Journal of Environmental Radioactivity 135 (2014) 63e66
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Journal of Environmental Radioactivity journal homepage: www.elsevier.com/locate/jenvrad
A new method for estimating the coefficients of diffusion and emanation of radon in the soil Nadezhda K. Ryzhakova* Tomsk Polytechnic University, 30 Lenin Ave., Tomsk 634050, Russia
a r t i c l e i n f o
a b s t r a c t
Article history: Received 17 June 2013 Received in revised form 19 March 2014 Accepted 6 April 2014 Available online
This paper describes a new method for determining the basic parameters of soil - diffusion and emanation coefficients related to the transfer of radon in the soil matrix, which are very useful for testing models, based on diffusion and characteristics of various soil matrices regarding the dangers of radon. The method is based on the measurement of radon in soil air on two small depths, differing twice. The paper presents the results of the determination of the parameters for covering loams and clays of Tomsk (Russian Federation), obtained by this method. Ó 2014 Elsevier Ltd. All rights reserved.
Keywords: Radon transfer Mathematical modeling Diffusion coefficient Emanation coefficient
1. Introduction In solving the problems associated with radon e evaluation of radon prone region, prospecting and exploration of radioactive ores, predicting seismic areas - the method of mathematical modeling of radon transport through porous media is widely used (Der Poel, 2002; Koarashi et al., 2000; Miklyaev et al., 2008; Novikov, 1989; Rogers and Nielso, 1991; Ryzhakova, 2009; Sahoo and Mayya, 2010; Savovi c et al., 2011; Sun et al., 2004). Moving in the soil, radon is involved in various physical processes of molecular diffusion in air and water phases of the soil, convection and turbulent mixing of air in the surface layers of soil due to changes in atmospheric conditions (pressure, temperature, wind speed and direction), filtration with the upward water flows; moving by gas lift force generated when the soil pores are filled with water, in the process of exchange between the air, water and solid soil phases. The diversity and complexity of these processes depending also on the constantly changing weather conditions, do not allow to build a precise mathematical model of transport of radon through soils. Therefore, in simulating the semi-phenomenological approach is used, where the dispersed porous medium is replaced by a continuous medium and geophysical properties of the soil and transport mechanisms are described by means of the effective parameters.
* Tel.: þ7 9059900827. E-mail address: [email protected]. http://dx.doi.org/10.1016/j.jenvrad.2014.04.002 0265-931X/Ó 2014 Elsevier Ltd. All rights reserved.
The best known are the diffusion and diffusion-convection models, the practical use of which is hampered by the ambiguous interpretation of the physical nature of simulation parameters, and, as a consequence, by the problems with the choice of methods for their determination. It is particularly difficult to interpret and determine the parameters, describing the movement of radon in soils, diffusion coefficient De e in diffusion model, and diffusion coefficient D and convection velocity y e in diffusionconvection model (Ryzhakova, 2012; Ryzhakova and Yakovleva, 2004a). In most papers on the transfer of radon, the physical meaning of these parameters (as well as the emanation coefficient Kem) is not disclosed, and the methods of their determination are not justified. Moreover, the values obtained under laboratory conditions, when there is no influence of the atmosphere, are often used in simulation. In addition, during the preparation of samples for measurement the physical properties of soils are changed, especially porosity and humidity that have a significant effect on the radon emanation and transport (Breitner et al., 2010; Chauhan et al., 2008; Ryzhakova and Ramenskaya, 2012; Ryzhakova and Shestak, 2009; Sakoda et al., 2010; Yu et al., 1993; Zhuo et al., 2006). The parameters used in the semiphenomenological description of the transfer of radon are empirical in nature and must therefore be determined under conditions of natural occurrence of soils (Ryzhakova, 2012; Sahoo et al., 2010). For example, the diffusion coefficient De, used in the diffusion model should take into account all the processes by which radon is moved to the soil surface,
64
N.K. Ryzhakova / Journal of Environmental Radioactivity 135 (2014) 63e66
