2-2 WCAP-18124-NP-A July 2018 Revision 0

2.2 GEOMETRIC

MODELING In developing an analytical model of the LWR reactor geometry, nominal design dimensions are normally employed for the various structural components. In some cases, as-built dimensions are available; in those instances, the more accurate as-built data are used for model development. However, most as-built dimensions of the components in the beltline region of the reactor are not available; instead, design dimensions are used. Likewise, water temperatures and, hence, coolant density in the reactor core and downcomer regions of the reactor are normally taken to be representative of full-power operating conditions. The reactor core is treated as a homogeneous mixture of fuel, cladding, water, and miscellaneous core structures such as fuel assembly grids, guide tubes, etc. The stainless steel former plates located between the core baffle and core barrel regions are also typically included in the model. Sensitivities of the analytical results to tolerances in the internals dimensions and fluctuations in water temperature are discussed and quantified in Section 4.4. The geometric mesh description of the reactor model is normally accomplished using 150 to 250 radial intervals, 80 to 150 azimuthal intervals, and 100 to 200 axial intervals depending on the overall size of the reactor and on the complexity required to model the core periphery, the in-vessel surveillance capsules, and the details of the reactor cavity. Mesh sizes are chosen to assure that proper convergence of the inner iterations is achieved on a pointwise basis. The pointwise inner iteration convergence criterion utilized in the transport calculations is set at a value of 0.001. The mesh selection process results in a smaller spatial mesh in regions exhibiting steep gradients, in material zones of high cross section (), and at material interfaces. In the modeling of in-vessel surveillance capsules, sufficient mesh are employed within the test specimen array to assure that accurate information is produced for use in the assessment of fluence gradients within the materials test specimens, as well as in the determination of gradient corrections for neutron sensors. Additional radial and azimuthal mesh are employed to model the capsule structure surrounding the materials test specimen array. In modeling the stainless steel baffle region at the periphery of the core, a relatively fine spatial mesh is required to adequately describe this rectilinear component in cylindrical geometry. In performing this Cartesian to cylindrical transition, care is taken to preserve both the thickness and volume of the steel region in order to accurately address the shielding effectiveness of the component. The geometric modeling described in this subsection complies with Regulatory Position 1.1.1 of Regulatory Guide 1.190.

Westinghouse Non-Proprietary Class 3 2-3 WCAP-18124-NP-A July 2018 Revision 0

2.3 CROSS

SECTIONS AND MATERIALS All of the transport calculations are carried out using the BUGLE-96 cross-section library (Reference 7). The BUGLE-96 library provides a 67-group coupled neutron-gamma ray cross-section data set produced specifically for LWR application. Anisotropic scattering is treated with a minimum P 3 Legendre expansion. Number densities used in the representation of material mixtures for LWR applications are taken from the documentation provided with BUGLE-96 for carbon steel, stainless steel, concrete, zircaloy-4, and uranium dioxide. Other mixtures, such as Inconel-718, come from internal Westinghouse data sources. The BUGLE-B7 cross-section library (Reference 12) is an update to the BUGLE-96 library. The primary difference between the two libraries is that the BUGLE-B7 library is derived from ENDF-B/VII.0 nuclear data, whereas BUGLE-96 is derived from older ENDF/B-VI nuclear data. The energy group boundaries and techniques used to construct both libraries are the same. In the documentation released with BUGLE-B7, Oak Ridge National Laboratory (ORNL) analyzed the H. B. Robinson Unit 2, Pool Critical Assembly (PCA), and VENUS-3 benchmarks using BUGLE-96 and BUGLE-B7. Calculations with both libraries were compared to measurements from reactions that cover high-energy portions of the neutron spectrum that are of greatest concern for reactor vessel integrity evaluations. The ORNL report demonstrates that the differences between BUGLE-96 and BUGLE-B7 for high-energy neutron applications are minor. This finding is corroborated by comparisons that Westinghouse has performed internally. Thus, for applications that concern Regulatory Guide 1.190, the differences between BUGLE-96 and BUGLE-B7 are not significant. Westinghouse has completed an additional comparative study that revealed differences between BUGLE-B7 and BUGLE-96 for low energy neutrons that resulted from discrepancies in the upscatter-removed BUGLE-B7 library in the lower energy range. This discrepancy does not affect the validity of the BUGLE-B7 library for reactor vessel integrity evaluations, but Westinghouse has chosen to continue using BUGLE-96 until the discrepancy with BUGLE-B7 is resolved. The use of the BUGLE-96 cross-section library with the P 3 Legendre expansion mode (or higher) and comparisons to the newer BUGLE-B7 library described in this subsection complies with Regulatory Position 1.1.2 of Regulatory Guide 1.190.

Westinghouse Non-Proprietary Class 3 2-4 WCAP-18124-NP-A July 2018 Revision 0 2.4 CORE SOURCE DEFINITION The spatial variation of the neutron source is generally obtained from a burnup-weighted average of the respective power distributions from individual fuel cycles. These spatial distributions include pinwise gradients for all fuel assemblies located at the periphery of the core and typically include a uniform or flat distribution for fuel assemblies interior to the core. The spatial component of the neutron source is transposed from Cartesian to cylindrical geometry by overlaying the mesh schematic to be used in the transport calculation on the pin by pin array and then computing the appropriate relative source applicable to each cylindrical mesh interval. The Cartesian-to-cylindrical transposition is accomplished by first defining a fine cylindrical mesh working array. The and mesh are usually chosen so that there is typically a 10x10 array of fine mesh over the area of each fuel pin at the core periphery. The coordinates of the center of each fine mesh interval and its associated relative source strength are assigned to the fine mesh based on the pin that is coincident with the center of the fine mesh. In the limit as and approach zero, this technique becomes an exact transformation. Each space mesh in the cylindrical transport geometry is checked to determine if it lies totally within the area of a particular fine working mesh. If it does, the relative source of that fine mesh is assigned to the transport space mesh. If, otherwise, the transport space mesh covers a part of one or more fine mesh, then the relative source assigned to the transport mesh is determined by an area weighting process as follows: (1) where: = the relative source assigned to transport mesh m = the area of fine working mesh i within transport mesh m = the relative source within fine working mesh i The energy distribution of the source is determined by selecting a fuel burnup representative of conditions averaged over the irradiation period under consideration and an initial fuel assembly enrichment characteristic of the core designs used over the applicable period. From the assembly burnup and initial U-235 enrichment, a fission split by isotope including U-235, U-238, Pu-239, Pu-240, Pu-241, and Pu-242 is derived; and, from that fission split, composite values of energy release per fission, neutron yield per fission, and fission spectrum are determined. These composite values are then combined with the spatial distribution to produce the overall absolute neutron source for use in the transport calculations. The core neutron source definition methodology described in this subsection complies with Regulatory Position 1.2 in Regulatory Guide 1.190.

Westinghouse Non-Proprietary Class 3 2-5 WCAP-18124-NP-A July 2018 Revision 0

2.5 DISCRETE

ORDINATES TRANSPORT CALCULATIONS WITH RAPTOR-M3G RAPTOR-M3G solves the time-independent Linear Boltzmann Equation (LBE) in the absence of fission in three dimensions via the discrete ordinates approximation. The method of discrete ordinates is described in detail in the DOORS manual (Reference 6). The following methodological differences exist between the RAPTOR-M3G code and the TORT code: RAPTOR-M3G does not use zero-weighted initiating directions. See Page 3-33 of the TORT manual in Reference 6 for a discussion of this difference. RAPTOR-M3G uses the technique of Lathrop and Brinkley. The consistency between RAPTOR-M3G and TORT in the calculated fast neutron (E > 1.0 MeV) fluence rate responses shown in WCAP-17993-NP, Justification for the Use of RAPTOR-M3G for the Catawba Unit 1 Measurement Uncertainty Recapture (MUR) Power Uprate Fluence Evaluations (Reference 13), indicates that this difference is insignificant for reactor vessel neutron fluence calculations. In particular, note the similarity of the values listed in the bottom two rows of Table 2-2 through Table 2-4 of WCAP-17993-NP. RAPTOR-M3G includes an implementation of the Directional Theta-Weighted (DTW) spatial differencing scheme, whereas TORT does not. The DTW scheme is discussed and endorsed in Regulatory Guide 1.190. (See Reference 34 of Regulatory Guide 1.190 for more information about the DTW scheme.) The DTW scheme generally produces improved results, as compared to traditional theta-weighted (TW) schemes. RAPTOR-M3G calculations are performed with an S 8 (or higher) level-symmetric angular quadrature set. Neutron fluence values are determined directly from the results of the radiation transport calculations performed with RAPTOR-M3G. The subsections that follow provide the theoretical basis for the discrete ordinates equations, and describe the parallelization and solution procedures implemented in RAPTOR-M3G. The methodological discussions are included here for completeness, but do not differ significantly from similar discussions in public literature (e.g. References 6 and 14). The RAPTOR-M3G calculations described in this subsection (and inputs described in previous subsections) comply with Regulatory Positions 1.3.1, 1.3.3, and 1.3.5 of Regulatory Guide 1.190. Regulatory Position 1.3.2 is not applicable because Monte Carlo calculations are not performed.

Regulatory Position 1.3.4 is not applicable because the synthesis technique is not used.

2.5.1 The Linear Boltzmann Transport Equation The LBE for a fixed source problem can be written as: (2) where the terms on the left-hand-side of Equation (2) are the neutron loss terms. The first term, Westinghouse Non-Proprietary Class 3 2-6 WCAP-18124-NP-A July 2018 Revision 0 , is the streaming, or leakage term, which represents the rate of change of the neutron angular flux along the streaming path. This is the only term in Equation (2) that varies for different geometries. In deriving Equation (2), is the expected particle angular flux in volume element about traveling in the solid angle about with energies between and . The independent (fixed) source term is defined such that is the number of particles emitted independently of the neutron density in the same phase space. is the macroscopic total cross-section; is the macroscopic differential scattering cross-section. The solution of Equation (2) via the discrete ordinates method is accomplished by discretizing the independent variables (energy, direction, and space). Common discretization methods are multigroup for the energy variable; discrete ordinates for the direction variables; and finite differencing for the space variables. The energy domain is partitioned into IGM energy intervals of width for = 1, 2, -, IGM, where group IGM represents the lowest energy group, and group 1 is the highest energy group. To discretize the angular domain, a set of discrete directions is chosen, where = 1 to MT, and each discrete direction is defined by its direction cosines, , and an associated weight . To evaluate the angular derivative in the streaming term in Equation (2) for cylindrical geometry, the angular flux is assumed to vary linearly over , and the angular flux at the "edges" of each angular bin associated with direction is defined with the superscripts/subscripts and . Directions and weights are included within the RAPTOR-M3G code. For spatial discretization, the spatial domain is partitioned into intervals defined by:

IT - or -direction intervals < < (or < < ) = 1, 2, -, IT JT - or -direction intervals < < (or < < ) = 1, 2, -, JT KT -direction intervals < < = 1, 2, -, KT The transport equation is now multiplied by , , and ( in cylindrical geometry; in Cartesian geometry) and integrated over one phase space cell to obtain the discretized form of the transport equation: (3) In Equation (3), is the average of the angular flux over the phase space areas in the - (or -) direction, is the average of the angular flux over the phase space areas in the - (or -) direction, and is the average of the angular flux over the phase space areas in the -direction; is the average of the angular flux over the phase space volume; are Westinghouse Non-Proprietary Class 3 2-7 WCAP-18124-NP-A July 2018 Revision 0 volume-averaged angular fluxes at the edges of the angular bin; is the spatial cell volume; are the - (or -) direction surface areas; are the - (or -) direction surface areas; are the z-direction surface areas. is the average external source over the phase space volume. The terms are the angular redistribution coefficients. These terms only apply in cylindrical geometry, and account for the fact that a particle traversing the geometry changes angle as a function of its position in the mesh array. For example, a neutron moving from west to east in a cylindrical coordinate system would change from an inward direction to an outward direction as it crosses the center of the geometry. The redistribution coefficients provide coupling between angles on each -level and are defined such that particles are neither gained nor lost. RAPTOR-M3G does not use zero-weighted initiating directions for cylindrical geometry calculations. For simplification, the cell center subscripts for position, direction, and energy are dropped from Equation (3) to obtain: (4) and dividing through by the quadrature weight yields: (5) 2.5.2 Weighted Difference Methods Equation (5) contains nine angular fluxes (, , , , ); the three incoming angular fluxes are known from spatial boundary conditions. An initializing angular "boundary condition" is supplied to eliminate one of the edge angular boundary fluxes, ; in RAPTOR-M3G, the step function method, which sets for the most negative on each -level, is used. To eliminate four of the remaining five unknown fluxes, four additional equations are introduced via the spatial differencing scheme to enable solution for the cell center angular flux, . General weighted differencing schemes express a general linear relationship between the cell center angular flux and the cell edge angular fluxes: (6) and rearranging to obtain: (7)

Westinghouse Non-Proprietary Class 3 2-8 WCAP-18124-NP-A July 2018 Revision 0 The signs of the subscripts in Equations (6) and (7) are selected based on which angular fluxes are known from boundary conditions. (Additional details and derivations are available in Reference 6.) Substituting Equation (7) into Equation (5) and solving for the cell center angular flux N gives: (8) where: For RAPTOR M3G, theta-weighted or directional theta-weighted differencing is used to determine the weighting coefficients , , , and . 2.5.2.1 Theta-Weighted Differencing For the theta-weighted formulation, the weighting coefficients , , , and are determined by relating them to the transport equation that would guarantee positivity of the extrapolated fluxes, and weighting factors are used to influence coefficient values. For example, to determine the coefficient , Equation (6) is substituted into Equation (8) for the cell center flux. To ensure positivity of , a condition on is: (9a) with cell center subscripts omitted for brevity. The variables in Equation (9a) are arbitrary parameters between zero and one that weight the source term and incoming boundary flux terms.

Westinghouse Non-Proprietary Class 3 2-9 WCAP-18124-NP-A July 2018 Revision 0 Conditions on , , and are similarly determined to be: (9b) (9c) (9d) In the theta-weighted differencing implementation in RAPTOR-M3G, the user supplies a single value for, with and set equal to 1.0. TORT (Reference 6) also uses this "consistent weighted" method. The calculated values of , , , and are then input into Equations (8) and (7) - with the angular flux values known from boundary conditions - to determine the unknown angular fluxes. Coefficients , , , and are always less than or equal to 1.0 and greater than 0.5. If any calculated , , , or value falls outside of , it will be reset to a value of 0.5. Note that, because the coefficients are initialized to 0.5, and Equations (9) are applied if incoming fluxes are greater than the maximum underflow, coefficient selection does not guarantee angular flux positivity.

2.5.2.2 Directional Theta-Weighted Differencing The directional theta-weighted differencing scheme (Reference 15) was developed to eliminate nonphysical flux oscillations that may occur when other differencing schemes - including the theta-weighted scheme - are used. With directional theta-weighted, the weighting factors in Equations (9) are no longer constants, but are dependent on direction: (10a) (10b)

Westinghouse Non-Proprietary Class 3 2-10 WCAP-18124-NP-A July 2018 Revision 0 (10c) (10d) In the directional theta-weighted formulation used by RAPTOR-M3G, the directionally-dependent values are defined as:

The calculated , , , and values are then input into Equations (8) and (7) - with the angular flux values known from boundary conditions - to determine unknown angular fluxes. The coefficients , , , and will always be less than or equal to 1.0 and greater than 0.5. If any calculated , , , and value falls outside of , it will be reset to a value of 0.5. Note that this selection of coefficients does not guarantee positivity.

2.5.3 Source

Term Calculations The right-hand side of Equation (2) is the source term, : (11) where the scattering source, , is defined as: (12) is the fixed source. In order to remove the dependence of the scattering cross-section data on relationships between specific directions, the angular variations in the scattering cross-section data are represented using an infinite series of Legendre polynomials:

Westinghouse Non-Proprietary Class 3 2-11 WCAP-18124-NP-A July 2018 Revision 0 (13) Using the Legendre addition theorem: (14) and substituting Equations (13) and (14) into Equation (12), the resulting scattering source is: (15) The angular flux variable, , can be represented with a spherical harmonic expansion: (16) where are moments of the angular flux, constructed analytically as: (17) Using Equation (17) in Equation (15), the scattering source becomes: (18) The scattering source is calculated using Equations (17) and (18) by first constructing flux moments from the angular flux. The flux moments are then combined with the Legendre-expanded cross-section data to calculate scattering into energy group across the energy spectrum. Finally, the scattering source is re-directionalized for use in the transport sweeps. The spherical harmonics expansions in Equations (15) through (18) are problematic because they contain complex components. The real expansion of employed by RAPTOR-M3G is: (19) where:

Westinghouse Non-Proprietary Class 3 2-12 WCAP-18124-NP-A July 2018 Revision 0 (20) The even and odd harmonic functions are: (21) are the associated Legendre polynomial functions and is the azimuthal coordinate of . For positive and : (22) The interested reader can find a detailed derivation in Reference 16.

