

ORIGINAL ARTICLE 

Year : 2016  Volume
: 39
 Issue : 4  Page : 177182 


A methodology for evaluation of absorbed gamma doserate factors for radionuclides distribution in soil
Kh A Allam
Department of Nuclear Law, Egyptian Nuclear and Radiological Authority, Cairo, Egypt
Date of Web Publication  13Feb2017 
Correspondence Address: Kh A Allam Egyptian Nuclear and Radiological Regulatory Authority, 3 Ahmed El Zommer, Nassr City, Cairo Egypt
Source of Support: None, Conflict of Interest: None  Check 
DOI: 10.4103/09720464.199975
After Fukushima accident, new approaches are found to be needed for the simulation of the absorbed doserate calculation due to different reasons; the large number of contaminated areas with different shapes, geometries, compositions, and densities. Furthermore, the effect of the depth profile of gammaemitting isotopes. In this work, a new home made computer software was developed based on a simple model for doserate factors computation of radionuclides distribution in soil. The software used Monte Carlo simulation for model solution. The developed software was used for studying the main factors that affect the exposure dose rate; among those are the contaminated soil (source term) geometries, the shape, the composition, and the density. In addition, the effect of radioactivity depth profile was studied using the soil layers' model. The results of the doserate factors show that (a) the variation of shape and the density has a slight effect on the calculation. The effect of source term composition was up to 7.4% from the standard one. (b) 98% of the dose rate comes only from the first 5 m lateral distance from the source term around the studied point. (c) The most important parameter was the depth profile of gamma emitters in soil, because about 50% of the dose rate comes from the first 5 cm of soil depth, about 20% from the second 5 cm layer, about 10% from the third 5 cm layer, and only less than 2% comes from the eighth 5 cm layer. Finally, besides the model simplicity in this work, the associated software is fast, and the calculated results are compatible with the international models. Keywords: Absorbed doserate factors, geometric variations, Monte Carlo simulation, soil radioactivity
How to cite this article: Allam KA. A methodology for evaluation of absorbed gamma doserate factors for radionuclides distribution in soil. Radiat Prot Environ 2016;39:17782 
How to cite this URL: Allam KA. A methodology for evaluation of absorbed gamma doserate factors for radionuclides distribution in soil. Radiat Prot Environ [serial online] 2016 [cited 2020 Feb 22];39:17782. Available from: http://www.rpe.org.in/text.asp?2016/39/4/177/199975 
Introduction   
After Fukushima accident, evaluating the radiation dose rates was needed in wide radioactive contaminated areas. The people living in Fukushima prefecture were expected to receive effective radiation doses of 1–10 mSv within the 1^{st} year of the catastrophe.^{[1]} Several “example locations” were identified, where the estimated radiation dose would exceed this range and reach levels between 10 and 50 mSv, two of which are cited by name: Namie and Iitate. In prefectures neighboring Fukushima, the estimated effective doses were calculated to be between 0.1 and 10 mSv/annum, whereas the effective dose for people in all other prefectures in Japan was estimated to be between 0.1 and 1 mSv/annum.^{[1]} The validity and reliability of these dose rate estimates are very important as it has impact on the dose assessment to people. New models are needed with simple methodologies which can be used in the calculation of results in several minutes by personal computer. The simulation models must have the ability to handle any source geometries, shape, density, composition, and gamma isotopes emitters.
The doserate calculations for external gamma exposure to photon emitters from contaminated soil were studied for more than four decades. The first methodology has been performed by Beck and Planque and Beck et al.^{[2],[3]} They used the polynomial expression matrix equation method for solving the soil/air transport problem to calculate the exposure rates 1 m above ground level for distributed sources of γ emitters in soil. The dose rates in the air were calculated for γ energies from 0.25 to 2.75 MeV for radionuclides commonly found in the natural environment. Furthermore, the dose rate was calculated by Kocher and Sjoreen using the pointkernel integration method by assuming the soil to be an infinite scattering medium for photons, and employing buildup factors to account for doses from uncollided and scattered photons.^{[4]} Soil properties, including the photon crosssectional data, were approximated to those of concrete. All the dose conversion factors were calculated, as usual, for a point receptor located 1 m above the ground. Recently, Monte Carlo techniques have been used almost exclusively to calculate absorbed dose rate in air. Chen developed a Monte Carlo algorithm to track the photon transport equation in the soil/air medium.^{[5]} One of the most important studies of air kerma rate per unit of soil mass for natural sources uniformly distributed in the ground was performed by Saito and Jacob.^{[6]} The photon transport calculations were carried out using the Monte Carlo program YURI,^{[7]} which has been verified through comparison with various experimental and theoretical data.
In all studies, the basic input calculation parameters are source term composition, shape, density, geometries, and the exposure point height. In earlier studies, many source term geometries, compositions, and densities were considered with different approaches.^{[2],[3],[4]}
In the Saito model, the source term simulated as an infinite slab.^{[6]} In the Clouvas models, two source term simulations were considered. In the first, source term simulated as a cylindrical shape of 40 m radius and 1 m depth.^{[8]} In the second, the source term simulated as a square slab with a side of 80 m and 1 m depth (the MCNP, MC, and GEANT codes used for calculations). Different source term compositions and densities used in Saito and Clouvas models.^{[6],[8]} In spite of the differences, the final results of Saito and Clouvas models were comparable.
