Journal of Environmental Radioactivity 127 (2014) 50e55
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Short communication
Modeling of indoor radon concentration from radon exhalation rates of building materials and validation through measurements Amit Kumar a, *, R.P. Chauhan a, Manish Joshi b, B.K. Sahoo b a b
Department of Physics, National Institute of Technology, Kurukshetra 136119, India Radiological Protection and Advisory Division, Bhabha Atomic Research Centre, Mumbai 400085, India
a r t i c l e i n f o
a b s t r a c t
Article history: Received 26 August 2013 Received in revised form 4 October 2013 Accepted 7 October 2013 Available online 22 October 2013
Building materials are the second major source of indoor radon after soil. The contribution of building materials towards indoor radon depends upon the radium content and exhalation rates and can be used as a primary index for radon levels in the dwellings. The radon flux data from the building materials was used for calculation of the indoor radon concentrations and doses by many researchers using one and two dimensional model suggested by various researchers. In addition to radium content, the radon wall flux from a surface strongly depends upon the radon diffusion length (L) and thickness of the wall (2d). In the present work the indoor radon concentrations from the measured radon exhalation rate of building materials calculated using different models available in literature and validation of models was made through measurement. The variation in the predicted radon flux from different models was compared with d/L value for wall and roofs of different dwellings. The results showed that the radon concentrations predicted by models agree with experimental value. The applicability of different model with d/L ratio was discussed. The work aims to select a more appropriate and general model among available models in literature for the prediction of indoor radon. Ó 2013 Elsevier Ltd. All rights reserved.
Keywords: Indoor radon concentration Wall flux Pin hole dosimeter Radon exhalation rates Sub-soil flux
1. Introduction Radon (222Rn) and its progeny are present in all dwellings, because radium is present in building materials as well as in the soil. It is important to understand the generation and migration process of radon from building materials, because it contributes to 55% of total radiation dose received by the population from the environment (UNSCEAR, 2000). Uranium, radium and thorium are present at trace levels with concentrations varying a wide range in different geological samples like soil and building materials (Patra et al., 2013). The soil and building materials are the main source of indoor radon (UNSCEAR, 2000; Nazaroff and Nero, 1988). The contribution of the exposure from building materials are assumed to be negligible, if they contain low radioactivity and exhalation rates than soil (Sahoo et al., 2011). Many studies have been performed for the measurement of radon exhalation from building materials and soil and extrapolated their results to the indoor radon concentration (Chen et al., 2010; Saad et al., 2013; Shweikani and Raja, 2009; Mahur et al., 2008,2009.) The indoor radon concentration and corresponding doses from the radon exhalation rates
* Corresponding author. Tel.: þ91 9812351248; fax: þ91 1744238050. E-mail address: [email protected] (A. Kumar). 0265-931X/$ e see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jenvrad.2013.10.004
were calculated without considering the physical change in the matrix during wall, floor and roof construction. While in actual practice, the radon exhalation from wall will change depending upon the value of radon diffusion length, thickness of wall and dimension of the building material used for measurements (Sahoo et al., 2011). The generation and transport process of the radon in wall is significantly different than that of its building materials. Hence, it is necessary to investigate this practice of extrapolating the radon exhalation data to indoor radon through a systematic analysis by carrying out both experimental measurements and model prediction. The calculation of radon flux from walls from the knowledge of the radium content, radon emanation coefficient and radon diffusion length in building materials was suggested by Nazaroff and Nero (1988) while Sahoo et al. (2011) suggested a semi-empirical model to predict the radon flux from wall using the radon exhalation rate and diffusion length in building materials. Another model suggested by Stoulos et al. (2003) predict the indoor radon concentration contributed by walls from values of radon exhalation rates from building material samples, surface fractional usage of building materials in wall construction and air exchange rate of the room. The present study focuses on the comparison of predicted indoor radon concentration applying above three models with the directly measured indoor radon concentration for selecting the best appropriate model among three. For this, radon
A. Kumar et al. / Journal of Environmental Radioactivity 127 (2014) 50e55
exhalation rates of various building materials were measured by an active technique using a continuous radon monitor and the results were extrapolated to indoor radon in order to compare with measured value of indoor radon concentration in some selected dwellings.
The indoor radon concentration due to the radon exhalation from surface fraction of building materials can also be estimated by the following formula (Stoulos et al., 2003)
" CRn ¼
n X
# wsi $Esi
i¼1
2. Existing theory and models description A one dimensional model for predicting the radon exhalation from wall was proposed by Nazaroff and Nero (1988) which is given by
Jw ¼ R$E$l$r$L$tanhðd=LÞ
(1)
where R radium contents in building materials, E radon emanation fraction depends upon the moisture contents, l radon decay constant, r density of building materials, L is radon diffusion length through materials and d is the half thickness of the wall. If it assumed that the entire radon atom reaching in pore volume of the building material could emanate into the indoor, then the analytical expression for radon mass exhalation rates can be written as (Sahoo et al., 2007)
Jm ¼ REl
(2)
Using Eqs. (1) and (2), one can write
Jw ¼ Jm rLtanhðd=LÞ
(3)
A model to predict the radon wall flux (Jw) using the data of radon surface exhalation rate (Jb) of the building material sample was suggested by the Sahoo et al. (2011), which is given by
Jw ¼ Jb
Sb d d þ1 1 exp k Vb L
(4)
where d, Sb and Vb are the wall half thickness, surface area and bulk volume of the building material sample, k is the regression parameter to be determined from least square fitting to the data points plotted between Jw/Jb and d/L and found to be 0.31 0.05 (Sahoo et al., 2011). Using Eqs. (3) and (4), the radon surface exhalation rate (Jb) of the building materials can be related to mass exhalation rate (Jm) as:
Jb ¼
Sb d Vb
Jm rLtanhðd=LÞ 1 exp k dL þ 1
(5)
If the diffusion length of the radon gas in the materials is much smaller than half thickness of wall, i.e. L> d, then the Eq. (4) reduced
Jw ¼ Jb
Sb d Vb
(6)
Once the radon flux from the wall become known, the indoor radon concentration can be calculated by knowing surface to volume ratio of the room and ventilation rates given by
C ¼
X i
Jwi Si VðlRn þ lv Þ
S V$lv
(8)
