ML20206K415
| ML20206K415 | |
| Person / Time | |
|---|---|
| Issue date: | 05/05/1999 |
| From: | Campe K NRC (Affiliation Not Assigned) |
| To: | Smith H AFFILIATION NOT ASSIGNED |
| References | |
| NUDOCS 9905130155 | |
| Download: ML20206K415 (17) | |
Text
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.i May 5. 1999 s
- Mr. Herschel Smith 6321 Pineburr Road Charlotte, NC 28211
SUBJECT:
REQUEST FOR DERIVATION NOTES FOR CONTROL ROOM HABITABILITY DOSE GEOMETRY FACTOR
Dear Mr. Herschel:
In response to your request, I am enclosing a copy of the derivation for the dose correction factor used in connection with control room dose calculations. Specifically, this derivation was the basis for the infinite-to-finite cloud dose correction factor that was described in the Murphy- 1
' Campe paper " Nuclear Power Plant Control Room Ventilation System Design For Meeting I
- General Criterion 19", presented at the 13* Air Cleaning Conference, August,1974. If you have any questions, please contact me at (301) 415-2858..
Sincerely, i O(iginalsigQ Kazimieras M. Campa, Senior Reactor Engineer Probabilistic Safety Assessment Branch Division of Systems Safety and Analysis Office of Nuclear Reactor regulation j l l DISTRIBUTION: ; F FILE CENTERfi SPSB FILE PDR
Enclosure:
As stated-cc w/ enclosure: MRubin , _KCampe - g (((g I ,
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. G:\CAMPE.WPD 3
OFC NRR/DSSA/SPSB NRR/DSSA/!p)SB (Q P NAME- KCampe;cff,f MRubird V DATE 5/f[/99 ' b 5//TT99 l e'"n 0' 015 OFFICIAL RECORD COPY
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' H- 9905130155 990505 NRRA i PDR ORO e
- - - ~ - . . .
.. - 1 8 . _. l INFINITE-TO-FINITE CLOUD DOSE ' _ . _ _ _ . . . _ ___ . . - ~
- - CORRECTION FACTORS FOR NUCLEAR POWER -- -
PLANT CONTROL ROOMS Accident Analysis Branch March 1974 . I An intermediate step in the calculation of the control room whole body gamma dose is the evaluation of an " unprotected dose" based on an infinite cloud immersion dose model. The fact that in most cases control rooms are surrounded by concrete walls reduces the dose contri- I butions from the contaminated air outside the control room to negligible levels.- Thus, a correction factor is required to take into account the ; I finite volume of the air within the control room boundary. The factor can be evaluated by ratioing the semi-infinite cloud flux at a point to a finite hemispherical cloud flux at the center of the sphere, where the radius of the hemisphere is determined by equating its volume to the control room volume. The correction factor CF is given by (See Appendix A for derivation) 1+ (1 - D)2 l CF= O r 3 (1) i (1 - e-p M) + 1 1 - [1 + (1 - D)#R] e-N - D)p R l j (1-D): ( j where i y = Linear gamma attenuation _ coefficient for air at some effective gamma energy E R = Control room equivalent hemisphere radius 1 C, D = Buildup coefficients for air at gamma energy E in i Berger's buildup fgg,tgr formula which is of the form j
. B(gR) = 1 + CpReD " l Figure 1 presents a graph of CF plotted versus control room volume V, [
where V is constrained by l 1 i V=ArR3 8 (2) i j 1 W
e - -- - 8 n c. E
- e.
c; E. c. c: _ g c ew c s .'
+
c: C L. t
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- 8 ul
- , 5l 4i E >E a
e el
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- o N 8 u Li e
cI
- 44 W1 E flLi
~
E .i s. f h -
, O e
. I . I . 1 . l . e @
n -
=
a s e a a a u dD 'J013*d A21*mO*D O O
, 8 w-
= -_. . . .
