Comparison between the measured and calculated exposures

Environment International, Vol. 14, pp. 181-184, 1988

0160-4120/88 $3.00 + .00 Copyright © 1988 Pergamon Press plc

Printed in the USA. All rights reserved.

COMPARISON BETWEEN THE MEASURED AND CALCULATED EXPOSURES D. Cesar, J. Kova~, and A. Bauman Institute for Medical Research and Occupational Health, 41000 Zagreb, Yugoslavia (Received 8 September 1987; Accepted 10 May 1988) The quickest way to detect a significant change in radioactivity in the atmosphere is by measuring exposure rate. These measurements enable elementary protective measures against radiation to be taken quickly, along with specific measurements of radioactivity in the environment. This study aims at determining the differences between the exposures obtained by direct measurement and the doses calculated from the measured specific activities of the radionuclides present in human environment.

In the e v e n t o f a nuclear accident it is n e c e s s a r y to estimate the dose received by a population during the accident and in the period that follows. Partly, the dose originates f r o m radioactive sources which are in the e n v i r o n m e n t and therefore have an effect upon man. This is called external radiation dose. Basic information for the determination of external radiation dose is e x p o s u r e (X) or, in case o f its change in time, e x p o s u r e rate (X). In this study the contamination caused by the Chernobyl accident was used for determination of the differences b e t w e e n the e x p o s u r e s obtained by direct m e a s u r e m e n t and the e x p o s u r e s calculated f r o m the m e a s u r e d specific activities o f the radionuclides present in h u m a n e n v i r o n m e n t (Turner, 1986). The data used w e r e e x p o s u r e rates and radionuclide specific activities m e a s u r e d at one place in the Rebulic o f Croatia in the period April 30th to M a y 31st, 1986. E x p o s u r e rates w e r e m e a s u r e d in the air 1 m a b o v e the ground by the instrumentation consisting of Phillips ZP 1451 Geiger-Miiller tubes, a " B o r i s Kidri~" Vin~a SVIT-10 c o u n t e r and an Apple II c o m p u t e r . M e a s u r e m e n t s were continuous and the data r e c o r d e d minutely were stored to be read at any time. The data r e c o r d e d for a certain period of m e a s u r e m e n t were: m e a n value, standard deviation, m a x i m u m and m i n i m u m values, time of m e a s u r e m e n t and total value. F r o m graphic record it was possible to d e t e r m i n e a value at any m o m e n t o f m e a s u r e m e n t . E x p o s u r e rates w e r e read out daily b e t w e e n 6:30 and 7:30 a.m. To calculate e x p o s u r e rates f r o m the m e a s u r e d spe-

cific activities in the e n v i r o n m e n t , a model illustrated in Fig. 1 was used ( K u r e p a , 1977). At point T at level 1 = 1 m a b o v e the ground the e x p o s u r e rate X is contributed by radionuclides f r o m the air in a part of the sphere of a radius R as well by radionuclides on the ground within a p0 radius. In the polar coordinate s y s t e m it generally stands:

ff(r, O,~b)r2 sinOdr dO d~b

(1)

provided that any functionf(r,O,~b) which depends on polar coordinates r, 0 and $, d o e s not depend on time. T h e functionf(r, 0,~b) is an expression used to calculate e x p o s u r e f r o m a point source:

X = k

A't

r~

(2)

where X = exposure k = constant of ionization for a certain g a m m a radiation energy A = activity o f a radioactive source t = time spent in the vicinity o f the source r = distance f r o m the source. Since e x p o s u r e rate is to be calculated in pA.kg -~ the t value c o r r e s p o n d s to t = 1 s. The A activity stands for the specific activity A 1 of a certain radionuclide in the air in Bq m -a assuming that it does not change during a day. Therefore: 181

182

D. Cesar, J. Kovar, and A. Bauman

1 R At A~

Fig. 1. Model for calculating exposure rates from the measured specific radioactivity in the environment.

1

f(r,O,qS) = kA~ T-~

(3)

Equations 1 and 3 are used to obtain exposure rates -~'1 originating from radionuclides in the air at point T:

=lm = 100m = specific acitivity of the air = specific activity on the ground.

