ML100910075

Response to Request for Additional Information - Revision to Technical Specification 4.3.1.1.a Concerning k-infinity

ML100910075
Person / Time
Site:	Peach Bottom
Issue date:	03/26/2010
From:	David Helker Exelon Generation Co, Exelon Nuclear
To:	Document Control Desk, Office of Nuclear Reactor Regulation
References
TAC MD9154, TAC MD9155
Download: ML100910075 (142)

Text

Exekrn Exelon Nuclear 200 Exelon Way Kennett Square, PA 19348 www.exeloncorp.coM Nuclear PROPRIETARY INFORMATION - WITHHOLD UNDER 10 CFR 2.390 10 CFR 50.90 March 26, 2010 U.S. Nuclear Regulatory Commission ATTN: Document Control Desk Washington, DC 20555-0001 Peach Bottom Atomic Power Station, Units 2 and 3 Renewed Facility Operating License Nos. DPR-44 and DPR-56 NRC Docket Nos. 50-277 and 50-278

Subject:

Response to Request for Additional Information - Revision to Technical Specification 4.3.1.1.a Concerning k-infinity

References:

1)

Letter from P. B. Cowan (Exelon Generation Company, LLC) to U.S.

Nuclear Regulatory Commission, "License Amendment Request -

Revision to Technical Specification 4.3.1.1.a Concerning k-infinity," dated June 25, 2008

2)

Letter from J. D. Hughey (U.S. Nuclear Regulatory Commission) to P. B.

Cowan (Exelon Generation Company, LLC), "Peach Bottom Atomic Power Station, Unit Nos. 2 and 3: Request for Withholding Information From Public Disclosure (TAC NOS. MD9154 and MD9155)" (concerning the Northeast Technology Corporation submittal), dated October 10, 2008

3)

Letter from J. D. Hughey (U.S. Nuclear Regulatory Commission) to P. B.

Cowan (Exelon Generation Company, LLC), "Peach Bottom Atomic Power Station, Unit Nos. 2 and 3: Request for Withholding Information From Public Disclosure (TAC NOS. MD9154 and MD9155)" (concerning the Global Nuclear Fuel submittal), dated October 10, 2008

4)

Letter from P. B. Cowan (Exelon Generation Company, LLC) to U.S.

Nuclear Regulatory Commission, "Response to Request for Additional Information - Revision to Technical Specification 4.3.1.1.a Concerning k-infinity," dated November 6, 2008 Attachments 1, 3, and 7 transmitted herewith contain Proprietary Information.

When separated from these attachments, this document is decontrolled.

Response to Request for Additional Information - Revision to Technical Specification 4.3.1.1.a Concerning k-infinity March 26, 2010 Page 2

5)

Letter from J. D. Hughey (U.S. Nuclear Regulatory Commission) to P. B.

Cowan (Exelon Generation Company, LLC), "Peach Bottom Atomic Power Station, Unit Nos. 2 and 3: Request for Withholding Information From Public Disclosure (TAC NOS. MD9154 and MD9155)," dated December 29, 2008

6)

Letter from J. D. Hughey (U.S. Nuclear Regulatory Commission) to P. B.

Cowan (Exelon Generation Company, LLC), "Peach Bottom Atomic Power Station, Unit Nos. 2 and 3: Request for Proprietary Review of Request for Additional Information Regarding License Amendment Request to Revise Technical Specification 4.3.1.1.a Concerning k-infinity (TAC NOS. MD9154 and MD9155)," dated January 21, 2009

7)

Letter from P. B. Cowan (Exelon Generation Company, LLC) to U.S.

Nuclear Regulatory Commission, "Response to Request for Additional Information - Revision to Technical Specification 4.3.1.1.a Concerning k-infinity," dated March 9, 2009

8)

Letter from J. D. Hughey (U.S. Nuclear Regulatory Commission) to P. B.

Cowan (Exelon Generation Company, LLC), "Peach Bottom Atomic Power Station, Units 2 and 3: Request for Withholding Information From Public Disclosure (TAC NOS. MD9154 and MD9155)" (concerning NET-264-02, Rev. 1), dated May 13, 2009

9)

Letter from J. D. Hughey (U.S. Nuclear Regulatory Commission) to P. B.

Cowan (Exelon Generation Company, LLC), "Peach Bottom Atomic Power Station, Unit Nos. 2 and 3: Request for Withholding Information From Public Disclosure (TAC NOS. MD9154 and MD9155)" (concerning NET-264-02, Rev. 2, NET-264-03, Rev. 0, and Response to RAI), dated May 13, 2009

10) Letter from P. B. Cowan (Exelon Generation Company, LLC) to U.S.

Nuclear Regulatory Commission, "Response to Request for Additional Information - Revision to Technical Specification 4.3.1.1.a Concerning k-infinity," dated June 12, 2009

11)

Letter from J. D. Hughey (U.S. Nuclear Regulatory Commission) to P. B.

Cowan (Exelon Generation Company, LLC), "Peach Bottom Atomic Power Station, Unit Nos. 2 and 3: Request for Withholding Information From Public Disclosure (TAC NOS. MD9154 and MD9155)" (concerning NET-264-02 P, Rev. 1), dated September 16, 2009

12)

Letter from J. D. Hughey (U.S. Nuclear Regulatory Commission) to P. B.

Cowan (Exelon Generation Company, LLC), "Peach Bottom Atomic Power Station, Unit Nos. 2 and 3: Request for Withholding Information From Public Disclosure (TAC NOS. MD9154 and MD9155)," (concerning NET-264-02, Rev. 3, NET-264-03, Rev. 1, and Response to RAI, Rev. 1), dated September 16, 2009

Response to Request for Additional Information - Revision to Technical Specification 4.3.1.1.a Concerning k-infinity March 26, 2010 Page 3

13) Letter from P. B. Cowan (Exelon Generation Company, LLC) to U.S.

Nuclear Regulatory Commission, "Revised Criticality Analysis - Revision to Technical Specification 4.3.1.1.a Concerning k-infinity," dated December 18, 2009

14)

Letter from J. D. Hughey (U.S. Nuclear Regulatory Commission) to C. G.

Pardee (Exelon Generation Company, LLC), "Peach Bottom Atomic Power Station, Units 2 and 3: Request for Additional Information Regarding License Amendment Request to Revise Technical Specification 4.3.1.1.a Concerning k-infinity (TAC NOS. MD9154 and MD9155)," dated March 4, 2010 In the Reference 1 letter, Exelon Generation Company, LLC (Exelon) requested an amendment to Appendix A, Technical Specifications, of the Renewed Facility Operating Licenses DPR-44 and DPR-56. The proposed change would revise the maximum k-infinity value contained in Technical Specification 4.3.1.1.a for the storage of fuel assemblies in the spent fuel storage racks. Additional correspondence concerning this issue is identified in References 2 through 13.

As discussed in public meetings between Exelon and U.S. Nuclear Regulatory Commission Staff on January 7, 2010 and March 18, 2010, additional information was requested as described in the Reference 14 letter. Attached is our response to this request.

Attachments 1 and 7 contain information proprietary to NETCO. NETCO requests that the information contained in Attachments 1 and 7 be withheld from public disclosure in accordance with 10 CFR 2.390(a)(4). An affidavit supporting this request is also contained in Attachment 1.

Attachments 2 and 8 contain a non-proprietary version of Attachments 1 and 7, respectively. contains information proprietary to Global Nuclear Fuel. Global Nuclear Fuel requests that the information contained in Attachment 3 be withheld from public disclosure in accordance with 10 CFR 2.390(a)(4). An affidavit supporting this request is also contained in. Attachment 4 contains a non-proprietary version of Attachment 3.

If any additional information is needed, please contact Tom Loomis at (610) 765-5510.

I declare under penalty of perjury that the foregoing is true and correct. Executed on the 26k" day of March 2010.

Respectfully, David P. Helker Manager, Licensing & Regulatory Affairs Exelon Generation Company, LLC

Response to Request for Additional Information - Revision to Technical Specification 4.3.1.1.a Concerning k-infinity March 26, 2010 Page 4 Attachments:

1) Response to Request for Additional Information - License Amendment Request to Revise Technical Specification 4.3.1.1.a Concerning k-infinity (NETCO Proprietary Version and Affidavit)

2) Response to Request for Additional Information - License Amendment Request to Revise Technical Specification 4.3.1.1.a Concerning k-infinity (NETCO Non-Proprietary Version)

3) Response to Request for Additional Information (GNF Proprietary Version and Affidavit)

4) Response to Request for Additional Information (GNF Non-Proprietary Version)

5) RAI 50 - Panel Degradation Maps

6) RAI 58 - Naval Reactor Physics Handbook Material

7) Panel Degradation Results (NETCO Proprietary Version)

8) Panel Degradation Results (NETCO Non-Proprietary Version)

9)

RAI 53.3 - ORNL-TM-1658 cc:

USNRC Region I, Regional Administrator USNRC Senior Resident Inspector, PBAPS USNRC Project Manager, PBAPS R. R. Janati, Commonwealth of Pennsylvania S. T. Gray, State of Maryland

NETCO 108 NWt *;,SEe*,

UM** BG'4 78' AFFIDAVIT 1, Kenneth 0. Lindquist, Director of NETCO Products and Services Division of Scientech, a business unit of Curtiss-Wright Flow Control Service Corporation, do hereby affirm and state:

1. I am a Director of NETCO Products and Services Division of Scientech, a business unit of Curtiss-Wright Flow Control Service Corporation, authorized to execute this affidavit on its behalf. I am further authorized to review information submitted to the Nuclear Regulatory Commission (NRC) and apply to the NRC for the withholding of information from disclosure.

2. The information sought to be withheld is contained in Attachment 1 (Response to Request for Additional Information - License Amendment Request to Revise Technical Specification 4.3.1. 1.a Concerning k-infinity) and Attachment 7 (Panel Degradation Results). The proprietary information is identified by the use of

brackets,

3. In making this application for withholding of proprietary information of which it is the owner, NETCO relies on provisions of NRC regulation 10 CFR 2.390(a)(4).

The information for which exemption from disclosure is sought is confidential commercial information.

4. The proprietary information provided by NETCO should be held in confidence by the NRC pursuant to the policy reflected in 10 CFR 2.390(a)(4) because:

a) The information sought to be withheld in the NETCO Attachments (see paragraph 2 above) is and has been held in confidence by NETCO.

b) This information is of a type that is customarily held in confidence by NETCO, and there is a rational basis for doing so because the information contains methodology, data and supporting information developed by NETCO that could be used by a competitor as a competitive advantage.

c) This information is being transmitted to the NRC in confidence.

Page 1 of 2 I

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NTy d) This information sought to be withheld, to the best of my knowledge and belief, is not available in public sources and no public disclosure has been made.

e) The information sought to be withheld contains NETCO developed methodology, data and supporting information that could be used by a competitor as a competitive advantage, and would result in substantial harm to the competitive position of NETCO. This information would reduce the expenditure of resources and improve his competitive position in the implementation of a similar product. Third party agreements have been established to ensure maintenance of the information in confidence. The development of the methodology, data and supporting information was achieved at a significant cost to NETCO. Public disclosure of this information sought to be withheld is likely to cause substantial harm to NETCO's competitive position and reduce the availability of profit-making opportunities.

5. Initial approval of proprietary treatment of a document is made by the Director of NETCO Products and Services Division of Scientech, the person most likely to be familiar with the value and sensitivity of the information and its relation to industry knowledge. Access to such information within NETCO is on a "need to know" basis.

6. Accordingly, NETCO requests that the designated document be withheld from public disclosure pursuant to 10 CFR 2.390(a)(4).

I declare under penalty of perjury that the foregoing affidavit and statements therein are true and correct to the best of my knowledge, information and belief.

Kenneth 0. Lindquist Director, NETCO Products and Services Division of Scientech, a business unit of Curtiss-Wright Flow Control Service Corporation Date:

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ATiACHMENT 2 Response to Request for Additional Information -

License Amendment Request to Revise Technical Specification 4.3.1.1.a Concerning k-infinity (NETCO Non-Proprietary Version)

Non-Proprietary Information in Accordance with 10 CFR 2.390 Response to Request for Additional Information -

License Amendment Request to Revise TS 4.3.1.1.a Page 1 Steam Generator Tube Integrity and Chemical Engineering Branch RAI Questions:

In the December 18, 2009, supplement, the licensee is proposing to lower the k-infinity value from 1.362 to 1.270. As part of the analysis to support this change, the licensee performed an analysis to predict the degradation of Boraflex in the SFP. In order for the NRC staff to have reasonable assurance that this analysis will conservatively predict the degradation of Boraflex, the NRC staff requires additional information.

Question:

RAI 26 - Discussion NET-264-02, Revision 4, describes an algorithm to predict Boraflex degradation. The NRC staff has the following questions regarding the algorithm:

RAI 26.1: Please discuss if the NET-264-03, Revision 1, Appendix A, algorithm or a similar algorithm, was used in the current, NET-264-02, Revision 4, analysis.

Response

The two algorithms are identical; however, the inputs differ with respect to the starting points for uniform thickness. The starting point for local dissolution was set to [ ]% for NET-264-02, Rev. 4 as opposed to [ ]% in NET-264-03, Rev. 1. The local dissolution patterns in Tables 3 and 6 of NET-264-03, Rev. 1 were scaled to reflect losses that would be seen in a panel with [ ]% uniform panel thinning.

Thus, the panel thickness in local areas degraded by uniform and local thinning is less than [ ]%. The uniform thinning values for each panel are read directly from a text input file from RACKLIFE and were adjusted to be [ ]% uniform thinning for all [ ] panels in the [

] Keno arrays. The details of the adjustment are described in RA126.3.

Question:

RAI 26.2: Discuss whether NET-264-03, Revision 1, Appendix A, is still applicable to the Licensing Amendment Request.

Response

Yes, with the modification for [ ]% uniform thinning described above in RAI 26.1 and scaling of the dissolution patterns in Tables 3 and 6 by the ratio of 2.25 (as described below in RAI 26.3).

Question:

RAI 26.3: Describe the methodology, conservatisms, and assumptions of the current, NET-264-02, Revision 4, algorithm to predict Boraflex degradation.

B

Non-Proprietary Information in Accordance with 10 CFR 2.390 Response to Request for Additional Information -

License Amendment Request to Revise TS 4.3.1.1.a Page 2

Non-Proprietary Information in Accordance with 10 CFR 2.390 Response to Request for Additional Information -

License Amendment Request to Revise TS 4.3.1.1.a Page 3

Non-Proprietary Information in Accordance with 10 CFR 2.390 Response to Request for Additional Information -

License Amendment Request to Revise TS 4.3.1.1.a Page 4

Non-Proprietary Information in Accordance with 10 CFR 2.390 Response to Request for Additional Information -

License Amendment Request to Revise TS 4.3.1.1.a Page 5 Question:

RAI 26.4: Describe the limitations, such as upper limits on % Boraflex loss, of the current, NET-264-02, Revision 4, algorithm.

Response

The upper limit on Boraflex loss for the algorithm is [ ]% dissolution as uniform thinning for the Peach Bottom spent fuel racks. This upper limit is due to a lack of BADGER data (for validation) at higher loss values.

Question:

RAI 26.5: Describe the differences, such as geometric considerations, of the current, NET-264-02, Revision 4, algorithm to the one described in NET-264-03, Revision 1, Appendix A.

Response: See responses to RA126.1 and RA126.2.

Non-Proprietary Information in Accordance with 10 CFR 2.390 Response to Request for Additional Information -

License Amendment Request to Revise TS 4.3.1.1.a Page 6 Question:

RAI 26.6: Discuss how the current, NET-264-02, Revision 4, algorithm was validated.

Response

The validation process involves comparison of the RACKLIFE results with BADGER measurements on a periodic basis.

Question:

RAI 27 - Discussion NET-264-02, Revision 4, mentions that the Peach Bottom Unit 2 RACKLIFE model was verified by BADGER campaigns; however, the verification of the RACKLIFE model for Unit 3 is not mentioned.

RAI 27.1: Please provide all of the BADGER results and RACKLIFE predictions for Unit 2 and Unit 3 racks.

Non-Proprietary Information in Accordance with 10 CFR 2.390 Response to Request for Additional Information -

License Amendment Request to Revise TS 4.3.1.1.a Page 7

Non-Proprietary Information in Accordance with 10 CFR 2.390 Response to Request for Additional Information -

License Amendment Request to Revise TS 4.3.1.1.a Page 8 Question:

RAI 27.2: Discuss the validation and verification of the RACKLIFE predictions by the BADGER results for the Unit 2 and Unit 3 racks.

Response

The Tables and Figures provided in response to RAI 27.1 provide the BADGER to RACKLIFE comparisons for all panels measured during the Unit 2 April 1996, February 2002, and February 2006 BADGER campaigns and the Unit 3 January 2001 and March 2005 BADGER campaigns.

The complete set of Unit 2 data is used to validate the Unit 2 RACKLIFE model and similarly all the Unit 3 data is used to validate the Unit 3 RACKLIFE model.

Using the results from all the measurements is a better indication of the validity of

Non-Proprietary Information in Accordance with 10 CFR 2.390 Response to Request for Additional Information -

License Amendment Request to Revise TS 4.3.1.1.a Page 9 the RACKLIFE model because a single measurement is subject to not only measurement variability, but also as-built B-10 areal density variability which can be as large as 15% of the nominal.

The first figure in RAI 27.1 shows the BADGER (measured) and RACKLIFE (predicted) average boron carbide loss for all panels tested during each BADGER campaign in the Peach Bottom spent fuel pools. The plot shows that for all campaigns except one, on an average basis the RACKLIFE predictions are conservative with respect to BADGER measurements. It is noted that for one test campaign (PBAPS, Unit 3, March 2005), the average measured boron carbide loss for the panels tested exceeded the average of the predicted boron carbide loss by approximately 10%, which is equivalent to the BADGER uncertainty. This was attributed to the selection of the reference unirradiated panels that had an areal density near the low range of the as-manufactured batch areal densities. The favorable agreement between BADGER and RACKLIFE validates the silica mass balance incorporated in the RACKLIFE model.

The Tables in Attachment 7 contain the individual panel measured and predicted boron carbide losses for each BADGER test campaign in the PBAPS, Units 2 and 3 spent fuel racks. On an individual panel basis there are variations between the measured and predicted panel loss. This may be attributed to any one or a combination of the following:

1. Implicit in the RACKLIFE model is the assumption that the escape coefficient for the volume of water surrounding each panel of Boraflex is the same. This is not necessarily true as even in the as-fabricated condition, variations in the escape coefficient exist due to the nature of attachment of the thin wrapper plates.

2. As the racks are used and fuel assembly movement impacts the wrapper plates, the escape coefficient of specific panels can change.

3. In the as-manufactured condition, the areal density of some panels can vary as much as +/- 15% from the nominal batch average areal density.

The second Figure in the response to RAI 27.1 shows the distribution of the difference between individual measured panel loss and individual panel predicted loss.

Question:

RAI 28

The NET-264-02, Revision 4, analyses is based on Unit 2 with the assertion that Unit 2 bounds Unit 3. The NRC staff is unaware of the bases that justify that Unit 2 bounds Unit 3. Please discuss the similarities and differences of the Unit 2 and 3 SFPs, spent fuel pool racks, and Boraflex material.

Response

A comparison of significant physical parameters between the Unit 2 and 3 spent

Non-Proprietary Information in Accordance with 10 CFR 2.390 Response to Request for Additional Information -

License Amendment Request to Revise TS 4.3.1.1.a Page 10 fuel racks was performed by reviewing the associated drawings. This review included a review of the rack layout, rack spacing, cell spacing, cell size, Boraflex sheeting, wrapper plate thickness, and wrapper plate placement between the Units. Based on a review of these drawings, no significant differences which could affect the effectiveness of the Boraflex were introduced during installation of the spent fuel pool racks.