7 J3-r The-equation for-the-curve-in-Figure 1-is -given by - - - -- CF = 33h (3) Appendix B" illustrates cha method of calculating the effective gamma energy for the airborne fission products. The calculation of p, C, and D is' outlined in Appendix C. The correction factor is used as follows: - I4I (DOSE),,g,yg = (DOSEL/CF If one of the dimensions of a control room, se.y the length, is significantly larger than the other.tvo dimensions, there is the possibility that a hemi-spherical representation is not appropriate. The use of an equivalent
- hemisphere for a long corridor, for example, may be overly conservative since the " ands" of the corridor may not be significant dose contributors.
In other words, the effective volume of an equivalent hemisphere in this case would be something smaller than the actual control room volume, V. Consequently, the actual CF would have to be larger than that predicted by. the equivalent hemisphere sof el in equation (1). A test of,this L .- possibility was performed with respect to a control room whose dimensions I- were 30' x 30' x 100' (assumed to be representative of a " slender" control
- room). Expressed as a ratio, the difference between the actual control room dose and its equivalent hemisphere dose is approximately (See Appendix D).
(DOSE),eyygg (5) (DOSE) HEMISPHERE a A simD tr test for a " flat" control room was performed using the dimensions 70' x 70' x 20'. The corresponding ratio was found to be (See Appendix D)
, (DOSE) ACTUAL =
0.96 (6) (DOSE)ggg,,,gg,,
,g4 g. ,.,ipw i me -. 'ag.ee m 9
w
r- ,
. = :=- - . - . .
i . 4
.w - - - - . . . ..w. , . . . ., . _ .
The ratios. (5) and (6) indicate that a hemispherical control room representation is adequate (and slightly conservative) for control ' room geometries encountered in practice. 9
-w ,
- 8
V . L' ' 5-Appendix A i Infinite-to-Finite Radioactive Cloud Dose Correction Factor The differential dose rate at the center of a spherical radiation
-source of radius R can be written as f
l i dD = K 2 e-8"B(g x)dV (A.1) 4rx where I l K = Flux to dose conversion factor j e Sy = Volumetric source strength j u = Linear attenuation coefficient for the source medium ! l X = Distance from a differential source volume dV to the center of the sphere B = Radiation dose buildup factor In a spherical coordinate system where $ is the azimuthal angle and 9 is the angle of elevation, the differential volume dV is of the form dV'= (dx)(xde)(x cos 6 d () (A.2) Substitution of A.2 into A.1, and integration over the volume of the sphere yields the following expression for the radiation dose rate as a function of' sphere size expressed in mean-free-paths, j i D(pR) = KS' CY B(y)dy (A.3) M 0 A particularly useful form of the buildup factor is given by Berger's formula (Ref.1), , B(y) = 1 + Cyeoy (A.4) l l
., -,-op.nespm-a ma mu-e4 e n n n- ' - ' W
_a_
,. l q
^*
. . 1 Applying equation A.4 to A.3 and carrying out the indicated integration, ._
we can write the dose as f D(pR) = KS' (1 - e-
- R ) + C !1 - [1 + (1 - D)gR] e-ti-olyRh (A.5)
(1 - D)2 4 j , The infinite cloud dose rate can be obtained by evaluating equation A.5 , as R approaches infinity. . Thus the infinite-to-finite cloud dose cor-rection factor is given by C 1+
'~' (1 ~ DI' CF = =
C f (A.6) D(pR) (1. .-p R g 4 1-l+( - D)p R] e-{1 - D)pRt (1 - D)2 ( l
)
i i i l l
n , .., i :
,f.... .- . . .
- 3. : - .
