Determination of Dose Factors for External Gamma Radiation in Dwellings

Transcription

1 Determnaton of Dose Factors for External Gamma daton n Dwellngs M.F. Maduar and G. Hromoto Insttuto de Pesqusas Energétcas e Nucleares, CP 049, São Paulo, Brazl INTRODUCTION e largest contrbuton for the global populaton exposure to onzng radaton arses from natural sources, especally from radonucldes present n terrestral crust. Certan human actvtes may eventually ncrease such exposure to sgnfcant levels, from the pont of vew of radologcal protecton (, 2). e presence of natural radonucldes n buldng materals may lead to an ncrement of both external and nternal radaton exposure of the nhabtants of dwellngs bult wth such materals (3). External exposure nsde dwellngs arses from gamma-emtter radonucldes exstng n the walls, floor and celng of the buldng. Mathematcal models can be used to predct external dose rates nsde the room, provded the radonuclde concentraton actvtes n dwellng consttuents are known (4, 5, 6). s paper presents a methodology for theoretcal evaluaton of external gamma doses due to radonucldes present n the walls of an hypothetcal dwellng. Assumng the dwellng as one compartment of rectangular secton and the radonucldes unformly dstrbuted wthn each wall, the most commonly cted expresson n the lterature for the evaluaton of the dose s expressed as a lnear combnaton of values of radonuclde concentratons and correspondng dose factors. Evaluaton of dose factors s carred out by varyng parameters of the model wthn a physcally reasonable range. Results are presented n a graphcal form. METHODOLOGY e dwellng s modeled as three pars of rectangular sheets wth fnte thckness. Assessment of doses was performed through the applcaton of photon transport model, takng nto account self-absorpton and buldup factors. As the external dose due to a partcular radonuclde s proportonal to ts actvty concentraton, results are presented as dose factors, defned as the quotent of absorbed dose rate (ngy.h - ) at a defned pont nsde a compartment, due to the presence of a gven radonuclde and ts daughter products, by the actvty concentraton (Bq.kg - ), for such radonuclde n the walls. e radonucldes are assumed to be unformly dstrbuted n the buldng materals. It was assumed attenuaton and radaton buldup factors of standard concrete. e studed nucldes are 40, 226, and 232, takng n account, for dose calculatons, all gamma emtters from 226 and 232 decay chans. Senstvty of the model s estmated by varyng four of ts nput parameters wthn a reasonable range of applcablty, whle leavng all other parameters at fxed selected values. e studed parameters and respectve ranges of varaton were: for thckness, 5 to 60 cm; for densty, to 4 g.cm -3 ; for the room length,.5 to 0 m; and for the dstance of the pont of calculaton to the nearest wall, 0 cm to the center of the room. Selected values left constant, for each parameter, were: thckness, 20 cm; densty, 2.35 g.cm -3 ; room length, 5 m; and for the poston of the calculaton pont, the center of the room. GEOMETRIC MODEL In order to calculate the dose rate at a gven pont O, t s assumed an unform dstrbuton of radonucldes wthn a fnte rectangular sheet wth thckness t. e pont O s n the orgn of the system of Cartesan coordnates, at a dstance h of the nferor surface of the sheet. In the present case, the analyss s lmted to the stuaton n whch the perpendcular to the sheet that crosses the pont O ntercepts the sheet. e model geometry s llustrated n Fgure.

2 t h O z y x Fgure. Geometry for the calculaton of the dose rate due to radonucldes dstrbuted n a rectangular sheet e geometrc modelng of a compartment can be made combnng dfferent sheets approprately. e dose rate functon s addctve, that s, the fnal dose s the sum of the doses of the sheets consdered separately. e absorbed dose s calculated by usng attenuaton coeffcents and takng nto account the contrbuton of the scattered radaton by means of expressons for the buldup factor. e dose rate D! n the ar n a certan pont due to the prmary and scattered photons, orgnatng from a source unformly dstrbuted wthn a generc volume V, s gven by S D! = 4π n = I µ en ( E ) ρ E V dv r 2 B ( E, µ r ) m e µ rm where D! : absorbed dose rate (Gy.s - ) : constant for unts converson, from (Bq.g - ).kev to Gy.s -, equal to.602 x 0-3. S : concentraton of a gven radonuclde, n the volume V (Bq.cm -3 ) n : number of gamma transtons beng consdered I : gamma photons per dsntegraton for the -th gamma transton µ ι : gamma attenuaton coeffcent correspondng to the energy E (cm - ) µ en ( E ) : ρ mass energy-absorpton coeffcent correspondng to the energy E (cm 2.g - ) ρ : densty of the materal (g.cm -3 ) E : energy of the -th gamma transton (kev) r m : dstance traveled n the absorber materal (cm) r a : dstance traveled n the ar (cm) r : total dstance, from the pont of nterest to each pont of the volume V (cm), equal to r m +r a B : buldup factor µ ι r m : number of mean free paths n the absorber materal correspondng to the energy E e prevous expresson should be appled to the geometrc model descrbed. By usng sphercal coordnates, wth O n the system orgn and the sheet s sdes defned by x, x2, y, y2, the absorbed dose rate s calculated n the pont O, for a gven radonuclde or a radoactve seres. Dvdng the sheet volume n 4 parts, each one beng a prsm wth trangular base, t s obtaned the varaton range for the ntegral n the expresson for the dose, as shown n Fgures 2 and 3. 2