where Esi is the measured surface exhalation rate of the building material; Wsi is the surface fractional usage of the building material; S/V is the surface to volume ratio of the room and lv is the annual average room ventilation rate. 3. Materials and methods 3.1. Measurement of indoor radon concentration in selected dwellings The indoor radon thoron concentration was measured by pin hole based radon thoron dosimeter in some dwellings to compare with theoretical results. The details and calibration of pin hole based radon thoron dosimeter was described elsewhere (Sahoo et al., 2013). The pin hole based radon thoron dosimeters (PRTMs) consisted of two compartments separated by a central pinholes disc made up of high density polyethylene material, acting as 220 Rn discriminator. Four pin holes each with dimension of 2 mm length and 1 mm diameter are made in this circular disc. The dosimeter has a single entry through which gas enters in first compartment namely “radon þ thoron” compartment through a glass fiber filter paper (pore size 0.7 mm) and diffuses to second compartment namely “radon” compartment through pin-holes cutting off 98% of entry of 220Rn and 98% transmission of radon into this compartment (Sahoo et al., 2013). Each compartment is cylindrical having a length of 4.1 cm and radius 3.1 cm. The solid state nuclear tracks detectors (LR-115, Type-2, strippable) of size (2 2 cm2) were fixed at opposite end of the entry face in each compartment. The LR-115 in first compartment measured the tracks produced by the alphas emitted from radon and thoron, while LR-115 in second compartment measured the tracks due to radon only. Eleven numbers of dwellings were selected for the measurement of indoor radon concentration having different construction type listed in Table 1. The measurement of dimension of dwellings, detail of door and window and thickness of wall were made during deployment of dosimeter. The dosimeters were deployed in the dwelling of area under study through a metallic chain at the average human height (1.5 m)
Table 1 Details of the dwellings used for measurement indoor radon concentration and their construction type. S. No
Type of dwelling
Dwelling code
Construction type
1. 2. 3 4 5 6 7 8 9
Mud House Mud house Mud house Mud house Brick house Brick house Brick house Brick house Cemented house
M1 M2 M3 M4 B1 B2 B3 B4 C1
10
Cemented house
C2
11
Cemented house
C4
Mud wall, soil floor, wooden ceiling Mud wall, soil floor, wooden ceiling Mud wall, soil floor, wooden ceiling Mud wall, soil floor, wooden ceiling Brick wall, wooden roof, soil floor Brick wall, brick roof, soil floor Brick wall, RCC concrete roof, soil floor Brick wall, brick roof, brick floor Plastered concrete wall, concrete roof, concrete floor Plastered concrete wall, concrete roof, marble floor Plastered concrete wall, concrete roof, granite floor
(7)
where Jwi and Si are the radon wall flux and surface area of wall, lRn þ lv is effective radon removal rates and V is volume of room.
51
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A. Kumar et al. / Journal of Environmental Radioactivity 127 (2014) 50e55
also measured by same technique in order to made correction in the measured indoor radon concentration. 3.2. Measurement of radon mass and surface exhalation rates of building materials and soil The radon exhalation rate from the building materials was carried out by the active measurement of radon growth in a closed sealed accumulator (Chen et al., 2010; Sahoo et al., 2007; Petropoulos et al., 2001, 2002). The samples were dried and sealed in the leak proof exhalation chamber shown in Fig. 1. The growth of the radon in accumulator was measured by the scintillation radon monitor (SRM) connected to chamber. The measurement of the radon growth was continued till a saturation radon concentration. The growth data was then fitted to following Eq. (10) for estimating radon mass exhalation rate (Jm) or surface exhalation rate (Jb)
X 1 ele t þ C0 ele t C t ¼ V le
Fig. 1. Experimental set-up used for the radon mass/surface exhalation rates from building materials.
where V is effective volume of the set-up i.e. sum of scintillation radon monitor volume and air volume inside the chamber. le is the effective decay constant, which is sum of radon decay constant, radon back diffusion constant and leakage rate of chamber, if any, X ¼ JmM or JbA, where M and A denote mass and surface area of sample and C0 is initial radon concentration inside the chamber at t ¼ 0.
at the centre of rooms for period of three months. After environmental exposure for the period of 90 days, the detectors were etched with 2.5 N sodium hydroxide solution in an etching bath at a temperature of 60 C for 90 min time for developing the registered tracks. This etching process removes a bulk thickness of 4 mm leaving a residual detector thickness of 8 mm. The detectors were washed and dried and the cellulose nitrates layers of the detector were pilled-off form the polyester base. The tracks densities produced by the alpha particles were counted with spark counter techniques. The detectors were first pre-sparked at 900 V twice and then tracks were counted at 500 V twice. The average of this tracks density converted into radon concentration according to following relations
CR ¼ T1 =ðd$KR Þ
3.3. Measurement of radon surface flux from floor The radon flux from walls is not only contributing to indoor radon but the sub-soil radon flux also contributes to it. Hence, measurements of radon surface flux from the floor of the dwellings under study were carried out by accumulator techniques. The accumulator having a radius of 20 cm and a height of 10 cm was placed on the surface of the floor. The mouth of the accumulator placed over the surface and rubber gasket of thickness 0.5 was sandwiched to avoid superficial leakage. In order to avoid further leakage, a heavy weight was placed over it. The measurement of radon growth in the accumulator was carried out by scintillation radon monitor with same procedure used by Sahoo et al. (2010) and Sahoo and Mayya (2010). The detail of the scintillation radon monitor and measurement principle described elsewhere (Gaware
(9)
where T1 is the track density observed in ‘radon’ compartment. KR is the calibration factor of radon in ‘radon’ compartment for radon (0.017 tr. cm2 d1/(Bq m3) and d is the number of days of exposure (Sahoo et al., 2013). The outdoor radon concentrations were Table 2 Radon exhalation rate, density and radon diffusion length of the material used in study. S. No
Building materials
Measured radon exhalation rates
1 2 3 4 5 6 7 8 9 10 10 11 12 13 14 15 16
Cement Portland Brick powder Soil1a Soil2a Soil3a Soil4a Sand Course aggregate Granite1 Marble Granite1 Granite2 Marble Concrete Fired brick Unfired brick Sandstone
3.74 9.57 58.6 34.6 49.7 68.4 27.6 5.39 13.2 10.3 0.82 2.27 0.74 1.44 0.23 3.30 1.82
a
0.56 (mBq/kg/h) 1.61 (mBq/kg/h) 0.65 (mBq/kg/h) 8.5 (mBq/kg/h) 3.9 (mBq/kg/h) 3.9 (mBq/kg/h) 5.7 (mBq/kg/h) 0.20 (mBq/kg/h) 1.2 (mBq/kg/h) 2.5 (mBq/kg/h) 0.22 (Bq/m2/h) 0.72 (Bq/m2/h) 0.01 (Bq/m2/h) 0.2 (Bq/m2/h) 0.01 (Bq/m2/h) 1.03 (Bq/m2/h) 0.36 (Bq/m2/h)
(10)
Measured density (kg/m3)
Radon diffusion length (m) taken from literature
1506 1623 1560 1340 1290 1250 1600 1580 2700 2600 2700 2526 2600 2200 2400 2400 1982
1.61 1.11 1.23 1.23 1.23 1.23 1.43 1.27 0.16 0.05 0.16 0.16 0.05 0.41 0.09 0.41 1.02
Soil1, soil2, soil3, soil4 were collected from the dwelling M1, M2, M3,M4, B1, B2, B3 and B4.
