Text

Calculation PM-1056, Rev. 0, Suppression Pool Ph Calculation for Alternative Source Terms
	ML072570190
Person / Time
Site:	Peach Bottom
Issue date:	03/28/2003
From:	Yemin L; Exelon Nuclear
To:	; Office of Nuclear Reactor Regulation
References
	CC-AA-309-1001, Rev 0 PM-1056, Rev 0
	Download: ML072570190 (57)
	v • d • e

002-PM-1 056 Rev 0 pH

Exelon.

Nuclear CC-AA-309-1001 Revision 0 ATTACHMENT 1 Design Analysis Cover Sheet Last Page No.fl%,6 Analysis No.

PM-1056 Revision 0 m-j.

EClECR No.

PB 02-00838 Revision 0

Title:

Suppresion Pool pH Calculation for Alternative Source Terms Peach Bottom Atomic Power Station(s)

Station Component(s)

Unit No.:

2 and 3 N/A Discipline SEAQ Description Code)

LOCA Keyword Safety Class S

System Code 912 Structure NIA CONTROLLED DOCUMENT REFERENCES Document No.

FromlTo Document No.

From/To PBAPS Tech. Spec. Bases B 3.6.2.2, From Rev. 0 Is this Design Analysis Safeguards?

Yes L] No U Does this Design Analysis Contain Unverified Assumptions?

Yes [] No [

ATI!AR#

Is a Supplemental Review Required?

Yes L] No [

If Yes, complete Is aSuplemetalAttachment 3

Preparer Lowell Yemin l

_J1.Q 3120/2003 Prni Name Sign Name Date Reviewer Harold Rothstein t1 3/20/2003 Phnnl Name Sign Name Date Method of Review

[J Detailed Review

[ Alternate Calculations E] Testing Review Noles:

Approver Harold Rothstein 3/20/2003 Prnt Name Sign Name Date (For Evter~I AnA8Vlyts Drily) _____________________________

Exelon Reviewer ML)_%

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rin t N a rr D r f v

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D d t*

Approver

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3/A0zi 3 Print Name Sign Name 1,O Dte Description of Revision (list affected pages for partials):

THIS DESIGN ANALYSIS SUPERCEDES: N/A

r(ýý,cuuvrjONNo. PM-1056 CALCLIATJON No. PM-1056 I REV No 0 I PAGE2ofI5 I REV. No. 0 I PAGE 2of 15 1.

2.

3.

4.

5.

6.

7.

8.

9-TABLE OF CONTENTS PURPOSE AND OBJECTIVE.........................................................................................................................................

3 M ETHODOLOGY AND ACCEPTANCE CRITERIA............................................................................................

3 ASSUM PTIONS/ENGINEERING JUDGEMENTS.......................................................................................................

3 DESIGN INPUT................................................

A................................................................................................................

3 REFERENCES....................................................................................................................................................................

4 CALCULATIONS.....................................................................................

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

5 SUM M ARY OF RESULTS AND CONCLUSIONS.....................................................................................................

11 OWNER'S ACCEPTANCE REVIEW CHECKLIST FOR EXTERNAL DESIGN ANALYSIS.................. 14 ATTACHM ENTS..........................................................................................................................................................

15 A -Determination of Total Exposed Cable.Quantities Inside Containment B - Dose Assessment, Core.Cs & I, and Gamma Mean Free Path Determination C - pH Transient Spreadsheet D - pH Transient Spreadsheel Ceil Formula*s E - pH Transient - Grand Gulf Reference Data F - Reference 5.1 G - Reference 5.2 H - E-Mail Memo and Attachments on SBLC from Mark Fry at PBAPS I - Computer Disclosure Sheet 49 PAGES 14 PAGES 4 PAGES 10 PAGES 7 PAGES 30PAGES 26 PAGES 16 PAGES 1 PAGE

CALCULATION No. PM-1056 REV. No. 0 PAGE 3 of 15

1. Purpose and Objective In order to prevent iodine re-evolution following an accident, the pH of the Suppression Pool should be maintained above 7.0. The chemistry of this phenomenon and methods of pH control are discussed in References 5.1 and 5.5.

The Objective of this calculation is to detenrmine the pH of the Suppression Pool following a Loss of Coolant Accident based on the use of Alternative Source Terms as deflned in References 5.4 and 5.6. The pH values are detennined, as a function of time, with and without the addition of the sodium pentaborate in Ihe Standby Liquid Control System. The conditins required to maintain the Suppression Pool at a pH above 7.0 are determined.

2. Methodology and Acceptance Criteria This calculation is based on the methodology developed for the equivalent calculation done for t'he Grand Gulf Nuclear Station, Unit I as revised December 2000. [Ref. 5.1 & 5.2]. The calculation formulas developed in these documents are accepted without independent verification. These references are included in this calculation as Attachments F and G. The accuracy of translation of the equations in these documents into spreadsheet cell formulas is verified by duplicating the Grand Gulf calcutation. This verification is presented as Attachment E and accurately duplicates all of the Grand Gulf results.

As noted in this calculation, injection of sodium pentaborate solution by the Standby Liquid Control System is a required function in order to control post-LOCA pH in the suppression pool, and prevent iodine re-evolution.

Based on the worst case beginning of cycle condition, injection should be completed within about. 30 hours3.472222e-4 days 0.00833 hours 4.960317e-5 weeks 1.1415e-5 months after the start of the DBA-LOCA. Therefore, manual initiation is acceptable. Manual initiation of SBLCS is expected early in a DBA-LOCA as a result of emergency operating procedures and severe accident guidelines, particularly for events resulting in fuel damage that would be consistent with AST source terms.

Acceptance Criteria: Per the guidance of Appendix.A of Regulatory Guide 1.183 [Ref. 5.6], the Suppression Pool pH should be controlled at values of 7 or greater following loss of coolant accidents.

3. Assumptions/Engineering Judgements The Suppression Pool is assumed to be well mixed so that the pH at any time can be represented by a single value.

For cable parameters, the cable data presented in Attachment A is used. It includes the exposed termination length of what is in a raceway. As a conservative estimale of the cable lengths in free air, an additional 5% of the raceway's totals are assumed to be in free air. A 10% contingency on the cable surface, reported in Attachment A, is also included. Radiolysis of surface coatings on the steel and concrete surfaces in the Drywell and Containment would not be significant contributors, since the coatings utilize non-chlorinaled polymers.

4. Design Input Cable Data Cable lengths, diameters, and average jacket thickness are developed separately and presented in Attachment A.

Temperature Suppression Pool temperatures are taken from UJFSAR, Rev.15 Figure 14.6.12A. Since this revised curve extends only to 14 hours1.62037e-4 days 0.00389 hours 2.314815e-5 weeks 5.327e-6 months , the older UFSAR, Rev 14 curve, Figure 14.6-12 was used to extend the data to 278 hours0.00322 days 0.0772 hours 4.596561e-4 weeks 1.05779e-4 months and extrapolate to 720 hours0.00833 days 0.2 hours 0.00119 weeks 2.7396e-4 months . The older curve gives slightly lower temperatures in the area of overlap and is therefore conservative (Lower temperatures give higher calculated pH values).

Extrapolation of the semilog plot is acceptable since the calculated pH is rather insensitive to temperature. At 30 days (720 hours0.00833 days 0.2 hours 0.00119 weeks 2.7396e-4 months ) it requires a 36 FP increase to reduce the pH by 0.1.

CALCULATION No. PM-1056 REV. No. 0 PAGE4 of 15 Sodium Pentaborate mass in SBLC Tank Per Technical Specification SR 3.1.7.7, the minimum B-10 stored in the SBLC tank is 162.7 lbs. In order to prepare this calculation, total boron is needed. The highest vendor supplied enrichment from Reference 5.7., included as attachment H, is 63.5 atom % B-10. For this calculation, 65 atom % B-i1] enrichment is assumed. Since B-10 has an atomic weight of 10.01, this gives 7373 gram-atoms of B-10 and 11,342 gram atoms of total boron. Since the formula of Sodium Pentaborate is Na2B,0Ot6X10H20, there are 1134 gram-mols of the pentaborate in the SBLC Tank. This calculation is performed on the pH calculation spread sheet at the top of columns U -Y.

Suppression Pool Volume The limiting Tech. Spec. volume [Ref.5.8] is 122,900 cu. ft. from Tech. Spec. Bases B3.6.2.2.

5.

References 5.1 GGNS-98-0039, Rev. 3, "Entergy Operations Engineering Report for Suppression Pool pH and Iodine Re-Evolution Methodology", Applicable Site: Grand Gulf Nuclear Station, 12/20/00 5.2 XC-Ql 111-98013, Rev. 2, Grand Gulf Design Engineering Calculation "Suppression Pool pH Analysis", 12/20/00 5.3 PBAPS UFSAR Figure 14.6.12 (Rev. 14) "LOCA - Suppression Pool Temperature Response" and Figure 14.6.12A (Rev. 15), "Long Term Suppression Pool Temperature Response - Nonnal ECCS Flows" 5.4 NIJREG-1465, "Accident Source Terms for Light-Water Nuclear Power Plants", February 1995 5.5 NUREG/CR-5950, "Iodine Evolution and pH Control", December 1992 5.6 U-tSNRC Regulatory Guide 1.183, "Alternative Source Terms for Evaluating Design Basis Accidents at Nuclear Power Reactors". July 2000 5,7 E-mail Memo, Mark G. Fry, Chemistry Manager-PBAPS, Exelon to Harold Rothstein WGI, "PBAPS Standby Liquid Control (SBLC) Data" (Transmission of Eagle Picher Technologies Boron-10 analysis and logs of Units 2 and 3 plant logs of pounds mass of Boron-10 in SBLC Tank), December 27, 2002 (Attachment H) 5.8 Peach Bottom Technical Specification Bases B 3.6.2.2, Rev. 0 Containment Systems - Suppression Pool Water Level (Minimum volume).

5.9 Not used 5.10 GE Report NEDC-32963A, "Prediction of the Onset of fission Gas Release From Fuel in Generic BWR", March 2000 (Allows a 121-second delay in timing of fission product release following design basis accidents) 5.11 Not used 5.12 Radioactive Decay Data Tables by David C. Kocher, Report DOE/TIC-1 1026 T'echical information Center U.S. DOE, Washington, D.C., 1981

I CA[.CULATHON No. PW-.1056 I REV. -No. 0 I PAGE 5of 15 CACLTO N.P-OEi RVN.

I PAEof

6.

Calculations pH - Fundamental Relationships pH = -1log[H]

6-1

[H'].[OH] = Kw(T) 6-2 where:

[HW]

concentration of hydrogen ions in moles/liter

[OH

= concentration of hydroxyl ions in moles/liter Kw,(T) ionization constant for water as a function of temperature T The data for Kw for T between 77 and 212 'F can be represented by the following correlation developed in Section 3.0 of Reference 5.1:

-LogjoKw(T) = 15.5129 - 2.24E-2

T + 3.352E-5

T2 6-3 Hydriodic Acid Production Iodine, accompanied by Cesium, is released during the Gap Release and Early In-Vessel Release phases.

Thfe following, equation, valid during the Early Vessel Release Phase, includes the release during the Gap Release Phase. See analysis in Reference 5.1 (Section 3.1 and Equation 3-1d).

Iodine and cesium core inventories are calculated for both beginning and end of cycle (BOC and EOC) conditions (See Attachnent B for a discussion of the assumed BOC conditions). Since EOC conditions result in increased inventory of both acidic (iodine) and basic (cesium) compounds, pH values are calculated for both conditions. For conservatism, the EOC radiation doses are used for the BOC calculation.

The hydriodic acid concentration is governed by the following equation:

[HJ](t) m i

(120* VPOoL) * [t - (0.5 + t,,)] + mi/

(400

Vl1,3,)

6-4 where:

[HI](t) = concentration of Hydriodic Acid at time t (moles/liter) m, = core iodine inventory (gram-moles)

VFoOi, Suppression Pool volume (liters)

I = time after start of accident (hrs) (includes tysp + Gap*Release [0.5 hrs] + Early In-Vessel Release [1.5 hrs] durations for a t,,,, = 2.0336 hrs)

[Ref. 5.6, Table 4, page 1.183-15]

i tgp-time of onset of gap release = 121 seconds = 0.0336 hrs [Ref. 5.6]

t,

= 2.0336 hrs = end of Early In-Vessel Release

[See Spreadsheet: Sheets 1 (EOC) and 5 (BOC), Col HI]

Nitric Acid Production

I CALCULATION No. PM-1056 1 REV. No. 0 1 PAGE 6 of 15 Nitric Acid is produced by radiolysis of the water in the Suppression Pool with a G value of 0.007 molecules HNO0

/ 100 eV absorbed dose or 7.3E-6 g moles / megarad-liter [Ref 5.1, Section 3.2, Equation 3-2b].

The nitric acid concentration is governed by the following equation:

[1N03](t) = 7.3E-6

D(i 0o, 6-5

[See Spreadsheet Col. 1]

where:

[I-NO 3](t) = nitric acid concentration at time t (moles/liter)

D(0pooJ = Total accumulated dose in Suppression Pool at time t (megarad)

Hydrochloric Acid Production Hydrochloric Acid is produced by radiolysis of chlorinated polymer cable jacketing. Radiolysis of surfthce coatings on the steel and concrete surfaces in the Drywell and Containment would not, be significant contributors, since the coatings utilize nonchlorinated polymers.

The calculation of the resulting concentration in the Suppression Pool is based on the equations in Section 3.3 of Reference 5.1 [see Ref. 5.2, Equations 5-1, 5-2, and 5-3]. These equations are in turn based on the following G value for HCI production in Hypalon chlorinated polymer given in Reference 5.5.

GI.,= 2.115 molectules/lOWeV = 3.512E-20 g moles HCI / MeV The hydrochloric acid concentration is governed by the following equations:

Doses from beta and gamma radiation are calculated separately.

[-ICI](I) = Guci / Vio*

0

(Stray / 2 + Sr,) / 40;,i,

Dp(t) 6-6 where the effective cable surface area for P dose is:

S,, / 2 +-

=f Do*1)

(f 2 2 + Lf0)

[See Spreadsheet Cols J & L]

[HCI]3(t) =.

c/ Vpw,. * (Sy. + Sfo) * (1-e

4W TX) /

i

(I -

e -

Iypal

D*(t) 6-7 where:

Struy + Sr, =i

Do * (Ltiy - Lfa)

[See Spreadsheet Cols K & MI where:

.. C..U IN~...

RE

.N.

U

... 15 I CALCULATTONNo. Fryl-1050 RE*JV. No. 0 I PAGE 7of 15 I

I

[HC15j(t) = HCI concenaration from Beta radiation at hime t (g m0oesiliter)

[HC1].(t) = HCI concentration from Gamma radiation at time t (g moles/liter)

Dt =

cable diameter (cm) 4,fy

= cable length in trays (raceways) (cm)

Lfý = cable length in free air (cm) pvt* = linear beta absorption coefficient in air (1/em) l..iairý linear gamma absorption coefficient in air (1/cm) rj. = gamma free path (cm)

PA hyat

= linear gamma absorption coefficient in Hypalon (1/cm) th

-lypalon jacket thickness (cm)

Dp(t) = accumulated beta dose per unit volume at time t (MeV/cmin)

Dy(t) - accumulated gamma dose per unit volume at time t (MeV/cnm)

GHcI= 3.512E-20 (g moles HCI / MeV)

VPCOL= Suppression Pool volume (Liters)

SY --= Cable surface area in trays (cm 2)

Sf, = Cable surface area in free air (cra2)

CesiumHydroxide Production Cesium, accompanied by Iodine, is released during the Gap Release and Early In-Vessel Release phases. The following equation, valid during the Early Vessel Release Phase, includes the release during the Gap Release Phase.

See analysis in Reference 5.1 (Section 3.4 and Equation 3-4d).

Iodine and cesium core inventories are calculated for both beginning and end of cycle (BOC and EOC) conditions (See Attachment B for a discussion of the assumed conditions). Since EOC conditions result in increased inventory of both acidic (iodine) and basic (cesium) compounds, pH values are calculated for both conditions. For conservatism, the EOC radiation doses are used for the BOC calculation.

The cesium hydroxide concentration is governed by the following equation:

[CsOHf](t) = (0.4

nec- 0.475

mi) / 3

VoTo.) * [t - (0.5 + tgap)]

+( 0.05

mc,- 0.0475

ill) / VFooL 6-8

[See Spreadsheet: Sheets 1 (EOC) and 5 (BOC), Col 0]

[CsOH](t) = concentration of Cesium Hydroxide at time t (g moles/liter) ml = core Iodine inventory (gram-moles) rnrc.- core Cesium inventory (gram-moles)

'ýFPOOL= Suppression Pool volume (liters) t = time after start of accident (hrs) (includes tgap + Gap Release [0.5 hrs] + Early In-Vessel Release

[1.5 hrs] durations for a t,*., = 2.0336 firs)

[Ref. 5.6, Table 4, page 1.183-15]

,,= time of onset of gap release = 121 seconds = 0.0336 hrs [Ref. 5.6]

= 2.0336 Irs = end of Early In-Vessel Release Final Pool pH Calculation (No SBLC Addition)

The net Suppression Pool pH can be calculated from the total of the [H+] and [O-] concentrations using the following equations developed in Reference 5.1, Section 3.5.

CALCULATION No-PM-1056

[H4](t) = [H'](ýt=0) + [Hfi](t) + [1-N0 3](i) + [1C](1)

I Tv. No, o 1 rAGE 8 of Is

__j

[H+](t) = 10-li(t=0) + [H11(t) + [llN0 3](t) + [HCI]()

6-9

[See Spreadsheet Cot N]

[OHJ(t) = [O1-]ct=0) A- [CSOH](I

[OI-F](t) = 10i1't'/1i

"(t=0) + [CsOlI](t) 6-10

[See Spreadsheet Col P1 Accounting for the concentration of neutralized ions [x]:

( ((] - [x] ) * { [OH] - [xJ )

KITr)

[]1

-'iH]

+ [OH-] - {([H1++[OH-])2 -4*([Hf]*[OH]-Kw)}I(2

} / 2 6-11

[See Spreadsheet Co] R]

note: Kw = 10 --LAlgw) [See Equation 6-3 and Spreadsheet Co] Q]

The equation for the net [H+j becomes

[H-lt, = [Hi - [xi 6-12

[See Spreadsheet Col S]

and pH =logJ5([H'Wj 6-13

[See Spreadsheet Col T]

CALCULATION No. FM-1056 REV. No.0 PAGE 9 of 15 Effect of Sodium Pentaborate (SBLC) Addition The pH of the suppression Pool can be increased by the addition of Sodium Pentaborale from the Standby Liquid Control (SBLC) System.

The limiting value (minimum weight) from Reference 5.7 is 210.6 lbs, but fbr conservative the more limiting value from Technical Specification SR 3.1.7.7 of 162.7 lbs is used. The limiting value is used since it minimizes the number of' moles available for buffering.

Addition of Sodium Pentaborate introduces a buffer into the Suppression Pool which will maintain the pool at a pH corresponding to the following equation: [Ref. 5.1, See. 6.1, p. 21].

pH = pK, + logio ([anion] / [acid])

6-14 with data for K. fitted by the equation K, =(0.0585

T+ 1.309)E-10 6-15

[See Spreadsheet Col U]

where:

K; = bonrc acid dissociation constant pK* -- negative of the log of the boric acid dissociation constant [See Spreadsheet Col.ZJ

[anion] = borate concentration of [2B(OH)4 -

[acid] - boric acid concentration of [SH 3 1B03]

based on the equation

+

Na2 B10O16 + 16H20 <-> 2Na

+

2B(OH)4- + 8H3B0 3 Therefore, Borate (g-equivalents) 2

Na2BoO,

10 H20 (g-moles)

Boric acid (g-equivalents) = 8

Na2B310O1

10 H20 (g-moles)

Using the methodology of Reference 5.1, the net strong acid equivalents [H4],,, calculated in Equation 5-12 are neutralized by the borate and the above equations become:

Borate (g-equivalents) = 2

Na 2B1 00 1 (g-moles)

[HWIne,

Vi 6-16

[See Spreadsheet Cot X]

Boric acid (g-cquivalents) - 8

Na2 BlcO 16 (g-moles) + [H-",t

VP-1 6-17

SL CALCULATION No. PM-1056

[See Spreadsheet Col Y]

And equation. 6-14 becomes:

I REV. No. 0 I PAUh 10 of 15 (2

Na2II, 00,6 (g-roles) -

[+].t

Vx.o) / V,,,o, pH

--logoKa +]og,o 6-18

[See Spreadsheet Col AA]

(8

NaB 1oO,6 (g-moles) [H],*j ' Vpoi) / Vp~1

CALCULATION No. PM-1056 REV. No. 0 PAGE I I of 15

7.

Summary of Results and ConcJusions The post accident Suppression Pool pH is calculated as a function of time after accident initiation. The results are shown below in Figures 7-1 and 7-2 for Beginning of Cycle (BOC) and End of Cycle (EOC) conditions respectively. These graphs are based on Excel spreadsheet calculations presented in Attachment C (Sheets I and 5). The inputs to the pH calculation of radiation. doses and the Iodine and Cesium inventories are presented in Attachment B.

The BOC (actually early cycle) condition produces the lowest pH and is therefore the limiting case.

Without addition of sodium pentaborate from the Standby Liquid Control (SBLC) System, the pH in the Suppression Pool could drop below pH 7 after 30 hours3.472222e-4 days 0.00833 hours 4.960317e-5 weeks 1.1415e-5 months , reaching pH 3.5 at 30 days. Therefore, SBLC addition is required to prevent iodine re-evolution.

With timely SBLC addition, the Suppression Pool remains above pH 8 at 30 days (720 hours0.00833 days 0.2 hours 0.00119 weeks 2.7396e-4 months ).

[ CALCULATION No. PM-1056 I.REV. No. 0 PAGE 12 of 15 Figure 7-1 pH vs. Time - BEGINNING OF CYCLE I-9.00 8.00 7.003 6.00 2.00 0.00 0.O0 47;

-L

--4H 1=* 1-3m 4:'ft 2

10--

105-t-1 F

EjtvI Iii-ii t -u i I -

flAil w/o SLCS with StCS 10F0 1000 ii 4:>-

I 100 Time IHours)

I CALCULATION No. PM-1056

! REV. No. 0 fPAGE 13of5 Figure 7-2 pH vs. Time - END OF CYCLE 10.00 8.00 7.00 6.00-M 5.00 I

L-m m,

4.00

-TI 3.00 2.00 1.00 0.00

~zzj 4,

w/o SLCS w-with SLGS 000

-~400 I

E I

I E

I I

i I

f I

L 1

10 100 Time (Hours)

I CALC.LATION No. PM-1056 I KEN.No. 0 I PAGE, 14 of 15

8.

OWNNER'S ACCEPTANCE REVIEW CHECKLIST FOR EXTERNAL DESIGN ANALYSIS DESIGN ANALYSIS NO. PM-1056 REV: 0

1. Do assumptions have sufficient rationale?

2, Are assumptions compatible with the way the plant is operated and with the licensing basis?.

3. Do the design inputs have sufficient rationale?

4. Are design inputs correct and reasonable?

5. Are design inputs compatible with the way the plant is operated and with the licensing basis?

6. Are Engineering Judgments clearly documented and justified?

7. Are Engineering Judgments compatible with the way the plant is operated and with the licensing basis?

8. Do the results and conclusions satisfy the purpose and objective of the design analysis?

9. Are the results and conclusions compatible with the way the plant i5-operated and with the licensing basis?

10. Does the design analysis include the applicable design basis documentation?

11. Have any limitations on the use of the resulls been identified and transmitted to the appropriate organizations?

12. Are there any tnverified assumptions?

13. Do all unverified assumptions have a tracking and closure mechanism in place'?

Yes No

[]

El

[]

N/A El C

El 0

El

[]

xr El El

~El E X

E El El EXELON REVIEWER: ".

