Finite element modeling of radon distribution in natural soils of different geophysical regions

Figures & data

Table 1. Exact and numerical solution for the patch test program

Distance (m)	Y-value
	Exact solution	Numerical value
x	Y	Y1	Y2	Y3
0.0	1.0000000000	1.0000000000	1.0000000000	1.0000000000
0.2	1.4000000000	1.3999999912	1.4000000012	1.4000000000
0.4	1.8000000000	1.7999999862	1.8000000027	1.8000000001
0.6	2.2000000000	2.1999999862	2.2000000023	2.2000000001
0.8	2.6000000000	2.5999999947	2.6000000012	2.6000000000
1.0	3.0000000000	3.0000000000	3.0000000000	3.0000000000
No. of elements	–	5	10	100

Figure 1. The experimental radon profile with soil depth for Greece 1 and Greece 2 data and radon experimental extrapolation to soil surface.

Figure 2. (a) and (b) The experimental radon profile with soil depth for Greece 1 and Greece 2 data, respectively, compared to the model calculations using one, two, and three-layered assumptions.

Table 2. The effective diffusion coefficient, D (cm² s⁻¹) of radon in natural soil for the different layers calculated for some countries

Country	Region	Data	1-Layer	2-Layers		3-Layers
			D1	D1	D2	D1	D2	D3
Greece	Greece 1		0.085	0.030	0.080	0.025	0.048	0.085
	Greece 2		0.070	0.035	0.075	0.030	0.090	0.070
Germany-Seik	BT-1			0.005	0.019
	BT-2			0.002	0.027
	FT-1			0.013	0.032
	FT-2			0.012	0.027
South Africa	M 1			0.003	0.016
	M 2			0.003	0.022
Jordan	AHP-Summer			0.0015	0.0120
	AHP-Winter			0.0015	0.0100
	Basalt-Summer			0.0030	0.0250
	Basalt-Winter			0.0030	0.0200

Table 3. The calculated soil surface radon concentration, C_o (Bq m⁻³) and radon surface flux, q_o (mBq m⁻² s⁻¹) for the different countries

Data		Co field data** (Bq m^−3)	Co Model (Bq m^−3)	Radon flux (mBqm^−2 s^−1)
Greece	Greece 1	550–950	850	1.68
	Greece 2	300–2,200	1,640	3.17
Germany-Seik	BT-1	NA^*	350	0.70
	BT-2	NA	103	0.21
	FT-1	1,000	1,025	2.05
	FT-2	NA	940	1.88
South Africa	M 1	NA	710	1.42
	M 2	NA	3,525	7.05
Jordan	AHP-Summer	3,000	3,320	6.64
	AHP-Winter	2,000	2,730	5.46
	Basalt-Summer	4,000	4,115	8.23
	Basalt-Winter	2,500	2,390	4.78

^* Not Available.

^** Extrapolated linearly from the radon concentrations close to the soil surface.

Figure 3. The experimental radon profile with soil depth and two-layered model calculation for Germany-Seik data.

Figure. 4. The experimental radon profile with soil depth and two-layered model calculation for South Africa data.

Figure 5. The experimental radon profile with soil depth and two-layered model calculation for Jordan data.

Figure 6. The diffusion coefficient as a function of the soil depth for Greece data.