A Stochastic Approach Towards a Post Closure Safety Assessment

A STOCHASTIC APPROACH TOWARDS A POST CLOSURE SAFETY ASSESSMENT

A Ramlakan1, GP de Beer1, A Abrahams2, R Schneeweiss2

1NECSA, PO Box 582, Pretoria 0001, South Africa, E-mail: [email protected] 2Rössing Uranium Ltd, Private Bag 5005, Swakopmund, Namibia.

Abstract. Following an extensive data acquisition programme to identify and characterize sources on the mine as well as some enhanced background sources around the mine site, a post-closure safety assessment has been performed for the Rössing uranium mine in Namibia. The transport of radioactivity from these sources to exposed critical groups was studied through atmospheric and simple aquatic pathway models together with analyzed data and estimated parameters. Using dose models the doses to pre-identified critical groups were assessed for the various pathways in a deterministic safety assessment. The effect of some dust mitigation options was also assessed, while the effect of post-closure institutional control of water seepage was considered in the aquatic model. A stochastic assessment was next attempted to provide information on the possible range and distribution of the assessed doses in terms of uncertainties in the experimental data and parameters used. While insufficient data caused some difficulties, various approximate distributions have been obtained for several of the parameters used. Techniques range from the utilization of the means and standard deviations of analytical data, published parameter ranges and other approximate methods to estimate parameter distributions. Using random selections from these distributions, the dose distributions for various exposure pathways and scenarios have been assessed. The deterministic doses were used to distinguish those critical groups where doses would likely be above the dose constraint from those where doses would likely be below the dose constraint or trivial. The stochastic results indicate 90-percentiles generally at around two times the mean values, but up to 6 times for very skew distributions. It is also indicated that the statistical comparison with the dose distributions from background sources and of the lower detection levels of analytical results are other important criteria to consider.

1. Introduction

In order to address uncertainties in assessment parameters, a stochastic safety assessment was performed for the post-closure conditions at the Rössing Uranium mine. The stochastic assessment was very similar to a deterministic assessment, which was first performed through a set of coupled spreadsheets, but instead of using fixed assessment parameters, parameter values were presented as so- called assumption distributions. The assessed doses were hence also provided as distributions (so- called forecast distributions), obtained through random (Monte Carlo) selections using the software package Crystal Ball, [1] from the assumption distributions. The forecast distributions were then evaluated statistically. Apart from presenting some measure on the uncertainties of the assessed doses, the stochastic assessment also allowed statistical significance tests on the dose contribution of mine- related sources to doses assessed for sources of natural background.

Details on an extensive data acquisition programme for the assessment and on the safety aspects of the assessment results have been presented elsewhere [2, 3]. While this presentation again summarizes important aspects of both the parameters used and the broad assessment methodology, it focuses on the methods used and problems experienced to specify assumption distributions for the stochastic assessment and on the results of statistical significance tests.

2. Site Description

The Rössing uranium mine is situated in the Namib desert of Namibia about 65 kilometres inland from the coastal town of Swakopmund. It performs open pit mining of low-grade ore (around 350 ppm uranium). Following various crushing and milling operations, extraction of uranium as ADU and calcination to U3O8 is performed at the mine. Apart from the open pit, the main impact features are various ore stockpiles and the tailings dam. The mine is situated next to the non-perennial Khan river and three dry gorges (Dome gorge, Panner gorge and Pinnacle gorge) drain from the mining area into the river. About 30 kilometres from the mine the Khan river flows into the Swakop river, which again

1 flows into the Atlantic ocean at Swakopmund. Arial pictures of the mine site and surrounding region are indicated in Figures 1 and 2 respectively.

FIG.1. Arial picture of the Rössing uranium mine site

FIG.1. Arial picture of the region surrounding the Rössing uranium mine

3. Source Terms

Generally the major source is the tailings dam, which is a source of radon, dust and seepage water. While the complete dam is regarded as a single radon source, salt patches remaining after water evaporation from the water-collection ponds on the dam contain higher concentrations of some radionuclides and are considered as separate dust sources, which will be mitigated to various degrees by covers of waste rock. Seepage water is presently collected in seepage dams and recycled. After closure seepage water will continue to be recycled to evaporation areas during an active institutional control period.