Additionally, a review of the fuel pool cooling suction and discharge piping was performed and no significant differences were identified that impact the performance of the spent fuel pool. The operational characteristics of the fuel pools (flow rates and temperatures) are essentially the same. Based on a review of historical records, it appears that the current Peach Bottom Unit 2 racks were placed in service starting in 1986, and the Unit 3 racks were placed in service starting in 1987.

Question:

RAI 29

NET-264-02, Revision 4, correlates the peak panel loss to an average panel boron carbide loss. The NRC staff is uncertain how this correlation was obtained.

Please discuss the correlation methodology.

Response

For a particular spent fuel pool configuration, RACKLIFE calculates the average boron carbide loss for each panel in the Peach Bottom spent fuel pool. The maximum is termed the peak panel boron carbide loss. The average boron carbide loss is the boron carbide loss averaged for each individual panel in the Peach Bottom spent fuel pool for the same spent fuel pool configuration.

Question:

RAI 30

NET-264-02, Revision 4, states, 'The original (RACKLIFE) model was updated by Exelon every 6 months to reflect actual fuel discharges into the spent fuel racks through 2008." Discuss whether the RACKLIFE model was updated in 2009 and if there are future plans to update the RACKLIFE model at a 6 month frequency. In addition, please describe plans for future BADGER testing for Units 2 and 3 to verify the RACKLIFE predictions.

Response

The RACKLIFE model at PBAPS, Units 2 and 3 is required by procedures to be updated eveny 6 months in accordance with Routine Tests Procedure RT-R-004-990-2(3), "Boraflex Surveillance Using the RACKLIFE Program". This conservative update frequency is reflected in NET-264-02, Rev. 4. In actuality, in 2009, the PBA PS, Unit 2 RACKLIFE model was updated on 1/16/09, 4/2/09, and 9/16/09. In 2009, the PBAPS Unit 3 RACKLIFE model was updated on 4/2/09 and 9/16/09. The next RACKLIFE model update for each unit is scheduled for March 2010. NET-264-02, Rev. 4 is based on a model update through 2008 and projections thereafter. The model was frozen at a point in time, and not updated, to allow final preparation of the report.

BADGER testing is performed on each PBAPS unit every 4 years in accordance

Non-Proprietary Information in Accordance with 10 CFR 2.390 Response to Request for Additional Information -

License Amendment Request to Revise TS 4.3.1.1.a Page 11 with Routine Tests Procedure RT-R-004-995-2(3), "Boraflex Surveillance Using the BADGER Test Device". This procedure enforces a minimum 4-year frequency for the testing. The BADGER test data is used to verify the RACKLIFE model and to determine if any adjustments to the model parameters are necessary.

The most recent PBAPS, Unit 3 BADGER test was performed in December2009, and the most recent PBAPS, Unit 2 BADGER test was performed in January 2010.

The next BADGER tests are scheduled for 2013 and 2014 for PBAPS, Units 3 and 2, respectively.

Reactor Systems Branch Questions:

RAI questions 31 through 35 pertain to the area of the applicability of the validation as discussed in NET-901-02-05, Revision 4.

Question:

RAI 31

Is Table 4-1 intended to state the ranges of parameters that the safety analysis fits within? If so, what is the basis for applying the bias and bias uncertainty up to 5 w/o U-235 when the CASMO validation only goes up to 4.31 w/o U-235? Similarly, H/U and EALF ranges in Table 4-1 are not substantiated by the CASMO validation ranges. Provide the basis for the extrapolation.

Response

No. Table 4-1 is intended to present a range of parameters that may exist for typical spent fuel storage configurations. The actual area of applicability for the CASMO-4 calculation methodology is listed in Table 5-6. The trend analysis for enrichment for the CASMO-4 validation showed a slightly positive slope with increasing enrichment. The CASMO-4 bias tends to become less negative with increasing enrichment. At the 4.31 w/o enrichment, the maximum enrichment evaluated in the CASMO benchmark, the trend analysis yields a bias of[

]

Ak which is less negative than the overall bias of[

1. However, as shown subsequently any trends are attributed to the randomness of the data. At the design basis final enrichment of 4.9 w/o 235U used in the Peach Bottom analysis, the trend analysis shows the bias is [

] Ak which would imply a reduction in the overall CASMO benchmark bias in item 1 of Table 5-4 of NET-264-02, Rev. 4, thus implying a reduction in the overall keff (95/95) shown at the bottom of that Table.

An additional CASMO benchmark "critical" (identified as CASL24CO1) has been performed to improve the trending analysis of the CASMO-4 bias. This additional critical benchmark was initially not evaluated as its enrichment of 9.83 w/o 235U is more than double the GNF reference design enrichment of 4.9 w/o 235U, while the highest enrichment of 4.31 w/o 235U included in the CASMO 24 case benchmark is within 0.6 w/o 235U of the enrichment of the GNF reference design. This additional CASMO benchmark also extends the area of applicability down to an H/U ratio of 41, bounding the values of the actual Peach Bottom racks. No statistically significant trend (i.e., the slope is not different than a slope of zero) appears to

Non-Proprietary Information in Accordance with 10 CFR 2.390 Response to Request for Additional Information -

License Amendment Request to Revise TS 4.3.1.1.a Page 12 exist based upon a Student's t-test of the means. (See RAI 40.)

Similarly for EALF, the additional CASMO critical benchmark experiment (CASL24C01) was performed to improve the trending analysis of the bias. This also extends the area of applicability for EALF up to 1.05. Again, no statistically significant trend (i.e., the slope of the Ak vs. EALF trend is not different than zero) appears to exist based upon a Student's t-test of the means. (See RAI 40.)

The additional CASMO critical benchmark experiment (CAS24C01) extends the area of applicability for pin pitch down to 0.62 cm. This bounds the actual pin pitch of the GNF2 design basis bundle.

Question:

RAI 32

Similar to RAI 31 above, H/U and EALF ranges in Table 4-1 are not substantiated by the SCALE validation ranges. Provide the basis for the extrapolation.

Response

As stated in RAI 31, Table 4-1 is intended to present a range of parameters that may exist for typical spent fuel storage configurations. The actual area of applicability for which the SCALE validation is applicable are shown in Table 5-3.

With respect to the range of applicability for EALF and H/U (denoted as H/X in Table 5-3) ratio, the values for both parameters in the validation database bound the actual parameter values for the Peach Bottom spent fuel racks shown in Appendix C of NET-264-02, Rev. 4.

Question:

RAI 33

In Table 4-1, there seems to be an omission for the absorber plate poison loading.

Please provide the missing data.

Response

Question:

The range of absorber plate loading is 0. 1 w/o boron to 32.74 w/o boron.

RAI 34

Why were experiments with soluble boron used when the analyzed system does not contain any soluble boron? What is the effect of soluble boron on the code bias and bias uncertainty? Justify your approach.

Response

In order to satisfy the geometry requirement of diagonal symmetry in CASMO, twenty-two critical experiments were selected from the B&W 1484 series of experiments that contain 3x3 arrays of fuel clusters. Only those experiments containing assemblies surrounded by no absorber plates or those with absorber plates along a uniform number of cell pitches (such that it could be reflected along the mid-plane) were available. While some of these experiments contained borated absorber plates, others did not, but all of them contained soluble boron.

The only suitable configurations that did not contain soluble boron, were two cases from PNL experiments that were at a higher uranium enrichment, but contained no

Non-Proprietary Information in Accordance with 10 CFR 2.390 Response to Request for Additional Information -

License Amendment Request to Revise TS 4.3.1.1.a Page 13 borated plates nor any soluble boron.

Calculations have shown that the presence of soluble boron tends to increase the negative bias. Consequently, the CASMO benchmark bias as shown in item 1 of Table 5-4 would be expected to be a smaller number had more measurements without soluble boron been available and included in the CASMO benchmark database.

The CASMO-4 bias becomes even more negative for critical experiments that contain bora ted absorber plates in conjunction with soluble boron, thereby maximizing the bias. In the absence of soluble boron or bora ted absorber plates, the relative bias is less negative while the bias becomes more negative with increasing soluble boron.

Question:

RAI 35

Discuss validation gaps (e.g., fission product validation) and, if appropriate, additional margin adopted to cover validation gaps.

Response

The CASMO-4 bias was determined based on comparisons to 95/95 bias corrected Keno V.a calculated knf values rather than nominal bias corrected kinf values that is standard practice. Thus, the CASMO values already contain an additional [

I (difference between CASMO-4 and Keno V.a nominal biases) Ak to account for gaps in the validation method. While explicit fission product validation was not performed, the adequacy of fission product isotopic production in CASMO-4 is confirmed by kinf comparisons to the results from the TGBLA06 code, shown in Appendix B of NET-264-02, Rev. 4.

RAI questions 36 through 37 pertain to the normality test performed for the CASMO validation as discussed in NET-901-02-05, Revision 4.

Question:

RAI 36

Section 5.2 states that the normality tests were performed for the Ak values. This approach seems to deviate from NUREG-6698 which uses the calculated keff values. Please justify your approach.

Response

The CASMO-4 bias is determined relative to the KENO V.a bias corrected values of knf (at the 95/95 level) and not relative to the critical condition of keff=1.0. As a result, it is more appropriate to show that the distribution of Ak, values is normal, rather than the distribution of the absolute values of kinf.

Non-Proprietary Information in Accordance with 10 CFR 2.390 Response to Request for Additional Information -

License Amendment Request to Revise TS 4.3.1.1.a Page 14 Question:

RAI 37

Section 5.2 states that Ak values were tested for normality and the data passed all tests. The staff could not confirm the normality of the Ak values based on the Shapiro-Wilk test described in NUREG-6698. In addition, the normality of the calculated keff values could not be confirmed. Re-evaluate the CASMO bias and bias uncertainty using the appropriate methods to handle non-normal data or justify not doing so.

RAI questions 38 through 39 pertain to the method used to determine the bias and bias uncertainty as discussed in NET-901-02-05, Revision 4.

Non-Proprietary Information in Accordance with 10 CFR 2.390 Response to Request for Additional Information -

License Amendment Request to Revise TS 4.3.1.1.a Page 15 Question:

RAI 38

The 3-dimensional SCALE bias was determined by comparing SCALE to critical experiments. The 2-dimensional SCALE models simulate a fictitious set of experiments used to validate CASMO. Justify using the SCALE bias determined in the 3D model to correct 2D SCALE models.

Response

The 3-dimensional SCALE bias is based upon actual 3-dimensional critical experiments that include neutron leakage. Neutron leakage inherently increases the statistical calculation uncertainty for a given experiment and results in a lower calculated kef due to neutron leakage. Also, the experimental (measurement) uncertainty for a 3-dimensional calculation would be larger than that for a 2-dimensional experiment infinite in the axial direction due to uncertainty in axial measurements (e.g., fuel height, moderator height, etc.). Therefore the weighted bias for a 3-dimensional critical experiment would be larger relative to a 2-dimensional critical experiment and assuming 2-dimensional systems include a 3-dimensional bias is thereby conservative.

Question:

RAI 39

The CASMO validation was performed in two steps. SCALE was validated against 103 critical experiments resulting in a SCALE bias and bias uncertainty. Then 24 of the 103 critical experiments were represented using the 2-dimensional SCALE models which were used to determine the CASMO bias and bias uncertainty. The 2-dimensional SCALE representation of the experiments corrects for the SCALE bias, but it does not seem to account for the SCALE bias uncertainty. Please explain how the SCALE bias uncertainty is accounted for in the maximum keff determination. Presently, it is not clear how the analysis links to the critical experiments.

Response

The CASMO bias was determined relative to the 95/95 bias corrected SCALE calculated knf values that inherently include the SCALE bias uncertainty. The SCALE bias was determined non-parametrically and therefore includes the bias uncertainty at the 95/95 level. The result is that the average CASMO bias is approximately [

]Ak larger than the SCALE average bias. The increase in Ak reflects the difference between the 3D and 2D biases.

RAI questions 40 through 43 pertain to the trend analysis of the validation as discussed in NET-901-02-05, Revision 4.

Question:

RAI 40

Please discuss what is to be concluded from the low "p" values of <1 E-4 in Tables 5-2 and 5-5. Does this indicate that the association between the response and predictor is statistically significant?

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License Amendment Request to Revise TS 4.3.1.1.a Page 16 The Table in RAI 37 contains data for corrected SCALE-5 Cases 3 through 10, as well as an additional benchmark experiment for trending analysis. Performing a Student's t-test on the revised values results in the revised CASMO-4 Trending Analysis Table (Table 5-5) shown below:

Response

Goodness Valid Parameter n

Intercept(b)

Slope (M) r2 T

t/2,n-2 P

of Fit Test Trend EALF(eV) 25

-0.0128 0.0097 0.101 0.19 2.398 0.12 YES No Enrichment (w/o 235U) 25

-0.016 0.0020 0.337 4.8 2.398 8E-5 No YES H/X 25

-0.0043

-3E-5 0.045

-1.04 2.398 0.31 YES No Soluble boron 25

-0.0087

-9E-6 0.173 1.28 2398 0.21 YES No (ppm)

The P-values shown indicate the probability of the data exhibiting a linear trend attributed to randomness of the data. The only parameter value that exhibits a less than 5% probability (of the trend being due to randomness) is enrichment.

However this parameter tends to cause the bias to become less negative with increasing enrichment. Accordingly, it is concluded that for the other parameters evaluated, any trends as indicated by regression analysis are attributable to the randomness of the data.

Question:

RAI 41

Please explain what is meant by "maybe" in Table 5-5. Does this indicate that a statistically significant trend exists? If so, justify its impact on the bias.

Response

Question:

The revised table in RAI 40 contains corrected conclusions relative to the presence of a valid trend.

RAI 42

The NRC staff could not confirm the r2 value for enrichment in Table 5-5. Please confirm that the correct value was determined in the submittal.

Response

The revised Table in RAI 40 contains corrected r2 values.

Question:

RAI 43

The trending analysis data provided in the submittal is not sufficient for the staff to independently verify that no statistically significant trends exist for CASMO. This is

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License Amendment Request to Revise TS 4.3.1.1.a Page 17 especially the case for enrichment and EALF. Please provide additional information to substantiate your claim that no trends exist for CASMO.

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License Amendment Request to Revise TS 4.3.1.1.a Page 18

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License Amendment Request to Revise TS 4.3.1.1.a Page 23 RAI questions 44 through 59 pertain to NET-264-02, Revision 4.

Question:

RAI 44

Provide 2-dimensional plots of the CASMO-4 and KENO V.a models used in the analysis.

Response: Figure 1 below contains a 2-dimensional color plot of the Keno V.a explicit geometry model used in the analysis as generated by Keno V.a. Figure 2 contains a 2-dimensional plot of the Keno V.a model of the CASMO geometry of the Peach Bottom storage cell. Figure 3 contains a 2-dimensional drawing of the CASMO model of the Peach Bottom storage cell.

The CASMO-4 model (and Keno V.a model of CASMO) differs from the exact geometry in that the midplane of the Boraflex panel lies on the reflected boundary and the thin gage wrapper plate is merged with the storage cell wall stainless steel to preserve the total stainless steel thickness between fuel assemblies and storage cell pitch.

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License Amendment Request to Revise TS 4.3.1.1.a Page 24 0OT AT CENTER LEGEND i l l

LIIIVOID hi~

M A

T ERIAL 1 FUEL 71MATERIAL 2 CLAD/CHANNEL 3' WATER 4 BORgFLEX

5. STAINLESS STEEL 7 WATER Own, ***(*:::I 0 C) (D (3) 3:1 Figure 1. 2-dimensional plot of Keno V.a model of explicit Peach Bottom rack geometry. The [

] arrays are an expansion of this model

,X-Yz PLOT AT CENTER LEGEND VOID LIIMATERIAL MATERIAL MATERIAL 71MATERIAL' 1

2 3

4

'5 FUEL CLAD/CHANNEL WATER

'BORAFLEX STAINLESS STEEL Figure 2. 2-dimensional plot of Keno V.a model of CASMO-4 Peach Bottom rack geometry

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License Amendment Request to Revise TS 4.3.1.1.a Page 25 00000 00000 00000 0000 000 00000O 00000........

00O0O 00000 00000 kJ' 11U)" ILIJ

\\~ J 0 Q(

000%

0000 00000 00000 00000 Figure 3. 2-dimensional rendering of CASMO-4 model of Peach Bottom rack geometry Question:

RAI 45

Describe how the asymmetries of the Peach Bottom SFP racks are modeled in CASMO-4.

Response

The CASMO model preserves the cell pitch of the storage rack. The Boraflex panel is reflected on the storage cell boundary. The stainless steel wrapper plates are combined with the storage cell wall such that when reflected, the total amount (thickness) of stainless steel in the storage cell walls and wrapper plates is preserved. An equivalent thickness for the fuel channel is determined to preserve the amount of zircaloy in the thick/thin region of the fuel channel, while the extra thick channel corners are defined explicitly by CASMO.

Question:

RAI 46 - Discussion The following questions pertain to how the gamma dose to an individual Boraflex panel was determined:

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License Amendment Request to Revise TS 4.3.1.1.a Page 26 RAI 46.1: Explain the use of the end-of-cycle relative power in calculating the gamma dose.

Response

MICROSHIELD, a shielding code that applies a point kernel approximation to gamma transport, was used to develop combined geometric and material attenuation coefficients and obtain nominal dose rates at a point in the center of a Boraflex panel assuming a nominal power density. Sensitivity studies were performed for a variety of water and stainless steel thicknesses, as well as power levels, to generate attenuation fit functions such that RACKLIFE could accommodate multiple assembly and rack designs. The dose rate to a Boraflex panel from its neighboring assemblies is adjusted to account for attenuation by the intervening water and stainless steel encapsulating the Boraflex and also for different source characteristics (e.g., power level, decay profile, burnup, enrichment, etc) to obtain a specific dose rate for the assemblies neighboring all Boraflex panels. The corrected dose rate is then integrated over time and corrected for cooling time based on a decay curve developed with ORIGEN.

Since fitted equations for the dose rate and attenuation coefficients were based on a nominal assembly average power, a correction factor must be applied to scale the dose rate for each specific assembly characteristic (burnup, enrichment, relative power, etc.). The actual assembly end-of-cycle dose rate is calculated as:

I--/ *(P/Nasbly) *RP*(Pre 1Nref)

Where:

I = nominal dose rate (rads/hr)

P= rated thermal power for the specific discharge cycle Nasly = number of assemblies in the core RP= assembly end-of-cycle relative power Pref = rated thermal power used to develop dose rate fits (251 1MWth for BWR)

Nref = number of assemblies in nominal reactor (724)

The actual end-of-cycle power level of each assembly is therefore required to determine the Boraflex panel dose rates, and the actual end-of-cycle power level for all assemblies is determined from the average end-of-cycle power level of all assemblies (P/Nasbly) times the assembly end-of-cycle relative power level. A sum of all end-of-cycle relative assembly power levels divided by the number of assemblies (Nasbly) would equal 1.0.

The above equation scales the dose rate from each assembly residing next to a Boraflex panel from the nominal value used to generate the dose rate and attenuation fit equations.

Question:

RAI 46.2:

Explain why the use of a weighted average end-of-cycle relative power is appropriate versus a bounding end-of-cycle relative power.

Response

The average power sharings for the discharged assemblies from Cycles 16 and 17

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License Amendment Request to Revise TS 4.3.1.1.a Page 27 were less than 0.53 (approximately 33% less than the value used). The analysis (NET-264-02, Rev. 4) is based on the peak panel boron carbide loss occurring in the central region of the fuel pool. The panels in the central region of the pool have already reached an integrated absorbed gamma dose greater than 1x101° rads, well in excess of the 2-3x10oP rads, where Boraflex degradation increases significantly. Therefore the predicted degradation in this region is increasing simply due to increased service life and is not impacted by the placement of discharge bundles in this region of the pool.

