Experience in radiological risk assessment of a surface waste disposal facility in Chişinău, Moldova

The facility consists of four reinforced concrete vaults (numbered I to IV), with total area around 80 m². The vaults are configured as shown in figure 2 with each having an openable lid for loading and to provide access. The size of the opening is about 700 × 1200 mm and although the internal volume of each of the four vaults is 42, 45, 36 and 42 m³, giving a total capacity of about 165 m³, the size and position of the openings means that the vaults cannot be filled completely. Waste was simply dropped through the opening with no special placement measures. The total volume occupied by the disposed waste is therefore about 75 m³. Records of the disposed waste packages characterise them as unstable waste form, stable waste form, or disused sealed radiation source. All details are taken from Anton (2017).

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Since construction of the facility the concrete structures of the vaults have been open to the elements and none of the four vaults provide satisfactory isolation (see figure 3). According to the operator's description an elevated groundwater table was observed inside Vault IV during the late 1990s. ⁹⁰Sr and ²²⁶Ra were detected in soil and groundwater in the vicinity of the disposal facility by the National Centre of Preventive Medicine in 1998 (NCPM 1998).

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The near-surface disposal facility is located in the Chişinău municipality, and the terrain adjacent to the facility (area 455 ha) falls within the city limits (figure 4). The location of the disposal facility is shown bordered by the white boundary and the area that defines the landscape context, local to the site, by the red boundary.

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Bogdevici (2019) reports the hydrogeological and geotechnical conditions at the site, as well as providing the digital elevation model for the site. The facility is located in a small valley ranging in elevation from 81 to 118 m with the upper elevations of the landscape around 130 m. In the valley, around the facility, local slopes are more than 6° but at the higher elevations the slopes are in the range 3°–6°.

The upper part of geological section is characterised by shallow thicknesses of Quaternary loam and Neogene sandy-clay formations. These are covered by agricultural and artificial soils. The Neogene formation comprises sandy loam layered with clay and clay layered with sands. The upper parts of the clays, located at slopes with high inclination, are intensively fractured. This clay is dense, dry, semi-dry, and fractured, with fine sand layers and carbonate inclusions. Groundwater can form seasonally at shallow depths due to the presence of clays at depths of 3–4 m.

Climate records have been maintained in the Republic of Moldova since 1886 and continue via the monitoring network of the State Hydrometeorological Service (Anton 2017). Current meteorological monitoring at the disposal site indicates an average precipitation of 573 mm yr⁻¹ with maximum 744 mm yr⁻¹ and minimum 425 mm yr⁻¹. Evapotranspiration in the vegetated areas is assessed as 80% of precipitation.

Projections of future climate conditions for the Republic of Moldova suggest that what are currently considered to be extreme rare events for absolute maximum temperatures (around 35 °C for the baseline period of 1961–1990) are likely to become mean maximum summer temperatures. Projections for Europe more generally indicate that the risk of floods increases in Northern, Central and Eastern Europe and that today's 100 year droughts will return every 50 years especially in Southern and South-Eastern Europe, including in the Republic of Moldova (Lehner et al 2006). The probability of flooding, particularly in the valley around the facility, is therefore expected to increase.

The general characterisation of land use around the site (figure 5) shows the dominance of infrastructure land (42.8% of the total area) mostly at lower elevations, towards the city boundary. Agricultural land is currently 38.1% and non-agricultural natural ecosystems 19.1%. Commercial arable production occupies 59.2% of the cultivated area, with individual plots a further 2.7%. Fruit cultivation (16.6%) and a small amount of grassland (2.5%) are also present. The land classified as non-agricultural just downslope from the facility could be suitable for cultivation as there is currently some cultivation adjacent to the facility boundary.

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The design scenario (ISAM SCE1, also called reference evolution) is based on the probable evolution of the system in respect of external conditions combined with realistic or, where justified, pessimistic assumptions with respect to internal conditions.

The disposal facility is located at a relatively high elevation so that it can be expected to be part of a groundwater recharge area. Design scenario, SCE1 with the initial state that the engineered barrier is partly degraded, is selected and a small farm assumed to be located at the disposal facility boundary. This design scenario is a relevant type of normal evolution scenario. The use of a farm system ensures that a comprehensive range of exposure pathways is assessed, maximising human interactions with potentially contaminated material. As described in section 2.5, the site context here suggests well water as the most likely source of drinking and domestic water supplies as well as for irrigation of cultivated land.

Scenarios that may deviate from the reference evolution for the long-term safety of the disposal facility are selected as alternative scenarios. Since the main safety function for the existing facility is provided by the concrete walls of the vault, possible routes to violation of the safety function are used to identify the alternative scenarios.