3.1. Radon Sources

The main radon sources are: — The open pit, including the waste rock dumps. — The crushing circuit, including the coarse and fine ore stockpiles. — The tailings dam. — Contaminated areas around the plants — Background locations including areas with enhanced levels.

3.2. Dust Sources

The fugitive dust sources identified were the entire tailings dam surface, waste piles, the salt deposits on the tailings dam, and areas where fine material is deposited from seepage.

3.3. Aquatic Sources

The primary sources were the tailings dam run-off and seepage.

4. Pathway Analysis

The atmospheric and the aquatic pathways are the two major pathways considered. At the points of impact at the receptors, the contributions from the atmospheric and aquatic pathways provide source terms for the secondary pathways. It is at these points where the public can get exposed to radiation through various modes, notably ingestion, inhalation and external exposure.

4.1. Scenario Description

The scenarios presented below represent both present as well as potential future scenarios with respect to human habitation in and around the mining grant. The eight scenarios are:

4.1.1. Scenario 1

Scenario 1 represents the present scenario of the township of Arandis whose residents live and work in the town. Arandis is located approximately 15 kilometres to the north-west of the mine site. The atmospheric pathway is of primary importance.

4.1.2. Scenario 2

Scenario 2 is similar to Scenario 1, except that the actual critical group is assumed to live and work in the immediate vicinity of Arandis airport. The atmospheric pathway is of primary importance.

4.1.3. Scenario 3

Scenario 3 considers a small farming community, living on the banks of the Khan River immediately downstream of the confluence to the Dome gorge catchment, receiving a potential dose through human inhalation, human ingestion, as well as external air and soil exposure. All the water is obtained from the Khan River as groundwater and the human ingestion pathway is extended to include the dose contribution from vegetable, fruit and animal consumption. Both the atmospheric and groundwater pathways are of primary importance.

4.1.4. Scenario 4

Scenario 4 is similar to Scenario 3, but the small farming community is located on the banks of the Khan River immediately downstream of the confluence of the Panner gorge.

4.1.5. Scenario 5

Under this scenario, it is assumed that a small community lives and works on the old Khan Mine site. It is assumed that all water at this site originates from the West Coast water supply scheme. As for scenarios 1 and 2, the atmospheric pathway is of primary importance.

4.1.6. Scenario 6

Scenario 6 is similar to Scenario 1, except that instead of working within the township of Arandis, it is assumed that some small industries make use of the existing office infrastructure present at Rössing after mine closure. This scenario therefore assumes a population living in the township of Arandis, but working (for an average of 2000 hours per annum) in an office block on the old Rössing mine site. The atmospheric pathway is of primary importance.

4.1.7. Scenario 7

This scenario involves residents of Swakopmund, 60 km from the mine who would be exposed through the atmospheric pathway only. Drinking water is pumped from the supply system of the aquifers of the Omaruru and Kuiseb rivers, which are not in any way linked to catchment area of the mine. Food is mainly brought in from outside the country and only very limited quantities of food are sourced from the market gardening done in the vicinity of the town. During wind events small quantities of radon and dust could potentially be dispersed from the mine to the town.

4.1.8. Scenario 8

A number of smallholdings are situated on the banks of the Swakop river, around 50 kilometres downstream of the mine. Farmers engage in market gardening and animal products which are mainly sold in Swakopmund. Drinking water for humans and animal comes from the aquifers of the Omaruru and Kuiseb rivers. Irrigation water is pumped from the Swakop river. It is estimated that 30 % of the fodder is produced at the farms. Exposure occurs through the atmospheric and the aquatic pathway. The aquatic pathway assumes that 50 % of the farmer’s diet would consist of farm products. Water quality is assumed to be worst-case, that is mixed, according to hydro-geologically modelled mixing proportions, of the Khan and Swakop river groundwater.