Question:

RAI 46.3: What is the basis for the gamma source term?

Response

ORIGEN-PC was used to develop multigroup gamma sources, principally as functions of:

reactor spectrum (i.e., BWR, PWR),

discharge burnup (6 GWD/MTU to 62 GWD/MTU),

Power density (30% to 150% of nominal), and Cooling time (1 day to 40 years)

Results were normalized per metric ton of uranium (MTU) so that they are generally applicable to all fuel types for a given reactor spectrum. Discharged fuel fission products are the dominant decay gamma source, with these and fuel actinides (and daughter products) contributing well over 2 orders of magnitude more to energy deposition to Boraflex panels than all other sources combined.

Thus, differences in clad and non-fuel-bearing components between assembly types were neglected in generating the source terms.

Question:

RAI 46.4:

The analysis assumes a 0.8 weighted average end-of-cycle relative power; describe the effect a higher weighted average end-of-cycle relative power would have on the analysis.

Response

An increase in weighted EOC relative power would have a minimal effect on the current analysis. Actual weighted average power sharings for Cycles 16 and 17 were less than 0.53 (approximately 33% less than the value used). The analysis is based on the peak panel boron carbide loss occurring in the central region of the fuel pool. The panels in the central region of the pool have already reached an integrated absorbed gamma dose in excess of lx101° rads; therefore, the predicted degradation in this region is increasing due to extended service life and increasing escape coefficient rather than additional gamma dose.

Question:

RAI 47

How are the KENO bias and bias uncertainty applied in the methodology for

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License Amendment Request to Revise TS 4.3.1.1.a Page 28 assessing the reactivity effects of Boraflex degradation? Justify the approach used and explain how it ensures the Boraflex degradation prediction meets at a 95 percent probability, 95 percent confidence level.

The reactivity effects of Boraflex degradation (for the Keno V.a [

] arrays, as well as the uniform panel thinning cases) are calculated on a relative basis to the reference case with all panels at the as-built boron-10 areal density and thickness.

Since the reactivity effects are calculated on a relative basis and not based on an absolute value of keff, the bias and bias uncertainty do not enter into the calculation of the reactivity effects of Boraflex degradation at the 95/95 level. While the reactivity effects of Boraflex degradation resulted in an equivalent uniform panel thinning of[

]%, the assumed uniform panel thinning amount of[ ]% provides approximately [

]lAk additional margin to account for uncertainties.

Response

Question:

RAI 48

Provide the data that is plotted in Figure 4-2.

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License Amendment Request to Revise TS 4.3.1.1.a Page 29 Question:

RAI 49

What trend analyses were performed on the data plotted in Figure 4-2 to reach the conclusion that no non-normal behavior was observed?

Response

The data were subjected to the Anderson-Darling, Cramer-von-Mises and Kolmogorov Smirnoff tests for normality. Each of the tests failed to reject the null hypothesis at a 95% probability level that the data followed a normal distribution.

Question:

RAI 50

Provide plots of the Boraflex degradation being modeled in the data in Figure 4-2 so that it is clear how the Boraflex degradation changes from one case to the next.

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License Amendment Request to Revise TS 4.3.1.1.a Page 30

Response

] are contained in Attachment 5. Whole numbers in each cell indicate the percent uniform panel thinning amount for each cell. Cells colored gray indicate local degradation features. Those cells containing only whole numbers pertain to local dissolution regions. Cells that contain a fractional inch along with a whole number in parenthesis are gaps occurring concurrent with dissolution.

Question:

RAI 51

What are the Boraflex loading reference points for Table 4-3?

Response

The Boraflex loading reference point is the nominal Boraflex areal density of 0.0235 gms B-0l/cm2 at the nominal thickness.

Question:

RAI 52

Provide the depletion parameters used in determining the limiting peak reactivity of the lattices evaluated. Justify those depletion parameters and identify how deviations from those parameters would affect the peak reactivity.

Response: See GNF response to RAI 52 in Attachment 3.

In addition to the GNF response, NUREG/CR-6665 contains guidance on the selection of LWR fuel depletion parameters. However, these pertain mainly to bumup credit and storage in casks and may not be appropriate for spent fuel pool criticality analyses. As a result, sensitivity studies were performed on depletion parameters to investigate their effects on the peak in-rack kinf at Peach Bottom.

NUREG/CR-6665 states that in BWR systems, moderator temperature changes very little axially and more significant is the effect on reactivity of moderator density (void fraction). The moderator temperature was increased from 569K to 600K and results in a decrease [

] in the peak kinf. With respect to fuel temperatures, NUREG/CR-6665 suggests a bounding fuel temperature (maximum pellet average temperature) of 1000K that would seem like an appropriate bounding fuel temperature for depletion calculations to maximize spectral hardening. Depleting the peak reactivity lattice at fuel temperature of 1 000K results in a small increase

[

] in the peak kin,.

Question:

RAI 53 - Discussion With respect to the determination of the reactivity equivalent fresh fuel enrichment (REFFE) fuel assembly, the cross-section bias and CASMO/KENO geometric bias, please provide the following information:

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License Amendment Request to Revise TS 4.3.1.1.a Page 31 RAI 53.11: How were the CASMO-4 and KENO biases and bias uncertainties applied?

Response

The REFFE is determined by applying the nominal biases to the calculated values of KENO V.a and iterating until the best estimate kinf of Keno V.a slightly exceeds the peak bias corrected knf calculated by CASMO-4 for the maximum reactivity.

lattice at peak reactivity. The bias uncertainties for both codes are nearly identical.

There is only a minor difference in the two codes when including the uncertainties.

If an additional [

] is included to account for the reactivity effect of the Keno V.a and CASMO-4 95/95 bias uncertainties, the REFFE would increase to [

] w/o 235U from [

] w/o 235U. The impact on the tolerances would result in the RMS combination of tolerances and uncertainties to decrease by less than [

]. This is due to the statistical uncertainty of the Keno V.a calculation. The self shielding bias would increase by [

] Ak.

Question:

RAI 53.2: How was xenon treated?

Response

The Xenon number density is set to 0 during the CASMO in-rack restart calculation.

Sensitivity studies have shown that the kinf at the burnup step of peak reactivity is a maximum at 0 cooling time. The reactivity decreases substantially around 3 hours3.472222e-5 days <br />8.333333e-4 hours <br />4.960317e-6 weeks <br />1.1415e-6 months <br /> post-shutdown and then increases until 150 days post-shutdown. At 100 hours0.00116 days <br />0.0278 hours <br />1.653439e-4 weeks <br />3.805e-5 months <br /> post shutdown, kinf reaches a local maximum that is [

]Ak less than the peak kinf at shutdown and slowly increases by [

]Ak reaching a peak around 150 days post shutdown before subsequently decreasing. The peak reactivity at 150 days post-shutdown remains [

]Ak lower than the maximum kinf at shutdown (0 cooling time). The figure below is a plot of knf as a function of cooling time (days) from shutdown to 1 year cooled for the peak reactivity GNF2 Vanished1 lattice depleted to 16 GWD/MTU.

The trend seen below is similar to the reactivity behavior of set 3 for fission products and actinides of Figure 3 in NUREG/CR-6781. The primary difference is that the initial kinf at 0 cooling time at the point of peak fuel assembly reactivity is at the no-xenon condition, whereas in Figure 3 of NUREG/CR-6781 Xenon-135 is included.

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License Amendment Request to Revise TS 4.3.1.1.a Page 32 Question:

RAI 53.3: How were the lumped fission products in CASMO-4 treated? Please provide the following information concerning those lumped fission products:

i) What actual fission products are represented in each lumped fission product?

Response

CASMO-4 handles some fission products explicitly (See table below), while the remaining fission products are lumped into two groups; the first group (ID=401) is for non-saturating isotopes while the second group (ID=402) is for slowly saturating isotopes. Any isotope not listed below is lumped into one of the two groups.

CASMO-4 Explicit Fission Products Kr-83 Rh-103 Rh-105 Ag-109 Xe-131 1-135 Xe-135 Cs-133 Cs-134 Cs-135 Cs-137 Ba-140 La-140 Nd-143 Nd-145 Pm-147 Pm-148 Pm-148m Pm-149 Sm-147 Sm-149 Sm-150 Sm-151 Sm-152

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License Amendment Request to Revise TS 4.3.1.1.a Page 33 Eu-153 Eu-154 Eu-155 Eu-156 Gd-155*

• Handled separately than burnable Gd-155 ii) What are the cross sections for each lumped fission product? What are the decay constants for each lumped fission product?

Response

The lumped fission product macroscopic absorption cross sections for both lumped fission products are shown in the table below for each of the 70 energy groups. The decay constant is 0 secI for all products.

Absorption Cross Sections for Lumped Fission Products Group Upper Energy (eV)

Sigma-A (401)(cm1)

Sigma-A (402)(cm1) 1 10000000.000 0.004 0.01 2

6065500.000 0.005 0.015 3

3679000.000 0.008 0.02 4

2231000.000 0.01 0.03 5

1353000.000 0.015 0.042 6

821000.000 0.018 0.065 7

500000.000 0.025 0.087 8

302500.000 0.033 0.12 9

183000.000 0.042 0.14 10 111000.000 0.056 0.18 11 67340.000 0.07 0.23 12 40850.000 0.095 0.28 13 24780.000 0.13 0.36 14 15030.000 0.16 0.44 15 9118.000 0.18 0.54 16 5530.000 0.23 0.66 17 3519.100 0.28 0.82 18 2239.500 0.35 1.1 19 1425.100 0.46 1.35 20 906.898 1.5 2.35 21 367.262 1.3 5.5 22 148.728 1.7 3.8 23 75.501 1

6 24 48.052 5

30 25 27.700 10 1

26 15.968 1

0.7 27 9.877 0.08 40 28 4.000 0.09 3.5 29 3.300 0.1 2

30 2.600 0.13 1.8 31 2.100 0.125 2.844 32 1.855 0.136 3.096 33 1.500 0.15 4

34 1.300 0.159 3.5 35 1.150 0.166 0.3 36 1.123 0.168 3.3

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License Amendment Request to Revise TS 4.3.1.1.a Page 34 37 1.097 0.17 3.3 38 1.071 0.172 3.3 39 1.045 0.174 3.3 40 1.020 0.176 3.3 41 0.996 0.178 3.3 42 0.972 0.181 3.03 43 0.950 0.184 3.07 44 0.910 0.188 3.16 45 0.850 0.196 3.29 46 0.780 0.212 3.56 47 0.625 0.237 3.97 48 0.500 0.265 4.45 49 0.400 0.289 4.85 50 0.350 0.305 5.13 51 0.320 0.318 5.34 52 0.300 0.328 5.51 53 0.280 0.344 5.78 54 0.250 0.365 6.13

55.

0.220 0.396 6.65 56 0.180 0.443 7.46 57 0.140 0.521 8.75 58 0.100 0.593 9.96 59 0.080 0.654 11 60 0.067 0.708 11.9 61 0.058 0.762 12.8 62 0.050 0.826 13.8 63 0.042 0.902 15.2 64 0.035 0.985 16.5 65 0.030 1.06 17.9 66 0.025 1.18 19.9 67 0.020 1.33 22.5 68 0.015 1.58 26.6 69 0.010 2.04 34.3 70 0.005 3.35 56.4 iii) Are there any neutron absorbers represented in the lumped fission products?

What are the cross sections for those neutron absorbers? What are the decay constants for those neutron absorbers?

Response

Yes. The absorption cross-sections are shown above in RAI 53.3.11. The decay constants are 0 sec7' since they saturate due to absorption.

iv) Are there any neutron sources represented in the lumped fission products?

What are the source terms? What are the decay constants for those neutron sources?

Resoonse: Yes. The table below lists the percent of all fissions for each isotope that leads to production of lumped fission product isotopes. For example, 235U, under heading 92235, 1.26% of all fissions lead to the production of isotopes in lumped

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License Amendment Request to Revise TS 4.3.1.1.a Page 35 fission product group LFP401. The decay constants are zero for all (they saturate and their number densities do not change).

Fission yields for Lumped Fission Products Isotope 92235 92236 93237 92238 94239 94240 94241 94242 LFP401 1.26 1.26 0.0 1.426 1.456 1.456 1.456 1.456 LFP402 0.298 0.298 0.0 0.267 0.301 0.301 0.301 0.301

Response

v) What is the basis for the cross section for each lumped fission product?

The cross-sections for the fission products provided in response to RAI 53.3 ii are from Figures 4 and 5 of ORNL-TM-1658, "Recommended Fission Product Chains for Use in Reactor Evaluation Studies," September 26, 1966 (Attachment 9).

vi) How do the cross sections of the lumped fission products respond to changes in temperature and spectral hardening?

There is no temperature dependence of the lumped fission products. Spectral hardening is accounted for when going from the single pin cell calculation to the 2-D assembly calculation. In this process, the flux weighted cross sections are collapsed from 70 energy groups to fewer (8 - 12 energy groups), taking into account number densities that have changed due to spectral hardening.

Response

Question:

RAI 53.4: Explain how normalizing KENO to CASMO-4 in determining the REFFE affects the determination of the cross-section bias and CASMO/KENO geometric bias.

Response

In determining the REFFE, the Keno V.a calculated knf is normalized to the CASMO calculated peak kinf. In so far as the two knf values are identical, the net difference (CASMO - Keno V.a) would be zero, therefore any effect on the cross-section bias would be zero. A slightly negative bias [

] is present simply because the REFFE was increased slightly from [

I to [

I w/o 235U. While this is conservative with respect to CASMO, no credit is taken for this bias and it is assumed to be zero.

The geometry bias was determined by calculating the difference in kinf values between two Keno V.a calculations. A Keno V.a model of the CASMO geometry was created and kinf was calculated to be [

]. A second Keno V.a model with the exact rendering of the Peach Bottom spent fuel rack geometry was created and kinf was calculated to be [

]. The difference in kinf of the exact geometry relative to the CASMO model is [

lAk. This verifies that the CASMO model of the Peach Bottom spent fuel rack is slightly more reactive (conservative) relative to the actual rack configuration.

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License Amendment Request to Revise TS 4.3.1.1.a Page 36 Question:

RAI 54 - Discussion The following questions pertain to Table 5-2. This table compares CASMO-4 and KENO V.a in a standard cold core geometry (SCCG) configuration, which both codes are capable of modeling.

RAI 54.1: Explain the differences in the information contained in the third and fourth columns and the differences in the information contained in the fifth and sixth columns of the table.

Response

Table 5-2 contains an in-core comparison of CASMO and KENO results for two lattices. KENO is not used in an in-core configuration in NET-264-02, Rev. 4.

Consequently, Table 5-2 is not relevant to the criticality analysis. This table and the applicable text in Section 5.3.2 can be deleted from NET-264-02, Rev. 4.

Question:

RAI 54.2: The number of examples provided is insufficient to draw conclusions; provide additional examples and include depleted fuel.

Response: See response to RAI 54.1; Table 5-2 has been deleted.

Question:

RAI 55 - Discussion The following questions pertain to Table 5-3, which compares CASMO-4 and KENO V.a in cold SFP rack geometry.

RAI 55.1: Since CASMO-4 cannot model the asymmetries associated with the Peach Bottom SFP rack design, explain what is being done in CASMO-4 to model the SFP rack geometry.

Response

See response to RAI 45.

Question:

RAI 55.2: Explain the differences in the information contained in the third and fourth columns and the differences in the information contained in the fifth and sixth columns of the table.

Response

Table 5-3 of NET-264-02, Rev. 4 including the associated text in Section 5.3.2 is superseded by the expanded code benchmark contained in NET-901-02-05P, Rev.

4; consequently, this portion of the report can be deleted.

Question:

RAI 55.3: The number of examples provided is insufficient to draw conclusions, provide

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License Amendment Request to Revise TS 4.3.1.1.a Page 37 additional examples and include depleted fuel.

Response: See response to RAI 55.2; Table 5-3 has been deleted.

Question:

RAI 56

Explain why the information provided in Table 5-3 doesn't match the information provided in Figure 5-1.

Response

As noted in RAI 55, Table 5-3 can be deleted from NET-264-02, Rev. 4. Figure 5-1 corresponds to the reference case k1nf in Table 5-4 which was determined for [ ]%

thinning.

Question:

RAI 57

Justify not using the KENO V.a uncertainty in the calculation of Keff as stated on page 39.

Response

The Keno V.a uncertainty was not included in the statistical combination of tolerances and uncertainties, since Keno V.a was used solely for determining certain reactivity effects due to variation in fuel rod and rack tolerances. Since this is a relative reactivity effect and not an absolute determination of kinf, the only uncertainties that need be included are the statistical Keno V.a calculation uncertainties of the reference calculation and the perturbed tolerance calculation and associated confidence factors. However, even including the Keno V.a 95/95 bias uncertainty in the statistical combination of tolerances and uncertainties, the increase in keg would be [

] and the maximum kff would be [

I.

There is still at least [

]Ak margin to the keg<O.95 limit. The CASMO-4 and KENO V.a bias uncertainties were demonstrated to have a negligible effect on the RMS combination of tolerances and uncertainties when included in the REFFE determination. Therefore, including the KENO V.a bias uncertainty would be redundant.

Question:

RAI 58

Please provide the applicable sections of Reference 25, Doub, W.B., "Particle Self-Shielding in Plates Loaded with Spherical Poison Particles," Part B of Section 4.2, Naval Reactors Physics Handbook, Volume 1: Selected Basic Techniques, Naval Reactors, Division of Reactor Development, United States Atomic Energy Commission: Washington, D.C.; 1964. Justify why this reference is applicable to the Peach Bottom SFP.

Response

The applicable section of Reference 25 is provided as Attachment 6. The referenced method was developed based upon experimental data for borated poison plates with typical light water reactor neutron energies from 0.03ev to 1.2263ev.

Non-Proprietary Information in Accordance with 10 CFR 2.390 Response to Request for Additional Information -

License Amendment Request to Revise TS 4.3.1.1.a Page 38 Question:

RAI 59

Please explain the large change in the fuel assembly misplacement accident from the previously supplied information.

Response

The difference in reactivity is due to the lower reactivity design basis bundle being used in the current analysis. The previous analysis was based upon a design basis bundle with an in-core kinf = 1.36. The current analysis was based upon a design basis bundle with an in-core knf = 1.27.

ENCLOSURE 3 JMD-EXN-HEQ-10-020 Responses to Request for Additional Information 52, 60, and 61 Affidavit I

Global Nuclear Fuel - Americas, LLC Affidavit I, Andrew A. Lingenfelter, state as follows:

(1) I am Vice President, Fuel Engineering, Global Nuclear Fuel - Americas, LLC ("GNF-A")

and have been delegated the function of reviewing the information described in paragraph (2) which is sought to be withheld, and have been authorized to apply for its withholding.

(2)

The information sought to be withheld is contained in the Enclosure 1 of GNF-A letter, JMD-EXN-HEO-10-020 from J. Michael Downs (GNF-A) to Tom Loomis (Exelon Nuclear),

Subject:

Responses to Request for Additional Information 52, 60 and 61 Related to License Amendment Request to Revise Technical Specification 4.3.1.].A Concerning K-Infinity for Peach Bottom Atomic Power Station, Units 2 and 3, dated March 24, 2010.

GNF-A proprietary text in Enclosure 1, which is entitled "Responses to Request for Additional Information 52, 60, and 61," is identified by ((a.doted.underlin.e.nside.d..u.bl

.s..quare brackets -3')).

Figures and other large objects are identified with double square brackets before and after the object. In each case, the superscript notation (3} refers to Paragraph (3) of this affidavit, which provides the basis for the proprietary determination.