Rogers et al. (1994) calculated Rogers et al. (1994) calculated Chauhan et al. (2008) Chauhan et al. (2008) Chauhan et al. (2008) Chauhan et al. (2008) Narula et al. (2009) Rogers et al. (1994) calculated Rogers et al. (1994) calculated Rogers et al. (1994) calculated Misdaq et al. (2000) Misdaq et al. (2000) Rogers et al. (1994) calculated Daoud and Renken (2001) Rogers et al. (1994) calculated Rogers et al. (1994) calculated Keller et al. (2001)
A. Kumar et al. / Journal of Environmental Radioactivity 127 (2014) 50e55
et al., 2011). The growth of radon in accumulator was measured by scintillation radon monitor coupled with it. The radon growth data was then fitted to following Eq. (11).
Jw A C t ¼ 1 ele t V le
(11)
where Jw is radon surface flux from floor contributed by sub-soil flux and building materials, V is total volume of chamber including the volume of scintillation cell (m3), le is the effective radon decay rate which is sum of radioactive decay constant of 222 Rn, back diffusion rate and leakage rate, if any, A is the surface area of floor covered with accumulator (m2). 4. Results and discussion The radon diffusion length in building materials was taken from data available in the literature. The samples for which radon diffusion length is not available in literature were calculated by the empirical relation of Rogers et al. (1994) listed in Table 2. The density of the building materials and soil were calculated by mass to volume ratio. The radon mass and surface exhalation rate from the building materials measured by scintillation radon monitor listed in Table 2. Radon exhalation rate from the wall was calculated using three models; Nazaroff and Nero, Stoulos et al. and Sahoo et al. by summing the radon exhalation rates contributed by wall floor and roof separately for eleven selected dwellings. The surface area due to door and window were 3e4% of the total surface area, thus assumed to be negligible. The contribution of the wooden roof for total radon flux was assumed to be negligible. From the calculated radon wall flux from three models the indoor radon concentration was calculated assuming ventilation rates 0.63 h1 (Uji c et al., 2010). However the actual ventilation rates of the dwellings were varied with their size, location, structure of construction and position of door and window. The radon surface flux from the floors measured by accumulator method was used in calculation as contribution from the floor. The outdoor radon concentration measured by pin hole dosimeter varied between 4 to 7 Bq/m3 with an average of 5.5 0.9 Bq/m3 and were subtracted from indoor radon concentrations considering as background. The comparison of theoretical calculated value of the indoor radon concentrations from three different models with experimental values is listed in Table 3. The dwellings M1, M2, M3 and M4 were the mud houses selected in four different places having different soil texture and. All these mud houses consists of mud wall, wooden roof and soil floor, the
thickness of wall varied from 0.20 m to 0.30 m and radon diffusion length in soil taken as 1.23 m (Chauhan et al., 2008). With these parameter d/L ratio varied from 0.122 to 0.406. The dwellings B1, B2, B3 and B4 were brick houses having different combination of roof and floor construction listed in Table 1. The radon diffusion length in the fired brick is of the order of 0.1 m, then d/L ratio are comparable and Jw/Jb ratio for brick wall is of the order of 1.77. The dwellings C1, C2 and C4 were the brick houses having wall covered with sand and cement paste of thickness 0.02 m and floor were constructed from the marble, concrete and granite. The surface exhalation rates from these materials are listed in Table 2. The radon diffusion length in concrete, marble and granite have values 0.41, 0.05 and 0.16 m and thickness of these materials used in the construction have values 0.3 m, 0.023, and 0.023 m. The d/L and Jw/ Jb ratio for these material wall were 0.365, 0.23, 0.072 and Jw/Jb ratio 1.71, 1.88 and 1.92 respectively. The comparison of measured Jw/Jb value with d/L ratio for radon along with predicted value calculated from Sahoo et al. (2011) for typical dwelling of Sbd/Vb ¼ 1.95 is shown in Fig. 2. The measured value for all dwellings differs slightly compared with the predicted values from any model as shown in Fig. 3, which may be due to difference in the actual ventilation rate than used in the calculation. The results of linear fit (passing through origin) to the plot between measured indoor radon concentration (X-axis) and predicted values from each models (Y-axis) are listed in Table 4. As may be seen from the Table 4, the R values obtained for Nazaroff and Nero model (0.86), Sahoo et al. model (0.87) and Stolous et al. model (0.85) are nearly same indicating that all three models have a good linear correlation with the measured indoor radon concentration. The slope of the regression line in the case of Sahoo et al. has a value of 1.04, while in the case of Nazaroff and Nero and Stolous et al. have values 0.81 and 0.77 respectively indicating that the prediction by Sahoo et al., is more close to measured radon concentration. But when the thickness of specimen is very smaller than the radon diffusion length in the specimen, all three models predict the radon values close to the measured values. Consider the case of mud dwellings (M1, M2, M3 and M4) the radon mass exhalation rates and density of the soil were 58.6, 34.6, 49.7, 68.4 Bq/kg/h and 1560, 1340, 1290, 1250 kg/m3 respectively. The radon diffusion length in soil is approximately 1.23 m (Chauhan, 2002). Thus if the floor is assumed a soil wall of half thickness 0.5 m, then with these parameter the predicted radon flux from floor have value 43.3, 21.98, 30.4 and 40.54 Bq/m2/h
Table 3 Measured and predicted indoor radon concentrations in test dwellings. S. No
1 2 3 4 5 6 7 8 9 10 11
Dwelling code
M1 M2 M3 M4 B1 B2 B3 B4 C1 C2 C4
Indoor radon concentration in Bq/m3 from Nazaroff and Nero model (1988)
Sahoo et al model (2011)
Stoulos model (2003)
Experimental value AM SE
34.5 21.9 24.3 34.5 23.9 15.1 25.5 10.1 5.9 6.1 5.1
36.0 28.3 35.8 49.5 26.7 20.2 28.8 18.1 8.7 8.3 9.1
33.6 20.7 24.3 34.7 23.6 13.4 22.7 7.1 5.9 3.1 2.6
31 25 29 39 29 34 27 21 10 7 7
AM ¼ Arithmetic mean, SE ¼ Standard error.
53
3 3 3 4 3 4 3 2 1 1 1 Fig. 2. Comparison of in experimental and theoretical Jw/Jb with d/L ratio.