including processes caused by the influence of the atmosphere (Ryzhakova and Shestak, 2009). A similar situation occurs with respect to the coefficient of emanation Kem, which is usually defined as the proportion of radon released to loose pores of the soil. In particular, just this value is measured by g-method (Miklyaev et al., 2005) in the measurement of emanation coefficient. However, under natural conditions not all radon, caught in the loose pores of the soil, comes to the surface. In the result of metabolic processes occurring in the air, water and solid phases of soil a part of radon is adsorbed on the surface of solid particles and is dissolved in the water contained in the pores. This is evidenced by, for example, the fact that the coefficients of emanation measured by a laboratory gmethod are 1.5 . 2 times larger than the values obtained under natural conditions (Krampit, 2004; Miklyaev et al., 2005). The purpose of this work is to determine the average values for the diffusion and emanation coefficients using measurements of radon volumetric activity in the soil air at two small depths (less than 1 m). Measurements were carried out in loams of Tomsk (Russian Federation) on 10 different sites with exposure time (3 . 4) days that allows to smooth spatial and temporal variations of radon (Iakovleva and Ryzhakova, 2003). 2. Definition of the radon transport related parameters of the soil in natural conditions The known methods for determining the diffusion and emanation coefficients under natural conditions are rather laborconsuming. An external source of radon and carrying out repeated (10 . 15) measurement of radon volumetric activity in soil air within a day are required in the method of “an instant source” (Bulashevich and Kartashov, 1957; Ryzhakova and Shestak, 2009) for determination of the diffusion coefficient. Other method of De determination is based on simultaneous measurement of radon volumetric activity at several depths (not less than 5 . 6) (Ryzhakova and Shestak, 2009). In paper (Krampit, 2004) the emanation coefficient was calculated by radon equilibrium activity measured at depth not less than 3 . 4 m. Tomsk Polytechnic University (Russian Federation) has developed a simple, cheap and reliable method for determining the diffusion and emanation coefficients of soil associated with the transfer of radon in the soil matrix, which are very useful for testing models based on diffusion and characterization of various soil matrices in terms of the radon risks. The method is based on the measurement of radon at two small depths, differing by half. The use of two depths, differing twice, allows to get simple formula to determine the radon transport related parameters of the soil on the basis of radon transport equation for a homogeneous porous medium (Ryzhakova, 2007; Ryzhakova and Yakovleva, 2004b). In our work, for this purpose we used the diffusion equation of radon transport in porous media:
l l d2 A Aþ Kem ARa rd ¼ 0; De h dz2 De
where AN ¼ Kem ARa rd =h e value of radon volumetric activity in the air of soil pores at large depths. Using expression (2) one can write the system of equations for two depths of measurements, differing twice. And formulae to determine radon transport related parameters of soils can be obtained from this system of equations:
l$h21 De ¼ h i2 ; ln AA21 1 Kem ¼
A1 $h ; 2 AA21 ARa rd
3. Measurement methods Measurements of radon volumetric activity in the air of soil pores were carried out simultaneously in two blast-holes by track detectors of IPRR type (individual passive radon radiometer) or by radiometer RRA-01M-03 on 10 sites of Tomsk in the Russian Federation. Recommended depths of measurements are w(1 . 2) of the diffusion length. To provide the homogeneity of soils on chosen sites, the upper soil layer with thickness of (0.3 . 0.5) m was taken off. For observable loose dispersed soils (clay sand, loam) the recommended depths h1 and h2 are (0.4 . 0.6) m and (0.8 . 1.2) m correspondingly. The passive track detectors or samplers were placed into both blast-holes with diameter of 5.5 cm. Then the
(1)
(2)
(4)
where A1, A2 e value of radon volumetric activity measured at the depths h1 and h2 respectively, h2 ¼ 2h1. The main condition of the method applicability e measured soils should be fairly uniform in depth, especially in mineralogical composition. This condition is nearly always fulfilled (except technogenic soil), since the thickness of the “active layer” in which the radon can come to the surface is relatively small and does not exceed a few meters. To obtain the most accurate results, the depth of measurements by the order magnitude pffiffiffiffiffiffiffiffiffiffiffi should be commensurate with the length of diffusion L ¼ De =l. For example, for the loose disperse soils, loams types, the depth h1 is about (0.4 . 0.6) m. At such depths the volumetric activity of radon varies with depth, and the dependence is nonlinear. At smaller depths, when the dependence of volumetric activity on the depth is close to linear one, formulae (3), (4) don’t work, and at larger depths the radon volumetric activity varies slightly, that can cause a large error in determination of parameters.
where A e radon volumetric activity in the air of soil pores, Bq/m3; ARa e specific activity of Radium, contained in the soil, Bq/kg; rd e density of dry soil, kg/m3, h e porosity of the medium, defining the volume share of soil, which is the share of pores filled with air; l ¼ 2.1$106 e radon decay constant, 1/s (coordinate z is calculated from the surface of porous medium). For the homogeneous soil layer under zero boundary conditions A(0) ¼ 0 the solution of Equation (1) is written as:
ffiffiffiffiffiffiffiffi p AðzÞ ¼ AN 1 e l=De z ;
(3)
Fig. 1. Diagram of pore activity measurement (D e radon detector).