LiT. 34v/C&3 Print

CALCULATION No. PNI-1056 REV. No. 0 PAGE 15 of 15

9.

Attachments (Unless noted, Attachments are Calculated By and Checked By the same individuals as the Calculation)

SPREADSHEET (ATh. D) INPUTS:

CALC. BY:

CHECKED BY Attachment A - Determination of Dale Shailcross/

Lowell Yemin Total Exposed Cable Quantities Harold Rothstein Inside CoDtainment Attachment B - Dose Assessment, Aleem Boatright Paul Reichert Core Cs & I Inventory, and Gamma Mean Free Path Determination Attachment C - pH Transient Spreadsheet Attachment D - pH Transient Spreadsheet Cell Formulas Attachment E - pH Transient - Grand Gulf Reference Data Attachment F - Reference 5.1 Attachment G - Reference 5.2 Attachment H - Computer Disclosure Sheet

"Suppression Pool pH Calculation for Alternative Source Term" Attachment A Determination of Total Exposed Cable Quantities Inside Containment for Assessment of Impact of Radiolytic Chlorine Releases on Suppression Pool pH I.

Purpose The purpose of this attachment is to provide a conservative basis for the calculation of Hydrochloric Acid addition to the suppression pool from radiolysis of exposed chloride-bearing materials inside the drywell during post-Loss of Coolant Accident (LOCA) conditions. The primary exposed chloride-bearing materials are the DuPont Hypalon (or Hypalon-like chlorosulfonated polyethylene rubbers from other manufacturers, such as Okonite) jackets typically used on containment power and control cable. Post-LOCA in-containment radioactivity exposure to these materials can lead to radiolytic breakdown with free chlorine radicals available for carryover as hydrochloric acid to the suppression pool by containment sprays or condensation, with resulting decreases in suppression pool pH. Cables in sealed metal conduits can be excluded from consideration, as there is no mechanism for any significant HCI produced to be released through the conduit (even if connections are assumed to leak, the HCI vapor formed is so chemically reactive that no significant amount would remain unreacted and available for release).

2.

Background and Approach PBAPS Station Electrical Engineer Dale Shallcross developed a listing of the total drywell exposed cable inventory from the INDMS database. The resulting data on cable types and codes, location and length were tabulated and provided to WGI. Following subsequent WGI discussions with Mr.Shallcross on December 26, 2002, he confirmed the data would be a conservative approximation if an additional 10% of cable area is used to account for any missed cable and ifa 5% free air addition is made. He also provided by fax of that date a listing of cable codes vs. their maximum cable outer diameter. This data for each unit were listed in the following spreadsheets with the formulas shown on the last 2 pages (corresponding to the first and last page of the spreadsheets for each unit).

Mr. Shallcross also indicated that there is no cabling underwater or in the air space of the suppression pool.

Hypalon may be used not only as an external cable jacket material, but also as a filler inside the jacket.

Therefore, to conservatively account for such Hypalon use and in accordance with the equivalent assumptions used by Grand Gulf in Reference 5.2 of Calculation PM-1056, an equivalent chlorine-containing material thickness of 80% of the cable radius is used, considered as 100% Hypalon. Additional conservatism is provided by inclusion of all cable types as if they are all Hypalon or Hypalon-equivalent jacketed.

3.

Results The data was used to develop individual and total cable volumes and the resulting volume-average cable radius [derived as the square root of the quantity (Total Cable Volume divided by pi and the Total Cable Length)]. The Hypalon thickness was then derived as 80% of this average cable radius. The calculations indicate that Unit 2 has the greater surface area of 1,837,364 square centimeters, and Unit 3 has the greater Hypalon average thickness of 0.70514 centimeters. For conservatism, this combination of the worst case from each unit is used.

PM-1056, Rev. 0, Attachment A Page A-I of A-49

PBAPS pH Calc., Draft Rev. 0 Attachment B Part 1: Determination of Post-LOCA Drywell/Torus and Suppression Pool Integrated y and 13 Energy, and Suppression Pool Integrated Doses for Suppression Pool pH Determination Part 2: Core Cesium and Iodine Determination Part 3: Drywell and Torus Gamma Mean Free Path Determination 1.

Part I Purpose The purpose of this analysis is to determine Post-LOCA Drywell/Containment and Suppression Pool Integrated y and 13 energies, and Suppression Pool Integrated Doses for Suppression Pool pH Determination. This data is used in Attachment C of this calculation to detennine the radiolytic generation of acid input to the suppression pool.

During a DBA-LOCA, analyzed using Alternative Source Terms (AST), radioactivity is released from the reactor, first during a 1/2 hour gap release period, and then during an early in-vessel release period. Activity is then removed froin containment by decay only for conservatism and simplicity.

2.

Approach This attachment calculates the total integrated ?y and 13 energy released into drywell/containment at specific points in time, and total y plus 13 Dose in the Suppression Pool water. For conservatism in this calculation, all activity is instantly distributed into the drywell and containment airspaces. The data is then used by the spreadsheets in Attachment C to calculate the change in the pH of the pool water as a function of time.

Initial activity in the core is taken from Reference 5.11. Release fractions and timing are per R.G.

1.183, Table 1. For simplicity, and because of its negligible effect, no credit is taken for the 121-second minimum anticipated time before the start of gap activity. No credit is taken for natural' deposition or suppression pool scrubbing. This maintains aerosols airborne to conservatively simulate theoretical plateout contributions. In general, significant amounts of plated-out material are likely to be washed into the suppression pool by condensed vapor flow or containment spray.

Simultaneously, all non-noble gas releases are assumed to be instantly transported to, and uniformly mixed in, the suppression pool water.

The calculation of the dose in the pool water, and the integrated energies from radiation in drywell/containment, parallel each other, up to the point of determining the total integrated y and 13 energy released into containment at the specific time-steps used by Entergy in their GGNS Suppression Pool pH Analysis Calculation (No. XC-Q1 111-98013); the basis for this part of the Peach Bottom AST analysis. First, for each isotope the following list of parameters must be calculated or acquired:

Parameter Origin Decay Constant RadTrad Standard Library Values Release Fractions from 0 to 0.5 hours5.787037e-5 days 0.00139 hours 8.267196e-6 weeks 1.9025e-6 months and Reg. Guide 1.183, Table 1 0.5 to 2 hours2.314815e-5 days 5.555556e-4 hours 3.306878e-6 weeks 7.61e-7 months PM-1056, Rev. 0, Attachment B, Page B-I of B-14

Initial Core Activity Reg. Guide 1.183 Activity in Drywell/Containment due to Calculated Herein, seebelow Gap Release at 0.5 hours5.787037e-5 days 0.00139 hours 8.267196e-6 weeks 1.9025e-6 months Time Integrated Activity through 0.5 hours5.787037e-5 days 0.00139 hours 8.267196e-6 weeks 1.9025e-6 months Calculated Herein, see below of Gap Release Activity in Drywell/Containnment due to Calculated Herein, see below Early In-vessel Release at 2 hours2.314815e-5 days 5.555556e-4 hours 3.306878e-6 weeks 7.61e-7 months Time Integrated Activity through 2 hours2.314815e-5 days 5.555556e-4 hours 3.306878e-6 weeks 7.61e-7 months of Calculated Herein, see below Early In-vessel Release Total Time Integrated Activity Released Calculated Herein, see below through 2 hours2.314815e-5 days 5.555556e-4 hours 3.306878e-6 weeks 7.61e-7 months Total Activity in Drywell/Containnment at 2 Calculated Herein, see below hours Gamma (Photon) Emission Energy Radioactive Decay Data Tables, by David C. Kocher [Ref. 5.12] as compiled in RadDecay program Beta Particle Emission Energy Radioactive Decay Data Tables, by David C. Kocher [Ref. 5.12] as compiled in RadDecay program Calculated Values In order to evaluate the activity in containment, and subsequently the concentration of activity, it was necessary to develop finctions that took into account the Peach Bottom conditions, while providing the necessary inputs for the analysis model of GGNS.

Activity in Drvwell/Containment up through 0.5 Hours (Due to Gap Release) a G(.5) = Ji05 X 0.5 0'e-0.5 =fo-0. x a'e -10.5 0.5 aG(;)

= 4fo-t a,-e 0.5 f,,= activity release fraction at 30 minutes, variable depending on isotope a,,= initial core activity, variable depending on isotope (Ci) e= constant 2= decay constant, variable depending on isotope (hours-')

t= time (hours)

('/t).5)= release fraction buildup over 0.5 hours5.787037e-5 days 0.00139 hours 8.267196e-6 weeks 1.9025e-6 months related linearly (as done in RadTrad)

Activity in Drywell/Containment up through 2 Hours (Due to Early In-vessel Release) 2-0.5 e-AM Ae-

-A aE(2 ) =.fS-2 x-x x

J'5-2 xa,e 1.5 t

a

_E(2)=J-x-

xa,e 1.5 PM-1056, Rev. 0, Attachment B, Page B-2 of B-14

f/*.5= activity release fraction at 2 hours2.314815e-5 days 5.555556e-4 hours 3.306878e-6 weeks 7.61e-7 months , variable depending on isotope a,,= initial core activity, variable depending on isotope (Ci) e= constant A= decay constant, variable depending on isotope (hours- )

t= time (hours)

(V1.5)= release fraction buildup over 1.5 hours5.787037e-5 days 0.00139 hours 8.267196e-6 weeks 1.9025e-6 months related linearly (as done in RadTrad)

Time Integrated Activity through 0.5 Hours (from Gap Release) 0.50.

aG(t) = ar, x./,-0.5 x< 0.

e 5

0.5 0.5 AGOO-S.= faG(t)d(-1t

'1 -=

0.

Jte-'dt 0

0 AGO-0O.

\\,-/0

[1 - e-°"

(0.52 + 1)]

0.5A.

:=activity release fraction at 2 hours2.314815e-5 days 5.555556e-4 hours 3.306878e-6 weeks 7.61e-7 months , variable depending on isotope (1/,.)= release fraction buildup over 0.5 hours5.787037e-5 days 0.00139 hours 8.267196e-6 weeks 1.9025e-6 months related linearly (as done in RadTrad) a,,= initial core activity, variable depending on isotope (Ci) e= constant 2= decay constant, variable depending on isotope (hours-)

t= time (hours) ac,(t)= activity in containment as a function of time, due to gap release (Ci)

AGo_, 5.= time integrated activity though 0.5 hours5.787037e-5 days 0.00139 hours 8.267196e-6 weeks 1.9025e-6 months due to gap release (Ci-hours)

Time Integrated Activity through 2 Hours (from Early In-vessel Release) aE (t) = a e-X.105 x

x x

[Note: Here i starts after 0.5 hour]

1.5 1.5 Sa,,e-

'x,/0.S-z te-Aldt AEO-, =

.E5 t)d,-t 0

0 A E0

-I.~5 IA 22

- e-""S(1.52 + 1) f.-0.5= activity release fraction at 2 hours2.314815e-5 days 5.555556e-4 hours 3.306878e-6 weeks 7.61e-7 months , variable depending on isotope

(//..)= release fraction buildup over 1.5 hours5.787037e-5 days 0.00139 hours 8.267196e-6 weeks 1.9025e-6 months related linearly (as done in RadTrad) a,,= initial core activity, variable depending on isotope (Ci) e= constant A= decay constant, variable depending on isotope (hours-)

t= time (hours) aE(t)= activity in containment as a function of time, due to early in-vessel release (Ci)

AEOI.5= time integrated activity from 0.5 to 2 hours2.314815e-5 days 5.555556e-4 hours 3.306878e-6 weeks 7.61e-7 months due to early in-vessel release (Ci-hours), after shutdown Total Time Integrated Activity Released in Drywell/Containment through 2 Hours A 2,,,,, = A GO0.5 + A E0-.5 PM-1056, Rev. 0, Attachment B, Page B-3 of B-14

AGO,,5= time integrated activity though 0.5 hours5.787037e-5 days 0.00139 hours 8.267196e-6 weeks 1.9025e-6 months due to gap release (Ci-hours)

AEOI-= time integrated activity froni 0.5 to 2 hours2.314815e-5 days 5.555556e-4 hours 3.306878e-6 weeks 7.61e-7 months due to early in-vessel release (Ci-hours), after shutdown Total Activity in Drywell/Containment at 2 Hours.

a(2),,,,=

a(2) + a(0.5) x e-'5 a(0.5)= activity present in containment at 0.5 hours5.787037e-5 days 0.00139 hours 8.267196e-6 weeks 1.9025e-6 months e= constant

,= decay constant, variable depending on isotope (hours-)

t= time (hours)

When the above values are obtained for each isotope, the Activity in Containment can be calculated at given times, and subsequently the energy from the activity can be calculated in the following manner:

Total Time Integrated Activity in Drywell/Containment at Specific Times (t hours) a,i,,, = (

') x (1 - eI't 2 ) + A, a(2)1,,,,,= total activity in containment at 2 hours2.314815e-5 days 5.555556e-4 hours 3.306878e-6 weeks 7.61e-7 months (Ci) a,,,,,,*= total time integrated activity released through 2 hours2.314815e-5 days 5.555556e-4 hours 3.306878e-6 weeks 7.61e-7 months (Ci-hours) 2= decay constant, variable depending on isotope (hours-')

t= time (hours)

At this point, the above equation is used to calculate the activity at the given timesteps, due to 7 and P3 radiation and the values are sunmmed for all contributing sources, as used in the GGNS analysis model. Finally, the activity's radiation energy concentration is calculated by dividing over the airspace volume of containment. Subsequently, this data is input into the spreadsheet of Attachment C to calculate the concentration of HCI that results in the pool (due to the release of chlorine from the radiolysis of cables in primary containment), and its contribution to the pH transient.

Of additional concern is the formation of Nitric Acid (HNO3), which contributes to the transient calculated in Attachment C, by serving to lower the pH in the pool. Any activity from sources found inunediately in the pool water is a factor in this acid's formation; therefore a dose to the water must also be calculated. Because the noble gas sources stay gaseous and do not mix with the pool water, we need only to consider non-noble gas sources in this calculation. As stated earlier, up to the point of determining the total integrated y and P3 energy released into containment at the specific time-steps, the calculation, of the dose in the pool water, and the integrated energies from radiation in containment parallel each other.

As before, the activities at given timesteps are summed for all contributing sources and the radiation energy concentration is calculated. However, the Entergy designed spreadsheet used in Attachment C uses a dose value for its calculation directly to HNO3 concentration, so it was necessary to convert the energy concentration (MeV/cm 3) to dose (Mrad). The conversion factor PM-1056, Rev. 0, Attachment B, Page B-4 of B-14

was detenrined to equal 1.60209E-14 (Mrad/(MeV/cm3)h. When all concentrations were converted to doses, the y and P3 values were sumnmed and input into Attachment C to calculate the concentration of HNO 3 formed, and its contribution to the pH transient.

Part 2: Core Cesium and Iodine Determination Cesium and Iodine released from the core during the DBA-LOCA have an impact on suppression pool pH.

lodines can contribute to the formation of hydriodic acid, HI, and cesiums contribute to formation of Cesium Hydroxide, CsOH. There is significantly more Cesium available and released from the core than Iodine. Therefore, these materials lead the suppression pool to be basic essentially from the beginning of fission product release. The quantities of Cesium and Iodine, tabulated on page B-14, were taken from the PBAPS Loss of Coolant Accident (LOCA) calculation's attached Source Terms.

Part 3: Drvwell and Containment Gamma Mean Free Path Determination Gamma mean free paths in the drywell are used to conservatively assess the size of the contained cloud that will irradiate cable. The determination of these values is perforned in a manner identical to that used for the GGNS assessment. That is, for the drywell, the entire radius of 34 feet from the reactor center to the drywell wall is used, neglecting shielding provided by the vessel and shield.

PM-1056, Rev. 0, Attachment B, Page B-5 of B-14

PM-1056. Re-. 0 Att-ah nl-B

PM.1056. Rv 0. Atmchmenl 6

If

41I IT I8

PM-.W56.

Rev.O. Attachment 8

U6?

6E 9E

PM 1056 Rev 0. Aih*thmen, B

Class 9

6 6

8 8

8 9

9 7

7 3

3 3

2 2

2 1

1 1

1 9

9 9

7 9

9 8

9.

8 8

3 7

7 7

7 4

4 5

5 5

5 7

4 4

Isotopic Nuclide Am-241 Ba-1 39 Ba-140 Ce-141 Ce-143 Ce-144 Cm-242 Cm-244 Co-58 Co-60 Cs-134 Cs-1 36 Cs-137 1-131 1-132 1-133 1-134 1-135 Kr-85 Kr-85m Kr-87 Kr-88 La-140 La-141 La-142 Mo-99 Nb-95 Nd-147 Np-239 Pr-143 PU-238 Pu-239 Pu-240 Pu-241 Rb-86 Rh-105 Ru-103 Ru-105 Ru-106 Sb-127 Sb-129 Sr-89 Sr-90 Sr-91 Sr-92 Tc-99m Te-127 Te-127m 24 Hours 1.31E-02 4.41E+02 9.05E+03 2.11 E+02 1.53E+02 1.81 E+02 5.96E+00 1.15E+00 3.63E+00 4.36E+00 1.14E+04 3.38E+03 1.01E+04 7.24E+04 1.11E+04 1.05E+05 3.76E+03 4.96E+04 3.56E+03 1.45E+04 5.34E+03 2.35E+04 7.85E+01 1.66E+01 4.68E+00 1.04E+03 8.70E+01 3.32E+01 2.72E+03 7.51E+01 1.22E+00 5.86E-02 1.26E-01 2.45E+01 1.11E+02 4.93E+02 9.89E+02 1.52E+02 3.71 E+02 9.90E+02 8.88E+02 4.94E+03 6.29E+02 2.77E+03 8.28E+02 3.24E+02 4.72E+02 1.81 E+02 96 Hours 5.47E-02 4.41 E+02 3.48E+04 8.52E+02 3.48E+02 7.49E+02 2.47E+01 4.79E+00 1.49E+01 1.82E+01 4.75E+04 1.31 E+04 4.24E+04 2.67E+05 1.11E+04 1.90E+05 3.76E+03 5.47E+04 1.48E+04 1.49E+04 5.34E+03 2.36E+04 1.95E+02 1.69E+01 4.68E+00 3.1OE+03 3.52E+02 1.26E+02 7.68E+03 2:90E+02 5.09E+00.

2.05E-01 5.28E-01 1.02E+02 4.39E+02 1.16E+03 4.01E+03 1.57E+02 1.54E+03 3.21 E+03 9.12E+02 2.02E+04 2.62E+03 3.42E+03 8.30E+02 3.50E+02 5.78E+02 7.45E+02 720 Hours 4.15E-01 4.41 E+02 1.45E+05 4.98E+03 4.03E+02 5.51 E+03 1.77E+02 3.63E+01 9.98E+01 1.37E+02 3.56E+05 5.51 E+04 3.21 E+05 8.56E+05 1.11 E+04 1.99E+05 3.76E+03

. 5.47E+04 1.12E+05 1.49E+04 5.34E+03 2.36E+04 2.42E+02 1.69E+01 4.68E+00 4.91 E+03 2.10E+03 4.86E+02 1.12E+04 1.24E+03 3.86E+01 1.47E+00 4.01 E+00 7.71 E+02 2.16E+03 1.37E+03 2.45E+04 1.57E+02 1.14E+04 6.28E+03 9.12E+02 1.29E+05 1.98E+04 3.43E+03 8.30E+02 3.50E+02 5.79E+02 5.21 E+03 24 Hours 1.10E+02 3.68E+06 7.55E+07 1.76E+06 1.28E+06 1.51E+06 4.97E+04 9.59E+03 3.03E+04 3.64E+04 9.49E+07 2.82E+07 8.46E+07 6.04E+08 9.22E+07 8.79E+08 3.13E+07 4.14E+08 2.97E+07 1.21E+08 4.45E+07 1.96E+08 6.55E+05 1.39E+05 3.91 E+04 8.71 E+06 7.26E+05 2.77E+05 2.27E+07 6.26E+05 1.02E+04 4.89E+02 1.05E+03 2.04E+05 9.26E+05 4.11 E+06 8.25E+06 1.27E+06 3.10E+06 8.26E+06 7.41 E+06 4.12E+07 5.25E+06 2.31 E+07 6.90E+06 2.70E+06 3.94E+06 1.51 E+06 96 Hours 4.56E+02 3.68E+06 2.90E+08 7.11 E+06 2.90E+06 6.25E+06 2.06E+05 3.99E+04 1.24E+05 1.52E+05 3.96E+08 1.09E+08 3.53E+08 2.23E+09 9.23E+07 1.59E+09 3.13E+07 4.56E+08 1.24E+08 1.25E+08 4.45E+07 1.97E+08 1.63E+06 1.41 E+05 3.91 E+04 2.58E+07 2.94E+06 1.05E+06 6.40E+07 2.42E+06 4.25E+04 1.71 E+03 4.40E+03 8.49E+05 3.66E+06 9.64E+06 3.35E+07 1.31 E+06 1.29E+07 2.68E+07 7.61 E+06 1.68E+08 2.18E+07 2.86E+07 6.92E+06 2.92E+06 4.83E+06 6.22E+06

4 Te-129 1.39E+02 1.39E+02 1.39E+02 1.16E+06 1.16E+06 4

Te-129m 7.73E+02 3.12E+03 1.84E+04 6.45E+06 2.61E+07 4

Te-131m 1.89E+03 4.11E+03 4.63E+03 1.58E+07 3.43E+07 4

Te-132 1.63E+04 5.08E+04 8.93E+04 1.36E+08 4.24E+08 1

Xe-133 4.81E+05 1.66E+06 4.01E+06 4.02E+09 1.39E+10 1

Xe-135 5.97E+04 7.24E+04 7.25E+04 4;98E+08 6.04E+08 9

Y-90 5.68E+00 1.67E+01 2.60E+01 4.74E+04 1.39E+05 9

Y-91 6.42E+01 2.63E+02 1.72E+03 5.36E+05 2.19E+06 9

Y-92 1.16E+01 1.18E+01 1.18E+01 9.71E+04 9.82E+04 9

Y-93 2.36E+01 2.98E+01 2.98E+01 1.97E+05 2.48E+05 9

Zr-95 8.68E+01 3.56E+02 2.35E+03 7.24E+05 2.97E+06 9

Zr-97 5.10E+01 8.23E+01 8.40E+01 4.25E+05 6.86E+05

720 Hours 3.46E+03 3.68E+06 1.21 E+09 4.16E+07 3.36E+06 4.60E+07 1.48E+06 3.03E+05 8.33E+05 1.14E+06 2.97E+09 4.60E+08 2.68E+09 7.14E+09 9.23E+07 1.66E+09 3.13E+07 4.56E÷08 9.37E+08 1.25E+08 4.45E+07 1.97E+08 2.02E+06 1.41E+05 3.91 E+04 4.1OE+07 1.75E+07 4.05E+06 9.32E+07 1.04E+07 3.22E+05

.1.23E+04 3.35E+04 6.43E+06 1.80E+07 1.14E+07 2.04E+08 1.31 E+06 9.52E+07 5.24E+07 7.61 E+06 1.08E+09 1.66E+08 2.86E+07 6.92E+06 2.92E+06 4.83E+06 4.35E+07 8.343E+03

1.16E+06 1.54E+08 3.86E+07 7.45E+08 3.35E+10 6.05E+08 2.17E+05 1.43E+07 9.82E+04 2.49E+05 1.96E+07 7.01 E+05

Class 9

6 6

8 8

8 9

9 7

7 3

3

.3 2

2 2

9 9

9 7

9 9

8 9

8 8

3 7

7 7

7 4

4 5

5 5

5 7

4 4

Isotopic Nuclide Am-241 Ba-1 39 Ba-140 Ce-141 Ce-143 Ce-144 Cm-242 Cm-244 Co.58 Co-60 Cs-1 34 Cs-1 36 Cs-1 37 1-131 1-132 1-133 1-134 1-135 La-140 La-141 La-142 Mo-99 Nb-95 Nd-147 Np-239 Pr-143 Pu-238 Pu-239 Pu-240 Pu-241 Rb-86 Rh-105 Ru-103 Ru-105 Ru-106 Sb-1 27 Sb-129 Sr-89 Sr-90 Sr-91 Sr-92 Tc-99m Te-127 Te-1 27m Te-129 Te-129m Te-131m Te-132 24 Hours 3.19E-02 1.07E+03 2.20E+04 5.14E+02 3.72E+02 4.39E+02 1.45E+01 2.80E+00 8.83E+00 1.06E+01 2.77E+04 8.22E+03 2.47E+04 1.76E+05 2.69E+04 2.56E+05 9.14E+03 1.21E+05 1.91 E+02 4.04E+01 1.14E+01 2.54E+03 2.12E+02 8.09E+01 6.62E+03 1.83E+02 2.97E+00 1.42E-01 3.06E-01 5.95E+01 2.70E+02 1.20E+03 2.41 E+03 3.70E+02 9.03E+02 2.41 E+03 2.1.6E+03 1.20E+04 1.53E+03 6.75E+03 2.01 E+03 7.89E+02 1.15E+03 4.40E+02 3.38E+02 1.88E+03 4.60E+03 3.97E+04 96 Hours 720 Hours 1.33E-01 1.01E+00 1.07E+03 1.07E+03 8.46E+04 3.52E+05 2.07E+03 1.21E+04 8.46E+02 9.80E+02 1.82E+03 1.34E+04 6.OOE+01 4.31E+02 1.16E+01 8.82E+01 3.62E+01 2.43E+02 4.42E+01 3.34E+02 1.16E+05 8.67E+05 3.18E+04 1.34E+05 1.03E+05 7.82E+05 6.50E+05 2.08E+06 2.69E+04 2.69E+04 4.63E+05 4.83E+05 9.14E+03 9.14E+03 1.33E+05 1.33E+05 4.74E+02 5.89E+02 4.12E+01 4.12E+01 1.14E+01 1.14E+01 7.54E+03 1.20E+04 8.57E+02 5.1OE+03 3.07E+02 1.18E+03 1.87E+04 2.72E+04 7.06E+02 3.03E+03 1.24E+01 9.39E+01 4.98E-01 3.58E+00 1.28E+00 9.76E+00 2.48E+02 1.88E+03 1.07E+03 5.26E+03 2.81E+03 3.33E+03 9.76E+03 5.95E+04 3.81E+02 3.81E+02 3.75E+03 2.78E+04 7.81E+03 1.53E+04 2.22E+03 2.22E+03 4.91E+04 3.14E+05 6.37E+03 4.83E+04 8.33E+03 8.34E+03

.2.02E+03 2.02E+03 8.51E+02 8.51E+02 1.41E+03 1.41E+03 1.81E+03 1.27E+04 3.38E+02 3.38E+02 7.60E+03 4.48E+04 1.OOE+04 1.13E+04 1.24E+05 2.17E+05 24 Hours 1.10E+02 3.68E+06 7.55E+07 1.76E+06 1.28E+06 1.51 E+06 4.97E+04 9.59E+03 3.03E+04 3.64E+04 9.49E+07 2.82E+07 8.46E+07 6.04E+08 9.22E+07 8.79E+08 3.13E+07 4.14E+08 6.55E+05 1.39E+05 3.91 E+04 8.71 E+06 7.26E+05 2.77E+05 2.27E+07 6.26E+05 1.02E+04 4.89E+02.