To address the problems above, in this work, a new methodology based on a simple dose rate equation and software program has been developed. Based on the used methodology, two soils (source term) simulations were provided and studied. In the first, the source term was simulated as a cylindrical shape of 40 m radius and 1.5 m depth. In the second, the source term was simulated as a square slab with a side of 80 m and 1.5 m depth. These two simulations can handle the source term variation in geometries, density, and composition. Furthermore, the effect of radioactivity depth profile using the soil layers' model.
This paper describes an overview of the methodology, comparison of test results and also present parameters which effect the dose rate. The developed model has been used to study the dose rate in air versus source term shape, geometries, density, composition, and depth profile with constant activity concentration (1 Bq/kg).
The Methodology Specification and Software Description   
For a uniformly distributed gammaemitting isotope, the dose rate at any point P due to the isotope radioactivity in the infinitesimal volume dV at any other point at a distance R from point P separated by i number of media with media thickness r_{i} and µ_{i} total attenuation coefficient with coherent scattering in m ^{− 1} where i donates the media number as shown in [Figure 1].  Figure 1: Diagram for calculating dose at pint P from the gamma rays emitted from the volume element dV passing through i media
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Where D (r, E) is the absorbed dose rate in Gy/s, A is the activity concentration of the radioactive isotope in MBq/m ^{3}, Γ is the specific gammaray emission in Gy.m^{2}/MBq/h, µ_{i} is the total attenuation coefficient with coherent scattering m ^{− 1}. This parameter depends on the energy of the photon, r_{i} is the gamma ray traveled distance in a layer number i, R is the total distance between the point source and the calculation point in (m).
The dose rate at point P due to the entire isotope in the soil is computed from all the infinitesimal volume elements.^{[9]}
Equation 1 can be rewritten as:
Where the geometry factor g is defined as,
It applies to a given point within a volume source. The geometrical factor takes into account the effects of both distance and energy absorption on the intensity of gamma photons as they penetrate the medium.
This work gives a solution for Equation 2 using Monte Carlo technique for the studied shapes. In addition, produce new software based on proposed models using the Delphi programming language. The software is very simple with a visual interface, and it is easily applicable for daily work.
Model Parameters   
Source term shapes and geometries
The source term has two shapes simulated models as in Clouvas.^{[8]} The first model was simulated as a slab with 80 m length, 80 m width, and 1.5 m depth as shown in [Figure 2]. The second model was simulated as a cylinder with 40 m radius, 1.5 m depth as shown in [Figure 3].
Source term composition
In the present work, three source terms compositions were used. The first was soil composed of 58.3% SiO_{2}, 16.7% Al_{2}O_{3}, 8.3% Fe_{2}O_{3}, and 16.7% H_{2}O as in Saito,^{[6]} the second was sand composed of 100% SiO_{2} and the third was limestone composed 100% CaCO_{3}. All source terms densities were taken 1.0 g/cm ^{3} to eliminate the density effect. All with a unitary activity concentration (1 Bq/kg) of ^{238} U,^{232} Th, and ^{40} K.
Air composition
The air above source term has the same shape and geometries of the calculated model with 1 m height. It has an atomic composition of 75.5% N, 23.2% O, and 1.3% Ar and a density 0.0012 g/cm ^{3}.^{[6]}
Mass attenuation
The total mass attenuation coefficients with coherent scattering (cm ^{2}/g) calculated using the XCOM program: Photon Cross Sections Database (National Institute of Standards and Technology).^{[10]} This software has a database that can be used to calculate photons crosssections for scattering, photoelectric absorption, and pair production, as well as total attenuation coefficients, for any element, compound or mixture (Z ≤ 100), at energies from 1 keV to 100 GeV.
In this work, 24 gamma lines in ^{238} U chain (^{226} Ra,^{214} Bi, and ^{214} Pb), 32 gamma lines in ^{232} Th chain (^{228} Ac,^{224} Ra,^{212} Bi,^{212} Pb, and ^{208} Tl), one gamma line for ^{40} K, one gamma line for ^{137} Cs, nine gamma lines for ^{134} Cs, and four gamma lines for ^{131} I are taken into consideration for the doserate calculation.
Specific gammaray emission (Γ)
The radiation intensity from any given gammaray source is used as a measure of the strength of the source. The gammaradiation exposure rate from a point source of unit activity at unit distance is called the specific gammaray constant and is given in units of Sieverts per hour at 1 m from a 1MBq point source (or in the traditional system, roentgen per hour at 1 m from a 1Ci point source). The source strength may be calculated if the decay scheme of the isotope is known.^{[11]}
Where f_{i} is the fraction of the transformations that yield a photon of the i^{th} energy, E_{i} is the energy of the i^{th} photon in MeV, and µ_{i} is linear energy absorption coefficient in air of the i^{th} photon.