N.K. Ryzhakova / Journal of Environmental Radioactivity 135 (2014) 63e66
65
Dried to constant mass and milled soil samples were placed in hermetically sealed vessels of Marinelli with a working volume of 1 L and held for w(14 . 20) days until a radioactive equilibrium is established between radium and its decay products. Specific content of 226Ra was determined by the lines of daughter products of radon decay: 295 keV and 352 keV, belonging to 214Pb, and line 609 keV, belonging to 214Bi. 4. Measurements results
Fig. 2. Diagram of measurement installation (1 e lead; 2 e iron; 3 e aluminum; 4 e soil sample; 5 e semiconductor detector; 6 e chamber filled with nitrogen).
blast-holes were closed in the top and covered with a layer of earth (distance between blast-holes is not more than 0.5 m) (Fig. 1). A necessary condition of measurements is the absence of water in blast-holes. Excluding the lowland and wetlands, the groundwater level is usually much lower than the recommended depths (deeper than 2 m). When measuring volumetric activity of radon by track detectors of IPRR type the exposure time was 3 . 4 days, and then removed from the radiometer detectors were subjected to chemical etching, drying and counting tracks in accordance with the procedure described in Nikolaev and Ilic (1999) and Durrani and Ilic, (1997). When using a sampler of radiometer RRA-01M03 the exposure time was one day. Therefore, at each point 3 measurements of radon volumetric activity were carried out sequentially and in calculations of emanation and diffusion coefficients according to formulae (3, 4) the average values were used. Simultaneously with the measurements of radon volumetric activity soil sampling was carried out to determine its physical properties: density of the dry soil rd, porosity h and radium content in the soil ARa. Measurement of radium’s content was carried out by gammaspectrometric method (Measurement methodology, 2013) with a help of germanium detector of DGDK e 100 V type with sensitivity of 200 mm2 and resolution of 3 keV on the line of cobalt 1332 keV. Protection of detector is provided by low-background chamber (LBC), which is a combined protection in the form of consecutive set of layers from protective materials with internal sizes (285 285 450) mm3 (Fig. 2). The main protective material is lead with density of 100 mm in all directions regarding to detector. To reduce the contribution in instrument spectrum of homoenergetic line of characteristic X-ray from lead, internal surface of chamber is coated with layer of steel (10 mm) and layer of aluminum (10 mm). A support under LBC, in which Dewar vessel with liquid nitrogen is placed, is also coated with lead with thickness of 50 mm.
Table 1 shows measured at two depths h1, h2 values of radon volumetric activity A1, A2, averaged over the two depths the physical properties of soils, and the parameters of Kem, De, defined by the formulae (3), (4), for 10 sites of Tomsk. The average values of the diffusion and emanation coefficients for loams of Tomsk are De ¼ 0:91$106 m2 s1 and K em ¼ 6:6%; confidential intervals for average values at sample of n ¼ 10 and a significance level 0.05 equal 0.59$106 m2 s1 and 2.9% respectively. The range of values of the diffusion coefficient (0.14 . 2.44)$106 m2 s1 is in good agreement with the results of other studies (Iscandar et al., 2004; Nazaroff and Nero, 1988; Yu et al., 1993) and the data obtained previously by other, more laborintensive methods - the method of instantaneous point source (Ryzhakova, 2012), and based on measurements of the distribution of radon volumetric activity of soil depth (Ryzhakova, 2009). The range of values of the loams emanation coefficients Kem of loose disperse soils of Tomsk (sandy loam, loam) (1.6 . 15) % is consistent with the data for this value reported in the literature for these types of soils (Krampit, 2004; Miklyaev et al., 2005; Nazaroff and Nero, 1988; Yu et al., 1993). The average value of emanation, obtained by in-situ method is about 6.6%, which is about twice less than the values obtained by the gamma method (Ryzhakova and Ramenskaya, 2012). The same difference in the values of Kem, determined by in-situ and gamma method is observed for the soils of Moscow (Krampit, 2004; Miklyaev et al., 2005). Most likely this difference is related to the fact that in using of gamma method the soils are dried and milled, i.e. change their moisture and porosity. Coefficient of variation V ¼ s$100=x for values De and Kem amounts to: 85% and 57% correspondingly; here sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n P s¼ ðxi xÞ2 =ðn 1Þ dispersion of sampling. As it was exi¼1