1.05E+03 2.04E+05 9.26E+05 4.11 E+06 8.25E+06 1.27E+06 3.1OE+06 8.26E+06 7.41 E+06 4.12E+07 5.25E+06 2.31 E+07 6.90E+06 2.70E+06 3.94E+06 1.51 E+06 1.16E+06 6.45E+06 1.58E+07 1.36E+08 96 Hours 4.56E+02 3.68E+06 2.90E+08 7.11 E+06 2.90E+06 6.25E+06 2.06E+05 3.99E+04 1.24E+05 1.52E+05 3.96E+08 1.09E+08 3.53E+08 2.23E+09 9.23E+07 1.59E+09 3.13E+07 4.56E+08 1.63E+06 1.41 E+05 3.91 E+04 2.58E+07 2.94E+06 1.05E+06 6.40E+07 2.42E+06 4.25E+04 1.71E+03 4.40E+03 8.49E+05 3.66E+06 9.64E+06 3.35E+07 1.31 E+06 1.29E+07 2.68E+07 7.61 E+06 1.68E+08 2.18E+07 2.86E+07 6.92E+06 2.92E+06 4.83E+06 6.22E+06 1.16E+06 2.61 E+07 3.43E+07 4.24E+08

9 9

Y-90 Y-91 Y-92 Y-93 Zr-95 Zr-97 1.38E+01 1.56E+02 2.83E+01 5.73E+01 2.11 E+02 1.24E+02 4.06E+01 6.40E+02 2.86E+01 7.24E+01 8.66E+02 2.OOE+02 6.33E+01 4.18E+03 2.86E+01 7.25E+01 5.73E+03 2.04E+02 4.74E+04 5.36E+05 9.71 E+04 1.97E+05 7.24E+05 4.25E+05 1.39E+05 2.19E+06 9.82E+04 2.48E+05 2.97E+06 6.86E+05

720 Hours 3.46E+03 3.68E+06 1.21E+09 4.16E+07 3.36E+06 4.60E+07 1.48E+06 3.03E+05 8.33E+05 1.14E+06 2.97E+09 4.60E+08 2.68E+09 7.14E+09 9.23E+07 1.66E+09 3.13E+07 4.56E+08 2.02E+06 1.41 E+05 3.91 E+04 4.10E+07 1.75E+07 4.05E+06 9.32E+07 1.04E+07 3.22E+05 1.23E+04 3.35E+04 6.43E+06 1.80E+07 1.14E+07 2.04E+08 1.31 E+06 9.52E+07 5.24E+07 7.61 E+06 1.08E+09 1.66E+08 2.86E+07 6.92E+06 2.92E+06 4.83E+06 4.35E+07 1.16E+06 1.54E+08 3.86E+07 7.45E+08 3.43E+03

2.17E+05 1.43E+07 9.82E+04 2.49E+05 1.96E+07 7.01 E+05

pH vs. Time - BEGINNING OF CYCLE.

10.00 9.00 8.00 7.00 6.00 5.00 4.00 3.00 2.00 1.00 0.00

.J - 77771 F

I

-- t-::: " ith S LC S 1

10 100

.1000 Time (Hours)

(PBAPS) PM-1056 Rev 0 AST pH Attachments C, D, E Main Calc Spreadsheets BOC Graph

pH vs. Time - END OF CYCLE 10.00 9.00 8.00 7.00 6.00

=

5.00 0.

4.00 3.00 2.00 1.00 0.00 I

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i L,

4Vq t-I I IN EH 1ý 4ý4

- T-t- Ll Tý 4 Eý Jý ýN ý 1t

+

A

/--wo SLOS WC2*_

with SLCS t44ývý 4ýq 44

- I Frtýý--

3fla 1

10 100 1000 Time (Hours)

(PBAPS) PM-1056 Rev 0 AST pH Attachments C, D, E Main Calc Spreadsheets EOC Graph

PEACH BOTTOM ATOMIC POWER STATION TRANSIENT POOL pH CALCULATION A

I B

C o

E 6F GH I

K L

MN 1 PEACH BOTTOM pH CALCULATION pH TRANSIENT BEGINNING OF CYCLE Cable Data 22 2

Linear Absorption Coefficients 4 SAt,-a [cm 2]

2.021.100 Cable Surface [trays]- Drywelt + 10% contingency 3

VpOOL 3.480E+06 Liters. 1122900 ft3 Ubeta air 1.980E-02 1/cm SA 1. [Cm!'l 101.055 Cable Surface [free air]- Drywell + 10% contingency 4,

mlT 1.700E.02 Iodine inventory [9-atoms] EOC 1

Uibea hypalon 52.08 1/cm Se e

[cm 2

]

0 Cable Surface [trays] -TORUS + 10% contingency 5

mcs

1.600E+03 Cesium inventory (g-atoms] EOC'9 Ugarma air 3.75E-05 1/cm S fa [cm 2]

0 Cable Surface [free air] - TORUS + 10% contingency 6

tap 3.361E-02 Onset of Gap release [hrsm 2Laanma hyPalon

.0090 1/cm I

7 r I.*re *

-ý!_r-,'OEL) 1036.32 cm th

[cm]

070514 Hypalon Jacket ThSckness 8

r

-re.

erTORUS-AIR]

464.82 cm 9

INTEGRATED DOSES 10 Beta+Gamma' 8

Gamma' 0

Beta"i Gammae Betar8 From Beta From Gamma From Beta From Gamma 11 TIME POOL Temp POOL DRYWELL DRYWELL TORUS AIR TORUS AIR

{Hi] -

[HNO,3

[HCL] -DRYWELL

[HCL] -DRYWELL [HCL] -CONTAIus [HCL] -CONTAIN" Total [H+]J

[CsOH j

12 Hours Dg F" Mrad MeVm MeV/cm g-mols/liter g-molstlsliter g-molslliter g-molts/liter 9-molstliter g-ionstliter g-mols/liter 13 0

80 0 OOE+00 5.012E-06 0.000E+0_

14 1

175 3 120E-07 5.324E-06 4.565E-05 15 2

187 1.435E-01 3415E+12 1.494E612 3+12 7.190E07 1.048E-06 8.077E-07 4.774L-06 0.00E+00 0.000E+00 1.236E-05 9.922E-00 16 2.0336 188 1.496E-01 3.557E+12 1.556E÷12 7071E+12 2.205E+12 7.327E-07 1.092E-06 8.414E-07 4.973E-06 0.OOOE.00 0.OOOE+00 1.265E-05 1.010E-04 17 3

192 3.093E-01 7.224E+12 3.184E+12 1.452E+13 4.654E+12 7.327E-07 2 258E-06 1.722E-06 1.010E-05 0.OOOEO00 0.000E+00 1.982E-05 1.010E-04 18 5

199 5.717E-01 1.299E+13 5.868E+12 2.658E+13 8.862E+12 7.327E-07 4.174E-06 3.173E-06 1.816E-05 0.000E+00 0.0006+00 3.125E-05 1.010E-04 19 12 204 1.189E+00 2.485E+13 1.227E+13 5.412E+13 1.958E+13 7.327E-07 8680E-06 6633E-06 3.473E-05 0.OOOE+00 0.000E+00 5.579E-05 1.010E-04 20 18 198 1.557E+00 3.103E+13 1.624E+13 7.012E+13 2.639E+13 7.327E-07 1.136E-05 8.782E-06 4.338E-05 0 OOOE+00 0.000E+00 6.927E-05 1.010E-04 21 24 197 1.852E+00 3.578E+13 1.953E+13 8.281E+13 3.199E61 3 7327E-07 1.352E-05 1.056E-05 5.002E-05 0.000E+00 0.000+E00 7.985E-05 1.010E-04 22 48 190 2.700E+00 4.929E+13 2.943E+13 1.194E+14 4801E+13 7.327E-07 1.971E-05 1.592E-05 6.890E-05 0.000E+00 0.0006+00 1.103E-04 1.010E-04 23 72 177 3.319E600 5.937E+13 3.686E+13 1.466E+14 5910E+13 7.327E-07 2.423E-05 1.993E-05 8.300E-05 0.000E+00 0.0006+00 1.329E-04 1.010E-04 24 96 160 3.839E600 6801E+13 4.306E613 1.700E+14 6.796E+13 7.327E-07 2802E-05 2.329E-05 9.506E-05 0.000E+00

.0.000+E00 1.521E-04 1010E-04 25 120 153 4.304E+00 7578E+13 4.847E613 1.912E+14 7.562E+13 7.327E-07 3.142E-05 2 621E-05 1 059E-04 0 000E+00 0.000E+00 1.693E-04 1.010E-04 26 150 149 4839E+00 8.466E+13 5.441E+13 2.157E+14 8.420E+13 7.327E-07 3 532E-05 2.943E-05

1.183E-04 0.0006+00 0.0006E00 1 BBE-04 1.010E-04 27 200 142 5.651E+00 9.801E613 6279E+13 2.534E+14 9.696E+13 7.327E-07 4.125E-05 3.396E-05 1.370E-04 0000E+00 00006+00 2.180E-04 1.010E-04 28 240 138 6.250E+00 1.077E+14 6.844E-13 2.813E+14 1.062E+14 7327E-07 4.562E-05 3.701E-05 1.505E-04 0.000E+00 00006+00 2.389E-04 1.010E-04 29 300 132 7.081E+00 1.209E+14 7.557E+13 3.202E+14 1.188E+14 7.327E-07 5.169E-05 4.087E-05 1.689E-04 0.000E+00 0.000E+00 2.672E-04 1.010E-04 30 360 127 7.847E+00 1.328E+14 8.146E+13 3.563E614 1 301E+14 7.327E-07 5.729E-05 4.406E-05 1.856E-04 0.000E+00 0.0006+00 2.927E-04 1.010E-04 31 400 124 8.328E+00 1.402E+14 8.486E+13 3.791E+14 1 37.1E+14 7.327E-07 6.079E-05 4.589E-05 1.960E-04 0.O00E+00 0.000E+00 3.084E-04 1.010E-04 32 480 123 9.230E+00 1 540E+14 9.071E613 4.221E+14 1.500E+14 7.327E-07 6.738E-05 4.905E-05 2.152E-04 0.000E+00 0.000E+00 3.374E-04 1010E-04 33 600 120 1.047E+01 1.727E+ 14 97806+13 4.817E+14 1.672E+14 7.327E-07 7.642E-05 5.289E-05 2.413E-04 0.000E+00 0.0006+00 37646-04 1.010E-04 34 700 1 119 1142E+01 1.870E614 1.027E+14 5.280E+14 1.801E+14 7.327E-07 8.338E-05 5.556E-05 2.613E-04 0.000E+00 0.000E+00 4060E-04 1010E-04 35 720 117 1.161E+01 1.897E+14 1.036E+14 5.369E+14 1.825E+14 7.327E-07 8472E-05 5.605E-05 2.652E-04 0.000E+00 0.000E+00 4.117E-04 1.010E-04 36 37 NOTES 141 Acid dissociation constant from: Entery Eng. Report GGNS-98_-0039 Rev.3, Sect.6.1.p.21 38 1 Entergy Eng. Report GGNS-98-0039 Rev.3, Equation 3-1d [30+90 min release duration]

15 Entergy CaIc. XC-011111-98013 Rev.2. Section 5.7 39 2 Ibid. Equation 3-25b16 See attachment B for gamma free paths 40 3 Ibid. 6uation 3E 4d 30.90 min release durationi PBAPS UFSAR Fig. 14.6.12 IRev.14) and Fig. I_4.6.12A (Rev. 15) 41 4 Ibid. Table A-1 18 A.ttachment B 42 5 Ibid. Equation 3-3a 19 Attachment B 43 6 Ibid, Equalion 3-3b 20 USNRC Reg. Guide 1 13

44.

7 Ibid, Equation 3-5a: Entergy Calc. XC-Q11111-98013 Rev.2, Section 5.7 21 Tech Spec SR 3.1 7.7 minimum B-10 stored in SBLC tank of 162.7 lbs, conservatively less than from 45 8 Ibid, Equation 3-5b: Entergy CaIc. XC-011111-98013 Rev.2, Section 5-7 plant chemistry data transmited via E-mail by Mark G. Fry on 12/27/2002, 46 9 Ibid. Equation 3-0a; Entergy CaIc. XC-O11111-98013 Rev.2, Section 5-7 ncluded as Attachment H. 65 atom % B-10 enrichment used, bounding 47 10 Ibid. Equation 3-5d, Entergy Cate. XC-Q11111-98013 Rev.2. Section 5-7 the =igbest 635 atom% B-10 from Attachment H 48 11 Ibid. Equation 3-5d; Entergy CaIc. XC-Q11111-98013 Rev.2. Section 5-7 22 Cable 1

ata from Attachment A.

49 12 I bid. Equation 3-5e: Entergy Calc. XC-Q11111-98013 Rev.2, Section 5-7 50 13 Min. Suppression Pool volume from PBAPS Tech. Spec. Bases B 3.6.2.2 PM-1056; Rev. 0, Attachment C, Page C-1 of C-4

PEACH BOTTOM ATOMIC POWER STATION TRANSIENT POOl. pH CALCULATION P

R S

T U

I V

W Y

Z AA.

AB 1

PH TRANSIENT BEGINNING OF CYCLE I

I 2 Cable Data 1

1134.24 g. mots Na 2B, 0O,6*10H2O Added 3

1.837,364 Cable Surface [Trays] - DRYWELL (cm2]

162.7 73799.09 lb/grams B-10"Y 10.01 atomic ml. B-10 4

91,868 Cable Surface [Free air] - DRYWELL [cm2]

65.60 atom % B-10" 7372.54 g. atoms B-10 5

0 Cable Surface [Free air] - TORUS [cm2]

11342.36 g.atoms total boron 6

0 Cable Surface [Trays) - TORUS [cm2]

8 pH EFFECT OF ADDITION OF SODIUM PENTABORATE STANDBY LIQUID CONTROL [SLC] SOLUTION 10 t

Strong Acid Total (OH.)

-LO(Kw)

-Root x

Net[H))

pH g-equiv.

Na2BoOlB't0H2Oj

. Borate Boric Acid pl<,

pH

12) g-ions/liter g-ions/liter Before SLC I Net [H+]

Vo, g-mols

. I a-ectuis. I a-oasis.

I *log.K, 15 131 1.995E-09 1.394E+01 I -3.197E-101 5 012E-06 14 1 4.565E-05 1.744E+0J1 1134.2

'1 2251 90911 "9.2 M.62 2072E-021 1134.2 2

9074 8.941 8.4 1.278E-02.

1134.2 2268 9074 8.911

.3 "151 "9.922E-05 8.431 1.231E-0E 1.285E-0:

1134.2 2266 90741 8.91 8.31 8.361 1.254E-091 1.528E-021 1134.2 2268 90741 890 8.30 18 1.010E-041 1.238E+01I 3.125E-051 5.938E-091 8.231 1.295E-00 2.066E-0; 191 1.010E-041 1.234E+01I 5.578E-05 1 014E-081 7.991 1.324E-091 3.530E-021 20 1.010E-04 1.239E+01I 6.926E-051 1.277E-081 7.891 1.289E-00 4 445E-0 iTI 1.010E-041 1.240E+01 I 7.983E-051 1.875E-1 7t.

1134.2 1134.2 1134.2 1134.2 1134.2 1134.2 2268 90741 8.89 2268 2268 2268 2236 2157 8.29 8.28 8.29 8.29 9074 22 1.010E-04 1.247E+01 1.010E-04 9.289E-06 5031 1.242E-00 1.2606+01 1.0106-04 3.189E-05 4 50 1.166E-00 9106 8.30 23 1.010E-04 1.110E+0; 9185 893 8.30 24 1.010E-04 1.0671-091 1 779E+021 11342 2091 9252 8.971 8.331 25 1

31 4.171 1.026E-09 2.377E+0:

1134.2 2031 9312 8 99 8.33 1

4.061 1.003E-091 3.056E+021 1134.2 1963 9380 9.00 8.32 27 1.010E-041 1.301E+01I 1.010E-041 1.169E-041 3.931 9.616E-10 4.070E+0; 1134.2 1862 94811 9.021 8.31 281 1.010E-041 1.306E+011 1.010E-.04 1.379E-041 3.861 9.382M-10 4.798E+02 1134.2 1789 29 1.010E-041 1.314E+011 1.010E-041 1:662E-041 3.781 9.031E-10 5.785E+0; 301 1.010E-041 1.321E+011 1.010E-04 1.917E-041 3 721 31 1.010E-041 1.325E+011 1 010E-041 2.074E-041 3.681 f

321 1.010E-041 1.326E+01 1.010E-04 2 364E-r4 1134.2 1134.2 1134.2 1134.2 1134.2 1134.2 1690 1446 98971 907 8.23 33 34 35 36 1.010E-041 1.331 E,01 I 1.010E-041 2.754E-041 1310 10032[

9.081 8.201 8.271E-10 1.061E+01 1207 101351 9.08 8.16 37 38 39 40 41 43~

_L5 PM-1056, Rev. 0, Attachment C. Page C-2 of C-4

PEACH BOTTOM ATOMIC POWER STATION TRANSIENT POOL pH CALCULATION A

B I

C I

F G

H I

J K

L M

N 0

1 PEACH BOTTOM pH CALCULATIONI pH TRANSIENT END OF CYCLE Cable Data 2

Linear Absorption Coefficients 4 SAtr1 [cm']

2.021.100 Cable Surface [trays)- Drywell + 10% contingency 3

VPOOL 3.480E+06 Liters [122900 ft'[

Ubeta air 1.960E-02 1/cm SA ra [cm 2

]

101.055 Cable Surface [free air]- Drywell + 10% contingency 4

mi 2.900E+0.2 Iodine inventory {g-atoms] EOC" Ubeta hypalon 52.08 1/cm Se _' [cm2[

0 Cable Surface [trays] - TORUS + 10% contingency 5

mIc 3.200E+03 Cesium inventory [g-atoms] EOCr Up-air 3.75E-05 1/cm Sea

[cm']

0 Cable Surface [free air] - TORUS + 10% contingency 6

tvap 3.361E-02 Onset of Gap release [hrs]

Ugamma hypalon 0099 1/cm.

I "

7 r l h1 RL-L]s l

1036.32 cm th [cm]

0.70514 Hypalon Jacket Thickness 8rig..

1-path TORUS AIR)"

464.82 cm

.9 INTEGRATED DOOSES 10 Beta+Gamma1 Gamma 0

Betaii Gamma1n Beta" From Beta From Gamma From Beta From Gamma 11 TIME POOL Temp POOL DRYWELL DRYWELL TORUS AIR TORUS AIR

[HI]

[HNO}

[HCL[ -ORYWELL [HCL[ -ORYVELL' [HCL[ -CONTAIN [HCL[ -CONTAIN5 Total [H.] r

[CsOH[

12 Hours beg F Mrad MeV/cm MeVeV/c m V/cm MeV/cm' g-mols/liter g-mols/liter g-molsiliter 9-moli/liter g-mol/ls/ier 13 0

80 O.00E+00 5.012E-06 0.000E -O-(

14 1

.175 5.322E-07 5.544E-06 9.304E-0,=

15 2

187 1.435E-01 3.415E+12 1.494E012 6.783E+12 2.113E+12 1.227E-06 1.048E-06 8.077E-07 4.774E-06.