2.5.4 Domain

Decomposition for Parallel-Processing The parallel processing capability of RAPTOR-M3G is its primary advantage over similar single-processor S N transport codes. The objective is twofold:

1. To reduce the memory requirements per processor

2. To reduce the computational time required for a given problem RAPTOR-M3G achieves parallelization by domain decomposition: dividing the problem into pieces that can be solved simultaneously by multiple processors. Two domain decomposition techniques are available to RAPTOR-M3G: spatial decomposition and angular decomposition.

2.5.4.1 Angular Domain Decomposition The S N method of solving the linear Boltzmann transport equation divides the continuous angle variable from Equation (2) into discrete angles. Figure 2-1 illustrates an example of such discretization: a symmetric S 8 quadrature set. The predominant computational task of RAPTOR-M3G is to calculate the angular flux in each discretized direction - for each mesh center and boundary location - for all energy groups. Angular domain decomposition takes advantage of the fact that the angular flux calculations are independent within a single flux iteration.

Westinghouse Non-Proprietary Class 3 2-13 WCAP-18124-NP-A July 2018 Revision 0 RAPTOR-M3G divides the angle domain into 8 octants, shown in Figure 2-2 for a single point in Cartesian geometry. Users can then divide the octants among 1, 2, 4, or 8 processors. Figure 2-3 illustrates an example of the angular domain being divided between two processors. Processor #1 calculates angular flux for all of the "up" ( > 0.0) directions, while processor #2 calculates angular flux for all of the "down" ( < 0.0) directions.

Figure 2-1: Symmetric S 8 Quadrature Set

Westinghouse Non-Proprietary Class 3 2-14 WCAP-18124-NP-A July 2018 Revision 0 Figure 2-2: Numbering of Octants in Cartesian Geometry Figure 2-3: Distribution of Angles Solved with Two Angle Domains

Westinghouse Non-Proprietary Class 3 2-15 WCAP-18124-NP-A July 2018 Revision 0 2.5.4.2 Spatial Domain Decomposition Spatial domain decomposition divides the problem into spatial segments. Processors assigned to each space domain only solve for flux values within their space domain. Figure 2-4 illustrates a problem divided into 4 space domains. As each flux iteration concludes, calculated flux values on the space domain boundaries are exchanged between processors. Because this communication occurs after the iteration is complete, problems with spatial domain decomposition typically require more inner iterations to converge to a solution. For example, imagine a source of neutrons placed in space domain #1 in Figure 2-4. RAPTOR-M3G requires three complete flux solution iterations for the neutrons to reach space domain #4. Typically, the number of additional iterations required is not significant, and is frequently less than 5% of the original number of iterations.

Figure 2-4: Conceptual Depiction of Four Space Domains

2.5.5 Solution

Process The discrete ordinates solution algorithm begins with the highest energy group, then "sweeps" through the space/angle mesh. All calculations use an S 8 level-symmetric quadrature set or higher. Cell center flux is calculated with Equations (8); then the extrapolation equations, Equations (7), are used to calculate cell boundary and directional bin boundary fluxes. This sweeping procedure then repeats for the next spatial cell or direction (or both). A sweep of the entire space/angle mesh within an energy group is termed an "inner," "flux", or "within-group," iteration. One sweep through all energy groups is termed an "outer" iteration. Because solving the scattering source depends on unknown fluxes, RAPTOR-M3G's solution to Westinghouse Non-Proprietary Class 3 2-16 WCAP-18124-NP-A July 2018 Revision 0 the transport equation is iterative (that is, after each inner iteration, sources are updated with newly calculated fluxes). Convergence is tested by calculating the infinity norm of the relative scalar flux error. For the p th inner iteration, convergence is achieved if: (23) where is the convergence precision defined by the user. If the denominator value is zero, the quantity within the absolute value expression evaluates to infinity and fails the convergence test. If the fluxes have not converged, the pass through the space/angle mesh for the energy group is repeated with the updated within-group scattering source term. After achieving a converged inner iteration solution for group , the procedure is then carried out for energy group . When all inner iterations for all energy groups have converged, the upscattering source terms are updated using the newly calculated fluxes for the energy groups. The zeroth moment of the scattering source solution is tested against the outer iteration convergence criterion, EPSSCT: (24) If unconverged, this outer/inner procedure continues. Note that, for fixed source problems without any upscattering, only one outer iteration is required; so, only one outer iteration is performed. See References 6 and 14 for comprehensive descriptions of the LBE and S N method.

Westinghouse Non-Proprietary Class 3 3-1 WCAP-18124-NP-A July 2018 Revision 0 3 LEAST SQUARES ADJUSTMENT WITH FERRET In this section, the methodology employed by Westinghouse to perform least squares adjustments for LWR applications is described in detail. Analysis details for least squares adjustments are outside the scope of Regulatory Guide 1.190. However, this section does describe measurement methods and measurement uncertainty assignments, which are discussed in Regulatory Position 2.1. Note that the methodology described in this section is identical to that described in WCAP-16083-NP-A. Minor updates were made to some of the uncertainty estimates to reflect the latest versions of ASTM standards and current practices. Minor updates were also made to some of the historical counting comparisons to reflect the best available data.

3.1 BACKGROUND

Least squares adjustment methods provide the capability to combine measurement data with the results of neutron transport calculations to establish a best estimate neutron energy spectrum with associated uncertainties at the measurement locations. Best estimates for key exposure parameters such as neutron fluence rate, (E > 1.0 MeV), or iron atom displacement rate, dpa/s, along with their uncertainties are then easily obtained from the adjusted spectrum. Using measurements in combination with detailed transport calculations results in a reduced uncertainty in the calculated spectrum, and provides a method to identify any biases or inconsistencies that may exist in the baseline transport calculation or in the measured data. The application of least squares adjustment methods in LWR dosimetry analysis is common throughout the dosimetry community. The ASTM International has addressed the use of adjustment codes in ASTM E944 "Application of Neutron Spectrum Adjustment Methods in Reactor Surveillance" (Reference 17), and many industry workshops have been held to discuss the various applications. For example, the ASTM-EURATOM Symposia on Reactor Dosimetry periodically holds workshops on neutron spectrum unfolding and adjustment techniques at its conferences. In ASTM E944, a comprehensive listing of available adjustment codes commonly employed in reactor surveillance programs including STAY'SL (Reference 18), LSL-M2 (Reference 19), LEPRICON (Reference 20), and FERRET is provided. Each of these codes is publicly available from the Radiation Safety Information Computational Center (RSICC) at ORNL. The FERRET code was initially developed at the Hanford Engineering Development Laboratory (HEDL) and has had extensive use in both the Liquid Metal Fast Breeder Reactor (LMFBR) program and the NRC-sponsored Light Water Reactor Pressure Vessel Surveillance Dosimetry Improvement Program (LWR-PV-SDIP). Examples of prior use of the FERRET code for LWR applications include: 1) a re-evaluation of the dosimetry from commercial pressurized water reactor (PWR) surveillance capsules (Reference 21) and 2) an evaluation of the dosimetry included in the PCA blind test experiments (Reference 22). Both of these applications were completed in support of the LWR-PV-SDIP program. The former evaluation was carried out to establish an updated surveillance capsule dosimetry database for use in the establishment of improved trend curves defining the radiation induced shift in reference nil ductility transition temperature and the decrease in upper shelf energy versus neutron fluence or Westinghouse Non-Proprietary Class 3 3-2 WCAP-18124-NP-A July 2018 Revision 0 displacements per atom (dpa). These updated correlations were later used in the development of the trend curve data appearing in Regulatory Guide 1.99, Revision 2 (References 23, 24, 25, and 26). The latter evaluation was completed to provide estimates of key exposure parameters (Fluence E > 1.0 MeV and dpa) for use in performing blind tests of neutron transport calculations in the PCA facility. This allowed blind test comparisons of calculated exposure parameters directly with the least squares results. It also allowed comparisons with measured reaction rates obtained from the multiple foil sensor sets included in the PCA irradiations. By participating in several cooperative efforts associated with the LWR-PV-SDIP, the FERRET approach was adopted by Westinghouse in the mid-1980s as the preferred approach to evaluating LWR surveillance dosimetry. The least squares methodology was judged to be superior to the previously employed spectrum averaged cross-section approach, which is dependent on the accuracy of the shape of the calculated neutron spectrum at the measurement locations. Further, applying the least squares methodology allowed for a rigorous treatment of the uncertainties associated with the dosimetry evaluation process.

Westinghouse Non-Proprietary Class 3 3-3 WCAP-18124-NP-A July 2018 Revision 0

3.2 APPLICATION

OF THE METHODOLOGY In general, the least squares methods, as applied to LWR dosimetry evaluations, act to reconcile the measured sensor reaction rate data, dosimetry reaction cross-sections, and the calculated neutron energy spectrum within their respective uncertainties. For example, (25) relates a set of measured reaction rates, , to a single neutron spectrum, , through the multigroup dosimeter reaction cross-section, , each with an uncertainty . The primary objective of the least squares evaluation is to produce unbiased estimates of the neutron exposure parameters at the location of the measurement. The application of the least squares methodology requires the following input:

1. The calculated neutron energy spectrum and associated uncertainties at the measurement location.

2. The measured reaction rates and associated uncertainty for each sensor contained in the multiple foil set.

3. The energy-dependent dosimetry reaction cross-sections and associated uncertainties for each sensor contained in the multiple foil sensor set. For LWR dosimetry applications, the calculated neutron spectrum is obtained from the results of plant-specific neutron transport calculations that follow the guidelines specified in Regulatory Guide 1.190, as described in Section 2. The sensor reaction rates are derived from the measured specific activities obtained using established ASTM procedures. The dosimetry reaction cross-sections and uncertainties are obtained from the SNLRML dosimetry cross-section library. Each of these critical input parameters and associated uncertainties are discussed in this section.

Westinghouse Non-Proprietary Class 3 3-4 WCAP-18124-NP-A July 2018 Revision 0

3.3 INPUT

SPECTRUM UNCERTAINTY The neutron spectrum input to the least squares adjustment procedure is obtained directly from the results of plant-specific transport calculations for each sensor location. The spectrum at each location is input in an absolute sense (rather than as simply a relative spectral shape). Therefore, within the constraints of the assigned uncertainties, the calculated data are treated equally with the measurements. The input uncertainties associated with the calculated spectrum must be consistent with the benchmarking results discussed in Section 4. The uncertainty matrix for the calculated spectrum is constructed from the following relationship: (26) where specifies an overall fractional normalization uncertainty, and the fractional uncertainties and specify additional random groupwise uncertainties that are correlated with a correlation matrix given by: (27) where (28) The first term in the correlation matrix equation specifies purely random uncertainties, while the second term describes the short-range correlations over a group range ( specifies the strength of the latter term). The value of is 1.0 when = and 0.0 otherwise. The normalization uncertainty pertains primarily to the magnitude of the spectrum, whereas the groupwise uncertainties pertain to the shape of the spectrum relative to energy. A typical set of parameters defining the input uncertainties for the calculated spectrum is as follows: Fluence Rate Normalization Uncertainty () 15% Fluence Rate Group Uncertainties (, ) (E > 0.0055 MeV) 15% (0.68 eV < E < 0.0055 MeV) 29% (E < 0.68 eV) 52% Short-Range Correlation () (E > 0.0055 MeV) 0.9 (0.68 eV < E < 0.0055 MeV) 0.5 (E < 0.68 eV) 0.5

Westinghouse Non-Proprietary Class 3 3-5 WCAP-18124-NP-A July 2018 Revision 0 Fluence Rate Group Correlation Range () (E > 0.0055 MeV) 6 (0.68 eV < E < 0.0055 MeV) 3 (E < 0.68 eV) 2 These uncertainty assignments provide an input covariance matrix that is consistent with the calculational uncertainties defined through the benchmarking process in Section 4.

Westinghouse Non-Proprietary Class 3 3-6 WCAP-18124-NP-A July 2018 Revision 0

3.4 MEASUREMENT

UNCERTAINTY Measurements at operating power reactors are generally accomplished with comprehensive multiple foil sensor sets including radiometric monitors (RM). In general, sensor sets employed in Westinghouse dosimetry programs include materials in which the following reactions can be measured:

In-Vessel Ex-Vessel Cu--60 Cu--60 (Cd-covered)

Ti-46 (n,p) Sc-46 Ti-46 (n,p) Sc-46 (Cd-covered)

Fe-54 (n,p) Mn-54 Fe-54 (n,p) Mn-54 (Cd-covered)

Ni-58 (n,p) Co-58 Ni-58 (n,p) Co-58 (Cd-covered)

U-238 (n,f) FP (Cd-covered) U-238 (n,f) FP (Cd-covered)

Np-237 (n,f) FP (Cd-covered) Nb--93m (Cd-covered)

Co- Co-60 Np-237 (n,f) FP (Cd-covered)

Co- Co-60 (Cd-covered) Co- Co-60 Co- Co-60 (Cd-covered)

These sensor sets provide adequate spectrum coverage in the fast neutron energy range greater than approximately 0.5 MeV and also include bare and cadmium covered cobalt sensors to provide an assessment of the thermal neutron fluence rate at the measurement locations. These sensor sets are fully consistent with the guidance specified in Section 2.1.1 of Regulatory Guide 1.190. Similar sensor set designs are also utilized by other vendors of LWR dosimetry programs. Following irradiation, the specific activity of each of the radiometric sensors is determined using the latest version of ASTM counting procedures for each reaction. In particular, the following standards are applicable to the radiometric sensors typically used in LWR programs: E523 Standard Test Method for Measuring Fast-Neutron Reaction Rates by Radioactivation of Copper E526 Standard Test Method for Measuring Fast-Neutron Reaction Rates by Radioactivation of Titanium E263 Standard Test Method for Measuring Fast-Neutron Reaction Rates by Radioactivation of Iron E264 Standard Test Method for Measuring Fast-Neutron Reaction Rates by Radioactivation of Nickel E704 Standard Test Method for Measuring Reaction Rates by Radioactivation of Uranium-238 E1297 Standard Test Method for Measuring Fast-Neutron Reaction Rates by Radioactivation of Niobium E705 Standard Test Method for Measuring Reaction Rates by Radioactivation of Neptunium-237 E481 Standard Test Method for Measuring Neutron Fluence Rates by Radioactivation of Cobalt and Silver E1005 Standard Test Method for Application and Analysis of Radiometric Monitors for Reactor Vessel Surveillance E181 Standard Test Methods for Detector Calibration and Analysis of Radionuclides

Following sample preparation and weighing, the specific activity of each sensor is determined using a germanium gamma spectrometer. In the case of multiple foil sensor sets, these analyses are usually Westinghouse Non-Proprietary Class 3 3-7 WCAP-18124-NP-A July 2018 Revision 0 completed by direct counting of each of the individual sensors, or, as is sometimes the case with U-238 and Np-237 fission monitors from in-vessel irradiations, by direct counting preceded by dissolution and chemical separation of cesium from the sensor. For ex-vessel dosimetry irradiations, gradient chains or wires are often included with the multiple foil sensor sets. For these gradient measurements, individual sensors are obtained by cutting the chains into a series of segments to provide data at appropriate intervals over the extent of the beltline region of the pressure vessel. The determination of sensor specific activities in these segments then proceeds in the same fashion as for individual foils from the multiple foil sensor sets. In general, data from the following reactions are obtained from the gradient chain measurements: Fe-54 (n,p) Mn-54 Ni-58 (n,p) Co-58 Co-59 (n,) Co-60 These data can be used in conjunction with high purity foil measurements to provide mappings of the neutron environment external to the reactor pressure vessel. For the radiometric sensors used in LWR irradiations, reaction rates referenced to full-power operation are determined from the following equation: (29) where: = measured specific activity (dps/g) = sensor reaction rate averaged over the irradiation period and referenced to operation at a core power level of (rps/atom) = number of target element atoms per gram of sensor (atom/g) = weight fraction of the target isotope in the target material = total number of monthly intervals comprising the irradiation period = number of product atoms produced per reaction = average core power level during irradiation period j (MW) = maximum or reference core power level of the reactor (MW) = calculated ratio of (E > 1.0 MeV) during irradiation period j to the time weighted Westinghouse Non-Proprietary Class 3 3-8 WCAP-18124-NP-A July 2018 Revision 0 average (E > 1.0 MeV) over the entire irradiation period = decay constant of the product isotope (s

-1) = length of irradiation period j (s) = decay time following irradiation period j (s)

In the above equation, the ratio accounts for month by month variation of power level within a given fuel cycle. The ratio is calculated for each fuel cycle using the neutron transport methodology described in Section 2 of this report and accounts for the change in sensor reaction rates caused by variations in fluence rate level due to changes in core power spatial distributions from fuel cycle to fuel cycle. For a single cycle irradiation, = 1.0. However, for multiple fuel cycle irradiations, the additional correction must be utilized. This additional correction can be quite significant for sensor sets that have been irradiated for many fuel cycles in a reactor that has transitioned from non-low leakage to low leakage fuel management. Because SSTR sensors are integrating devices not susceptible to radioactive decay of a product isotope, measurements of fissions per target atom, , are converted directly to reaction rates using the following equation: (30) where the denominator represents the total effective full-power seconds (EFPS) of reactor operation during the irradiation period of the solid state track recorders. Prior to using the measured reaction rates for direct comparison with the results of transport calculations or as input to the least squares adjustment procedure, additional corrections must be made to U-238 measurements to account for the presence of U-235 impurities in the sensors and for the build-in of plutonium isotopes over the course of the irradiation. These corrections are location and fluence dependent, are obtained from a combination of calculated data from the plant-specific discrete ordinates analysis described in Section 2 of this report and, when available, measurements are made with U-235 foils or solid state track recorders. In addition to the corrections for competing neutron induced reactions in the U-238 sensors, corrections must also be made to both the U-238 and Np-237 sensor reaction rates to account for gamma-ray induced fission reactions that occur during the irradiation. These photo-fission corrections are also location dependent and are obtained from the transport calculational methodology discussed in Section 2. Typical corrections to the measured fission rates at in-vessel and ex-vessel sensor locations are summarized as follows:

Westinghouse Non-Proprietary Class 3 3-9 WCAP-18124-NP-A July 2018 Revision 0 Typical Correction In-Vessel Ex-Vessel U-235 Impurities 8-12% <1% Pu Build-In 7-20% <1% U-238 (,f) 4-6% 3-5% Np-237 ( ,f) 1-2% 1% The corrections listed are typical values for a PWR plant with in-vessel capsules mounted on the outer radius of the thermal shield. These values cannot be used with a plant-specific sensor set. Rather, the appropriate corrections must be determined for each sensor set based on the actual plant-specific geometry and irradiation history. Along with the reaction rates, the uncertainty associated with each of these measurements is also an important input to the least squares adjustment procedure. The overall uncertainty in the measured reaction rates includes components due to the basic measurement process, the irradiation history corrections, and the corrections for competing reactions. A high level of accuracy in the reaction rate determinations is assured by using laboratory procedures that conform to the ASTM National Consensus Standards listed earlier in this section. In all cases, the latest available versions of the applicable standards are used in the dosimetry evaluations.