4.1.9. Scenarios 9

This scenario looks at the background dose near the mine. It is similar to the radon and aquatic pathway parts of scenario 3, but uses the identified radon background sources and analytical water data for the Khan river upstream of the mine.

4.1.10. Scenario 10

This scenario looks at background dose near Swakopmund. It is similar to the radon and aquatic pathway parts of scenario 7, but uses the identified radon background sources and the analytical water data for the Swakop river upstream of the smallholdings.

4.1.11. Scenario 11

This assesses doses from the lower level of detection (LLD) for the aquatic pathway.

5. Distribution Data

Reliable data on the distributions of the various parameters are not readably available whereas available data mostly provide only limited information. In most cases only parameter ranges are

4 provided with expected values presented only in some cases. For others only ratios of expected and maximum values are presented. In the training manual for Crystal Ball the code distributor provides various suggestions on the use of distributions for cases where limited data are available. These were followed in some cases but other methods were also used. The manual for instance favoured triangular distributions in cases of insufficient information with minimum and maximum values at the range boundaries provided for the parameters and the median value at the provided or deduced expected value. In many cases it was felt, however, that the parameters should be described by a log-normal distribution and this was hence preferred. Attempts to fit such a distribution to available data (for instance to radio-analytical results) often failed, however, because a sufficient number of data values were not available while the available data favoured no particular distribution. In some of these cases estimates of the mean and standard deviation were rather obtained initially and used to describe the log-normal distribution. Where no data was available, the deterministic parameters were rather used without a distribution. The purpose of the stochastic assessment should hence rather be seen as an attempt to obtain some lower bound of the uncertainties in assessed doses, based on available information, rather than to provide quantitatively accurate results. The methodologies used to obtain assumption distributions are presented and discussed below.

5.1. Distribution Data Methodologies

5.1.1. Radon

The means and standard deviations of the mine contributions to the radon concentrations for all the scenarios were obtained from [4]. Log-normal distributions were assumed with these means and standard deviations. The means and standard deviations of the radon background concentrations were obtained from [5]. These were again assumed for log-normal distributions.

5.1.2. Aquatic Pathway

Water distributions were obtained as follows: Nuclide concentration measurements were provided, for a number of years, for the three gorges as well as the Khan river in [6]. A mean value was determined for the seepage flow by averaging the contributions from the Dome, Pinnacle and Panner gorges. A standard deviation was also calculated from the distribution of the concentration values. Similarly, a mean and standard deviation for the Khan river was calculated. These distributions were assumed to follow a log-normal distribution. A mixing model was used to obtain the mixed Khan and mixed Swakop river nuclide concentrations. The Khan river flow was taken to have a mean of 900 kL/day whilst for the Seepage flow a rate of 70 kL/day was used. The unmixed Swakop river water quality was calculated by assuming that the ratio of nuclide concentrations between the Swakop and Khan rivers is the same as the ratio between their alpha- activity concentration, namely (1.27) Bq/L/(2.04) Bq/L The mixed Swakop river quality was taken to be half of the Khan river quality. Standard deviations for the mixed Swakop river quality and the mixed Khan river quality were obtained by running Crystal Ball simulations on the mixing model. The water analysis database goes back to 1993 with initial high LLD’s for Th-230, Pb-210 and Ra-228. Thus, Ra-226 values were used for Th-230 and Pb-210 while Th-228 values were used for Ra-228.

5.1.3. Inhalation and Ingestion Dose Coefficients

As the dust inhalation pathway was not considered in the stochastic assessment, no distributions were obtained for the inhalation dose coefficients. Uncertainties in ingestion dose coefficients were extracted from [7, 8] and only addressed the uncertainty in the fraction f1 of the ingested activity absorbed from the gastro-intestinal tract into the blood. The level of confidence in individual absorbed fractions was estimated in terms of lower and

5 upper bounds, A and B, such that there is judged to be roughly a 90% probability that the true central value is no less than A and that there is no probability that it is greater than B. However, radionuclides used in [8] were different to those needed. Thus, (sigma/ dose coefficient mean) was calculated for all radionuclides used in [8]. To obtain uncertainties for radionuclides used in the safety assessment, the following principle was applied: For U-234, the ratio given for U-238 was used. For Th-230, Po-210, Pa-231, Ac-227, Th-232 and Th-228 the ratio given for Pb-210 was used. For Ra-223, Ra-228 and Ra-228 the same ratio given for Ra-226 was used. Using the presented f1 value as mean µ, the upper bound was calculated as µ.B/A and the lower bound as µ.A/B.