The frequency of flooding is expected to increase in line with the climate predictions outlined in section 2.3.2, so we select flooding and associated landslides as alternative scenarios. Anton (2017) notes that today's 100 year droughts in Europe are likely to occur on timescales of 50 years the cumulative frequency of this rare event, $P\left( t \right)$ can be written as:

$$\begin{equation}P\left( t \right) = 1 - {0.98^t}\end{equation} \tag{ 1 }$$

in which $t$ is time (year AP). No frequency function is assigned to the landslide scenario.

Two human intrusion scenarios are also selected based on figure B-1in the ISAM report (IAEA 2004a) to assess the disturbed evolution of the disposal facility:

• (a)  
  on-site residence scenario (SCE6), and
• (b)  
  the road construction scenario (SCE7), used to assess risks to humans intruding into the disposal facility after institutional control.

The ISAM RADON example (IAEA 2004b) uses an interaction matrix to express the conceptual model for the site. The interaction matrix is a convenient and compact technique for developing models since it promotes the screening of interactions for specific applications. Furthermore, Kłos and Thorne (2020) have illustrated how interaction matrices can be used to define compartmental mathematical models and we adopt this method here.

Figure 8 is an interaction matrix based on the original ISAM (IAEA 2004a) generic description but processed to include four levels of screening, including those in the IAEA (2004b) documentation. Aggregation and nesting has been used to define the matrix for development into mathematical models for the assessment. We identify the vault and geosphere submodel as distinct from the biosphere submodel. As shown, many interactions are ruled out by generic considerations and others from the description in the ISAM example documentation. Site-specific considerations are used to rule out the interactions as a final stage before translation into mathematical form, thus, we assume that there is no interaction (in terms of radionuclide transport) from the aquifer back to the unsaturated zone and, similarly, that the aquifer is not in contact with the lower soils. Contamination reaches them only via irrigation of the rooting zone soils. Drainage from the system is via the local aquifer. In this form the mathematical models for the vault and geosphere and for the biosphere are defined.

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The vault/geosphere sub-model describes the release of radionuclides from the waste and transport through saturated media to the site boundary using the ISAM model. Output from the vault/geosphere model is to the Local aquifer defined by the upstream catchment area in figure 6. The interaction matrix indicates that three dynamic compartments are used for the biosphere—the local aquifer (used as a well) the rooting zone soil for crops and the unsaturated soil above the aquifer layer. Xu and Kłos (2021) considered the role played by dynamic soils with equilibrium conditions assumed for the well aquifer, concluding that the dynamics of accumulation of radionuclides in soil was of little significance in the calculation of dose. Here we take the opportunity to add a dynamic aquifer compartment in which accumulation of radionuclides can build up over time with the input from the geosphere aquifer.

The compartmental model equation is used for dynamic compartments:

$$\begin{equation}\frac{{{\text{d}}{N_i}}}{{{\text{d}}t}} = {S_i}\left( t \right) + {\lambda _N}{M_i} + \sum\limits_{j \ne i} {{\lambda _{ji}}{N_j}} - \left( {{\lambda _N} + \sum\limits_{i \ne j} {{\lambda _{ij}}} } \right){N_i}\end{equation} \tag{ 2 }$$

where the external time-dependent source term to the ith compartment is ${S_i}\left( t \right)$ Bq yr⁻¹, ingrowth from precursor radionuclide (in the decay chain) is ${\lambda _N}{M_i}$ Bq yr⁻¹, and transfers to the ith compartment from the other compartments is denoted by $\mathop \sum \limits_{j \ne i} {\lambda _{ji}}{N_j}$ Bq yr⁻¹, representing the sum of fractional transfers from the other ($j$) compartments. Losses are by radioactive decay ${\lambda _N}{N_i}$ Bq yr⁻¹, and the sum of all transfers to the other compartments including the sink compartment, $\mathop \sum \limits_{j \ne i} {\lambda _{ij}}{N_i}$ Bq yr⁻¹. The elements ${\lambda _{ij}}$ of the transfer matrix can be linked to the off-diagonal elements of the interaction matrix (Kłos and Thorne 2020).

Release of radionuclides from the waste is driven by the infiltration of net precipitation through the vault cover, with subsequent percolation to the unsaturated zone and geosphere aquifer. The concentration of radionuclides in the aquifer is constrained by the dimensions of the vault system and the flowpath to the site boundary where mixing with the wider aquifer in the watershed is assumed to take place.

