1. Introduction

The assessment of the 2^nd phase disposal facility for the safe long-term storage of radioactive wastes critically depends on the performance of (1) the engineered containment system, and (2) the natural, geologic system underlying the repository. The inventory of radionuclides, their mobilization and release from the repository, and their transport through the unsaturated zone (UZ) to the groundwater table and eventually to the accessible environment are key factors and processes affecting the long-term performance of the system [1, 2].

The objective of the study is to evaluate the radionuclide transport simulations, focusing on examining the release and migration of tritium (³H) and volatile radiocarbon (¹⁴C). Radionuclides transport analysis were performed based on the previous results [3], and domains were constructed based on the cell-centered finite volume method for numerical analysis [4], and the mass and energy conservation equations of each grid were analyzed. The EOS7r module of TOUGH2 code was used to track the physical characteristics of water-air-radionuclides and the movement of radionuclides dissolved groundwater [5], and Tecplot was used as a post-processing program to visualize the modeling results [6].

2. Simulations

2.1 Model assumptions

In order to model the radionuclide transport, it is necessary to consider the phenomenon of dissolving and moving in groundwater, so groundwater flow must also be considered. Since the groundwater flow in this study was referenced under the same conditions as in the previous study. In the previous study, groundwater flow was simulated including a series of artificial and natural barriers to the disposal vault, unsaturated zone and saturated zone in the lower part of the repository, including the cover of the repository to be installed after the closure of the second-phase disposal facility. As shown in Table 1, the material property values of the eight multiple cover layers constituting the cover were not experimental or measured values, but assumed values were used.

Table 1

Radioactive properties and inventory

The simulations are concerned with the fate of two radionuclides: tritium (³H) and carbon-14 (¹⁴C). Basic properties of these two isotopes are shown in Table 1. Both isotopes are contained in the waste being stored at Wolsong. However, the specific location, chemical form, and partitioning between the solid, liquid and gas phases, are unknown. It can be assumed that the bulk of the radionuclide activity is contained in solid material comprising the waste. The process by which these isotopes (or molecules that underwent an oxidation or exchange reaction with an isotope) are transported from within the material to its surface (e.g., by solid diffusion) is essential as it determines the rate (equilibrium or kinetic) with which it becomes available for desorption, dissolution into groundwater, evaporation into gas, or direct outgassing from the solid phase [8].

Moreover, the partitioning between the liquid and gas phase determines the process and thus mobility with which the radionuclides are transported out of the containment system from where they migrate through the natural system either to the atmosphere, groundwater, or a surface water body [9].

Most of these critical processes and associated parameters are currently unknown for the specific conditions at Wolsong. This lack of information is dealt with by (a) making assumptions that are either considered reasonable or conservative, and (b) reporting only relative isotope concentration values, as no defensible statements about activities in the various mobile phases can be made at this point.

The following simplifying assumptions regarding radionuclide inventory and phase partitioning are made:

The phase partitioning coefficients of the radionuclides impact the migration mechanism, i.e., they determine whether a specific radionuclide is predominantly transported by advection in the liquid phase or diffusion in the gas phase. Moreover, the actual activity of a radionuclide depends on the (absolute) concentration in the given phase, along with the mass flow rate of that phase. For example, even a high relative concentration in the gas phase may have insignificant activity if the saturation and porosity at that location is low, or if the flow rate to a receptor is low.

Despite the absence of accurate adsorption and phase partitioning coefficients for ¹⁴C and ³H, values are chosen that represent the expected behavior, specifically the fact that ¹⁴C may be volatile and thus be transported through the gas phase. In addition, the total inventory of a radionuclide in the waste vault shall be represented. To achieve this, the following approach was chosen to initialize radionuclides in the model:

Due to these many assumptions, model convergence was limited, and to solve this problem, modeling was optimized using iTOUGH2, an inverse code of TOUGH2 [11].

2.2 Simulation scenarios

As analysis scenarios, the nuclear species migration was evaluated for four scenarios derived from the two barriers of the disposal cover and vault. Multiple scenarios were set up and simulated to examine the design case as well as bounding configurations. The reference case is referred to as the design case, as it contains all the engineered features and properties. In particular, the cover consists of a sequence of layers that form multiple permeability and capillary barriers to divert infiltration water sideways, reducing the percolation flux encountered by the waste vault. The waste vault itself acts as an additional barrier, reducing water in-and outflows and radionuclide migration by advection and diffusion. It also provides structural strength and serves as a chemical barrier.