3 y vertcal secton y 2 x b x φ x 2 x a y c Fgure 2. Top vew of the sheet, showng ts dvson n four parts for the ntegraton. z c sec φ t θ lm h θ max x Fgure 3. Vertcal secton x' at a generc angle φ, llustratng the varaton range of r (n blue) and angle θ. us, the absorbed dose rate s gven by D! = ( E ) n 4 µ en I E = V= S 4π ρ A, V where A,V s defned, for each gamma transton and part V of the sheet, by the expresson where b ( φ ) ( h+ t) arctan θ θ θ φ φ θ c lm sec max c sec cosec a f ( r θ ) dr dθ f ( r θ ) dr dθ θ, + = r= h θ θ φ, 0 sec r h sec θ φ = arctan lm = c θ c secφ h + t lm () φ = arctan ; θ () φ ( ) ( ) c secφ max = arctan h dφ 3

4 f ( r θ ) = B( E, µ r ) exp( µ r ) snθ, m m r m = r - h secθ and the a, b, c values are defned for each part V. e dose rate calculated takng n account only non-scattered photons would lead to an underestmate of the real dose. A commonly used way for takng nto account the scattered radaton contrbuton s the ntroducton of the so-called buldup factor, B ( E, µ r), where B s the buldup factor, E s the energy of the prmary photon and µ r s the number of mean free paths n the scatterng materal. Esenhauer & Smmons (6) presented, only for concrete, calculated values of B for dscrete energy values, n the 5 kev 5 MeV range, and for mean free paths from 0 to 30. In order to obtan B values for both generc energy values and mean free paths wthn those ranges, n the present paper the evaluaton of the buldup s made by means of an nterpolaton appled to the logarthms of the energy and to the mean free paths, on the B values suppled n that paper. So, gven the values of B = B( E, µ r ), B 2 = B( E, µ r2 ), B 2 = B( E2, µ r ) and B 2 = B( E2, µ r2 ), the buldup factor B for E and µ r, for E < E <E 2 and µ r < µ r < µ r 2, s ftted by B ( E, µ r) = B( E, µ r ) B exp ln B ( E, µ r2 ) µ r µ r ( E, µ r ) µ r µ r e values of E that are the values of energy of the prmary gamma transtons, compose a spectrum of dscrete values, whle the values of r vary contnuously when one performs the ntegraton of the functon that contans the B ( E, µ r m ) factor. us, the nterpolaton s made frst on the logarthms of the tabulated values of energy, n order to obtan a set of buldup factors for the tabulated values of r, for each value of prmary gamma energy; when t s made the calculaton of the dose factor, that data set s used to obtan the values of B for r varyng contnuously. It was obtaned values for the mass attenuaton and for energy-absorpton coeffcents for dscrete values of energy, wthn the kev to 20 MeV range (8). Agan, t s used the nterpolaton n order to obtan the coeffcents for a generc energy E. us, the coeffcents for E < E < E 2 were obtaned by means of the expresson ln( E E ) µ ( E ) = µ ( E ) [ ( ) ( )] exp ln µ E2 µ E ln( E2 E ) Defned the methodology for the calculaton of the dose, the dose factor q for each radonuclde or radoactve seres s gven by the expresson 2 q = D! ρ S In the prevous expresson, t s assumed the use of an unque type of materal n the walls, wth both homogeneous densty ρ and actvty by volume S. RESULTS AND DISCUSSIONS In each smulaton s studed the varaton of one parameter of the model, n a physcally reasonable range, keepng all other parameters at selected values. Table shows the studed parameters, where the frst lne shows the constant values and the second lne the respectve varaton ranges. 4

