Uranium Mill Tailings Cover Calculator - HELP
(last updated 26 May 2012)
Contents:
This calculator determines the radon fluxes and concentrations in multi-layer uranium mill tailings and cover systems, and it optimizes the cover thickness to satisfy a given flux constraint.
The calculator is a clone of the RAECOM code (Radiation Attenuation Effectiveness and Cover Optimization with Moisture Effects), as described in [Rogers 1984]. It performs one-dimensional, steady-state radon diffusion calculations for a multi-layer system.
In addition, the calculator optionally estimates the long-term moisture contents in each layer based on rainfall and evaporation, and adjusts the diffusion coefficients correspondingly.
For calculating radon flux from bare and/or water covered tailings, see the Uranium Mill Tailings Radon Flux Calculator
For calculating the gamma radiation attenuation from a uranium mill tailings pile cover, 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 layers may vary in the long term, depending on climatic conditions.
- Note that the optimization only concerns radon flux, while other factors, such as mitigation of infiltration, or resistance against erosion, biointrusion, etc., also affect the cover construction.
The properties of the tailings and cover system are defined in the Input Data table.
The Result field repeats the input data and shows the calculation results.
The contents of the Result field can be highlighted and copied for further use.
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 parameters to the values of the example given in [Rogers 1984], typical for a dry climate. It comprises the tailings (Layer 1), a clay cover (layer 2), and an overburden cover (layer 3). The thickness of the overburden layer is to be optimized to satisfy the permissible surface radon-222-flux of 20 pCi/m^{2}s (0.74 Bq/m^{2}s).
This table contains parameters describing the properties of each layer. Layer 1 is the tailings layer, covered by one or more cover layers.
- Thickness [m]
- Layer thickness
If the thickness of a layer is empty or 0, this and all following layers are discarded.
- Ra-226 Activity Concentration [Bq/g] · [pCi/g]
- Activity concentration of Radium-226 in the layer.
If no entry is made, a default of 0 is used.
A value can not only be entered for the tailings layer, but also for each other layer.
In case the value for the tailings layer 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)
- Rn-222 Emanation Fraction
- fraction of the total amount of radon-222 produced by radium decay that escapes from the soil particles and gets into the pores of the soil.
It depends on the soil 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.
- Porosity
- ratio of the pore volume (air- and water-filled) to the total volume of the soil
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 soil weight
- Fraction Passing #200 Mesh (75 µm)
- fraction by weight of the soil passing a No. 200 Mesh, corresponding to a particle diameter of 75 µm or less.
If no value is entered, no estimate for long-term moisture is performed for this layer.
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.
> 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 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 x 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.
- Entrance Radon flux to Layer 1 [Bq/m^{2}s] · [pCi/m^{2}s]
- Radon-222-flux from the subsoil into the tailings layer.
If -1 is entered, then a value is computed internally for infinitely thick subsoil.
If no value is entered, a default of 0 is used.
- Surface Radon concentration at top of system [Bq/m^{3}] · [pCi/L]
- Radon-222-concentration in air above the top cover.
If no value is entered, a default of 0 is used.
- Layer No. to be optimized
- No. of the layer, the thickness of which is to be optimized to meet the surface flux constraint.
The tailings layer (Layer 1) cannot be optimized.
If no value, or 0, is entered, no optimization is performed.
- Surface flux constraint for optimization [Bq/m^{2}s] · [pCi/m^{2}s]
- value that is to be attained for the radon-222-flux from the top layer to the atmosphere.
If no value, or 0, is entered, no optimization is performed.
The U.S. EPA standard set in 40 CFR 192 is 20 pCi/m^{2}s (0.74 Bq/m^{2}s) (see also legislation).
- Surface flux convergence criterion (fraction)
- error allowance for the surface flux from the constraint, expressed as fraction.
Enter 0.01 for a permissible error of 1%, for example.
If no value is entered, a default value of 0.001 is used.
- Annual Precipitation [cm]
If no value, or 0, is entered, no estimate for long-term moisture is performed.
- Annual Lake Evaporation [cm]
If no value, or 0, 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 contains some minor modifications vs. RAECOM:
- The activity unit can be selected (pCi or Bq).
- Some units have been changed to more convenient ones.
- The pore space radon source term for each layer, other than in RAECOM, is not entered directly, but it is calculated from the Ra-226 activity concentration and the radon emanation fraction. The layer bulk density rho_{b} (required for this calculation) is calculated from the porosity p using an assumed specific gravity g of 2.7 g/cm^{3}, as follows: rho_{b} = g * (1 - p),
- If no diffusion coefficient is entered for a tailings layer, a value is estimated from porosity and moisture data, according to [Rogers 1991].
- The calculator optionally estimates the long-term moisture contents in each layer, and adjusts the diffusion coefficients correspondingly.
- The number of optimization iterations has been limited to prevent hang-up in case no convergence occurs.
Apart from that, the calculator is a strict clone of the RAECOM code [Rogers 1984].
[Rogers 1980] V.C. Rogers, R.F. Overmyer, K.M. Putzig, et al.: Characterization of Uranium Tailings Cover Materials for Radon Flux Reduction , prepared for U.S. Nuclear Regulatory Commission, Washington, D.C., NUREG/CR-1081, March 1980, 172 p.
[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.
[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.