.g . f.c
- M l
---- - J.ppendix B -- 1 Effective Gamma Energy Table B.1 lists the radioisotopes that are considered in accident analysis 3 dose calculations for airborne contaminants, along with the corresponding '
energies of the photon spectrum amitted by each radionuclide. The energies correspond to those found in the ORIGEN (Ref. 2) photon library. In general, the average photon energy for the ib radioisotope can be defined as 9 Es "Eli Ej ,/Dji * (B.1) -1 1 1 1 1 where i f g
= Emission rate of the jb photon energy for the ib l radioisotope E
p
= Thejb photon energy for the ib radioisotope l If N gand F are i the equilibrium inventory and the accident release fraction for the ith radioisotope, respectively, then the average gamma energy I for a group of radioisotopes can be calculated from i = $N, F,I,/ [ N, F, (B.2) i i The above method was used to evaluate the average gamma energy for the radioisotopes listed in Table B.l. The calculated average energy is E = 0.733 May gwwe. -
se =w+a =+a..ea .m - w -. c.smae we ab - --e-9 D
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T A F _ L _ U C _ L A * ) C y e r v 7 E o i 8 2 37 6 S t t 6168 42152210524 _ O D n e l a 80285 2 50580124819 _ v e 4554 01110051054 . S n R ( I I S Y , g L A N N A 5 ' 7 8 T 8 N 2 0 E D 0 I . C C 3 _ A 8 39 3 57 _ N 30 _ I 2 00 D E ) S e U v 3 i 9 5 5 A t 9 5 9 35 6 T a 2 9 96 8 A l 1 0 0 10 0 D e . R 0 0 00 0 T ( C U e D t _ O a 5 R R 5 7 31 18 1 P 2 81 40 1 n 1 1 12 13 1 N o O i 0 00 00 0 I s S s S i _ m I 7 _ F E 1 525 5 3821 0 _ E n 1 3031 2 . N o t l t 0001 0 O o B h R P 6 I 3 2 9 3 3 6949 A 6 931 519 3284 0 1.799 0 . . . 736 8040 202 000 0000 1 f v B e M E L 3 B 78 3 2 27773 - 9 2 A 0 00 0 3 64477 0 5 T 0 2 1 22572 8 1
= 1 0 0 0 00000 0 0 E
e p o t o s mm m i mmmm1335578 o 12345 57893333333 i 33333 88881111111 d 11111 a rrrreeeeeee R III1I KKKKXXXXXXX
k
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C-Evaluation of the Parameters y, C, and D in Equation '(1) l The value of' the linear attenuation coefficient for air obtained from
~
i the y versus gamma energy enzve in Ref. 3. is p = 0.00955 m'1 The parameters C and D in Berger's buildup. factor formula were evaluated ~ j by interpolating Trubey's data (ref. 4) for the appropriate gamma energy l for air. Figure C.1 shows a graph of C and D versus gamma energy E based en data in Raf. 4. The parameter values were found to be I C = 1.35 ! ] 1 j = 0.076 j
.D ;
A test of the accursey of the above parameters can be made by comparing l the infinite' cloud doses as given "oy equation (A.5) and l l l l t D., = 0.507 Y x (c.1) j i presented in Ref. 3. Since E is 0.733 Mev, (C.1) yields
- l 4
D., = 0.372 X (C.2) l ! l. t I For an infinite cloud, (A.5} reduces to 1 I s e [ D** - K , 1 1+ r > j
# ( (1 - 0)2 j (C.3) 4 %.M.e g 4
. . . ,~ - ,,, .
- . = = = = = = . . = - -
e : . . _. ; . , , f.g o
..c.-. . .
i j ?, . To have s. (C.1) and (C.3) in a consistent set of variables we observe that
.g dI8 .
1d om8 , Ci , y cf,3 cm3 - we m-3 3.7 x 10 2$ or
'S, = 3.7 x 104X
. Furthermore,-K is about 1.25 x 10.s rAr at 0.733 Mev (Ref. 5),
7/cm _ ,,, 2
'/"*
K = 1.25 x 10-8/3600 7/em _ ,, So that Eq. C.3 becomes o l' D = 1.25 x 10 4
, 3.7 x 108 X 1+-
1.35 I 1 scoo 0.omss (1 - c.076)*/ l L ! Thus 1 D., = 0.347 X (C.4) r whr .h is in fair agreement with the value in eq.. (C.2) . 9*
, r y , .