(3)

In making this application for withholding of proprietary information of which it is the owner, GNF-A relies upon the exemption from disclosure set forth in the Freedom of Information Act ("FOIA"), 5 USC Sec. 552(b)(4), and the Trade Secrets Act, 18 USC Sec. 1905, and NRC regulations 10 CFR 9.17(a)(4), and 2.390(a)(4) for "trade secrets" (Exemption 4). The material for which exemption from disclosure is here sought also qualify under the narrower definition of "trade secret", within the meanings assigned to those terms for purposes of FOIA Exemption 4 in, respectively, Critical Mass Energy Project v. Nuclear Regulatory Commission, 975F2d871 (DC Cir. 1992), and Public Citizen Health Research Group v. FDA, 704F2d1280 (DC Cir. 1983).

(4) Some examples of categories of information which fit into the definition of proprietary information are:

a. Information that discloses a process, method, or apparatus, including supporting data and analyses, where prevention of its use by GNF-A's competitors without license from GNF-A constitutes a competitive economic advantage over other companies;

b. Information which, if used by a competitor, would reduce his expenditure of resources or improve his competitive position in the design, manufacture, shipment, installation, assurance of quality, or licensing of a similar product;

c. Information which reveals cost or price information, production capacities, budget levels, or commercial strategies of GNF-A, its customers, or its suppliers; Affidavit for Enclosure 1 of GNF-A letter, JMD-EXN-HEO-10-020 Affidavit Page I of 3

d. Information which reveals aspects of past, present, or future GNF-A customer-funded development plans and programs, of potential commercial value to GNF-A;

e. Information which discloses patentable subject matter for which it may be desirable to obtain patent protection.

The information sought to be withheld is considered to be proprietary for the reasons set forth in paragraphs (4)a. and (4)b., above.

(5) To address the 10 CFR 2.390 (b) (4), the information sought to be withheld is being submitted to NRC in confidence. The information is of a sort customarily held in confidence by GNF-A, and is in fact so held. Its initial designation as proprietary information, and the subsequent steps taken to prevent its unauthorized disclosure, are as set forth in (6) and (7) following. The information sought to be withheld has, to the best of my knowledge and belief, consistently been held in confidence by GNF-A, no public disclosure has been made, and it is not available in public sources. All disclosures to third parties including any required transmittals to NRC, have been made, or must be made, pursuant to regulatory provisions or proprietary agreements which provide for maintenance of the information in confidence.

(6) Initial approval of proprietary treatment of a document is made by the manager of the originating component, the person most likely to be acquainted with the value and sensitivity of the information in relation to industry knowledge, or subject to the terms under which it was licensed to GNF-A. Access to such documents within GNF-A is limited on a "need to know" basis.

(7) The procedure for approval of external release of such a document typically requires review by the staff manager, project manager, principal scientist or other equivalent authority, by the manager of the cognizant marketing function (or his delegate), and by the Legal Operation, for technical content, competitive effect, and determination of the accuracy of the proprietary designation. Disclosures outside GNF-A are limited to regulatory bodies, customers, and potential customers, and their agents, suppliers, and licensees, and others with a legitimate need for the information, and then only in accordance with appropriate regulatory provisions or proprietary agreements.

(8) The information identified in paragraph (2) is classified as proprietary because it contains details of GNF-A's fuel design and licensing methodology for the Boiling Water Reactor (BWR). Development of the analytical models and methods, including computer codes, were achieved at a significant cost to GNF-A.

The development of the evaluation methodology along with the interpretation and application of the analytical results is derived from an extensive experience database that constitutes a major GNF-A asset.

Affidavit for Enclosure 1 of GNF-A letter, JMD-EXN-HEO-10-020 Affidavit Page 2 of 3

(9)

Public disclosure of the information sought to be withheld is likely to cause substantial harm to GNF-A's competitive position and foreclose or reduce the availability of profit-making opportunities. The fuel design and licensing methodology is part of GNF-A's comprehensive BWR safety and technology base, and its commercial value extends beyond the original development cost. The value of the technology base goes beyond the extensive physical database and analytical methodology and includes development of the expertise to determine and apply the appropriate evaluation process. In addition, the technology base includes the value derived from providing analyses done with NRC-approved methods.

The research, development, engineering, analytical, and NRC review costs comprise a substantial investment of time and money by GNF-A or its licensor.

The precise value of the expertise to devise an evaluation process and apply the correct analytical methodology is difficult to quantify, but it clearly is substantial.

GNF-A's competitive advantage will be lost if its competitors are able to use the results of the GNF-A experience to normalize or verify their own process or if they are able to claim an equivalent understanding by demonstrating that they can arrive at the same or similar conclusions.

The value of this information to GNF-A would be lost if the information were disclosed to the public. Making such information available to competitors without their having been required to undertake a similar expenditure of resources would unfairly provide competitors with a windfall, and deprive GNF-A of the opportunity to exercise its competitive advantage to seek an adequate return on its large investment in developing and obtaining these very valuable analytical tools.

I declare under penalty of perjury that the foregoing affidavit and the matters stated therein are true and correct to the best of my knowledge, information, and belief.

Executed at Wilmington, North Carolina this 24th day of March 2010.

Andrew A. Lingenfelter Vice President, Fuel Engineering Global Nuclear Fuel - Americas, LLC Affidavit for Enclosure 1 of GNF-A letter, JMD-EXN-HEO-10-020 Affidavit Page 3 of 3

ATTACHMENT 4 Response to Request for Additional Information (GNF Non-Proprietary Version)

Global Nuclear Fuel A Joint Venture ol GE, Toshiba, & Hilachi J. Michael Downs Global Nuclear Fuel - Americas, LLC Customer Project Manager Castle Hayne Road, Wilmington, NC 28401 March 24, 2010 JMD-EXN-HEO-10-020 Mr. Tom Loomis Exelon Nuclear 200 Exelon Way KSA-3E Kennett Square, PA 19348

Subject:

Responses to Request for Additional Information 52, 60 and 61 Related to License Amendment Request to Revise Technical Specification 4.3.1.1.A Concerning K-Infinity for Peach Bottom Atomic Power Station, Units 2 and 3

Dear Mr Loomis:

This letter transmits the Global Nuclear Fuel - Americas (GNF-A) responses to Request for Additional Information (RAI) 52, 60, and 61 Related to License Amendment Request to Revise Technical Specification 4.3.1.1.A Concerning K-Infinity for Peach Bottom Atomic Power Station, Units 2 and 3. contains the GNF-A response to the RAls 52, 60 and 61. Please note that Enclosure 1 contains proprietary information of the type that GNF-A maintains in confidence and withholds from public disclosure. The information has been handled and classified as proprietary to GNF as indicated in the enclosed affidavit. The affidavit contained in Enclosure 3 identifies that the information contained in has been handled and classified as proprietary to GNF-A. GNF-A hereby requests that the information in Enclosure 1 be withheld from public disclosure in accordance with the provisions of 10 CFR 2.390 and 9.17. Enclosure 2 is a non-proprietary version of Enclosure 1.

GNF-A requests that any transmittal of this proprietary information to the NRC be accompanied by the enclosed affidavit and proprietary notice. In order to maintain the applicability of the affidavit and to meet the requirements of 10CFR2.390, the transmittal to the NRC should:

1) Faithfully reproduce the proprietary information,

2) Preserve the proprietary annotations, and

3)

Include the words similar to "GNF-A Proprietary information" at the top of first page and each page containing the proprietary information.

Further, 10CFR2.390 requires that the proprietary information be incorporated, as far as possible into a separate paper. Therefore, Enclosure 1 hereto contains the proprietary information, and the non-proprietary and redacted information is provided in Enclosure 2.

JMD-EXN-HE0-10-020 Page 2 of 2 Based on past discussions with the NRC, GNF-A has been encouraged to request its customers to provide a paragraph similar to the following in the customer letters transmitting proprietary information to the NRC in order to clearly indicate the proprietary nature of the information and to document the source of the proprietary information as indicated in the GNF-A affidavit.

"The enclosed RAI responses contain proprietary information as defined by 10CFR2.390. GNF-A, as the owner of the proprietary information, has executed the enclosed affidavit, which identify that the enclosed proprietary information has been handled and classified as proprietary, is customarily held in confidence, and has been withheld from public disclosure. The proprietary information was provided to Exelon Nuclear in a GNF-A transmittal that is referenced by the affidavit. The proprietary information has been faithfully reproduced in the enclosed RAI responses such that the affidavit remains applicable. GNF-A hereby requests that the enclosed proprietary information be withheld from public disclosure in accordance with the provisions of 10CFR2.390 and 9.17. A non-proprietary version of the RAI responses also is provided."

A signed copy of this letter is also included in eDRF Section 0000-0115-7070. If you have any questions, please do not hesitate to contact me.

Sincerely, Customer Project Manager Enclosures

1. Responses to Request for Additional Information 52, 60, and 61, GNF-A Proprietary Information

2.

Responses to Request for Additional Information 52, 60, and 61, Non-Proprietary Information

3.

Affidavit for Enclosure 1

ENCLOSURE 2 JMD-EXN-HE0-10-020 Responses to Request for Additional Information 52, 60, and 61 Non-Proprietary Information IMPORTANT NOTICE This is a non-proprietary version of Enclosure 1 to JMD-EXN-HEO-10-020, which has the proprietary information removed. Portions of the document that have been removed are indicated by white space with an open and closed bracket as shown here ((

I].

JMD-EXN-HEO-10-020 Non-Proprietary Information Page 1 of 3

RAI 52

Provide the depletion parameters used in determining the limiting peak reactivity of the lattices evaluated. Justify those depletion parameters and identify how deviations from those parameters would affect the peak reactivity.

GNF Response:

The GNF2 lattices are depleted in the in-core infinite lattice critical configuration with the GNF standard depletion parameters from the GNF2 design basis document. These parameters are provided in Table 1 below and Table 9 of GNF-0000-01 10-5796-P Revision 0.

Table 1: Depletion Parameters Depletion Conditions Volumetric Power Density (kw/I) 50.0 Fuel Temperature (0C)

See Table 9 of GNF-0000-0110-5796-P Rev 0 Moderator Temperature (°C) 286.0 Moderator Liquid Density (g/cc) 0.73749 Moderator Vapor Density (g/cc) 0.03733 The lattice depletions are performed at three in-channel void fractions to simulate the variation in in-core operating conditions. The three in-channel conditions used to deplete the lattice are 00%, 40%, and 70% void fractions. These conditions form the parameter "void history". These three void histories create three sets of isotopic content as a function of lattice exposure (depletion). The isotopic content is then evaluated in the cold (200C), uncontrolled (control blade withdrawn) in-core configuration to determine the in-core cold reactivity as a function of exposure and void history. The maximum value of the in-core cold reactivity over this set of evaluations is determined to be the "peak in-core cold reactivity".

For high reactivity, high enrichment lattices, the gadolinium depletion rate is the dominant factor in determining the point of maximum cold reactivity. For lattices with gadolinium present, the peak in-core cold reactivity generally occurs in the 00% void history condition. This is a direct result of the rate of gadolinium depletion being maximized in the 00% in-channel void fraction condition.

In the BWR, the moderator temperature is effectively constant (saturation temperature). The variation of the in-channel void fraction accounts for the variation of the moderator density in the depletion process.

Sensitivity studies of the storage system reactivity to these depletion parameters are presented in Section 6.5 of NEDC-33374P, Rev. 3 "SAFETY ANALYSIS REPORT FOR FUEL STORAGE RACKS CRITICALITY ANALYSIS FOR ESBWR PLANTS", ADAMS No. ML093421411. These studies demonstrate that modifying the depletion parameters from their nominal values has a combined effect of less than 0.0014 Ak on the BWR spent fuel storage rack ker.

JMD-EXN-HE0-10-020 Non-Proprietary Information Page 2 of 3

RAI 60

GNF-0000-01 10-5796, Revision 0, states, "For fuel pool storage evaluations, the 95/95 bias uncertainty is used as a bias applied to the TGBLA in-core peak cold reactivity." This is the effect of an uncertainty when it is the only uncertainty considered. Please provide the justification for not considering the other uncertainties.

GNF Response:

It is recognized that the in-rack analysis is performed with a method that is different from the method used for in-core maximum cold reactivity evaluations. However, the in-core method (TGBLA) and the in-rack method (MCNP) can be used to analyze identical in-core conditions.

By modeling identical in-core conditions with these methods, a bias and uncertainty for differences in reactivity results between the two methods can be determined. This bias and uncertainty provides assurance that the TGBLA generated in-core cold reactivity is conservative relative to reactivity generated with the MCNP criticality method.

This bias and uncertainty is based on evaluations of a series of GNF2 lattice designs in the in-core configuration with both TGBLA and MCNP and includes the numerous dominant, and vanished bundle zones. This bias is based on an analysis of over 200 GNF2 TGBLA06 to MCNP in-core configuration comparisons over an extensive range of GNF2 designs. The evaluated exposure range was from beginning of life (0.0 GWd/st exposure) to 60.0 GWd/st and for depletions over the range of in-channel void fractions up to 70% in-channel void fractions.

Typical GNF2 design configurations with lattice average enrichments from 2.96% to 4.25%,

gadolinium rods from 2.0% to 7.0%, and part lengths rods were included in the evaluations.

This bias and uncertainty is incorporated in the design of the GNF2 design basis bundle such that the in-core reactivity limit (1.27) will conservatively limit the in-core reactivity of future lattice/bundle designs.

Other uncertainties such as depletion effects, geometry variations, and material variations are accounted for in the NETCO in-rack evaluations.

JMD-EXN-HEO-10-020 Non-Proprietary Information Page 3 of 3

RAI 61

GNF-0000-01 10-5796 indicates that the TGBLA06 bias and the 95/95 bias uncertainty are extracted from NEDE-24011-P-A-16, "General Electric Standard Application for Reactor Fuel (GESTAR II)", October 2007 (ADAMS Accession No. ML091340075). However, the NRC staff could not locate the TGBLA06 bias and the 95/95 bias uncertainty in NEDE-24011-P-A-16. Please provide clarification regarding the location of the TGBLA06 bias and the 95/95 bias uncertainty in a document currently on the NRC docket, or provide the information for the NRC staff s review.

GNF Response:

The "{3}" superscript associated with the in-core bias and uncertainty value is a component of the GNF proprietary markup as described in the affidavit. The bias and uncertainty values are not extracted from NEDE-2401 1-P-A-16. The internal GNF evaluations performed to determine this in-core bias and uncertainty are described in RAI 60 response.

The GNF bias and uncertainty evaluations for the ESBWR GE14E fuel product was reviewed by the NRC in 2009. The evaluation process for GNF2 is identical except for fuel product to the evaluation process for GE14E. In the review process for NEDC-33374P,"SAFETY ANALYSIS REPORT FOR FUEL STORAGE RACKS CRITICALITY ANALYSIS FOR ESBWR PLANTS", an NRC staff audit of the spent fuel storage rack methodology was performed. The NRC and ORNL participates in the review were Dennis Galvin, NRC - Project Manger, Bruce Bavol, NRC

- Project Manger, Jim Gilmer, NRC - Reviewer, Don Mueller, ORNL - Reviewer (contractor to NRC), and Davis Reed, ORNL - Reviewer (contractor to NRC), Jay Lee (part time)

NRC -

Reviewer. The following section was provided in the "LTR Rev 3 Feedback 101" dated 12/01/2009 as follow-up to this audit. Note that the bias and uncertainty in the following section are GE14E values.

2) Provide additional information on the calculation of the TGBLA06A eigenvalue uncertainty reported in Section 3.3 of NEDC-33374P.

The in-core characteristics of the design basis bundle/lattice are generated with the GNF lattice physics system TGBLA06. As part of a previous GNF proprietary analysis, a bias of ((

)) and a 1-sigma bias uncertainty of ((

)) have been calculated for in-core, peak, cold reactivities defined by this code for GE14 fuel types. These values are based on an analysis of TGBLA06 to MCNP comparisons. The TGBLA eigenvalue 95/95 uncertainty value of ((

)),

which will be used to update Revision 3 of the LTR and RAI responses, is based on the previously reported 1-sigma value of ((

)) with the application of a one-sided 95/95 upper tolerance limit multiplier.

In the GNF analysis, independent studies were performed to determine the bias and bias uncertainty values of both GNF2 and GE14 fuel types over an extensive range of application for in-core depletion. The evaluated exposure range considered was from beginning-of-life (0.0 exposure) to 60.0 Gwd/ST and for depletions at 0% in-channel void fractions through 70% in-channel void fractions.

Typical design configurations with lattice average enrichments from 2.96% to 4.25%, gadolinium rods from 2.0% to 7.0%, and part-length rods were included in the evaluation. The bias and bias uncertainty for both fuel types were shown to be similar, and overall good agreement with results calculated using the validated MCNP code was demonstrated.

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ATTACHMENT 6 RAI 58 - Naval Reactor Physics Handbook Material

NAVAL REACTORS PHYSICS

,HANDBOOK VOLUME I Selected Basic Techniques Volume Editor A. RADKOWSKY V.,

c,1 1964 Naval Reactors, Division of Reactor Development United States Atomic Energy Commission POLYTECHNV,[,

and pi ling detailed comments. Reactor physics today is such a +/-apidly growing field that future editions of this hand-book will undoubtedly be necessary. Criticism and suggestions by the readers will be welcomed and, if practicable, incor-porated in later editions.

The writer wishes to express his appreciation to Vice Admiral H. G. Rickover for suggesting the preparation of this handbook and for giving encouragement at all times. Special thanks are also due to Theodore Rockwell, il, Technical Director, Naval Reactors, for many helpful suggestions.

Finally, the writer is most grateful to all members of the Editorial Board and to all authors and chapter editors whose effort was essential to the preparation of these volumes.

A. Radkowsky Chairman, Editorial Board Naval Reactors Physics Handbook TABLE OF CONTENTS Page Chapter 1 REACTOR PHYSICS AND ITS APPLICATION TO NUCLEAR POWER REACTORS 1.1 Introduction......................

1.2 Reactor Physics and Nuclear Design of Naval Reactors........

1.3 Numerical Analysis and Digital Computer Programs.................

1.4 Selection and Verification of Calculational M odels............

1.5 Dependence of Design Detail on Performance Requirements....................

1.6 Summary.......................

Chapter 2 THE NEUTRON SLOWING-DOWN PROBLEM 2.1 Introduction......................

2.2 Calculation of Nuclear Cross Sections....

A.

Introduction...................

B.

General Considerations...........

C.

Optical Model.

D.

The Compound Nucleus Model.......

E.

The Direct Interaction Model.......

F.

Unified Treatment of Optical Model and Resonance Reactions...........

G.

Models of Nuclear Bound States.....

H.

Cross-Section Calculations 2.3 Slowing-Down Theory in a Uniform M edium........................

A.

Introduction...................

B.

Decomposition of the Transport Equation...................

C.

The Source Due to Elastic Scattering..

D.

Heavy Moderator Approximations....

E.

Expansion Coefficients for Heavy Mass Approximation....

F.

Termination of Series............

G.

Calculation of 7nL'..............

1 3

6 10 13 15 24 24 27 38 51 60 73 75 77 89 89 90 91 94 95 96 98 ix Viii

H.

Explicit Forms and Recursion Relations for the Quantities ThL..........

I.

Slowing-Down Density and the General-ized Greuling-Goertzel Approximation...................

J.

Slowing Down by Hydrogen..........

2.4 Monte Carlo Age Calculations in a Uniform Medium...............................

A.

Introduction.......................

B.

Theory...........................

C.

Neutron Distribution from a Plane Fission Source in Water..........

2.5 Resonance Capture A.

Introduction...................

B.

The Resonance Cross Sections......

C.

Analytical Models...............

D.

The One-Energy Problem.........

E.

The Practical Width.............