Compartment modelling is an approximation since it is a discretisation of a continuous transport process. Increasing the number of compartments increases accuracy but at the cost of model run-time and model complexity. Based on the guidance of Kirchner (1998) and Xu et al (2007) the optimal number of compartments can be determined. As shown in figure 9, the waste form is modelled by a single compartment, the unsaturated zone by three and the aquifer downstream from the disposal facility by five compartments.

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The compartment structure in the interaction matrix (figure 8) is a disaggregation of the soils/sediments leading diagonal element of the ISAM (IAEA 2004b) interaction matrix. Figure 10 shows the transfer processes in the GBI/soil submodel. The source term to the biosphere model is defined by the radionuclide flux from the vault/geosphere model. This constitutes a time series into the biosphere and the transfer coefficients are defined as shown in figure 10.

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From equation (2), the radionuclide inventories in the compartments L, D, T, E vary as shown in figure 10 and the solute mediated transfers from compartment i to compartment j are given by Kłos and Thorne (2020) as

$$\begin{equation}{\lambda _{ij}} = \frac{{{F_{ij}}}}{{{s_i}{\varepsilon _i}{R_i}{V_i}}}\end{equation} \tag{ 3 }$$

where the water flux is ${F_{ij}}$, the compartment saturation is ${s_i}$, the porosity ${\varepsilon _i}$, the density ${\rho _i}$. The thickness of the compartment is ${z_i}$ and plan area ${A_i}$, giving an overall compartment volume ${V_i} = {z_i}{A_i}$. ${\lambda _N}$ is the radionuclide decay. The retardation factor for the radionuclide in the compartment is

$$\begin{equation}{R_i} = 1 + \frac{{\left( {1 - {\varepsilon _i}} \right){\rho _i}}}{{{s_i}{\varepsilon _i}}}{K_i}\end{equation} \tag{ 4 }$$

where ${K_i}$ is the K_d-value for the radionuclides in the ith compartment and ${\rho _i}$ the grain density of the solid material in the compartment.

The area of the soil layer, ${A_{{\text{obj}}}}$, corresponds to that of the biosphere object defined in figure 7 and the annual precipitation ($P$), evapotranspiration ($E$) and irrigation (${d_{{\text{irri}}}}$) amounts are defined by the site context, so that water conservation gives water fluxes in the soil as

$$\begin{equation}{F_{{\text{TD}}}} = {F_{{\text{DL}}}} = \left( {P - E + {d_{{\text{irri}}}}} \right){A_{{\text{obj}}}}.\end{equation} \tag{ 5 }$$

The water flux from well to topsoil is the irrigation demand,

$$\begin{equation}{F_{{\text{LT}}}} = {d_{{\text{irri}}}}{A_{{\text{obj}}}}.\end{equation} \tag{ 6 }$$

The justification of a suitable dilution parameter for wells—here ${F_{{\text{LE}}}}$—is a well-known problem in site-generic studies or in cases with limited site characterisation. The well dilution is not well defined in the ISAM documentation. A value of 8300 m³ yr⁻¹ is used as the flow rate in the well but the site context differs somewhat from that considered here. Similarly, the volume of the well compartment is not precisely defined in the ISAM examples. Here, however, we are able to bound these key parameters from the site-description. For the volumetric flow in the well there are two bounding cases.

2.6.3.1. Minimum dilution in local aquifer.

2.6.3.2. Maximum dilution in local aquifer.

2.6.3.3. Maximum well compartment volume.

2.6.3.4. Minimum well compartment volume.

2.6.3.5. Equilibrium solution.

2.6.3.6. Exposure submodel.

Doses to the human exposed group are expressed as a linear sum over the exposure all pathways arising from water and soil via the different exposure routes,

$$\begin{align}{D_{{\text{total}}}} = \sum\limits_{\begin{array}{*{20}{c}} {{\text{pathways}},} \\ p \end{array}} {\sum\limits_{\begin{array}{*{20}{c}} {{\text{exposure}}} \\ {{\text{routes}},r} \end{array}} {{H_p}} } \left( {{a_{{\text{well}},rp}}{I_{{\text{water}},rp}}{C_{{\text{well}}}} + {a_{{\text{soil}},rp}}{I_{{\text{soil}},rp}}{C_{{\text{soil}}}}} \right).\end{align} \tag{ 7 }$$

The pathways include those identified in the column for humans in figure 8, namely ingestion, inhalation and external irradiation. The conversion factors ${a_{{\text{well}},rp}}$, ${a_{{\text{soil}},rp}}$ depend on the description of the exposure route r and the intake (exposure) rates, ${I_{{\text{well}},rp}}$, ${I_{{\text{soil}},rp}}$, combine different processes. For example, consumption of meat from domesticated animals requires the transfer factors from the intake of radionuclides in the animal in fodder as well as the consumption of water. The intake of radionuclides in crops depends on the uptake of radionuclides in the soil via the roots as well as the intercepted radionuclides that originate in well water used for irrigation. In the equilibrium biosphere, equation (7) reduces to a sum over all exposure routes only from the source term to the biosphere submodel in figure 10.