Westinghouse Non-Proprietary Class 3 3-10 WCAP-18124-NP-A July 2018 Revision 0 From these standards, the achievable uncertainties in the measured specific activities of each of the sensors comprising typical LWR multiple foil sensor sets are as follows: Reaction Precision Bias Cu-63 (n,) Co-60 1% 3% Ti-46 (n,p) Sc-46 1% 3% Fe-54 (n,p) Mn-54 1% 3% Ni-58 (n,p) Co-58 1% 3% U-238 (n,f) FP 1% 5% Nb--93m 1% 2% Np-237 (n,f) FP 1% 5% Co-59 (n,) Co-60 3% 0% These uncertainties included the effects of counting statistics, sample weighing, detector calibration, source/detector geometry corrections, and product nuclide branching ratios. In determining reaction rates from the measured specific activities, the following additional uncertainties are incurred: Reaction Fission Yield Product Half-Life Competing Reactions Cu-63 (n,) Co-60 0.01% Ti-46 (n,p) Sc-46 0.05% Fe-54 (n,p) Mn-54 0.06% Ni-58 (n,p) Co-58 0.08% U-238 (n,f) FP 3% 0.30% 4% Nb--93m 0.74% Np-237 (n,f) FP 4% 0.30% 1% Co-59 (n,) Co-60 0.01%

Westinghouse Non-Proprietary Class 3 3-11 WCAP-18124-NP-A July 2018 Revision 0 After combing all of these uncertainty components, the sensor reaction rates derived from the counting and data evaluation procedures typically result in the following net uncertainties associated with the sensor reaction rates that are input to the least squares evaluation: Reaction Reaction Rate Uncertainty (1) Cu-63 (n,) Co-60 5% Ti-46 (n,p) Sc-46 5% Fe-54 (n,p) Mn-54 5% Ni-58 (n,p) Co-58 5% U-238 (n,f) FP 10% Nb--93m 5% Np-237 (n,f) FP 10% Co-59 (n,) Co-60 5% In addition to the adherence to ASTM National Consensus Standards in the evaluation of sensor reaction rates, the procedures used by Westinghouse have been periodically tested via round robin counting exercises included as part of the LWR-PV-SDIP as well as by evaluation of fluence counting standards provided by the National Institute of Science and Technology (NIST). A summary of the results of these counting validations is as follows: 1980 Round robin counting of the foil sets irradiated at the Thermal Shield Back (TSB) and Pressure Vessel Face (PVF) positions of the PCA simulator. 1981 Round robin counting of additional foil sets included in the first metallurgical simulated surveillance capsule, also irradiated in the PCA benchmark mockup.

These two counting exercises involved direct comparisons with measurements obtained by HEDL. At the time of these irradiations, HEDL was a prime contractor providing measurement services for the PCA benchmark and was cross calibrated with NIST and the MOL laboratory in Belgium. 1985 Counting and evaluation of Ti-46 (n,p) Sc-46, Fe-54 (n,p) Mn-54, and Ni-58 (n,p) Co-58 certified fluence standards supplied by NIST.

Comparisons with fluence standards involve the determination not only of the reaction rate of each foil, but also of the spectrum averaged cross-section in the NIST U-235 irradiation facility. Thus, the comparisons with certified fluence standards test both the measurement process and the energy dependent reaction cross-sections used in the evaluation. 1992 Counting of NIST foils irradiated in an ex-vessel dosimetry experiment at the Trojan power reactor.

Westinghouse Non-Proprietary Class 3 3-12 WCAP-18124-NP-A July 2018 Revision 0 This exercise involved duplicate counting of a subset of irradiated foils by both Westinghouse and NIST to assure adequate cross-calibration of the laboratories so that data could be confidently mixed in the overall fluence evaluations performed by NIST and ORNL. 1998 Round robin counting of U-238 and Np-237 certified fluence standards irradiated by NIST in the MDRF facility at the University of Michigan.

As in the case of the 1985 radiometric sensor evaluations, the fluence standard involved the determination of the reaction rate of each sensor, but also of the spectrum averaged cross-sections in the MDRF facility. The results obtained from these counting comparisons are summarized as follows:

[West]/[HEDL] [West]/[NIST]

Average 1980 1981 1985 1992 1998 Cu-63 (n,) Co-60 1.014 1.018 0.969 1.000 Ti-46 (n,p) Sc-46 1.035 1.012 1.030 1.026 Fe-54 (n,p) Mn-54 0.992 1.008 1.011 1.056 1.017 Ni-58 (n,p) Co-58 1.008 0.990 1.028 1.029 1.014 U-238 (n,f) FP 1.019 1.014 1.017 1.017 Np-237 (n,f) FP 1.010 1.017 1.095 1.041 Co-59 (n,) Co-60 1.013 1.017 1.015 These comparisons demonstrate that the procedures used by Westinghouse in the determination of sensor reaction rates have produced accurate and stable results over an extended period of time. The cross-comparisons with HEDL and NIST support the reaction rate uncertainties used by Westinghouse in performing LWR fluence evaluations. In addition to these periodic comparisons, laboratory calibrations with NIST-supplied sources are also carried out on a routine basis.

Westinghouse Non-Proprietary Class 3 3-13 WCAP-18124-NP-A July 2018 Revision 0

3.5 DOSIMETRY

CROSS-SECTIONS AND UNCERTAINTY The third key set of input data for the least squares procedure includes the reaction cross-sections for each of the sensors included in the multiple foil dosimetry packages. The reaction rate cross-sections used by Westinghouse are taken from the SNLRML library (Reference 27). This data library provides reaction cross-sections and associated uncertainties, including covariances, for 66 dosimetry sensors in common use. Both the cross-sections and the uncertainties are provided in a fine multi-group structure for use in least squares adjustment applications. These cross-sections were compiled from cross-section evaluations including ENDF/B-VI and IRDF-90 (Reference 28) and have been tested with respect to their accuracy and consistency for least squares analyses. Further, the library has been empirically tested for use in fission spectra determination as well as in the fluence and energy characterization of 14 MeV neutron sources. Detailed discussions of the contents of the SNLRML library along with the evaluation process for each of the sensors is provided in Reference 27. For the sensors of interest to LWR dosimetry applications, the following uncertainties in the fission spectrum averaged cross-sections are provided in the SNLRML documentation package: Reaction Uncertainty Cu-63 (n,Co-60 4.08-4.16% Ti-46 (n,p) Sc-46 4.51-4.87% Fe-54 (n,p) Mn-54 3.05-3.11% Ni-58 (n,p) Co-58 4.49-4.56% U-238 (n,f) FP 0.54-0.64% Nb--93m 6.96-7.23% Np-237 (n,f) FP 10.32-10.97% Co-59 (n, Co-60 0.79-3.59%

These tabulated ranges provide an indication of the dosimetry cross-section uncertainties associated with typical sensor sets used in LWR irradiations.

Westinghouse Non-Proprietary Class 3 4-1 WCAP-18124-NP-A July 2018 Revision 0 4 FLUENCE CALCULATION METHODOLOGY QUALIFICATION This section describes the methodology qualification evaluations performed for the fluence calculation process. The material in this section addresses Regulatory Position 1.4 of Regulatory Guide 1.190.

4.1 OVERVIEW

The validation of the transport methodology (using RAPTOR-M3G) is based on the guidance provided in Regulatory Guide 1.190. In particular, the validation consists of the following stages:

1. Simulator Benchmark Comparisons: Comparisons of calculations with measurements from simulator benchmarks, including the PCA simulator at ORNL and the VENUS-1 experiment.

2. Operating Reactor and Calculational Benchmarks: Comparisons of calculations with surveillance capsule and reactor cavity measurements from the H. B. Robinson power reactor benchmark experiment. Also provided are comparisons of calculations performed with RAPTOR-M3G to results published in the NRC fluence calculation benchmark (Reference 29).

3. Analytic Uncertainty Analysis: An analytic sensitivity study addressing the uncertainty components resulting from important input parameters applicable to the plant-specific transport calculations used in the exposure assessments. At each subsequent application of the methodology, comparisons are made with plant-specific dosimetry results to demonstrate that the plant-specific transport calculations are consistent with the uncertainties derived from the methods qualification. The first stage of the methods validation addresses the adequacy of basic transport calculation and dosimetry evaluation techniques and associated cross-sections. This phase, however, does not test the accuracy of commercial core neutron source calculations nor does it address uncertainties in operational or geometric variables that affect power reactor calculations. The second stage of the validation addresses uncertainties that are primarily methods related and would tend to apply generically to all fast neutron exposure evaluations. The third stage of the validation identifies the potential uncertainties introduced into the overall evaluation due to calculational methods approximations as well as to a lack of knowledge relative to various plant-specific parameters. The overall calculational uncertainty is established from the results of these three stages of the validation process.

Westinghouse Non-Proprietary Class 3 4-2 WCAP-18124-NP-A July 2018 Revision 0

4.2 SIMULATOR

BENCHMARK CALCULATIONS Several simulator benchmark experiments have been performed for the purpose of providing a qualification basis for neutron fluence analysis methods. The experiments were performed in laboratory settings, and simulate the configuration of an operating nuclear reactor on a smaller scale. This section provides the results of comparisons of simulator benchmark measurement results with calculations performed with RAPTOR-M3G. These simulator benchmark comparisons contribute to addressing Regulatory Position 1.4.2 of Regulatory Guide 1.190.

4.2.1 PCA The PCA Pressure Vessel Facility Benchmark (Reference 30) is an industry-standard benchmark that can be used to partially qualify a fluence determination methodology according to Regulatory Guide 1.190.

The PCA facility provides a small-scale simulation of the configuration of a PWR. The geometry, material compositions, and neutron source for this experiment were all well-characterized, and accurate dosimetry measurements were collected at several locations of interest. A complete description of the benchmark is available in Reference 30. Table 4-1 shows the distribution of measurement locations. The RAPTOR-M3G analysis of the PCA problem with the 12/13 configuration is modeled on a 67 x 139 x 102 Cartesian mesh grid. Angular quadrature is modeled with an S 8 level-symmetric quadrature set, and anisotropic scattering is treated with a P 3 Legendre expansion. The transport cross-section set was constructed from the BUGLE-96 library, and dosimetry reaction rate cross-sections are taken from the SNLRML library. The PCA problem was analyzed in RAPTOR-M3G using the TW and DTW differencing schemes. Results of the benchmark comparisons using RAPTOR-M3G are presented in Table 4-2 for TW differencing and Table 4-3 for DTW differencing.

Table 4-1: PCA Experimental Measurement Locations Position Y (cm) Location Description A1 A2 A3 A4 A5 A6 A7 12.0 23.8 29.7 39.5 44.7 50.1 59.1 Thermal Shield (Front) Thermal Shield (Back) Pressure Vessel (Front) Pressure Vessel (1/4 T)

Pressure Vessel (1/2 T) Pressure Vessel (3/4 T) Void Box Westinghouse Non-Proprietary Class 3 4-3 WCAP-18124-NP-A July 2018 Revision 0 Table 4-2: M/C Comparisons for the PCA 12/13 Blind Test Experiment (TW Differencing) Reaction M/C Ratio for Dosimetry Position Noted A1 A2 A3 A4 A5 A6 A7 27Al (n,) 24Na (Cd) 0.99 1.00 0.95 0.95 0.96 0.98 -

58Ni (n,p) 58Co (Cd) 1.03 1.03 0.99 1.00 1.01 0.97 - 115115mIn (Cd) 1.03 1.03 0.97 0.97 0.99 1.00 1.06 103103mRh (Cd) 1.01 0.98 0.98 0.98 1.04 1.06 1.07 238U (n,f) FP (Cd) - - 0.92 1.01 1.03 1.06 1.06 237Np (n,f) FP (Cd) - - 1.07 1.00 0.99 1.03 0.98 Average 1.02 1.01 0.98 0.99 1.00 1.02 1.04 % std dev 1.9 2.4 5.2 2.3 2.9 3.9 4.0 Table 4-3: M/C Comparisons for the PCA 12/13 Blind Test Experiment (DTW Differencing) Reaction M/C Ratio for Dosimetry Position Noted A1 A2 A3 A4 A5 A6 A7 27Al (n,) 24Na (Cd) 0.98 0.99 0.95 0.97 0.99 1.00 -

58Ni (n,p) 58Co (Cd) 1.02 1.02 0.99 1.01 1.02 0.98 - 115115mIn (Cd) 1.02 1.02 0.96 0.97 1.00 1.00 1.06 103103mRh (Cd) 1.00 0.97 0.98 0.98 1.04 1.07 1.08 238U (n,f) FP (Cd) - - 0.92 1.01 1.04 1.06 1.07 237Np (n,f) FP (Cd) - - 1.06 1.01 1.00 1.03 0.99 Average 1.01 1.00 0.98 0.99 1.02 1.02 1.05 % std dev 1.9 2.4 4.9 2.1 2.1 3.5 3.9

Westinghouse Non-Proprietary Class 3 4-4 WCAP-18124-NP-A July 2018 Revision 0 4.2.2 VENUS-1 Benchmark The VENUS-1 experiment (Reference 31) is another commonly-used qualification benchmark. As with the PCA benchmark, the critical variables affecting the measurements were carefully measured and recorded. The VENUS-1 benchmark correctly represents the heterogeneities in a PWR, and includes a stainless steel core baffle, core barrel, and neutron pad. The benchmark experiment was performed at room temperature (300 K). Forty-one measurement locations exist in the benchmark, which are given in Table 4-4. The RAPTOR-M3G analysis of the VENUS-1 problem is modeled on a 192 x 123 x 65 cylindrical mesh grid. Angular quadrature is modeled with an S 8 level-symmetric quadrature set, and anisotropic scattering is treated with a P 3 Legendre expansion. The transport cross-section set was constructed from the BUGLE-96 library, and dosimetry reaction rate cross sections are taken from the SNLRML library. Results of the benchmark comparisons using RAPTOR-M3G are presented in Table 4-5 for TW differencing and Table 4-6 for DTW differencing.