2.6 Multigroup Diffusion Theory...........

A.

Introduction...................

B.

The Group Diffusion Equations......

C.

Time Dependence and Criticality.....

D.

Computation Strategy............

E.

Boundary Conditions: Continuity at Interfaces..

F.

Adjoint Equations...............

G.

Space and Energy Self-Shielding.....

H.

Illustrative Example:

P, Multigroup,.

2.7 Multigroup Transport Theory..........

A.

Introduction...................

B.

Description and Discussion of the M ethod....................

C.

Angular Differencing...............

D.

Lethargy Differencing............

E.

Conclusions..

2.8 Few-Group Approximations.............

A.

Introduction...................

B.

Single Mode Model..............

C.

Group Equations D.

Special Forms of the Group Equations.

E.

The Time-Dependent Problem......

F.

Computation of Few-Group Constants.

2.9 Fast-Group Fitted Constants in Few-Group Theory.........................

A.

Introduction...................

B.

Fitted Cross-Section Scheme.......

C.

Computational Results............

D.

Variational Procedure for Calculating Fast Group Constants...........

Page 108 120 123 125 125 126 132 137 138 141 147 153 154 154 155 161 162 163 164 165 166 175 175 175 177 182 197 197 197 199 203 209 214 218 229 229 230 251 256 Chapter 3 TtIE NEUTRON THERMALIZATION PROBLEM 3.1 3.2 Introduction......................

Inelastic Scattering of Thermal Energy Neutrons.

A.

Introduction...................

B.

Theory of Scattering.............

C.

Applications..................

D.

Conclusions...................

3.3 Sensitivity to the Neutron Scattering Kernel.........

A.

Analysis of Thermal Neutron Spectra.

B.

Analysis of Thermal Diffusion Length.

3.4 Multigroup Theory.....................

A.

Introduction.......................

B.

Multienergy Transport Equation.....

C.

Solution of the Multigroup Equations in One Dimension.....

D.

Multigroup Monte Carlo Techniques...

3.5 Application of Monte Carlo Methods to Neutron Thermalization..............

A.

Introduction...................

B.

One-Group Thermal Model: TUT-T5.

C.

Three-Dimensional, Multigroup Program: TRAM.............

D.

One-Group Thermal Model with Slowing-Down: TRAC-1.........

E.

Normal and Adjoint Multithermal Group Model: MARC-I..............

3.6 Blackness Theory for Slabs...........

A.

Introduction...................

B.

Blackness Coefficients...........

C.

Matching Conditions.............

D.

Double Blackness...............

E.

Applications and Results..........

F.

Convenient Forms and Conclusions...

3.7 Approximations to Multigroup Methods...

A.

Introduction...................

B.

One-Group Models..............

C.

Conventional Few-Group Approximations...............

D.

Variational Approachto Thermal-Group Calculations.................

3.8 A Two-Mode Variational Procedure for Calculating Thermal-Diffusion Theory Parameterss......................

A,' Introduction...................

B.

General Formulation.............

Page 285

291, 291 293 312 330 332 332 339 351 351 353 365 379 381 381 382 388 395 403 411 411 414 419 436 439 443-450 450 452 459 480 496 496 500 xi x

C.

Procedure for Calculating Thermal Constants.......................

D.

Results..........................

Pagt 506 512 Chapter 4 REACTOR DESIGN TECHNIQUES V

4.1 Introduction......................

4.2 Treatment of Self-Shielding in Isolated P lates.........................

A.

Introduction...................

B.

Particle Self-Shielding in Plates Loaded with Spherical Poison Particles....

C.

Generalized Treatment of Particle Self-Shielding....................

D.

Representation of Plate Self-Shielding in Diffusion Theory............

4.3 Homogenization Techniques...........

A.

Introduction...................

B.

Methods of Obtaining Homogenized Constants from Cell Theory C.

Arrays of Epithermal Self-Shielded Absorbers..................

D.

The Validity of Cell Theory for Arrays of Absorbing Plates............

E.

The Validity of Cell Theory for Full Core Calculations....

F.

Cell Calculations with Nonzero-Current Boundary Conditions...........

G.

Summary.....................

4.4 Synthesis Methods....

A.

Introduction...................

B.

Single Channel Synthesis..........

C.

Multichannel Synthesis...........

D.

Variational Synthesis 4.5 Gross Fission Product Poisoning........

A.

Introduction.......................

B.

Analysis.........................

C.

Representative Numerical Results....

D.

Discussion of Results...............

4.6 Depletion Methods.

A.

Introduction...................

B.

Effective Microscopic Cross Sections..

C.

Number Density Calculations.......

D.

Depletion of Natural Uranium.......

E.

Integrated Depletion Systems.......

531 535 535 537 552 595 620 620 621 636 645 650 653 655 656 656 657 678 710 728 728 728 744 748 751 751 753 756 777 782 4.7 Burnable Poisons......................

A.

Introduction.....................

B.

Elementary Theory of Homogeneous Burnable Poisons in Thermal Reactors.....................

C.

Materials Suitable for Use as Burnable Poisons........................

D.

Self-Shielded Burnable Poisons.......

E.

Nonuniform Depletion Effects and Zoning.........................

F.

Application of Burnable Poisons to Cores with High U238 Content Fuels.

G.

Advanced Applications of Burnable Poison.........................

H.

Use of Burnable Poisons in Epithermal Reactors.....................

Chapter 5 REACTOR KINETICS 5.1 Introduction..........................

5.2 Neutron Kinetics......................

A.

Derivation of the Kinetics Equations B.

Physical Interpretation of the Adjoint Flux: Iterated Fission Probability C.

The Utility of the Kinetics Equations D.

Computation of Parameters in the Kinetics Equations................

5.3 Reactor System Kinetics................

A.

Inherent Stability...................

B.

Boiling Induced Reactivity Feedback C.

Self-Shutdown of Reactor Power Excursions......................

5.4 Space-Time Kinetics...................

A.

Introduction.......................

B.

The Instantaneous Tilt Method........

C.

Nodal Analysis.....................

D.

Modal Analysis....................

E.

Modal Analyses of Xenon Stability....

F.

Summary.........................

5.5 Kinetics of Low Source Level...........

A.

Introduction.......................

B.

Analysis of Low Source Startup.......

C.

Multiplicative Process with Feedback -

D.

Natural Reactor Sources............

Chapter 6 COMPARISONS OF INTEGRAL EXPERIMENTS WITH THEORY 6.1 Introduction..........................

Page 800 800 802 815 821 831 840 843 844 853 855 855 864 869 873 877 878 915 933 955 955 957 961' 966 977 1007 1010 1010 1013 1079 1085 1143 Xiii xii

6.2 Highly Enriched Clean Critical Experiments At Ambient Temperatures...............

A.

Clean Slab Experiments with Small Bundle Box Geometry.............

B.

Clean Slab Experiments with Repeating Plane Geometry..................

C.

Plastic-Moderated Critical Experiments....................

6.3 Highly Enriched Clean Critical Experiments at Elevated Temperatures..........

A.

Introduction........... *...........

B.

Description of Experiments..........

C.

Calculational Model................

D.

Results of Core Reactivity Calculations.

E.

Results of Activation Distribution Comparisons...................

F.

Conclusions......................

6.4 Investigations of Neutron Peaking in Highly Enriched Clean Critical Experiments A.

Introduction......................

B.

Experimental Arrangement..........

C.

Characteristics of Lattices..........

D.

Experimental Results...............

E.

Analysis.........................

F.

Conclusions......................

6.5 High U 28Content Critical Experiments at Ambient Temperature..................

A.

Introduction......................

B.

Effective U2 3 8 Resonance Capture In-tegrals in Rods and Lattices.......

C.

The Relative U2 3 5 Fission Activationas a Function of Energy in Slightly Enriched Uraniium-Water Lattices D.

Relative Pu and U2 3 5 Fission Rates in Water-Uranium Reactor Spectra..

6.6 Pulsed Neutron Source Measurements...

A.

Introduction......................

B.

Theory..........................

C.

Experimental Method...............

D.

The Far Subcritical Pulsed Neutron Technique......................

E.

Reactivity without Critical Calibration.

6.7 Low Energy Measurements of the Neutron Spectrum............................

A.

Introduction......................

B.

Experimental Method...............

C.

Details of the Chopper Design........

D.

Experimental Corrections...........

E.

Comparison of Calculated and Measured Spectra........................

F.

Conclusions......................

Page 1148 1148 1193 1203 1218 1218 1220 1229 1234 1238 1243 1245 1245 1246 1252 1254 1258 1271 1275 1-275 1276 1298 1308 1319 1319 1321 1332 1336 1351 1357 1357 1360 1369 1376 1390 Chapter 7 REACTOR PHYSICS COMPUTATION 7.1 Introduction..........................

A.

Digital Computers.................

B.

Programming Techniques...........

C.

Role of Analysis...................

7.2 Iteration Procedures in Neutron-Diffusion Calculations.........................

A.

Introduction......................

B.

Source Iterations...................

C.

Solution of the Group Equations.......

D.

The Time-Dependent Problem........

7.3 The Mathematics of Monte Carlo for Re-actor Calculation......................

A.

Introduction......................

B.

Random Walk Processes............

C.

Analog Processes..................

D.

Importance Sampling and Related Methods.......................

7.4 Digital Computer Programs for Reactor Physics Calculations...................

A.

Introduction......................

B.

Few-Group One-Dimensional Diffusion Theory...............

C.

Few-Group Two-Dimensional Diffusion Theory........................

D.

Few-Group Three-Dimensional Diffusion Theory.................

E.

Few-Group One-, Two-, and Three-Dimensional Depletion............

F.. Few-Group Constants Calculations..

G.

Approximations to Transport Theory..

H.

Monte Carlo Calculations............

I.

Theoretical Cross-Section Calculations.

J.

Perturbation Calculations...........

K.

Modal Calculations.................

CONTRIBUTING AUTHORS...........................

INDEX............................................

-,age 1405 1405 1410 1412.

1414 1414 1418 1426 1439 1441 1441 1442 1448 1455 1461 1461 1461 1463 1473 1475 1484 1489 1499 1507 1509-1509 1519 1521 XiV KV

'i30

'4A1VA L R E'A. rLfZr PHYlSIC:S f(ANDBOOK: ';I-Tf;I BASI. TEiNIQIt 126. F. D. FederighN and G. P. Calame, "Reactor Code Abstract No. 8," Nucl. Sci. Eng. 9, 416 (1961).

127. A. J. Buslik, "The Description of the Thermal Neutron Spatially Dependent Spectrum by Means of Variational Principles" in "Bettis Technical Review, Reactor Technology, " WAPD-BT-25, May 1962, pp. 1-24.

128. S, L. Shufler, "A Comparison of a Self-Adjoint Variational Method to 36-Group Thermal Spectrum Calculations of Heterogeneous Arrays," Trans. Am. Nucl. Soc. 5 (1), 37-39 (1962).

129. W. B. Wright and F. Feiner, "Spectrum Effects to the Surface of Water Gaps and Black Slabs," Trans. Am. Nucl. Soc. 2 (1),

246 (1959).

130. G.

P. Calame, F. D. Federighi, and P. A. Ombrellaro, "A Two Mode Variational Procedure for Calculating Thermal Diffusion Theory Parameters," Nuel. Sci. Eng. 10, 31-39 (1961).

131. J. A. Archibald, Jr., "The KARIR System for Computing Life Studies Automatically," Trans. Am. Nucl. Soc. 3 (1), 64-65 (1960).

I Chapter 4 REACTOR DESIGN TECHNIQUES R, S. Wick, Editor

4.1 INTRODUCTION

In this chapter the application of the theoretical concepts heretofore discussed on slowing-down theory and thermal spectra to determine the nuclear characteristics of reactors is described. The heterogeneous and three-dimensional nature of actual reactors must be taken into account by properly extending the appropriate theory to the particular case, which is usually far from the idealized case. After the various cal-culational techniques are discussed, the chapter concludes with a description of how the depletion characteristics of burnable poisons may be advantageously used by the nuclear designer to achieve desirable reactor characteristics, thus unifying the application of the calculational techniques. The general steps in a typical reactor analysis are shown in Fig.

4,1. These steps encompass progressively less microscopic detail of the reactor, and the topics in this chapter follow the same pattern.

Section 4.2, Treatment of Self-Shielding in Isolated Plates, presents a description of the determination of macroscopic cross sections, taking into account the fact that neutron absorb-ing material may be in the form of plates, rods, or discrete particles embedded in structural elements. The discussion includes an approximate technique for treating discrete parti-cles, in which a calculation model is assumed and compared to experiment, and a more sophisticated treatment of this problem, in which a theoretical and experimental basis for selecting a calculational model is developed. The section con-cludes with a descriptionof how the macroscopic cross sections are determined, taking into account the fact thatthe bulk of the principal neutron absorbing material is in the form of fuel plates or rods, control rod blades, and burnable poison ele-rnents which are surrounded by a moderator. These explicit elements often causeý major perturbations in the neutron flux.

531

532 NAVAL RE(ACTORS PH1YSICS HIANDBOOK: SELECTED IIA) C Es

-n"V n

tREACTOR DESIGN TECHNIQUES 533 In many calculations, larger regions of a core than se discussed in Sect. 4.2 can also be described by macroscopic 0 3 cross sections representative of the region containing discrete neutron absorbing elements. Section 4.3, Homogenization Tech-niques, treats the problem of determining the macroscopic cross sections of the larger regions. These larger regions, isolated as a basic unit for study, usually include a group of fuel elements and associated poison plates, control rods, structural supporting material, and moderator. (In many cases the fuel elements and associated coolant are first treated as a 9 S ag 7 0 V

-ogroup, as in Sects. 4.2.B and 4.2.C, before the larger unit is 4

considered.) Many of the same approximations described in the Ai 0: 0 section on self-shielding techniques, such as cell theory Ej _o boundary conditions, are also used to determine the macro-scopic cross sections of the larger regions. However, since qthe validity of the underlying assumptions of cell theory is more questionable for regions containing isolated absorbers, con-2 siderable discussion is devoted to the inaccuracies inherent g

EI Cd

_*in the use of cell theory to obtain effective cross sections for O

such regions.

1.1V 3U" The next topic, Synthesis Methods (Sect. 4.4), describes how, given an arbitrary spatial distribution of diffusion theory param-eters, the kinetic (see Chap. 5) and static characteristics of 14_,the core can be calculated from sets of calculations encom-

o.

0 passing less than the complete core. For example, it is often V

0 X

.*possible (because of computer limitations) or desirable (for E

economic reasons) to perform only two-dimensional radial cal-Z S W-culations through a core and then axially to combine a number

,of these calculations to describe the entire core, a procedure 2

0 CY

• termed synthesis. The availability of three -dimensional compu-ter codes permits the checking of the accuracy of synthesis W

techniques for test cases (see Chap. 7). In most practical

-C coupling of these planes is sought. Where the fuel and poison 4

't*

have been partially depleted, or where control rods have been moved in or out of various axial regions of the core, or both, a core with a continuous variation in the composition of each axial plane results. Thus, as is brought out in detail in the next section, synthesis calculations over reactor life usually "Y =are not isolated from the concurrent depletion calculations.

So'

,However, to emphasize the synthesis technique, it is assumed 2

• for the purpose of discussion that the macroscopic cross sec-14, Q W tions in each plane are known at the particular time of interest 0

0 and that a three-dimensional steady-state power distribution 9

is desired. The section discusses single channel synthesis and advanced techniques. The single channel synthesis method, the simplest approach to coupling together axially the radial slices

,4 NAVAL REACTORS PHYSICS HIANDBIOO)K: SELECTED BASIC TECIINIQ1.

of the core, uses only a single set of axial coupling factors.

Discussion of advanced techniques for coupling together axially the radial slices, such as the multichannel approach and variational techniques, deals with improved descriptions of more complicated configurations, especially for those cases where radial and axial separability of the flux is not a good approximation.

The next step in the reactor analysis sequence is to determiine the depletion characteristics of the core. Before this can be done, information on the cross sections of the fission fragments must be available, because their poisoning effect is an important factor in the design of cores with high fuel depletions and long lifetimes. In Sect. 4.,5, a method of combining experimental information on individual fission products into a total fission product treatment is described.

Section 4.6, Depletion Methods, answers the question:

Given a spatial distribution of fuel and poison inventory (fixed and movable), the corresponding spatial distribution of cross sec-tions, and the average temperature and powerlevel of the core, what will the spatial distribution of fuel and poison inventory and the corresponding spatial distribution of cross sections be at a later time?

It is assumed that some method of calculating the spatial distribution of flux, given the spatial distribution of cross sections corresponding to the fuel and poison inventory, is available; but such a calculation is not in itself considered to be part of the depletion calculation in this section, since It has been discussed in Sect. 4.4. The depletion calculation for a core is usually broken down into a number of time intervals, depending on the rapidity of the changes in core characteristics.

Thus, the calculation of the depletion process defined here has been divided into: (1) the calculation of the change in the spatial distribution of the fuel and poison inventory with time and (2) the calculation or, more properly, the recalculation of the spatial distribution of macroscopic cross sections at the end of the time interval. These will be emphasized separately by first discussing the time dependence of the effective micro-scopic cross sections, considering separately those cross sec.-

tions which vary relatively rapidly with time, because of either neutron spectrum changes or inventory changes, and those which vary relatively slowly. The limitations of computer capacities, the accuracy of various theoretical approaches, and the economics of computer utilization dictate the use of many approxidmate methods in depletion calculations. The approximate methods used to incorporate the changing cross sections and fluxes during a time interval into the calculation of the inventory change during the same time interval are, thus, described for REACTOR DESIGN TECHNIQUES 535 the case where the changes in cross section with time are relatively rapid. Next, the determination of the time dependence, ile., the actual depletion equations, of the number densities is treated, taking into account the time variation of the cross sections. Finally, two integrated depletion systems, which actually include the spatial synthesis described in Sect. 4.4 and the depletion described in this section, are described.

Section 4.7, Burnable Poisons, describes, from a conceptual point of view rather than from a detailed calculational point of view, the special features of cores which employ burnable poisons as a means of obtaining desirable reactor characteris-tics. Thus, this section complements the preceding analysis techniques by illustrating how these techniques may be used in the development of a specific type of core design.

4.2 TREATMiENT OF SEI.F-SIIIF.LOING IN ISOLATED PLATES A. Introduction Neutron absorbing materials (fuel, burnable poisons, non-burnable poisons, and parasitic poisons) are present in pressur-ized water reactors in the form of plates or cylinders cooled by water and supported by associated structure. These plates (or rods) may be placed in the core in a manner such that they are relatively isolated from similar plates of the same type (for Kexample, cruciform or cylindrical control rods), or they may be placed in uniform arrays (such as fuel plates or rods posi-tioned on a more or less uniform array within a cluster or module which makes up the basic fueled assembly of the core).

Further, neutron absorbing material in the form of discrete particles may be embedded in different elements of the clusteI7_

(For a description of the mechanical arrangement of fuel plates, fuel rods, and cruciform control rods in the Pressurized Water Reactor (PWR) core which, for the purpose of discussion tn this volume, may be considered as typical of pressurized water reactors, see Chap. 4 of Ref. 1.) A basic problem in the analysis of such geometric arrangements of neutron absorbing material is the appropriate determination of spatially and energy-averaged macroscopic cross sections which, when multiplied by the appropriately averaged neutron flux, yield the neutron absorption rates of these components. (These macroscopic cross sections are hereafter referred to as the effective macroscopic cross sections.) Thus, the true absorp-t, ion must first be determined for these cases of nonuniform flux and material distribution.

5.