Analytical models are used for the two human intrusion scenarios selected, namely the on-site residence scenario SCE6 and the road construction scenario SCE7, taken from the ISAM RADON test case. Two further alternative scenarios are included: the flooding scenario and the landslides scenario. The model used for the flooding scenario is the so-called bathtubbing model adapted from the ISAM test cases, employing an analytical expression describing radionuclides in overflowing leachate. For landslides we assume that results of the on-site residence scenario SCE6 are appropriate. Xu and Kłos (2019, 2021) give details.

The limits on the aquifer and well parameters can be used to define the range of doses in the biosphere dose object, the results are plotted in figure 11 showing the four combinations in table 2 for the flow and volume parameters and the ISAM reference flow rate as well as the equilibrium dose result for accumulations of radionuclides in the biosphere submodel.

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As there is no site-specific preferred value for either aquifer dilution or well volume, the actual doses can be expected to lie somewhere between these cases. There are three distinct peaks—for ³⁶Cl around 10 years, ¹⁴C (1 kyear) and ²³⁹Pu (20 kyear), as well as an increasing dose, towards the end of the simulation period, arising from ²¹⁰Po, the short lived progeny of the ²²⁶Ra initially present in the repository. The ratio of maximum dose to minimum is around a factor of 20 in each case and this is close to the ratio of the limits of the overall dilution factor. The size of the well compartment has less of an influence but this has the most impact in the low dilution cases where the ratio of volumes (=2.3) corresponds to the reduction of dose in the two low dilution cases. As may be anticipated, the ISAM dilution gives results close to the upper limit since it is close to the minimum determined by site-specific considerations.

The dynamic aquifer plays a role in determining the timing of dose. This is most apparent in the low dilution cases where the larger the aquifer compartment volume, the longer the time to equilibrium required. Although the effect is small it is clear that the assumption of equilibrium conditions in the aquifer compartment as well as the soils (see Xu and Kłos 2019) would give slightly earlier dose peaks for the less strongly sorbing ³⁶Cl and ¹⁴C and the higher sorbing ²³⁹Pu and ²²⁶Ra peaks would occur much earlier. This indicates that understanding the groundwater system is of more importance than the soil system in this case whereby the soils become contaminated via the use of well water.

These deterministic results show that the maximum doses for the unremediated facility could approach the 0.3 mSv yr⁻¹ dose limit specified by the IAEA but this would be after several thousand years (¹⁴C) and far in the future for ²³⁹Pu and the ²²⁶Ra chain (after 10 kyear). In each of these cases the dilution is at the lower extreme of the site-specific values. This prompts further consideration of the model. The behaviour of ¹⁴C in the biosphere means that it is not well represented by the kind of model described here and more detailed ¹⁴C-specifc models are required for more reliable dose estimation. The models for ²³⁹Pu and the ²²⁶Ra chain are appropriate for the purposes but the timescale for the peak doses to arise is over 10 kyear and, on such a timescale, major change to the biosphere system would be likely to take place, not least there might be erosion and redistribution of contaminated material in the vault-aquifer-biosphere system. Nevertheless the results from the SCE1 deterministic case suggest that remedial action to safeguard the site should be considered.

Avila et al (2010) categorise parameters used in simulations as (a) time-independent parameters considered to be certain, (b) time-independent parameters with uncertain values, and (c) time-dependent parameters. Parameters in the first category are those representing habits and properties of the exposed individuals, such as inhalation rates, water ingestion rates food ingestion rates and dose coefficients. Other time-independent parameters fall into the second category and the effect of their uncertainty on the calculated total dose is studied by performing probabilistic simulations. These parameters are distribution coefficients and parameters used in determining transfer factors illustrated in the conceptual model in figure 8.

