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Determination of Max Permissible Concentrations in Water for Xe-133 & Xe-135 for Mar 1975.Prepared for Met Ed
	ML19210A605
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Site:	Three Mile Island
Issue date:	03/31/1975
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. 1 A DETERMINATION OF THE MFC.,'S .-

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I. Introduction

Xenon-133 and Xenon-135 are radio-noble gases which can be found in power reactor liquid effluents. It is the purpose of this report to detemine the Maximum Pemissible Concentration in Water (MPC y )' of these radionuclides for the general population.

II. Xenon In The Water Environment A. Maximum Specific Activities Attainable in Water The maximum specific activities of Xenon-133 and Xenon-135 attainable in the water environment are functions of solubility and intrinsic specific activi-ties. The concentration of Xenon in water can be detemined by Henry's Law.

This law states that the solubility of a gas in a liquid is directly propor-tional to the pressure of the gas above the liquid at equilibrium. Mathema--

t':: ally Henry's Law may be expressed as, C = kP ,

1.

. :

where C is the weight of gas in the liquid, P is the atmospheric partial ^

pressure, and k is Henry's constant for a given gas and a given temperature.

At 0 C and 1 atmosphere partial pressure,242 ml of Xenon will be soluble -

in 1 liter of water (1). And, by extrapolation it can be shown that I lit er of water at 10 C can absorb approximately 210 ml of Xenon at 1 atmosphere pressure. Since the density of Xenon is 5.85 mg/ml (2) Henry's constant at -

10* C for Xenon is 1.23 g/1-ata. The mole fraction of Xenon in the atmos-phere is 8 x 10-a(3); therefore,substitutin3 into equation 1, C = (1.23g/1-atm)(8 x 10-3 atm) = 9.8 x 10-89/1 2.

.

it is fcund that I liter of water can absorb up to 9.8 x 10-8 g/l of Xenon a- 10 C. .

i The intrinsic specific activities of Xeno1-133 and Xenon-135 are 1.85 x 105

~

,

Ci/g and 2.55 x 105 C1/g, respectively. As such each liter of water can ab-sorb a maximum of either 1.8 x 10-2 Ci of Xenon-133 or 0.25.Ci of Xenon-135. .

These values are equivalent to 18 uCi/mi of Xenon-133 or 250 pCi/mi of Xenon ,

-135. '

,,

III. Detemination of MPC, .

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The calculation of an adult MpCyequal to 5000 mrem / year for the drinking -

water pathway is based on the following equation (4):

1.3x10-6 mRA D .

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MPC" 3. .

f,(i - e-l t)o I E F gj (RBE)jng .

Each tem in this equation is discussed below.

1492 (07 1

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m-

~ m is the mass in grams of the critical organ. It has been shown that Xenon is concentrated in the body fat approximately ten to twenty times above the level in the blood stream (5). Thus the body fat is considered to be the critical organ; its mass is 10,000' g(4).

-

R- R is the permissible dose rate to the organ in rems / week. Since the body fat is the critical crgan, and since it is distributed through the whole body, R is taken as 0.1.

Ao -lo is the effe:tive decay constant, it is a combination of the physicai

-

and biological decay constants. In order to calculate lo the bie'agi- -

cal half life (T ) bmust be determined. .

Tb =0.693mC/ 4,

/ Ifw i

where, '

m = cass of critical organ = 10,000 g I i

C = average tissue concentration = 1.1 x 10-s g/kg based on equation 1 with k equal to 0.68 g/1-atm at 37.8a C and .

j:

a concentration factor of 20 ..

I = average daily ingestion rate = 2.3 x 10-7 g based on a water plus fluid uptake of 2200 cc/ day and 300 cc/ day .

of water of oxidation produced in the body, therefore -3 J

intake is 2.21(9.8 x 10-a g/l) + 0.31(0.68 g/l-atm)(8 -

x 10-8 atm) f y= 0.95 based on a fraction from GI tract to blood of 1.0 f.

p and a concentration factor of 20 in the body fat ,

h t' .