NAVAL R TA(IORS PIlYSI(S IIANDBO)K: SL.FCr'TI):j BASIC TECIINIQI~..S Since, in general, the spatial and energy dependence of the flux obtained from an exact solution of the neutron transport equations is not separable, and since the solution depends on the boundary conditions, approximations must be made regarding the degree to which neutron absorption and the effective macroscopic cross sections can be geometrically localized.

In addition, assumptions regarding separability of space and energy must often be made to permit a mathematically tractable solution.

A reasonable basis for determining the degree of detail with which a particular localized portion of a reactor can and should be examined is the degree to which the spatial and energy dependence of the neutron flux is separable. As the area des-cribed in the calculation is increased, a coarser description of the spatial and energy interdependence can often be assumed.

Generally, more refined calculations for simple one-dimen-sional geometries can be performed and the effect of assuming separability estimated for the more complicated geometries on the basis of this comparison.

The effect of portions of a physical particle, plate, or rod shielding the other portions from the incident flux is defined as spatial self-shielding. There is an additional energy self-shielding phenomenon caused by the suppression of the neutron flux level at the energy under consideration because of the strong neutron absorption at a somewhat higher energy which acts as a source of neutrons for the energy in question (see Chap.

2). The discussion of self-shielding starts with the smallest units of neutron absorbing material, the particle, and then progresses to the larger units, such as rods and plates, arrays of plates, control rods, etc. Section 4.2.B presents a relatively simple method of treating particle self-shielding along with a comparison to experiment.

Since experimental results are limited as to the range of the neutron optical diameters of the particles, the volume fraction of highly absorbing particles in the plates or rods, and the number of types of absorbing particles, a more generalized treatment is given in Sect. 4.2. C. (In general, however, because of materials limitations it is expected that the formulation of Sect. 4.2.B will be adequate for most applications.) The discus-sion in Sect. 4.2.C is a much more elaborate and generalized treatment of particle self-shielding, stressing the theoretical aspects. In addition, it also discusses how the geometric factors which describe the particle distribution in space may be estimated experimentally, as contrasted to the technique in Sect 4.2.B which assumes a particle distribution. This verygeneral.

ized treatment is shown in the limiting condition of zero volume fraction to reduce to the resultof Hurwitz and Zwelfel 2 REACTOR DESIGN TECHNIQUES 507 and also, in the case of a single particle type, to the resu. A Doub described in Sect. 4.2.B. At present the theoretical approach of Sect. 4.2.C with its potential flexibility due to a larger number of parameters must be considered exploratory in nature. Section 4.2.D discusses the explicit representation of self-shielded plates in diffusion theory.

B, Particle Self-Shielding in Plates !Loaded with Spherical Poison Particles W. B. Doub

1. rntroduction The self-shielding properties of an unordered system of small poison spheres bound together in a neutral plate-type matrix are investigated in this discussion.

The problem has been solved by Case, et al,, 3 for the case of one poison sphere placed in a uniform neutron flux. The results of Ref. 3 have been extended exactly by Hurwitz and Zweifel 2 to the general case, with the restriction that the volume fraction of poison particles in the plate be small. For this case, Hurwitz and Zweifel found that the transmission of the plate is duplicated by another plate of the same size having a factor f. times as much poison material distributed homogeneously in it.

The factor fo (particle self-shielding factor) is identical to the disadvantage factor P, (escape probability) which Case, et al., computed for the case of a single sphere in a uniform flux. An attempt to extend these results to the case of arbitrary volume fraction has been made by Burrus 4, 5 using heuristic arguments. He assumed the plate to be composed of slices, each of thickness equal to the average chord length of the spherical poison particles (= 4/3 radius).

The average transmission of a single slice was computed on the basis of the fractional voids in the slice (= I - V, where v =

poison volume fraction) and also by the expression of Case, etal., for average transmission through a poison sphere. Then, the total transmission was taken to be the product of all the slice transmissions. As will be seen shortly, his formulation, though giving fair agreement with experiment, apparently neg-lects the ordering of the poison spheres due to the geometrical shape of the spheres themselves. The term ordering is used to denote any process which tends to make the neutron path lengths in the poison material in the plate less variable (i.e.,

it tends to make the plate poison apparently more homogeneous).

In this discussiop, an alternative approximate method has been used to compute the case of arbitrary poison volume fraction. It gives good agreement with experiment.

NAVAL REACTONS PH~icsjC JIANDJ3OOK: SEM).C(TED BASIC TECHfNIQr.

. JEACTOR DESIGN TECHNIQVES 39

[:!}!

In Sect. 4.2.B.2, a theoretical expression is derived for the particle self-shielding factor, f, for a set of uniform poison spheres of radius r randomly distributed ina matrix composed of nonabsorbing spheres of radius r. The above expression is extended to include the case when the matrix is also absorb.

ing. In Sect. 4.2.B.3, an experiment is described and analyzed in which the particle self-shielding factor for a mixture 01 boron carbide spheres and aluminum spheres is determined, using measured transmissions of monoenergetic neutrons. In Sect. 4.2.B.4, the experimentally determined particle self-shielding factor referred to above is compared with the theoretical particle self-shielding factors of Burrus, 4, 5 Hurwitz and Zweifel, 2 and this discussion.

2.

Theory The model is as follows:

The purely absorbing poison parti-cles of radius r are assumed to be embedded randomly in a plate of thickness a and having a homogeneous binding material with absorption but no scattering. The average transmission per neutron through the plate for neutrons incident at an angle '; = arc cos u is (Fig. 4.2) there C = total neutron path length contained in poison particles Y= macroscopic absorption cross section of a poison particle

[2= macroscopic absorption cross section of the binder

= oa ip = length of the neutron path in the plate PfC)dC fraction of neutron paths (at fixed angle of incidence) which pass through a length C to C t dC of poison particles.

Equation (4.1) reduces to T (2 Y-,) =

2 T(

1 2'0)

Eq. (4.2)

Thus, the problem is reduced to finding the transmission of the tame set of poison particles, but with macroscopic absorption I-2 and with a binder having no absorption. The trans-mission in this case is T(YI, 2 T v-T(Z 0) = fp(CQe_2CdC.

Eq. (4.3)

P(C exp [

C-g -C}X Y, dC Eq. (4.1)

I it is now assumed that when a neutron path intersects a poison particle the neutron is transmitted through the particle with a probability

- (the average neutron transmission per neutron-particle collision), Eq. (4.3) takes the form NEUTRON LINE OF FLIGHT M

r P-()

Eq. (4.4) where number of poison particles whose centers lie in a volume element formed by the intersection of the plate and a cylinder of radius r whose axis coincides with the neutron path (Fig. 4.2) p(w = probability that the above type volume element contains the centers of x poison particles (keeping the angle of incidence fixed)

A= maximum number of poison particles possible in the volume element under consideration (Fig. 4.2).

FIGURE 4.2. Schematic Showing Plate Geometry and Typical Neutron Line of Flight with its Associated Volume Element. (Any sphere whose center lies in the volume element will be intersected by the neutron line of flight [not to scale].)

NAVAL RVA(

fTORS PHYSICS IHANDBOOK: 5lLI.-1 7E1)D IASIC TECHJNIQVI To determine prx), the following model is postulated which allows the poison particle positions tobe influenced by crowding (i.e., two particles may not occupy the same position).* The division of the plate into cells is postulated. Each cell may contain either a poison particle or a portion of the matrix mate rial. The total number of cells in the small volume element referred to above (Fig. 4.2) is set equal to M. The above model implies that the binding matrix consists of spheres of the same radius as the poison spheres. In this case, the appropriate distribution, p(xj, is hypergeoxnetric 6 or, what is essentially equivalent, Bernoulli's binomial distribution. 5,6 However, the initial Eqs. (4.1) and (4.2) depend on the postulate of a homo-geneous binding matrix. Thus, to obtain a workable solution to the problem, two mutually exclusive assumptions have been used, i.e., that the binding matrix is homogeneous and that it is particulated. However, if the spheres of a particulated bind-ing matrix are nonself-shielded with respect to both absorption and scattering, they may be homogenized to allow the applica-tion of Eqs. (4.1) and (4.2). This is a very good approximation for the experimental sample discussed in Sect. 4,2.B. 3. It is not certain whether one can reconcile the above two contradictory assumptions for the case of a homogeneous binding matrix; for, though Eqs. (4. 1) and (4.2) apply, one no longer has the assump-tion of a particulated binding matrix and can no longer apply the same rules of probability to obtain a hypergeometric or binomial distribution for p (z). In the limit of very high volume fraction of poison spheres, the distribution p1fx) is uninfluenced by whether the binder is particulated or not, since almost every cell is occupiedby a poison sphere. Also, as will be seen, the hypergeometric or binomial distribution leads to an exact expression for the particle self-shielding in the limit of zero volume fraction. Thus, for very high and very low volume fractions, the above model is insensitive to whether the binding matrix is particulated or homogeneous. However, for volume fractions away from these limits (near 0.5, for instance),,,(,)

will depend upon the particulation of the binding matrix.

The binomial distribution is chosen because it is easier to work with:

I REACTOR DESIGN TECHNIQUES 541

" umber fraction = fraction of cells in the sample ccupied by poison spheres. Since the number of cells in the sample has been set equal to the maximum numberOf poisOn spheres which could be packed into the sample volume, one W the following relatiow.

I V = gV1 Eq. (4.6) rhere V fraction of the geometrical sample 'volume occupied by the poison spheres.

A fraction of the geometrical sample volume which is occupied by the set of poison spheres plus matrix spheres.

The theoretical value of 9 for perfectly packed spheres is 0.707 However, for loosely packed spheres this value may drop as low as 0.5 to 0.6. Since the sample used in the present exriment was firmly packed, the maximum theoretical value 0.740 was used.

'Now, substituting Eq. (4.5) into Eq. k4. 4) 1}:

M M~

Eq..(4.7 Eq.. (4.7)

-. (V} )

+ l-VI)if

'here the binomial theorem has been used. There is also the obvious relationship P (X) = (,X,)

IVf(i VI).V-x Eq. (4.5) or 41-g 0/0~r 4

Eq. (4.8) where (a b b!(a-b)!

The particle self-shielding factor f will now be defined:

T 7ep(-1VY'J.

Eq. (4.9)

• lThis derivauon is somewtiat stmdiar to that presentedh by EBurrus.

5

j 542 AVAI. RU-AMTORS PHYSICS HANDBlOOK: SlAJ.-CrTl) 11ASI: TE*:CfNJQUFS Since i j - represents the optical path of the homogenized poison,

/ may be interpreted as the fraction of the original poison material which, when homogenized, will give the same trans-mission as the original sample.

Combining Eq. (4.6), (4.7), (4.8), and (4.9), one has for the particle sell-shielding factor f = 2 y(V/)

-(P/g)(I-i)

Eq. (4.10) where r 2rl, From now on take g 0,740, so that V = 0.740 V Eq. (4.11)

A reasonable assumption for 7 is that it is the same as the transmission of a uniform current incident on a poison particle: 3 *

'ACTOR DESIGN TECHNIQUES t ý Y

- ( 1

+ Y )e - j.

Eq. (4.121 2

3 4

Yodl CE)

The particle self-shielding function f in Eq. (4.10) is plotted in Fig. 4.3 as a function of the optical diameter y and the number fraction V1.

3. Experimental Results Transmission measurements were performed on a sample containing 37 volume percent natural boron carbide spheres t of 87 A mass-average radius. The measurements were per-formed at Brookhaven National Laboratory using a high resolu-tion neutron crystal spectrometer. The transmission of this sample was measured at five neutron energies ranging from 0.03 to 1.23 ev. The measurements at 0.03 ev corresponded to an optical diameter (2, 2) in the boron carbide particles of approximately 0.5 to 0.6. Using the experimentally determined transmissions, the particle self-shielding factor was computed from an expression equivalent to Eq. (4.9).

A) SAMPLE DESCRIPTION. The various physical param-eters of interest in the sample are presented in Table 4.1.

• Reference 3 derives Eq. (4.12) for a sphere placed in a uniform isotropic flux, but the same expression holds for a uniform current.

f Obtained from the American Lava Corporation.

FIGURE 4.3. Particle Self-Shielding Factor vs Optical Diameter of Particle and Volume Fraction of Poison.

The sample contains a mixture of natural boron carbide spheres and aluminum spheres. The aluminum is used to dilute the boron carbide to the proper volume percent. This mixture is contained in an aluminum form of well-defined geometry, so that the thickness of the target mixture is uniform. An alterna-tive method of holding the sample together by compacting the mixture under high pressure was not preferred for fear of cracking the boron carbide spheres, thus risking vitiation of measurements.

The density of the boron carbide particles was measured by comparing their density to that of a known fluid. The density of the fluid mixture (acetone and acetylene tetrabromide

!C1,a/ 2 1I) was varied until the particles were balanced, i.e.,

half the particles floated and half did not. A volume displace-ment type measurement was not feasible because of the limited quantity of particles available.

The size distribution of the boron carbide spheres was measured by analyzing a photomicrograph of a portion of the sample (Fig. 4.4). An average mass-weighted diameter was computed from the measured distribution (Fig. 4.5).

NAVAL RFA CUTO RS PHIYIJ('S 1IANI)MIO

,K: S

'I.E'( TII) BASIC TI TABLE 4.1 -

PHYSICAL PARAMETERS OF THE SAM Thickness of boron carbide in mixture, g/cm 2 Thickness of aluminum in mixture, g/cm 2 al, thickness of mixture, cm a 3, thickness of aluminum in beam but external to mixture, cm Density of aluminum, g/cm3 Density of boron carbide, g/cm 3 VAI, volume fraction of aluminum in mixture V

volume fraction of boron carbide in mixture BC' d.,

average mass-wei hted particle diameter of A'4boron carbide, 10-cm Particle diameter range of aluminum spheres, 10-4 cm Boron in boron carbide particles, weight percent Carbon in boron carbide particles, weight percent Boron-to-carbon atom ratio in boron carbide particles E(.1INIQIi PLE

0. 1377 0.09124

0. 1529

0. 3259 2.70 2.41 0.2210

0. 3737 86.9 53-74 72.4 24.0 3.35

• a.

FIGURE 4.4. photomicrograph of a Portion of the Spheres Used in the Transmission Sample: 100 X.

1EACTOR DESIGN TECHNIQUES Boron Carbide The boron-to-carbon atom ratio in the particles was deter-mined from chemical analyses of a portion of the sample. It will be noted that this ratio and the density of the particles are not the book values. Presumably, this is caused by an excess of carbon present during the manufacture of the particles.

B) EXPERIMENTAL ARRANGEMENT AND PROCEDURE.

A description of the crystal spectrometer used for the trans-mission measurements is given in Ref. 8. A schematic of the experimental arrangement is shown in Fig. 4.6. After adjusting the Bragg angle P to give the desired neutron energy, the following measurements were made on the sample:

1. Sample out of beam (a)

C0, on-Bragg counts and M0, monitor counts (b) 8L?, off-Bragg counts and At %, monitor counts

2. Sample in beam (a) C, on-Bragg counts and Al, monitor counts (b) 8, off-Bragg counts and At., monitor counts The off-Bragg counts were obtained by rotating the crystal off the Bragg angle by an amount slightly larger than the resolution 0W 12 10 a

55 58

& 64 67 707376 798285 88 9 94 97 100 03 106 09 PARTICLE DIAMETERI microns FIGURE 4.5. Histogram Showing Size Distribution of the Boron Carbide Spheres in the Sample.

INCIDENT NEUTRON SOLLER M_

EIZOETECTOR COLLIMATORS FIGURE 4.6. Schematic Showing Experimental Arrangement for the TransmissiOrI Measurements.

547 546

.\\AI. RIACT.1'OR' PHYSI( S HIANDIBOOK: S1.1 I

1:1CTI)D HASIC TI-(CHN1Il P6 of the instrument. This measured the background associated with the on-Bragg counts. The experimental transmission Is C

I T

Al Al8 CM Bo M0 M0 Eq. (4.13)

,-OR DESIGN TECHNIQUES

, each section is equal to the gross boron carbide volume

!mction, i.e., b a,(V'/V C).

The model shown can now be

&alyzed. The total transmission is the product of the transmis-dons of each section shown in Fig. 4.7 (C). The transmission d the section containing boron carbide particles of diameter d, igiven by Eq. (4.2), i.e.,

Ti(

BC,. if ) -

(exp -

b-F11) Tj 0711C -' 111, )

Eq. (4.15)

TABLE 4.2 -

EXPERIMENTAL TRANSMISSIONS Table 4.2 presents the experimental results.

C) ANALYSIS OF EXPERIMENT.

The interpretation of the transmission data in terms of a particle self-shielding factor equivalent to Eq. (4.9) is complicated by:

1. Scattering as well as absorption is present.

2.

The neutron beam traverses a portion of the aluminum sample holder as well as the mixture of boron carbide and aluminum particles.

3.

The boron carbide particles are distributed in size.

In transmission measurements a scattering produces the same result as an absorption, i.e., removal from the incident beam. Thus, all results will hold if the absorption cross sec-tions used previously are replaced with total cross sections.

The effect of the pure aluminum structure in the path of the beam is subtracted out by computing its transmission from the known aluminum macroscopic cross section. Finally, the parti-cle size distribution is accounted for by reducing the real sample to one which can be analyzed. The steps in this process are shown in Fig. 4.7, where the upper part (A) schematically shows the real arrangement and the middle part (B) shows that the aluminum particles have been homogenized over the region of the mixture but outside the boron carbide particles. The macroscopic cross section of the homogenized aluminum is Y' and is related to the pure aluminum cross section by A) e goo VAl 1

!4 H I I/8 Eq. (4.14)

S)

C)

EDIm

• Vi bi

-ot "vac vi Vac V1 VAI ZAV where v,

= volume fraction of aluminum in the mixture

• RC = volume fraction of boron carbide in the mixture 2Al

= pure aluminum macroscopic cross section.

In Fig. 4.7 (C), the boron carbide particles with diameters d!.

2....

and partial volume fractions V. V2,

, have been grouped in separate sections of the sample. The thickness, bi, of each section has been adjusted so that the volume fraction FIGURE 4.7. Schematic Showing Progressive Approximations Made in the Model of the Sample.

V

'48 NAVAL RKFA(U()RKS PhYSICS IIANDIlIOOK: SI"LI{C(T:.IE)

BASIC T"ECHNI*"'

-nere Ic

= macroscopic cross section of the boron carbide spheres. Using Eq. (4.9),

Ti.(2Bc,-1 H', 0)> exp [-bj(XBC-*,) 'Scf. I - Eq. (4.16)1 Since the total transmission through the sample is the product of the individual element transmissions, UACTOR DESIGN TECHNIQUES perior to chemical analysis, for even if the cheml SUpio te (actuall about 3 percent) the final value of Walysis is accurate (actually au dfr h

sooi will depend upon the value assumed for the isotopic Sjndance of B1 0 (an uncertain number). Thevalueof aVBCC I8? the highest energy El(= 1.23 ev) is given by inverting t4.(4.17):

1 8C B)-a1),/E 1

[-

VcfrE1

)

_ A Wl "

<9 7'-- exp {-a 3.y 41i-a1-2 H-1 VC( (BC-- 2 )T }

where i

B C yj =di(Z8 c-28)

Eq. (4.171 Eq. (4.18a)

Eq. (4.18b)

Eq. (4. 180 from Eq. (4.10), and By inverting Eq. (4.17) and using the experimental transmis-sions T = T given in Table 4.2, one may solve for f= To, the experimental particle self-shielding factor. Then, according to the model, this experimental value should be compared to a volume fraction-weighted (or mass-weighted) theoretical f =

as given by Eqs. (4.10) and (4.18).

D)

SUMMARY

OF COMPUTATIONS.

A summary of the method used to obtain the results shown in Fig. 4.8 is given below.

The experimental 7, i.e., f[,

is given by inverting Eq. (4.17):

i N

r'q, I,.

