Uranium Mill Tailings Radon Flux Calculator - HELP
(last updated 4 Apr 2023)
Contents:
This calculator determines the radon flux from a bare and/or water-covered uranium mill tailings pile.
The calculator is based on the paper [Nielson 1986]. It performs one-dimensional, steady-state radon diffusion calculations for the following zones of the tailings deposit: the zone submerged under ponding water, the saturated beach zone, and the unsaturated zone:
In addition, the calculator optionally estimates the long-term moisture contents in each tailings zone based on rainfall and evaporation, and adjusts the diffusion coefficients correspondingly.
For calculating the effects of soil covers, see the Uranium Mill Tailings Cover Calculator.
For calculating the gamma radiation from a uranium mill tailings pile, see the External Radiation Dose Calculator.
- Note that some of the parameters show wide ranges of variation. Meaningful results for actual sites can only be obtained, if site-specific data is used.
- Note that the moisture contents of the tailings may vary in the long term, depending on climatic conditions.
The properties of the tailings are defined in the Input Data table.
The Result field repeats some input data and shows the calculation results.
The contents of the Result field can be highlighted and copied for further use.
1 Ci = 10^{12} pCi
1 TBq = 10^{12} Bq
The values in the "Total/Avg." row are either totals (Surface Area and Total Rn-222 Release), or area-weighted averages (others). Therefore, the "Avg. Ra-226 Act.Conc." may differ from the overall (weight-averaged) Ra-226 Activity Concentration.
This calculator is suitable for offline use.
The Activity unit can be selected for the whole calculator as pCi (pico-Curie = 10^{-12} Ci) or Bq (Becquerel). This selection must be made before any other entry, since it resets the complete calculator.
The button "Sample Data" initializes the tailings parameters to example values, most of which are given in [Nielson 1986].
- Ra-226 Activity Concentration in tailings [Bq/g] · [pCi/g]
- Overall activity concentration of radium-226 in the tailings material.
In case the value is unknown, it can be estimated from the grade of the ore processed in the uranium mill. Assuming secular equilibrium in the ore between uranium-238 and radium-226, and that all radium goes into the tailings, an ore grade of 0.1% U (or 0.1179% U_{3}O_{8}) corresponds to a Ra-226-concentration of 12.4 Bq/g (334 pCi/g). (see also Unit Converter)
- Ra-226 Activity Ratio in slimes vs. sand
- Ratio of radium-226 activity concentrations in the slimes fraction vs. the sand fraction of the tailings material.
The activity concentrations typically increase with decreasing particle size. [Nielson 1986] uses a value of 4.
- Rn-222 Emanation Fraction in slimes
- fraction of the total amount of radon-222 produced by radium decay that escapes from the slimes fraction of the tailings particles and gets into the pores of the material.
It depends on the tailings material and the moisture content. It varies over a range of 0.1 - 0.4 or more; typical values are in the range of 0.2 - 0.3.
- Rn-222 Emanation Fraction in sand
- fraction of the total amount of radon-222 produced by radium decay that escapes from the sand fraction of the tailings particles and gets into the pores of the material.
It depends on the tailings material and the moisture content. It varies over a range of 0.1 - 0.4 or more; typical values are in the range of 0.2 - 0.3.
- Fraction Passing #200 Mesh (75 µm)
- fraction by weight of the overall tailings material passing a No. 200 Mesh, corresponding to a particle diameter of 75 µm or less.
Since 75 µm particle diameter marks the sand/silt dividing line, this figure denominates the fraction that is not sand, or the fraction of combined silt and clay contents ("slimes").
> See also U.S. Department of Agriculture (USDA) diagram of soil textures [Yu 1993]
- Fraction of pond area with less than 1 m depth
- Average pond depth for areas greater than 1 m deep [m]
- Ra-226 Activity Concentration in ponding water [Bq/L] · [pCi/L]
- activity concentration from dissolved radium-226 in the ponding water
If no value is entered, the value is calculated using the following parameter.
- Ratio of radium in solution to radium in tailings solids [g/cm^{3}]
- used to determine radium-226 concentration in the ponding water, if no value is entered for the previous parameter; otherwise any ratio entered is discarded.
[Nielson 1986] uses a value of 8.92 x 10^{-4} g/cm^{3}.
- Effective stagnant water transport coefficient [m^{2}/s]
- describes radon transport in water
[Nielson 1986] determined a value of 3 x 10^{-7} m^{2}/s
This table contains parameters describing the specific properties of each tailings zone, that is the zone submerged under ponding water, the saturated beach zone, and the unsaturated zone.
- Surface Area [m^{2}]
- Area covered by the zone
If this field is empty or 0, this zone is discarded.
- Bulk Density [g/cm^{3}]
- Dry bulk density of the tailings material in this zone
If no value, or 0, is entered, a value is estimated using the porosity and a specific gravity of 2.7 g/cm^{3}.
- Porosity
- ratio of the pore volume (air- and water-filled) to the total volume of the tailings
If no value, or 0, is entered, a value of 0.4 is used.