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A. Kumar et al. / Journal of Environmental Radioactivity 127 (2014) 50e55
utilizing radon exhalation data of building materials sample which is relatively simple and fast to measure as compared to radium content. 5. Conclusions
Fig. 3. Comparison of measured and predicted radon concentration from different models.
respectively, while the measured radon flux from the floor by accumulator technique were 60, 52, 46 and 69 Bq/m2/h respectively. The ratio of measured and predicted flux for these varied with 1.74 043 which is comparable to the ratio 1.68 for Sbd/ Vb ¼ 1.95 and d/L ¼ 0.5 calculated by Eq. (4). This difference occurred because in prediction of radon flux, soil floor assumed to be of finite thickness, but in actual it extends to infinity. If the radon diffusion length become twice or thrice than thickness of specimen, then the predicted indoor radon concentration will be 39 Bq/m3 for B1 dwellings i.e. 1.7 times higher than predicted from d/L equals 0.14. In case of Stolous et al. model, the radon surface exhalation rates from materials were extrapolated to wall flux using surface fractional usage in order to find indoor radon concentrations. This model deviated if thickness of the specimen becomes larger than the radon diffusion length, then the wall flux will be different depending upon the values of diffusion length and Sbd/Vb. This suggests that the above said model may not be applicable for thicker wall made by high density material. On the other hand Sahoo et al. model is a more general model applicable to all d/L values. From Eq. (7), that as d/L ratio increases and become large enough (10 times), then the two value (Jb and Jw) become equal and for smaller value of d/L (i.e larger diffusion length), wall flux increases by a factor depending upon values of diffusion length and Sbd/Vb. For d/L less than one, the Sahoo et al. model reduced to Stolous et al. model. Also Nazaroff and Nero model requires knowledge of radium content, density and emanation fraction of building materials to estimate wall flux. It may be noted that the measurement of these input parameters (especially radium content and emanation coefficient) is always a difficult task and time consuming (e.g. measurement of radium content requires a sample storage time of at least one month to ensure secular equilibrium between parent and daughter nuclides). In view of this, Sahoo et al., model is more useful for quick estimation of radon flux from walls and indoor radon concentration by
Table 4 Results of linear regression between measured radon concentrations and model predicted data. Model
Slope
R
p Value
Nazaroff and Nero Sahoo et al. Stolous et al.
0.81 0.17 1.04 0.07 0.77 0.07
0.86 0.87 0.85
3.7 104 1.7 104 5.4 104
The indoor radon concentration from the measured radon exhalation rate from different building materials was calculated by three different models described in the literature. In order to validate these models predictions, measurement of indoor radon concentration in some selected dwellings were carried out by calibrated pin hole based radon thoron dosimeter. The radon surface flux from floors of selected dwelling was measured by accumulator techniques. The radon mass and surface exhalations were measured by the scintillation radon monitor. The results showed that the predicted radon concentrations from all three models were closed to measured radon concentration. The comparison of results from three models showed that the Nazaroff and Nero model is applicable in case, when sample thickness is finite, otherwise it gives an underestimate of the exhalation rates and hence indoor radon concentrations. As d/L ratio increase and become large enough, then the two value (Jb and Jw) become equal and for smaller value of d/L, wall flux increases by a factor depending upon values of diffusion length and Sbd/Vb. For very small value of d/L the predicted value of radon flux and indoor radon concentration can be explained by Stoulos et al. model. Sahoo et al. is a model to be applicable for all d/L ranging from 0.01 to 10 or more for radon and thoron. The measured radon concentrations are 2e3 times higher than for cemented house, when sub-soil contribution was neglected. However the measured radon concentrations agreed with predicted value, after considering the contribution from soil gas flux. Acknowledgment The authors are thankful to Board of Research in Nuclear Science, Department of Atomic Energy, Mumbai, India, for providing the financial support to carry out this work. References Chauhan, R.P., Nain, M., Kant, K., 2008. Radon diffusion studies through some building materials: effect of grain size. Radiat. Meas. 43, S445eS448. Chauhan, R.P., Chakarvarti, S.K., 2002. Radon diffusion through soil and fly ash: effect of compaction. Radiat. Meas 35, 143e146. Gaware, J.J., Sahoo, B.K., Sapra, B.K., Mayya, Y.S., 2011. Indigenous development and networking of online radon monitors in the underground uranium mine. Radiat. Protect. Environ. 34, 37e40. Daoud, W.Z., Renken, K.J., 2001. Laboratory assessment of flexible thin-film membranes as a passive barrier to radon gas diffusion. Sci. Total Environ 72, 127e 135. Keller, G., Hoffmann, B., Feigenspan, T., 2001. Radon permeability and radon exhalation of building materials. Sci. Total Environ. 272, 85e89. Mahur, A.K., Kumar, R., Sengupta, D., Prasad, R., 2009. Radon exhalation rate in Chhatrapur beach sand samples of high background radiation area and estimation of its radiological implications. Indian J. Phys. 83, 1011e1018. Mahur, A.K., Kumar, R., Sengupta, D., Prasad, R., 2008. An investigation of radon exhalation rate and estimation of radiation doses in coal and fly ash samples. Appl. Radiat. Isotopes 66, 401e406. Misdaq, M.A., Ktata, A., Bakhchi, 2000. A new method for studying the transport of radon and thoron in various building materials using CR-39 and LR-115 solid state nuclear track detectors. Radiati. Meas. 32, 35e42. Narula, A.K., Goyal, S.K., Saini, S., Chauhan, R.P., Chakarvarti, S.K., 2009. Calculation of radon diffusion coefficient and radon diffusion length for different building construction materials. Indian J. Phys. 83, 1171e1175. Nazaroff, W.W., Nero Jr., A.V., 1988. Radon and its decay products in indoor air. John Wiley and Sons, New York. Patra, C., Sahoo, S.K., Tripathi, R.M., Puranik, V.D., 2013. Distribution of radionuclides in surface soils Singhbhum Shear Zone, India and associated dose. Environ. Monitor. Assess. 185, 7833e7843. http://dx.doi.org/10.1007/s10661-013-3138-y.
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Sahoo, B.K., Sapra, B.K., Gaware, J.J., Kanse, S.D., Mayya, Y.S., 2011. A model to predict radon exhalation from walls to indoor air based on the exhalation from building material samples. Sci. Total Environ. 409, 2635e2641. Sahoo, B.K., Sapra, B.K., Kanse, S.D., Gaware, J.J., Mayya, Y.S., 2013. A new pin-hole discriminated 222Rn/220Rn passive measurement device with single entry face. Radiat. Meas.. http://dx.doi.org/10.1016/j.radmeas.2013.08.003. Shweikani, R., Raja, G., 2009. Radon exhalation from some finishing materials frequently used in Syria. Radiat. Meas. 44, 1019e1023. Stoulos, S., Manolopoulou, M., Papastefanou, C., 2003. Assessment of natural radiation exposure and radon exhalation from building materials in Greece. J. Environ. Radioact. 69, 225e240. Uji c, P., Celikovi c, I., Kandi c, A., Vukanac, I., Durasevi c, M., Dragosavac, D., Zuni c, Z.S., 2010. Internal exposure from building materials exhaling 222Rn and 220Rn as compared to external exposure due to their natural radioactivity content. Appl. Radiat. Isotopes 68, 201e206. UNSCEAR, 2000. United Nation Scientific Committee on the Effects of Atomic Radiation: sources, effects and risks of ionizing radiation. New York, United Nations: Report to the General Assembly.