Ion 0.96 M

CAORBD SPHERESNG

/NATURAL BORON CRI S

E S

DISPERSED NALUMINUM PLATE

/

TYPE MATRIX

/

S M sASWEIGHTED DIAMETER 86ORIN

/

VOLUME FRACTION T 0.375T7

~0.9 EX 7PERIMENTAL Vu O.74V 1

O

.373 T

0 " ~

pE~

A

,(SELF

-SHIELDING THEORETICAL FACTO CODN

• ,86 NORMALIZATIONý TO DOUBRT 0.84EXPERIMENTAL (SE LF.-SN'iELDiNG 0.8k.

THEORETICAL rFACTOR ACCORDING

-a NORMALIZATION)

To SURRUS) 0.82 EXPERIMENTALJ I(SECLýFt;HIELOiNG I

THERETCA FACTOR ACCORDING TO 0,60 I NORMALIZATIO 9 1IURWITZ ANDWEEL 0.7 o.1 1.0 10.0 0.01 INCIDENT NEUTRON ENERGY, av T

I

)

a A -

a, Y11 I V 8c BC. _a-V8c*j Eq. (4.19)

The value of the term aIV/BCc in Eq. (4.19) is inferred at the highest energy (1.23 ev) from the experimental transmission (Table 4.2) and a theoretical f given by Eq. (4.18), i.e., the values of the experimental and theoretical particle self-shielding factors are normalized at the highest energy. The value of the term aIV/C BC at all lower energies is computed using the I,

law for the boron cross section. This method for determining, in effect, the total amount of boron is accurate, even though it depends upon the use of an f whose validity is being tested, because / is close to one at high energy (1.23 ev) and will be insensitive to errors in theory. It is believed that this method 7

F.comarison of Experimental and Theoretical Self-FIGURE 4 8.

a G by Eq. (4.10) Burru.,4' 5 and Hurwitz and iel RespectvelY. (All experimental points at the same energy are inferred from the same data. The separation of points in the figures is caused by the different self-shielding factors used in the normalization 4Lt the highest energy-)

I.' ~

NAVAl. R[A CT(

URS PiYsIC:s HIAN DOf OK: sBAjSr'r ) I CASl(:

TI-CHNIQ[J The value of f(E,) is given by Eqs. (4.10) and (4.18). The value of T, (E ) is given in Table 4.2. The value of aIV8CIBC at any other energy is given by REACTOR DESIGN TECHNIQUES 551 where 1 C )

I BC C

LR(E)

J

,)B

+

+

)c R (E)

+

%7

= boron-to-carbon atom rat the boron carbide particle (a + %)c = 4. 8 barns (o,)B = 4 barns Eq. (4.21b) io in s

(,c(2200 m/sec) ) = 755 barns Equation (4.21) expresses the I/,, absorption law andalso con-tains scattering terms.

The theoretical value of f is given by Eqs. (4.10), (4.12), and (4.18) and is to be compared with the experimental value in Eq. (4.19). The computations indicated in these equations are tedious; an approximation has been made. One makes the approximation that f is linear in Y over the range covered in the experiment (o '- Y !- 0.65; Fig. 4.3), i.e.,

The volume fraction V,,,: in the denominator of Eq. (4.23) is determined from the measured mass and density of the boron carbide and the known volume of the sample container.

4. Discussion of Results The experimental and theoretical values of T expressed in Eqs. (4.19) and (4.22), respectively, are compared in Fig. 4.8.

The experimental and theoretical points have been forced to-gether at the highest energy, as explained in Sect. 4.2.B.3.

As can be seen, the agreement is good, thus validating the expression in Eq. (4.10) for the particle self-shielding. The particle self-shielding expression in Eq. (4.10) reduces in the limit of zero volume fraction to that given by Hurwitz and Zweifel. Since the Hurwitz-Zweifel calculations were exact in the same limit, the expression in Eq. (4.10) is exact for zero volume fraction. Also, experiment has verified the expression in Eq. (4.10) at 0.37 volume fraction. Thus, the expression in Eq. (4.10) is accurate at least in the zero to 40 volume percent range (and at least for optical particle diameters up to 0.7).

The shaded area in Fig. 4.3 is a reasonable extrapolation of the range of I1 and y for which Eq. (4.10) is likely to be valid.

In general, because of materials limitations it can be expected that most applications will be in this range.

For purposes of comparison and to ensure that the experi-mental method employed here is a fairly sensitive check, two alternative expressions for f have also been compared with experiment. The first expression is that given by Hurwitz and Zweifel, 2 and the second is that given by Burrus. 4,5 The com-parisons were made in the same manner as for the particle self-shielding factor of this discussion. These are shown also in Fig. 4.8, where all experimental points at the same energy represent the same experimental data. The separation of the points is induced by different theoretical f's used in the normal-izations at the highest energy. It is seen that the Hurwitz-Zweifel expression gives quite poor agreement and underesti-mates the particle self-shielding factor. The Burrus expression gives much better agreement with experiment but still not as good as Eq. (4.10). It also underestimates the particle self-shielding factor.

The particle self-shielding expression in Eq. (4.10) reduces to that of Hurwitz and Zweifel if one sets V = o. The same expression reduces to the Burrus' expression if one sets g = 1.

These observations are consistent with the following interpretation.

1?

~

441' f()=f(Y A +

f)

(Y - Y)

Y _Y where YA = mass-averaged value of y

= da(sBC-a g

d) daa = mass-averaged diameter of the boron carbide spheres.

Then, it follows that

=h

= f(d, [Y c..- T'/, 8c)

Eq. (4.22) that is, the theoretical T is computed as if all the poison spheres had a uniform diameter d,,. The value of XB,* in Eq. (4.22) is given by Eq. (4.21), i.e.,

aI VRC *BC(E)

BSC a VEq.

(4.23) a 1BC

'5 NAVAL REACTORS PHYSICS HANDBOOK: SELECTED BASIC TECHNIQUE' The Hurwitz-Zweifel expression is derived on the basis of complete freedom of placement of the poison particles in the sample (true for low volume fractions) and does not allow for the mutual exclusion of one particle by another from a given position in the sample. The Burrus expression, on the other hand, does take into account the mutual exclusion of one particle by another, but does so only on the basis of aligned particles which are cubic in shape. If the particles are spherical in shape, the resulting extra effectiveness of mutual exclusion is reflected by choosing g = 0.74 (or less for loosely packed samples). This, in effect, increases the volume excluded from the last poison particle placed in the sample from v to v/0.74.

In any case, too great a freedom of position of the poison parti-cles implies too great a variation in poison particle number density from point to point which, in turn, implies that the plate optical thickness has too much variation. Hence, the particle self-shielding factor is too small. As can be seen from Fig. 4.8, both the magnitudes and directions of the dis-crepancies of the Hurwitz-Zweifel and Burrus self-shielding expressions from experiment are consistent with the above interpretation. It is evident that the particle self-shielding factor must depend upon the volume fraction of poison particles in the sample, since near zero volume percent the factor is given by the Hurwitz-Zweifel expression, and near 100 volume percent it is 1.0.

It is of interest to note that, in the expression in Eq. (4.10) for the particle self-shielding factor, no parameters appear which depend upon the geometry, i.e., one may take the particle self-shielding function E(effective, object)

Y(homogeneous, object) to be independent of the object geometry for most normal geometries and, hence, equal to Eq. (4.10).

C. Generalized Treatment of Particle Self-Shielding C. H. Randall

1. Introduction In this section a more general technique than the preceding one is described for predicting the nuclear characteristics of heterogeneous mixtures of materials. It should be pointed out that the calculational models of Doub (Sect. 4.2.B) and Hurwitz and Zweifel 2 are based on assumed material characteristics gEACTOR DESIGN TECHNIQUES which could be dependent on the manufacturing process..he model of Doub (binomial distribution) assumes essentially a random distribution of particles of approximately the same size and shape. Since it is not inconceivable that particular applications could lead to manufacturing processes where some of these simplifying assumptions may not be valid, it is worth indicating how one would develop a calculational model from more general principles. The particular example discussed in detail should not be construed as the ultimate and most general model, since each individual material will have its own characteristics. It should be noted that, as the volume fraction of particles increases, the shape deviates from a sphere, the range of particle sizes present increases, neutron optical diameters increase, and the need for a more gener-alized treatment becomes necessary. A specific character-istic of this type of material for which the model of Doub (Sect. 4.2.B) may be inaccurate is evidence of considerable large scale inhomogeneity in the material.

A particular model is developed in the following pages in detail for a particular case of particles embedded in a matrix material. Figure 4.9 is a sketch of a mixture containing two particle phases in contrast to the preceding analysis. A phase is defined as a spatially uniform medium exhibiting distinctive macroscopic nuclear properties. Specifying these spatially independent properties defines a phase. The method of approach is to determine when and how such complex mixtures can be represented by homogeneous materials. A homogeneous ma-terial is a single phase medium. The process of representing a mixture of materials by a homogeneous medium is generally referred to as homogenization. The defining properties of a homogeneous representation will be referred to as effective homogeneous properties or simply as effective properties.

The nature of the materials should be understood from the start. The fabrication processes always leave uncertainties concerning the microgeometry of any particular heterogeneous element. Microgeometry will refer to the detailed distribution of phases in a particular element. In Fig. 4.9 it refers to the exact shape, size, orientation, and location of the particles.

Although it is unlikely that two elements produced by a given fabrication process will possess the same microgeometry, it is almost certain that they will share a common microstruc-ture. Microstructure will be reserved to describe those average structural properties common to a collection (ensemble) of elements, e.g., phase volume fractions, mean particle diameter, etc. Since the nmicrogeometry of a heterogeneous material can-not be controlled or measured in detail, the heterogeneous elements and their behavior can only be described statistically.

553 4,

NETCO r ~orteastTechnology AFFIDAVIT I, Kenneth 0. Lindquist, Director of NETCO Products and Services Division of Scientech. a business unit of Curtiss-Wright Flow Control Service Corporation, do hereby affirm and state:

1. I am a Director of NETCO Products and Services Division of Scientech, a business unit of Curtiss-Wright Flow Control Service Corporation, authorized to execute this affidavit on its behalf. I am further authorized to review information submitted to the Nuclear Regulatory Commission (NRC) and apply to the NRC for the withholding of information from disclosure.

2. The information sought to be withheld is contained in Attachment 1 (Response to Request for Additional Information - License Amendment Request to Revise Technical Specification 4.3. 1.1.a Concerning k-infinity) and Attachment 7 (Panel Degradation Results). The proprietary information is identified by the use of brackets.

3. In making this application for withholding of proprietary information of which it is the owner, NETCO relies on provisions of NRC regulation 10 CFR 2.390(a)(4).

The information for which exemption from disclosure is sought is confidential commercial information.

4. The proprietary information provided by NETCO should be held in confidence by the NRC pursuant to the policy reflected in 10 CFR 2.390(a)(4) because:

a) The information sought to be withheld in the NETCO Attachments (see paragraph 2 above) is and has been held in confidence by NETCO.

b) This information is of a type that is customarily held in confidence by NETCO, and there is a rational basis for doing so because the information contains methodology, data and supporting information developed by NETCO that could be used by a competitor as a competitive advantage.

c) This information is being transmitted to the NRC in confidence.

Page 1 of 2 I

CURZTISS 1,FPiw Conte o Compauny

TC_ d) This information sought to be withheld, to the best of my knowledge and belief, is not available in public sources and no public disclosure has been made.

e) The information sought to be withheld contains NETCO developed methodology, data and supporting information that could be used by a competitor as a competitive advantage, and would result in substantial harm to the competitive position of NETCO. This information would reduce the expenditure of resources and improve his competitive position in the implementation of a similar product. Third party agreements have been established to ensure maintenance of the information in confidence. The development of the methodology, data and supporting information was achieved at a significant cost to NETCO. Public disclosure of this information sought to be withheld is likely to cause substantial harm to NETCO's competitive position and reduce the availability of profit-making opportunities.

5. Initial approval of proprietary treatment of a document is made by the Director of NETCO Products and Services Division of Scientech, the person most likely to be familiar with the value and sensitivity of the information and its relation to industry knowledge. Access to such information within NETCO is on a "need to know" basis.

6. Accordingly, NETCO requests that the designated document be withheld from public disclosure pursuant to 10 CFR 2.390(a)(4).

I declare under penalty of perjury that the foregoing affidavit and statements therein are true and correct to the best of my knowledge, information and belief.

Kenneth 0. Lindquist Director, NETCO Products and Services Division of Scientech, a business unit of Curtiss-Wright Flow Control Service Corporation Date:

?'/2-Page 2 of 2 OMS.

OS NOTARY PUIMTATE O NEW YORK QQunt,&ihedmU Au oust 26,

,4,*

Co't" immisIion &xpiro$ August 26,

ATTACHMENT 8 Panel Degradation Results (NETCO Non-Proprietary Version)

Non-Proprietary Information in Accordance with 10 CFR 2.390 Panel Loss Tables Page 1

Non-Proprietary Information in Accordance with 10 CFR 2.390 Panel Loss Tables Page 2

Non-Proprietary Information in Accordance with 10 CFR 2.390 Panel Loss Tables Page 3

Non-Proprietary Information in Accordance with 10 CFR 2.390 Panel Loss Tables Page 4

Non-Proprietary Information in Accordance with 10 CFR 2.390 Panel Loss Tables Page 5

ATTACHMENT 9 RAI 53.3 - ORNL-TM-1658

'0"A MASTE.R OAK RIDGE NATIONAL LABORATORY 0operated by 0UNION CARS1IO

• 'RPORATION for ihg.

U.S. ATOMIC ENEIGY COMMISSION ORNL-TM-1658 COPYNo.-

C I

W=

FOR A IgOU'NCSM DATE -September. 26, 196C EN F4C T. AI' SCIESU O ABSTI

,CTS t

RSCON4ENDED FISSION PWWCT CHA3NS FOR USE IN REAMTOR EYAWATIO*

STUDIES L. Bennett Abstract A brief review of fission product poisoning in thermal reactors was made, and a nuclide chain description is recom-mended for use in reactor evaluation studies at OEMR.

Deple-tion calculations show that this treatment is a sa".1factory representation of the time-dependent fission product poisoning.

The recamended fission product description treats 26 nuclides explicitly in 3.1 nuclide chains having a total of 12 interconnecting routes.

In addition, two pseudo-elements are used to include the lumped poisoning effects of those nuclides not treated explicitly.

Recommended values for yields and cross sections are presented.

Th~sdcuimat amto~oinb imAWN4A Oof prIlfatwn woare60 a 1

. imrim~lly for ihata ums at 00 Oak Ridge Nationad Leioomy. It is alet to roelon or trolijaa and 0"wforea do,, not represent a anal mport.

I

(Page 2 Missing From Original)

3 Table of Contents Page Sununary.

5 Conclusions and Recommendations.........

5 Introduction...

8 Background Information..............................

Long Fission-Product Treatment..........

8 Short Fission-Product Treatment 10 Need for Revised Fission Product Treatment........

10 Proposed Revisions in Fission Product Treatment 10 Properties of Lumped Pseudo-Elements........

13 Average Yields and Cross Sections for Lumped Pseudo-Elements...................................

l....4 Results of Depletion Calculations 20 References....

23 Appendix A...........

25 I

Uzr0ASE FOR ii"OUNEMJJI5 IN NUCLEAR SemrC3 ABSTPACIS LEGAL NOTICE A-Usk" o.f 00 th.ame aiud.@I.

&WisI~

la w

1USrp t

0.

10..tU 00-0",

N

.4 5

Si144A1RY A brief review of fission product poisoning in thermal reactors was made, and a nuclide chain description is recomended for use in t

for e in,". r.*

o..

evaluation studies at ORIU.

Depletion calculations wereperformud to verify that this treatment is a good representation of the time-dependent fission product poisoning.

The recomnended fission product description shown in Figure 1 treats 7

26 nuclides explicitly in 11 nuclide chains having a total of 12 inter-t'I-connecting routes.

In addition, two pseudo-elements are used t include the lumped poisoning effects of those nuclides not treated ekplicitly..-

In order to avoid very long nuclide chains, the lsaSm.-.156Zspox.tjn of the 1 4 7Nd-1 SSEu chain has been treated as a separate short chai-h.

This has the effect of omitting all secondary capture contributions to the europium isotopes from nuclides to the left of 1 820m. In describing the chains, the fission yield to 152 8m is placed on the s 158m-USSEu chain, and omitted from the 147 Nd-1 62Sm chain.

This avoids the possible error of including the 1S2Sm fission yield contribution twice.

Yield and cross section properties for the nuclides shown in Figure 1 are presented in Table 1.

The identification numbers are applicable for GAN and THEVS libraries in common usage at OREL.

Conclusions and Recc.amendations It is recommended that the fission product chains shown in Figure 1 be used with the yield fractions presented in Table I to describe fission products in depletion calculations performed for reactor evaluation.purý.

poses at ORNL.

This. description appears adequate for this purpose withou" requiring the long computer time that would be needed for more elaborate explicit chain treatments.

However, these yield fractions and cross section data should be re-viewed frequently, and revisions should be made when new data are obtained.

Also, this treatment should be checked against experimental data. for fission product poisoning as a final verification of*tis adequacy.

S..

.. ~.....

6 11&4-455-ORNL-DWG 66-3243 I

I,

---

(n,---

YIELD"ri;'"

Ir "l

149 mrN

't 135....

=__-.*

N.

N.

Kr 8 2 -. Kr 8 3 --.

N.

Rh t 0 3 -'

~RhtO5~.

Nd\\14 5 -"

Nd t 5

CS N.

4g1 0 9 -*

NSFP---

(NON-SATURATING FISSION PRODUCT)

SSFP---.

(SLOWLY-SATURAT1NG FISSION PRODUCT) for Use in Evaluation Fig. 1.

Fission Product Chains Recommended Studies.

~-...

Table 1.

Properties of Nuclides Included in Recommended Fission Product Treatment 3m go

",wA h~ ?3drI3 jM ph

-t If 8.36 1

.ao 106.o o

0.@

o.69 0.96 o.W0 O.ar 0.o4 Iw-63 35 8336 1

9s.

i1,.

0 1.99

3.

2L 0.5"

.0.090 0,9 0.10 31-3o3 1 I0" 1

139.0 1,059.0 0 0

.6 o,

1.6 3.0

6.

.*,6 6.9 31-303 14 3458 1

"3oo000.

7,261.o 36 b 5.363 x W0 0.005 0.50 0490 3.7

55.

5.8 AM-109 69

1050, 1

87.0 1,44T.0 0

0.055 0.0k 0.03 0.30.

1.55 3.1 U.-131 8k 13X0 1

M2.0 812.4 0

1.7 3.1 9.93 2.3 3.8 3.4 26-233 133 1335 1

190.0o 9.33 5-.-T d

.M x 1076 3.7 s566 6."

s.2 6.9 6-0 Ca-133 69 13355 1

28.0 3M1.1 4

0 9

0 0

0 0

0 s-l#

M35 13,55 1

1I'f.o (6.8D 2.3 y 9.55 x 1 c9 0

0 0

a 0

0 Z.35A 0

0 6.7%

.87*k x 105 5.39 5.*

6.

518 693 6.26 Xu.135 87 1355k I

26A x 3o6 22,M.0 9.1,

2.093 x 1'5 0.21 0.2 Oa.k 0.22 0.0?

o.0 Cs-U, 99 IS" 1

8.70 35.33 a

0 0

0 0

0 0

0 39-183 101 IA360 1

368.0 138.0 a

a L.0 591.

6.03

.8.

8.6 5.6 9.1k 203.

2.8.ko 1

60.0 30.6 a

o 6.6f 3.38 3.98 L.9 3.1 3.6 m2-147 0

0 M2 *t 7MG x o 7 3.8 L.93 2.36 2.8 2.0 S.8,

,-17.

