Measurement of exhalation and diffusion parameters of radon in solids by plastic track detectors

Nuclear Tracks, Vol. 12, Nos I-6, pp. 701-704, 1986. Int. J. Radiat. Appl. Instrum., Part D Printed in Great Britain.

0191-278X/86 $3.00+.00 Pergamon Journals Ltd.

M E A S U R E M E N T OF E X H A L A T I O N AND D I F F U S I O N P A R A M E T E R S OF RADON IN SOLIDS BY P L A S T I C T R A C K D E T E C T O R S

G. ScEsDgyi, Abdel-Fattah Hafez*, I. Hunyadi and M. T6th-Szil~gyi Institute of Nuclear Research, Debrecen, Hungary, 4OO1 *On leave from Alexandria University, Faculty of Science, Department of Physics, Eclvpt

~ C T There are large discrepancies in data available in the literature for the exhalation and diffusion behaviour of radon in various materials. Therefore there is a need for more studies in this field. For this purpose we have developed and used track methods to measure mass and areal exhalation rates of radon from different fly ashes and sand. In addition, methods were also developed to determine the diffusion length of radon and the porosity of materials. For getting the radon emanation coefficient we have applied the autoradiographic method and the "can-techniqu4' for determining the real and effective radium contents. The disturbing effect expected from the geometry of measuring cans and samples is discussed. Relations are derived for the correction of such effect. KEYWORDS Plastic track detectors; e-activity measurement; radon; areal a~d mass exhalation rate; diffusion length; fly ash; effect of measuring geometry ~T~ROD~ST ION

Recently different waste materials produced by power plants, chemical and metallurgical industry are ~mmcnly used as building materials. Scme of them (furnice slag, fly ash, by-product gyps~n, etc) contain appreciable amount of natural radionuclides from the uranium and thoriL~n series and may present potential radiation hazards to the population. Therefore, at present, there is a need for developing simple and efficient measuring methods and performing extensive studies to get representative data about the radiation levels due to typical waste and construction materials. For prediction of the level of radiation hazard of various solids an estimation of the rate of their radon exhalation is of prime importance. For this purpose one of the most sinplest and efficient methods is to place the specimen to be studied in the lower part of a sealed cylindrical can and to fasten a piece of alpha-sensitive etQh-track detector on the inner upper surface of the can (Abu-Jarad, 1980). By using this simple passive measuring ~evice, at low cost, a large number of tJJTe--integratedradon exhalation measurements can be performed with using only relatively small amount of specimen. The "sealed-can technique" for measuring radon exhalation and diffusion parameters of solids has been used in combination with several active measuring techniques too. (Panastefanou and Charalambous, 1979; Greiner, 1980; Folkerts et al., 1984; Kalkwarf et al., 1985). In all of these studies, where generally limited anount of ~nanating specimen is used in a closed ccntainer, it is to be expected that the measurer~=_ntwill be influenced by the geoP~etry and ~ i o n s of both the specimen and the measuring can. The reduction in radon exhalation of a sample under steady-state oondition in a sealed can is recently reported by Jonassen (1983) and Stranden (1983) and referred to as "back-diffusion" phencmenon. In our present studies particular emphasis is laid on the discussion of the commonly used measuring condition when the sample is sealed in a can of cylindrical gecr~try. In this case we have tried to estimate the effect of the can and sample dimensions on the radcn exhalation measurements, that in our opinion has not been treated with the necessary carefulness in the literature. Relations derived from the one-dimensional diffusion model will be given to correct for this effect. It will also be shown that by using the technioue of sealed-can ec~ipped with track detector all the ini0ortant parameters (areal and mass exhalation rates, effective diffusion length, porosity, e~anation coefficient) of the radon transport in solids can be determined with reasonable accuracy. In such measurements the disturbing effect arising from 701

702

G. SOMOGYI ~t ~ .

the plated-out alpha-activity of radon daughters, wi~h may cause an overestimation of radon concentraticns (Abu-Jarad, 1981), can also be ignored by using LR-II5 type track detectors. THEOB~TICAL CONSIEERATIONS In our present treatment it is ass~T~d that a slab of specimen of L thickness and Vs=A.L voltlne is closed in a cylindrical can of A cross-sectional area, an air vol~me Va=A h. is over the specimen and an alfa-sensitive plastic track detector is mounted to the centre of the inner upper wall of the can (see Fig.L). Ass~m~ing that under steady-state condition radon ooncentraticn gradient exists only in the direction of depth, the diffusion inside the specimen is governed by the differential ~ a t i o n (i), and the rate of radon exhalation (radon flux density) from the surface of specimen is given bv the Fick,s first law (2) : dC(z) D s d2C(Z)dz 2 IC(z)+IC =0, (i); ~A= - u a ~ Iz=L (2) _

where C(z) and C~ are the radon ccncentrations in the L-z and infinite depth of the specimen, Ds and Da=PD s are the diffusion ooefficients of radon in the specimen of porosity p and in the air, and I is the decay ccnstant of ~n-222 (2.1.10-6 s-I ) • The solution of eq. (I) foz the radon concentration can be written as d% (z/z d) C(z) = C (i - k~h(L/z d )