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Journal of Environmental Radioactivity journal homepage: www.elsevier.com/locate/jenvrad
Short communication
Modeling of indoor radon concentration from radon exhalation rates of building materials and validation through measurements Amit Kumar a, *, R.P. Chauhan a, Manish Joshi b, B.K. Sahoo b a b
Department of Physics, National Institute of Technology, Kurukshetra 136119, India Radiological Protection and Advisory Division, Bhabha Atomic Research Centre, Mumbai 400085, India
a r t i c l e i n f o
a b s t r a c t
Article history: Received 26 August 2013 Received in revised form 4 October 2013 Accepted 7 October 2013 Available online 22 October 2013
Building materials are the second major source of indoor radon after soil. The contribution of building materials towards indoor radon depends upon the radium content and exhalation rates and can be used as a primary index for radon levels in the dwellings. The radon flux data from the building materials was used for calculation of the indoor radon concentrations and doses by many researchers using one and two dimensional model suggested by various researchers. In addition to radium content, the radon wall flux from a surface strongly depends upon the radon diffusion length (L) and thickness of the wall (2d). In the present work the indoor radon concentrations from the measured radon exhalation rate of building materials calculated using different models available in literature and validation of models was made through measurement. The variation in the predicted radon flux from different models was compared with d/L value for wall and roofs of different dwellings. The results showed that the radon concentrations predicted by models agree with experimental value. The applicability of different model with d/L ratio was discussed. The work aims to select a more appropriate and general model among available models in literature for the prediction of indoor radon. Ó 2013 Elsevier Ltd. All rights reserved.
Keywords: Indoor radon concentration Wall flux Pin hole dosimeter Radon exhalation rates Sub-soil flux
1. Introduction Radon (222Rn) and its progeny are present in all dwellings, because radium is present in building materials as well as in the soil. It is important to understand the generation and migration process of radon from building materials, because it contributes to 55% of total radiation dose received by the population from the environment (UNSCEAR, 2000). Uranium, radium and thorium are present at trace levels with concentrations varying a wide range in different geological samples like soil and building materials (Patra et al., 2013). The soil and building materials are the main source of indoor radon (UNSCEAR, 2000; Nazaroff and Nero, 1988). The contribution of the exposure from building materials are assumed to be negligible, if they contain low radioactivity and exhalation rates than soil (Sahoo et al., 2011). Many studies have been performed for the measurement of radon exhalation from building materials and soil and extrapolated their results to the indoor radon concentration (Chen et al., 2010; Saad et al., 2013; Shweikani and Raja, 2009; Mahur et al., 2008,2009.) The indoor radon concentration and corresponding doses from the radon exhalation rates
* Corresponding author. Tel.: þ91 9812351248; fax: þ91 1744238050. E-mail address: [email protected] (A. Kumar). 0265-931X/$ e see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jenvrad.2013.10.004
were calculated without considering the physical change in the matrix during wall, floor and roof construction. While in actual practice, the radon exhalation from wall will change depending upon the value of radon diffusion length, thickness of wall and dimension of the building material used for measurements (Sahoo et al., 2011). The generation and transport process of the radon in wall is significantly different than that of its building materials. Hence, it is necessary to investigate this practice of extrapolating the radon exhalation data to indoor radon through a systematic analysis by carrying out both experimental measurements and model prediction. The calculation of radon flux from walls from the knowledge of the radium content, radon emanation coefficient and radon diffusion length in building materials was suggested by Nazaroff and Nero (1988) while Sahoo et al. (2011) suggested a semi-empirical model to predict the radon flux from wall using the radon exhalation rate and diffusion length in building materials. Another model suggested by Stoulos et al. (2003) predict the indoor radon concentration contributed by walls from values of radon exhalation rates from building material samples, surface fractional usage of building materials in wall construction and air exchange rate of the room. The present study focuses on the comparison of predicted indoor radon concentration applying above three models with the directly measured indoor radon concentration for selecting the best appropriate model among three. For this, radon
A. Kumar et al. / Journal of Environmental Radioactivity 127 (2014) 50e55
exhalation rates of various building materials were measured by an active technique using a continuous radon monitor and the results were extrapolated to indoor radon in order to compare with measured value of indoor radon concentration in some selected dwellings.
The indoor radon concentration due to the radon exhalation from surface fraction of building materials can also be estimated by the following formula (Stoulos et al., 2003)
" CRn ¼
n X
# wsi $Esi
i¼1
2. Existing theory and models description A one dimensional model for predicting the radon exhalation from wall was proposed by Nazaroff and Nero (1988) which is given by
Jw ¼ R$E$l$r$L$tanhðd=LÞ
(1)
where R radium contents in building materials, E radon emanation fraction depends upon the moisture contents, l radon decay constant, r density of building materials, L is radon diffusion length through materials and d is the half thickness of the wall. If it assumed that the entire radon atom reaching in pore volume of the building material could emanate into the indoor, then the analytical expression for radon mass exhalation rates can be written as (Sahoo et al., 2007)
Jm ¼ REl
(2)
Using Eqs. (1) and (2), one can write
Jw ¼ Jm rLtanhðd=LÞ
(3)
A model to predict the radon wall flux (Jw) using the data of radon surface exhalation rate (Jb) of the building material sample was suggested by the Sahoo et al. (2011), which is given by
Jw ¼ Jb
Sb d d þ1 1 exp k Vb L
(4)
where d, Sb and Vb are the wall half thickness, surface area and bulk volume of the building material sample, k is the regression parameter to be determined from least square fitting to the data points plotted between Jw/Jb and d/L and found to be 0.31 0.05 (Sahoo et al., 2011). Using Eqs. (3) and (4), the radon surface exhalation rate (Jb) of the building materials can be related to mass exhalation rate (Jm) as:
Jb ¼
Sb d Vb
Jm rLtanhðd=LÞ 1 exp k dL þ 1
(5)
If the diffusion length of the radon gas in the materials is much smaller than half thickness of wall, i.e. L> d, then the Eq. (4) reduced
Jw ¼ Jb
Sb d Vb
(6)
Once the radon flux from the wall become known, the indoor radon concentration can be calculated by knowing surface to volume ratio of the room and ventilation rates given by
C ¼
X i
Jwi Si VðlRn þ lv Þ
S V$lv
(8)