5.1.4. Transfer Coefficients

Uncertainty ranges for transfer coefficients were obtained from [9]. Where values were not available, values from a chemically similar radionuclide were used. Where these were not available the 10% lower bound was calculated by dividing the mean by 10 and the 90% upper bound by multiplying the mean by 10. Standard deviations were calculated from the ranges and log-normal distributions were assumed with the published expected values as means and these standard deviation values. Corrected transfer coefficients are used in the case where one needs the transfer coefficient of the wet mass of fresh products. The IAEA transfer coefficients in these cases are defined for dry mass of fresh products and the corrected transfer coefficients takes this into account by correcting with the ratio of wet and dry weights from [9] also presented in the table.

6. Stochastic Assessment Assumptions

The stochastic assessment was performed on an adapted copy of the spreadsheet used for the deterministic assessment. Adaptation involved the following: (a) Spreadsheet pages for the different dust sources and dust mitigation options were deleted beforehand as to save calculation time. (b) Assumption distributions were fitted only to those parameters for which published data on uncertainties could be found (consumption figures were for instance not varied). (c) Scenarios 9 and 10 were used to describe the dose from background. This was done as to eventually determine whether the mine-plus-background contribution was statistically distinguishable from the background-only distribution. For radon, the background dose distribution was obtained by repeating the dispersion assessment as for the mine sources, but using as a source measured radon exhalation rates from identified background areas near the mine. Scenario 11 was used to describe the dose originating from the lower detection limit. Assessment results are meaningless where concentrations below the minimum detection levels are recorded. A comparison with aquatic doses at the lower detection levels is thus also useful. (d) Different sets of identical parameters (e.g. a set of identical ingestion dose coefficients for each pathway with the other data for the relevant pathway) in the deterministic assessment spreadsheets were moved to a single page as suggested in the Crystal Ball training manual. This is required to allow repetitive Monte Carlo sampling, using the same random number sequence. (e) Merged cells were unmerged to prevent locked cells to be generated, because problems arise in Crystal Ball when such cells contain assumption distributions. (f) The various forecast distributions were defined with proper names and units for the variable. (g) A total of 10 000 Monte Carlo selections were made from each assumption distribution.

7. Stochastic Assessment Results

A stochastic assessment was first completed only for the additional doses from mine sources. This assessment was done for all scenarios, first considering the radon pathway, then the water- consumption pathway and finally the total dose due to radon as well as all (primary and secondary) aquatic pathways. The assessment was than repeated considering only background and LLD sources. Forecast distributions were plotted for the above. Examples are shown in Figure 3 to Figure 5.

7 Forecast: All- Swakopmund resident

10,000 Trials Frequency Chart 9,761 Displayed

.042 421 10 % Percentile 6.9E+00 µSv/a

.032 25 % Pecentile 1.1E+01 µSv/a 315.7 50 % Percentile 1.7E+01 µSv/a 75 % Percentile 2.9E+01 µSv/a .021 210.5 90 % Percentile 4.7E+02 µSv/a

.011 105.2

Mean = 2.4E+1 .000 0

1.9E+0 2.4E+1 4.7E+1 6.9E+1 9.1E+1 uSv/a

FIG.3. Distribution and statistics of aquatic plus radon for Swakopmund (scenario 8).

Forecast: Radon- Khan river downstream of Dome Gor

10,000 Trials Frequency Chart 9,753 Displayed

.026 262 10 % Percentile 3.5E+02 µSv/a 25 % Pecentile 4.6E+02 µSv/a .020 50 % Percentile 6.5E+02 µSv/a 196.5 75 % Percentile 9.2E+02 µSv/a .013 90 % Percentile 1.2E+03 µSv/a 131

.007 65.5

Mean = 7.4E+2 .000 0

9.7E+1 5.3E+2 9.6E+2 1.4E+3 1.8E+3 uSv/a

FIG. 4. Distribution and statistics of radon Dose for Dome gorge (scenario 3).