Table 4-4: VENUS-1 Measurement Locations Point Description 1 Central Water Hole 2-3 Inner Baffle 4-10 Outer Baffle 11-14 Along 45° in 3/0 fuel region 15-19 Along 45° in Water Gap I 20-27 Core Barrel (0-45°) 28-36 At a radius of 55.255 cm in Water Gap II 37-41 Neutron Pad

Westinghouse Non-Proprietary Class 3 4-5 WCAP-18124-NP-A July 2018 Revision 0 Table 4-5: M/C Reaction Rate Comparisons for the VENUS-1 Experiment (TW Differencing) Point M/C Ratio 58Ni (n,p) 115In (n,n')

103Rh (n,n')

238U (n,f) 237Np (n,f) 1 1.01 0.99 0.97 1.11 - 2 0.97 0.97 0.93 1.03 0.98 3 0.96 0.97 0.93 1.02 0.96 4 0.98 0.97 - 1.05 1.06 5 0.98 0.96 0.94 1.02 - 6 0.99 0.96 0.93 1.04 1.03 7 1.01 0.97 0.94 - 1.02 8 1.03 0.97 0.94 1.03 1.03 9 0.96 0.96 0.93 1.04 1.00 10 0.97 0.98 0.95 1.01 1.01 11 - - - - 0.98 12 - - - - 1.00 13 - - - - 0.98 14 - - - - 1.08 15 - 0.98 0.97 1.04 0.98 0.97 - 0.98 17 - 0.98 0.99 1.06 0.99 18 - 1.00 0.93 - 1.02 19 - 0.99 1.01 1.08 - 20 0.97 0.99 - 1.06 0.98 21 0.99 0.98 - 1.06 0.99 22 1.00 0.98 0.93 1.08 1.07 23 1.03 0.99 - 1.07 1.07 24 1.05 0.98 - 1.10 1.05 25 1.07 0.98 - 1.11 0.99 26 1.07 0.99 - 1.05 1.06 27 1.08 0.99 0.98 1.07 1.05 28 - 1.03 - 1.13 1.07 29 - 1.01 - 1.08 1.10 30 - 1.02 - 1.16 1.02 - 1.08 1.06 32 - 1.04 - 1.10 1.11 33 - 1.01 - 1.10 1.05 34 - - - 1.12 1.11 35 - 1.08 - - 1.00 - 1.09 1.13 37 - - - - 1.12 - - - - - - - - 1.09 - - -

Westinghouse Non-Proprietary Class 3 4-6 WCAP-18124-NP-A July 2018 Revision 0 Table 4-6: M/C Reaction Rate Comparisons for the VENUS-1 Experiment (DTW Differencing) Point M/C Ratio 58Ni (n,p) 115In (n,n')

103Rh (n,n')

238U (n,f) 237Np (n,f) 1 1.00 0.98 0.95 1.10 - 2 0.98 0.98 0.94 1.04 0.99 3 0.97 0.98 0.93 1.03 0.97 4 0.98 0.98 - 1.05 1.06 5 0.98 0.97 0.95 1.03 - 6 1.00 0.97 0.94 1.05 1.03 7 1.03 0.98 0.95 - 1.04 8 1.03 0.98 0.95 1.04 1.04 9 0.96 0.97 0.93 1.04 1.01 10 0.97 0.97 0.95 1.01 1.01 11 - - - - 0.98 12 - - - - 1.00 13 - - - - 0.99 14 - - - - 1.08 15 - 0.98 0.97 1.04 0.98 0.97 - 0.99 17 - 0.99 1.00 1.07 0.99 18 - 1.01 0.94 - 1.03 19 - 1.00 1.02 1.09 - 20 0.99 1.00 - 1.08 0.99 21 1.01 1.00 - 1.08 1.01 22 1.01 1.00 0.95 1.10 1.09 23 1.05 1.01 - 1.08 1.09 24 1.07 1.00 - 1.12 1.07 25 1.08 0.99 - 1.13 1.01 26 1.09 1.02 - 1.07 1.08 27 1.11 1.01 1.00 1.09 1.08 28 - 1.04 - 1.14 1.08 29 - 1.02 - 1.10 1.11 30 - 1.03 - 1.17 1.03 - 1.09 1.07 32 - 1.05 - 1.12 1.12 33 - 1.02 - 1.11 1.06 34 - - - 1.14 1.12 35 - 1.09 - - 1.01 - 1.11 1.14 37 - - - - 1.15 - - - - - - - - 1.11 - - -

Westinghouse Non-Proprietary Class 3 4-7 WCAP-18124-NP-A July 2018 Revision 0

4.2.3 Summary

of Simulator Benchmark Results Results of the PCA and VENUS-1 simulator benchmarks, grouped by reaction, are summarized in Table 4-7 for the TW differencing scheme and Table 4-8 for the DTW differencing scheme. Also included in both tables are the energy response ranges between which 90% of activity is produced in a U-235 fission spectrum, taken from ASTM E844 (Reference 32). The U-238 and Np-237 measurements exhibit slightly worse agreement with the calculations; however, as indicated in Section 3.4, the U-238 and Np-237 reactions are subject to higher uncertainties in the measurement process. The simulator benchmarks test the adequacy of the transport and dosimetry evaluation techniques, and the underlying nuclear data. The simulator benchmark comparison results demonstrate that, when the configuration of the system is well-known, the level of agreement between RAPTOR-M3G calculations and measurements is within the uncertainties associated with the measurements, themselves. The uncertainty assigned to the calculational methodology from simulator benchmarks is 3%.

Westinghouse Non-Proprietary Class 3 4-8 WCAP-18124-NP-A July 2018 Revision 0 Table 4-7: Summary of Simulator Benchmark M/C Reaction Rate Comparisons (TW Differencing) Reaction Neutron Energy Response Number of Observations Average M/C % std dev 27Al (n,) 24Na (Cd) 6.45 - 11.9 MeV 6 0.97 2.2 58Ni (n,p) 58Co (Cd) 1.98 - 7.51 MeV 24 1.01 3.6 115115mIn (Cd) 1.12 - 5.86 MeV 40 1.00 3.7 103103mRh (Cd) 0.731 - 5.73 MeV 23 0.97 4.4 238U (n,f) FP (Cd) 1.44 - 6.69 MeV 33 1.06 4.2 237Np (n,f) FP (Cd) 0.684 - 5.61 MeV 35 1.03 4.4 Total 161 1.02 5.0 Table 4-8: Summary of Simulator Benchmark M/C Reaction Rate Comparisons (DTW Differencing) Reaction Neutron Energy Response Number of Observations Average M/C % std dev 27Al (n,) 24Na (Cd) 6.45 - 11.9 MeV 6 0.98 1.8 58Ni (n,p) 58Co (Cd) 1.98 - 7.51 MeV 24 1.01 4.0 115115mIn (Cd) 1.12 - 5.86 MeV 40 1.01 3.9 103103mRh (Cd) 0.731 - 5.73 MeV 23 0.98 4.4 238U (n,f) FP (Cd) 1.44 - 6.69 MeV 33 1.07 4.5 237Np (n,f) FP (Cd) 0.684 - 5.61 MeV 35 1.04 4.5 Total 161 1.02 5.2

Westinghouse Non-Proprietary Class 3 4-9 WCAP-18124-NP-A July 2018 Revision 0

4.3 OPERATING

REACTOR AND CALCULATIONAL BENCHMARKS In addition to measurements from laboratory-scale simulator benchmark experiments, Regulatory Guide 1.190 recommends that methods qualification should be based on comparisons with measurement data from operating power reactors and comparisons with reference results from calculational benchmark problems. This section provides the comparisons of power reactor measurements to calculations performed with RAPTOR-M3G and FERRET, and details the results of two calculational studies. These comparisons contribute to addressing Regulatory Position 1.4.2 of Regulatory Guide 1.190.

4.3.1 H.B. Robinson Unit 2 Benchmark H. B. Robinson Unit 2 is a Westinghouse 3loop PWR. As part of the LWR-PV-SDIP, a comprehensive set of surveillance capsule and exvessel neutron dosimetry measurements were performed during Cycle 9 (Reference 33). For the Cycle 9 benchmark, a replacement surveillance capsule was installed in a vacant surveillance capsule holder at the 20° azimuth with respect to the nearest cardinal axis. The dosimetry sets were placed at the geometric center of the surveillance capsule such that all measurements were taken within 30 cm of the core midplane. The exvessel neutron dosimetry was installed in the reactor cavity, between the concrete biological shield and the reactor vessel insulation. Multiple foil sensor sets were placed in capsules that were attached to gradient wires. The gradient wires were installed in the reactor cavity and axially spanned the length of the reactor core. Only the midplane capsule from the Cycle 9 exvessel neutron dosimetry set was analyzed. H. B. Robinson Unit 2 was modeled in cylindrical geometry with 158x136x172 mesh using RAPTOR-M3G. Angular quadrature was modeled with an S 8 level-symmetric quadrature set, and anisotropic scattering was treated with a P 3 Legendre expansion. Detailed geometry data for H. B. Robinson Unit 2 can be found in Reference 33. Neutron spectra obtained from the transport calculations were input into the FERRET code to apply the least squares adjustment procedures described in Section 3. The FERRET results are presented in Table 4-9 and Table 4-10 for transport results obtained with TW and DTW differencing schemes, respectively. These comparisons show that in both cases, the adjustments performed by the FERRET analysis are small and consistent with the input uncertainty bounds for the reaction rates and calculated neutron fluence rate. The 2 per degree of freedom associated with each of the analyses indicate good data consistency for all cases. In Table 4-11 and Table 4-12, the neutron fluence rate (E > 1.0 MeV) at each measurement location is provided before and after adjustment for each transport case (TW and DTW). The data in Table 4-11 and Table 4-12 show that the net adjustment in the fast neutron fluence rate was 4-5% for the in-vessel dosimetry and 0-2% for the ex-vessel data set. Further, the inclusion of the measurement information has Westinghouse Non-Proprietary Class 3 4-10 WCAP-18124-NP-A July 2018 Revision 0 reduced the uncertainty in the magnitude of the fast fluence rate from 15%

to 6% and 7% at the in-vessel and ex-vessel locations, respectively. This improved uncertainty in the fast neutron fluence rate is consistent with the corresponding improvement in the calculated sensor reaction rates. Table 4-9: FERRET Results for the H. B. Robinson Unit 2 Cycle 9 Dosimetry Benchmark Experiment (TW Differencing) In-Vessel 2/Degree of Freedom = 0.34) Reaction Reaction Rate [rps/atom] M/C Ratio Adjustment % of Calc. Measured Calculated Adjusted Cu-63 (n,Co-60 3.86E-17 3.67E-17 3.96E-17 1.05 7.9% Ti-46 (n,p) Sc-46 6.92E-16 5.83E-16 6.53E-16 1.19 12.0% Fe-54 (n,p) Mn-54 3.81E-15 3.67E-15 3.93E-15 1.04 7.1% Ni-58 (n,p) Co-58 5.34E-15 4.97E-15 5.35E-15 1.07 7.6% U-238 (n,f) FP 1.74E-14 1.64E-14 1.74E-14 1.06 6.1% Np-237 (n,f) FP 1.19E-13 1.14E-13 1.19E-13 1.04 4.4% (E > 1.0 MeV) [n/cm 2-s] - 4.47E+10 4.70E+10 - 5.1%

Ex-Vessel 2/Degree of Freedom = 0.83) Reaction Reaction Rate [rps/atom] M/C Ratio Adjustment % of Calc. Measured Calculated Adjusted Cu-63 (n,Co-60 3.86E-19 4.05E-19 4.02E-19 0.95 -0.7% Ti-46 (n,p) Sc-46 6.55E-18 5.81E-18 6.11E-18 1.13 5.2% Fe-54 (n,p) Mn-54 3.55E-17 3.76E-17 3.76E-17 0.94 0.0% Ni-58 (n,p) Co-58 5.85E-17 5.65E-17 5.77E-17 1.04 2.1% U-238 (n,f) FP 2.74E-16 2.60E-16 2.64E-16 1.05 1.5% (E > 1.0 MeV) [n/cm 2-s] - 1.01E+09 1.03E+09 - 1.7%

The 15% uncertainty reported for the calculated values represents the normalization uncertainty assigned to the trial spectrum input to the FERRET code.

Westinghouse Non-Proprietary Class 3 4-11 WCAP-18124-NP-A July 2018 Revision 0 Table 4-10: FERRET Results for the H. B. Robinson Unit 2 Cycle 9 Dosimetry Benchmark Experiment (DTW Differencing) In-Vessel 2/Degree of Freedom = 0.34) Reaction Reaction Rate [rps/atom] M/C Ratio Adjustment % of Calc. Measured Calculated Adjusted Cu-63 (n,Co-60 3.86E-17 3.68E-17 3.96E-17 1.05 7.6% Ti-46 (n,p) Sc-46 6.92E-16 5.84E-16 6.53E-16 1.18 11.8% Fe-54 (n,p) Mn-54 3.81E-15 3.68E-15 3.92E-15 1.04 6.5% Ni-58 (n,p) Co-58 5.34E-15 4.99E-15 5.34E-15 1.07 7.0% U-238 (n,f) FP 1.74E-14 1.65E-14 1.74E-14 1.05 5.5% Np-237 (n,f) FP 1.19E-13 1.16E-13 1.19E-13 1.03 2.6% (E > 1.0 MeV) [n/cm2-s] - 4.53E+10 4.73E+10 - 4.4%

Ex-Vessel 2/Degree of Freedom = 0.80) Reaction Reaction Rate [rps/atom] M/C Ratio Adjustment % of Calc. Measured Calculated Adjusted Cu-63 (n,Co-60 3.86E-19 4.10E-19 4.03E-19 0.94 -1.7% Ti-46 (n,p) Sc-46 6.55E-18 5.87E-18 6.10E-18 1.12 3.9% Fe-54 (n,p) Mn-54 3.55E-17 3.78E-17 3.75E-17 0.94 -0.8% Ni-58 (n,p) Co-58 5.85E-17 5.71E-17 5.77E-17 1.02 1.1% U-238 (n,f) FP 2.74E-16 2.66E-16 2.67E-16 1.03 0.4% (E > 1.0 MeV) [n/cm 2-s] - 1.05E+09 1.06E+09 - 0.5%

Westinghouse Non-Proprietary Class 3 4-12 WCAP-18124-NP-A July 2018 Revision 0 Table 4-11: Summary of Least Squares Adjustment Results for the H. B. Robinson Unit 2 Benchmark (TW Differencing)

Location (E > 1.0 MeV) [n/cm 2-s] A/C Calculated Adjusted In-Vessel 4.47E+10 (15%) 4.70E+10 (6%) 1.05 Ex-Vessel 1.01E+09 (15%) 1.03E+09 (7%) 1.02 Note: Numbers in parentheses represent one standard deviation. The 15% uncertainty reported for the calculated values represents the normalization uncertainty assigned to the trial spectrum input to the FERRET code.

Table 4-12: Summary of Least Squares Adjustment Results for the H. B. Robinson Unit 2 Benchmark (DTW Differencing)

Location (E > 1.0 MeV) [n/cm 2-s] A/C Calculated Adjusted In-Vessel 4.53E+10 (15%) 4.73E+10 (6%) 1.04 Ex-Vessel 1.05E+09 (15%) 1.06E+09 (7%) 1.00 Note: Numbers in parentheses represent one standard deviation. The 15% uncertainty reported for the calculated values represents the normalization uncertainty assigned to the trial spectrum input to the FERRET code.

Westinghouse Non-Proprietary Class 3 4-13 WCAP-18124-NP-A July 2018 Revision 0 4.3.2 NRC Fluence Calculation Benchmark The NRC's fluence benchmark (Reference 29) is a calculational exercise, developed by Brookhaven National Laboratory at the request of the NRC, which provides reference solutions for typical PWR and BWR pressure vessel fluence calculations. The PWR problem models a typical 204 fuel assembly PWR core including the core baffle and barrel, thermal shield, and a pressure vessel. Three types of fuel loadings are defined, including a standard out-in core loading, a low-leakage core loading, and a core that includes partial length shield assemblies (PLSAs). The BWR problem models an 800 fuel bundle BWR core including the radial reflector, shroud, jet pumps, riser columns, and a pressure vessel. Reference solutions derived from multigroup synthesis and Monte Carlo simulations are provided in Reference 29. The PWR and BWR problems were analyzed with RAPTOR-M3G. The PWR model analysis presented herein considers the standard core loading configuration. In all cases, angular quadrature is modeled with an S 8 level-symmetric quadrature set, and anisotropic scattering is treated with a P 3 Legendre expansion. Comparisons relative to the fast (E > 1.0 MeV) fluence rate synthesis solutions published in Reference 29 are provided in Table 4-13 and Table 4-14 for the PWR and BWR problems, respectively.