Sand | 0.25 - 0.50 |
Silt | 0.35 - 0.50 |
Clay | 0.40 - 0.70 |
- Moisture Contents [dry wt_%]
- percentage of water weight to dry tailings weight
This value is only required for the unsaturated zone, since moisture saturation is assumed for the submerged and the saturated zones.
- Fraction Passing #200 Mesh (75 µm)
- fraction by weight of the tailings passing a No. 200 Mesh, corresponding to a particle diameter of 75 µm or less.
Since 75 µm particle diameter marks the sand/silt dividing line, this figure denominates the fraction that is not sand, or the fraction of combined silt and clay contents ("slimes").
> See also U.S. Department of Agriculture (USDA) diagram of soil textures [Yu 1993]
- Rn-222 Effective Diffusion Coefficient [m^{2}/s]
- defined from Fick's equation as the ratio of the diffusive flux density of radon activity across the pore area to the gradient of the radon activity concentration in the pore or interstitial space.
If no value, or 0, is entered, a value is calculated from porosity and moisture contents according to [Rogers 1991].
Caution: The effective (or interstitial) diffusion coefficient D_{e} is not to be confused with the bulk radon diffusion coefficient D. D is obtained by multiplying D_{e} by the total soil porosity. The use of the terminology for the diffusion coefficients in literature is highly inconsistent - in some cases, the symbols of D and D_{e} are used reversely!
The diffusion coefficient in porous media is a property of the diffusing species, the pore structure, the type of fluids present in the pores, the adsorption properties of the solid matrix, the fluid saturations, and temperature.
The effective radon diffusivity values in porous media (soils and concrete included) vary over a wide range of several orders of magnitude depending on the porous material and particularly on its degree of water saturation. Typically, the effective diffusion coefficient of radon in unconsolidated soil material with a low moisture content is about 10^{-6} m^{2}/s. The upper limit is represented by the radon diffusion coefficient in open air, D_{o}, which is about 1.1 · 10^{-5} m^{2}/s. At the lower extreme, in a fully saturated soil material the radon diffusion coefficient may be as low as 10^{-10} m^{2}/s.
Values ranged from 7.4 · 10^{-7} to 6.0 · 10^{-9} m^{2}/s, averaging 1.42 · 10^{-7} m^{2}/s at four uranium waste disposal sites in the western United States (Fuhrmann 2023).
- Annual Precipitation [cm]
If no value is entered, no estimate for long-term moisture is performed.
- Annual Lake Evaporation [cm]
If no value is entered, no estimate for long-term moisture is performed.
- Depth to Water Table [m]
- If no value, or 0, is entered, a deep water table is assumed. This parameter is only used for estimating long-term moisture.
The calculator performs the calculations described in [Nielson 1986]. For the submerged zone, it considers (1) radon transport from the tailings through the ponding water to the surface, and (2) radon released from radium dissolved in the ponding water. It assumes that all radon reaching the top 1 meter layer of the water is released into the air, as well as all radon produced from dissolved radium in this top layer.
In addition, the calculator offers the following two features:
- If no diffusion coefficient is entered for a tailings zone, a value is estimated from porosity and moisture data, according to [Rogers 1991].
- If precipitation and evaporation data is entered, the calculator estimates the long-term moisture contents in each zone, and adjusts (or estimates) the diffusion coefficients correspondingly, according to [Rogers 1984]. (The Rn-222 emanation fractions are not adjusted, however; but this introduces errors only for very low moisture contents of less than approx. 10 dry wt_%.)
If evaporation is higher than precipitation, then the calculator assumes that the pond disappears; otherwise it assumes that the extension and depth of the pond is unchanged, and adjustments are only performed for the initially saturated and unsaturated zones.
[Nielson 1986] Nielson, K.K., V.C. Rogers: Surface water hydrology considerations in predicting radon releases from water-covered areas of uranium tailings ponds, in: Geotechnical & Geohydrological Aspects of Waste Management / Fort Collins / 1986, p. 215-222
[Rogers 1984] Rogers, V.C., K.K. Nielson, D.R. Kalkwarf: Radon Attenuation Handbook for Uranium Mill Tailings Cover Design , prepared for U.S. Nuclear Regulatory Commission, Washington, D.C., NUREG/CR-3533, PNL-4878, April 1984, 87 p.
[Rogers 1991] Rogers, V.C., K.K. Nielson: Correlations for Predicting Air Permeabilities and Rn-222 Diffusion Coefficients of Soils, in: Health Physics Vol. 61, No. 2 (August 1991), p.225–230.
[Silker 1979] W.B. Silker, P.G. Heasler, Laura E. Santos: Diffusion and Exhalation of Radon from Uranium Tailings , prepared for U.S. Nuclear Regulatory Commission, Washington, D.C., NUREG/CR-1138, PNL-3207, October 1979, 140 p.
[Yu 1993] C. Yu, J.J. Cheng, et al.: Data Collection Handbook To Support Modeling Impacts Of Radioactive Material In Soil , Environmental Assessment and Information Sciences Division, Argonne National Laboratory, Argonne, Illinois, ANL/EAIS-8, April 1993, 165 p.