107

.?

7.1 1

.235.0 2,279.0 2.63.y 6.2.

x20'T 0

0 0

0 0

0 No. 1b 1,IV:

1286 I

twmo 3:..

m,.o ko.6

.976

3. -

0 0

0 0

0 pam:

131 38861 21,500.0*

h8,059.0.

M 4-.49..810~

x 0

a 0

0 0

0

.0 81-0k9 9

o 0,

3

.183.0 it6 30 0.98

.-I0T 1.13

,.1 1.3 Le.:

8-1449.

o

.149%

1 "0,6O0.0 3,14.0 0

a 0

0 0 o 0

b1 111 1509 1

6". R 109.7

.0 0

0,a o

0 0

0 0

m.151 1i.3 21,(9

1 W00.0 2

0

0.

0.3s'..1"8*

O 0.9 0.60 0.0 1 39

"+

113 532 1

20* 0

i.

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0 o.o_0 0.6.6

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85.0 831.1

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0.90

'20158 317 15"i6

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118+.

3563 1i*

&.7;ro

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o.opqg 0.03.

0.33 0.13 0.6

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..111*

1 9 *

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in*.

34 J

D.-,

74, 8 0

• ,,L 4g.

9 Oltft A

abacptlMS, 0092 8% 1.9f -to U*

1-*

U.RSW Is=

=6 1.0 la to *A 5.8.dt iwi~~olan.

i A

INTRODUCTION The time-dependent behavior of neutron absorptions in fission products is a major concern in any reactor depletion calculation.

The degree of complexity required for an adequate treatment of fission product buildup depends on several factors, including the neutron energy spectrum, ruel isotopic composition, and cycle length.

When making comparative studies on a number of different reactor types, the fission products must be describeil in sufficient detail to be "adequate" for all the reactors being considered.

To provide a margin of safety, this usually requires the chain descriptions to be more complex than would be needed when studying a single reactor type.

In the latter case, a "lumped fission product" could be used with its yield and cross section properties normalized to more exact "explicit" descrip-tions.

When this normalization is required for more than one reactor type, it is usually easier to just use the more complex treatment.

3ACKGROUND INFORMATION In the advanced converter study reported in ORNL-3686 (Ref. 1), numer-ous fission product nuclides and chains were examined and those of signifi-cance in depletion studies were described in as much detail as possible.

The discussion in the next two sections is taken almost verbatim from OMUl-ý 3686 in order to provide background for the present analysis.

Long Fission-Product Treatment The basic approach involved a description of all the important fission-product nuclides in explicit isotope chains that were followed during the depletion calculation.

This description treated 54 explicit fission-product nuclides in 13 chains having a total of 22 connecting routes (shown in Figure 2).

The nuclides not treated in these explicit chains were lumped together as a single nonsaturating pseudo-element JFP(1).

This limped fission product constitutes pcrhaps 5% of the total fission-product poisoning.

This description was dubbed the "Long Fission-Product Treatment -

(LPP)" to distinguish it from a simpler treatment derived from it, and was taken as the standard against which simpler treatments were compared.

9 I

I smL,,,

'q6.,,,I..

mom--IN

-0

.,,,.ango$.*

m--.o no Tome NiP

-F d

40-',

w pp.#

I I

II. I,".

I

• m mu.Ima.

'S" 1

.k. -., T_.

Cd--e.I Km Xe Fig. 2.

Iugilide Chainis Used in long Ftaaion-Product (I)Treatmenit in ouuL-368.

10 Short Fission-Product Treatment Since the computer time required for a depletion problem is dependent on the number of nuclide chains being treated, a simplified fission product description was used in many of the physics calculations.

The nuclide chains for this treatment (called the Short Fission-Product Treatment, SUP) are shown in Figure 3.

It is obvious that many of the nuclide chains shown in Figure 2 are not treated explicitly here.

The nuclides involved in the omitted chains were lumped into F. slowly-saturating pseudo-element FP(2).

The energy distributions of these lumped nuelide cross sections were estimated by weighting the point cross sections for the individual nuclides by their yield fractions.

Preliminary normalization calculations were performed for a pressurized-water reactor to determine the effective fission yield for FP(2) which would produce the same neutron losses to fission products in the SFP treatment as predicted by the L"P treatment.

The yields given for MP2) in Table 2 are based on this normalization.

As further check the HTGR was analyzed with both treatments, and the calculated lifetimes and fission-product poisoning were in good agreement.

Need for Revised Fission Product Treatment The short fission product treatment described above appeared to be satisfactory when the normalized yields and effective cross sections were used.

However, this treatment is a bit more abbreviated than one would really like to use.

With the long burnups of interest to advanced con-verters, some of the secondary fission-product routes (notably in the Nd-Pa-Sm chain) become important and should be included exactly.

On the other hand, use of the long treatment is not Justified in most reactor evaluations.

Thus, a compromise appears in other.

That is, it seems desirable to have more of the fission products included in explicit nuclide chains, but not to the extent of the long treatment described above.

In particular, the Nd-Pm-Sm chain needs to be described in more detail, including the branched capture from -41pm to 14LimpM and 14SPm.

Proposed Revisions in Fission Product Treatment A study of fission product poisoning has been made recently by T. R. EnglandO at Bettis Atomic Power Laboratory.

As a result of his

~r-

-. r.Vy.~..,t.

~r-r.v~rr.

..~.%

13

\\ I"\\ 1*

Ndff Nrr4 149 oum.z*v-6.5 6 "T 6

lYield I

I q (Sa"7 I

'U I L

\\ %

S F.g. 3.

in OMM-,76%.

FP (1) ---- P FP(2) ---- W rL*uapd FPJ FPL) fPJ lucLidb, Chaine Used in Short Fission-Product (SiF)

Treatment

12 Table 2.

Effective Fission Yields end Cross Section Data for Lumped Pseudo-Elements in OMeL-3686 Fis sioning Nuclide Yield aa Yield ai Fraction (2200) a Fraction (2200) 2s3U 1.41 3.86 7.0 0.88 33.7 l2J*

23sU 1.31 2.74 5.7 1.02 34.2 158*

239pu 1.06 2.74 5.7 1.4 49.1 210' 2,,pu 1..06 2.7 4 5.7 1.4 49.1 210

• The values given In OROL-3686 for these two !umbers were in error and have been corrected here.

calculations, England concluded that a set of 12 fission product chains, con-taining 26 nuclides, would provide an excellent repres'ntation for alaost any reactor optimization purpose.

To the 12 explicit chains, one or more pseudo-nucli..es representing the remainig poison must be added.

England's analysis indicated that at an exposure of 5000 EFFE (about 0.2 fifa)* these explicit chains would account for about 84 percent of the total resonance absorptions in s3su fission products and about 90 percent of the thermal poison (exclusive of 13 6 Xe and the direct mass yield to 149 Sm).

This representation of the fission products (shown in Figure 1) in-cludes 28 nuclides in 13 chains having a total of 14 connecting routes (2 for the branched 13-4'd-l5aSm chain).

By comparison', the long treatment used in the advanced converte",study contained 55 nuclides in 23 connecting routes.

For the Nd-Pm-Sm-Eu chains alone, 8 chain equations were required.

The short treatment included 14 nuclides and required 5 connecting routes.

• Epp

= Eqrui,!,,

t Full-Power Hours; fifa = fissions per initial fissile atom.

.1..

Properties of Lumped Pseudo-Elements In addition to the fission product nuclides included explicitly in nuclide chains, we have chosen to have two pseudo-elements.

These are needed to include the poisoning contributed by those nuclides not explicitly..

shown in Figure 1.

The first of these pseudo-elements is identified as :a Nn-Saturat.in Fission Product, NSFP.

It includes the summed poison contribution by tose:*_-..

fission product nuclides which have significant fission yield.fraction bu'..

low absorption cross section (less than about 10 barns at 0.C053 ev.),}x,.

Hence, there is a large nuclide production rate but relatively low neutrn.-,

capture rate.

The second pseudo-element includes the sumned poison contribution:by..,.-.',.

those fission products which have both a significant yield fraction and a:!ý.,.

relatively large capture cross section.

This pseudo-element is a Slowly-Saturating jission Product, seFP, which will slowly approach -an eq iib-iu condition at which its neutron capture rate is equal to its production rate from fission yield.

At this point, its poison contribution is determined entirely by the yield fraction applied to this pseudo-element, since at equilibrium each atom produced results in a neutron capture.

The effective yield fraction, y, for each lumped pseudo-element was defined to be the sum of the individual yields for those nuclides included.

where, the summation is over all nuclides included in the lumped pseudo.-r,._-.

element.

The effective cross section, 0 a' for the lumped nuclides was obtaineq..-

by weighting the cross sections for the individual nuclides by. their yield, fractions.

Thus, we require that a Yja (2)

1S4o Solving Eqs. I and 2 for the effective cross sectiony we obtain U--

1 ytai a

a-

' (3)

Energy-dependent cross sections-for the lumped pseudo-elements were ob-tained by applying Eq. 3 to each group in the OMIL cross section libraries for GANl and THEEIE3.

Tables A-1 and A-2 list the individual nuclides which were included in the lumped pseudo-elements NSFP and SFP, respectively, together with their yields and cross sections.

All cross section data presented in Appendix A was taken from the GAM and THEMM6S libraries currently used at OlL.

Average Yields and Cross Sections for Lumped Pseudo-Elements The effective yields and cross sections calculated for NSF and SSP are presented in Table 3 below for the different fissioning nuclides.

Table 3-Summed Yields and Effective Cross Sections for Lumped Fission Products Fissioning Nuclide Yield a(2200) 1 Yield a(2200) 1 Fraction a

a Fraction a

3 38Th 1.241 1.018 4.ce8 0.319 15.168 64.936 2s 3U 1.271 0.978 5.573 0.2.99 19.036 75.854 135U 1.260 1.111 7.354 0.298 28.664 76.744 2saU 1.135 1.396 9.208 0.277 17.985 78.932 239FU 1.157 1.398 8.754 0.329 17.o81 8i.848 a

The results shown in Table 3 indicate that the properties of the lumped nuclides are not strongly dependent on the fissioning element.

Thus, it was decided that the lumped pseudo-element, for* 33UWtjssi OW:pro-ducts could be used for all the other fission-ing nuclides. witih their -

yields.adjusted to give the proper product of y oa(2200)1 IAecior g,

the recommended set of properties for lumped pseudo-elements is given in Table 4.

Although the cross sections presented in Table 4. chactre -the thermal cross sections by their 2200 rn/sec value and the epitherwal'. ckbaa sections by a total resonance integral, the cross sectionsagrefat-.al W

incorporated into the data libraries of GhM and THERMWS as energy.rdepndent group cross sections.

Figures 4 and 5, show the energy. dependence, of' the cross sections which were placed on the library tapes.i"+.

Table 4.

Recommended Data for Lumped Pseudo'-Nements-Non-Saturating Blov2Lyf-Stura&tIn'g Product Pro-uct NSP SBFV

-+2.:iY++?

Effective Cross Section oa(2200), barns

1. 111

18. 66k.-

I&E o.414), barns T.354 76 i4.

Yield.Fraction atoms/fission Fissioning fuels:

23 2 Th I.1in 0'.259.,

2l

.U9 0.3p, 30.-

3SUt

ý1.260

.9o 2 3 8u 1.4.26 o.267 23 U1.456, 0.301

a0 a

as a

114 1

111,4 11 a

a 4s 8 a

a lotS 1 11dU sP I oo.o.oi.

o.mO1o 3.0

.O

~

lOO.

-00 1

0 Fig I.

rosNecIon o

o-auaigFsso

rdcNPD, grip mtYT I

10.0 91 4_

91

• 1 8~i 21 a stee l

3 a

ltoll

Ti sii 1:

'+

T T

t ti Lf.4 cn')

rs etosfrNnStrt FsinPou T,

NSFPI~~~~~~~~~~~~~

7'mi0e o1 e...*

it I aiu

..:..i ":..

-I..:-

.n:;,;;..;*

ou.111111-2046" (flit z) tK*

1-1.0 0

0....m 1

e010 v

=UL-bwrg-e"4i3J (part 0) z a a 0 57 li'll a

a a 9 wwwl 4

771 77

'77 1

i W

W A

rV am!

if,

ýjj 2 It 7Z

.LL W 47, I Ll tj:

wa

r, rn UP 7 7 sip" r

r 1.4 7A

ý211 Jr.

I.;

4W ljý m

W IA 4i:

9' JA dt.

0.11 iOT ev Fig.

(cont'd).

Cross Sections for.. M: owl'Y-Saitdrating. Fission z':Prddudt SBPPj from IOD ev to 10 Nev.

20 Results of Depletion Calculations An evaluation of heavy-water moderated, organic-cooled reactors was underway at the soe time this memo was being prepared.

Hence, the HWOCR was uzed as a model for depletion calculations with the different fission product descriptions.

Depletion calculations vere performed for the uranium-fueled design proposed by Al/CE.

The continizous-fueling operation was simulated by treating the reactor as a 15-batch scatter-reload core which was kept critical by feeding 335U as needed.

Discharge fuel exposure was 17,000 Results of these calculations are sumarized in Figures 6 and 7, Figure 6 shows the total poison fraction of all the fission products except 1 3aXe.

Figure 7 shows the ratio of fertile-to-fissile absorptions.

It is clear that the short treatment is somewhat pessimistic relative to the long treatment.

The fission product description recomended in this report is in very close agreement with the long treatment.

N

- - 1 1 ;

0.06 IS F4 Mils! Elli EmEii uno. -IS %T!,:;;=

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n.

H.

ý;Trloo xMnN W

I

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.7

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In Ro HE III H*

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i

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23 Referencee

1.

M. W. Rosenthal et al., "A CoMParative Evaluation of Advanced Converters," UBAE Report O01L-3686, Oak Ridge Nationil Laboratory, January 1965.

2. T. IR. 34nlend, "Time-Dependent Fiasion-Product Thermal and Resonance Absorption Cross Sections (Data Revisions and Calculational Ertensions)," USAZC Report VAPD-TM-333, Addendum No. 1, Bettis Atomic Poaer Laboratory, January 1965.

(Page 24 Missing From Original)

25 APPEDIX A Yield and cross section data for fission products included in lumped pseudo-elements.

• 26 Table A-1.

Properties of Nuclides Included in the Non-Saturating Pseudo-Blement, NKrP ReiOn.,

Peft.

Yield fm Fra1u auclie -a(o~e ntegm'*

NUdAboe Bonn

.U Ma M°U "Oft*

O.414 00-76 Be-76 Oe-jo k-SO Dw-811 xr-85 Krn-O Rb.8T7 Y-89 ar-90 zr-91 zr-w ZP-93 zr,96 Zr.96 No-200 66-101 RU-206 Pd-oh0 ca-ha Cd-In*

66-116 c-12%

On-l,7

-6.120 A.-122 TO-128 oe-230 1e-1*

XG-136 Cu-]3?

Cm -I%

Ce-I4O CO-1110 U-1548 Gd-156 Od-MS 0.36 0.40 0.61 3.30 0.16 7.0 0.91 o.o6 0.22 1.31.

1.0 1.58 0.25 1.1 2.20o 0.51 0.50 5.0 9.0 0.21 2.0 0.03 0.24 1.70 2.5 0.141 0..161 o.30 0.50 0.20 0.20 0.15 0.11 0.70 o.66 5.0 3-.

3.0 5.'

4.0 3.9 0.150 o.i6..

0.83..

57.63 14.1,T o.6T1 0.056 o.166 0.760 2.182 7.453 0.264 7.9fe 0.15 0.324 15.30 5.953 7.6 78.6 31.99 1.6.23, 10.49 51.09 32.99 111.38 1.20" 16.060 6.6..

0.8614 2.517 2.009 2.14" 0.63 0.368 o.11*7 13.85 10.149 10.86 2.7%6 33.97 32o03 O.o00 0.03 0.15 0.36 3.65 1.014 3.4"8 6.0 6.6 7.2 7.T3 7.2 6.8 6.3.

5.7 4.8 4.53 3.6 1.04 0.62 0.36 0.0111 0.001 O.041 o.o614 o.o6yS o.o685 O.067 o.o6B 0.058 0.0115 2.87 5.1 6A1 6.7 7.3 7.7 7.5 1.8 0.4 0.018 0.00001, 0.01 0.10 0.28 0.1#6 1.91 0.58 I-88 3.20 6.28 6.3B 6.57 6.63 7.02 6*70 5.03 5.38 5.25 4.49 2.84

2. 6 0.92 0.22 0.03 0.03 0.00 0.Ce 0.01 0.01 0.00 6.71 4.51 1.28 0.55 0.047 0.01 0.00001 0.015 0.10 o.06 0.21 1.00 0.293 2.02 2.149 h.79 5.TT 5.8h 6.03 6.45 6.4o 6.33 6.09 5.78 6.30 5.0 4.1 1.8 0.38 o.011 0.019 0.01 oXII 0.011.

0.01 0.011 0.013 O.W9) 2.0 8.06 6.1,6 6.15 5.74 6.4141 5.62 1.71 0.67 0,077 0.013 0.002 0.03 o.oo6 0.006 o.o18 0.030 o.16 0.061 0.209 0.80 2.5 3.-° 11.4 b.5 14.6 14.7 5.1.

5.,

5.9 6.3 6.3 6.3 It.$

2.9 0.O14 0..07 0.014 0.04 0.01 0.04 0.04 0.26 1.1 5.*

6.0 6.0 6.0 14.5 2.11 1.3 0.22, 0.0am 0.017 0.01 6.6e 0.01 0.11 0.47 O.1R2 0.418 0.75 0.91 1.7 2.2 2.55 3.1 3.9 4.5 5.1 5.6 5.9:

.-1.

5.9 5.9 5.9 4.5 0.55 0.20 0.12 o.0C 0.035 0.035 0.035 0.03" 0.035 0.74 2.5 5.3 7.5

&6.

6.5 6.3 5.6 3.8 0.25 0.10 o.035 KAU o,

,etios Muami to be 1/v i, 8ni Iumaz.

"Cror Uactm

,amaM to be 1/v " GM 1"..Wmr.

.d Table A-2.

Properties of Nuclides Included in the Slowly-Saturating Pseudo-Element,' SOP Resonance Percent Yield. From Fission Nuclide 47a(2200)

Integral Aave2 aaU 235U 2

5'U 29pU 0.AA ev Se-77 42.041 29.0**

0.022 0.02 0.0083 o.0o4 0.01 Be-79 4o.o*

i6.o*.

o.056 o0

.9 o.o56 0.010 0.010 Mo-95 13.9*

.11.3 5.15 6.22 6.27 4.80 5.o Tc-99 22.0 198.0 Z.53 5.48 6.09 5-5 5.6 Pd-107 10.0*

45.27 0.049 0.22 0.19 1.3 3.6 Pd-108 1o.4*

169.3 0.053 0.07 0.09 o.64 2.6 In-U5 20T.0 3305.0 o.o69 0.02 0.011 0.04 0.035 Sb-121 5.9*

20e.o**

0.055 o.02 0.015 o.o4 0.035 sb-123 4.1*

16i.o*

0.035 0.03 0.0227 0.04 0.035 1-127 7.0*

155.9 0.091 o.61 0.25 0.13 0.37 1-129 28.7 39.45 O.1.0 1.70 0.80 0.53 1.4 LS-139 8.9*

11.0 7.51 6.61 6.55 6.o 6.0 Pr-141 11.6*

24.08 8.1.

6.2A 6.4 5.14 5.6 Nd-146 10.0*

8.78 5.5 2.58 3.07 3.3 2.6 T.b-159 46.0*

1438.0 0.00107 0.008 0.015

• cross section "Cross section assumed to be 1/v in TMDCS library.

assumed to be 1/v in GAN library.