where Esi is the measured surface exhalation rate of the building material; Wsi is the surface fractional usage of the building material; S/V is the surface to volume ratio of the room and lv is the annual average room ventilation rate. 3. Materials and methods 3.1. Measurement of indoor radon concentration in selected dwellings The indoor radon thoron concentration was measured by pin hole based radon thoron dosimeter in some dwellings to compare with theoretical results. The details and calibration of pin hole based radon thoron dosimeter was described elsewhere (Sahoo et al., 2013). The pin hole based radon thoron dosimeters (PRTMs) consisted of two compartments separated by a central pinholes disc made up of high density polyethylene material, acting as 220 Rn discriminator. Four pin holes each with dimension of 2 mm length and 1 mm diameter are made in this circular disc. The dosimeter has a single entry through which gas enters in first compartment namely “radon þ thoron” compartment through a glass fiber filter paper (pore size 0.7 mm) and diffuses to second compartment namely “radon” compartment through pin-holes cutting off 98% of entry of 220Rn and 98% transmission of radon into this compartment (Sahoo et al., 2013). Each compartment is cylindrical having a length of 4.1 cm and radius 3.1 cm. The solid state nuclear tracks detectors (LR-115, Type-2, strippable) of size (2 2 cm2) were fixed at opposite end of the entry face in each compartment. The LR-115 in first compartment measured the tracks produced by the alphas emitted from radon and thoron, while LR-115 in second compartment measured the tracks due to radon only. Eleven numbers of dwellings were selected for the measurement of indoor radon concentration having different construction type listed in Table 1. The measurement of dimension of dwellings, detail of door and window and thickness of wall were made during deployment of dosimeter. The dosimeters were deployed in the dwelling of area under study through a metallic chain at the average human height (1.5 m)
Table 1 Details of the dwellings used for measurement indoor radon concentration and their construction type. S. No
Type of dwelling
Dwelling code
Construction type
1. 2. 3 4 5 6 7 8 9
Mud House Mud house Mud house Mud house Brick house Brick house Brick house Brick house Cemented house
M1 M2 M3 M4 B1 B2 B3 B4 C1
10
Cemented house
C2
11
Cemented house
C4
Mud wall, soil floor, wooden ceiling Mud wall, soil floor, wooden ceiling Mud wall, soil floor, wooden ceiling Mud wall, soil floor, wooden ceiling Brick wall, wooden roof, soil floor Brick wall, brick roof, soil floor Brick wall, RCC concrete roof, soil floor Brick wall, brick roof, brick floor Plastered concrete wall, concrete roof, concrete floor Plastered concrete wall, concrete roof, marble floor Plastered concrete wall, concrete roof, granite floor
(7)
where Jwi and Si are the radon wall flux and surface area of wall, lRn þ lv is effective radon removal rates and V is volume of room.
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also measured by same technique in order to made correction in the measured indoor radon concentration. 3.2. Measurement of radon mass and surface exhalation rates of building materials and soil The radon exhalation rate from the building materials was carried out by the active measurement of radon growth in a closed sealed accumulator (Chen et al., 2010; Sahoo et al., 2007; Petropoulos et al., 2001, 2002). The samples were dried and sealed in the leak proof exhalation chamber shown in Fig. 1. The growth of the radon in accumulator was measured by the scintillation radon monitor (SRM) connected to chamber. The measurement of the radon growth was continued till a saturation radon concentration. The growth data was then fitted to following Eq. (10) for estimating radon mass exhalation rate (Jm) or surface exhalation rate (Jb)
X 1 ele t þ C0 ele t C t ¼ V le
Fig. 1. Experimental set-up used for the radon mass/surface exhalation rates from building materials.
where V is effective volume of the set-up i.e. sum of scintillation radon monitor volume and air volume inside the chamber. le is the effective decay constant, which is sum of radon decay constant, radon back diffusion constant and leakage rate of chamber, if any, X ¼ JmM or JbA, where M and A denote mass and surface area of sample and C0 is initial radon concentration inside the chamber at t ¼ 0.
at the centre of rooms for period of three months. After environmental exposure for the period of 90 days, the detectors were etched with 2.5 N sodium hydroxide solution in an etching bath at a temperature of 60 C for 90 min time for developing the registered tracks. This etching process removes a bulk thickness of 4 mm leaving a residual detector thickness of 8 mm. The detectors were washed and dried and the cellulose nitrates layers of the detector were pilled-off form the polyester base. The tracks densities produced by the alpha particles were counted with spark counter techniques. The detectors were first pre-sparked at 900 V twice and then tracks were counted at 500 V twice. The average of this tracks density converted into radon concentration according to following relations
CR ¼ T1 =ðd$KR Þ
3.3. Measurement of radon surface flux from floor The radon flux from walls is not only contributing to indoor radon but the sub-soil radon flux also contributes to it. Hence, measurements of radon surface flux from the floor of the dwellings under study were carried out by accumulator techniques. The accumulator having a radius of 20 cm and a height of 10 cm was placed on the surface of the floor. The mouth of the accumulator placed over the surface and rubber gasket of thickness 0.5 was sandwiched to avoid superficial leakage. In order to avoid further leakage, a heavy weight was placed over it. The measurement of radon growth in the accumulator was carried out by scintillation radon monitor with same procedure used by Sahoo et al. (2010) and Sahoo and Mayya (2010). The detail of the scintillation radon monitor and measurement principle described elsewhere (Gaware
(9)
where T1 is the track density observed in ‘radon’ compartment. KR is the calibration factor of radon in ‘radon’ compartment for radon (0.017 tr. cm2 d1/(Bq m3) and d is the number of days of exposure (Sahoo et al., 2013). The outdoor radon concentrations were Table 2 Radon exhalation rate, density and radon diffusion length of the material used in study. S. No
Building materials
Measured radon exhalation rates
1 2 3 4 5 6 7 8 9 10 10 11 12 13 14 15 16
Cement Portland Brick powder Soil1a Soil2a Soil3a Soil4a Sand Course aggregate Granite1 Marble Granite1 Granite2 Marble Concrete Fired brick Unfired brick Sandstone
3.74 9.57 58.6 34.6 49.7 68.4 27.6 5.39 13.2 10.3 0.82 2.27 0.74 1.44 0.23 3.30 1.82
a
0.56 (mBq/kg/h) 1.61 (mBq/kg/h) 0.65 (mBq/kg/h) 8.5 (mBq/kg/h) 3.9 (mBq/kg/h) 3.9 (mBq/kg/h) 5.7 (mBq/kg/h) 0.20 (mBq/kg/h) 1.2 (mBq/kg/h) 2.5 (mBq/kg/h) 0.22 (Bq/m2/h) 0.72 (Bq/m2/h) 0.01 (Bq/m2/h) 0.2 (Bq/m2/h) 0.01 (Bq/m2/h) 1.03 (Bq/m2/h) 0.36 (Bq/m2/h)
(10)
Measured density (kg/m3)
Radon diffusion length (m) taken from literature
1506 1623 1560 1340 1290 1250 1600 1580 2700 2600 2700 2526 2600 2200 2400 2400 1982
1.61 1.11 1.23 1.23 1.23 1.23 1.43 1.27 0.16 0.05 0.16 0.16 0.05 0.41 0.09 0.41 1.02
Soil1, soil2, soil3, soil4 were collected from the dwelling M1, M2, M3,M4, B1, B2, B3 and B4.