pected, the spread in values of De is greater than for value Kem, because of the emanation coefficient depends only on physical properties of soil (measurement are carried out in different points), and values of diffusion coefficient are influenced in addition by atmospheric conditions. 5. Conclusion This paper describes a new method for determining the radon transport related parameters of the soil associated with the transfer of radon in the soil matrix, which are very useful for
Table 1 The measured values of radon volumetric activity, the physical properties and the basic parameters clay soils of Tomsk. Site N
1
2
3
4
5
6
7
8
9
10
h1, m A1, kBq m3 A2, kBq m3 , % $103, kg m3 , Bq kg1 Kem, % De$106, m2 s1
0.5 3.85 1.15 6.04 1.8 50 1.3 23 15 1.81
0.5 3.6 1.08 5.21 1.56 41.5 1.5 61 3 0.78
0.5 1.18 0.35 1.64 0.49 58 1.1 22.5 4.2 0.43
0.5 1.9 0.57 2.34 0.7 53 1.25 25.5 4 0.22
0.5 1.78 0.53 2.20 0.66 59.5 1.1 24 5.2 0.23
0.5 2.57 0.77 3.23 0.97 59 1.05 24 7.9 0.24
0.5 5.73 1.72 6.53 1.96 45.5 1.4 27 8 0.14
0.6 1.80 0.54 2.70 0.81 56 1.1 17 10.8 1.54
0.5 1.70 0.51 2.60 0.78 50.5 1.3 23.5 6 1.31
0.6 1.40 0.42 2.20 0.66 25.5 2.05 25 1.6 2.44
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N.K. Ryzhakova / Journal of Environmental Radioactivity 135 (2014) 63e66
testing models based on diffusion and characterization of various soil matrices regarding the dangers of radon. The method is based on the measurement of radon volumetric activity in soil pore space at two small, differing by half, depths. The method allows to determine the average value of the diffusion coefficient De and emanation coefficient Kem under conditions of natural occurrence in soil. De parameters and Kem parameters, defined by the proposed method, consider physical properties of soil and climatic conditions of the district, where measurements are carried out. Parameter De characterizes the speed of radon movement to the surface of the soil and takes into account all possible mechanisms for transport of radon to the surface of the soil, including those related to the effects of the atmosphere. Parameter Kem determines the amount of radon coming to the surface of the soil, and therefore can be used to estimate the radon potential of areas. It should be noted that the use of this method makes it possible to significantly reduce the labor intensity and cost of determination of the radon transport related parameters of soils under natural conditions.
References Breitner, D., Arvela, H., Hellmuth, K.-H., Renvall, T., 2010. Effect of moisture content on emanation at different grain size fractions e a pilot study on granitic esker sand sample. J. Environ. Radioact. 101 (11), 1002e1006. Bulashevich, YuP., Kartashov, N.P., 1957. Determination of radon diffusion coefficient in rocks using a method of instant source. Phys. Earth 10, 71e76. Chauhan, R.P., Nain, M., Kant, K., 2008. Radon diffusion studies through some building materials: effect of grain size. Radiat. Meas. 43, S445eS448. Der, Poel, V., 2002. Radon Transport in AAC. Einhazard University, p. 84. Durrani, S.A., Ilic, R. (Eds.), 1997. Radon Measurements by Etched Track Detectors: Applications in Radiation Protection, Earth Science, and the Environment. World Scientific, Singapore, 387 p. Iakovleva, I.S., Ryzhakova, N.K., 2003. Spatial and temporal variations of radon concentration in soil air. Radiat. Meas. 36, 385e388. Iscandar, D., Iida, T., Nakashima, S., 2004. Determination of Rn222 Diffusion Coefficient in Japanese Soils. Department of Nuclear Enginering, Graduate School of Enginering, Nagoya University. Koarashi, J., Amano, H., Iida, T., Yamazawa, H., Nagai, H., 2000. Development of model for dynamical behavior of water and Rn222 in unsaturated soil. In: Proc. 10th Intern. Congr.Intern.Rad.Prot. Association (IRPA e 10) «Haronization of Radiation, Human Life and the ECOSYSTEM», Hiroshima, Japan. Krampit, I.A., 2004. About measurement emanation of soil factor. ANRI 3, 51e52.