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.3 A w. ,1 ,...,% . _... ~._ .e .. . . . . , , _ . , . . - , . . . , - _ _ . - . - . _ , _ . _
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Figure Col. _ Berger's Buildup Factor Coefficients versus Cama Energy d
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{ 4 _ _ . _ .. _ . - _ . . _ - _ _ _ JLppendix D _ _. __ ___ _ _. .- .. . . ._ _ . - _ _ . _ _ Control Room Equivalent Geometry Tests Consider a " slender" control room having the dimensions H = Height = 30' W = Width = 30' . L = Length = 100' The radius R of an equivalent hemisphere is obtained by equating volumes, namely h r R 8 i = HWL (D.1) or R = 10.676 m. If, instead, the control room is replaced by a cylinder of radius R' and length L, such that f r R'2L = HWL (D.2) then the radius R' = 7.296m. An estimate of the discrepancy between the two geometries can be made by ratioing the corresponding uncollided fluxes at the center of the respective geometries, l'.e. G i 2
- p R';
p , cHALF-CYLINDER ,2g (D.3) HEMISPHERE S f i 1 -o'8 L
l
- I
.O__
. . . _ - . . . - - . . . . . - - - - -- - - - - - - - - - - - - ' - - - - - - ~ ~ ~
where (Raf. 4) - h
.G (6,b) m F (tan-1$, y)dy (p,4) .
Y a and F (w, a) a e*8 d#
-o (D.5)
For = 0.00955 m-1, the ratio can be written as p do.1455, ONE = 10.3165 G(0.1455,0.06908) 3 , c.102 or 0.00088 9 = 10.3165 F(tandA% Y)dY (D.6) o Using 12 point Gaussian quadrature, equation (D.6) yields p= 0.915 e
+
~
. ' -+ u-.. - - - . . --- .,
-_14 -
' ~ ~ ' -
- The other extreme for control wom geometry is-the flat, or " pillbox" -
configuration. Consider, for axample, the control room dimensions H = Height = 20' W = Width = 70' L = Length = 70' The radius R of an equivalent hemisphere for the above control room, as determined by equation (D.1), is . R = 10.9 8m. Replacing the control room by an equivalent upright cylinder of radius R' and height H we have w R'2 H = HWL (D.7) f or -R = 12.04 m The cylindcr to hemisphere flux ratio is given by d"hG(yH,pR') kD.8) h(1 - e*"")
~1 Again, for = 0.00955 m , the ratio is p _G(0.058n,0.11M) *= 10.05 G(0.05822,0.11498)
, ,, , o.1os or 0.1149s (D.9) 9 = 10.05 F (tan-1 U$8",y)dy 0
. - ~ , _ .
't i . 7 15 - APPl ying 12 point Gaussian quadrature to equation (D.9) we obtain p= 0.955. I l 4 4 4 t e
*~ .am.w,,
,:?;
.l/
l $ , :3 -
~
i
.t.
t
... _ _ . _ _ _ . . - - - -.__ _.._ REFERENCES. _ ._ _,__. . _. _,, _ . . , _ .
- 1. ' Jaeger, R. G., et al., " Engineering Compendium on Radiation Shielding" Vol. I - Shielding Fundamentals and Methods, Springer -
Verlag,1968. - -
- 2. Belt, M. T., "0RIGEN - The ORNL Isotope Generation and Depletion Code," ORNL-4628, May 1973.
- 3. Slade, D. H., Ed., " Meteorology and Atomic Energy 1968," TID-24190, July 1968 (p. 338).
- 4. . Rockwell III, Th., 'Ed., " Reactor Shielding Design Manual," TID-7004, 1 March 1956. I I
- 5. Schaeffer, N.M., " Reactor Shielding for Nuclear Engineers," TID-25951, 1973. -
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