Development of Two-Dimensional Near-field Integrated Performance Assessment Model for Near-surface LILW Disposal

중·저준위 방사성폐기물 천층처분시설 근계영역의 2차원 통합성능평가 모델 개발

Abstract

Wolsong Low- and Intermediate-level radioactive waste (LILW) disposal center has two different types of disposal facilities and interacts with the neighboring Wolsong nuclear power plant. These situations impose a high level of complexity which requires in-depth understanding of phenomena in the safety assessment of the disposal facility. In this context, multidimensional radionuclide transport model and hydraulic performance assessment model should be developed to identify more realistic performance of the complex system and reduce unnecessary conservatism in the conventional performance assessment models developed for the $1^{st}$ stage underground disposal. In addition, the advanced performance assessment model is required to calculate many cases to treat uncertainties or study parameter importance. To fulfill the requirements, this study introduces the development of two-dimensional integrated near-field performance assessment model combining near-field hydraulic performance assessment model and radionuclide transport model for the $2^{nd}$ stage near-surface disposal. The hydraulic and radionuclide transport behaviors were evaluated by PORFLOW and GoldSim. GoldSim radionuclide transport model was verified through benchmark calculations with PORFLOW radionuclide transport model. GoldSim model was shown to be computationally efficient and provided the better understanding of the radionuclide transport behavior than conventional model.

월성원자력환경센터 중저준위방사성폐기물 처분시설은 서로 다른 방식의 처분시설이 혼재하고, 월성 원자력발전소와도 인접해있다. 이와 같은 높은 복잡성으로 인해 처분시설 안전성 평가 시 보다 면밀한 현상이해가 필요하다. 기존 1단계 사일로 처분시설의 성능평가모델들에 포함된 불필요한 보수성을 줄이고 복합처분시설에 대한 보다 실제적인 성능을 파악하기 위해서는 다차원 수리/핵종이동 모델이 필요하다. 이와 함께 향후 복합처분시스템의 특성에 기인한 다양한 불확실성을 관리하고 파라미터의 중요도를 분석하기 위해 많은 계산이 필요할 것으로 예상하며, 이를 위해 보다 효율적인 성능평가 모델이 요구된다. 본 논문에서는 두 요건을 충족시키기 위해 수리성능 모델과 핵종이동 모델을 연계한 2단계 천층처분시설의 근계영역 2차원 통합성능평가 모델을 개발하였다. 수리 및 핵종이동은 PORFLOW와 GoldSim 전산 코드를 이용해 평가하였으며, GoldSim 핵종이동 모델은 PORFLOW 핵종이동 모델과의 벤치마크를 통해 검증하였다. GoldSim 모델은 계산효율이 뛰어났으며 기존의 모델에 비해 핵종이동거동을 이해하는데 용이하였다.

1. Introduction

Korea Radioactive Waste Agency (KORAD) has developed the Wolsong Low- and Intermediate-level Radioactive Waste (LILW) Disposal Center located in the south eastern coastal area of the Korea peninsula. The total capacity of Wolsong LILW disposal center is about LILW 800,000 drums. In the first stage, KORAD completed the constructions of the underground silo-type disposal facility of 100,000 packages and launched the new project developing near-surface vault-type disposal of 125,000 drums as the 2nd stage.

As shown in the Fig. 1, Wolsong LILW disposal center has two different kinds of disposal facilities and interacts with the neighboring Nuclear Power Plant(NPP). These situations impose a high level of complexity and eventually cause the difficulty of safe assurance. Therefore, the Wolsong LILW disposal center and NPP should be considered as a complex system and safety cases should be developed in this point of view.

Fig. 1.Panoramic view on Wolsong LILW disposal center in Korea.