'b (XS)" 0.693(10,000)(1.1x10-9) /

/(2.3x10-7)(0.95) = 35 days 5.

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E eff Tb+T p 6.

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3 2, T3ff(133Xe) = = 4.53 days 7. ,

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eff(13sXe) =( f( g) = 0.38 days

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0.693 -

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.l g(133Xe) = 0.693/4.58 = 0.151/d 10. !

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- 0.693 (13sxe}= 0.38 " 1*

t_ - t is the time which in this case is 365 days 133Xe ,f reference IEjfj(RBE)ingand - effective energy for organ o 0.090 for 135Xe (4) drinking are, y

Referring back to equation 3 the adult MPC 's for .

12.

(1.3x10-6 )(10,000)(0.1'l(0. t st l = 7.7x10-2u ci/ml 13 Xe MPCv (0.95)(1-e-(0.143)(365))(0.0027) 13.

(1.3x10-6)(10,000)(0.1)(1.821 2.8x10-2pCi/ml 13sxe HPC u (0.95)(1-e-(1.82)(365))(0.090) i and are not repre-The MPCy's calculated above are for the adult l populat tion must be onIn orde sentative of MPCv's for the general population. the for the general population the age discribution of the popu a considered.

However, it would be impractical toatadd to arrive gen- this v

!!PC . calculationalThescheme.10

.

MPCy 's for 133XeCFR 20, the und 13sXe adult MPCy's ar are then:

eral population MPCy's.

= 8 x 10-3 pCi/mi 133XeMPCy pCi/mi 13sXegp q = 3 x 10-3

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IV. Conclusions MPCy

's were calcusated for 133Xe and 13sXe in water. The critical organ was the body fat. The MPC y val es found were lower than the solubility of Xenon in water. Ft.rther analysis has shown that drinking water is the critical dose pathway. Apper. dix A of this report reviews other dose pathways.

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i References Lange, N.A. Handbook of Chemistry _,. Ninth Edition. Handbook Publi-1.

shers, Inc. Sandusky, Ohio. 1956. .

Eshback, 0.W. Handbook of Engineering Fundamentals. John Wiley &

2.

Sons, Inc. New York, 1952.

3. Gray,D.E.(Ed.) American Institute of Physics Handbook. McGraw-Hill Book Company, Inc. New Yort. 1957. ..

~

4. Recomr.endations of the International Commission on Radiological Pre-te::fon. ICRP Publication 2. Report of Committee New II on Permissible York. 1959.

Dose for Internal Radiation. Pergamon Press.

5. Itaghissi, A.A. Personal Communication.

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Appendix A

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I. Introduction .

In this appendix general population MPC.,,'s are calculated for dose pathways other than drinking for Xenon in water. These pathways are swiming and shine at the shoreline. Adult dose conversion factors are also calculated '

for these pathways as well as the drinking water pathway. General popula-

tion MPC.,'s and adult dose conversion factors were chosen to agree with 10 CFR 20 and ALAP philosophy respectively. 1 II. Swimino Pathway _

The calculation of an MPCy equal to 5000 mres/ year for the swiming path-way is based on the following assumptions- l

'

1. The maximum individual swims 107 hours0.00124 days 0.0297 hours 1.76918e-4 weeks 4.07135e-5 months per year (1)

2. The critical organ is the whole body

3. Adult dose conversion factcr. (DCF)are(1):

5.7 x 10-8 mrem /hr/pCi/l for 133Xe 4.5 x 10-7 mrem /hr/pCi/l for 135Xe ,

The equation for calculating an MPC. s based en a dose conversion factor is,

.

p MFC..(uCi/ml) = (5000 mrem / year)(10-3 Ci/ml/pCi/1)

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/ (D /, CF)(t) 1; ;

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Therefore the adult MPC.,'s are, .

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132x*M?C y

= (5000)(10-3)!(5.7x10-a)(100)=0.88pCi/mi ,

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. 2. .

I'#X0 (4.5x10-7)(100) = 0.11 pCi/ml 3.

MPCy ,

and the general population MPC y 's are,

.