Rogers et al. (1994) calculated Rogers et al. (1994) calculated Chauhan et al. (2008) Chauhan et al. (2008) Chauhan et al. (2008) Chauhan et al. (2008) Narula et al. (2009) Rogers et al. (1994) calculated Rogers et al. (1994) calculated Rogers et al. (1994) calculated Misdaq et al. (2000) Misdaq et al. (2000) Rogers et al. (1994) calculated Daoud and Renken (2001) Rogers et al. (1994) calculated Rogers et al. (1994) calculated Keller et al. (2001)
A. Kumar et al. / Journal of Environmental Radioactivity 127 (2014) 50e55
et al., 2011). The growth of radon in accumulator was measured by scintillation radon monitor coupled with it. The radon growth data was then fitted to following Eq. (11).
Jw A C t ¼ 1 ele t V le
(11)
where Jw is radon surface flux from floor contributed by sub-soil flux and building materials, V is total volume of chamber including the volume of scintillation cell (m3), le is the effective radon decay rate which is sum of radioactive decay constant of 222 Rn, back diffusion rate and leakage rate, if any, A is the surface area of floor covered with accumulator (m2). 4. Results and discussion The radon diffusion length in building materials was taken from data available in the literature. The samples for which radon diffusion length is not available in literature were calculated by the empirical relation of Rogers et al. (1994) listed in Table 2. The density of the building materials and soil were calculated by mass to volume ratio. The radon mass and surface exhalation rate from the building materials measured by scintillation radon monitor listed in Table 2. Radon exhalation rate from the wall was calculated using three models; Nazaroff and Nero, Stoulos et al. and Sahoo et al. by summing the radon exhalation rates contributed by wall floor and roof separately for eleven selected dwellings. The surface area due to door and window were 3e4% of the total surface area, thus assumed to be negligible. The contribution of the wooden roof for total radon flux was assumed to be negligible. From the calculated radon wall flux from three models the indoor radon concentration was calculated assuming ventilation rates 0.63 h1 (Uji c et al., 2010). However the actual ventilation rates of the dwellings were varied with their size, location, structure of construction and position of door and window. The radon surface flux from the floors measured by accumulator method was used in calculation as contribution from the floor. The outdoor radon concentration measured by pin hole dosimeter varied between 4 to 7 Bq/m3 with an average of 5.5 0.9 Bq/m3 and were subtracted from indoor radon concentrations considering as background. The comparison of theoretical calculated value of the indoor radon concentrations from three different models with experimental values is listed in Table 3. The dwellings M1, M2, M3 and M4 were the mud houses selected in four different places having different soil texture and. All these mud houses consists of mud wall, wooden roof and soil floor, the
thickness of wall varied from 0.20 m to 0.30 m and radon diffusion length in soil taken as 1.23 m (Chauhan et al., 2008). With these parameter d/L ratio varied from 0.122 to 0.406. The dwellings B1, B2, B3 and B4 were brick houses having different combination of roof and floor construction listed in Table 1. The radon diffusion length in the fired brick is of the order of 0.1 m, then d/L ratio are comparable and Jw/Jb ratio for brick wall is of the order of 1.77. The dwellings C1, C2 and C4 were the brick houses having wall covered with sand and cement paste of thickness 0.02 m and floor were constructed from the marble, concrete and granite. The surface exhalation rates from these materials are listed in Table 2. The radon diffusion length in concrete, marble and granite have values 0.41, 0.05 and 0.16 m and thickness of these materials used in the construction have values 0.3 m, 0.023, and 0.023 m. The d/L and Jw/ Jb ratio for these material wall were 0.365, 0.23, 0.072 and Jw/Jb ratio 1.71, 1.88 and 1.92 respectively. The comparison of measured Jw/Jb value with d/L ratio for radon along with predicted value calculated from Sahoo et al. (2011) for typical dwelling of Sbd/Vb ¼ 1.95 is shown in Fig. 2. The measured value for all dwellings differs slightly compared with the predicted values from any model as shown in Fig. 3, which may be due to difference in the actual ventilation rate than used in the calculation. The results of linear fit (passing through origin) to the plot between measured indoor radon concentration (X-axis) and predicted values from each models (Y-axis) are listed in Table 4. As may be seen from the Table 4, the R values obtained for Nazaroff and Nero model (0.86), Sahoo et al. model (0.87) and Stolous et al. model (0.85) are nearly same indicating that all three models have a good linear correlation with the measured indoor radon concentration. The slope of the regression line in the case of Sahoo et al. has a value of 1.04, while in the case of Nazaroff and Nero and Stolous et al. have values 0.81 and 0.77 respectively indicating that the prediction by Sahoo et al., is more close to measured radon concentration. But when the thickness of specimen is very smaller than the radon diffusion length in the specimen, all three models predict the radon values close to the measured values. Consider the case of mud dwellings (M1, M2, M3 and M4) the radon mass exhalation rates and density of the soil were 58.6, 34.6, 49.7, 68.4 Bq/kg/h and 1560, 1340, 1290, 1250 kg/m3 respectively. The radon diffusion length in soil is approximately 1.23 m (Chauhan, 2002). Thus if the floor is assumed a soil wall of half thickness 0.5 m, then with these parameter the predicted radon flux from floor have value 43.3, 21.98, 30.4 and 40.54 Bq/m2/h
Table 3 Measured and predicted indoor radon concentrations in test dwellings. S. No
1 2 3 4 5 6 7 8 9 10 11
Dwelling code
M1 M2 M3 M4 B1 B2 B3 B4 C1 C2 C4
Indoor radon concentration in Bq/m3 from Nazaroff and Nero model (1988)
Sahoo et al model (2011)
Stoulos model (2003)
Experimental value AM SE
34.5 21.9 24.3 34.5 23.9 15.1 25.5 10.1 5.9 6.1 5.1
36.0 28.3 35.8 49.5 26.7 20.2 28.8 18.1 8.7 8.3 9.1
33.6 20.7 24.3 34.7 23.6 13.4 22.7 7.1 5.9 3.1 2.6
31 25 29 39 29 34 27 21 10 7 7
AM ¼ Arithmetic mean, SE ¼ Standard error.
53
3 3 3 4 3 4 3 2 1 1 1 Fig. 2. Comparison of in experimental and theoretical Jw/Jb with d/L ratio.