0 O0OE+00 O.OO0E+00 1.287E-05 2.024E-01 16 2.0336 188 1.496E-01 3.557E+12 1.556E+12 7.071E+12 2.205E-12 1.250E-06 1.092E-06 8.414E-07 4.973E-06 O.0OE00 0.0O00000 1.317E-05 2.061E-01 17 3

192 3.093E-01 7.224E+12 3.184E+12 1.452E+13 4.654E. +12 1.250E-06 2.258E-06 1.722E-06 1.010E-05 0.OOOE00 O.O000.00 2.034E-05 2.061E-O' 18 5

199 5.717E-01 1.299E-13 5.868E+12 2 6580+13 8.862E0,12 1.250E-06 4.174E-06 3.173E-06 1.816E-05 0.000E+00 0.OOOE+00 3.177E-05 2.061E-0' 19 12 204 1.189E+00 2.485E+13 1.227E+13 5.412E-13 1.958E+13 1.250E-06 8 680E-06 6.633E-06 3 473E-05 O.OOOE+00 O.OOOE+00 5.631E-05 2.061E-0' 20 18 198 1.557E000 3.103E+13 1.624E+13 7.012E+13 2.639E+13 1.250E-06 1.136E-05 8.782E-06 4 338E-05 0 OOOE+00 O.OOOE+00 6.979E-05 2.061E-0' 21 24 197 1 852E+00 3.578E+13 1.953E+13 8.281E+13 3.199E+13 1.250E-06 1.352E-05 1.056E-05 5.002E-05 O.00O0OO+

0.OO0E+00 8 037E-05 2 061E-0-1 22 48 190 2.700E+00 4.929E+13 2 943E+13 1.194E+14 4.801E+13 1.250E-06 1.971E-05 1.592E-05 6.890E-05 0 0000+00 O.O0OE+00 1.108E-04 2.061E-04 23 72 177 3.319E+00 5.937E013 3686E+13 1.466E+14 5.910E+13 1.250E-06, 2.423E-05 1.993E-05 8.300E-05 O.0000+00+

000010+00 1.334E-04 2.061E-04 24 196 160 3.839E+00 6.801E+13 4.306E013 1.700E+14 6.796E+13 1.250E-06 2.802E-05 2.329E-05 9.506E-05 O.OOE+0000 0.OE000 1.526E-04 2.061E-04 25 120 153 4.304000 75780+13 4.847Eu13 1.9120+14 7.5620+13 1.250E-06 31420-05 2 621E-05 1.059E-04 O.0OOE00 O.OO0E+00 1.698E-04 2.061E-04 26 150 149

. 4 839E+00 8.466E+13 5.4410E13 2.1570+14 8.420E+13 1.2500-06 3.532E-05 2.943E-05 1.183E-04 0.OOOE+00 0.0000+00 1.894E-04 2.061E-04 27 200 142 5.651E000 9.801E+13 6 279E+13 2.534E+14 9 696E+13 1.250E-06 4.125E-05 3.396E-05 1 370E-04 0.000+00 0.00+00 2.1950-04 2.0610-0' 28 240 138 6.250E+00 1.077E+14 6 844E+13 2.813E+14 1.062E+14 1.250E-06 4.562E-05 3.701-05 1.505E-04 0000OO+00 2.3940-04 2.0610-04 29 300 132 7.081E+00 1.209E+14 7.557E+13 3.202E+141 1.188E+14 "1.250E-06 5.169E-05 4.087E-05 1.689E-04 0.0000+00 0.000E000 2.678E-04 2.061E-04 3601 400 480 600 1271 7.847E+OC 1.328E0141 8.146E+13 3 563E+14 1.301E+141 1 250E-061 5.729E-05 4.406E-051 1.856E-04 0.00OE+00 O.00OE+00 2 932E-041 2.061E-04 33 1201 8.328E+00 1.402E+14 8.486E+13 3.791E+141 1.371E+14

. 1 2500-06 6.0790-05 4.589E-05 1.960E-0 0.000E+00 00000+00 3089E-04 2.061E-04 9.230E+00 1.540E+14 9.071E+13 4.221E+14 1.500E+14 1.2500-06 67380-05 4.905E-05 2 152E-04 0O00OE+00 0.O00E+00 3.379E-04 2.061E-0' 1.047E+01 1.727E+14 9.780E+13 4.817E+14 1.672E+14 1.250E-06 7 642E-05 5.289E-05 2.413E-04 0.0000.00

. 0.00E+00 3.769E-04 2.061E-0' 1.142E+01 1.870E+14 1.027E+14 5.280E+144 1.801E+14 1.250E-06 8.338E-05 5.556E-05 2.613E-04 0.0000E00 O.O00E+00 4.065E-04 2.061E-0'z 1.161E+01 1.897E+14 1.036E+14 5.369E+141 1.825E014 1.250E-06 8.472E-05 5.605E-05 2.652E-04 O.000E+00 0.O00E+00 4.122E-04 2 061E-0/

34 700 119 35 T6 37 38 720 1171 14 Acrd dissocialion constant from: Entergy Eng. Report GGNS-98-l 039 Rev.3, Sect.6.1,p.21 v.3, Equalton 3-1d [30+90 min release duration]

1:

XC-011111-98013 Roy.2 Section5.

39 1,

I B for gamma free paths 40 3 Ibid. E 6 12 Rev 14) and Fin 14 6 12A Rev 1,1 411 4 Ibid, I 42 5 Ibid. Equation 3-3a 18 Attachmenlt 19 Attachment B 20 USNRC Reg Guide 1.183 21 Tech Spec SR 3 1.7.7 minimum B-10 ston 43_-_--_--_

6Fb-id. Equation 3-3b I_______

______I_________

44 45 46 47 7

bid. Equation 3-5a: Entergy Caic. XC-Q11111-98013 Ren.2. Section 5.7 red in SBLC tank of 162.7 lbs, conservatively less than fron iquation 3n5b: Entergy Calc. XC-O11111-98013 Rev.2, Section 5-7 Y

iplant chemistry data transmitted via E-mail by Mark G. Fry on 12/27/2002.

1 1

1 Eguation 3-0a; Entergy Calc. XC-Q11111-98013 Rev.2. Section 5-7 included as Attachment H. 65 atom % B-10 enrichment used, bounding 10 Ibid, E 111-98013 Re..2. Section 5-7 the hiohest 63.5 atom% B-10 from Attachment 48 11 Ibid. E 111-98013 Rev.2. Section 5-7 22 Cable Data from Attachment A.

49 12 Ibid, Equation 3-5e; Entergy Calc. XC-Q1 111 mi

_______ I

[

______ I 50o _--_

13 Min Suppression Pool volume from PBAPS -

PM-1056, Rev. 0, Attachment C. Page C-3 of C4

PEACH BOTTOM ATOMIC POWER STATION TRANSIENT POOL pH CALCULATION p

0 R

S I

T I

U I

v W

x Y

z AA AEB 1

pH TRANSIENT END OF CYCLE 2 Cable Data 22 1134.24 g. mols Na.1B,00, 10H20 Added 3

1.837,364 Cable Surface [Traes] -

DRYWELL (cm21 1627 737999.09 lbgram% B-102' 10.01 atomic m. B-10 4

91,868 Cable Surface [Free air] -DRYWELL [cm2[

65.00 atom % B-102 7372.54 g atoms B-10 5

0 Cable Surface [Free air] - TORUS [cm2[

11342.36 g atoms lotal boron 6

0 Cable Surface [Trays] - TORUS [cm2]

8 pH EFFECT OF ADDITION OF SODIUM PENTABORATE STANDBY LIQUID CONTROL [SLC] SOLUTION 9I 10 Strong Acid 11 T.

g-equiv.

Na 2B,.O16"10H 20 Borate Boric Acid pK.

pH 12 9-isosfiter g-ionslliter Before SLC Net (H+]

V

" g-mobs g-eqLiv.

g-equa.

-IogsK.

13 1.995E-09 1.394E+01

-3.197E-10 5.012E-06 5.30 5.989E-10 1.744E+01 1134.2 2251 9091 9.22 8.62 14 9.305E-05 1.262E01 5.541E-06, 2.745E-09 9.56 1.155E-09 9.553E-03

.1134.2 2269 9074 8.94 8.34 15 2.025E-04 1.250E-01 1 287E-05 1.682E-09 877 1.225E-09 5.855E-03 11342 2269 9074 9.91 8.31 16 2061 E-04 1.249E01 1.317E-05 1 691E-09 8.77 1.231E-09 5.884E-03 1134.2 2268 9074 8.91 8.31 17 2.061E-04 1.245E01 2.034E-05 1.920E-091 972 1.2549-09 6 680E-03 1134.2 2269 9074 990 8.30 18 2.0619E-04 1 236.01 3.177E-05 2.376E-09 9.62 1.295E.09 8.268E-03 1134.2 2269 9074 699 8.29 19 2.061E-04 1.234E+01 5.630E-05 3.063E-09 9.51 1.324E-09 1.066E-02 1134.2 2269 9074 9.69 8.28 20 2.061E-04 1.239E+01 6.979E-05 2.975E-09 8.53 1.289E-09 1.035E-02 1134.2 2269 9074 6.89 8.29 21 2.061E-04 1.240E.01 8.036E-05 3.158E-09 6.50 1.283E0-9 1.099E-02 1134.2 2269 9074 9.89 8.29 22 2.0616-04 1.247E.01 1.108E-04 3.579E-09 8.45 1.242E-09 1.245E-02 1134.2 2269 9074 6.91 8.30 23 2.0616E-04 1.260901 1.3346-04 3.469E-09 8.46 1.166E-09 1.207E-02 1134.2 2269 9074 6.93 8.33 24 2.0616-04 1.279E+01 1.526E-04 3.0536-09 952 1.067E-09 1 062E-02 11342 2269 9074

.97 8.37 25 2.0619E-04 1.287991 1.698E-04 3712E-09 8.43 1.026E-09 1 292E-02 11342 2269 9074 6.99 8.39 26 2 2061E-04 1.292E01 198949-04 7.174E-09 9.14 1003E-09 2.497E-02 1134.2 2268 9074 900 8.40 27 2.0616E-04 1 301901 2.0619-04 1 235-05 4.91 9.6166-110 4.299E+01 1134.2 2225 9117 9.02 8.40 29 2.061E-04 1 3069.01 2.061E-04 3.3269-05 4.46 9.382E-10 1.158E+02 1134.2 2153 9190 9.03 8.40 29 2.0616E-04 1.314201 2.0619E-04 6.164-05 4.21 9.031E-10 2.145E+02 1134.2 2054 9288 9.04 8.39

30.

2.061E-04, 1.32101 2.0619E-04 8.711-05 4.06 8.7399-10 3.032E+02 1134.2 1965 9377 9.06 8.38 31 201E0

.2E0

.6E0

.2E0

.9853-0 3.578E +02*

1134.2 191 9432 9.07 8.37 3 2.6E0 1.2E0 2.6E0

.1E0 3.885510 4.587E+02 1134.2 1101 9533 9.071 8.35 5.944E+02 1134.2 74 9668 8.32 3,

.6

-4 132+1 201 -4 204-4 30

.7E1 6 974E+02 1134.2 1711 9771 9.88.29 35 201E0

.3E0 6

-0

.6E0 618 5

7 172E+02 1134 2 1551 9791 9.98.29 46 47 49, 490 41

[-

42 i-43i 44i 45I 46i 47i 48i M5i PM-1056, Reo 0, Attachment C, Page C-4 of C-4

PEACH BOTTOM ATOMIC POWER STATION TRANSIENT POOL pH CALCULATION A

B

[

C I

D E

E I

F7 I

G I

H I

1 2

3 4

PEACH BO1 I

pH TRANSIENT

'EGINNING OF CYCL I Linear Absorption I VPOOL MI

=122900"28.3168

Liters [122900 ft 3 3

=170 Iodine inventory [g-atoms]

Ueta *ir 6

6 Mi.

=1600 Cesium inventory [g-atom Uteta hypalon Ugamma air Uarmm. hvynnlu

0.0198 152.08 0.0000375 10.099 I.

t-aa :121/3600 IlOnset of Gap release [hrs 7

8 r (w-f-P-,

mDRWJELLI" =

34 -30.48 r [g,,. tr p.,

TORUS Ae!=15.25*30.48 Beta" 9

INTEGRATEI)D td 3my 18 10 11 12

,Beta-Gamma In TIME POOL Temp i

POOL Hours I

Mrad iTRATE Beta n

m

....... 8 DRYWELL DRYWELL TORUS AIR TORUS AIR g-mols/liter MeV/cm' MeV/cm" MeV/cm" MeV/cm' I

13 0 80 10 14 1 175

_1

-=$B$41(120*$B$3)'($A14-(0.5-$B$S6))_$B$41(400.$B$3) 15 2 187 0.143500086508842 3415252526559.5 1493516901702.39 16782790405603.09 2112853924362.65

=$B$4/(120*$B$3y*($A15-(0.5+$B$6))+$B$4f(400"$B$3) 16 =0.5+1.5+B6 188 0.149634733015881 3557433766582.65 1555848397608.08 17070702227895.83 2205232001151.76

$B$4/1120 $B$31($At16-0.5+$B$6)).$B$4/(400$B$3) 17 3 192 0.309341836086142 7223665685898.47 3184466482938.89 14522270407907.7

.4653989461673.07 H$16 18 5 199 0.571714238137557 12993742725588.9 5867592321860.4 26579195436675.8

'8861664876224.85

=H$16 19 12 204

1.18897340652801 24846754835583.8 12285274440332.4 54124658556267.7 19580415772096.5

=H$16 20 18 198 11.55683327582913 31033162634725.7 16238511537328.7 70115732616255 26393164623873.5

'=H$16 21 24 197 11.85191915601109 3578387807763.8 19532321678811.2 F82812650068300.5 31988772986659.7

ý=H$16 22 48 190

'2.69999350899574 49289591172808.2 29429378072763.1 119362761252454 48011228084913.2 H$16 23 72 177 13.31896426382511 59373911524643.9 36857885649250 146641045030486 59103260447932.9

-H$16 24 96 160 3.839025927095 68006216910072.3 43061765946118.8 170021885936274.

67961305910172.6 H$16 25 120 153

[4.30449745517556 75777204350529.3 48460947167744.3 191216585122999 75621430881437

'=H$16 26 150

]149 14.83863042922377 84663108071843.2 54411194958229.2 215749512205084 84199682180048.8 IH$16 27 200

[142 ----------- 15.65123374775693 98005925381916

!62794391540543.6 1253363489030894 96959403927412.6 H$16 28 240

[138 6.24993554889672 107669540194174 68442614993399.4 1281251300182045 106185426030441

[=H$16 29 300 132

7.08123504117198 120857131002314 75570313182062.1 1320201031278407 118768378954490 H+/-$16 30 360 127 7.84729286641128 1132800350275133 81462258405056.5

!356330536069072 130127193615785

!=H$16 1/cm 1/cm 1/cm 1/cm cm cm

[HNO3] 2 g-mols/fiter

=0.0000073"$C1 5

=0.0000073"$C16

=0.0000073"$C17

=0.0000073-$C18

=0 0000073*$C19

=0.0000073"$C20

=0.0000073*$C21

=0 0000073"$C22

=0.0000073'$C23

=0.0000073"$C25 0 000n7~$2 000000073$C26

=0.0000073"$C28

=0.0000073"$C29

=0.0000073"$C30

=.000073"$C31 0.000073"$C32

=.000073"$C33 0.000073"$C34 __

=0.0000073"$C35 31 1400 124 8.32796771895153 32 480 123 33 600 120 19.23016582533999

.10.4680366999075 140208197049268 184862166864990.9 379118949506557 137136062051670

=H$16 153971254659635 90707083398776.2 422140895644603 150041841567683 1 H$16 172651749035525 97804662138577.5 481694348263629 167224642525045 j=H$16 186955852261398 102732737437929 1527952520751998 180060583153812

=H$16 189712487101709 103642526077636 1536915254530628 182499580739728

'=H$16 34 35 36 700 720 119 111.4213133856566 117 11.6052404151638 371I NOTES 381 Ester En.e orlC 39 12 Ibd Euton 3-2 14

.Acid dissociation constant from: EntergyEng. Report GGNS-98-00 15 111-980.13 Rev.2. Section 5.7 16 1See attachment B for gamma free paths 1j7

'PBAPSULFSAR Fi.1..21 S(

AtRev.a14c B14.6.1 A Rev. 5) 18

ýAttachment B 40 41 42 4ý3 44 45 3

5 7

6

lbid, Eguatiofl3-4dL3.

-bid, Table A-iý bid, Equation 3-3a E bhid. Equation 3-3b bid, Equation 3-nLa

[bid, Equation 3S:Ej CIF 19 IAttachment B 120 U..

SNRC Re Guide 1. 183 21 Tech Spec SR 3.1.7.7 minimum B-10 stored in SBLC tank of 162.7 i

.... la ntchemistr d-ata tra~ns~mitted via E-mail by Mark G.Fry on 12127_

.p p.7. r

-. dt tas ite i

il..by..

a.......

.ry.o...2.....

!included as Attachment H. 65 atom % B-10 enrichment used, bou_

jthe highest 63.5 atom% B-10 from Attachment H 22

[Cable Data from Attachment A. Assume 5% of Tray cable surface 4-6 -------

uation 3-6a 47]10 lbid, Equation 3-5d: Ei Equation 3-5d E-'

49 L12 Ibid. Equation 3-5e; E6 ccn 1" NUin 'I11nnrnninn Pnn 51 13 Supression Poo PM-1056, Rev. 0, Attachment D, Page D-1 of D-10

PEACH BOTTOM ATOMIC POWER STATION TRANSIENT POOL pH CALCULATION I

K L

1ICable Data 22 I

2 SAtray [cm]i=$P$3"1.1 lCable Surface [trays]- Drywell+ 10% contingency 3

SAfa (cm 2]1=$P$4.1 1 1Cable Surface [free air]- Drywell + 10% contingency 4

SB tray [cmr] =$P$60.-95 1.1 J

Cable Surface [trays] - TORUS + 10% conlingency 5

SBf. [cm 2] =P6*1.1*0.05

[Cable Surface [free air] - TORUS + 10% contingency 7

0.61865 Hypalon Jacket Thickness

__9I 10 From Beta From Gamma From Beta 11

[HCL[ -ORYWELL

[HCL[

-DRYWELO

[HCL[ -CONTAINW 12 g-mols/iter g-mols/liler g-mols/liter 13 14 15 =3.512E-201$B$3"($K$20.9512-=$K$3)I$H$3*$E15

=3.512E-20/$6$3 ($K$2*0.95$K$3) (1-EXP(-$H$5*$H$7)) $H$5*(1-EXP(-$H$6*$K$7)$D15

=3.512E-201SB$3*$K$4O.9512+$K$5)/$H$3*$E15 16 =3.512E-2015B$3*($K$2"0.9512+$K$3)/$H$3'$E16

=3.512E-20/$B$3*($K$2"0.95+$K$3)*1-EXP(-$H$5*$H$7))/$H$5(1-EXP(-$H$6*$K$7)y$D16

=3.512E-20/5B$3"($K$4*0.9512+$K$5)/$H$3*$E16 17 =3.512E-2015B$3*($K$2"0.95/2+$K$3)ISH$3"$E17 3 512E-20$6$$3*($K$2*0.95+$K$3)'(1-ExP(-$H$5*$H$7))/$H$5*(1-ExP(-$H$6$K$7)$D17

=3.512E-20153($K$4"O.95I2+$K$5)I$H$3$E17 18 =3.512E-201$B$3*($K$2*0.9512+$K$3)/$H$3*$E18

=3.512E-20$B$3($K$2095+$K$3)[1-EXP(-$H$5**$$7)[f$H$5[1-ExPP($H$6s$K$7))*$D18

[=3.512E-20/$B$3"($K$4-0.9512+$K$5)/$H$3*$E18 19 =3.512E-20/$B$3*($K$2"0.9512+$K$3)IH$33$E1 9

=3.512E-20/$B$3"($K$2*0.95+$K$3)[(1-EXP(-$H$5*$H$7))/$H$5*(1EXP-$H$6$K$7))$D9 I=3.512E-20/5B$3[($K$4*0.9512+$K$5)/$H$3-$E19 20 =3.512E-2015B$3[($K$2*O.9512=$K$3)I$H$3*$E20

=3.512E-20/$B$3"($K$2*0.95+$K$3)*(1-EXP(-$H$5SH$7))/$H$5[1l-EXP(-$H$6*$K$7)SO$D20 j=3.512E-20/1B$3ý_$K$4"95/2$K$5)_$H$3"$E20 21 =3.512E-201$B$3"($K$2*O.9512+$K$3)/$H$3*$E21

=3.512E-20/$8$3"($K$2"0.95+$K$3)*(1-EXP(-H*ý$H7 H

-EXP(-$H$6*$K$7)'$D21 1=3.512E-20153($K$40.9512.$K$5)I$H$3$E21 22 =3.512E-2015B$3 $K$2".9512+$K$3)I$H$3$E22

=3.512E-201$B$3($K$2*095.$K$3)(1-EXP(-$H$5*$H$7))/$H$5*(1-EXP(-$H$6$K$7[)$022

[=3.512E-20/5B$3($K$4O.9512+$K$5)/SH$3$E22 23 =3.512E-2015B$3°($K$2*0.95I2.$K$3)I$H$3"$E23

=3.512E-201$B$3*Z $

$31-EXP(-$H$5"$H$7 I$H$5*(1-EXP(-$H$6$K$_7)$D23

-3.512E2015B$3($K$4*0.9512+$K$5)I$H$3*$E23 24 43.53.51E K($K$220095$K$3).(1-E9XP.-$H$5*$H$7.9/$H$5/{EXPP(2 H7)S$E 1=3.512E320$B

($K$4*0.95/2+SK$5)[/$H$3$E24 25 =3.512E-20/$B$3"($K$2*0.95/2+$K$3)I$H$3"$E25 1=3.512E-201$B$3($K$20.95u$K$3)'(1-ExP(-$H$5 $H$7))$H$5(1-ExP(-$H$6$K$7))$D25 1=3.512E-2015B$3"($K$4*0.9512$K$5)I$H$3-$E25 26 =3.512E-2015B$3"($K$2*O9512u$K$3)y$H$3$E26 I=3.512E.20$B$3[($K$2.0.5+$K$3)*(1.EXP[*$H$-5*$H$7[)$H$-5-(1*ExP[$.$H$6s$-K$-7-))$D26 I =3.512E-20/$ B$3*($K$4¶0.=95/2+$K$5)/$H$3"$E26 27 =3.512E-201$B$3"[$K$2°0.9512÷$K$3)/$H$53$E27

-3.512E-20/$B$3($K$2'0.g5+$K$3)'(1-EXP(-$H$5*$H$7))/$H$5(1-EXP-$H$6$K$$

W$D27 1=3.51 2E-205B$3($K$4*.95/2+$K$5 )$H$3"$E27 28 =3.512E-20/$B$3($K$2".95/2+$K$3)/$H$3$E28

=3.512E-20__B$3 SK$2* g5u$K$3 1-EXP P-$H$5$H$7)/$H$5[1-EXP(-$H$6$K$7))$028 l=3.512E-20153($K$4*0.952+$K$5)I$H$3"$E28 29 =3.512E-2015B$3($K$2O.9525+K$3)/$H$3'$E29

=3.512E-201$B$3 ($K$2"0.95+$K$3(1-EXP -$H$5*$H$7 )H$5(.1-EXP(-

'$K57)'$D29 1=3.512E-2015B$3($K$4O.95/2$K$5)/$H$3*SE29 30 =3.512E-20/$B$3*($K$2"0.95/2+$K$3)I$H$3*$E30

=3.512E-20/$B$3[$K$20.g5$K$3' 1-EXP(-$H$5$H$7))I$H$5(I-EXP(-$H$6$K$7))$030

=3.512E.20tS3($K$4*.95f2.SK$5)ISH$3$E30 31 =3.512E-2015B$3*($K$2*0.95/2+$K$3)I$H$3"$E31

=3.512E-20/$B$3*($K$2"0.95+$K$3)[(1-EXP(-$H$5$H$7)/$H$5§(1-EXP(-$H$6*$K$7))$D31 1=3.512E-20/5B$3*3$K$4*0.95/2+$K$5)/$H$3*$E31 32 =3.512E-201$B$3*($K$2*0.95/2+$K$3I$H$3"$E32

=3512E-20/$B$3-($K$2'0.g5+$Kt*S3(1-EXP(-$H$5*$Fj

[$H$5(1-EXP(-$H$6$1K$7)$)$D32 i=3.512E-20/1B$3*($K$4*0.95/2+$K$5)f$H$3"$E32 33 =3.512E-201$B$3-($K$/20.952+$K$

H$3*$E33

($K$20.5K3

-EXP(-5$

H$5$

H$S(-EXP(-$H$6"$K$7)) $D33 1=3.512E-20/5B$3"($K$4"0.95/2÷$K$5)/$H$3"$E33 34 =3.512E-20/$B$3*[$K$2*0.9512+$K$3)I$H$3*$E34

=3.512E-20/$B$3"($K$20.95$K$3)(1-*-E-$H5H7 XP-$H6$K$7))'$D34

=3.512E-20/$B$3°($K$4*0.95/2+$K$5 YSH$3$E34 35 =3.512E-201$B$3"($K$2*0.95/2.$K$3)/$H$3*$E35

=3`512E-201$8$3($K$2*0.95a$K$3)[(1-EXP(-SHS5*$H$7))[SHH$S1*EXP(-$H$6*$K$7)(($S35

=3.512E-20fSB$3*(SK$4.9512+SK)/$H$3"SE35 37 3,88 39 40 41 43 44 45 47 48 49 50 PM-1056, Rev. 0, Attachment D, Page D-2 of D-10

PEACH BOTTOM ATOMIC POWER STATION TRANSIENT POOL pH CALCULATION M.