Isotopes data
The isotopes data such as decay gamma lines and the fraction of the transformations were taken from the isotope project. The isotopes project compiles evaluates and disseminates nuclear structure and radioactive decay data for basic and applied research.^{[12]}
Results   
Dose rate in air versus the source term shape
By considering the recent changes in decay data in present work, the results of conversion factors are compared with the international models and listed in [Table 1]. A comparison between this work and the international models are given in [Figure 4]a, [Figure 4]b, [Figure 4]c, the average values of the international models are given in solid straight lines. The differences between the studied slab model and the international models average values are 0.9% for ^{238} U series, 3.0% for ^{232} Th series and 1.9% for ^{40} K isotope, and for the studied cylindrical model, the differences are 2.15% for ^{238} U series, 0.114% for ^{232} Th series, and 0.67% for ^{40} K isotope. These results show that this work provides comparable results with the main international models, besides the simplicity of Equation 2. Now for the symmetry, the cylindrical simulated model will be used in all subsequent evaluations.  Table 1: Dose.rate conversion factors (nGy/h per Bq/kg) for different models
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 Figure 4: Comparison of dose conversion factors for ^{238}U (a), ^{232}Th (b), and ^{40}K (c) using different models (vertical axis is × 10 ^{−1})
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Dose rate in air versus the source term geometries
In the present work, the effect of source term geometries was studied by varying the radius of the cylindrical model. Starting from 5 to 40 m radius and 1.5 m depth with 5 m step, the percentage of change in the doserate conversion factors was calculated and plotted against the cylinder diameter as shown in [Figure 5]. The percentage of change in the dose rate from 5 to 40 m radius does not exceed 2.5%. Therefore, the most effective area around the calculation point is the first 5 m radius, which represents more than 97.5% of the dose rate values for ^{238} U,^{232} Th, and ^{40} K. As shown in [Figure 5], the three sets of conversion factors for ^{238} U,^{232} Th, and ^{40} K nearly have the same behavior with the source term geometries change.  Figure 5: Percent of change in doserate conversion factor with cylinder diameter
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Dose rate in air versus the source term density
Saito and Clouvas ^{[6],[8]} have used different densities of 1 g/cm ^{3} and 1.3 g/cm ^{3} respectively. Both the studies showed a comparable set of the doserate conversion factors in spite of density difference.
In the present work, the effect of density change on the dose rate was studied by varying the density from 1 to 2.5 g/cm ^{3} with 0.1 g/cm ^{3} increasing step. The results show that there is no change in the doserate conversion factors, which can be explained by as selfattenuation increases, the activity concentration in unit volume also increases with increasing density.
Dose rate in air versus the source term composition
Saito and Clouvas used two slightly different source terms compositions.^{[6],[8]} In the present work, the effect of source term composition on the dose rate was studied by using the three source term compositions. Results of doserate conversion factors tabulated in [Table 2]. The results show that the differences due to source term composition (between standard soil composition and other compositions) were up to 7.4% as shown in [Table 2]. The airborne fission products such as ^{131} I,^{134} Cs, and ^{137} Cs were observed in the soil following the Fukushima Daiichi Nuclear Power Plant.^{[13]} Due to their importance for the doserate calculation, the doserate conversion factors for ^{137} Cs,^{134} Cs, and ^{131} I are also computed and listed in [Table 2].  Table 2: Dose.rate conversion factors (nGy/h per Bq/kg) values for different source term composition
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Dose rate in air versus the source term layers' contribution
In the present work, the effect of different source term layers on the dose rate was studied by dividing the source term thickness into slabs. Each slab with 0.05 m depth, then the dose rate was calculated due to each slab separately as shown in [Figure 6]. The calculations carried out for eight slabs with 0.4 m depth, and its contribution was about 95% of the total dose rate. The first slab contribution is about 50% of the total dose rate as shown in [Figure 7]. Each slab contribution was decreasing with increasing slab depth due to the shielding effect of the upper slabs as shown in [Figure 6]. From above results, we can conclude that the upper layer (0.4 m depth) is the most effective layer in the doserate calculation.
Discussion and Conclusions   
The results of the study of the parameters for absorbed doserate factors for 1 m above the ground for gamma emitters show that:
 The used model gives very comparable results with complicated international models
 In addition, the shape of the source term (cylindrical, slab) has an insignificant effect on the doserate factors. Those results can be taken as a model result verification
 98% of the dose rate comes only from the first 5 m around the studied point
 The source term density has a very small or negligible effect on the dose rate factors because as selfattenuation increases the activity concentration in unit volume also increases (the activity per unit weight is constant)
 The most important parameter in the doserate calculation was the gamma emitters depth profile. About 50% of the dose rate comes from the first 5 cm of soil depth, about 20% from the second 5 cm layer, about 10% from the third 5 cm layer, and only <2% comes from the eighth 5 cm layer
 In the light of its simplicity, the developed model is suitable for assessment of the dose rate in case of nuclear and radiological accidents.
Financial support and sponsorship
Nil.
Conflicts of interest
There are no conflicts of interest.
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[Figure 1], [Figure 2], [Figure 3], [Figure 4], [Figure 5], [Figure 6], [Figure 7]
[Table 1], [Table 2]