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A. Kumar et al. / Journal of Environmental Radioactivity 127 (2014) 50e55
utilizing radon exhalation data of building materials sample which is relatively simple and fast to measure as compared to radium content. 5. Conclusions
Fig. 3. Comparison of measured and predicted radon concentration from different models.
respectively, while the measured radon flux from the floor by accumulator technique were 60, 52, 46 and 69 Bq/m2/h respectively. The ratio of measured and predicted flux for these varied with 1.74 043 which is comparable to the ratio 1.68 for Sbd/ Vb ¼ 1.95 and d/L ¼ 0.5 calculated by Eq. (4). This difference occurred because in prediction of radon flux, soil floor assumed to be of finite thickness, but in actual it extends to infinity. If the radon diffusion length become twice or thrice than thickness of specimen, then the predicted indoor radon concentration will be 39 Bq/m3 for B1 dwellings i.e. 1.7 times higher than predicted from d/L equals 0.14. In case of Stolous et al. model, the radon surface exhalation rates from materials were extrapolated to wall flux using surface fractional usage in order to find indoor radon concentrations. This model deviated if thickness of the specimen becomes larger than the radon diffusion length, then the wall flux will be different depending upon the values of diffusion length and Sbd/Vb. This suggests that the above said model may not be applicable for thicker wall made by high density material. On the other hand Sahoo et al. model is a more general model applicable to all d/L values. From Eq. (7), that as d/L ratio increases and become large enough (10 times), then the two value (Jb and Jw) become equal and for smaller value of d/L (i.e larger diffusion length), wall flux increases by a factor depending upon values of diffusion length and Sbd/Vb. For d/L less than one, the Sahoo et al. model reduced to Stolous et al. model. Also Nazaroff and Nero model requires knowledge of radium content, density and emanation fraction of building materials to estimate wall flux. It may be noted that the measurement of these input parameters (especially radium content and emanation coefficient) is always a difficult task and time consuming (e.g. measurement of radium content requires a sample storage time of at least one month to ensure secular equilibrium between parent and daughter nuclides). In view of this, Sahoo et al., model is more useful for quick estimation of radon flux from walls and indoor radon concentration by
Table 4 Results of linear regression between measured radon concentrations and model predicted data. Model
Slope
R
p Value
Nazaroff and Nero Sahoo et al. Stolous et al.
0.81 0.17 1.04 0.07 0.77 0.07
0.86 0.87 0.85
3.7 104 1.7 104 5.4 104
The indoor radon concentration from the measured radon exhalation rate from different building materials was calculated by three different models described in the literature. In order to validate these models predictions, measurement of indoor radon concentration in some selected dwellings were carried out by calibrated pin hole based radon thoron dosimeter. The radon surface flux from floors of selected dwelling was measured by accumulator techniques. The radon mass and surface exhalations were measured by the scintillation radon monitor. The results showed that the predicted radon concentrations from all three models were closed to measured radon concentration. The comparison of results from three models showed that the Nazaroff and Nero model is applicable in case, when sample thickness is finite, otherwise it gives an underestimate of the exhalation rates and hence indoor radon concentrations. As d/L ratio increase and become large enough, then the two value (Jb and Jw) become equal and for smaller value of d/L, wall flux increases by a factor depending upon values of diffusion length and Sbd/Vb. For very small value of d/L the predicted value of radon flux and indoor radon concentration can be explained by Stoulos et al. model. Sahoo et al. is a model to be applicable for all d/L ranging from 0.01 to 10 or more for radon and thoron. The measured radon concentrations are 2e3 times higher than for cemented house, when sub-soil contribution was neglected. However the measured radon concentrations agreed with predicted value, after considering the contribution from soil gas flux. Acknowledgment The authors are thankful to Board of Research in Nuclear Science, Department of Atomic Energy, Mumbai, India, for providing the financial support to carry out this work. References Chauhan, R.P., Nain, M., Kant, K., 2008. Radon diffusion studies through some building materials: effect of grain size. Radiat. Meas. 43, S445eS448. Chauhan, R.P., Chakarvarti, S.K., 2002. Radon diffusion through soil and fly ash: effect of compaction. Radiat. Meas 35, 143e146. Gaware, J.J., Sahoo, B.K., Sapra, B.K., Mayya, Y.S., 2011. Indigenous development and networking of online radon monitors in the underground uranium mine. Radiat. Protect. Environ. 34, 37e40. Daoud, W.Z., Renken, K.J., 2001. Laboratory assessment of flexible thin-film membranes as a passive barrier to radon gas diffusion. Sci. Total Environ 72, 127e 135. Keller, G., Hoffmann, B., Feigenspan, T., 2001. Radon permeability and radon exhalation of building materials. Sci. Total Environ. 272, 85e89. Mahur, A.K., Kumar, R., Sengupta, D., Prasad, R., 2009. Radon exhalation rate in Chhatrapur beach sand samples of high background radiation area and estimation of its radiological implications. Indian J. Phys. 83, 1011e1018. Mahur, A.K., Kumar, R., Sengupta, D., Prasad, R., 2008. An investigation of radon exhalation rate and estimation of radiation doses in coal and fly ash samples. Appl. Radiat. Isotopes 66, 401e406. Misdaq, M.A., Ktata, A., Bakhchi, 2000. A new method for studying the transport of radon and thoron in various building materials using CR-39 and LR-115 solid state nuclear track detectors. Radiati. Meas. 32, 35e42. Narula, A.K., Goyal, S.K., Saini, S., Chauhan, R.P., Chakarvarti, S.K., 2009. Calculation of radon diffusion coefficient and radon diffusion length for different building construction materials. Indian J. Phys. 83, 1171e1175. Nazaroff, W.W., Nero Jr., A.V., 1988. Radon and its decay products in indoor air. John Wiley and Sons, New York. Patra, C., Sahoo, S.K., Tripathi, R.M., Puranik, V.D., 2013. Distribution of radionuclides in surface soils Singhbhum Shear Zone, India and associated dose. Environ. Monitor. Assess. 185, 7833e7843. http://dx.doi.org/10.1007/s10661-013-3138-y.
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Sahoo, B.K., Sapra, B.K., Gaware, J.J., Kanse, S.D., Mayya, Y.S., 2011. A model to predict radon exhalation from walls to indoor air based on the exhalation from building material samples. Sci. Total Environ. 409, 2635e2641. Sahoo, B.K., Sapra, B.K., Kanse, S.D., Gaware, J.J., Mayya, Y.S., 2013. A new pin-hole discriminated 222Rn/220Rn passive measurement device with single entry face. Radiat. Meas.. http://dx.doi.org/10.1016/j.radmeas.2013.08.003. Shweikani, R., Raja, G., 2009. Radon exhalation from some finishing materials frequently used in Syria. Radiat. Meas. 44, 1019e1023. Stoulos, S., Manolopoulou, M., Papastefanou, C., 2003. Assessment of natural radiation exposure and radon exhalation from building materials in Greece. J. Environ. Radioact. 69, 225e240. Uji c, P., Celikovi c, I., Kandi c, A., Vukanac, I., Durasevi c, M., Dragosavac, D., Zuni c, Z.S., 2010. Internal exposure from building materials exhaling 222Rn and 220Rn as compared to external exposure due to their natural radioactivity content. Appl. Radiat. Isotopes 68, 201e206. UNSCEAR, 2000. United Nation Scientific Committee on the Effects of Atomic Radiation: sources, effects and risks of ionizing radiation. New York, United Nations: Report to the General Assembly.