N

-I.

1 2

3 4

5 6

7 8

10 From Gamma 11 12 13 14 15 16

[HCL] -CONTAINt g-molsfliler

=3.512E-20/$B$3"($K$4°0.95+$K$5)*(1-EXP(-$H$5*$H$8))/$H$5*(1-EXP(-$H$6*$K$7)1$D 1

=3.512E-20/$B$3*($K$4'0.95+$K$5)*(1-EXP(-$H$5*$H$8))/$H$5(1-EXPI-$H$6*$K$7G)*$D16 Total [H., 7 9-ions/liter

=POWER 05

+1

$H134 F=POWER(10,-$T$13)+$H14

]=POWER(10,-$T$1)_I$Hl4

- =POWE R(10,-$T$1-3)+$H 16-17 =3.512E-20/$B$3_($K$4*0.95+$K$

-E PX

$H-$H$E$K$7)

'$17

=POWER(T 3$H1 7 18 =3.512E-20/$B$3*($K$4*0.95v$K$5)l(1-EXP(-$H$5*$H$8))/$H$5*(1-EXP(-$H$6*$K$7) K$018

=POWER(10,-$T

+$H18 19 =3.512E-20I$B$3*($K$4*0.95+$K$5)*l1-EXP(-$H$5*$H$8))/$H$5*(1-EXP(-$H$6*$K$7))*$D19

=POWER1-T$13

$H19 20 =3.512E-20/$B$3*($K$4*0.95+$K$5)1-EXP(-$H$51$H$8))/$H$5* 1-EXP(-$H$6*$K$7))*$D20

=POWER 105

+11$H20+

21 =3.512E-20/$B$3'($K$4-0.95.$K$5) (1-EXP(-$H$5*$H$8))/$H$51-ExP(-$H$6'$K$7

$021

=POWERl

-$$13)+$H21+

22 =3.512E-20/$B$3 $K$40.95+$K$5)*(--EXP($H$5'$H$8))/SH$5*(l.EXP(-$H$6*$K$7))*$D22

$POWER 10,-$TS13).$H22+

23 =-3.512E-20/*B$3*($K$4.*.95-$K$5)'(l-EXP(-$H$5'$H$8))/$H$5-(--EXP(-$H$6*$K$7))_-$D23 P

.O S,-$T$13).$H234 24 =3.512E-20/$B$S3*$K$40.95 +$K$5)*(1-EXP(-$H$5 $H$8))/$H$_5( 1-EXP(-$H$6*$K$7))*SO -D24 J=POWER(10,-_$T$13)+$H24+

25 =3.512E-2/E3$B$3'*$K$4*0.95+$K$5)*(1-EXP(-$H$5'$H$8))/$H$5*(1-EXP(-$H$6'$K$7))*$D25 I=POWER(

-$ $H25 26 =3.512E-20/$B$3*($K$4*0.95+$K$5)-(1-EXP(-$H$5'$H$8) /$H$51-E-xP(-$H$6$K$7))*$D26*3........

POWER(10$T$13).$H26+

27 =3.512E-20/$B$3" $K$4t0.95+$K$5)*S1-EXP(-$H$5'$H$8))/$H$5*(1-EXP(-$H$6'$K$7 )'$D27

=POWER(10,-$T$13)VS$H27-28 =3.512E-20/$B$3'($K$4*0.95+$K$5)*(1-EXP(-$H$55$H$8))/$H$5*(1-EXP(-$H$6S$K$7))*$D28 P

E 0

)+$13 128+

29 =3.512E-201$B$3*($K$4*0.95+$K$5)* 1-EXP(-$H$5*$H$8))/$H$5*(1-EXP(-$H$6*$K$7))*$D29

=POWER 10,-$T$13)$H 30 =3.512E-20/$B$3*($K$4*0.95+$K$5)*(1-EXP(-$H$5*$H$8 ))$H$5(1-EXP(-$H$6*$K$7 )*$D30

=POWER

,T$13)+$H30.

31 =3.512E-20/$B$3*($K$4*0.95+$K$5)*(1-EXP(-$H$5*$H$8))/$H$5*(1-EXP(-$H$6°$K$7))*SD31

=POWER(10.-$T$13)+$H31.

32 =3.512E-20/$B$3" $K$4"0.95.$K$5)*(1-EXP(-$H$5*$H$8))/$H$5*(1-EXP(-$H$6*$K$7))*$D32

=POWER(10,-$T$13)+$H32,

+$113+$J13*$K13+$L13+SM13

-$114+$J14+$K14+$L14+SM14

-5115SJ 15. SK 15+$St 5e5M 15

'$116-$J16+$K16+$L16+$5M16

$117+$J17+$K17+$L17.$M17

+$11 8+$J 1 8+$K1 8÷$L 18+$SM 18

+$119+$J19+$K19+$L19--+$M19

+$120+$J20s$K20-$L20+$M20

+$121+$J21 ; $K21+$L21+$M21

+$122+$J22+$K22+$L22+$M22

+$123+$J23_$K23+$L23+$M23..

-$124+$J24+$K24+$L24+$M24

+$125+$J25÷$K25+$L25+$M25

+$126+SJ26+$K26+$L268$M26

$127+$J27+$K27÷$L27.$M27

+$130+$J30+$K30+$L30+$M30

+$131+$J31 +$K31 ÷$L31+$M31

+$132+$J32+$K32.$L32+$M32

+$133+$J33+$K33+$L33$M33 33J=3.

S341=3 812P-2O/SRS3'lSKS4'09B.8KS5t'l1.FXPl-SHH8RltfSH'll.Pt(P(-SI-/CR7~t'Sfl33

=PCIWF R~tO.T$13t+$H/3,

( K $4 -

\\....

i X

.. \\..

ii....

\\.

. \\...

t....

-P W R 1

\\

H!

Ida-

+

(-

(1-

- H F, K 711 4

35 =3.512E-20$B$3"($K$4'0.95+$K$5)*(1-EXP(-$H$55$H$8))/$H$5*(1-EXP(-$H$6*$K$7))*$D35

=POWER(10,-$T$13)+$H34+$134+$J34+$K34+$L34+$M34

=POWER(10,-$T$13)+$H35+$135+$J35+$K35+$L35+$M35 36 37 38 39 4 1 43 44 4 54.

46 47 48 49 150 PM-1056, Rev. 0, Attachment D, Page D-3 of D-10

PEACH BOTTOM ATOMIC POWER STATION TRANSIENT POOL pH CALCULATION 0

P__

2

-Ca bIeý Da ta 22

}________

3 1837364 Cable Surface [Trays] - DRYWELL lcm2]

4

=$P$3-0.05 Cable Surface [Free air] - DRYWELL lcm2[

5 1=P6*0.05 iCable Surface [Free air]- TORUS [cm2]

6 0

iCable Surface [Trays] - TORUS ()cm2[

11 jCsOH]

Total [OH.J

-LOG[Kw) 12 g-mols/liler g-ions/niler

=15.5129-0.0224"$B_13+0.00003352*POWERB_13,2) 13 0 i=POWER 10,-14 /POWER 10,-$T$13)+$013

=15.5129-0.02245Bl3.0.00003352'POWER(B13.

14 =(0.4$B$5-0.475$B$4)(3'$B$3)

$A14-(0.5+$B$6))-(0.05$B$5-0.0475$B$4)/$B$3

=POWER(10,-14)/POWER(10,-$T$13+$014

=15.5129-0.02245$B14.0.00003352*POWER(E1.2 15 =(.4*$B$5-0.475*$$4 I 3

$B$3

($A15-(0.5+$B$6))÷(0.055$B$5-0.0475*$B$4)/$B$3

=POWER(10,-14)IPOWER(10,-$T$13)+5015

=15.5129-0.0224$B 15+0.00003352*POWER 615.2) 18 =(0.4"$B$5-0.475*$B$4)/(3*$B$3)*($Al6-(0.5+$B$6))+(0.05*$B$5-0.0475*$B$4)/SB$3

=POWER(10,-14)/POWER(10,-$T$13)+$016

=15.5129-0.0224"$S16+0.00003352°POWER(B16,2)

=$O517

=POWER10,-014 /POWER10,-$T$13)+$O17

=15.5129-0.0224$B 17+0.00003352"POWER(B 17,2) 18 =$O516

=POWER 10,-1"Z)/POWER(10,-$T$13)+$ 018

=15.5129-0.0224S$B18+0.00003352"POWER(B18,2 19 =$O516

=POWER 10,4 1POWER 10,-$T$13 +$O19

= 15.5129-0.0224"$B19+0.00003352"POWER[B19,2) 20 =$O$16

=POWER(10,-14)/POWER(10,-$T$13)+$020

=15.5129-0.0224"$B20+0.00003352°POWER(B20.4) 21 =$O$16

=POWER(10,-14)/POWER(10,-$T$13)+$021

=15.5129-0.0224"$B21+0.00003352"POWER(B21,2) 22 =$O$16

=POWER(10044 POWER(10.-$T$13)+$022

{ =15.5129-0.0224*$B22+0.00003352*POWER(B22,2)_

24$0_$_16......

=POW.ER_)10,-14)IPOWER)10O-$T$1 3)_$_024_

=1 15.5129-0.0224 5$B24 ÷0.00003352"POWER.B24.42)......

25 =$O516

=POWER)(1,-14)/POWER(1 0,-$T$13 -025

=15.5129-0.0224*$B25+0.00003352*POWER(B23.2) 26_=$0516 pOW

=P 0

W ER)10,-14)/POWER( 0,-$T$13)$ 5 26_........

15.5129-0.0 224*.SB24 +0.00003352POWER(B26*,2) 7=$518

=POWER-

-/POWER(10,-$T$13)$-27

=15.5129-0.0224$E27+0 00003352-POWER)EB272)_____

8=$5016

=POWER 10,-14*.POWER10,-$T13)+$O28

=15.5129-0.0224"$28+0 00003352POWE RB28,2) 29$7 16

=POWER=104

,-4POWER 10.

+$O29

-15.5129-0.0224$B29+0.00003352'POWER(B27,2) 30 =$O516

=POWER)10,-$T$13)+$030

=15.5129-0.02245$630+0.00003352*POWEfR(B30,2) 31 =S0516 f=POWER)ý1041)POWVER)10-T$1 31502 1=1 5:51 29-0.02245E31.0.00003352'P0WER)E31.2 32 =$O516

=POWER(10,-14)/POWER(10,-$T$13)+$031

=15.5129-0.0224"$B31÷0.00003352*POWERB30.2) 31=$O$16 I=POWER(10,- 14)/POWER( 10.-$T$13)+$O32 552-.241B2÷.0032 OER*

33 =$O516

=POWER(10,-14)/POWER(10,-$T$13)+$O33

{=15.5129-0.0224"$B33+0.00003352*POWER(B33,2) 34 =$S516

=POWER(10,-14)/POWER 10,-$T$13)+$O34

=1 5.5129-0.02245$B34+0.00003352"POWER(B34,2) 35 =$O516

=POWER(10,-14)/POWER(10,-$T$13)-$035

=15.5129-0 0224"$B35+0.00003352*POWER(B35,2) 36I 40 4141 432

~

423 I_________________

454___________________________________

465 476____________________________

497____________________________

10481_____________________

PM-1056, Rev. 0, Attachment D, Page D-4 of D-10

PEACH BOTTOM ATOMIC POWER STATION TRANSIENT POOL pH CALCULATION R

S T

[u v

W x

y IPH TRANSI ENT

.BEGINNING OF CYCLE______

2

=.1

________________9si

. mols Naý 3

127=U3*453 59 15./grams B3110.01 atomic wI. B-t10 4_______

65 6.atom

% B-1I=V3/X3 Lg.atoms B-t0 5

=X4N4*100 Igatoms toIJ_______

8

_________________________________J_____________pH EFFECT OF ADDITION OF SODIUM PENTABORATE STANDBY 11 Roots x Neti iH+Y pH K,

g-equiv.

61B,00,6101 Borate Boric Acid 12 j,-3i ons/lit er Before SLC 14 Net (H-i VpsL g-mols g-egoiv.

g-equiv.

13 EJN13.P1 3.SQRT(POWER(($Nl3+$P13).2)-(4*(N 3*Pl3-POWER(10.-$Q13)(f/

$13_$R1 153i008B31 39/00000

=Sl3*$B$3

=$V$2

=W13'2-Vl 3

=W1 r8sV13 14 =(Nl4.Pl4.SORT(POWER ($Nl4.$P14L,2)-(4'(Nl4'P4-POWER(10,-$Ql4)))))/2 1=N4-$R14 I=-LOG10($514)

=0.0585*B14+1.309 )/10000000000

=S14*$B53

=$V$2

=W14*2-Vl4 W14'8.V14 15 =(Nl5.P1 5-SORT(POWER(($N1 5+$P15(,2)-(4t(Nl5SPl5-POWER(10.4$015))))/

I=$NtS-$RIS I=-LOG1O($S1 5)

=0.0585*B15.1.309 /10000000000

=S 15$ rB-S-3

=$V$2

=W 5*2-Vt S

=W1 5*8+V15 16 =( N16+ P 16-SORT(POWE R(1$N1 6+$P B,)((1P6PWR1.$16))))/

=16-$R16 I=-LOG1g($516

=(0.05850816-1.309)/10000000000

=S16'$B$3

=$V$2

=W16*2-V1B

=W16*8.V16 17 =(Nl7+-Pl7.SORT(POWERtdSN17+SP17),2)-(4'(N17.P17POWFlR(10,-$017 )))))2 I=SN1i7-$R17 1=-LOG10($517)

=(0.0585*B17+1.309)/11000000000D

=517*$B$3

=V2

=W17*2-V1 7

=W17*8+Vl7 18 =tNl8+Pl8-S0RT(POWER(($Nl8+$P18), H

.N818PWE(0-$Q18

)~)D/2 1S$N18-$R18 1=-LOG1O($51

=0.0585*B818.130 )/10000000000

-=518$B$3

=$V$2

=W182-V18

=W1808V18 19 = N19-P19-SORT(POWER $SNl9n$P19.2)- 4* N19*Pl9-POWER 10,.6019)J)))/12 1=$Nl9-$R19

=-LOG(10(LS19

=(0.0585'B19+1.309)110000000000

=519S$B$3

=$V$2

=W192-V19

=W19*8-V19 20 =(N20'P20-SORT(POWER(($N20.$P20).2)-

4*(N20*P20-POWER 10,-$020 ))))12 I=$N20R2 3-O1 S2 08 20+.1309)/10000000000 I-S20'$B$3

=$V$2

=W20'2-V20-

=W20*8-.V20 21 =(N21.P21-SORT(POWER(($N21.$P21 ),2)-(4*(N21*P21-POWER(10,-$Q21 )))))/2

--$N21-$R21 1=-LOG10($S21) 0058 B2 +1.309)/10000000000

=S21

-'B$3 =$V$2

=W21 2-V21

=W21 8.V21 22 =(N22.P22-SORT(POWER((SN22.$P22).2)-(4'(N22*P22-POWER(10.-$022

)D)(/2 1=$N22-SR22 i =-LOG 10 $S22) 08I2.

0)100000=522*$B$3

=$V$2

=W22*2-V22

=W22*8+V22 23.

23P3-?S9RT(POWR($N3

?2)?:.('*(N23R(1$OWE20-93))))Y)2

-42S2 KO 0953 0085B3 Q-L29.9IQP

=S23$B$3

=$V$2

=W23-2-V23

=W38+

24 =(N24.P24-SQRT(POWER(($N24+$P24),2J-(4(CN24'P24-POWER(10.-$O24)))))/2 4-R2

=-LOG1O($S24)

. (0.0585*824+1.309(/iO000000

..... =S24*$BS3

=$- V=$.$2

=W2-4*2-V24 _

=W2-4'8+V 24 25 =jN25.P25-SORT(POWER(($N25.$P25).2 - 4*N25*P25-POWER 10,-$025 ))))L2

ý=$N25-$R25 I1=-LOG1O(j52-5) 0(Q0585 925+1.309)/10000000000

=S25-jB$3 ---- =$V$2 W5

=VW258.V25 26 =(N26+P26-SQRl(POWER(($N26+SP26),2)-(4*(N26-P26-POWERý(10.-$O26)))))/2

___________5B6+.0)/000000 S6$B3

=V$

W6*-

27 =(N27.P27-SORT(POWER(($N27+SP27).2)-(4'(N27'P27-POW+/-fR(10.-$027)))fl12

=$N27-$R27

=-LOG1O($527)......... ~0585 B27-.1309 /100(00000000

=S27'$8$3

=$V$2

=W27*2-V27

=W27'8.V27 28 f(N28oP28-SORT(POWER(($N28+$P28).2)-(4*(N28*P28-POWER(10,-$O28)))))/2

=$N28-$R28 LG1(5)__

0585 B328ý+1.30. 10000000000

=58B3

=$V$2

=W28*2-V28

=W28'8.V28 29 =(N29.P29-SORT(POWEBt($N29.SP29).2)-(4'(N29'P29-POWER(10.-SQ29)D)))l2

=$2-R9

=LOO829)......

=0.05815-129,1.309)l10100000000I

=529'SB$3

=$V$2

=W29*2-V29

=W29*8=V29 30 fý(N30.P30-SQRT(POWER(($N0$P0.2-ýN30*P30-POWER(10.-$Q30(fl))/2

=$N30-$R3

=_LOG1O SS3O fJO 0585 B30+1.309 /110000000000

=530S$B$3

=$V$2

=W30*2-V30 I=W30*8=V30 31 =(N31.31SRTPOWER(($N31.$P31) 2(-(4* N3P'P31-_POWER(10-$Q31 )))))/2

=$

31-R1

-- LOG10 $S31)

=00585*B31 1.309)/10000000000

=S31 *$B$3

=$V$2

=W31"24V31

=W31*8+V31 32 = N32.P32-SORT(POWER(($N32+$P32),2)-(4tN32*P32-POWER'n0-$032)

)t)2 1=$N32$3

=_LOG1O($S32)

-055B239/10000000000

=32;$B$3

=$V$2

=W322-V32

=W32*8=V32 33 =(N33-+P33-SORT(POWER(($N33+$P33t,2)-(4*(N33*P33-POWER(10.-$O33tt)1t2 1=$N33-$R33 1=-LOGJO $S33) 008 3+

0100000=S33*$BS3

=$V$2

=W33*2-V33

=W33*8.V33 34 =(N34.P34-SORT(POWER(($N34+$P34),2)-(4*(N34*P34-POWER 10,4$034) )))/2 1=$N34-$R34 I=-LOGJO($531......-055344.

0 100000

=S34*0$3

=$V$2

=W34*2-V34

=W34*8.V34 35 =(N35.P35-SOR1(POWER(($N35+SP35),2)-(4'(N35*P35-POVVER(10,-SO35)))))/2 1=$N35-$R35 I=-LOC1O($535) 1(0.0585*B351.1309)/10000000000

=535*$B$3 1$V$2

-W35*2-V35'

-W15*8+V35 36

.I 37 4038_

1_______________

389 3940 _________________________________________

41 4?

-~

t 1

44 45 46 479 49 PM-1056, Rev. 0, Attachment D, Page D-5 of D-10

PEACH BOTTOM ATOMIC POWER STATION TRANSIENT POOL pH CALCULATION z

AA Z

Pi 2

3I 4

5 67 8

LIQUID CONTROL [SLC] SOLUTIOP 10 11 pK.

pH 12

-Ilog K.

15 14 =-LOG10(Ul3)

=Z14+LOGIO((X14SS)(Y4$S))

15 =-LOG10 U1)

!=Z14+LOGIO((Xl4/$B$3)i(Y151S8S3))

16 =-LOG 10 U16)

=Z16+LOGIO((X1I5$B$ )t(M 5BS$3 ))_______

17 =-LOG10(Ul67

=Zl6+LOGIO (X16/$B$ )10LI ISB$3))________

189 E-LOG10 U18 ZE184LOG1O((XI8ISBS3)t(Y181$BS3))________

20O =-LOO 10(U20)

[Z20+LOGl0 ((X20$3I(Y2OISBS3))

21iLGO(2)

!Z21+LOG1O((X21/$B$3)/(Y21/$B$3))

__~

22 =-LLX31 0(U22)

= Z22+LOG1 O(X21B3iY183) 2ý3 =.LOG12(U23)_

=Z23+ LOG1IO((X231S0$33y(Y23/!!$B3)L_

25 =ý-LOG 10(U-24)_

'Z25+LOG1 O((X25/$El3)!(Y2/$ 83))

26 =-LOG10(U25)

!=Z25+LOG10((X25/$B$ )/(Y25l$B$3))

2L7- =-LOI0( 27)

I=Z27+LOGIO (X27/$B$ )I(Y27Lý1SB3) 28 =-LOG 1 0(U28L__[1-Z28+LOG1 0((X281$8$3)!(Y_28/SBS3))

29 _=-LOG10(U2 )

I=z29.LOG1O((X291SBS3)ffI28IBS3))

30 =-LOG10(U30)

=Z30OLOGl0

((301S8$21)tC1301$B$3))

3

-O1(3 1

Z3+OI(XISS)j(YjjI$R$31) 32 -LG0U2 Z3LO1(X25S)f(Y32,S8$3))

313 =-LOG11 2(33'

ýZ33+LZOG1O(3I83IY3 3

34 =-LOO10(U34 I=Z34.LOGIOftX34/S8S3I/Cv34/SBS3fl 35 =-LOGIO(U35) 1=Z35.LOG10((X35(S653)/(Y3515BS3))

39I 41 42 43 44 45 76___________-

467

~____

48 F________

49 501______________________

PM-1056, Rev. 0, Attachment D, Page D-6 of D-10

PEACH BOTTOM ATOMIC POWER STATION TRANSIENT POOL pH CALCULATION A

B C

D E

F G

1 PEACH B50 pH TRANSIENT END OF CYCLE 2

Linear Absorption Coe 3

VpooL =122900*28.3168 Liters 1122900 tf1 U beta 4

mi =290 Iodine inventory [g-atom Ubeta hypalon 5

mcs =3200 Cesium inventory [g-ato Ugamma air 6

teap =12113600 Onset of Gap release [h Ugamma hypalon 7

r f-ama Ihe ypalo I"

8 r

ft-m p-t1TORUS AIR)1 9

INTEGRATED DO 16 Be0a+Gamma.