The effectiveness of the engineered cover barrier is contingent on the integrity of each of the layers over the 300- year compliance period. This implies that the geometry and material properties, as well as the continuity and homogeneity of each of the layers remain intact. Even relatively minor disturbances of the design may lead to a breach of the barrier system, thus reducing the flow-diversion capacity of the cover system. As a result, higher percolation fluxes reach the vaults holding the radioactive waste.

Similarly, the vaults may be breached, specifically through cracking or other degradation of the concrete. Table 2 summarizes the main four scenarios, which include the design cases (Case A) and three combinations of barrier failure. Additional scenarios (omitting multi-phase diffusion; assuming long-term averaged net infiltration) were also examined.

Table 2

Main simulation scenarios

2.3 Initial conditions and constraints

It is normalized to the maximum concentration found in the waste storage vault, separate for each phase. The initial conditions for transport simulations are therefore by definition represented by relative concentrations of 1.0 in the vault, and 0.0 elsewhere, as shown in Fig. 1.

Fig. 1

Initial conditions for transport simulations; figures are identical for each radionuclide in each of the considered phases.

As the condition of the model area, the top grids were set to a constant atmospheric pressure, thereby eliminating the possibility of affecting the disposal facility through pressure and mass transfer. In addition, the lowermost part of the domain was set to a constant head as a saturation region in order to prevent the reverse raising phenomenon causing saturation to the upper part of the unsaturated zone by inflow of groundwater. The rainfall conditions flowing into the disposal facility were used as input data for the multiple cover system by utilizing the water balance analysis data in the southern Ulsan area of the Korean peninsula [12]. In the total rainfall, 46.1% of rainfall infiltration was applied, excluding evapotranspiration, and the rainfall conditions for 300 years were set as the 30-year rainfall data were repeated 10 times.

Performing coupled multiphase flow and transport simulations of five components (water, air, brine, ³H, and ¹⁴C) in a system with property contrasts that cover many orders of magnitude and a highly variable net infiltration rate that leads to many phase changes due to pulses of water migrating through the system is computationally very demanding and time-consuming. Results are therefore only obtained for relatively short simulation periods that depend on the numerical convergence behavior and time-stepping rates attainable for each case.

3. Results and disccusion

3.1 Case A

The release and transport of partitioning radionuclides is a complex process that involves multi-component diffusion with phase partitioning, as well as advection in the gas and liquid phase driven by pressure gradients and density effects. Superimposed on these flow and transport processes is radioactive decay.

The volatile ¹⁴C is released from the enclosed waste canisters predominantly by gas diffusion. It spreads throughout the vadose zone until it encounters a diffusion barrier such as the clay layers above, the water table at the bottom, and laterally the high-flux, high-saturation water curtain that develops at the edge of the repository due to the diversion of infiltrating water within the engineered cover system (Fig. 2). The ¹⁴C released by gas diffusion also partitions into the liquid phase according to Henry’s law, i.e., the presence of dissolved ¹⁴C relatively far away from the repository may have likely been transported through the gas phase. Advective transport is comparatively small in the shadow zone of the cover system.

Fig. 2

Case A: Evolution of relative ¹⁴C concentrations in the gas phase (color) and liquid saturation (contour lines).

By contrast, the main mechanism for the release of ³H is liquid diffusion and should the barrier system be breached, advective transport. For the reference case, where the concrete vault is assumed to prevent water inflow, the low liquid diffusion coefficient (see Table 1) limits releases (note that relative concentrations are shown on a logarithmic scale in Fig. 3). ³H appears to be contained within the intact vault, where it decays. Due to the small release rates, the change of the ³H inventory in the vaults shows the exponential curve describing radioactive decay of ³H (see Fig. 4).

Fig. 3

Cas e A : Evolutio n o f relativ e log(³H ) concentration s i n th e liqui d phas e (colo r) an d liqui d saturatio n (contou r lines).

Fig. 4

Case A: Change of radionuclide activity in vaults and vadose zone with respect to initial inventory.