Westinghouse Non-Proprietary Class 3 4-14 WCAP-18124-NP-A July 2018 Revision 0 Table 4-13: NRC Fluence Benchmark Comparisons with RAPTOR-M3G PWR Problem with Standard Core Loading Pressure Vessel Inner-Wall Lower Weld Location (R=219.393 cm, Z=67.1048 cm) Theta (Degrees) Fast (E > 1.0 MeV) Neutron Fluence Rate [n/cm 2-s] RAPTOR-M3G with DTW Relative Diff. (%) RAPTOR-M3G with TW Relative Diff. (%) Reference 29, Table 4.1.2.4 RAPTOR-M3G with DTW RAPTOR-M3G with TW 1.125 2.71E+10 2.57E+10 2.55E+10 -4.99% -5.86% 3.375 2.76E+10 2.64E+10 2.63E+10 -4.48% -4.96% 5.625 2.87E+10 2.77E+10 2.75E+10 -3.49% -4.38% 7.875 3.04E+10 2.96E+10 2.94E+10 -2.78% -3.36% 10.125 3.31E+10 3.18E+10 3.16E+10 -4.03% -4.59% 12.375 3.49E+10 3.39E+10 3.38E+10 -3.01% -3.11% 14.625 3.62E+10 3.53E+10 3.52E+10 -2.44% -2.81% 16.875 3.64E+10 3.55E+10 3.56E+10 -2.29% -2.07% 19.125 3.45E+10 3.35E+10 3.32E+10 -2.79% -3.92% 21.375 3.18E+10 3.15E+10 3.11E+10 -0.97% -2.24% 23.625 2.95E+10 2.90E+10 2.87E+10 -1.75% -2.94% 25.875 2.79E+10 2.73E+10 2.67E+10 -2.48% -4.56% 28.125 2.74E+10 2.68E+10 2.64E+10 -2.04% -3.65% 30.375 2.77E+10 2.72E+10 2.68E+10 -1.95% -3.22% 32.625 2.77E+10 2.71E+10 2.72E+10 -2.01% -1.68% 34.875 2.67E+10 2.56E+10 2.57E+10 -4.00% -3.88% 37.125 2.36E+10 2.35E+10 2.34E+10 -0.77% -1.18% 39.375 2.08E+10 2.07E+10 2.06E+10 -0.59% -1.10% 41.625 1.88E+10 1.80E+10 1.77E+10 -4.31% -5.85% 43.875 1.72E+10 1.66E+10 1.62E+10 -3.70% -5.93%

Westinghouse Non-Proprietary Class 3 4-15 WCAP-18124-NP-A July 2018 Revision 0 Table 4-14: NRC Fluence Benchmark Comparisons with RAPTOR-M3G BWR Problem Pressure Vessel Inner-Wall (R=321.786 cm, Z=239.93 cm) Theta (Degrees) Fast (E > 1.0 MeV) Neutron Fluence Rate [n/cm 2-s] RAPTOR-M3G with DTW Relative Diff. (%) RAPTOR-M3G with TW Relative Diff. (%) Reference 29, Table 4.2.2.4 RAPTOR-M3G with DTW RAPTOR-M3G with TW 1.125 7.27E+08 7.18E+08 7.26E+08 -1.24% -0.03%

3.375 6.45E+08 6.53E+08 6.58E+08 1.25% 2.06%

5.625 5.74E+08 5.90E+08 5.92E+08 2.88% 3.16%

7.875 5.09E+08 5.17E+08 5.03E+08 1.58% -1.27%

10.125 5.10E+08 5.10E+08 5.13E+08 0.16% 0.68%

12.375 4.88E+08 4.98E+08 5.00E+08 1.93% 2.42%

14.625 4.88E+08 5.09E+08 4.96E+08 4.50% 1.78%

16.875 5.60E+08 6.03E+08 5.98E+08 7.64% 6.67%

19.125 6.74E+08 6.87E+08 6.80E+08 1.84% 0.83%

21.375 6.87E+08 7.01E+08 7.18E+08 2.14% 4.60%

23.625 7.30E+08 7.35E+08 7.44E+08 0.67% 1.96%

25.875 8.42E+08 8.35E+08 8.28E+08 -0.90% -1.76%

28.125 9.13E+08 9.00E+08 9.11E+08 -1.41% -0.27%

30.375 9.15E+08 9.26E+08 9.21E+08 1.19% 0.65%

32.625 9.66E+08 9.65E+08 9.71E+08 -0.08% 0.50%

34.875 9.61E+08 9.75E+08 9.71E+08 1.51% 1.08%

37.125 1.03E+09 1.03E+09 1.02E+09 0.23% -0.23%

39.375 1.14E+09 1.18E+09 1.20E+09 3.71% 5.85%

41.625 1.30E+09 1.27E+09 1.27E+09 -2.41% -2.14%

43.875 1.26E+09 1.24E+09 1.23E+09 -1.51% -1.65%

Westinghouse Non-Proprietary Class 3 4-16 WCAP-18124-NP-A July 2018 Revision 0

4.3.3 Summary

of Operating Reactor and Calculational Benchmark Results The H. B. Robinson Unit 2 benchmark represents an experimental configuration that is broadly reflective of most operating reactors: data was collected during full-power operation at a commercial LWR; the power distribution and power history data supporting the analysis were derived using methods similar to those employed by most operating LWRs; geometric dimensions specified are nominal dimensions, and not necessarily identical to their as-built configuration. These characteristics make the H. B. Robinson Unit 2 benchmark a compelling data set. The best-estimate fast (E > 1.0 MeV) neutron fluence rate, derived from the application of the least squares process, differs from the calculated values at the measurement locations by a maximum of 5%. Therefore, the uncertainty assigned to the calculational methodology from H. B. Robinson Unit 2 benchmark is 5%. The calculational study performed in Section 4.3.2 does not provide real measurement data, and the methods and data used in the reference results are somewhat dated by contemporary standards. Therefore, results of these evaluations are not used as a direct input to the overall bias and uncertainty assessment for the fluence determination methodology. Nonetheless, the consistency of the RAPTOR-M3G results, both with the reference calculations provided by Brookhaven and the self-consistency demonstrated by the two differencing schemes in RAPTOR-M3G, provides additional confidence that RAPTOR-M3G is correctly applying the S N method.

Westinghouse Non-Proprietary Class 3 4-17 WCAP-18124-NP-A July 2018 Revision 0

4.4 ANALYTIC

UNCERTAINTY ANALYSIS Operating reactors are subject to several uncertainties that may influence the validity of the calculated neutron fluence results. The most significant among these are: Uncertainties in the core neutron source Uncertainties in the as-built thicknesses and locations of the reactor vessel and internal components Uncertainties in the full-power coolant temperatures (water density) This listing of parameters is consistent with the findings of other neutron fluence uncertainty studies (References 34, 35, and 36). This section presents the results of a sensitivity study performed using RAPTOR-M3G that evaluate the impacts of variations in the parameters listed above on calculated neutron fluence values. These comparisons address Regulatory Position 1.4.1 of Regulatory Guide 1.190. Note that the uncertainty analysis was performed for both the TW and DTW differencing schemes. In general, the analytic uncertainty values are consistent between the two differencing schemes; however, in cases where there are differences, the higher uncertainty values were selected.

4.4.1 Core Neutron Source Uncertainties To assess the impact of uncertainties in the core neutron source on calculated neutron fluence results, changes in the following parameters were evaluated: Absolute source strength of peripheral fuel assemblies - Studies have shown that the neutron fluence rate in regions external to the core is dominated by the neutron source from fuel assemblies on the core periphery. In-core measurements indicate that a source magnitude uncertainty of 5% is bounding. Pin-by-pin spatial distributions of neutron source at the core periphery - Core management studies indicate that uncertainties in the relative pin powers in peripheral fuel assemblies can be on the order of 10%. This parameter is evaluated by holding total assembly power constant while diminishing and intensifying the peripheral pin power gradients. Burnup of the peripheral fuel assemblies - Perturbations in fuel assembly burnup impact the fission spectrum, neutron yield per fission, and energy released per fission for each peripheral fuel assembly. A 5000 MWD/MTU uncertainty in the peripheral fuel assembly burnups is considered conservative. The sensitivity study is performed using a series of calculations starting with mid-cycle burnup at 3000 MWD/MTU, and 5000 MWD/MTU to 50,000 MWD/MTU with 5000 MWD/MTU delta mid-cycle burnup between each run. Axial power distribution - Based on variations in axial peaking factors over the course of a fuel cycle, a 10% uncertainty in the shape of the axial power distribution is considered conservative.

Westinghouse Non-Proprietary Class 3 4-18 WCAP-18124-NP-A July 2018 Revision 0 This parameter is evaluated by holding total assembly power constant while diminishing and intensifying the axial power gradients. Each case evaluated as part of the sensitivity study is described in Table 4-15. The base case consisted of a low-leakage power distribution cycle from a Westinghouse 4-Loop reactor. Table 4-16 through Table 4-18 provides the differences between calculated fast neutron (E > 1.0 MeV) fluence rate results at several locations for each permutation case, each normalized to the corresponding base case result. The overall uncertainty estimates are summarized in Table 4-19 through Table 4-21.

Westinghouse Non-Proprietary Class 3 4-19 WCAP-18124-NP-A July 2018 Revision 0 Table 4-15: Summary of Core Neutron Source Sensitivity Study Case Number Description 1 Peripheral source strength biased by a factor of 0.95 2 Peripheral source strength biased by a factor of 1.05 3 Pin power distribution gradient diminished according to: 4 Pin power distribution gradient intensified according to: 5f Mid-cycle burnup at 3000 MWD/MTU 6f Mid-cycle burnup at 50,000 MWD/MTU 7 Axial power distribution gradient intensified according to: 8 Axial power distribution gradient diminished according to: Table 4-16: Source Permutation-to-Nominal Fast Neutron (E > 1.0 MeV) Fluence Rate Difference at Surveillance Capsule Locations Case Number Surveillance Capsule Location 1 -4% 2 4% 3 1% 4 -1% 5 -7% 6 1% 7 1% 8 -1% f Cases 5 and 6 span a mid-cycle burnup range of 47000 MWD/MTU. The uncertainty in the neutron fluence attributable to a 5000 MWD/MTU uncertainty in burnup is obtained by scaling the difference between Cases 5 and 6 accordingly by F = (5000 / 47000).

Westinghouse Non-Proprietary Class 3 4-20 WCAP-18124-NP-A July 2018 Revision 0 Table 4-17: Source Permutation-to-Nominal Fast Neutron (E > 1.0 MeV) Fluence Rate Difference at Pressure Vessel Inner Radius Locations Case Number RPV Inside Radius +42 cm Relative to Top-of-Core Elevation RPV Inside Radius +12 cm Relative to Middle-of-Core Elevation RPV Inside Radius -26 cm Relative to Bottom-of-Core Elevation 1 -4% -5% -4% 2 4% 5% 4% 3 0% 1% 0% 4 0% -1% 0% 5 -7% -7% -7% 6 4% 2% 3%

7 -10% 1% -8% 8 10% -1% 8%

Table 4-18: Source Permutation-to-Nominal Fast Neutron (E > 1.0 MeV) Fluence Rate Difference at Reactor Cavity Locations Case Number Reactor Cavity Top-of-Core Elevation Reactor Cavity Middle-of-Core Elevation Reactor Cavity Bottom-of-Core Elevation 1 -4% -5% -5% 2 4% 5% 5% 3 1% 1% 1% 4 -1% -1% -1% 5 -7% -7% -7% 6 2% 2% 2%

7 -3% 1% -2% 8 3% -1% 2%

The selected locations on the inner radius of the reactor pressure vessel are typical of circumferential welds that join the upper and intermediate shell courses.

Westinghouse Non-Proprietary Class 3 4-21 WCAP-18124-NP-A July 2018 Revision 0 Table 4-19: Summary of Neutron Fluence Rate Uncertainties at Surveillance Capsule Locations Resulting from Core Neutron Source Uncertainties Uncertainty Component Surveillance Capsule Location Peripheral Assembly Source Strength 4% Pin Power Distribution 1% Peripheral Assembly Burnup (+/-5000 MWD/MTU) 1% Axial Power Distribution 1%

Table 4-20: Summary of Neutron Fluence Rate Uncertainties at Pressure Vessel Inner Radius Locations Resulting from Core Neutron Source Uncertainties Uncertainty Component RPV Inside Radius +42 cm Relative to Top-of-Core Elevation RPV Inside Radius +12 cm Relative to Middle-of-Core Elevation RPV Inside Radius -26 cm Relative to Bottom-of-Core Elevation Peripheral Assembly Source Strength 4% 5% 4% Pin Power Distribution 0% 1% 0% Peripheral Assembly Burnup (+/-5000 MWD/MTU) 1% 1% 1% Axial Power Distribution 10% 1% 8%

Table 4-21: Summary of Neutron Fluence Rate Uncertainties at Reactor Cavity Locations Resulting from Core Neutron Source Uncertainties Uncertainty Component Reactor Cavity Top-of-Core Elevation Reactor Cavity Middle-of-Core Elevation Reactor Cavity Bottom-of-Core Elevation Peripheral Assembly Source Strength 4% 5% 5% Pin Power Distribution 1% 1% 1% Peripheral Assembly Burnup (+/-5000 MWD/MTU) 1% 1% 1% Axial Power Distribution 3% 1% 2%

Westinghouse Non-Proprietary Class 3 4-22 WCAP-18124-NP-A July 2018 Revision 0

4.4.2 Geometric

and Temperature Uncertainties To assess the impact of uncertainties in the location and thickness of reactor components, as well as uncertainties in reactor coolant temperature, on calculated neutron fluence results, changes in the following parameters were evaluated: Reactor internals dimensions - Thickness tolerances on stainless steel reactor internals components (e.g., core baffle, core barrel, thermal shield/neutron pad) are typically specified as 1/16 inch or tighter. Reactor vessel inner radius - Reactor vessels typically specify an inner radius with tolerance bounds of -0.00 inches and +1/32 inches. A tolerance of +/- 1/8 inch is considered. Reactor vessel thickness - Some techniques for fabricating reactor vessels result in larger-than-nominal reactor vessel base metal plate thicknesses. A tolerance of +/- 1/16 inch is considered. Dosimetry Positioning - Surveillance capsules have a tolerance of +/- 1/16 inch associated with the positioning of the dosimetry in radial, azimuthal, and axial directions. A larger positioning uncertainty of +/- 2 inches is associated with ex-vessel neutron dosimetry in radial azimuthal, and axial directions. Coolant Temperature - Variations in water temperature over the course of a fuel cycle are expected to be less than +/- 10 °F. Core Peripheral Modeling - The modeling of the rectilinear core baffle in cylindrical geometry represents another potential source of uncertainty in the geometric modeling of the reactor. The sensitivity of the solution to the modeling approach is determined by a direct comparison of the results of a cylindrical geometry calculation with those of a Cartesian geometry calculation in which the baffle region and core periphery were modeled explicitly. The comparisons of interest were taken at various locations external to the core baffle, but inside the core barrel. Each case evaluated as part of the sensitivity study is described in Table 4-22. The base case consisted of a low-leakage power distribution from a Westinghouse 4-Loop reactor. Table 4-23 through Table 4-25 provide the differences between calculated fast neutron (E > 1.0 MeV) fluence rate results at several locations for each permutation case, each normalized to the corresponding base case result. The overall uncertainty estimates are summarized in Table 4-26 through Table 4-28.

Westinghouse Non-Proprietary Class 3 4-23 WCAP-18124-NP-A July 2018 Revision 0 Table 4-22: Summary of Geometry and Temperature Sensitivity Study Case Number Description 1 Baffle plates, core barrel, and neutron pad thickness decreased by 1/16 inch 2 Baffle plates, core barrel, and neutron pad thickness increased by 1/16 inch 3 Reactor coolant temperatures decreased by 10 °F 4 Reactor coolant temperatures increased by 10 °F 5 Reactor vessel radius decreased by 1/8 inch 6 Reactor vessel radius increased by 1/8 inch 7 Reactor vessel thickness decreased by 1/16 inch 8 Reactor vessel thickness increased by 1/16 inch 9 Surveillance capsule position adjusted by 1/16 inch, ex-vessel dosimetry position adjusted by 2 inches 10 Cartesian versus cylindrical geometry modeling difference in core periphery Table 4-23: Geometry and Temperature Permutation-to-Nominal Fast Neutron (E > 1.0 MeV) Fluence Rate Difference at Surveillance Capsule Locations Case Number Surveillance Capsule Location 1 1% 2 -1% 3 -4% 4 5% 5 0% 6 0% 7 0% 8 0% 9 2%(a) 10 5%(b) (a) Surveillance capsule positioning uncertainty includes radial, azimuthal, and axial position variations (b) Core periphery modeling uncertainty determined from direct comparison between cylindrical and Cartesian results in bypass region

Westinghouse Non-Proprietary Class 3 4-24 WCAP-18124-NP-A July 2018 Revision 0 Table 4-24: Geometry and Temperature Permutation-to-Nominal Fast Neutron (E > 1.0 MeV) Fluence Rate Difference at Pressure Vessel Inner Radius Locations Case Number RPV Inside Radius +42 cm Relative to Top-of-Core Elevation RPV Inside Radius +12 cm Relative to Middle-of-Core Elevation RPV Inside Radius -26 cm Relative to Bottom-of-Core Elevation 1 6% 5% 5% 2 -3% -3% -3% 3 -8% -6% -7% 4 10% 6% 8% 5 3% 4% 4% 6 -3% -4% -3%

7 2% -1% 1% 8 2% -1% 1% 9 N/A N/A N/A 10 5%* 5%* 5%*

Core periphery modeling uncertainty determined from direct comparison between cylindrical and Cartesian results in bypass region

Westinghouse Non-Proprietary Class 3 4-25 WCAP-18124-NP-A July 2018 Revision 0 Table 4-25: Geometry and Temperature Permutation-to-Nominal Fast Neutron (E > 1.0 MeV) Fluence Rate Difference at Reactor Cavity Locations Case Number Reactor Cavity Top-of-Core Elevation Reactor Cavity Middle-of-Core Elevation Reactor Cavity Bottom-of-Core Elevation 1 3% 3% 3% 2 -4% -3% -3% 3 -6% -6% -6% 4 7% 6% 6% 5 1% 1% 1% 6 -4% -4% -4%