Gamma18 Beta1 9

Gamma7 8

Beta2 0

11 TIME POOL Temp POOL DRYWELL ORYWELL TORUS AIR TORUS AIR 12 Hours D

[eg

ýF lrMrad MeV/cm' e/m MeV/cm' MeV/cm' 13 5 80 14 T175 15 2 187 0.143500086508842 3415252526559.5 1493516901702.39 16782790405603.09 2112853924362.65 16 =0.5+1.5+B6 188 0.149634733015881 3557433766582.65 1555848397608.08 7070702227895.83 2205232001151.76 17 3 192 0.309341836086142 7223665685898.47 3184466482938.89 14522270407907.7 4653989461673.07 18 5 199 0.571714238137557 12993742725588.9 5867592321860.4 26579195436675.8 8861664876224.85 19 12 204 1.18897340652801 24846754835583.8 12265274440332.4 54124658556267.7 19580415772096.5 20 18 198 1.55683327582913 31033162634725.7 16238511537328.7 70115732616255 26393164623873.5 21 24 197 1.85191915601109 35783878087763.8 19532321678811.2 82812650068300.5 31988772986659.7 22 48 190 2.69999350899574 49289591172808.2 29429378072763.1 119362761252454 480112280849132 23 72 177 3.31896426382511 59373911524643.9 36857885649250 146641045030486 59103260447932.9 24 96 160 3.63902585927095 68006216910072.3 43061765946118.8 170021885936274 67961305910172.6 25 120 153 4.30449745517556 75777204350529.3 48469947167744.3 191216585122999 75621430881437 26 150 149 4.83863042922377 84663108071843.2 54411194958229.2 215749512205084 84199682180048.8 27 200 142 5.65123374775693 98005925381916.4 62794391540543.6 253363489030894 96959403927412.6 28 240 138 6.24993554889672 107669540194174 68442614993399.4 281251300182045 106185426030441 29 300 132 7.08123504117198 120857131002314 75570313182062.1 320201031278407 118768378954490 30 360 127 7.84729286641128 132800350275133 81462258405056.5 356330536069072 130127193615785 31 400 124 8.32796771895153 140208197049268 84862166864990.9 379118949506557 137136062051670 32 480 123 9.23016582533999 153971254659635 90707083398776.2 422140895644603 150041841567683 33 600 120 10.4680366999075 172651749035525.

97804662138577.5 481694348263629 167224642525045 34 700 119 11.4213133856566 186955852261398 102732737437929 527952520751998 180060583153812 35 720 117 11.6052404151638 189712487101709 10364252607763E 536915254530628 182499580739728 36 37 NOTES 14 38 1 Entergy Eng. Report 15 39 2 Ibid. Equation 3-2b 16 40 3 Ibid, Equation 3-4d [3 17 41 4 Ibid, Table A-1 18 42 5 Ibid. Equation 3-3a 19 43 6 Ibid, Equation 3-3b 20 44 7 Ibid, Equation 3-5a; 21 45 8 Ibid, Equation 3-5b; 46 9 Ibid. Equation 3-2a:

47 10 Ibid. Equation 3-5d: E 22 4811 Ibid, Equation 3-5d: E.

49112 "D 113 I

PM-1056, Rev. 0, Attachment D, Page D-7 of D-10

PEACH BOTTOM ATOMIC POWER STATION TRANSIENT POOL pH CALCULATION H

N 0

2 3 0.0198 1 /cm 4

52.08 l/cm 5 0.0000375 1/cm 6 0.099 1/cm 7 =34*30.48 cm 8 =15.25*30.48 cm 9

10 11

[HI]

[HNO3] 2 Total [H+] *

[CsOH] "

12 g-mols/liter g-tools/liter g-ions/liter g-mols/liter 13 0

=POWER(10,-$T$13)+$H13+$113+$SJ13+$K13+$L13+$M1=3 14 =$B$4/(120H$B$3)*($A-14-0.5+$B$6))+$B$4/(400*$B$3)

=POWER(10,-$T$13)+$H14+$114+$J14+$K14+$L24+$M24

=(0.4'$B$5-0.475"6$B$4)/(3"$B$3)($A14-(0.5+$B$6))+(0 05*$B$5-O.0475"$B$4)/$B$3 15 =$B$41(1206$B$3)-($A15-(O.5ý:$B$6))+$B$41(400*$B$3)

=0.0000073"$C15

=POWER(10,-$T$13)+$H15+$115+$J15+$K 15+$L5+$M15

=(0.40$B$5-0.475*$B$4)/136$B$3)*($A15-(0.5+$B$6)/+(0.05"$B$5-0.0475'$8$4)/$B$3 16 =$B$416120*$B$3)'($A16-10.5+$B$6))÷$B$4/{400*$B$3)

=0.0000073'$C16

=POWER(10.-$T$13)+$H16+$116+$J16+$K16+$L16+$M16

=(0.4"$B$5-0.475"$B$4)/(3"$B$3)'($A16-(0.5+$B$6))+(0.05*$B$5-0.04756$B$4)/$B$3 317 =H$16

=0.0000073"$C17

=POWER(10,-$T$13)+$H317+$117+$J17+$K17+$L 17+$M17

=$O516 18 =H$16

=0.0000073"$C18

=POWER(10,-$T$13)+$H18+$118+$J18+$K18+$L18+$M18

=$O516 19 =H$16

=0.0000073"$C19

=POWER(10;-$T$13)+$H19+$119+$J19+$K19+$L19+$M19

=$O516 20 =H$16

=0 0000073"$C20

=POWER( 10,-$T$13)+$H20+$120+$J20+$K20+$L20+$M20

=$5016 21 =H$16

=0.0000073"$C21

=POWER 10,-$T$13)+$H21+$121+$J21+$K21+$L21+$M21

=$0516 22 =H$16

=0.0000073"$C22

=POWER(10,-$T$13)+$H22+$122+$J22+$K22+$L22+$M22

=$5016 23 =H$16

=0.0000073"$C23

=POWER(10,-$T$13)+$H23+$123+$J23+$K23+$L23+$M23

=$5016 24 =H$16

=0.0000073"$C24

=POWER(10,-$T$13)+$H24+$124+$J24+$K24+$L24+$M24

=$5016 25 =H$16

=0.0000073"$C25

=POWER(10,-$T$13)+$H25+$125+$J25+$K25+$L25+$M25

=$O516 26 =H$16

=0.0000073*$C26

=POWER(t 0,-$T$13)+$H26+$126+$J26+$K26+$L26+$M26

=$O$16 27 =H$16

=0.00000736$C27

=POWER(10,-$T$13)+$H27+$127+$J27+$K27+$L27+$M27

=$O516 28 =H$16

=0.0000073"$C28

=POWER(10,-$T$13)+$H28+$128+$J28+$K26+$L28+$M28

=$O$16 29 =H$16

=0.0000073"$C29

=POWER(10.-$T$13)+$H29+$129+$J29+$K29+$L29+$M29

=$0$16 30 =H$16

=0.0000073'$C30

=POWER(10.-$T$13)+$H30+$130+$J30+$K30+$L30+$M30

=$0$16 31 =H$16

=0.0000073"$C31

=POWER(10,-$T$13)+$H31+$131+$J31+$K31÷$L31÷$M31

=$O$16 32 =H$16

=0.0000073"$C32

=POWER(10,-$T$13)+$H32+$132+$J32+$K32+$L32+$M32

=$0$16 33 =H$16

=0.0000073"$C33

=POWER(10,-$T$13)+$H33+$133+$J33+$K33+$L33+$M33

=$O516 34 =H$16

=0.0000073"$C34

=POWER(10,-$T$13)+$H34+$134+$J34+$K34+$L34+$M34

=$O516 35 =H$16

=0.0000073"$C35

=POWER(10,-$T$13)+$H35+$135+$J35+$K35+$L35+$M35

=$O516 36 37 Acid dissociation constant from: Entergy Eng. Report GGNS-986 38 Entergy CaIc. XC-Q11111-98013 Rev.2, Section 5.7 39 See attachment B for gamma free paths 40 PBAPS UFSAR Fig. 14.6.12 (Rev.14) and Fig. 14.6.12A (Rev. 1E 41 Attachment B 42 Attachment B 43 USNRC Reg. Guide 1.183 44 Plant chemistry data transmitted via E-mail by Mark G. Fry 12127, 45 minimum lbs. mass of boron-10 used (PBAPS Unit 2 - 12/0711 46 atom% B-1 0 from Eagle Picher Report of Analysis Job #00-0771 47 Cable Data from Attachment A. Assume 5% of Tray cable surfac 48 PM-1056, Rev 0. Attachment D, Page D-8 of 0-10

PEACH BOTTOM ATOMIC POWER STATION TRANSIENT POOL pH CALCULATION P

Q R

S T

1 pH TRANSIENT 2 Cable Data 22 3

1837364 Cable Surface [Trays] - DRYWELL

[cm2]

4

=$P$3"0.05 Cable Surface [Free air. - DRYWELL [cm2]

5 =P6'0.05 Cable Surface [Free air] - TORUS [cm2]

6 0

Cable Surface [Trays] -TORUS

[cm2]

7 8

9 10 11 Total [OH+]

-LOG(Kw)

Root x Net [H+]

pH l'

12 g-ions/liter g-ions/liter Before SLC 13 =POWER(10,-14)/POWER(10.-$T$13)+$013

=15.5129-0.0224*$B13+0.00003352"POWER(B13,2)

=(N13+P13-SORT(POWER(($N13+$P13).2)-(4*(N13"P13-POWER(10,-$013)))))/2

=$N13-$R13 5.3 14 =POWER(10,-14)/POWER(10,-$T$13)+$014

=15.5129-0.0224*$B14+0.00003352*POWER(B14,2)

=(N14+P14-SORT(POWER(($N14+$P14).2)-(4*(N14"P14-POWER(10,-$014)))))/2

=$N14-$R14

=-LOG10($S14) 15 =POWER(10,-14)/POWER(10,-$T$13)+$015

=15.5129-0.0224"$B15+0.00003352*POWERB615,2)

=(N15+P15-SQRT(POWER(($N15+$P15),2)-(4*(N15*P15-POWER(10,-$015)))))/2

=$N15-$R15

=-LOG10($S15 16 =POWER(10,-14)/POWER(10,-$T$13)+$016

=15.5129-0.0224*$B16+0.00003352'POWER(B16.2)

=(N16+P16-SORT(POWER(($N16+$P16),2)-(4 (N16"P16-POWER(10,-$Q16)))))/2

=$N16-$R16

=-LOG10($S16) 17 =POWER 10,-14)/POWER(10,-$T$13)+$017

=15.5129-O.0224"$B17+O.00003352*POWER B17.2)

= N17+P17-SORT(POWER ($N17+$P17),2)-(4"{N17"P17-POWER 10,-$017)))))/2

=$N17-$R17

=-LOG10D$S17) 18 =POWER( 10.-14)/POWER( 10.-$T$13)+$018

=15.5129-0.0224"$B18+0.00003352*POWER(B18.2)

=(N18+-P18-SORT(POWER(($N18+$P18).2)-(4'(N 18*P18-POWER(10.-$Q18)))))/2

=$N18-$R18

-LOG10($S18) 19 =POWER(10,-14)/POWER(10,-$T$13)+$O19

=15.5129-0.0224*$B19+0.00003352*POWER(B19,2)

=(N19+P19-SORT(POWER(($N19+$P19).2)-(4'(N 19*P19-POWER(10,-$019)))))/2

=$N19-$R19

=-LOG10($S19) 20 =POWER(10,-14)/POWER(10.-$T$13)+$020

=15.5129-0.0224'$B20+0.00003352*POWER(B20,2)

=(N20+P20-SORT(POWER(($N20+$P20).2)-(4*(N20*P20-POWER(10,-$020)))))/2

=$N20-$R20

=-LOG10($S20) 21 =POWER(10,-14)/POWER(10,-$T$13)+$O21

=15.5129-0.0224*$B21+0.00003352'POWER(B21.2)

=(N21+P21-SORT(POWER(($N21+$P21).2)-(4'(N21'P21-POWER(10,-$021)))))/2

=$N21-$R21

=-LOG10($S21) 22 =POWER 10,-14)/POWER(10,-$T$13)+$O22

=15.5129-0.0224*$B22+0.00003352'POWER(B22,2)

=(N22+P22-SORT(POWER(($N22÷$P22),2)-(4*(N22"P22-POWER(10,-$022)))))/2

=$N22-$R22

=-LOG10($S22) 23 =POWER(10,-14)/POWER(10,-$T$13)+$O23

=15.5129-0.0224'$B23+0.00003352'POWER(B23.2)

=(N23+P23-SQRT(POWER(($N23+$P23),2)-(4*(N23*P23-POWER(10,-$Q23)))))/2

=$N23-$R23

=-LOG10($S23) 24 =POWER(10,-14)/POWER(10,-$T$13)+$024

=15.5129-0 0224'$B24+0.00003352*POWER]B24.2)

=(N24+P24-SQRT(POWER(]$N24+$P24),2)-(4*(N24'P24-POWER(10,-$024)))))/2

=$N24-$R24

=-LOG10($S24) 25 =POWER(10,-14)/POWER(10,-$T$13)+$025

=15.5129-0.0224"$B25+0.00003352*POWER(B25.2)

=(N25+P25-SQRT(POWER ($N25+$P25),2)-(4"(N25*P25-POWER(10.-$Q25)))))/2

=$N25-$R25

=-LOG10($S25) 26 =POWER( 10-14)/POWER( 10,-$T$13)+$026

=15.5129-0.0224*$B26+0.00003352'POWER(B26.2)

=(N26+P26-SORT(POWER(($N26+$P26),2)-(4*(N26"P26-POWER(10,-$026)))))/2

=$N26-$R26

=-LOG10($S26) 27 =POWER(10.-14)/POWER(10,-$T$13)+$027

=15.5129-0.0224*$B27+0.00003352'POWER(B27,2)

=(N27+P27-SORT(POWER(($N27+$P27),2)-(4*(N27*P27-POWER 10,-$027)))))/2

=$N27-$R27

=-LOG10($S27) 28 =POWER(10,-14)/POWER(10.-$T$13)+$028

=15.5129-0.0224*$B28+0.00003352*POWER(628.2)

=(N28+P28-S0RT(POWER(($N28+$P28).2)-(4"(N28*P28-POWER( 10.-$O28)))))/2

=$N28-$R28

=-LOG10($S28) 29 =POWER(10,-14)/POWER(10.-$T$13)+$029

=15.5129-0.0224*$B29+0.00003352*POWER(B29,2)

=(N29+P29-SORT(POWER(($N29+$P29).2)-(4*(N29*P29-POWER(10,-$029)))))/2

=$N29-$R29

=-LOG10($S29) 30 =POWER(10.-14)/POWER(10.-$T$13)+$030

=15.5129-0.0224*$B30+0.00003352*POWER(B30,2)

=(N30+P30-S0RT(POWER(($N30+$P30),2)-(4'(N30'P30-POWER(10,-$030)))))/2

=$N30-$R30

=-LOG10($S30) 31 =POWER(10,-14)/POWER(10.-$T$13)+$O31

=15.5129-0.0224*$B31+0.00003352"POWER(B31.2)

=(N31+P31-SQRT(POWER(($N31+$P31),2)-(4*(N31"P31-POWER(10,-$031)))))/2

=$N31-$R31

=-LOG10($S31) 32 =POWER(10,-14)/POWER( 10,-$T$13)+$032

=15.5129-0.0224'$B32+0.00003352'POWER(B32.2)

=(N32+P32-SORT(POWER(($N32÷$P32),2)-(4*(N32'P32-POWER(10,-$Q32)))))/2

=$N32-$R32

=-LOG10($S32) 33 =POWER( 10,-14)/POWER( 10,-$T$13)+$033

=15.5129-0.0224'$B33+0.00003352"POWER(B33.2)

=(N33+P33-SORT(POWER(($N33+$P33),2)-(4'(N33"P33-POWER(10,-$Q33)))))/2

=$N33-$R33

=-LOG10($S33) 34 =POWER(10,-14)/POWER( 10,-$T$13)+$034

=15.5129-0.0224'$B34+0.00003352*POWER(B34.2)

=(N34+P34-SORT(POWER(($N34+$P34),2)-(4'(N34"P34-POWER(10.-$Q34)))))/2

=$N34-$R34

=-LOG10($S34) 35 =POWER(10,-14)/POWER(10.-$T$13)+$035

=15.5129-0.0224"$B35+0.00003352*POWER(B35.2)

=(N35+P35-SORT(POWER(($N35÷$P35).2)-(4"(N35*P35-POWER(10,-$035)))))/2

=$N35-$R35

=-LOG10($$35) 36 37 38 39 4O 41 42 43 44 45 4§ 471 48 49 50 PM-1056, Rev. 0, Attachment D, Page D-9 of D-10

PEACH BOTTOM ATOMIC POWER STATION TRANSIENT POOL pH CALCULATION U

V

.W X

Y Z

AA AB 1

END OF CYCLE 2

=V5/10

g. mols Na 2 B, 0 01610H2 0 A 3 210.6

=U3'453.59 lb./grams B-1021 10.01 atomic wt. B-10 4

62.98 atom % B-10"

=V3/X3

g. atoms B-10 5

=X4N4"100 g.atoms total boron 6*

7 8

pH EFFECT OF ADDITION OF SODIUM PENTABORATE STANDBY LIQUID CONTROL [SLCI SOLUTION 9

10 Strong Acid 11 K.

g-equiv.

NaB,*oO*10H 20 Borate Boric Acid pK, pH 12 14 Net [H +]

VPOOL g-mols g-equiv.

g-equiv.

-IogloK.

15 13 (0.0585B13+1.309)/10000000000 S$13"$B$3

=$V$2

=W13*2-V13

=W13*8+V13

=-LOG10(U13)

=Z13+LOG10((XI315B$3)I(Y1315B$3))

14 =(0.0585"B14+1.309)/10000000000

=S14"$B$3

=$V$2

=W14"2-V14

=W14"8+V14

=-LOG10 U 14)

=Zl4+LOG10(X 141$B$3)I(Yl41$B$3))

15 =(0.0585"B15+1.309)/10000000000

=S15"$B$3

=$V$2

=W15"2-V15

=W15"8+V15

=-LOG10U15)

=Z15+LOG10(Xl51$B$3)/(Y1S/$B$3))

16 =(0.0585"B16+1.309)/10000000000

=S16"$B$3

=$V$2

W16"2-V16

=W16*8+V16

=-LOG10(U16)

=Z16+LOG1O((X16/B$3)/(Y16/$B$3))

17 =(0.0585"B17+1.309)/10000000000

=S17"$B$3

=$V$2

=W17"2-V17

=W178+V17

=-LOG10(U17)

=Z17+LOG10((X17/$B$3)/(Y17/$B$3))

18 =(0.0585"B18+1.309)/10000000000

=S18*$B$3

=$V$2

=W18*2-V18

=W18*8+Vl8

=-LOG10(U18)

=Z18+LOG1O((X1lB$B$3)/(Y18/$B$3))

19 =(0.0585"B19+1.309)/10000000000

=S19"$B$3

=$V$2

=W19"2-V19

=W19*8÷V19

=-LOG10(U19)

=Z19+LOG1O((X19/$B$3)/(Y19/$B$3))

20 (0.0585"B20+1.309)110000000000

=S20"$B$3

=$V$2

=W20"2-V20

=W20*8+V20

=-LOG10(U20)

=Z20+LOG10((X2015B$3)/(Y20/$B$3))

21 =(0.0585"821+ 1.309)/10000000000

=$21"$8$3

=$V$2

=W21*2-V21

=W21"8+V21

=-LOG10(U21)

=Z21+LOG10((X21/$B$3)/(Y21/1B$3))

22 =(0.0585"B22+1.309)/10000000000

S22"$B$3

=$V$2

=W22*2-V22

=W22*8+V22

-LOG10(U22)

=Z22+LOG10((X22/$B$3)/(Y22/1B$3))

23 =(0.0585"B23+1.309)/10000000000

=S23"$B$3

=$V$2

=W23*2-V23

=W23"8+V23

=-LOG10(U23)

=Z23+LOG10((X23/$B$3)/(Y23/1B$3))

24 =(0.0585"B24+1.309)110000000000

=S24'$B$3

=$V$2

=W24"2-V24

=W24*8+V24

=-LOG10(U24)

=Z24+LOG1O((X2415B$3)/(Y24/1B$3))

25 =(0.0585"B25+1.309)/10000000000

=S25"$B$3

=$V$2

=W25*2-V25

=W25*8+V25

=-LOG10U25)

=Z25+LOG10((X25/$B$3)I(Y25/$B$3))

26 = 0.0585*B26+1.309)/10000000000

=S26"$B$3

=$V$2

=W26"2-V26

=W26*8+V26

=-LOG10U26)

=Z26+LOG1O (X2615B$3)I(Y26/1B$3))

27 = 0.0585"B27+1.309)/10000000000

=S27"$B$3

=$V$2

=W27*2-V27

=W27*8+V27

=-LOGlO(U27)

=Z27+LOG10((X271$B$3)/(Y27/$B$3))

28 =(0.0585"B28+1.309)/10000000000

=S28"$B$3

=$V$2

=W28*2-V28

=W28'8+V28

=-LOG10(U28)

=Z28+LOGI0((X28/1B$3)/(Y28/$B$3))

29 =(0.0585"B29+1.309)/10000000000

=S29"$B$3

=$V$2

=W29*2-V29

=W29"8+V29

=-LOG10(U29)

=Z29+LOGI8((X29/1B$3)/(Y29/$B$3))

30 =(0.0585"830+1.309)/10000000000

-S30"$B$3

=$V$2

=W30*2-V30

=W30"8+V30

=-LOG10(U30)

=Z30+LOGIO((X30/1B$3)/(Y30/$B$3))

31 =(0.0585"B31+1.309)/10000000000

=S31"$B$3

=$V$2

=W31"2-V31

=W31*8+V31

=-LOG10(U31)

=Z31+LOGIO((X31/1B$3)/(Y31/1B$3))

32 =(0.0585"B32+1.309)/10000000000

=S32"$B$3

=$V$2

=W32*2-V32

=W32'8+V32

=-LOG10(U32)

=Z32+LOGIO((X32/$B$3)/(Y32/1B$3)).

=(0.0585"B33+1.309)/10000000000

=S33"$B$3

=$V$2

-W33*2-V33

=W33*8+V33

=-LOG10(U33)

=Z33÷LOG10((X33/1B$3)/(Y33/1B$3))

34 =(0.0585"B34+1.309)/10000000000

=S34"$B$3

=$V$2

=W34*2-V34

=W34*8+V34

=-LOG10(U34)

=Z34+LOG10((X34/$B$3)/(Y34/1B$3))

_L =0.0585"B35+ 1.309)/1000000000C

$35*$B$3

=$V$2

=W35*2-V35

=W36*8+V35

=-LOG10(U35)

=Z35+LOG10((X3515B$3)1(Y3515B$3) 46 47 48 PM-1056, Rev. 0, Attachment 0, Page D-10 of D-10

GRAND GULF REFERENCE CALCULATION A

B C

D E

F G

H I I J

K L

M N

0 P

1 CASE 1 GRAND GULF REFERENCE DATA pH TRANSIENTI I

I I

Ibs

2.