Measurement Methodology of Specific Activity of Natural and Technogenic Radionuclides 226Ra, 228Ra, 224Ra, 40K, 137Cs, 134Cs, 60Co, 241Am, 152Eu in Firm Loose Tests by a Gamma and Spectrometer Method with Use of Semiconductor Detectors, 2013. http://www.fundmetrology.ru/06_metod/list.aspx?tk¼40. Miklyaev, P.S., Petrova, T.B., Okhrimenko, S.E., 2005. Research of soil emanation factor of Moscow city. ANRI 2, 30e38. Miklyaev, P.S., Petrova, T.B., Tsapalov, A.A., 2008. Estimation principles of potential radon-danger of territories. ANRI 4, 14e19. Nazaroff, W.W., Nero, A.V., 1988. Radon and Its Decay Products in Indoor Air. Lawrence Berceley Laboratory, University of California, 518 pp. Nikolaev, V.A., Ilic, R., 1999. Etched track radiometers in radon measurements: a review. Radiat. Meas. 30, 1e13. Novikov, G.F., 1989. Radiometric Exploration. L.: Subsurface, p. 407. Rogers, V.C., Nielso, K.K., 1991. Multiphase radon generation and transport in porous materials. Health Phys. 60 (6), 807e815. Ryzhakova, N.K., 14.05.2007. Way of Determination of Effective Radon Diffusion Factor in the Land. The patent for the invention N 2332687. Ryzhakova, N.K., 2009. On the issue of modeling of radon transport through porous media. Geoecol. Eng. geol. Hydrogeol. Cryopedol. 1, 1e5. Ryzhakova, N.K., 2012. Parameters of modeling radon transfer through soil and methods of their determination. J. Appl. Geophys. 80, 151e157. Ryzhakova, N.K., Ramenskaya, G.A., 2012. Methods and results of the coefficients emanation clay soils Tomsk. Geoecol. Eng. geol. Hydrogeol. Cryopedol. 2, 168e176. Ryzhakova, N.K., Shestak, A.P., 2009. Methods and results of measuring the effective diffusion coefficient of radon in soil. Geoecol. Eng. geol. Hydrogeol. Cryopedol. 6, 555e563. Ryzhakova, N.K., Yakovleva, V.S., 2004a. Estimation of radon convection rate in soils by the measured values of pore activity. Geoecol. Eng. geol. Hydrogeol. Cryopedol. 1, 1e5. Ryzhakova, N.K., Yakovleva, V.S., 27.11.2004b. Way of measurement of radon-222 emanation factor in the land. The patent for the invention N 2239207. Sahoo, B.K., Mayya, Y.S., 2010. Two dimensional diffusion theory of trace gas emission into soil chambers for flux measurements. Agric. For. Meteorol. 150, 1211e1224. Sahoo, B.K., Mayya, Y.S., Sapra, B.K., Gaware, J.J., Banerjee, K.S., Kushwaha, H.S., 2010. Radon exhalation studies in an Indian uranium tailings pile. Radiat. Meas. 45, 237e241. Sakoda, A., Ishimori, Y., Hanamoto, K., Kataoka, T., Kawabe, A., Yamaoka, K., 2010. Experimental and modeling studies of grain size and moisture content effects on radon emanation. Radiat. Meas. 45, 204e210. Savovi c, S., Djordjevich, A., Tse, P.W., Krsti c, D., 2011. Radon diffusion in an anhydrous andesitic melt: a finite difference solution. J. Environ. Radioact. 102 (2), 103e106. Sun, K., Guo, Q., Zhuo, W., 2004. Feasibility for mapping radon exhalation rate from soil in China. Nucl. Sci. 41 (1), 86e90. Yu, C., Loureiro, C., Cheng, J.eJ., et al., 1993. Data Collection Handbook to Support Modeling Impacts of Radioactive Material in Soil. Environ. Assessment and Information Sci. Division. Argonne National Laboratory, Argonne, Illinois. Zhuo, W., Iida, T., Furukawa, M., 2006. Modeling radon flux density from the Earth’s surface. J. Nucl. Sci. Technol. 43 (4), 479e482.
Contents lists available at ScienceDirect
Journal of Environmental Radioactivity journal homepage: www.elsevier.com/locate/jenvrad
A new method for estimating the coefficients of diffusion and emanation of radon in the soil Nadezhda K. Ryzhakova* Tomsk Polytechnic University, 30 Lenin Ave., Tomsk 634050, Russia
a r t i c l e i n f o
a b s t r a c t
Article history: Received 17 June 2013 Received in revised form 19 March 2014 Accepted 6 April 2014 Available online
This paper describes a new method for determining the basic parameters of soil - diffusion and emanation coefficients related to the transfer of radon in the soil matrix, which are very useful for testing models, based on diffusion and characteristics of various soil matrices regarding the dangers of radon. The method is based on the measurement of radon in soil air on two small depths, differing twice. The paper presents the results of the determination of the parameters for covering loams and clays of Tomsk (Russian Federation), obtained by this method. Ó 2014 Elsevier Ltd. All rights reserved.
Keywords: Radon transfer Mathematical modeling Diffusion coefficient Emanation coefficient
1. Introduction In solving the problems associated with radon e evaluation of radon prone region, prospecting and exploration of radioactive ores, predicting seismic areas - the method of mathematical modeling of radon transport through porous media is widely used (Der Poel, 2002; Koarashi et al., 2000; Miklyaev et al., 2008; Novikov, 1989; Rogers and Nielso, 1991; Ryzhakova, 2009; Sahoo and Mayya, 2010; Savovi c et al., 2011; Sun et al., 2004). Moving in the soil, radon is involved in various physical processes of molecular diffusion in air and water phases of the soil, convection and turbulent mixing of air in the surface layers of soil due to changes in atmospheric conditions (pressure, temperature, wind speed and direction), filtration with the upward water flows; moving by gas lift force generated when the soil pores are filled with water, in the process of exchange between the air, water and solid soil phases. The diversity and complexity of these processes depending also on the constantly changing weather conditions, do not allow to build a precise mathematical model of transport of radon through soils. Therefore, in simulating the semi-phenomenological approach is used, where the dispersed porous medium is replaced by a continuous medium and geophysical properties of the soil and transport mechanisms are described by means of the effective parameters.