After about 3 years, the diffusive transport of ¹⁴C reaches a first quasi-steady state, where the releases balance the amount being washed into the groundwater, and the amount of ¹⁴C residing in the vadose zone stabilizes (see Fig. 4 and Fig. 5). Releases to the atmosphere are comparatively small. Moreover, they diminish as gas diffusion is inhibited during the initial wetting of the cover system. No releases of ³H to either the atmosphere or water table were calculated.

Fig. 5

Case A: Activity fluxes to atmosphere and water table.

3.2 Case B

Radionuclide releases from the vault is likely to depend on the integrity of the concrete vault. Diffusion in the gas phase is the main escape mechanism for ¹⁴C. The concrete is an effective barrier for gas diffusion mainly due to its strong capillarity, which ensures that the pores remain almost completely liquid saturated, reducing gas diffusion. In Case B, this diffusion barrier is absent, leading to a fast release of ¹⁴C, diffusing readily through the shadow zone towards the water table and through the initially unsaturated cover towards the atmosphere (Fig. 6). As previously discussed, the absolute concentrations of ¹⁴C in the gas and liquid phase depend on the Henry coefficient, which is not known for the ¹⁴C waste form stored at Wolsong.

Fig. 6

Case B: Evolution of relative ¹⁴C concentrations in the gas phase (color) and liquid saturation (contour lines).

Release of ³H occurs predominantly by liquid diffusion, which is substantially small than gas diffusion (see Table 1). Fig. 7 shows that ³H migrates away from the vaults with the expected diffusive penetration depth, which is a function the square-root of time. Note that these simulations only show the early-time behavior with an intact cover barrier leading to very small advective transport. No ³H reaches the atmosphere or water table for the considered time frame. The advective component is more relevant for ³H, as will be mentioned in Case C.

Fig. 7

Case B: Evolution of relative log(³H) concentrations in the liquid phase (color) and liquid saturation (contour lines).

Due to the small release rates, the change of the ³H inventory reflects the decay, reducing the amount of ³H remaining in the vault by a factor of 2 every 12 years. Fig. 8 shows the exponential curve describing radioactive decay of ³H. By contrast, the change of the ¹⁴C inventory is almost entirely due to the diffusive release, which is initially very high because of the strong concentration gradient from the vault to the backfill. The release rate diminishes with time and approaches a near-steady flux that is equivalent to the rate with which ¹⁴C is washed into the water table (Fig. 9).

Fig. 8

Case B: Change of radionuclide activity in vaults and vadose zone with respect to initial inventory.

Fig. 9

Case B: Activity fluxes to atmosphere and water table.

Releases to the atmosphere are relatively small and decline as the cover becomes more liquid saturated within the first 5 years.

3.3 Case C

The initially relatively dry conditions around the vaults, and the arrival of the water front after about 2 years, have a strong impact on the ¹⁴C migration mechanism and resulting concentration distribution at early times, as shown in Fig. 10. The highly volatized ¹⁴C is instantly released from the waste vault by gas diffusion, spreading throughout the vadose zone and reading the water table in approximately 2 years. Note that lateral spreading beyond the footprint of the repository is inhibited by the higher liquid saturations encountered for X > 60 m. This transport behavior is similar to that seen in Cases A and B.

Fig. 10

Case C: Evolution of relative ¹⁴C concentrations in the gas phase (color) and liquid saturation (contour lines).

Shortly after 2 years, however, the initial water pulse arriving at the horizon of the repository leads to high liquid saturations around the vault, thus curtailing ¹⁴C diffusion in the gas phase. The high water flux between the vaults effectively washes out the radionuclides. As the panels for 5, 10, and 30 years show, ¹⁴C is still being released by gas diffusion to the shadow zones beneath the vaults, where they are diluted by the percolating water that spreads horizontally due to capillary pressure gradients. No fundamental change in the transport mechanism occurs after 5 years. ¹⁴C content in the vaults is slowly depleted, with concentrations in the gas and liquid phases in the vadose zone changing slightly in response to the fluctuations in net infiltration, but essentially remaining constant over time.

The normalized ¹⁴C concentrations in the liquid phase (Fig. 11) shows accumulation of dissolved ¹⁴C at each leading edge of a saturation front, as the radionuclide is scrapped from the gas phase. Concentrations are lower in the tail of each plume where ¹⁴C has been washed out. This is specifically evident in the panel of Fig. 11 that shows the distribution after 3 years.