4 tLinear Absorption Coefficients 4 LA 5

[tb]y 873.65 Cable Length [trays]- Zone A SLC 5800

.VpooL.4.841E+06 Liters [Min.Tech Spec Basis B 3.6.2.2m Ubeta air 1980E-02, LA Ib]

873.65 Cable Length [free air]- Zone A 4

M~ 1 325 Iodine inventory [g-atoms]

Ubeta hyrpalon 52.081 /cm LB ray VIb]

14049.27 Cable Length [trays] - Zone B 5

2400 Cesium inventory [g-atoms]

Ugann ai.r 3.75E-05 1/cm LB f. [Ib]l 1561.03 Cable Length [free air] - Zone B 6

tgan 0.0336 Onset of Gap release [hrs]

Uga...a hypalon 0.099 1/cm R0 [cm 2]/IbI 800 Cable Area 7_r_

kL tr. pat-A]

1112.51cm th [cm]l 0.7112 Hypalon Jacket Thickness 8

1 rl.....

a.. I 13841cm F -o am 1a INTEGRATED DOSES i

I CONCENTRATIONS i

10 Beta+Gamma Gamma Beta Gamma Beta

]

From Beta iFrom Gamma From Beta From 11 TIME POOL Temp POOL DRYWELL DRYWELL :ONTAINMEN1 CONTAINMENT

[HI]

[HNO 3] 2

[HCL}-A

[HCL]-A

[HCL]

CL-B '

Total [H+]

[C

]

TlOGK 12 Hours Deg F Mrad MeV/cm MeV/cm'iT MeV/cm MeV/cm' g-mols/liter g-mols/liter g-mols/liter g-mols/liter g-mols/Iiter g-mols/liter g-ions/liter g-mols/liter g-ions/liter 13 77 0.OOE+00 5.012E-06 O.0O00E+00 2.00E-09' 1,399E+01 14 1]

160 4.288E-07 5.4418-06 4.7472E-05 4.75E 05l 1.279E+01 15 2

. 160 1.3783E+00 1.4200E+12 2.8733E+12 0.0000E+00 1.1220E+12j 9.8825E-07 1.00E-5 1.104E-061 1.067E-06 2.824E-06 0.000E+00 2.106E-05 1.0295E-04 1.03E 04 1.279E+01 16 2.03361 160 1.3792E+00 1.4506E+12 2.8784E+12 0.0000E+001 1.2148E+12 1.0071E-06 1.0078-05 1.106E-06]

1.090E-06 3.057E-06 0.000E+00 2.134E-05 1.0481E-04 1.05E-041 1,279E+01 17 3

159.1 1.4049E+00 2.16308+12 3.0235E+12 6.6925E+10 1.2908E+121 1.0071E-06 1.026E-05 1.161E-06 1.625E-06 3.249E-06 5.560E-07 2.287E-05 1.0481E-04 1.05E-041 1,280E801 18 5]

155.5 1.4581E+00 3.0991E+12 3.32088+12 6.4671E+11 1.4468E+12i 1.0071E-061.1.064E-051 1.276E-06 2.328E-06 3.641E-06 5.373E-06 2 928E-05 1.04818-04 1.05804 1.284E+01 19 12]

149.2 1.64258+00 4.7032E+12 4.33128+12

+1 1.9789E+12 1.0071E-061 1.199E8-5 1.664 E-06[

3.533E-06 4.980E-06 1.363E-05 4.181E-05 1.04818-04 1.058-04 1.2928+01 20 181 146.4 1.79858+00 5.44628+12 5.16098+12 2.10068+12]

2.4183E+12! 1.0071E-06 1.313E-05 1.982E-061 4.091E-06 6.086E-06 1.745E-05

.4.876E-05 1.0481E-04 1.05E-041 1.295E+01 21 241 144.3 1.9526E+00 5.9733E+12 5.9584E+12 2.4271E+12 2.8430E+12ý 1.0071E-061 1.425-05 2.289E-061 4.487E-06 7.155E-06 2.0168-05 5.437E-05 1 0481E-04 1.05E-041 1.298E+01 22 481 139.4 2.5509E+00 7.2434E+12 8.8503E+12 3.2138E+12 4.4038E+12 1.0071E-061 1.862E-051 3.400E-061 5.442E-06 1.108E-05 2.670E-05 7.126E-05 1.0481E-041 1.05E-04i 1 304E+01 23 72]-

136.5 3.12138+00 7.98638+1 11319E+13 367408+12 5.76498E12 1.0718-06]229-05 4.348E-6r 6.0-008-6

.151 3.528-05t 8.418E-05 1.0481E-04 1.058-041 1.3088+01 24 96 134.4 3.6648E+00 8.5135E+12 1.3425E+13 4.0005E+12 6.9521E+121 1.0071E-08 2.6758-05 5.1578-06' 6.396E-06 1.750E-051 33238-05 9 506E-05 1.0481E-04 1.05E-041 1.311E+01 25" 12 132.8 4.18308-E0-8.92248+1 1.5-224+3 4.

8+12-7.9874E+1;1.0071E06 3.0 5.8488-06 6.7038-06 2.010E-051 3.5348-05 1.045E-04 1.04818-04 1.05E-041 1.3138+01 26 150i 131.3 4.7966E+00 9.3312E+12 1.7105E+131 4.5071E+121 9.0975E+12ý 1.0071E-06i 3.502E-05 6.571E-061 7.010E-06 2.290E-05 3.744E-05 1.150E-04 1.0481E-04_

1.05E-04 1.3158+01 27 200 129.2 5.7409E+00 9.8584E+12 1.9521E+13 4.8336E+12' 1.0574E+131 1.0071E-061 4.191E-05 7.499E-061 7.406E-06 2.661E-05 4.016E-05 1.296E-04 1.0481E-04 1.05E-041 1.318E+01 28 240 127.9 6.4313E+00 1.0192E+13 2.0955E+13 5.04058+12 1.1486E+131 1.0071E-06 4.695E-05 8.050E-06!

7.657E-06 2.891E-05 4.187E-05 1.395E-04 1.0481E-04

.1.05E-041 1.320E+01 29 300 126.3 7.3686E+00 1.0601E+13 2.2506E+131 5.29388+12 1.25198+13 1.00718-06 5.3798-05 8.645E-061 7.964E-06 3.151E-051 4.398E-05 1.519E-04 1.0481E-04 1.05E-04!

1.322E+01 30 3601 125 8.1999E+00 1.0935E+13-2.3551E+13, 5.5007E+121 1.3252E+13! 1.0071E-061 5.986E-05l 9.

0 4 7 E-0 6l 8.215E-06 3.335E-05 4.5700-05 1.6220-04 1.0481E-04 1.05E-04, 1.324E+01 3

O-124.3 8.70118E+00 1.1128E+13 2.40409-31 5620-3E+12 1.36f8E+1Y.6 -0671E 06.352E-05 9.!23-88E--06--

E-06 3.427E-05 4.669E-05 1.681E:04* *.0481E-04 05E-04; 1.325E+01 32 480 123 9.5911E+00 1.1463E+13 2.4727E+13 5.8272E+121 1.4143E+131 1.0071E-06 7.002E-05 9.4998-06 8.612E-06 3.559E-05 4.841E-05

.1.781E-041 1.0481E-04 1.05E-041 1.326E+01 33 6001 121.4' 1.0685E+01 1.1871E+13 2.52598+13 6.08058+12' 1.4592E+13ý 1.0071E-06 7.8E-05 9.703E-06 8.918E-06 3.672E-051 5.051E-05 1.899E-04ý 1.0481E-04 1.05E-041 1,329E+01

-34.

700 120.31 1417E+01 1.2154E+131 2.5472E+131 6.2555E+12 1.4791E+13 1.0071E-06 8.334E-05 9.785E-06, 9.131E-06 3.722E-051 5.197E-05 1.975E-04 1.0481E-04 1.05E-04T 1.330E+01 35 720 1 120.11 1.15468+01 1.22058+131 2.55008+1 6.28758+12E 1.4 E04 13 !.06 7 1 O4..... 1.0-9495-063 9.1698-0637 5

38 1 Entergy Eng. Report GGNS-98-0039 Rev.3, Equation 3-1d [30+90 min release duration]

14 Acid dissociation constant from: Entergy Eng. Rep. GGNS-98-0039 Rev.3, Sect.6.1,p.21 715 Entergyac. XC-011111-98013 Rev.2, Section 5.7 T

A 3Ii qaio -d[09 min release duration]

42 5 1bid, Equation 3-3a; Enterg y CaIc. XC-Q11111-98013 Rev.2, Equation 5-1 43 6 Ibid, Equation 3-3b: Entergy Calc. XC-01 1111-98013 Rev.2, Equation 5-2 44 7 Ibid, Equation 3-5a: Enter Cabc. XC-Q1 1111-98013 Rev.2, Section 5.7 45 8 bid, Equation 3-Sb; EnteryCalc. XC-Q11111-98013 Rev.2, Section 5.7 46 9 Ibid, Equation 3-0a; Entergy Calc. XC-Q11111-98013 Rev.2, Section 5.7 47 10 Ibid, Equation 3-5d; Entergy Caic. XC-Q11111-98013 Rev.2. Section 5.7 ---- --

48 12 Ibid, Equation 3-Se; Entergy CaIc. XC-Q11111-98013 Rev.2, Section 5.7 49 12 Ibid, E uation 3-5e; Enter y Calc. XC-Q11111-98013 Rev.2, Section 5.7 "50 13 Entergy Calc. XC-Q11111-98013 Rev.2, Section 5.2.2 1

PM-1056, Rev. 0, Attachment E, Page E-1 of E-7

GRAND GULF REFERENCE CALCULATiON R

I s I T

I U

I V

I w

Ix I Y I Z I A I AB I AC 1

2

-i

~1

-~

\\Ia2B1 0O16 Added [MW=410]

3 4

5

+

~r~-4 67 -7i

_pH EFFECT OF ADDITION OF SODIUM PENTABORATE STANDBY LIQUID CONTROL [SLC] SOLUTION 8

_ I_

ODU

-0 ;

StrongAcidI 11 Root x

Net [H+)

7PHiT K.

g-equiv.

Na 2B10oO 6 Borate Boric Acid p1<

pH 12 9-ions/liter.

.Net

[H+]

Vpoo g-mols g-equiv.

g-equiv. i -log,.iK 13

-61360E-11:

5.0119E-06 5.300 5.8135E-10 2.4262E+01 6416.8 12809 513591 9.24 8.63 14 _5.4368E-06 3.8846E-09 8.411 1..0669E-09J 1.8805E-02 6416.8 12834 51334...... 8W97 8.37 15 2.1054E-05 1.99406E-09 8.700 1.669K-0 9.65296-03 6416.8 12834 513341 8.97 8.37 16 2.1338E-05 1.9563E-09 8.709 1.0669E-09 9 4701E-03 6416.8 12834 51334:

8.971 8.37 17 2.2864E-05' 1.9450E-09 8.711 1.0616E-09 9.4153E-03 6416.8 12834 513341 8.97 8.37 18 2.92796-05 1.9127E-09 8.718 1 0406E-09 9.2569E-03 6416.8 12834 513341 8.98 8.38 19 4.1812E-05 1.9216E-09 8.716 10037E-09 9.3022E-03 6416.8 12834 51334-9.00 8.40 20 4.8757E-056 1.9925E-09.

8.701 9.8734E-10 9.6456E-03 64168 12834 513341 9.01 8.40(

21 5.4365E-051 2.0826E-09 8.681 9.7506E-10 1.0082E-02 6416.8

. 12834 51334]

9.01 8.41 22 7.1261E-05:;

2.7075E-09 8.567 9.4639E-10 1.3107E-021 6416.8 12834 51334:

.9.02 8.42 23 8.4179E-05!

4.0324E-09 8.394 9.2943E-10 1.9520E-02 6416.8 12834 51334 9.03 8.43 24 9.5048E-05!

7.9891E-09 8.098 9.1714E-10 3.86746-02 6416.8 12834; 5133 9.04 8.44 25 1.0438E-04, 1.7016E-07 6.769 9.0778E-10 8.23736-01 6416.8 12833 5 13351 9.04 8.44 1

26 1.0481E-041 1.0148E-05 4.994 8.9901E-10 4.9124E+011 641.6.8 12784 513831 9.05 8.44 1

27 1.0481E-041 2.4789E-05 4.606 8.8672E-10 1.2000E+02 6416.8 127141 514541 9.05 8.45 28 1.0481E-04, 3.4644E-05 4.460 8.7912E-10 1.677"6E02 64168 12666 51502 906 8.45 29 1.0481E-04!

4.7093E-05 4.3271 8.6976E-10 2.2797E+02 6416.8 12606 51562i 9.06i 8.45 30 1.0481604 5.73776-05 4.241 8.6215E-1 2.7775E+021 6416.8 12556 51612 906 8.45 31

1.0 481E-04

6.3287E-05 4.199 8.58066-10 3.0636E+02 6416.8 12527 51641 9.07 8.45 32 1.0481E-04!

7.3336E-05 4 135 8.5045E-10 3.5501E+02.

6416.8 12479

51689i, 9.07 8.45 33 1.0481-04 8 5066E-05 4.070 8.4109E-10 4.1179E+02 6416.8 12422 51746 908 8.46 34 1.0481604 92659E-05 4.033 8.3466E-10 4.4855E+02 64168 12385 517831_

9.08 8.46 3_5

.0481604 9.39866-0 4.0278.33496-10 4.5497E+02 6416.8 12379 51789; 9.08 8.46 36 _______

______1_____

38 40 41

______1______1 42 43 4,4 46 _______

74-I 7915-5o76!

PM-1056, Rev. 0, Attachment E, Page E-2 of E-7

GRAND GULF REFERENCE CALCULATION A

I B

I C

ID pH TAsEEI F

Lier G

H CASE 1 A GRAND GULF REFEREI

[

TNEN 2

=

-ijna Absorption Coefficiý,

3 VpOOL =170954"28.3168_

tLiters [Min'zech Spec Basis E TRANSIENTair 100198 4m]=325

-iIodine inventory [g-atoms].

1 Ubta 52.08 Ubeta hypalon 5

mc=2400 Cesium inventory [g-atoms) air 10.0010375 6

t ap =121/3600 Onset of Gap release [hrs]

Ua.a..

hypalon 0.099 8

F 11..

.....,*384 9

INTEGRATED DOSES.

I i

-1.

Beta+Gamma-.-

Gamma I

Beta l

Gamma Betal*

10~~

aGam amaBt amaBt-------------

11 TIME POOL-Temp POOL DRYWELA DRYWELL-A

[

DRY WELL-B DRYWELL-B

[..]

H 12 Hours Deg Mrd..

MeV/c 3

MeV/cF

.eV/cm*

--MVc3-g-m-os/litr..

130 77

_*_*_I I

10 1466

.16=$B$4/(120"$B$3)ý(A1-(0 5+$B$6)+L$B$4/(400"$3 121611.3783 1420000000000

ý2873300000000 i0 1122000000000

=$B$4/(120"$EB53) "($A 15-(().5+$B$6)) +$B$41(400"$8$3)-

16 =0.5+1.5-B6 160 11.3792 11450600000000 12878400000000 0

1214800000000 0=$B41(120$B$3)*$A16-(O.5+$B$6))+$B$4/(400*$B$

17 3 159.1 1.4049.2163000000000 13023500000000 66925000000 12908000000 18 5 155.54581 3099100000000 3320800000000 64671000000066bo 144680000(0000

________H$16___________

19 12 149.2 1.6425 14703200000000 4331200000000 1640400000000 1978900000000

=H$16 20 18 146.4 1.7985 5446200000000 5180900000000 2100600000000 12418300000000

=H$1-6 21 24

-1443 1.9528 5973300000000 595840000000 2427100000000 o284300000000 7=$16 22 48 139.4

.5509 72434000000 850300000000 80000 3213800000000 14403800000000 I=H$16 72

ý136.5 3.1213 7986300000000 111319000000000 3674000000000.

5764900000000 4=H$t6 24 96 134.4 6648 8513500000000 13425000000000 4000500000000 6952100000000

=H$16 25 120 1132.8 14.183 8922400000000 15224000000000 14253800000000 7987400000000

=H$16 26 150 131.3 4.7966 9331200000000 117105000000000 14507100000000 19097500000000

=H$16 200 129.2_

5.7409

9.

858400000000

_l 19521000000000 14833600000000

'10574000000000 I=H$16_

28 240 127.9 6.4313 10192000000000 20955000000000 5040500000000 11486000000000

=H$16 29 300 1126.3 7.3686 10601000000000 22506000000000 15293800000000 12519000000000 I=H$16 30 360 125 8.1999 10935000000000 23551000000000 5500700000000 13252000000000

!=H$16 31 400 124.3 8.7011 11128000000000 124049000000000 5620300000000 13618000000000 1=H$16 32 480 123 9.5911 11463000000000 124727000000000 J582720000000 14143000000000

,=H$16 33 600 121.4 10.685 11871000000000 2525900000000 6080500000000 14592000000000 I=H$16 34 700 1120.-3-...............

11.417 12154000000000 2547200 -60000 --

- -555*00-660000 - --------

1479100000000 -=H 720 120.1 12205000000000__oo 125500000000000 6...

_r287500000000 14819000000000 oH$16 NOTES I I

/

IJ__

38 1 Enterg nE. Report GG

[

I_*

14 39 Ibid, Equation 3-2b

__*__15 40

3Ibid, Equation 3-4d [30+d*

41 4 Ibid. Table A-1

_1 42 5 bid, Equation 3-3a; Ent*

736Ibid

, Equation 3-3b: Ent*

43~ 6 bd qua-tio-n 3-3b:---

Eut 44 7 Ibid, Equation 3-5a: Entel 45 8 Ibid, Equation 3-5b; Ente!

4619

]Ibid, Equation 3-0a; E_

47 10 Ibid. Equation 3-5d: Entt_

48111 Ibid, Equation 3-5d; Ent_

49 12

Ibbid, Equation 3-5e; Ent_

50113 Enterqy Catc. XC-Q111' I

1 I

PM-1056, Rev. 0, Attachment E, Page E-3 of E-7

GRAND GULF REFERENCE CALCULATION I

L JK L

2 3

4 1/cm 1/cm Laney [Ib]1873.65 LRo [Ib 873.65 rth [Ib] 14049.27 Cable Length [trays]- Zone A Cable Length [free air]- Zone A Cable Length [trays] - Zone B Cable Length [tree air[ - Zone B

'able Area

-ylon Jacket Thickness 5

6 7

1/cm 1/cm cm R5

[cm ]IIb 800 9

CONCENTRATIONS__

10

[From Beta IFrom GammaFrmBt 11

[HN0 3[ 2

[HCL] -A

-[HCL]

A

-c

[HL--6 12 g-mots/titer g-mols/liter I..

-mols/titer g-mots/liter 16 10.0000073*$C16

=3.512E-20/$B$3$~iks$6(i$K$21+$K 3)/H $E18

=351 E2/B3K6$$+K3

-EXP-$H5H7)$$XP(P($$$$)

$06 31

-20I$B$3*$K$6*($K$4/2.$K$5)I$H$3'$G16 0.0007'C17 351E.01Br$$6(K$/2$K3/$$3E 71351220$B3K$($$2$$3 1X2:H$$t$)

Y$H5 1

FX($H$'$K$7))'$017 = 3.512E:0$3K6(K4/$$5$H3G1 18 =0.0000073'$C16

=3.512E-20/$8$3*$K$6*($K$2/ +$K$3)/$H$3*$E 18=.1E_ 0/$B$3*$K$6*($K$2+$K$3)y(l-EXP(-$H$5*$H$7))/$H$5s(1-EXP(.$H$I

$)

$08;312-0$$$$(K$4/2+$K$5)I$H$3*$G 18 19 =0.0000073-$C17

=-3.512E-20/$B$3_*$K$6($K$2/2+$K$3)/$H$3*$El7 I=3.512E-20/$B$3*$K$6]$ýK$2+$K$3)(

"-E F(-$H$5'$H$7))/ý$H$5t-EXP(-$H$68$K$7

$0Dl719I3.51 2E-20/$B$3*$K$6*($K$4/2+$K$5)/$H$3r$G 19 20 =0.0000073-$C18

352-0$$~K6$

$2/+$$3)/$I-Mý$E0 1=3.512E-20/$B$3*$K$6'($K$2+$K$3)*(l-EXP(-$H$5*$H$7))/$H$5*(1-EXF(-$H$6*$KS7))$020 T=351 2EýY-0/fd$B$K-$-6'($K$4/2+$K$5)/$H$3*$Gl0 1=0.0000073'$C19

=3.512E-20/$B$3*$K$6*($K$2/2.-$K$3)/$H$3*$El91'=3.51 2E-20/$B$3*$K$6]($K$2+$K$3)*(l-EXP(-$H$5'$H$7))/$H$5(1l-EXP(-$H$6*$K$7))

$0291=I3.51 2E-20/$B$3*$K$6*($K$4/2+$K$5)/$H$3*$Gl1 22 =0.0000073*$C22

=3.512E-20/$B$3*$K$6*($K$212+$K$3)/$H$3*$E 22 1=3512E-201$ B$3*$K$6']$K$2+$K$3y*(l-EXP(-$H$5*$H$7))/$H$5*(l-EXP(-$H$6'$K$7 ) $D02J =3.512E-20/$B$3X$K$6*($K$4/2+$K$5)/$H$3*$G22 23 =0.0000073'$C21

=3.512E-20/$B3$3*$K$6*($K$2/2-$K$3)/$H$3*$E23

=3.ý1,2E-20/ý$B$3:$K$6'($K$2.$K$3)*(l-EXP(-$H$5'$H$7))/$H$5*(1-EXP(-$H$6*$K$7))

$023 J 3.51 2E-20/$B$3*$K$6*($K$4/2+$K$5)/$H$3*$G23 24 =0.0000073*$C24

=3.512E-20/$B$3*$K$6]($K$2/2+$K$3)/$H$3*$E24

_3.51 2E_20/$B$3 K$6 ($K$2-$K$3)*(l-EXP(-$H$5*$H$7))/$H$5*(l-EXP(-$H$6*$K$7)J

$024 13.51 2E-20/$B$3*$K$6]($K$4/2-$K$5)/$H$3*$022 25 =0.0000073*$C25

=3.512E-20/$B$3*$K$68($K$2/2f-$K$3)/$H-$3'$E23

=-3.51 2E-20/$B3$3*$K$6*($K$2v$K$3)*(l-EXP(-$H$5'$H$7

)/$H$5*(l-EXP(-$H$6*$K$7)) $025 I 3 51 2E-20/$B$3*$K$6*($K$4/2.$K$5)I$H$3*$G25 26 =0.0000073:$C26

=3.512E-20/$B$3'$K$6'($K$2/2+$K$3)/$H$3"$E24 1=3.51 2E-20/$B$3*$K$6*($K$2+$K$3y:(1 -EXP(-$H$5*$H$7))/$H$5*(l-EXP(-$H$6*$K$7)

$026 3.51 2E-20/$B$3*$K$6*($K$4/2r-$K$5]/$H$3*$G24 27 =0.0000073 $C25

=3:5 12E-20/$B$3'$K$6-$K$2/2+$K$3)/$H$3*$E25 1=3.512E-20/$B$3X$K$6*($K$2.$K$3)*(l-EXP(-$H$5*$H$7))/$H$5'(l-EXP(-$H$6*$K$7))

$027

=351 2E-20/$B$3'$K$6*($K$4L2.$K$5)/$H$3*$G27 28 =0.0000073*$C28

=3.512E-20/$B$3'$K$6*($K$2/2+$K$3)/$H$3*$E28 1=3.51 2E-20/$B$3*$K$6*($K$2--$K$3y*(1-EXP(-$H$5*$H-$7))/$H$5*(1-EXP(-$H$6'$K$7))

$028 J 3.512E-20/$B$3*$K$6*($K$4/2+$K$5)/$H$3*$G26 29 =0.0000073'$C27

=3.512E-20/$B$3*$K$_($K$2/2-$K$3)/$H$3r$E27

=-3.512E-20/$B$3*$K$6*($K$2+$K$3)*(1-EXP(-$H$5*$H$7

)/$H$5*(1-EXP(-$H$6*$K$7)) $029 I 3.51 2E-20/$B$3$K$6($K$4/2+$K$5)/$H$3*$G29 30 =0.0000073*$C30

=3.512E-20/$B$3-$K$6-($K$2/2+$K$3)/$H$3i$E3 I3.512E-20/$B$3'$K$6*($K$2+$K$3)(l-EXP(-$H$5*$H$7))/$H$5*(l-EXP(-$H$6*$K$7))

$03 1E2/B3K6(K42$$)$2$3 31 =0.0000073*$C31

=3.512E-20/$B$3*$K$6*($K$2/2+$K$3)/$H$3'$E391=3.512E-20/$B$3'$K$6- $K$2+$K$3)(1-EXFP(-$H$5'$H$7]/H51-EXP(-$H$6*$K$7)*$03 29 13.512E-20/$B$3*$K$6*($K$4 2+$K$5)/$H$3*$G29 32 =0 0000073*$C32

=3.512E-20/$B$3'$K$6'($K$2/2.-$K$3)/$H$3*$E30 1=3.512E-20/$B$3*$K$6 ($K$2.$K$3(1X-EXP(-$H$5*$H$7))/$H$5* 1-EXP(-$H$6*$K$7 )$D03 1=3.512E-20/$B$3*$K$6*($K$4/2+$K$5)/$H$3*$G32 33 =0.0000073*$C31

=3.12E-20/$B$3*$K$6*($K$2/2+$K$3)/$H$3*$E33 1=3.512E-20/$B$3*$K$6'($K$2+-$K$3)'(-EXP(-$H$5*$H$7))/$H$5*(_- EXP($H$6*$K$7 )jO33 i=3.512E-20/$B$3*$K$6*($K$4/2+$K$5)Iýý$H$3*$G33 34 =0.0000073*$C34

=3.512E-20/$B$3*$K$6-($K$2/2.-$K$3)/$H$3'$E32 T=3.512E-20/$B$3*$K$6*($K$2.$K$3y*(1-EXP(-$H$5'$H$7 )/$H$5*(1 EXP(-$$$$]$3

=3.51 2E-20/$B$3r$K$6*($K$4/24$K$5)/$H$3'$G32 35 =0.0000073*$C35

=3.512E-20/_$B$3*$K$6ý($K$2/2vý$KK$3)/$$H4$$E353

-=3.51 2E.20/$B$3*$K$6'($K$2.$K$3)-(1-EXP]-$H$5*

$7))LkH$L( 1-EXP](-$H$6$K$7)r$D35 1=3.51 2E-20/$B$3X$K$6'($K$4/2+$K$5)/$H$3*$G35

=352

$ $3)/-----E

-=----

-3

))$$5(-EXP-$H6*K$--

$3--

I 38 Acid dissociation coasti 39_ teg2a9.X-O 1En_______________________

____________11_________

40

_ 1 __

44 45 46

________________1.________________

4847 48 491 PM-1056, Rev. 0, Attachment E, Page E-4 of E-7

GRAND GULF REFERENCE CALCULATION M

N 0N.