Specific activities of the air were measured by pumping the 650 m a of air through a filter (General Metal Works 6013 M E A D - E L O white) during 24 hours. The filter was changed daily between 6:30 and 7:30 a.m. Specific activities on the ground were determined as a sum of dally specific activities from fallout. The values of previous days were reduced each day taking into account half-lives of radionuclides and to a value obtained thus, the fallout activity o f the last day was added. The wet fallout collected during 24 hours was taken daily between 6:30 and 7:30 a.m. using a funnel with the opening area 1 m z. On the days with dry fallout the funnel was rinsed with I 1 distilled water. The samples of the air (filters) and fallout were analysed using a Ge(Li) detector with a 4K analyzer and were processed by means of a lie Apple computer. The measured values were corrected with respect to the half life using the following expression:

A-

A,,,ktl

eXt2

(8)

1 -- e -xtl

271"

X,=kA,

R

1

fdcb(

f dr [sinOdO

0

1

+ ~ dr [sinOdO)(4)

0

0

0

The exposure rate from radionuclides deposited on the ground is estimated using A2 specific activity of radionuclides from fallout assuming that it does not change during a day. F r o m Fig. 1 and Eq. 2 the following equation is made up:

f(p,O)

= kAz

1

12 + p2

(5)

Using Eqs. 1 and 5 exposure rate)?5 at point T from radionuclides deposited on the ground is obtained: 2~

PO

dp J(~. = kAz f dqb f P o o 1~ + p2

(6)

Total exposure rate at point T originating from radionuclides in the environment is determined as a sum o f expressions obtained by integrating Eqs. 4 and 6:

.~=k'rr 2A~I 1 + - ~ - + In

+ A2 In

T

(7)

The values used to calculate exposure rate X are as follows:

where A = A,,, = = tl = tz =

corrected activity measured activity constant of half-life of a radionuclide time of sampling time between sample collecting and the end of measurement.

The assumption of this correction was that the activity o f the air and in fallout was constant throughout the period of sample collecting. Specific activity of the air and in fallout did not include rBe and naturally occurring radionuclides which means that the exposure rate calculated using Eq. 7 originated only from the man made radioactive sources. The measured exposure rates were therefore reduced by 0.94 pA kg -a which was the average exposure rate between January 1 and April 29, 1986 on the place of measurment. The maximum values of specific activities measured in the air and in the fallout, together with total specific activities in fallout measured in the period April 30 to May 31 are shown in Table 1. Exposure rates from the specific activities of the air and fallout were calculated for the radionuclides presented in Table 1. Results obtained are shown in Table 2 and in Fig. 2. Exponential functions of exposure rate changes were made up for both the measured and calculated values, and are shown in Fig. 3. Exponential function for the values measured in the period May 4 to 31 is as follows:

183

Comparison of measured and calculated exposures

Table 2. Measured (X~a) and calculated (Xc) exposure rates (pA.kg 1).

Table 1. Measured specific activities in air (Bq m -3) and fallout (Bq m-Z). Radionuclide

Date Airm~x

Z4Na '~lCr 54Mn 5~Co 5e~2o 6°(20 5~Fe 65Zn a~Nb asZr 99Mo ~gmTc l°aRu l°~Ru "°mAg 124Sb 12~Sb 1311 13~I 13~I'e 134Cs 1arCs IzTCs 14°Ba 14°La 141Ce 14aCe 239Np

3.2E-

2

1.0 E 4.8 E 1.4E1.4E1.7E +

1 3 1 1 2

1.7 E + 3.4 1.4 E 1.6 E 2.1 E 2.8E + 1.4E + 6.8 E + 3.6 3.9 E 8.1 4.1 4.1 3.3 E 2.4E9,0 E +

1 1 2 1 l 2 1

Falloutm~

Fallouttota I

3.6 E 3.1 E 4.4E 2.4 E 9.5E 2.3 E

+ + + + + +

2 2 1 2 2 2

6.6 E 3,1 E 4,4E 3.8 E 1.4E 4.0 E

+ + + + + +

2 2 1 2 3 2

8.5E 8.5E 1.1 E 7.3 E 6.1 E 2.7 E 7.4

+ + + + + +

2 2 3 3 3 3

9.0E 9.0E 1.1 E 1.2 E 1.4 E 5.5 E 7.4

+ + + + + +

2 2 3 4 4 3

9.0 1.5E 5.6E 1.8 E 4.4 E 5.7 E 9.0E 2.3 E 2.1 E 8.8 E 8.1 E

1

1 1 2

9.0 3.0E 8.8E 3.0 E 1.9 E 1.5 E 1.2E 4.0 E 4.9 E 9.2 E 1.0E

+4 + 5 + 4 + 2 + 1 + 3 + 3 + 3 + 2 + 2

3.04.-0.1.05. 01 .-02. 02.-03. 03.-04. 04 .-05. 05.-06. 06.-07. 07.-08. 08.-09. 09.-10. 10.-11. 11.-12. 12.-13, 13.-14. 14.-15. 15.-16. 16.-17. 17.-18. 18.-19. 19.-20. 20.-21. 21.-22. 22.-23. 23.-24. 24.-25. 25.-26. 26.-27. 27.-28. 28.-29. 29.-30. 30,-31.