= 0.1 pCi/ml 4.

133XeMPC

= 0.01 pCi/ml 5.

135XeMPC v

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III. Direct Radiation At The Shoreline Xenon is a noble gas and will not absorb in the ~ sediments; therefore the ex-posure is limited to the shine dose from the dissolved gas. The following

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F assumptions are made,

1. The problem is defined as primary ionization above an infinite disc where buildup due to scatter and absorption cancel each other out

2. At a point above the center of the disc the dose is equal to the 2r air imersion dose minus a correction factor, F (2)

3. Then at a point above one edge of this infinite disc the dose is the 2x irmersion dose minus a correction factor, that is, (2x imersion dose)(1-F) 6. ?(;.

Dshine =

where, ..

F = e-Vo - vo[Euo ) 7.

and, ,

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=fe-vt t

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therefore by integration, ,

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vDtn Eu = log t + + + 9. s 0 11 2 2! 3 3! n n!

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apply limits with, .

p o(133Xe)=0.2cm/g 2 (3) 10.

5 11.

and 9 0 (135Xe) = 0.12 cm2 /g (3) then,

.

12.

Euo(1334e) = 0.19 and Eva (13sXe) = 0.12 13..

and from equation 7, F (133Xe) = e-o.2 - 0.2(0.19) = 0.78 14.

and F (13sXe) = e-o.12 - 0.12(0.12)~= 0.87 15.

Therefore from equation 6 and utilizing the 2n ir=ersion DCF's in reference 1 the dose conversion facto,rs a' re, DCF(133Xe)= (2.8x10-8 mrem /hr/pCi/1)(0.22)=3.1x10-9 mrem /hr/pCi/l 16.

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DCF(13sXe)=b(2.2x10-7 mrem /hr/pCi/1)(0.;3)=1.4x10-emrem/hr/pCi/l 17. ,

And the adult P.PC/s for 5000. mrem / year are, in a fashion analagous to equa- ,

'

tion 1, t

32 1492 113

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133XeMPC y

" (5000)(10-9)

, / /(3.1x10-9)(365)(24) = 0.18pCi/ml 18. ,

135Xe MPCy

"( }(

,

p (1.4x10-8)(365)(24) = 4.1x10-2 Ci/ml 19.

And the general population MPC y 's are,

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133Xe = 0.02 pCi/ml 20. h, ,

MPC y 135Xegp q = 4 x 10-3 uCi/ml 21.

These MPC y 's are overly conservative in that they assume an individual would stand at the shoreline all year, which is unrealistic. The dose rate drop.s off very rapidly with distance from the shoreline.

IV. Deterniination of Dose Conversion Factorr (DCF's) ,

A. Drinking Water Pathway '

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,

The OCF's are determined by rearranging equation 1 to, nr.e

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, (5000 mrem / year)(10-9 uCi/ml/cCi/1) 22*

(MFCw pCi/ml)(hours / year) and substituting the appropriate values. The DCF's are,

" ^*0CF * (5000)(10-9)!(7.7x10-2)(365)(24)v 7.4x10-9 mrem /hr/pCi/l

.

23.

13sz

2.8x10-2)(365)(24)= 2.0x10-8 mrem /hr/pCi/l 24.

GCF B. Swimino Pathway The DCF's are given in reference 1. They are, based on whole body dose, 133Xe = 5.7 x 10-8 mrem /hr/pCi/l 25. -

g7 13sXeDCF = 4.5 x 10-7 mrem /hr/pCi/l 26.

C. Direct Radiation At The Shoreline [

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These values are as calculated in equations 16 and 17. They are,

, ; 13 3X DCF ~~ * * """

1 135Xe0CF = 1.4 x 10-8 mrem /hr/pCi/l 28.

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General Population MPCy Values '

based on 5000 mrem / year (uCi/ml) Solubility in Water ..