2 3

4 5

6 7

8 10 From Gamma 11

[HCL

-B--- ----------------------------

Toa [-+

-C--

12 g-mols/liter g-ions/liter g-mols/liter 13

=POWER(10,-$T$13)+$H13+$113+$J13+$K13+$L13+$M13 0

14 _=POWER10,_-$T$13)+$H14+$114+$J14+$K14+$L14+$M14

=

-(.4*$B$5-0.475"$B$4)I(3X$$3)*($Ai4-(0 5+$B$6))+(0.05*$B$5-0.0475*$B$4)/$B$3 15 =3.512E-20/$B$r3$K$6'($K$4+$K$5)r(1-EXP(-$H$5'$H$8))/$H$5*N1-EXP(-$H$68$K$7))

$F15

=POWER(10,-$T$13)+$HI5+$115+$J15+$K15+$L15+$M15

=(0.4*$B$5-0.475*$B$4)I(3*$B$3)'($A15-(0.5+$B$6))+(0.05*$B$5-0.0475*$B$4)/$B$3 1T =3.512E-20/$B$3r$K$6*($K$4+$K$5)*(1-EXP(-$H$5*$H$8))/$H$5*(1-EXP(-$H$6*$K$7))p$F16

=POWER(10,-$T$13)+$H16+$116+$J16+$K16+$L16+$M16

=(0 4"$B$5-0.475*$B$4)/(3*$B$3)-($A16-(0.5+$B$6))+(0.05*$B$5-0.04751$B$4)/$B$3 17 -3.512E-20/$B$3_$K$6.($K$4+$K$5y(1-EXP(-$H$555H$8))/$H$5(1_(EXP(-$H$6$_

$K$7))p$F 17

=POWER(10,-$T$13)+$H 17+$t17 +$J 17+$1 K 7+$L 17+$M 17

=$C$16 1.8 =3512E-20/$-B$3*$K$6*($K$4+$K$5)*(1-EXP(-$H$5*$H$8))/$H$5*(1-EXP(-$H$6*$K$7))*$F18

=POWER(10,-$T$13)+$H18+$118+$J18+$K18+$L18+$M18

=$O$16 19 =3.512E-20/$B$3*$K$6*($K$4+$K$5)jl-EXP(-$H$5'$H$8))/$H$5*(1-EXP(-$H$61$K$7))-$P19

=POWER 10.-$T$13)v$H19+$I19+$J19+$K19+$L19+$M19

=$O$16 20 =3.512E-20/$B$3*$K$6*($K$4+$K$5) (1-EXP(-$H$5*$H$8))/$H$5*(1-EXP(-$H$6*$K$7))p$F20

=POWER(10,-$T$13)+$H20+$120+$J20+$K20+$L20+$M20

=$O$16 21 =3.512E-20/$B$3*$K$6*($K$4+$K$5)*(1-EXP(-$H$5*$H$8))/$H$5*(1-EXP(-$H$6*$K$7))*$F21

=POWER(10,-$T$13)+$H21+$121+$J21+$K21+$L21+$M21

=$O$16 22 =3.512E-20/$B$3*$K$6($K$4+$K$5)`y(1-EXP(-$H$5*$H$8))/$H$5*(1-EXP(-$H$6*$K$7))*$F22

=POWER(10,-$T$13)+$H22+$122+$J22+$K22+$L22+$M22

=$O$16 23 =3.512E-201$B$3*$K$6*($K$4+$K$5)*(1-EXP(-$H$5*$H$8))/$H$5*(1-EXP(-$H$6*$K$7))*$F23

=POWER(10,-$T$13)+$H23+$123+$J23+$K23+$L23.$M23

=$O516 24 =3.512E-20/$B$31$K$6*($K$4v$K$51-EXP(-$H$5*$H$8))/$H$5*1-EXP(-$H$6*$K$7))$F24

=POWER 10,-$T$13)+$H24+$1244-$J24+$K24+$L24+$M24

=$O516 25 =3.512E-20/$B$3Y$K$6*($K$4+$K$5)*(1-EXP(-$H$51$H$8))/$H$5*(l1-EXP(-$H$6*$K$7))*$F25

=POWER(10,-$T$13)+$H25+$125+$J25+$K25+$L25+$M25

=$O516 26 =3.512E-20/$B$3*$K$6*($K$4+$K$5)'(1-EXP(-$H$5*$H$8))/$H$5*(l1-EXP(-$H$6*$K$7))*$F26

=POWER(10,-$T$13)+$H26+$126÷$J26+$K26+$L26+$M26

=$O516 27 =3.512E-20/$B$3*$K$6*($K$4+$K$5)1-EXP(--$-H$5$H$8))I$H$5*(i-EXP($H-$-6*$K$7))$F27

=POWER(10,-$T$13)+$H-27+-$27+$J27+$K27+$L27+$M27

=$0$16 28 =3.512E-20/$B$3*$K$6U($K$4+$K$5)-(1-EXP(-$H$5 $H$8))/$H$5 (1-EXP(-$H$6 MK$7))'$F2

=POWER(10,-$T$13)+$H28+$126+$J28+$K28+$L28 +$M28

=50516 29 =3.512E-20/$B$3*$K$ 6($K$4+$K$5)p(1-EXP(-$H$5 $H$8))/$H$5*(1-EXP(-$H$6-K$K7))-$F29

=POWER(10,-$T$13)+$H29+$129+$J29+$K29+$L29+$M29

=$5016 30 =3.512E-20/$3

$$ K$ 6($K$4+$K$5)*(1 -EXP(-$H$5*$H$8))/$H$5*(1-EXP(-$H$6$

K$7))*$F30

=POWER(10,-$T$13)+$H30+$130+$J30+$K30+$L30+$M30

=$5016 31 =3.512E-20/$B$ 3$K$6 ($K$4+$K$5) (1-EXP(-$H$55$H$8))/$H$5 (1 -EXP(-$H$6$K$7)) $F31

=POWER(10,-$T$13)+$H31+$131+$J31+$K31+$L31+$M31

=$O$16 32 =3.512E-20/$B$3*$K$6*($K$4+$K$5)'(1-EXP(-$H$5*$H$8))/$H$5*(1-EXP(-$H$6'$K$7))'$F32

=POWER(10,-$T$13)+$H32+$132+$J32+$K32+$L32+$M32

=$O516 33 =3;.512E-20-/$8$3'$K$6' $K$4+$K$$5Y(1-EXPL5H$5'$H$8))/--$5'-1-EXP-4H$ý6$K$7))*$F33

=POWER_04-$T$13)+$H33+$133+$J33+$K33+$L33+$M33

=$O$16 34 =3.512E:20/$B$3*$K$6*($K$4+$K$5) (1-EXP(-$H$5'$H$8))/SH$5*(1-ExP(-$H$6'$K$7)) $F34

=POWER(10,-$T$13)+$H34+$134+$J34+$K34+$L34+$M34

=$O516 35 =3._512E-2O/$B$3K-$6$-($K$4+$K$5-)(1-EXP(--$*H5$5*$H$8))/$H$5-'(1-EXP(-$H$6S$K$7))p$F35-

=POWER(10,$T$13)-$H35+$135+$J35+$K35+$L35+SM35

=$O$16 36 37 3T 39 4F 41 42 43 44 45 46 47 48 4950 PM-1056, Rev. 0, Attachment E, Page E-5 of E-7

GRAND GULF REFERENCE CALCULATION 1

Q R

s S

T U

2 SLC [Ibs] 5800 Na2BIO110HO Added [MW=410J

-___I____

4 8 --------- -

iL---------------

77 8

________________pH EFFECT OF ADDITION OF SODIU 10---------

[

t 11 Total [OF-+

-L(G(Kw)

Rotx Net[0;1-pH

~

i K,

12 g-ions~liter g-ions/liter 13 =POWER(10,-14)/POWER(10,-$T$13)+$013

=15.5129-0.0224*$813+0.00003352*POWER(Bl3,2)

=(Nl3+P13-SORT(POWER(($N1 3v$P1 3(.2)-(4C(Nl3*Pl3-POWER(10.-$013)((((/2_

=$N13-$R1 3 15.3

=(0.0585 813+1.309)/10000000000 14 =POWýRJ1_0A4lýPOWERj10c$T$13+$O14_

=15.5129-0.0224'$B14+0.000033521'OWER(B14,2L

=(N 14+P14-SQRTAPOWER(($N14+$Pi~j.)1 4( j4P14-POWER(.0,-§O14j))))i2

=$N 4-$R14

--LOG1O($S14LAO 0585 B314+1.30 -9)/10000000000 -

15 =POWER(10.-14)/POWER(10,-$T$13)+$015

=15.5129-0.0224581l5+0.00003352*POWER(Bl5.2)

=(Nl5+Pl5-SORT(POWER(($Nl5+$P1 5),2)-(4*(N15*P15-POWER(10,-$O15)(/2

=CN1 5-$R5415 =LG _$S5 (0.0585-615+1.309)/10000000000 16 =POWER(10,-14)/POWER(10,-$T$13)+$016

=15.5129-0.0224*$Bl6+0.00003352*POWER(Bl6.2)

.=(Nl6+Pl

-SORT(POWER(($N16+$Pl6),2)-(4*(N1 6*P16-POWER(10,-$Ql6())))/2

=$Nl6-$Rl6

--LOG1O($S16)' =(0.0585 816+1.309(/10000000000 17 =POWER(10.-14)/POWERý(10,-$T$13)+$017

=15.51 29-1.022411317+0.00003352 POWER(Bl7,2aL

[t1,7+P17-SORT(PýOWERý(($N17+SP!7J.2)-(4K(N17'P1 7-_POWER(10..$Oi 7))D

~

=$1-R7

-LOG1O($S17)

_(0.0585 B17+1.309)/10000000000 18 POWR 0-1 /PWE 10-$T1 +$1~=1.519-.024'$18-0.00035P0WR(18,-2

[=(N8.P_-SRT(POWER(($N18.$Pl8(,2)-(4*(Nl8*P8-POWER(10.-$018)~)I I$8-R8I-LOG10($S18) =(0.0585 8lB1-.309)/10000000000 19 =POWER 10,-14 /POWER(10.-$T$1 3)-soig 1=15.5129-0.0224*$B19+0.00003352*POWER(Bl9,2)

[=(N 19-Pl9-SQRT(POWER(($N19+$Pl9).2)-(4*(Nl9*Pl9-POWER(10.-$Ql9)))))/2

[=$N19-$R19 ILG1(S9 (055B91.0)0000000000 20 =POWER 10,-14)/POWER 10.-$T$13)+$020 1=15.5129-0.0224*$B20--0.00003352*POWER(B20.2)

=(N20+P20-SQRT(POWER(($N20--$P20),2)-(4C(N20*P20-POWER(10,-$020)))))/2

[=$N20-$R20 I=-LOG1O($S20) =(0.0585*820+1.309)/10000000000 21 =POWER(10,-14)/POWER(10,-$T$13).$021 1=15.5129-0.0224*$B21 +0.00003352-POWER(B21.2) =(N21 +P21-SQRT(POWER(($N21 +$P21 (.2(-(4*(N21-P21-POWER(10,-$Q21 ))()/2 [=$N21-$R21 1=-LOG 10($S21) =(0.0585-821+1.309(l10000000000 22 =POWER 10,-14)/POWER 10,-$T$13)+$022 I =15.5129-0.0224*$B22+0.00003352*POWER(B22,2)

=(N22+P22-SORT(POWER(($N22-$P22),2)-(4'(N22*P22-POWER(10,-$022())))(/2

[=$N22-$R22 J=-LOG1O($S22) ý(0.0585 B22+1.309)/10000000000 23 =POWER 10,-14)/POWER 10,-$T$13)+$023

=15.5.129-0.0224'$B23+0.00003352-POWER(B23.2)

=(N23-P23-SORT(POWE R(($N23+$P23),2)-(4*(N23*P23-POWER(10$2))(/

1 N2$R3I-L 10($S23) !=(0.0585'B23+1 309)/10000000000 24 =POWER(10,-14)/POWER(10,-$T$1 3)+$024

=1 5.5129-0.0224'$B24+0.00003352-P0WER(B24.2)

=(N24-P24-SORT(POWER ((N24+$P24),2)-(41(N24P24-POWýER(10. $024))())/ý2 I=$N245-$R224 I-LOG 10($S24) '(0.0585*1324+1

.309(/10000000000 25 =POWER 10,-14)/POWER 10,-$T$13)+$025

=15.5129-0.0224*$B25+F0.00003352-POWER(B25,2)

=(N25.P25-SQRT(POWER(($N25+$P25),2)-(4*(N25*P25-POWER( 10,_$02,)()(/

IN25-R5

_LOG10($Sý25( I' (05ý85 B 5.130g)/10000000000 26 =POWER 10,-14 /POWER 10.-$T$13(+$026

=15.5129-0.0224*$B26+0.00003352*POWER(B26,2)

=(N26-.P26-SORT(POWER(($N26-$P26),2)-(4C(N26*P26-POWER(10,-$Q26)))))/2 I=$N26-$R28 I=-LOG10($S6 (0058 RB256--109)/10000000000 2 PWR0..................i)+/-$O27

=15.5129-.242700032PWRB,2

=(2+2-OTPWR$2+P7.(C(2P27-O EýR(10.-$Q27)((((/2

[=$N27-$R27 1-LOG10($S27)

-(00585 E327+1.39/OOO00 28 POER(0.14(VOER(1,$$1)$2

=552-0.0224'$828.0.00003352-P0WERý(B728_.2

=(N28+P27-SORT(POWER(($N28.$P28(,2)-(4(ýN28P27-POWR

.0-08~(2I$2-R8!-O1(S8 055881 39/OOOOO 29 =POWER(10.-14)/POWER(10,-$T$13).$029

=15.5129-0.0224*$B82+0.00003352*POWER(828.2)

=(N28+P28-SQRT(POWER(($N28+$P29),2)-(4'(N29;P28-POWER(10,-$O298fl(2 j=$N29-$R29 1=-LOG 10)($S22 =(0.0585 B82+1.309(/10000000000 30 =POWER 10,-14)/POWER 10,-$T$13)+$030

=15.5129-0.0224*$B30+0.00003352*POWER(B30.2)

=(N30+P30-SQRT(POWER(($N30.$P30),2)-(4*(N30nP3O-POWER(10,-$030())((/2_ I=$30-R3 1-O1O130 0.0585*830+1.309)/10000000000 31 =POWER(10,-14)/POWER(10,-$T$13)+$031

=15.5129-0.0224*$B31 +0 00003352*POWER(B31.2)_=jN3l +P31-SQRT(POWER(($N31 v$P31),2)-(i

ý 3P1-OE(0S3)))2I$3-R1

-O1 S31)

=(0.0585-B31 +1.309)/10000000000 32 =POWER(10,-14)/POWER(10,-$T$13)+$032

=15.5129-0.0224*$B32+0.00003352*POWER(B32,2)

=(N32+P32-SQRT(POWER( SN32+$P32),2)-(4*(N32*P32-POWER 10,-$Q32~)()l2

=$N32-$R32

ý=-LOG1O($S32) ý= 0:0585*B32+1.309)/10000000000 33 =PWR(0-15.5129-0.0224-$B33+0.-00-003352rPOWER(B33,2)_

=N -------

3-S-QRT(POWER(($N33+$P33(.2J)-ý4(-N-33-'P33-POWERý(10.-$033))J))/2

-$N33-$R3.3

.LOGj1O($S33)_

9-------------

34 =-POWER 10,-14 /POWER 10,-$T$13)+$034

=15.5129-0.0224*$B34-0.00003352*POWER(834,2

(

N34+P34-SQRT(POWER(($N34+$P34),2)-(4*(N34*P34-POWER 10,-$Q34) )))12 =$N34S$R_406

=-O1($341 =0085*1334+1 309)/10000000000

-35 RM-E55519002$3..0035PWRB52 R(N35.P35-SQRT(POkWER(($N35+$P35)(2(-(4*(N35P3-PWR O-$Q35)))))/2

=$N35-$R3 1=LG O

+

3 PWR10_-1.4(/POWER 10,-$T$1)$3

-1.12---------------

0003-- -POWE (B52 R35 L

10( S3 8

309)/10000000000

______-~~~-

Tj-

-i6 37___

38_

_I__

39_

_I_

47 481 491 50I I-

-I

_ I _

PM-1056, Rev. 0, Attachment E, Page E-6 of E-7

GRAND GULF REFERENCE CALCULATION v

w

[

x y

z AA___________

4

_L0_

S_

+ __9__

__,d 11 --

g-equiv.

__Na2B.1OH20t-2 Borate Boric Acid PIK pH 12 Net [H+] *Vpo0 L g-mols g-equiv.

g-equiv.

-log, 0K.

13 =S13*$B$3

=$0$2'453.6/410 =W13*2-V13 j=W138+V13

=-LOG1 U13) =Zl3+LOG10((Xl3/$B$3)/(Yl3/$B§3))_

14 =S14S$BS3

=$_Q$2453 6/410 =W14*2-V_14_ =Wl4*8+V14- =-LOG10)U14)_

Z14+_-LOGi0((Xl4/$B$3)/(Y14/$B$3))

1T5 ~S5 3

=$0S2*453.6l410 =W15*2-VI5 I=Wl568+V5

=-LOG 10(Ul 5) fZ15 kG1 (X51$B$3)i Y15/$B$3))

16 =S16*$B$3

=$0$2*453.6/4 10 =W16*2-V16 =W16*8+V16

=-LOG10(U 16) =Z16+LOG10((Xl6/$B$3)/(Yl6/$B$3) 17 =Sl7r$B$3

=$Q$2*453.6/410 =Wl7*2-V17 =W17*8+V17

=-LOG-10(U1-7)

=Z17+LOG!O((Xl7/$B$3)/(Yl7L$8$3))_

18 =S1&$B$3 W$Q245.B410 =W182-18 =W1868+V18

=-LOG1O U18) =Zl8+LOG10()Xl8/$B$3)/(YlB/$B$)

19 =S19*$B$3

=$Q$2*453 6/410 =W19*2-19 =W19*8+V19 =-LOG10 Ul 9) =Z19+LOG10((X19IB3)U 1 /$$))

20 S20'$B$3

=$O$2*453.6/410 =W20*2-V20 =W20*8.V20 =-LOG10)U20)

=Z20+LOG10((X20/$B$3)/(Y20/$B$3)ý 21 I=S21-$B$3

=$O$2*453.6/410 =W21*2-V21

=W21*8+V21 =-LOG10(U21) I Z21 +LOG 10((X21/$B$3)/(Y21/SB$3) 22-S22*$B$3

=$O$2*453.61410

=W22*2-V22

-=W2268+V22

= -LOG10 U22) L=Z22+L0G10((X22/$B$3)/(Y22/$B$3)1 23 =S23*$B$3

=$Q$2*453 6/410 =_W23*2-23 =W23*8+V23 =-LOG10(U23)

=Z23.LOG10( X23/$B$3L/Y Y23$B$3))

24 =S24*$B$3

=$Q$2*453 6/4 10 =W24*2-V24

=W24*8vV24 =-LOGIO(U24)

-Z24 +LOG I0((X241$B$3)1(Y241$B$3) 25 =S25*$B$3

=$Q$2*453.6/410 =W25*2-V25 =W25* +2

=-LOG10 U25) =_:Z25+LOG10((X25/$B$3)/(Y25/$B$3))

26 =S26*$B$3

=$O$2*453.6/410

=W26*2-V26 j =W2668+V26 =-LOG10(U26)

=Z26+LOG1O((X26/$B$3)I(Y26/$B$3))

27 =S27*$B$3

=$QS2*453.61410 =W27*2-V.27 I=W27'8+V27

-LOG.1O(U27)_

=Z27+LOG1O1((X?7-/$B$3)/(Y2.7/ý$B$.3))

28 -S-28-$B-$3 --

=$Q$2-*45-3.-6/410-

=W2&82-V28TJ=W26&86+V28

=-LOG1O)U28)

-Z28+L0G10( X28/$B$3)/(Y28/$B$3))

29 =S29*$B$3

=$O$2*453.6/410 =W29*2-V29 I =W2968+V29 =-LOG1O U29) [=Z29+LOG10((X29/$B$3)/(Y29/$B$3))

30 =S30*$B$3

=$0$2*453.6/410 =W30*2-V30]I=W30n6.V30

=-LOG10 U30 [=Z3 +ýLOG1O(30/$B$3))/(Y30/$B$3L) 31 =S31*$B$3

=$O$2*453.6/410

=W31*2-V31

=W31*8+V31

=-LOG10 U 31) =Z31.LOG10)(X3 I$B$3 /Y31/$B$3)ý 32 =S32*$B$3

=$0$2'453.6/410 =W32*2-V32 J=W32*8+V32

=-LOG1O(U32) L=Z32+LOGIO((X32/$B$3)/(Y32/$B$3)ý 33 =S33*$B$3

$0$2*453.6/410 =W33*2-V33 I=W33*8+V33

=-LOG10 U33~ =Z33+LOGl0(tX33(SB$3)1)Y 3j/

3))

§34 ýf S34SB$3

=$Q'453.6/410 =W4-V3 W3 4*.8+V 3-4 -=-

L0-G 10(U 34) fZ34+O1I)X4

$)/)Y 34 1 B $3))

35 =S3.5-$B$3

=$QO$2*453.6/4 10 =W35*2-V35 _=W_35*8+V35

=-LOG iO(Y3)_ =Z35+LOG10)(X35/$3)(Y35L$B$3))

36 371________

36 8

39 40___________________

l_____

421_______

46 47 48

____________{_______________

49.I___________________________

50 PM-1056. Rev. 0, Attachment E, Page E-7 of E-7

ML072570190

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Title:

1.0 481E-04

.LOGj1O($S33)_

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Title:

1.0 481E-04

.LOGj1O($S33)_

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