+4 + 5 + 4 + 3 + 2 + 4 + 3 + 3 + 2 + 3

X~

Xc

Pa (%)*

0.43 0.78 1.14 1.59 2.04 1.86 1.65 1.51 1.50 1.38 1.26 1.16 1.10 1.06 0.94 0.91 0,83 0,80 0.75 0,72 0.68 0.67 0.66 0.58 0.58 0.55 0.53 0.53 0.53 0.51 0.51

1.69 18.33 1.51 41.11 I. 13 1.48 1.47 2.34 1.18 1.05 1.00 1.02 0.89 0.86 0.83 0.81 0.79 0.78 0,76 0.75 0.73 0.72 0.71 0.69 0.69 0.68 0.67 0.66 0.65 0.65 0.64

18.9 1.1 16.4 0.2 4.3 2.8 0.6 0.4 0.5 0.04 0.1 0.05 0.04 0.04 0.03 0.003 0.002 0.002 0,002 0,0007 0.002 0.001 0.002 0.0006 0.0009 0.001 0.01 0.001 0.02 0.0007 0.0001

*PA = Percentages of the calculated exposure rates of radionuclides in the air in relation to the total exposure rates.

Y 2-

ln~ 3-

1 ---~(c

2.

I rI I

-I

2

YM " 2.16 e"O'Os3 x

~

,

6

,

10

,

lt,

1 DAYS

,

,

22 2 IN MAY

Fig. 2. Measured (XM) and calculated ()(c) exposure rates (pA kg-l),

X ,

I

J

2

6

I0

I',

26

3'o

Fig. 3. Exponential functions of measured (YM) and calculated (Y,.) exposure rates (pA kg-1).

184

D. Cesar, J. Kova~, and A. Bauman YM = 2.16 e -°'°Sax

P(t) < 0.001

(9)

and for the calculated values, May 3 to 31, 1986: Yc = 2.58 e -°'°58x

P(t) < 0.001

(10

Value P(t) stands for a degree o f probability that exponential functions will not correspond to the data from which they have been derived. In both our cases the probability is less than 0.001, that is, less than 0.1%. In Eqs. 9 and 10 YM and Yc denote exposure rates expressed in p A kg -1 and x stands for the date. A disagreement between the measured and calculated exposure rates is obvious. Among various possible causes we consider the following ones to be responsible: 1. Significantly higher values o f the calculated exposure rates in the period April 30 to May 4 and May 7 to 8 are most probably due to the correction based on the assumption that the activity was assumed to be constant throughout the period o f sampling. Thus, a radioactive fallout at the end of the sampling period could cause the correction (8) to increase actual activity. Similarly, for the period May 4 to 7, due to fallout at the beginning o f the sampling period the correction (8) reduced the actual activity. This refers only to the short lived radionuclides such as 1321 (Tl/2 = 2.3 h). 2. The exposure rate in the period April 30 to May 8 was greatly contributed by 1321, which has not been in any significant amounts since, either in fallout or in the air. The calculated exposure rate was therefore suddenly reduced. Probably, certain amounts o f 1321 were still present but could not be recorded by our fast method o f measurement. F o r that reason the measured exposure rates in the period May 8 to 18 were somewhat higher than those calculated.

3. The higher values for the calculated than for the measured exposure rates for the period May 20 to 31 could be accounted for by certain quantities o f radioactive matter which entered the soil so that less radioactivity reached the measuring equipment. In case o f the c a l c ~ a t e d exposure rates the assumption was that all radioactivity was deposited on the ground. 4. Basic assumption when calculating exposure rates was that exposure rate at point T originated from radionuclides in the air in the part o f the sphere of radius 100 m as well as from radionuclides from the ground within the radius o f approximately 100 m. H o w e v e r , the fact that the measuring equipment was not situated in an identical, geometrically defined sp'ao: undoubtedly contributed t o a certain disagreement between the measured and calculated data. Exponential Eqs. 9 and 10 (Fig. 3) show a better agreement because in the investigated period their values differed by not more than 20% which could be tolerated. Contribution to the calculated exposure rates from radionuclides in the air was small especially after May 6. This can b e seen from the last column in Table 2 (PA), which show~ percentages o f the calculated exposure rates o f radiormctides in the air in relation to the total exposure rates.

Conclusion Taking into account the actual situation during the Chernobyl accident it may be concluded that the measured exposure rates in the environment were a b e t t e r h~dicator o f the actual exposure o f a population than the catculated values.

Reference~ Kurepa, S. (1977) Matemati(ka analiza, p. 331. Tehni~ka knjiga, Zabreb, Yu. Turner, J. E. (1986)Atoms, Radiation and Radiation Protection, p. 191. Pergamon Press, New York.