(3)

where k=l for "free exhalation" (Va+ ~) ~nd Zd=(Ds/~) ½ is the effective diffusion length of radon in the specimen. The areal exhalation rate of radon, by using Eqs. (2) an@ (3), is given by C Da

C~IZ~

oo

where #A is the m a x ~ value of CA" The gec~etrical correction factor k for the "sealed-can technicn/e" can be derived frQm the boundary condition ~A.A=XVaC(Z) Iz=L ,

(5) ;

k= l+(PZd/h)'th(L/Zd),

(6)

Now one can derive the most important relationships for the radon measurements in a closed ccntainer. For the bound areal e~halation rate expressed in terms of Bqm-.2s-I we have the relation C~lpzd- th (L/zd)

C A ( b ~ ) = i+ (~a/h) th (n/Zd) = C A ( ~ ) / k

(7)

fram where the maxirsan exhalation rate (L+ ~, so th(L/Zd)~- i) is C~I pzd "A (bound) = l+(PZd/h )

(8)

and hence #A (bOund) _ rA= CA(bOund )

l+(PZd/h)

• th(L/Zd) .

(9)

l+(PZd/h)'th(L/z d) --I

--I

For the bound mass exhalaticn rate in terms of Bqkg .s

, by definition,~ have the relaticn

#M (bound) = #A (b°und)A = ~A(b°und)/Ly

(I0)

where M ~md y are the mass and density of the specimen studied. By using Eqs. (7) and (I0) finally we have C~Ipz d

from where the ~

th (L/zd )

mass exhalation rate (I~O, so the (L/Zd)= O) is

EXHALATION AND DIFFUSION PARAMETERS OF RADON

703

#M (bound) = C I p/l,

(12)

and hence CM(bOund)

rM_- ~M (b°und) 0o

z~/L i+ (DZd/h) th (L/Zd)

th (L/Zd).

(13)

The effect of can and sa~ole size on the me~sure of radon exhalation is calculated by Eqs. (9) and (13) and illustrated in Fig.l. From the relationships obtained for radon exhalation in a sealed can one can derive several n ~ methods for the detemaination of both the diffusion length (Zd) and porosity (p).We will consider here only few typical cases. From the condition rA(Lo)=rM(Lo), for example, we have the simple relation Zd=Lo-[l-(plo/h)] -I . If Lo>z d we have y z d - ~ / % M • The diffusion length and the porosity may be obtained frcm Eq. (9) [or Eq. (13)] too, if one determines " rA (or rM) at two different thicknesses of the 1.0 2.0 3.0 L / Z d . somp~e thickness / diffusion length specimen. At low L values (L<
ol

ships it is necessary to relate the measured track density, p, to the radon exhalation rate. For this _rxlrpose one can easily derive the equation S= 0/#A= (~/hl) • (T-I-I (l-e-IT)) = (~/hl).Tef f

(15)

if one takes into account that the track detector will measure the total radon decayed in the can during an exposure time T with a track detection efficiency_ of D (expressed in terms of s-tracks cm-a.day-I/Bq-m-3). The value of q will depend on the radius ~nd height of the measuring can according to the equations given bv Sanogyi and co-workers (1984). Using a can of 3.5 cm radius and i0 an height and L~-II5 (f3~m) track detector etdned to 5~m residual thid~ness we have ~ (LR)=i/30-track hole. cm-a.day-I/(Bq-m-3) almost indeDe_ndentlv on the degree of radioactive equilibria. For CR-39 detector this factor, asstm~ina total ec~ilibrium,theoretically is about 9 times higher than n (LR), from whic~ about 1/3 part ccmes frcm the s-activity of airborne radon and 2/3 part arises from Po-218 and Po-214 Dlated-ont on the can wall and detector surface. According to our ~ r i e n c e s , however, in a closed can practically the ratio (CR)/~ (LR)= 6-+20 % is realized. If we know ~M(Bq kg-ls -I) , or ~A(Bqm-2s-1) and y(kgm -3) , the effective radium content (i.e. Ra in equilibri~ with the Rn ~nanated from the specimen) can be calculated from IeC~ff(Bq kg-1 )= CM-- ~A/LY "

(16)

Finally, the emanation coefficient of the specimen is given by_ the ratio of effective and real radish content where the real r a d i ~ content can be estimated from e-autoradiographic measurements by etch-track detectors in direct contact with the snecimen. MEASUreMenTS AND RESULTS We have systematically collected fly ash samples from five different coal-fired power plants in Hungary. The samples were dried and placed into vessels which were than tightly mounted to the lower end of cylindrical cans of I0 cm height and 3.5 an radius. To the inner upper wall of the cans LR-II5 and CR-39 track detetors were fixed and the devices were sealed to prevent any significant leakage effect. The track density produced by the radon gas diffusing into the air volume was then measured after 30 day exposure. Using the theoretical relations derived in the previous section we have determined several radon exhalation and diffusion paraneters for fly ashes of Hungarian origin. Typical results obtained are s~mTn~rized in Table i. The frequency distribution of emanation coefficients measured for 8 fly ash samples with thicknesses of i. 2, I. 8 and 2.4 c~n is shown in Fig. 2.

