ML16257A078

Revision 309 to Final Safety Analysis Report, Chapter 11, Radioactive Waste Management, Section 11.1A

ML16257A078
Person / Time
Site:	Waterford
Issue date:	08/25/2016
From:	Entergy Operations
To:	Office of Nuclear Reactor Regulation
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WSES-FSAR-UNIT-311.1A-iAPPENDIX 11.1ADERIVATION OF RESIDENCE TIMES WSES-FSAR-UNIT-311.1A-iiAPPENDIX 11.1ATABLE OF CONTENTSSECTIONTITLEPAGE11.1ADERIVATION OF RESIDENCE TIMES11.1A-111.1A.1CIRCULATING CRUD11.1A-111.1A.2DEPOSITED CRUD11.1A-3 WSES-FSAR-UNIT-311.1A-1APPENDIX 11.1ADERIVATION OF RESIDENCE TIMESThe derivation of the core residence times for circulating crud and deposited crud as shown in Subsection11.1.2 is as follows:11.1A.1CIRCULATING CRUD:

The number of radioactive atoms (N f) in the crud film on in-core surfaces at any time is:

1)-(A N-dt dN f i i f=Solving for N f yields the following:

()2)-(A atom/g e 1=N res i t-i i fwhere:i=the activation rate for each isotope i (d/g-sec)i=the decay constant for each isotope (sec

-1) and t res=the desired core residence time (sec).The number of radioactive atoms (N c) released to the reactor coolant at any time is:

[]()N++-A ER N=dt dN c i c f c atoms/secSolving for N c yields the following:

[]()()()t++-i c f c i e-1++A ER N=N (A-3)where:ER=the erosion rate (g/cm 2)A c=the core surface area (cm 2)=the plateout rate (sec

-1)=the purification cleanup rate (sec

-1)i=the decay constant (sec

-1)

WSES-FSAR-UNIT-311.1A-2Revision 11 (05/01)The total amount of crud (M c) released to the reactor coolant any time is:

[]()c T c M+-A ER=dt dM (A-4)where:(DRN 99-2361)

M cincludes both radioactive and nonradioactive material(DRN 99-2361)Solving for M c yields:[]()()()grams e-1+A ER=M t+-T c (A-5)where:ER=the erosion rate (g/cm 2)A T=the total system area (cm 2)=the plateout rate (sec

-1)=the purification cleanup rate (sec

-1)The activity (A i) of the crud released to the reactor coolant is:

coolant reactor in crud of gram per dps , M N A c C i i= (A-6)Substituting the values of N c and M c into the above expression and assuming i is small when compared to and , the activity of the crud is as follows:

()()0.06 A A e 1=A T c t-i i res idpm/mg-crud (A-7)where:0.06= a constant changing dps/g-crud to dpm/mg-crudThis activity (A i) is also assumed to be the activity of the crud which plates out on out-of-core surfaces.Solving equation (A-7) for t res yields equation (3).11.1A.2DEPOSITED CRUDThe activity (A j) of the deposited crud is:

()()0.06 e 1 N A res i t-i f i j== (A-8)Solving equation (A-8) for t res yields equation (4).