Fig. 11

Case C: Evolution of relative ¹⁴C concentrations in the liquid phase (color) and liquid saturation (contour lines).

The relative ³H concentrations in the liquid phase are shown in Fig. 12. It is immediately evident that the reduction of the ³H inventory in the waste vaults is predominantly due to radioactive decay rather than migration out for the containment system. The distributions after 12 and 24 years (corresponding to the passage of 1 and 2 half-lives), show the expected ³H relative concentrations of 0.5 and 0.25, respectively. The arrival of the initial water pulse and saturation of the waste (mainly driven by capillarity) result in a ring-shape region within the waste of increased ³H concentration. This structure, however, should not be over-interpreted, as the assumption of a homogenized waste form is most likely unrealistic.

Fig. 12

Case C: Evolution of relative ³H concentrations in the liquid phase (color) and liquid saturation (contour lines).

Fig. 13 shows the change in the total activity of ³H and ¹⁴C in the waste vaults and in the vadose zone, relative to the initial conditions. As mentioned above, the change of ³H inventory in the vault declines following the exponential curve describing radioactive decay. The amount of activity from ³H in the vadose zone is comparatively small. Fig. 14 indicates that comparatively small amounts of ³H are transported to the water table at an initial rate on the order of 10¹⁰ Bq·yr^-1 per waste vault. This rate declines with time due to radioactive decay of the source.

Fig. 13

Case C: Change of radionuclide activity in vaults and vadose zone with respect to initial inventory.

Fig. 14

Case C: Activity fluxes to atmosphere and water table.

By contrast, due to its long half-life of ¹⁴C, all the changes seen in the vault indicate the cumulative amount of ¹⁴C that escaped the waste and vault, initially mainly due to gas diffusion, and later by reduced diffusion to the shadow zone and advective transport in the liquid phase. The release rate of ¹⁴C is almost linear after the initial transient response to the arrival of the first liquid pulse. This is also confirmed by an essentially constant amount of ¹⁴C in the vadose zone, indicating near-steady transport of ¹⁴C through the natural system. The same conclusion can be reached by looking at the flux of ¹⁴C across the water table (see Fig. 14), which remains constant after the initial pulse. Gaseous releases to the atmosphere are smaller by a factor of about 10⁶. From 10 year onward, a ¹⁴C release rate of approximately 10¹³ Bq·yr^-1 is obtained per vault. Assuming this rate remains constant, less than 1% of the initial ¹⁴C inventory will be released from the repository during the compliance period of 300 years.

3.4 Case D

In this case, the scenario is examined where both engineered barrier systems have degraded. This may be considered a worst-case scenario even though the benefits of high liquid saturations around the vaults on diffusive ¹⁴C releases has been demonstrated in case C.

Fig. 15 shows the evolution of relative ¹⁴C concentrations in the gas phase. Similar to the previous case, ¹⁴C is initially released by gas diffusion and spreads through a significant portion of the vadose zone. After approximately 5 years, however, the infiltration front engulfs the vaults, effectively limiting gas diffusion, with the exception of the region beneath the vault floor, where a shadow zone develops. Since no lowpermeability concrete vault is present, the waste saturates after about 10 years, and the shadow zone disappears, curtailing all gas diffusion. After this initial period, a quasi-steady state is achieved, where ¹⁴C is washed out of the vaults by water dissolving the adsorbed ¹⁴C mass and transporting it towards the water table.

Fig. 15

Case D: Evolution of relative ¹⁴C concentrations in the gas phase (color) and liquid saturation (contour lines).

Fig. 16 shows the evolution of relative log(³H) concentrations in the liquid phase. During the initial few years, ³H is essentially immobile. Only after the water pulse arrives is ³H transported by advection to the water table. The concen-trations of ³H arriving at the water table reach a maximum at around 12 years, when infiltration fluxes are at quasi-steady state and the ³H as a source in the vaults has not yet decayed or been washed out. After 2, 3, and 4 half-lives, the concentration fluxes decrease exponentially, as expected.

Fig. 16

Case D: Evolution of relative log(³H) concentrations in the liquid phase (color) and liquid saturation (contour lines).