Forecast: Water- Lower Detection Level at Dome Gor

10,000 T rials Frequency Chart 9,805 Displayed

.025 250 10 % Percentile 2.2E+01 µSv/a 25 % Pecentile 2.7E+01 µSv/a .019 50 % Percentile 3.4E+01 µSv/a 187.5 75 % Percentile 4.3E+01 µSv/a .013 90 % Percentile 5.4E+01 µSv/a 125

.006 62.5

Mean = 3.7E+1 .000 0

1.4E+1 3.0E+1 4.5E+1 6.0E+1 7.6E+1 uSv/a

FIG. 5. Distribution and statistics of aquatic + radon dose at the lower detection level (scenario 11).

8 Lastly, an assessment considering the total dose from mine plus the background sources was run. Overlay charts were generated to evaluate whether the mine-plus-background distributions are statistically distinguishable from the background-only distributions. Typical results are indicated in Figure 6 and Figure 7.

Radon Pathway - Arandis Resident

0.25

0.2

y Radon- Arandis resident t i

l 0.15 (background) bi Arandis resident (mine +

oba 0.1 r backgnd) P

0.05

0 127 287 447 607 767

uSv/a

FIG. 6. Overlay chart for radon doses of Arandis (scenario 1).

All Pathways - Arandis Airport Resident

0.45 0.4 0.35

y 0.3 All- Arandis airport it il 0.25 (background) b a

b 0.2 All- Arandis airport(mine + o r 0.15 background) P 0.1 0.05 0 83 583 1083 1583 2083

uSv/a

FIG. 7. Overlay chart for total radon plus aquatic doses at Arandis airport (scenario 2).

8. Discussion of Results

8.1. Distributions of Additional Dose from Mine

The importance of these distributions relates to the indication they provide on the uncertainty of the assessed doses. The relation between the mean and 90 percentile may be a useful indicator of this uncertainty. This ratio generally seems to range from 1.5 to 2.2, but a value of around 6 was also obtained for one very skew distribution. Considering the fact that distributions were only considered for those parameters for which published uncertainty data could be found, uncertainties around or

9 somewhat above a factor of two may hence be relevant for most of the assessed dose contribution from the mine.

8.2. Criteria for Statistical Significance of the Mine Contributions

Generally statistical significance testing is a tool used to assess whether samples originate from specific populations. For this study one wants to assess whether the total doses (from the background + mine sources) could be distinguished as significantly different from the background doses (excluding the contribution from mine sources) at some confidence level α. In distinguishing between the background and total distributions, two types of errors can be made and the use of critical levels LC and decision levels LD provide a very practical basis in confidence-level assessments to quantify the errors above. The levels are defined as (refer to Figure 8):

Critical level LC = Level below which one will falsely conclude > 100×(1-α) % of the time that a high background dose is not from background but a mine contribution. This is indicated as a type 1 error.

Decision level LD = Level (above LC) below which one will falsely conclude >100×α % of the time that a real dose from the mine is actually background. This is indicated as a type 2 error.

Representation of Background-Dose and Total-Dose Distributions

0.6 µ B µ T 0.5

y L C L D

t Total-Dose

i Background- l 0.4 Dose Distribution Distribution bi 0.3 oba

r 0.2

P L C error 0.1 L D error 0 0.4 0.5 0.6 0.8 0.9 1.0 1.1 1.2 1.4 1.5 Dose (arbitrary units)

FIG. 8. Graphical representation of critical and decision levels for statistical significance tests.

The confidence levels for a mean value depend not only on the distribution of the variable, but generally also decrease with the reciprocal of the square root of the number of readings from which the mean is determined. This study is done, however, with distributions derived in various ways. For the atmospheric pathway the distribution is already that of the average dose calculated from the annual mean weather data for a specific year. In other cases the distributions were deduced from confidence intervals obtained from the literature without statistical information.