704

G. SOMOGYI et

TA~J~ 1

~xhalatlo~

Rad~

amd D i f f u s i o n

MAXIMUM ~ SAMPLE CODE

Parmterl

EXHALATI(A~

for

F l y A~hes C o l l e c t e d

EFFF~TI~IE DZ~F~81{~ LENGTB

RATES

~.

E ~ S I T y OF FLY ~H

fr~la Three Sunqartan Coal-Fired

EImFECTIVE DIFt~SIO~ L~G~I~ Rd

[Bq'm-a's "~ ]

[Bq.kg.... -'] R d - y . z ~

Y'L.~

Po~er P!ant

~IVE DENSITY OF DIPI~J~IOM FLy ASH LENGTH SOLID PHASE the

talc.

POBOSIT~

m~d

Z~" T

e ~ .[lO . ~ (am] ~

7s= v_~M~p

P" 1" ~--y

A-7

fly

ash

5. O. 10"4

20.3 • 10- 6

24.6

13CO

1.89

1.86

2660

A-ll(1)

fly

ash

4.O-10 -4

4 7 , 0 . 1 0 -6

8.5

900

0.95

1.00

2520

O.66

&-11(2)

fly

ash

6.3-10 -4

116.O.10 - 6

5.4

560

O.96

0.95

2730

0.79

A-12

fly

ash

2.4-10 -4

14.O,10 - 6

17.1

1650

1.14

1.25

2630

0.65

G-2-3

fly

ash

1.O.10 -4

88.0,10 -6

1.1

490

0.23

0.26

1690

O.71

I-1-6

fly ash

O. 51

1.O. 10-4

8.2"10-6

12.2

1140

1.O6

O.91

1620

0.30

ash

1.2.10 "4

46.O. 10- 6

2.7

870

O.31

0.32

970

O. 10

A-12 econamlzer

1.O. 10. 4

7.5.10_ 6

13.3

llOO

1.21

I.05

2600

O. 58

I-1 bottom ash

.~

II t

/ 2

I

s.

F/A [/ /~

~'= °=)

O-

-/ /

i,~

iv

I

"~T -

/

-

I

/

/ _ _ Z 1 h=012

1

i

(fry o~h)

/

,

~ - ~

~.........

i iJ",,/ •

,

,

0,5 ~.0 £ , rodor~ ernor~otion coefficient

,

,

m

t5 ['&]

. . . . . .

0

0

1.0 L/Zd,

Fig. 2. Frequency_ distribution of amanaticn coefficients measured for fly ash samples collected from two Hungarian coal-fired ~ r plants (Ajka and Inota). The mean emanation coefficient of 8 san~ples measured at three different thicknesses is indicated.

-;.L]

-

2D

3.0

samplethickne~s/diffusion !ength

Fig. 3. CQmparison of the measured and calculated mass and areal radon exhalation rates for sanples possessing s~all and large diffusion length 1.25 cm for fly ash and 140 cm for sand. The m e a s ~ t s are carried out in closed cans with IO cm air gad over the sa~oles.

The mean value of emanation coefficients calculated for each thickness is also indicated frcm which the thickness dependence of e is obvious. We note that here CR-39 track detectors were exposed in cc~taot with the samples and a factor flT=O.8 ~-track-fya-a-day-I/(Bq-kg -I ) calculated for radioactive equilibri~n and for a typical fly ash composition (35% CaO+30% SIO2+15% AI~O3+20% other oxides) is used to calculate the CrP~eal values. For samples of identical origin a mean Th content was also estimated from X-ray fluorescence measurements and the effect of Th was taken into account by a factor fTh=O.3 fu" Our experiments indicated that,in spite of their enhanced radiL~n concentratioms, the emanation power of fly ashes collected frQm different Hungarian coal-fired power plants is unusually low (in average O. 5% for thin san~les). To illustrate the shape of radon exhalation curves cbtained experimentally two typical examples are given in Fig. 3. The Figure clearly shows the different effect of the can ge~etry on the m e a s ~ t s in case of fly ash (Zd/h=0. i) and sand (Zd/h=14). REFE-~CES Abu-Jarad, F., J. H. Fremlin, and R. Bull (1980). Ph~zs.Med.Biol., 25, 683-694. Abu-Jarad, F., C. K. Wilson, and J. Ho Fremlin (1981). Nucl. Tracks, 5, 285-290. Folkerts, K. H., G. Keller, and H. Muth (1984). Rad.Prot.Dos., 7, 41-74. Greiner, N. P. (1980). Health Phys., 48, 283-288. Jcnassen, N. (1983). Health Phys., 45, 369-376. Kalkwarf, D. R., P. O. Jackson, and J. C. Kutt (1985)° Health Phys., 48, 429-436. Papastefanou, C., and St. C~ara]ambous (1979). Z. Naturfors~h, 43a, 53--3-537. Sc~aogyi, G., B. Parip~s, and Zs. Varga (1984). Nucl. TraCks, 8, 423-427. Stranden, E., (1983). Health Phys., 44, 145-153.