* Tel.: þ7 9059900827. E-mail address: [email protected]. http://dx.doi.org/10.1016/j.jenvrad.2014.04.002 0265-931X/Ó 2014 Elsevier Ltd. All rights reserved.
The best known are the diffusion and diffusion-convection models, the practical use of which is hampered by the ambiguous interpretation of the physical nature of simulation parameters, and, as a consequence, by the problems with the choice of methods for their determination. It is particularly difficult to interpret and determine the parameters, describing the movement of radon in soils, diffusion coefficient De e in diffusion model, and diffusion coefficient D and convection velocity y e in diffusionconvection model (Ryzhakova, 2012; Ryzhakova and Yakovleva, 2004a). In most papers on the transfer of radon, the physical meaning of these parameters (as well as the emanation coefficient Kem) is not disclosed, and the methods of their determination are not justified. Moreover, the values obtained under laboratory conditions, when there is no influence of the atmosphere, are often used in simulation. In addition, during the preparation of samples for measurement the physical properties of soils are changed, especially porosity and humidity that have a significant effect on the radon emanation and transport (Breitner et al., 2010; Chauhan et al., 2008; Ryzhakova and Ramenskaya, 2012; Ryzhakova and Shestak, 2009; Sakoda et al., 2010; Yu et al., 1993; Zhuo et al., 2006). The parameters used in the semiphenomenological description of the transfer of radon are empirical in nature and must therefore be determined under conditions of natural occurrence of soils (Ryzhakova, 2012; Sahoo et al., 2010). For example, the diffusion coefficient De, used in the diffusion model should take into account all the processes by which radon is moved to the soil surface,
64
N.K. Ryzhakova / Journal of Environmental Radioactivity 135 (2014) 63e66
including processes caused by the influence of the atmosphere (Ryzhakova and Shestak, 2009). A similar situation occurs with respect to the coefficient of emanation Kem, which is usually defined as the proportion of radon released to loose pores of the soil. In particular, just this value is measured by g-method (Miklyaev et al., 2005) in the measurement of emanation coefficient. However, under natural conditions not all radon, caught in the loose pores of the soil, comes to the surface. In the result of metabolic processes occurring in the air, water and solid phases of soil a part of radon is adsorbed on the surface of solid particles and is dissolved in the water contained in the pores. This is evidenced by, for example, the fact that the coefficients of emanation measured by a laboratory gmethod are 1.5 . 2 times larger than the values obtained under natural conditions (Krampit, 2004; Miklyaev et al., 2005). The purpose of this work is to determine the average values for the diffusion and emanation coefficients using measurements of radon volumetric activity in the soil air at two small depths (less than 1 m). Measurements were carried out in loams of Tomsk (Russian Federation) on 10 different sites with exposure time (3 . 4) days that allows to smooth spatial and temporal variations of radon (Iakovleva and Ryzhakova, 2003). 2. Definition of the radon transport related parameters of the soil in natural conditions The known methods for determining the diffusion and emanation coefficients under natural conditions are rather laborconsuming. An external source of radon and carrying out repeated (10 . 15) measurement of radon volumetric activity in soil air within a day are required in the method of “an instant source” (Bulashevich and Kartashov, 1957; Ryzhakova and Shestak, 2009) for determination of the diffusion coefficient. Other method of De determination is based on simultaneous measurement of radon volumetric activity at several depths (not less than 5 . 6) (Ryzhakova and Shestak, 2009). In paper (Krampit, 2004) the emanation coefficient was calculated by radon equilibrium activity measured at depth not less than 3 . 4 m. Tomsk Polytechnic University (Russian Federation) has developed a simple, cheap and reliable method for determining the diffusion and emanation coefficients of soil associated with the transfer of radon in the soil matrix, which are very useful for testing models based on diffusion and characterization of various soil matrices in terms of the radon risks. The method is based on the measurement of radon at two small depths, differing by half. The use of two depths, differing twice, allows to get simple formula to determine the radon transport related parameters of the soil on the basis of radon transport equation for a homogeneous porous medium (Ryzhakova, 2007; Ryzhakova and Yakovleva, 2004b). In our work, for this purpose we used the diffusion equation of radon transport in porous media:
l l d2 A Aþ Kem ARa rd ¼ 0; De h dz2 De
where AN ¼ Kem ARa rd =h e value of radon volumetric activity in the air of soil pores at large depths. Using expression (2) one can write the system of equations for two depths of measurements, differing twice. And formulae to determine radon transport related parameters of soils can be obtained from this system of equations:
l$h21 De ¼ h i2 ; ln AA21 1 Kem ¼
A1 $h ; 2 AA21 ARa rd
3. Measurement methods Measurements of radon volumetric activity in the air of soil pores were carried out simultaneously in two blast-holes by track detectors of IPRR type (individual passive radon radiometer) or by radiometer RRA-01M-03 on 10 sites of Tomsk in the Russian Federation. Recommended depths of measurements are w(1 . 2) of the diffusion length. To provide the homogeneity of soils on chosen sites, the upper soil layer with thickness of (0.3 . 0.5) m was taken off. For observable loose dispersed soils (clay sand, loam) the recommended depths h1 and h2 are (0.4 . 0.6) m and (0.8 . 1.2) m correspondingly. The passive track detectors or samplers were placed into both blast-holes with diameter of 5.5 cm. Then the
(1)
(2)
(4)
where A1, A2 e value of radon volumetric activity measured at the depths h1 and h2 respectively, h2 ¼ 2h1. The main condition of the method applicability e measured soils should be fairly uniform in depth, especially in mineralogical composition. This condition is nearly always fulfilled (except technogenic soil), since the thickness of the “active layer” in which the radon can come to the surface is relatively small and does not exceed a few meters. To obtain the most accurate results, the depth of measurements by the order magnitude pffiffiffiffiffiffiffiffiffiffiffi should be commensurate with the length of diffusion L ¼ De =l. For example, for the loose disperse soils, loams types, the depth h1 is about (0.4 . 0.6) m. At such depths the volumetric activity of radon varies with depth, and the dependence is nonlinear. At smaller depths, when the dependence of volumetric activity on the depth is close to linear one, formulae (3), (4) don’t work, and at larger depths the radon volumetric activity varies slightly, that can cause a large error in determination of parameters.
where A e radon volumetric activity in the air of soil pores, Bq/m3; ARa e specific activity of Radium, contained in the soil, Bq/kg; rd e density of dry soil, kg/m3, h e porosity of the medium, defining the volume share of soil, which is the share of pores filled with air; l ¼ 2.1$106 e radon decay constant, 1/s (coordinate z is calculated from the surface of porous medium). For the homogeneous soil layer under zero boundary conditions A(0) ¼ 0 the solution of Equation (1) is written as:
ffiffiffiffiffiffiffiffi p AðzÞ ¼ AN 1 e l=De z ;
(3)
Fig. 1. Diagram of pore activity measurement (D e radon detector).
N.K. Ryzhakova / Journal of Environmental Radioactivity 135 (2014) 63e66
65
Dried to constant mass and milled soil samples were placed in hermetically sealed vessels of Marinelli with a working volume of 1 L and held for w(14 . 20) days until a radioactive equilibrium is established between radium and its decay products. Specific content of 226Ra was determined by the lines of daughter products of radon decay: 295 keV and 352 keV, belonging to 214Pb, and line 609 keV, belonging to 214Bi. 4. Measurements results
Fig. 2. Diagram of measurement installation (1 e lead; 2 e iron; 3 e aluminum; 4 e soil sample; 5 e semiconductor detector; 6 e chamber filled with nitrogen).
blast-holes were closed in the top and covered with a layer of earth (distance between blast-holes is not more than 0.5 m) (Fig. 1). A necessary condition of measurements is the absence of water in blast-holes. Excluding the lowland and wetlands, the groundwater level is usually much lower than the recommended depths (deeper than 2 m). When measuring volumetric activity of radon by track detectors of IPRR type the exposure time was 3 . 4 days, and then removed from the radiometer detectors were subjected to chemical etching, drying and counting tracks in accordance with the procedure described in Nikolaev and Ilic (1999) and Durrani and Ilic, (1997). When using a sampler of radiometer RRA-01M03 the exposure time was one day. Therefore, at each point 3 measurements of radon volumetric activity were carried out sequentially and in calculations of emanation and diffusion coefficients according to formulae (3, 4) the average values were used. Simultaneously with the measurements of radon volumetric activity soil sampling was carried out to determine its physical properties: density of the dry soil rd, porosity h and radium content in the soil ARa. Measurement of radium’s content was carried out by gammaspectrometric method (Measurement methodology, 2013) with a help of germanium detector of DGDK e 100 V type with sensitivity of 200 mm2 and resolution of 3 keV on the line of cobalt 1332 keV. Protection of detector is provided by low-background chamber (LBC), which is a combined protection in the form of consecutive set of layers from protective materials with internal sizes (285 285 450) mm3 (Fig. 2). The main protective material is lead with density of 100 mm in all directions regarding to detector. To reduce the contribution in instrument spectrum of homoenergetic line of characteristic X-ray from lead, internal surface of chamber is coated with layer of steel (10 mm) and layer of aluminum (10 mm). A support under LBC, in which Dewar vessel with liquid nitrogen is placed, is also coated with lead with thickness of 50 mm.