The assessment below will hence rather focus on single estimates from a distribution. In this case the confidence levels will approximately coincide with the corresponding percentile values of the distribution from which the single estimates were selected. The distributions would hence be regarded as significantly different in terms of a type 1 error if the mean µB of the background distribution is below the relevant lower percentile value of the total (mine + background) distribution. Similarly the distributions would be regarded as significantly different in terms of a type 2 error if the mean µT of the total (mine + background) distribution is above the relevant upper percentile value of the background distribution. Estimates of the 25 % and 10 % percentiles of the total distribution are used below to assess type 1 errors at a low and high confidence level respectively. Similarly estimates of the 75 % and 90 % percentiles of the lower distribution are used below to assess type 2 errors at a low and high confidence level respectively. The results for Figure 6 and Figure 7 are presented below.

8.2.1. Results from overlay chart of radon dose distribution at Arandis

LC (25 %) = 3.4E+02 LC (10%) = 2.9E+02 µB = 3.9E+02. µB is hence > LC (25 %) and > LC (10 %) and the distributions are not significantly different at low and high confidence levels in terms of type 1 errors.

LD (75 %) = 4.6E+02 LD (90%) = 5.5E+02 µT = 4.5E+02. µT is hence < LD (75 %) and < LD (90 %) and the distributions are not significantly different at low or high confidence levels in terms of type 2 errors.

8.2.2. Results from overlay chart of total dose distribution at Arandis airport

LC (25 %) = 7.9E+02 LC (10%) = 6.6E+02 µB = 5.6E+02. µB is hence < LC (25 %) and < LC (10 %) and the distributions are significantly different at low and high confidence levels in terms of type 1 errors.

LD (75 %) = 6.2E+02 LD (90%) = 7.9E+02 µT = 1.1E+03. µT is hence > LD (75 %) and > LD (90 %) and the distributions are significantly different at low and high confidence levels in terms of type 2 errors.

9. Conclusion

A deterministic as well as a stochastic dose assessment was performed for Rössing uranium mine. The former was used to distinguish those critical groups where doses would likely be above the dose constraint from those where doses would likely be below the dose constraint or trivial. The stochastic results indicate 90-percentiles generally at around two times the mean values, but up to 6 times for very skew distributions. It is also indicated that the statistical comparison with the dose distributions from background sources and of the lower detection levels of analytical results are other important criteria to consider.

10. References

1. Decisoneering, Risk Analysis Using Crystal Ball CD-ROM, 2001. 2. Abrahams A and Schneeweiss R, Data Acquisition Programme for a Post Closure Public Dose Assessment, IRPA Regional Radiation Protection Congress, 5- 8 May 2003, Misty Hills, South Africa. 3. De Beer G P, Ramlaken A J and Schneeweiss R, A Stochastic Approach Towards a Post- Closure Safety Assessment for the Rössing Uranium Mine, IRPA Regional Radiation Protection Congress, 5- 8 May 2003, Misty Hills, South Africa. 4. EnviroSolutions, An Assessment of the dose attributable to radon at a number of receptor locations surrounding Rössing Uranium Mine, Final Report (2001). 5. EnviroSolutions, Excel table ‘RADONBG.XLS’ (2002) provided through personal communication. 6. Schneeweiss R, Excel table ‘Ground Water Nuclide Quality Distributions.xls’ provided through personal communication. 7. Gilby D, Gribi P and Noszke D, Quantifying the reliability of calculated ingestion dose coefficients, Radiation Protection Dosimetry, Vol 79,Nos 1 – 4, pp 283 – 286 (1998). 8. Harrison et al, Reliability of the ICRP’s Dose Coefficients for Members of the Public, II. Uncertainties in the Absorption of Ingested Radionuclides and the Effect on Dose Estimates, Radiation Protection Dosimetry, Vol 95, No. 4, pp 295-308 (2001). 9. IAEA Handbook of Parameter Values for the Prediction of Radionuclide Transfer in Temperate Environments, Technical Reports Series No. 363 (1994)