Fig. 17 succinctly summarizes the case where engineered barriers fail. At early times, releases of radioactivity are dominated by ¹⁴C, which is transported to the atmosphere and the water table mainly by gas diffusion. After gas diffusion is severely suppressed by the increased liquid saturation throughout the model domain, ¹⁴C is dissolved and advectively transported in the aqueous phase; after approximately 10 years, both release fluxes reach a quasisteady state at lower rates.

Fig. 17

Case D: Change of radionuclide activity in vaults and vadose zone with respect to initial inventory.

The first arrival of ³H at the water table is around 7 years. Activity fluxes to the water table show a sharp arrival front, which coincides with the water pulse from infiltration, which has been interrupted by the construction of the repository and cover system. The sharp rise in ³H activity flux to the water table is curtailed after about 12 years, when the source term becomes weaker due to decay and depletion. No ³H escapes to the atmosphere. Peak activity releases to the water table are due to ³H after about 12 years.

As shown in and Fig. 18, the very large ¹⁴C inventory is slowly depleted by wash-out and some gas diffusion at an approximately constant rate of 3×10¹² Bq·yr^-1 per vault.

Fig. 18

Case D: Activity fluxes to atmosphere and water table.

Absent disruptive events, approximately 10¹⁵ Bq of ¹⁴C will be leased within a compliance period of 300 years, which is less than 1% of the initial inventory. These estimates strongly depend on the release and mobilization processes within the waste and vaults, and the phase-partitioning properties, which are highly uncertain.

The ³H inventory initially follows the exponential decay curve. After about 5 years, inventory reduction speeds up as the washed-out of ³H is initiated. After about 20 years, most of the ³H initially placed in the vaults is washed out or has decayed; the activity change curve reaches a constant value that is equal to the initial ³H activity of 1.35×10¹⁶ Bq stored in the vaults.

4. Conclusions

From case A with intact engineered barriers, gas diffusion is the main release mechanism of ¹⁴C which spreads throughout the shadow zone due to gas diffusion. The highsaturation plume at the edge of the repository prevents lateral spreading of ¹⁴C in the gas phase. Percolating water and wet layers in cover system limit diffusive ¹⁴C releases to the atmosphere. ³H migration is limited due to small advective and diffusive flows in the aqueous phase. Most ³H mass decays while being contained in the repository. There are no ³H releases to the atmosphere or water table.

From the degraded concrete vault case, diffusive releases of ¹⁴C are accelerated due to absence of concrete vault. ¹⁴C release is effectively curtailed by increased liquid saturations in the vicinity of the vaults in no engineered cover barrier system release rate of ¹⁴C is approximately 1013 Bq·yr^-1 per vault. Less than 1% of the initial ¹⁴C inventory will be released from the repository during the compliance period of 300 years. ³H is essentially contained in the repository. Its inventory follows the exponential curve that describes radioactive decay.

From the result of case D, the waste is almost fully saturated after 10 years, effectively reducing gas diffusion. Dissolved ¹⁴C is washed out by advective transport in the aqueous phase at a constant rate of approximately 3×10¹² Bq·yr^-1 per vault. ³H is washed out by advective transport in approximately 20 years. Peak activity releases to the water table are due to ³H after about 12 years.

The mobilization mechanism of radionuclides within the vaults is essentially unknown. While the chosen as-sumptions are expected to lead to conservative results, the source term, which drives transport in the near field, remains highly speculative. It is therefore recommended to develop a detailed source-term model that accounts for the composition and geometry of the waste, along with submodels on hydro-geochemical processes and scenarios on breaching mechanisms.

Concentrations of both radionuclides in the gas and liquid phase depend on the assumptions about adsorption and phase partitioning coefficients, which are highly uncertain. The properties need to be characterized for a reliable estimation of phase partitioning behavior. Phase partitioning is essential because it determines the transport mechanism (diffusion, advection, and potential retardation) of the radionuclides as well as the absolute concentrations (and thus activity) of the fluids migrating to the accessible environment. It is expected that this study will provide a good way to predict the movement of radionuclides in terms of the safety of the disposal facility. This can be considered as a methodology for radionuclide transfer in the long-term as well as operation of the disposal facility. In particular, it seems that the direction of future radioactive waste management was indirectly suggested by using a method that considers both gaseous and liquid leakage.