7 2% 2% 2% 8 -3% -3% -3%

9 12%(a) 4%(a) 14%(a) 10 5%(b) 5%(b) 5%(b) (a) Cavity capsule positioning uncertainty includes radial, azimuthal, and axial position variations (b) Core periphery modeling uncertainty determined from direct comparison between cylindrical and Cartesian results in bypass region Table 4-26: Summary of Neutron Fluence Rate Uncertainties at Surveillance Capsule Locations Resulting from Geometry and Temperature Uncertainties Uncertainty Component Surveillance Capsule Location Internals Dimensions 1% Vessel IR 0% Vessel Thickness 0% Dosimetry Position 2% Coolant Temperature 5% Core Periphery Modeling 5%

Westinghouse Non-Proprietary Class 3 4-26 WCAP-18124-NP-A July 2018 Revision 0 Table 4-27: Summary of Neutron Fluence Rate Uncertainties at Pressure Vessel Inner Radius Locations Resulting from Geometry and Temperature Uncertainties Uncertainty Component RPV Inside Radius +42 cm Relative to Top-of-Core Elevation RPV Inside Radius +12 cm Relative to Middle-of-Core Elevation RPV Inside Radius -26 cm Relative to Bottom-of-Core Elevation Internals Dimensions 6% 5% 5% Vessel IR 3% 4% 4% Vessel Thickness 2% 1% 1% Coolant Temperature 10% 6% 8% Core Periphery Modeling 5% 5% 5%

Table 4-28: Summary of Neutron Fluence Rate Uncertainties at Reactor Cavity Locations Resulting from Geometry and Temperature Uncertainties Uncertainty Component Reactor Cavity Top-of-Core Elevation Reactor Cavity Middle-of-Core Elevation Reactor Cavity Bottom-of-Core Elevation Internals Dimensions 4% 3% 3% Vessel IR 4% 4% 4% Vessel Thickness 3% 3% 3% Dosimetry Position 12% 4% 14% Coolant Temperature 7% 6% 6% Core Periphery Modeling 5% 5% 5%

Westinghouse Non-Proprietary Class 3 4-27 WCAP-18124-NP-A July 2018 Revision 0

4.4.3 Summary

of Analytic Uncertainty Analysis Table 4-29 through Table 4-31 summarize the analytic uncertainties determined from a reference Westinghouse 4-Loop reactor model with calculations performed with RAPTOR-M3G. The total analytic uncertainty is derived by combining the individual uncertainty components in quadrature using the "root-sum-of-the-squares" method. The analytic uncertainty analysis was performed with both the TW and DTW differencing schemes. In general, the analytic uncertainty values are consistent between the two differencing schemes; however, in cases where there are differences, the higher uncertainty value was selected. Table 4-29: Summary of Neutron Fluence Rate Uncertainties at Surveillance Capsule Locations Uncertainty Component Surveillance Capsule Location Peripheral Assembly Source Strength 4% Pin Power Distribution 1% Peripheral Assembly Burnup (+/-5000 MWD/MTU) 1% Axial Power Distribution 1% Internals Dimensions 1% Vessel IR 0% Vessel Thickness 0% Dosimetry Position 2% Coolant Temperature 5% Core Periphery Modeling 5% Total Analytic Uncertainty 9%

Westinghouse Non-Proprietary Class 3 4-28 WCAP-18124-NP-A July 2018 Revision 0 Table 4-30: Summary of Neutron Fluence Rate Uncertainties at Pressure Vessel Inner Radius Locations Uncertainty Component RPV Inside Radius +42 cm Relative to Top-of-Core Elevation RPV Inside Radius +12 cm Relative to Middle-of-Core Elevation RPV Inside Radius -26 cm Relative to Bottom-of-Core Elevation Peripheral Assembly Source Strength 4% 5% 4% Pin Power Distribution 0% 1% 0% Peripheral Assembly Burnup (+/-5000 MWD/MTU) 1% 1% 1% Axial Power Distribution 10% 1% 8% Internals Dimensions 6% 5% 5% Vessel IR 3% 4% 4% Vessel Thickness 2% 1% 1% Dosimetry Position N/A N/A N/A Coolant Temperature 10% 6% 8% Core Periphery Modeling 5% 5% 5% Total Analytic Uncertainty 17% 11% 15%

Westinghouse Non-Proprietary Class 3 4-29 WCAP-18124-NP-A July 2018 Revision 0 Table 4-31: Summary of Neutron Fluence Rate Uncertainties at Reactor Cavity Locations Uncertainty Component Reactor Cavity Top-of-Core Elevation Reactor Cavity Middle-of-Core Elevation Reactor Cavity Bottom-of-Core Elevation Peripheral Assembly Source Strength 4% 5% 5% Pin Power Distribution 1% 1% 1% Peripheral Assembly Burnup (+/-5000 MWD/MTU) 1% 1% 1% Axial Power Distribution 3% 1% 2% Internals Dimensions 4% 3% 3% Vessel IR 4% 4% 4% Vessel Thickness 3% 3% 3% Dosimetry Position 12% 4% 14% Coolant Temperature 7% 6% 6% Core Periphery Modeling 5% 5% 5% Total Analytic Uncertainty 17% 12% 18%

Westinghouse Non-Proprietary Class 3 4-30 WCAP-18124-NP-A July 2018 Revision 0

4.5 ESTIMATE

OF BIAS AND UNCERTAINTY The simulator benchmark comparison results demonstrate that, when the configuration of the system is well-known, the level of agreement between RAPTOR-M3G calculations and measurements is within the uncertainties associated with the measurements, themselves. Therefore no systematic bias is assigned to the calculational methodology. The following summarizes the uncertainties applicable to pressure vessel beltline locations, determined from the results of the methodology qualification process: Simulator Benchmark Comparisons 3% H. B. Robinson Benchmark Comparisons 5% Analytic Sensitivity Studies 11% Peripheral Assembly Source Strength 5% Pin Power Distribution 1% Peripheral Assembly Burnup 1% Axial Power Distribution 1% Internals Dimensions 5%

Vessel IR 4% Vessel Thickness 1% Coolant Temperature 6% Core Periphery Modeling 5% Other Factors 5%

Net Uncertainty 13%

The category designated "Other Factors" is intended to attribute an additional uncertainty to other geometrical or operational variables that individually have an insignificant effect on the overall uncertainty, but collectively should be accounted for in the assessment. The uncertainty components tabulated above represent percent uncertainty at the level. In the tabulation, the net uncertainty from the analytic sensitivity studies has been broken down into its individual components. When the four uncertainty values listed above are combined in quadrature with the "root-sum-of-the-squares" method, the resultant overall calculational uncertainty is estimated to be bounded by 13% for pressure vessel inner radius within the beltline region. To date, this methodology has been used in the evaluation of dosimetry sets from 69 in-vessel surveillance capsules and 87 dosimetry sets from the midplane of the reactor cavity from 18 PWRs. The comparisons of measurements to calculations are summarized in Section 5.4. The comparisons of the plant-specific calculations with the results of the capsule dosimetry are used to further validate the Westinghouse Non-Proprietary Class 3 4-31 WCAP-18124-NP-A July 2018 Revision 0 calculational methodology within the context of a 1 calculational uncertainty at corresponding vessel locations. This uncertainty quantification addresses Regulatory Position 1.4.3 of Regulatory Guide 1.190.

Westinghouse Non-Proprietary Class 3 5-1 WCAP-18124-NP-A July 2018 Revision 0 5 VALIDATION OF LEAST SQUARES ADJUSTMENT PROCEDURES Regulatory Guide 1.190 does not provide guidance on qualifying a least squares adjustment process. However, the material provided in this section is similar to material that was previously presented and approved in WCAP-16083-NP-A. The underlying methods and processes have not changed. New in this report is a discussion and evaluation of the characteristics of Nb-93 as a neutron sensor. In addition, the inputs sensitivity study was re-evaluated using a different reference data set, but the conclusions remain the same.

5.1 OVERVIEW

This section describes the methodology qualification evaluations performed for the least squares adjustment process. These evaluations consist of the following stages:

1. Data Comparisons in the NIST U-235 Fission Field: Comparisons of published spectrum-averaged cross-sections calculated with the SNLRML library to measurements from NIST, and corresponding comparisons of Westinghouse-calculated spectrum-averaged cross-sections to data published in ASTM standards.

2. FERRET Sensitivity Studies: Sensitivity studies examining the relative importance of commonly-used neutron sensors to outputs of the least squares adjustment process and the effects of input uncertainties on final calculated uncertainties.

3. Operating Power Reactor Comparisons: An extensive database of evaluations performed with the methodology described in this report. These comparisons are intended to provide support for the validation of the transport calculation itself as well as validation for the uncertainties assigned to the results of those calculations.

Westinghouse Non-Proprietary Class 3 5-2 WCAP-18124-NP-A July 2018 Revision 0 5.2 DATA COMPARISONS IN THE NIST U-235 FISSION FIELD The sensor reaction cross-sections and associated uncertainties play a key role in the least squares evaluation of dosimetry data sets. Therefore, it is important to assess both the overall accuracy of these cross-sections and the impact on that accuracy of any data processing included in the evaluation procedure. The least squares approach used by Westinghouse makes use of the SNLRML dosimetry cross-section library. This comprehensive library meets the requirements identified in ASTM E1018, "Standard Guide for Application of ASTM Evaluated Cross-Section Data File" (Reference 37) for use in LWR applications, and has been explicitly recommended in previous versions of the standard. The library is provided by RSICC in a 640 neutron group format spanning an energy range from thermal to 20.0 MeV. Prior to use in the least squares adjustment, this fine group library is collapsed to a broad group structure consisting of 53 groups using the calculated neutron spectrum at the measurement location as a weighting function. The data comparisons from the standard field irradiations were used to determine the level of accuracy of the base cross-section library, as well as to demonstrate the adequacy of the collapsing procedure used to generate the 53 group library. In ASTM E261, "Standard Practice for Determining Neutron Fluence, Fluence Rate, and Spectra by Radioactivation Techniques" (Reference 38), fission spectrum averaged cross-sections applicable to the U-235 thermal fission field and the Cf-252 spontaneous fission field are provided for a variety of threshold activation detectors that are used in power and research reactor irradiations. In this data compilation, both calculated and measured spectrum averaged cross-sections are provided along with their evaluated uncertainties. The magnitude of errors in the processed dosimetry cross-section library can be judged by the observed disagreement between the calculated spectrum averaged cross-sections and the corresponding measured values for the standard U-235 and Cf-252 fields. The data listed in Table 5-1 and Table 5-2 have been extracted from Table 3 of ASTM E261, and are representative of the foil sets used in power reactor irradiations and in the PCA benchmark irradiations. This subset of the ASTM E261 information includes the threshold reactions typically used in LWR surveillance capsule and ex-vessel dosimetry irradiations. For the comparisons shown in Table 5-1 and Table 5-2, the authors of ASTM E261 based the calculated spectrum averaged reaction cross-sections on data from the recommended SNLRML library. Because the Westinghouse methodology and the evaluations provided in ASTM E261 are both based on the same dosimetry cross-section library, the calculated spectrum averaged cross-sections produced by the SAND/FERRET processing procedure should closely match the calculated values cited in the standard.

Significant differences between the two sets of calculated spectrum averaged cross-sections would indicate errors in the processing procedure. Comparisons of the calculated spectrum averaged cross-sections from ASTM E261 with the corresponding cross-sections processed by Westinghouse are listed in Table 5-3. The calculation to measurement comparisons given in Table 5-1 indicate that for the U-235 thermal fission field, the C/M ratios except for Ti-46 (n,p) Sc-46 fall within one standard deviation of the combined uncertainty in the calculation and measurement. For these reactions, the agreement between calculation and measurement is within 5%. In the case of the Ti-46 (n,p) Sc-46 reaction, the C/M ratio Westinghouse Non-Proprietary Class 3 5-3 WCAP-18124-NP-A July 2018 Revision 0 falls within two standard deviations of the combined uncertainty with the calculation falling within 11% of the measured value. For the Cf-252 spontaneous fission field, the comparisons provided in Table 5-2 show that, with the exception of the U-238 (n,f) FP, In-115 (n,n') In-115m, and Ti-46 (n,p) Sc-46 reactions, the C/M comparisons fall within one standard deviation of the combined uncertainty in the calculations and measurements. The C/M ratios for the U-238 (n,f) FP and In-115 (n,n') In-115m reactions fall within two standard deviations and the C/M ratio for the Ti-46 (n,p) Sc-46 reaction falls within three standard deviations of the combined uncertainty. For reactions other than Ti-46 (n,p) Sc-46, the agreement between calculation and measurement is within 6%. The calculated spectrum averaged cross-section for the Ti-46 (n,p) Sc-46 reaction falls within 11% of the measured value. The comparisons provided in Table 5-1 and Table 5-2 demonstrate that the SNLRML dosimetry cross-sections as processed by the authors of ASTM E261 produce accurate representations of the spectrum averaged cross-sections in the NIST standard fission fields. The Westinghouse least squares approach uses this same base dosimetry cross-section library, but a somewhat different processing procedure. To compare the cross-section processing procedure used in the Westinghouse approach to expand the calculated input spectrum, spectrum weight the dosimetry cross-sections, and re-collapse the spectrum and dosimetry cross-sections to the FERRET 53 energy group structure, the ASTM E261 calculations for the U-235 thermal fission field were duplicated for the foil reactions contained in both the power reactor sensor set and PCA sensor set. In performing this calculation, the ENDF/B-VI U-235 fission spectrum supplied with the BUGLE-96 cross-section library was input to the SAND/FERRET procedure as the calculated spectrum. The dosimetry cross-sections for were taken directly from the SNLRML library. Comparisons of the Westinghouse-processed spectrum averaged cross-sections with the calculated values from ASTM E261 are listed in Table 5-3 for both the power reactor and PCA sensor sets. An examination of the data given in Table 5-3 shows that the spectrum averaged cross-sections calculated by Westinghouse using the SAND pre-processing module are essentially identical to the calculated values given in ASTM E261, with the largest difference being at the 1% level. The comparison results summarized in Table 5-3 combined with the C/M results listed in Table 5-1 and Table 5-2 demonstrate that using the SNLRML dosimetry cross-section library combined with the algorithms included in the SAND pre-processing module to produce a spectrum weighted broad group library, results in an appropriate cross-section representation for use in the FERRET least squares adjustment algorithm.

Westinghouse Non-Proprietary Class 3 5-4 WCAP-18124-NP-A July 2018 Revision 0 Table 5-1: U-235 Fission Spectrum Averaged Cross-Sections from ASTM E261 Typical Power Reactor Sensor Sets Reaction Spectrum Average Cross-Section [millibarns] C/M Calculation Measurement Cu-63 (n,) Co-60 0.521 (2.85%, 6.05%) 0.50 (11.0%) 1.042 (12.87%) Ti-46 (n,p) Sc-46 10.43 (2.46%, 5.4%) 11.6 (3.45%) 0.899 (6.86%) Fe-54 (n,p) Mn-54 80.18 (2.17%, 4.69%) 80.5 (2.86%) 0.996 (5.91%) Ni-58 (n,p) Co-58 105.69 (2.43%, 4.52%) 108.5 (5.0%) 0.974 (7.16%) U-238 (n,f) FP 306.23 (0.53%, 4.21%) 309.0 (2.6%) 0.991 (4.98%) Nb--93m 139.97 (3.06%, 4.14%) 146.2 (8.6%) 0.957 (10.02%) Np-237 (n,f) FP 1330.1 (9.33%, 4.31%) 1344.0 (4.0%) 0.990 (11.0%)

PCA Sensor Sets Reaction Spectrum Average Cross-Section [millibarns] C/M Calculation Measurement Al-27 (n,) Na-24 0.727 (1.40%, 6.95%) 0.706 (3.97%) 1.030 (8.13%) Ni-58 (n,p) Co-58 105.69 (2.43%, 4.52%) 108.5 (5.0%) 0.974 (7.16%) In-115 (n,n') In-115m 186.35 (2.17%, 4.17%) 190.3 (3.84%) 0.979 (6.07%) Rh-103 (n,n') Rh-103m 706.02 (3.1%, 4.14%) 733.0 (5.2%) 0.963 (7.33%) U-238 (n,f) FP 306.23 (0.53%, 4.21%) 309.0 (2.6%) 0.991 (4.98%) Np-237 (n,f) FP 1330.1 (9.33%, 4.31%) 1344.0 (4.0%) 0.990 (11.0%)

Notes: 1. The tabulated data were taken from Table 3 of ASTM E261.

2. For the calculated values, the cross-section and spectrum components of the uncertainty, respectively, are shown in parentheses.