5 Table : varaton ranges and constant values used for each model parameter ckness (cm) Densty (g.cm -3 ) Dmensons (m) Fxed value L x W x H a : 5 x 4 x x 4 x 2.8 Dstance from the pont of nterest to the nearest wall (m) Center of the compartment nge L a : a L: length; W: wdth; H: heght. e graphs show the dose factors for each radonuclde. By varyng the thckness of the walls n the range from 5 cm to 60 cm, t s observed that the dose factors ntally ncrease rapdly and then tend to an upper lmt. For a 35 cm thckness, the dose factor already reaches a value only 2% nferor to the correspondng factor for a 60 cm thckness (Fgure 4) q (ngy h - )/(Bq kg - ) ckness (cm) Fgure 4. Graph of the dose factors q n functon of the thckness of the walls of the compartment. By varyng the densty of the materal, the dose factor ncreases lnearly wth the densty of the wall materal (Fgure 5). In fact, ths property can be drectly deduced from the expresson for the dose factor. 5

6 q (ngy h - )/(Bq kg - ) densty (g cm -3 ) Fgure 5. Graph of the dose factors q n functon of the materal densty eepng constant both the heght, at a value of 2.8 m, and the wdth, at 4 m, and varyng the length wthn the.5 m 0 m range, the dose factor slghtly decreases (2%), from.5 m to 3 m, and slghtly ncreases from 3 m to 0 m untl a value 4% greater than the mnmum at 3 m (Fgure 6). q (ngy h - )/(Bq kg - ) Length (m) Fgure 6. Graph of the dose factors q n functon of the compartment length Calculatng the dose factor n postons along the axs that crosses the centers of two parallel walls, startng from the center of the compartment and approachng to a poston 0 cm off the wall, t s observed that, for a compartment of 5 m x 4 m x 2.8 m (Fgure 7), the dose factor remans practcally constant (wthn an % range) from the center of the compartment to approxmately m off the wall; for a dstance from the wall varyng n the m 0. m range, the dose factor slghtly ncreases, but no more than 6% of the value at the compartment center. 6

7 q (ngy h - )/(Bq kg - ) p (cm) Fgure 7. Graph of the dose factors q n functon of the dstance p from the pont of nterest to the closest wall (5 x 4 x 2.8 m compartment). For a 0 m x 4 m x 2.8 m compartment (Fgure 8), there s a change n the behavor of the curve. From the center of the compartment (5 m apart from the wall) and approachng the wall, the factor decreases untl a mnmum value at a pont.4 m off the wall (.6% less than the value n the center). From.40 m to 0 cm off the wall, t ncreases untl a value 3.5% greater than that n the center. q (ngy h - )/(Bq kg - ) p (cm) Fgure 8. Graph of the dose factors q n functon of the dstance p from the pont of nterest to the closest wall (0 x 4 x 2.8 m compartment). CONCLUSIONS It was found that the most senstve parameters are the densty, that shows a lnear dependency to the dose factor, as expected, and wall thckness. Model senstvty for the room length and dstance from the calculaton pont to the walls was neglgble n the studed range of varaton. It was also observed that the 7

8 qualtatve behavor of the dose-parameters relatons does not change sgnfcantly from one radonuclde to another, for all the studed parameters, although the gamma energy spectra of the consdered radonucldes vary consderably. REFERENCES. Internatonal Commsson on dologcal Protecton, Prncples for lmtng exposure of the publc to natural sources of radaton. ICRP-39, Pergamon, Oxford (984). 2. Unted Natons Scentfc Commttee on the Effects of Atomc daton, Sources, effects and rsks of onzng radaton. UNSCEAR, New York (993). 3. Nuclear Energy Agency, Exposure to radaton from the natural radoactvty n buldng materals. NEA, Pars (979). 4. E.Stranden, doactvty of Buldng Materals and the Gamma daton n Dwellngs. Phys. Med. Bol., v. 24, n. 5, p (979). 5. J.G.Ackers, B.F.M.Bosnjakovc and L.Strackee, Lmtaton of radoactvty concentratons n buldng materals based on a practcal calculaton model. d. Prot. Dos., v. 7, n. -4, p (983). 6. L.oblnger, Mathematcal models of external gamma radaton and congruence of measurements. d. Prot. Dos., v. 7, n. -4, p (984). 7. C.M.Esenhauer and G.L.Smmons, Pont sotropc gamma-ray buldup factors n concrete. Nucl. Scence and Engneerng, n. 56, p (975). 8. J.H.Hubbell and S.M.Seltzer, Tables of X-y Mass Attenuaton Coeffcents and Mass Energy- Absorpton Coeffcents (verson 2), [Onlne]. Avalable: [2000, January 22]. Natonal Insttute of Standards and Technology, Gathersburg, MD (997). 8