Table 1 shows measured at two depths h1, h2 values of radon volumetric activity A1, A2, averaged over the two depths the physical properties of soils, and the parameters of Kem, De, defined by the formulae (3), (4), for 10 sites of Tomsk. The average values of the diffusion and emanation coefficients for loams of Tomsk are De ¼ 0:91$106 m2 s1 and K em ¼ 6:6%; confidential intervals for average values at sample of n ¼ 10 and a significance level 0.05 equal 0.59$106 m2 s1 and 2.9% respectively. The range of values of the diffusion coefficient (0.14 . 2.44)$106 m2 s1 is in good agreement with the results of other studies (Iscandar et al., 2004; Nazaroff and Nero, 1988; Yu et al., 1993) and the data obtained previously by other, more laborintensive methods - the method of instantaneous point source (Ryzhakova, 2012), and based on measurements of the distribution of radon volumetric activity of soil depth (Ryzhakova, 2009). The range of values of the loams emanation coefficients Kem of loose disperse soils of Tomsk (sandy loam, loam) (1.6 . 15) % is consistent with the data for this value reported in the literature for these types of soils (Krampit, 2004; Miklyaev et al., 2005; Nazaroff and Nero, 1988; Yu et al., 1993). The average value of emanation, obtained by in-situ method is about 6.6%, which is about twice less than the values obtained by the gamma method (Ryzhakova and Ramenskaya, 2012). The same difference in the values of Kem, determined by in-situ and gamma method is observed for the soils of Moscow (Krampit, 2004; Miklyaev et al., 2005). Most likely this difference is related to the fact that in using of gamma method the soils are dried and milled, i.e. change their moisture and porosity. Coefficient of variation V ¼ s$100=x for values De and Kem amounts to: 85% and 57% correspondingly; here sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n P s¼ ðxi xÞ2 =ðn 1Þ dispersion of sampling. As it was exi¼1
pected, the spread in values of De is greater than for value Kem, because of the emanation coefficient depends only on physical properties of soil (measurement are carried out in different points), and values of diffusion coefficient are influenced in addition by atmospheric conditions. 5. Conclusion This paper describes a new method for determining the radon transport related parameters of the soil associated with the transfer of radon in the soil matrix, which are very useful for
Table 1 The measured values of radon volumetric activity, the physical properties and the basic parameters clay soils of Tomsk. Site N
1
2
3
4
5
6
7
8
9
10
h1, m A1, kBq m3 A2, kBq m3 , % $103, kg m3 , Bq kg1 Kem, % De$106, m2 s1
0.5 3.85 1.15 6.04 1.8 50 1.3 23 15 1.81
0.5 3.6 1.08 5.21 1.56 41.5 1.5 61 3 0.78
0.5 1.18 0.35 1.64 0.49 58 1.1 22.5 4.2 0.43
0.5 1.9 0.57 2.34 0.7 53 1.25 25.5 4 0.22
0.5 1.78 0.53 2.20 0.66 59.5 1.1 24 5.2 0.23
0.5 2.57 0.77 3.23 0.97 59 1.05 24 7.9 0.24
0.5 5.73 1.72 6.53 1.96 45.5 1.4 27 8 0.14
0.6 1.80 0.54 2.70 0.81 56 1.1 17 10.8 1.54
0.5 1.70 0.51 2.60 0.78 50.5 1.3 23.5 6 1.31
0.6 1.40 0.42 2.20 0.66 25.5 2.05 25 1.6 2.44
66
N.K. Ryzhakova / Journal of Environmental Radioactivity 135 (2014) 63e66
testing models based on diffusion and characterization of various soil matrices regarding the dangers of radon. The method is based on the measurement of radon volumetric activity in soil pore space at two small, differing by half, depths. The method allows to determine the average value of the diffusion coefficient De and emanation coefficient Kem under conditions of natural occurrence in soil. De parameters and Kem parameters, defined by the proposed method, consider physical properties of soil and climatic conditions of the district, where measurements are carried out. Parameter De characterizes the speed of radon movement to the surface of the soil and takes into account all possible mechanisms for transport of radon to the surface of the soil, including those related to the effects of the atmosphere. Parameter Kem determines the amount of radon coming to the surface of the soil, and therefore can be used to estimate the radon potential of areas. It should be noted that the use of this method makes it possible to significantly reduce the labor intensity and cost of determination of the radon transport related parameters of soils under natural conditions.
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