3. The measurement uncertainty is also shown in parentheses.

4. The uncertainty in the C/M ratio represents a sum in quadrature of the measurement and calculational uncertainty.

Westinghouse Non-Proprietary Class 3 5-5 WCAP-18124-NP-A July 2018 Revision 0 Table 5-2: Cf-252 Fission Spectrum Averaged Cross-Sections from ASTM E261 Typical Power Reactor Sensor Sets Reaction Spectrum Average Cross-Section [millibarns] C/M Calculation Measurement Cu-63 (n,) Co-60 0.678 (2.83%, 1.38%) 0.689 (1.98%) 0.984 (3.72%) Ti-46 (n,p) Sc-46 12.56 (2.45%, 1.18%) 14.09 (1.76%) 0.891 (3.24%) Fe-54 (n,p) Mn-54 88.12 (2.14%, 0.79%) 86.92 (1.34%) 1.014 (2.65%) Ni-58 (n,p) Co-58 115.31 (2.40%, 0.73%) 117.6 (1.3%) 0.981 (2.83%) U-238 (n,f) FP 315.39 (0.53%, 0.4%) 325.0 (1.63%) 0.970 (1.76%) Nb--93m 142.65 (3.04%, 0.36%) 149.0 (7.0%) 0.957 (7.64%) Np-237 (n,f) FP 1335.0 (9.2%, 0.23%) 1361.0 (1.58%) 0.981 (9.43%)

PCA Sensor Sets Reaction Spectrum Average Cross-Section [millibarns] C/M Calculation Measurement Al-27 (n,) Na-24 1.04 (1.36%, 1.61%) 1.017 (1.47%) 1.019 (2.57%) Ni-58 (n,p) Co-58 115.31 (2.40%, 0.73%) 117.6 (1.3%) 0.981 (2.83%) In-115 (n,n') In-115m 189.8 (2.16%, 0.38%) 197.6 (1.3%) 0.961 (2.55%) Rh-103 (n,n') Rh-103m 714.45 (3.08%, 0.27%) 757.0 (4.0%) 0.944 (5.06%) U-238 (n,f) FP 315.39 (0.53%, 0.4%) 325.0 (1.63%) 0.970 (1.76%) Np-237 (n,f) FP 1335.0 (9.2%, 0.23%) 1361.0 (1.58%) 0.981 (9.43%)

Notes: 1. The tabulated data were taken from Table 3 of ASTM E261.

2. For the calculated values, the cross-section and spectrum components of the uncertainty, respectively, are shown in parentheses.

3. The measurement uncertainty is also shown in parentheses.

4. The uncertainty in the C/M ratio represents a sum in quadrature of the measurement and calculational uncertainty.

Westinghouse Non-Proprietary Class 3 5-6 WCAP-18124-NP-A July 2018 Revision 0 Table 5-3: Comparison of Calculated U-235 Fission Spectrum Averaged Cross-Sections Typical Power Reactor Sensor Sets Reaction Spectrum Average Cross-Section (millibarns)

Ratio FERRET/E261 ASTM E261 SAND/FERRET Cu-63 (n,) Co-60 0.521 0.523 1.003 Ti-46 (n,p) Sc-46 10.43 10.28 0.985 Fe-54 (n,p) Mn-54 80.18 80.28 1.001 Ni-58 (n,p) Co-58 105.69 105.76 1.001 U-238 (n,f) FP 306.23 305.76 0.998 Nb--93m 139.97 139.89 0.999 Np-237 (n,f) FP 1330.114 1329.917 1.000

PCA Sensor Sets Reaction Spectrum Average Cross-Section (millibarns)

Ratio FERRET/E261 ASTM E261 SAND/FERRET Al-27 (n,) Na-24 0.727 0.729 1.003 Ni-58 (n,p) Co-58 105.69 105.76 1.001 In-115 (n,n') In-115m 186.35 186.17 0.999 Rh-103 (n,n') Rh-103m 706.02 705.88 1.000 U-238 (n,f) FP 306.23 305.76 0.998 Np-237 (n,f) FP 1330.114 1329.917 1.000

Westinghouse Non-Proprietary Class 3 5-7 WCAP-18124-NP-A July 2018 Revision 0

5.3 FERRET

SENSITIVITY STUDIES The information discussed in this subsection provides an understanding of how the composition of the multiple foil sensor sets and the input values for the uncertainties in the calculated neutron spectrum and measured reaction rates affect the results of the least squares analysis in terms of both the magnitude and uncertainty of the adjusted spectrum. The threshold foils comprising typical LWR sensor sets respond to different portions of the neutron energy spectrum. These multiple foil measurements are a set of partial measurements of the fluence rate rather than a group of complete and independent determinations. Of particular interest for weighting and averaging threshold detector measurements is the spectrum coverage of the individual foils, which recognizes that such measurements do not form an equivalent observation set; therefore, they are not easily matched to the principle of maximum likelihood. This response is shown in Figure 5-1 and Figure 5-2 for the neutron spectra characteristic of an in-vessel surveillance capsule location and an ex-vessel dosimetry location. The graphical representations shown in Figure 5-1 and Figure 5-2 provide response profiles for the Cu-63 (nFe-54 (n,p), U-238 (n,f), Np-237 (n,f), and Nb-93 (n,n) threshold reactions, as well as for the neutron fluence rate (E > 1.0 MeV). The Ti-46 (n,p) and Ni-58 (n,p) reactions exhibit behavior similar to the Cu-63 (n,Fe-54 (n,p) reactions, respectively. From Figure 5-1 and Figure 5-2, it is evident that the response of the higher threshold reactions exhibits significantly different behavior than does the neutron fluence rate (E > 1.0 MeV); the fission monitor and niobium response shows a better match to the spectral behavior of the neutron fluence rate. This behavior suggests that in order to validate a calculation of the neutron fluence rate (E > 1.0 MeV), a significant spectral weighting of measured reaction rates should be included in the comparisons. The least squares approach allows for this spectral weighting to be included in a rigorous manner. The data from Figure 5-1 and Figure 5-2 also indicate that the makeup of the foil set could affect the final results of the dosimetry comparisons.

5.3.1 Composition

of the Multiple Foil Sensor Set To assess the effect of the makeup of the sensor set on the least squares adjustment final solution, parametric studies were performed for typical LWR dosimetry data sets. In each parametric study, the calculated neutron spectrum and uncertainty was held constant along with the uncertainties associated with the measured reaction rates. The base case consisted of an evaluation, including the threshold reactions, whereas the variations in the analysis were accomplished by deleting foil reactions individually and in combination. The 11 cases analyzed in the parametric study with fission monitors are summarized in Table 5-4. The results of the least squares evaluations for each of these 11 cases are shown in Table 5-5. The 7 cases analyzed in the parametric study with niobium are summarized in Table 5-6. The results of the least squares evaluations for each of these 7 cases are shown in Table 5-7. This data in Table 5-5 shows that in terms of the magnitude of the adjusted solution the results for all cases are within the uncertainty of the base case (Case 1). However, the uncertainty in the adjusted Westinghouse Non-Proprietary Class 3 5-8 WCAP-18124-NP-A July 2018 Revision 0 fluence rate increases as the content of the foil set is reduced with the highest uncertainties occurring when only a single foil is used in conjunction with the transport calculation. The data in Table 5-5 further shows that for a minimum uncertainty solution the foil set should consist of at least Fe, U, and Np foils (Case 4). The addition of Cu, Ti, and Ni do not enhance the capability of the foil set. This is because the very high threshold of the Cu-63 (n,and Ti-46 (n,p) reactions places their response well above the important energy range for the neutron fluence rate (E > 1.0 MeV) and the Ni-58 response is so similar to Fe-54 (n,p) that the reaction is redundant. Further reductions in the foil set from the Fe, U-238, Np-237 package results in an increased uncertainty in the adjusted fluence rate. As with the fission monitor sensitivity study, the data in Table 5-7 shows that the uncertainty in the adjusted fluence rate increases as the content of the foil set is reduced. Similar to the fission monitor sensitivity study, a minimum uncertainty solution the foil set should consist of at least Fe and Nb-93 foils (Case 4). Further reductions in the foil set results in an increased uncertainty in the adjusted fluence rate.

5.3.2 Input

Uncertainties A second sensitivity study was completed to evaluate the effect of the input uncertainties in the measured reaction rates and the calculated neutron fluence rate on the adjusted solution and the final uncertainties determined by the FERRET least squares procedure. In performing this sensitivity study, the uncertainty matrix in Table 5-8 was evaluated for the reaction rates and calculated spectra. In this sensitivity study, the "High" category would tend to overstate achievable uncertainties, the "Medium" category would represent a routinely achievable case, and the "Low" category would be equivalent to values achievable in the laboratory or benchmark environment. The results of the input uncertainty sensitivity study are summarized in Table 5-9. Considering the "Medium"-"Medium" case as the baseline, the magnitude of the adjusted fluence rate varies by less than 2% for all of the cases evaluated, indicating that the magnitude of the adjusted fluence rate is dependent primarily on the magnitude of the inputs, rather than on the input uncertainties. However, the associated uncertainty varies in a predictable trend from 4% for the "Low"-"Low" case to 11% for the "High"-"High". The indications from this sensitivity study are that the FERRET least squares algorithm is operating as anticipated.

Westinghouse Non-Proprietary Class 3 5-9 WCAP-18124-NP-A July 2018 Revision 0 Table 5-4: Dosimeter Foil Composition Sensitivity Study Case Descriptions (with Fission Monitors)

Case Foils Included in the FERRET Analysis Cu Ti Fe Ni U-238 Np-237 1 X X X X X X 2 X X X X X 3 X X X X 4 X X X 5 X X 6 X X 7 X X 8 X 9 X 10 X 11 X Table 5-5: Dosimeter Foil Composition Sensitivity Study Results (with Fission Monitors)

Case (E > 1.0 MeV) [n/cm 2-s] A/C % Diff From Case 1 Calculated Adjusted 1 4.53E+10 (15%) 4.73E+10 (6%) 1.04 - 2 4.53E+10 (15%) 4.73E+10 (6%) 1.04 0.0% 3 4.53E+10 (15%) 4.69E+10 (6%) 1.04 -0.8% 4 4.53E+10 (15%) 4.69E+10 (6%) 1.04 -0.8% 5 4.53E+10 (15%) 4.66E+10 (7%) 1.03 -1.4% 6 4.53E+10 (15%) 4.70E+10 (7%) 1.04 -0.6% 7 4.53E+10 (15%) 4.69E+10 (8%) 1.04 -0.7% 8 4.53E+10 (15%) 4.61E+10 (12%) 1.02 -2.6% 9 4.53E+10 (15%) 4.71E+10 (9%) 1.04 -0.4% 10 4.53E+10 (15%) 4.67E+10 (9%) 1.03 -1.3% 11 4.53E+10 (15%) 4.70E+10 (12%) 1.04 -0.6%

Note: Numbers in parentheses represent one standard deviation.

Westinghouse Non-Proprietary Class 3 5-10 WCAP-18124-NP-A July 2018 Revision 0 Table 5-6: Dosimeter Foil Composition Sensitivity Study Case Descriptions (with Niobium)

Case Foils Included in the FERRET Analysis Cu Ti Fe Ni Nb-93 1 X X X X X 2 X X X X 3 X X X 4 X X 5 X 6 X 7 X Table 5-7: Dosimeter Foil Composition Sensitivity Study Results (with Niobium)

Case (E > 1.0 MeV) [n/cm 2-s] A/C % Diff From Case 1 Calculated Adjusted 1 4.73E+08 (15%) 4.79E+08 (6%) 1.01 - 2 4.73E+08 (15%) 4.79E+08 (6%) 1.01 0.0% 3 4.73E+08 (15%) 4.88E+08 (6%) 1.03 1.9% 4 4.73E+08 (15%) 4.87E+08 (6%) 1.03 1.5% 5 4.73E+08 (15%) 4.92E+08 (8%) 1.04 2.6% 6 4.73E+08 (15%) 4.75E+08 (10%) 1.01 -0.9% 7 4.73E+08 (15%) 4.46E+08 (13%) 0.94 -7.4%

Note: Numbers in parentheses represent one standard deviation.

Westinghouse Non-Proprietary Class 3 5-11 WCAP-18124-NP-A July 2018 Revision 0 Table 5-8: Least Squares Adjustment Input Uncertainty Sensitivity Study Reaction Rate Uncertainties Reaction Type Uncertainty Category High Medium Low Non-Fission 10% 5% 2.5% Fission 20% 10% 5.0%

Neutron Spectrum Uncertainties Reaction Type Uncertainty Category High Medium Low Normalization 30% 20% 10% Spectrum Groups 1-53 30% 20% 10% Spectrum Groups 28-48 50% 25% 10% Spectrum Groups 49-53 100% 50% 25%

Table 5-9: Input Uncertainty Sensitivity Study Results - Adjusted (E > 1.0 MeV) and % Standard Deviation Spectrum Uncertainty Reaction Rate Uncertainty High Medium Low High 4.72E+10 (11%) 4.67E+10 (7%) 4.66E+10 (5%) Medium 4.76E+10 (9%) 4.70E+10 (6%) 4.67E+10 (5%) Low 4.79E+10 (6%) 4.76E+10 (5%) 4.72E+10 (4%)

Westinghouse Non-Proprietary Class 3 5-12 WCAP-18124-NP-A July 2018 Revision 0 Figure 5-1: Cumulative Sensor Response as a Function of Neutron Energy at In-Vessel Surveillance Capsule Locations

Westinghouse Non-Proprietary Class 3 5-13 WCAP-18124-NP-A July 2018 Revision 0 Figure 5-2: Cumulative Sensor Response as a Function of Neutron Energy at Ex-Vessel Dosimetry Locations

Westinghouse Non-Proprietary Class 3 5-14 WCAP-18124-NP-A July 2018 Revision 0

5.4 OPERATING

POWER REACTOR COMPARISONS In addition to the sensitivity studies described above, the radiation transport methodology in RAPTOR-M3G and the least squares dosimetry evaluations in FERRET have been extensively compared with data from operating power reactors. These comparisons are intended to provide support for the validation of the transport calculation itself as well as validation for the uncertainties assigned to the results of those calculations. There are 69 in-vessel surveillance capsules with 295 threshold foil measurements from 18 nuclear power plants that have been analyzed with RAPTOR-M3G and FERRET. In addition to the in-vessel surveillance capsules, 87 ex-vessel neutron dosimetry (EVND) capsules with 454 threshold foil measurements from locations in the reactor cavity opposite the core midplane have been analyzed with RAPTOR-M3G and FERRET. The comparisons between the plant-specific calculations and the database measurements are provided on two levels. In the first instance, the average M/C reaction rate ratio over all the fast neutron sensors from each reactor is listed. This tabulation provides a direct comparison, on an absolute basis, of measurement and calculation. The results of this comparison are listed in Table 5-10. For surveillance capsules, these comparisons show an average M/C ratio of 1.03 with a standard deviation of 5% at the level. For ex-vessel dosimeters irradiated opposite the core midplane, these comparisons show an average M/C ratio of 0.92 with a standard deviation of 6% at the level. The second level of comparison is based on the least squares adjustment procedure, which provides a weighting of the individual sensor measurements based on spectral coverage and allows a comparison of the neutron fluence rate (E > 1.0 MeV) before and after adjustment. The neutron fluence rate and fluence (E > 1.0 MeV) is the primary parameter of interest in the overall pressure vessel exposure evaluations. The results are presented in Table 5-11 for surveillance capsules and Table 5-12 for ex-vessel dosimetry. The overall database average best estimate-to-calculation (BE/C) ratio for surveillance capsules is 0.98 with an associated standard deviation of 6% for fast neutron fluence rate, and 0.99 with an associated standard deviation of 5% for iron atom displacement rate (DPA/s). For ex-vessel dosimetry, the average BE/C ratio is 0.92 with an associated standard deviation of 6% for fast neutron fluence rate, and 0.93 with an associated standard deviation of 7% for DPA/s. These results show that the BE/C and M/C ratios are essentially unbiased and well within the +/- 20% acceptance criteria for the in-vessel capsules and +/- 30% for the cavity capsules given in Regulatory Guide 1.190.