2

/ \ at 10*C and Drinking Swiming Shoreline 80 nata. Xe ,

133Xe 8 x 10-3 0.1 0.02 18 , ,

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i 13sXe 3 x 10-3 0.01 4 x 10-3 250 -

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Adult Dose Conversion Factors mrem /hr/oCi/l Drinking Swinaing Shoreline -

,

133Xe 7.4 x 10-9 5.7 x 10-8 3.1 x 10-9 -

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13sXe 2.0 ,: 10-8 4.5 x 10-7 1.4 x 10-8

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References t

1. U.S.A.E.C. Final Environmental Statement. 'fiumerical Guides For Design Objectives and Limiting Conditions For Operation To Meet The Criterion "As Low As Practicable" For Radioactive Material in Light-Water Cooled fluclear Reactor Effluents. Volume 2. Analytical Itodels and Calcula-tions. WASH-1253. July, 1973.

2. Evans, R. The Atomic flucleus. McGraw-Hill Book Company, Inc. flew York. ' -

1955.

3. Lapp, R.E. and H.L. Andrews. fluclear Radiation Physics. Prentice-Hall, In:. Englewood Cliffs. 1964.

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Appendix B I. Introduction ,

In this appendix adult dose conversion factors specific to TMINS are calculated for the applicable pathways. Adult dose conversion factors were chosen to agree with the ALAP philosophy. These pathways include the maximum individual drink-ing, the closest realistic drinking individual supplied by a water company, Brunner Island, the individual swirming, and the individual on the shoreline.

All values are in mrea/hr/pCi/l for the effluent concentration.

m -

II. Drinkinc Pathway

.

The licuid outfall at TMINS is submerged and is diluted approximately 1.7 x 104 tices. This dilution factor is based on a maximum pump flow of 30 gpm, a min-imum blowdown flow of 5000 gpm and a river dilution factor of 100. Therefore the concentration of radio-Xenon in the river water (C y ) is

"

v 1.7 x 10 4 '

,

where CE is the concentration of radio-Xenon in the station effluent.

A. Maxitum Individual The caximum individual drinks 1200 ml of river water per day at the point of discharge. If credit is taken only for dilution and not for physical decay the TMINS site specific dose conversion factors are,

/

1200 133Xe n = (7.4x10-9)(2

( M = 2.4 x 10-13 uCr- 1.7x10g

.

C 13 sX e ,,.

'

= E(2.0x104)h = 6.4 x 10-13 1.7x104

.

B. Individuals That Work At Brunner Island The individuals who work at Brunner Island drink 600 ml of water during their work day. The Brunner Island river intake is 4.2 miles below the TlilNS out-fall and as such the travel time is about 9 hours1.041667e-4 days 0.0025 hours 1.488095e-5 weeks 3.4245e-6 months . For calculation of these dose conversion factors crc - for radioactive decay equal to the travel time' is taken. The dose :onver';i; factors are, 9

13 3Xe =C( 4*lW)2 E '

e-blM M = 1.1 x 10-13 DCF 1,7xtwq

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135Xe DCF

= CE (2.0x10-a) 2 0 e~ = 1.6 x 10-13 1.7x104

.

II. Swi m ing Pathway

'

133Xe 4= ~4 x 10-12 DCF

=(5.7x10-s)/1.7x10 ,

..

13sXe = (4.5x10-7) = 2.6 x 10-11 DCF 1.7x104

.

III. Direct Radiation At The Shoreline 133Xe0CF * (3.1x10-9) 1.7x10g= 1.8 x 10-13

,

13sXe =(1.4x10-8) = 8*2 x 10-13 OCF 1.7x104 IV. Samole Problem If the effluent at TMINS contained 10-2 pCi/ml (107 pCi/ 1) each of 133Xe.and 135xe the resultant doses to the adult population are as in the table below.

Max Ind Brunner Is Swimming Shoreline Drinking Drinkinc 100 hours0.00116 days 0.0278 hours 1.653439e-4 weeks 3.805e-5 months /yr all year 133Xe 2.1x10-2 9.5x10-3 3.4x10-3 1.6x10-2 crem/yr 235Xe 5.6x10-2 1.4x10-2 2.6x10-2 7.2x10-2 mrem /yr

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