Six parameters connected with the transfer rates were studied using 3000 sample sets generated using Latin hypercube sampling:

• volume of the well compartment (uniform: 5.65 × 10⁴–1.3 × 10⁵ m³),
• well capacity (uniform: 6.3 × 10³–1.24 × 10⁵ m³ yr⁻¹),
• hydraulic conductivity in the geosphere aquifer (uniform: 0.2–0.5 m d⁻¹, best estimate 0.35 m d⁻¹),
• effective porosity in the geosphere aquifer (uniform: 0.2–0.4, best estimate 0.35),
• irrigation rate (uniform: 0.25–0.4 m yr⁻¹, best estimate 0.3 m yr⁻¹),
• K_d values for radionuclides in the clay, saturated layers and soils. The values from IAEA (2003b) are here used as the geometric mean and we assume—for purposes of sensitivity analysis—the geometric standard deviation is 2.0 for all elements and for all media.

Uncertainty analysis results are plotted in figure 12, showing that the range from the 2.5th to the 97.5th percentile encompasses the deterministic results, thereby indicating that the uncertainty in vault and geosphere parameters contributes significantly to overall uncertainty. The probabilistic results spread out the time dependence of calculated doses by virtue of the retardation effects of the sampled K_d values. Overall, however, the peak doses in this probabilistic uncertainty analysis are similar to those as determined by the range of values determined by the uncertainty in the aquifer/well characteristics. The arithmetic mean and median doses imply peak doses around 5 × 10⁻² mSv year⁻¹. It should be remembered, however, that the distribution assumed for the well dilution parameter is uniform between the limits defined from the site-specific conditions and, as such, the range of results is a more reliable indicator of the radiological hazard. This is suitable for scoping studies but the central values in the probabilistic analysis are heavily influenced here by the uniform distribution and there is no preferred value for well dilution on the basis of the information available.

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A probabilistic sensitivity analysis was carried out using standardised rank regression coefficients (SRRCs). The higher the absolute SRRC for an input parameter, the greater the effect on the output. A positive SRRC value indicates that input and output move in the same direction, whereas a negative SRRC value shows that they move in the opposite sense. Results for the three main peaks in figure 12 are shown in table 3.

Table 3. Result for standardised rank correlation coefficients (SRRC >≈ 0.1) in the probabilistic analysis at 10 year, 1 kyear and 20 kyear.

10 years (36Cl)		1 kyear (14C)		20 kyear (239Pu)
Parameter	SRRC	Parameter	SRRC	Parameter	SRRC
Well dilution, ${F_{{\text{LE}}}}$	−0.79	Well dilution, ${F_{{\text{LE}}}}$	−0.63	Saturated aquifer Kd, 239Pu	−0.71
Soil Kd, 36Cl	0.28	Soil Kd, 14C	0.58	Darcy velocity in geosphere aquifer	0.42
Darcy velocity in geosphere aquifer	0.17	Saturated zone Kd, 14C	−0.18	Unsaturated zone Kd, 239Pu	−0.29
Irrigation demand, ${d_{{\text{irri}}}}$	0.14	Irrigation demand, ${d_{{\text{irri}}}}$	0.09	Saturated zone Kd, 226Ra	−0.21
				Well volume	−0.13
				Well dilution, ${F_{{\text{LE}}}}$	−0.13

Doses at earlier times (up to 1 kyear) come from the more weakly sorbing radionuclides in the vaults and, as might be expected, the well dilution has the greatest influence, acting to flush any radionuclides reaching the aquifer rapidly out of the biosphere dose object. Retention in the rooting zone soil is positively correlated for the ³⁶Cl and ¹⁴C peaks and irrigation demand is seen to have a relatively small influence on dose. Flow in the geosphere aquifer has the effect of transporting ³⁶Cl to the biosphere object and retention of ¹⁴C in the saturated zone of the geosphere flow path is negatively correlated.

The later peak is more complex, since retardation in the geosphere aquifer dominates with a high negative correlation, acting to delay the arrival of ²³⁹Pu into the biosphere object, as does the K_d in the unsaturated zone. These contrast with the positive correlation of the aquifer's Darcy velocity. The saturated zone K_d for ²²⁶Ra is flagged as influencing the dose at this later peak via its effect on the progeny, ²¹⁰Po. For the more strongly sorbing radionuclides that appear at this peak, the well characteristics are of lesser importance.

The uncertainties in the SCE1 scenario are emphasised in the analysis. ³⁶Cl could possibly be detectable at boundary of the site in the present day but doses would be low as the biosphere object is not currently cultivated. The inherent uncertainties in the dose assessment for ¹⁴C means that the results here are indicative of the potential for ¹⁴C to be of interest but at around 1 kyear after present. Action by the local authorities may be anticipated well before this could become an issue, as is also the case for ²³⁹Pu and ²²⁶Ra. Results from the SCE1 scenario therefore suggest that remediation of the site should be considered and this feeds into the assessment of the other exposure scenarios.