Westinghouse Non-Proprietary Class 3 5-15 WCAP-18124-NP-A July 2018 Revision 0 Table 5-10: In-Vessel and Ex-Vessel Capsules Threshold Reactions M/C Reaction Rate Ratios Plant Number In-Vessel M/C EVND Midplane M/C Domestic Plant #1 1.05 0.96 Domestic Plant #2 0.99 0.97 International Plant #1 1.13 1.03 International Plant #2 1.06 1.00 International Plant #3 N/A 0.97 International Plant #4 0.99 0.89 International Plant #5 1.09 0.88 International Plant #6 0.95 0.87 International Plant #7 0.95 0.86 Domestic Plant #3 1.02 0.89 Domestic Plant #4 1.01 0.89 Domestic Plant #5 1.00 0.93 International Plant #8 0.96 0.87 International Plant #9 1.08 0.83 Domestic Plant #6 1.01 0.90 Domestic Plant #7 1.07 N/A Domestic Plant #8 1.11 N/A Domestic Plant #9 1.07 N/A Average 1.03 0.92 Std. Dev. % 5% 6% Total Number of Capsules 69 87 Total Number of Threshold Foils 295 454

Westinghouse Non-Proprietary Class 3 5-16 WCAP-18124-NP-A July 2018 Revision 0 Table 5-11: In-Vessel Surveillance Capsules BE/C Reaction Rate Ratios Plant Number BE/C Fluence (E>1.0 MeV) BE/C DPA Number of Threshold Foils Number of Capsules International Plant #1 1.04 1.05 8 3 International Plant #2 0.99 0.99 8 3 International Plant #3 N/A N/A N/A N/A Domestic Plant #1 1.03 1.04 20 4 International Plant #4 0.92 0.90 14 4 Domestic Plant #2 0.96 0.97 20 4 International Plant #5 1.05 1.06 19 4 International Plant #6 0.90 0.93 13 3 International Plant #7 0.89 0.92 12 3 Domestic Plant #3 0.97 0.99 30 6 Domestic Plant #4 0.96 0.96 29 6 Domestic Plant #5 0.93 0.95 25 5 International Plant #8 0.94 0.95 14 4 International Plant #9 1.04 1.04 16 4 Domestic Plant #6 0.98 0.99 19 5 Domestic Plant #7 1.02 1.03 13 3 Domestic Plant #8 1.08 1.08 11 3 Domestic Plant #9 1.02 1.02 24 5 Average 0.98 0.99 295 (Total) 69 (Total) Std. Dev. % 6% 5%

Westinghouse Non-Proprietary Class 3 5-17 WCAP-18124-NP-A July 2018 Revision 0 Table 5-12: EVND Core Midplane BE/C Reaction Rate Ratios Plant Number (# of EVND Sets) BE/C Fluence (E>1.0 MeV) BE/C DPA Number of Threshold Foils Number of Capsules Domestic Plant #1 (1) 0.93 0.90 15 4 Domestic Plant #2 (1) 0.92 0.88 16 4 International Plant #1 (2) 1.03 1.03 40 8 International Plant #2 (2) 1.00 1.01 40 8 International Plant #3 (1) 0.99 1.02 28 4 International Plant #4 (1) 0.89 0.88 20 4 International Plant #5 (1) 0.92 0.97 15 3 International Plant #6 (2) 0.89 0.91 48 8 International Plant #7 (2) 0.85 0.85 32 8 Domestic Plant #3 (2) 0.89 0.90 48 8 Domestic Plant #4 (2) 0.89 0.92 48 8 Domestic Plant #5 (1) 0.96 0.98 24 4 International Plant #8 (2) 0.86 0.88 40 8 International Plant #9 (1) 0.84 0.84 20 4 Domestic Plant #6 (1) 0.93 0.94 20 4 Average 0.92 0.93 454 (Total) 87 (Total) Std. Dev. % 6% 7%

Westinghouse Non-Proprietary Class 3 6-1 WCAP-18124-NP-A July 2018 Revision 0 6

SUMMARY

, CONCLUSIONS, AND CONDITIONS In this report, the use of the RAPTOR-M3G code for neutron fluence determination and the FERRET code for the least squares evaluation of LWR surveillance dosimetry have been described and benchmarked. The fluence determination methodology, based on the RAPTOR-M3G code, has been shown to follow the guidance of Regulatory Guide 1.190. The least squares procedure has been validated by benchmark comparisons in the NIST U-235 and Cf-252 standard fission fields and demonstrating satisfactory sensitivity study results. The fluence determination methodology is used to derive calculated values of neutron exposure at reactor vessel material locations of interest. The practices used to define the model geometry, the nuclear data, the core neutron source, and the radiation transport solution parameters have been described. The theoretical foundation of the RAPTOR-M3G code and its solution process is detailed. The results of the methodology qualification process, based on extensive comparisons to experimental measurements and a detailed analytic sensitivity study, are provided. The least squares procedure combines calculations of the neutron spectrum with available measurements to determine the best estimate spectrum with reduced uncertainties at the measurement locations. The importance of the key input parameters to the Westinghouse least squares procedure (the neutron spectrum, the measured reaction rates, and the dosimetry cross-sections) and their associated uncertainties have been discussed and the values used have been described and justified. The sensitivity of the adjustment procedure to the makeup of the foil set and the input uncertainties in the calculated spectrum and the measured reaction rates has been provided. The conclusions from these studies are as follows:

1. The fluence determination process operates as intended and meets the 20% fluence uncertainty criterion (at the level) discussed in Regulatory Guide 1.190 for RT NDT and RT PTS determination.

2. The FERRET code operates as intended as a least squares adjustment code for reactor dosimetry analyses.

3. The input parameters (calculated neutron spectrum, measured reaction rates, and dosimetry reaction cross-sections) and their associated uncertainties are appropriate for use in LWR dosimetry evaluations.

4. The adjusted neutron fluence rate (E > 1.0 MeV) from the FERRET evaluations can be used to develop a database for use in validating plant-specific neutron transport calculations for LWR pressure vessels. This adjustment process provides a rigorous spectrum weighting of individual reaction rate M/C comparisons. The comparison database developed from the least squares evaluation of the dosimetry sets can be used along with the guidance in Regulatory Guide 1.190 to validate neutron transport calculations and to determine any calculational biases that may be present.

Westinghouse Non-Proprietary Class 3 6-2 WCAP-18124-NP-A July 2018 Revision 0 The following conditions must be met in order to apply the methodology described in this report: The neutron fluence calculations must be adequately benchmarked. Calculations of neutron fluence must be benchmarked against plant-specific measurements or measurements from a similar reactor if plant-specific measurements are not available.

Any adjustments to calculated neutron fluence values using the least squares technique must be justified. The adjustments must be consistent with the uncertainties assigned to the calculated neutron spectra, the measured reaction rates, and the dosimetry cross-section data.

Westinghouse Non-Proprietary Class 3 7-1 WCAP-18124-NP-A July 2018 Revision 0 7 REFERENCES

1. Code of Federal Regulations Title 10 Part 50, "Domestic Licensing of Production and Utilization Facilities," Appendix G, "Fracture Toughness Requirements" and Appendix H, "Reactor Vessel Material Surveillance Requirements."

2. Code of Federal Regulations Title 10 Part 50.61, "Fracture Toughness Requirements for Protection Against Pressurized Thermal Shock Events."

3. Regulatory Guide 1.190, "Calculational and Dosimetry Methods for Determining Pressure Vessel Neutron Fluence," U.S. Nuclear Regulatory Commission, Office of Nuclear Regulatory Research, March 2001.

4. Westinghouse Report WCAP-16083-NP-A, Revision 0, "Benchmark Testing of the FERRET Code for Least Squares Evaluation of Light Water Reactor Dosimetry," May 2006. (Available as ADAMS Accession Number ML061600256.)

5. Westinghouse Report WCAP-14040-A, Revision 4, "Methodology Used to Develop Cold Overpressure Mitigating System Setpoints and RCS Heatup and Cooldown Limit Curves," May 2004. (Available as ADAMS Accession Number ML050120209.)

6. RSICC Computer Code Collection CCC-650, "DOORS 3.2a, One- Two- and Three Dimensional Discrete Ordinates Neutron/Photon Transport Code System," Radiation Safety Information Computational Center, Oak Ridge National Laboratory (ORNL), May 2007.

7. RSICC Data Library Collection DLC-185, "BUGLE-96, Coupled 47 Neutron, 20 Gamma-Ray Group Cross Section Library Derived from ENDF/B-VI for LWR Shielding and Pressure Vessel Dosimetry Applications," Radiation Shielding Information Computational Center, Oak Ridge National Laboratory (ORNL), July 1999.

8. RSICC Code Package PSR-145, "FERRET Least Squares Solution to Nuclear Data and Reactor Physics Problems," Radiation Shielding Information Computational Center, Oak Ridge National Laboratory (ORNL), March 1984.

9. F. Schmittroth, "FERRET Data Analysis Code," HEDL-TME-79-40, Hanford Engineering Development Laboratory, September 1979.

10. Gulf General Atomic Report GA-8747, "TWOTRAN, a FORTAN Program for Two Dimensional Transport," July 1968.

11. WANL-PR-(LL)-034, "Nuclear Rocket Shielding Methods, Modification, Updating and Input Data Preparation. Vol. 5 - Two-Dimensional Discrete Ordinates Transport Technique," August 1970.

Westinghouse Non-Proprietary Class 3 7-2 WCAP-18124-NP-A July 2018 Revision 0

12. RSICC Data Library Collection DLC-245, "VITAMIN-B7/BUGLE-B7, Broad-Group and Fine-Group and Coupled Neutron/Gamma Cross-Section Libraries Derived from ENDF/B-VII.0 Nuclear Data," Radiation Safety Information Computational Center, Oak Ridge National Laboratory (ORNL), October 2011.

13. Westinghouse Report WCAP-17993-NP, Rev. 0-B, "Justification for the Use of RAPTOR-M3G for the Catawba Unit 1 Measurement Uncertainty Recapture (MUR) Power Uprate Fluence Evaluations," April 2015. (Available as ADAMS Accession Number ML15117A012.)

14. Lewis, E.E., Miller, W.F. Jr, "Computational Methods of Neutron Transport," La Grange Park: American Nuclear Society, 1993.

15. Petrovic B. and Haghighat A., "Analysis of Inherent Oscillations in Multidimensional S N Solutions of the Neutron Transport Equation," Nuclear Science and Engineering, Vol. 124, pp. 31-62, 1996.

16. U.S. Department of Energy Report CASL-U-2015-0080-000, Revision 0, "Exnihilo Transport Methods Manuals," Evans et al., Oak Ridge National Laboratory, 2015.

17. ASTM Designation E944, 2013, "Standard Guide for Application of Neutron Spectrum Adjustment Methods in Reactor Surveillance," ASTM International, West Conshohocken, PA, 2013, DOI: 10.1520/E0944-13, www.astm.org.

18. RSICC Code Package PSR-113, "STAY'SL Least Squares Dosimetry Unfolding Code System," Radiation Shielding Information Computational Center, Oak Ridge National Laboratory (ORNL),

December 1991.

19. RSICC Code Package PSR-233, "LSL-M2 Least Squares Logarithmic Adjustment of Neutron Spectra," Radiation Shielding Information Computational Center, Oak Ridge National Laboratory (ORNL), February 1991.

20. RSICC Code Package PSR-277, "LEPRICON PWR Pressure Vessel Surveillance Dosimetry Analysis System," Radiation Shielding Information Computational Center, Oak Ridge National Laboratory (ORNL), June 1995.

21. R. L. Simons, et. al, "Re-Evaluation of the Dosimetry for Reactor Pressure Vessel Surveillance Capsules," in NUREG/CP-0029, "Proceedings of the Fourth ASTM-EURATOM Symposium on Reactor Dosimetry," F. B. K. Kam, Editor, July 1982.

22. W. N. McElroy, et. al, "LWR PV Surveillance Dosimetry Improvement Program: PCA Experiments and Blind Test," NUREG/CR-1861, July 1981.

23. Regulatory Guide 1.99, Revision 2, "Radiation Embrittlement of Reactor Vessel Materials," U. S. Nuclear Regulatory Commission, Office of Nuclear Regulatory Research, May 1988.

Westinghouse Non-Proprietary Class 3 7-3 WCAP-18124-NP-A July 2018 Revision 0

24. G. L. Guthrie, "Uncertainty Considerations in Development and Application of Charpy Trend Curve Formulas," in REACTOR DOSIMETRY Dosimetry Methods for Fuels, Cladding, and Structural Materials, Proceedings of the Fifth ASTM-Euratom Symposium on Reactor Dosimetry, GKSS Research Centre, Geesthact, F. R. G., J. P Genthon and H Rottger, Editors, D. Reidel Publishing Company, 1985.

25. G. L. Guthrie, "Charpy Trend Curve Development Based on PWR Surveillance Data," in NUREG/CP-0048 Proceedings of the U. S. Nuclear Regulatory Commission Eleventh Water Reactor Safety Research Information Meeting, Volume 4 - Materials Engineering Research," U. S. Nuclear Regulatory Commission, Office of Nuclear Regulatory Research, January 1984.

26. G. L. Guthrie, "Charpy Trend Curves Based on 177 PWR Data Points," NUREG/CR-3391, Volume 2, LWR-PV-SDIP Quarterly Progress Report, April 1983.

27. RSICC Data Library Collection DLC-178, "SNLRML Recommended Dosimetry Cross Section Compendium," Radiation Shielding Information Computational Center, Oak Ridge National Laboratory, July 1994.

28. N. P. Kocherov, et. al, "International Reactor Dosimetry File (IRDF-90)," International Atomic Energy Agency, Nuclear Data Section, IAEA-NDS-141, Rev. 0, August 1990.

29. BNL Report BNL-NUREG-52395, "PWR and BWR Pressure Vessel Fluence Calculation Benchmark Problems and Solutions," (NUREG/CR-6115), September 2001.

30. ORNL Report ORNL/TM-13204, "Pool Critical Assembly Pressure Vessel Facility Benchmark," (NUREG/CR-6454), July 1997.

31. Nuclear Energy Agency (Organization for Economic Co-Operation and Development), "Prediction of Neutron Embrittlement in the Reactor Pressure Vessel: VENUS-1 and VENUS-3 Benchmarks," 2000.

32. ASTM Designation E844, 2009 (2014), "Standard Guide for Sensor Set Design and Irradiation for Reactor Surveillance," ASTM International, West Conshohocken, PA, 2014, DOI: 10.1520/E0844-09R14E01, www.astm.org. 33. ORNL Report ORNL/TM-13204, "H. B. Robinson-2 Pressure Vessel Benchmark," (NUREG/CR-6453), February 1998.

34. Westinghouse Report WCAP-13348, "Consumers Power Company Palisades Nuclear Plant Reactor Vessel Fluence Analysis," May 1992.

35. Westinghouse Report WCAP-13362, "Westinghouse Fast Neutron Exposure Methodology for Pressure Vessel Fluence Determination and Dosimetry Evaluation," May 1992.

Westinghouse Non-Proprietary Class 3 7-4 WCAP-18124-NP-A July 2018 Revision 0

36. R. E. Maerker, "Application of LEPRICON Methodology to LWR Pressure Vessel Surveillance Dosimetry," Reactor Dosimetry, Proc. 6th ASTM-Euratom Symposium, Jackson Hole, Wyoming, May 31 - June 5, 1987, American Society for Testing and Materials (1989).

37. ASTM Designation E1018, 2013, "Standard Guide for Application of ASTM Evaluated Cross Section Data File, Matrix E706 (IIB)," ASTM International, West Conshohocken, PA, 2013, DOI: 10.1520/E1018-09R13, www.astm.org. 38. ASTM Designation E261, 2015, "Standard Practice for Determining Neutron Fluence, Fluence Rate, and Spectra by Radioactivation Techniques," ASTM International, West Conshohocken, PA, 2015, DOI: 10.1520/E0261-15, www.astm.org.

v t e Letter Sequence Other
CAC:MF9141, (Approved, Closed)
Initiation Request, Request Acceptance... Administration Questions Answers Results Approval, Approval, Approval Other: ML18204A010
MONTHYEAR2018-06-15 [Table View]

ML18204A010

Text

SUBJECT:

Dear Mr. Gresham:

SUBJECT:

Dear Mr. Gresham:

Enclosure:

1.1 BACKGROUND

1.2 CURRENT

SUMMARY

2.1 BACKGROUND

2.2 GEOMETRIC

2.3 CROSS

2.5 DISCRETE

2.5.2 Weighted

2.5.3 Source

2.5.4 Domain

2.5.5 Solution

3.1 BACKGROUND

3.2 APPLICATION

3.4 MEASUREMENT

3.5 DOSIMETRY

4.1 OVERVIEW

4.2.3 Summary

4.3 OPERATING

4.3.3 Summary

4.4 ANALYTIC

4.4.2 Geometric

4.4.3 Summary

4.5 ESTIMATE

5.1 OVERVIEW

5.3 FERRET

5.3.1 Composition

5.3.2 Input

5.4 OPERATING

SUMMARY

1.1 BACKGROUND

1.2 CURRENT

SUMMARY

2.1 BACKGROUND

2.2 GEOMETRIC

2.3 CROSS

2.5 DISCRETE

2.5.3 Source

2.5.4 Domain

2.5.5 Solution

3.1 BACKGROUND

3.2 APPLICATION

3.3 INPUT

3.4 MEASUREMENT

3.5 DOSIMETRY

4.1 OVERVIEW

4.2 SIMULATOR

4.2.3 Summary

4.3 OPERATING

4.3.3 Summary

4.4 ANALYTIC

4.4.2 Geometric

4.4.3 Summary

4.5 ESTIMATE

5.1 OVERVIEW

5.3 FERRET

5.3.1 Composition

5.3.2 Input

5.4 OPERATING

SUMMARY

Navigation menu

Search