KORAD has developed the safety case program as one of follow-up actions to the 1st stage construction and operation license since July 2008. A part of the safety case program is to develop the performance assessment methodologies which include tools for integrated performance assessment and treatment of different kinds of uncertainties in parameter, scenario, and model [1]. KORAD should focus on the development of advanced modeling to find out the potential performance of the complex disposal system through the detailed analysis on the function of radionuclide confinement [2]. To secure enough safety margins in the context of the complex disposal system, unnecessary conservatism should be reduced through the development of models in an appropriate level of detail with careful approach to management of model uncertainty which can be achieved by conservative or bounding models, or by stylized approaches to representing complex phenomena [3].

This paper deals with the development of a systemlevel model to be applied to future performance assessment activities in a safety case and describes the latest developments in modeling of near-field radionuclide transport phenomena for LILW near-surface disposal. Although it’s possible to develop highly refined three dimensional (3-D) models with the minimum assumption and mathematical manipulation, the efficient 2-D model allows a stochastic approach covering a greater number of safety calculation cases while ensuring a high level of accuracy and scalability. The two-dimensional (2-D) approach was selected and an integrated near-field performance assessment model combining hydraulic performance assessment model and radionuclide transport model was developed. The hydraulic performance assessment models were used to assess the hydraulic behavior of near-field and provide an understanding of the water flow infiltrating into the storage vaults and the flow distributions inside vault system according to the degradation of the confining concrete. Eventually, the flow fields of the near-field abstracted from the outputs of the hydraulic performance assessment were applied for the evaluation of the radionuclide transport behavior.

 

2. Near-surface disposal concept

The total number of waste drums to be disposed in the 2nd disposal facility is expected to be about 125,000. As shown in Fig. 2, the near-surface disposal system consists of two key subsystems, final capping system and vault system. The final capping system adopted by KORAD is the multi-layer cover concept such as used at Andra’s Centre de la Manche disposal site. After storage closure, the multicover layer encapsulates the storage vaults. Fig. 3 shows a schematic of the KORAD multi-layer cover concept and the design features considered for assessment. The vaults are designed to prevent the migration of radionuclide via groundwater and release into the atmosphere. The concrete vault is a physical barrier limiting water ingress to the waste and the encapsulating matrix (backfill). The waste packages are arranged on a triangular lattice with 10 cm gap between the vault wall and waste packages to allow for handling operations. This waste package density in a single vault is an important assumption for the safety analysis. Waste packages are disposed of in the vault layer by layer as shown in Fig. 4. When one layer is completed the backfill material is poured in the vault until a 10 cm layer covers the waste packages. Backfill keeps the waste packages stable from external impacts and makes the operation convenient. The backfill layer also contributes to the long-term structural stability of the vault since the steel drums are expected to lose their structural strength in the future.

Fig. 2.KORAD Near-surface disposal concept.

Fig. 3.KORAD multi-layer cover concept.

Fig. 4.Concrete filled disposal vault concept.

 

3. Model development

An integrated 2-D near-field performance assessment model composed of linked sequences of models which together present the near-field evolution of the disposal system over time was developed as shown in Fig. 5. Three main components are dealt with to implement an integrated performance assessment: evaluation of water flow through the multi-layer cover system; evaluation of water flow through the vault system; and radionuclide transport through the system.

Fig. 5.Modeling code integration for LILW near-surface disposal assessment model.

Fig. 6.Conceptual model and hydraulic boundary conditions of cover system (not to scale).

For the hydraulic performance assessment on the engineering barriers of the near-surface disposal system, the infiltration rate at the bottom of the first layer of the multi-cover system was determined by water balance analysis considering evapotranspiration and direct runoff on the top surface via HELP code simulation and flow calculations throughout the engineering system were performed via PORFLOW code considering a 2-D near-field section consisting of the engineering barriers, multi-layer cover and storage vault.

A radionuclide transport model was developed with 2-D approach through GoldSim code. The 2-D GoldSim radionuclide transport model (2DGTM) provides the radionuclide fluxes from the storage vault to its main outlets through different surfaces. The accuracy of the results of 2DGTM for which simplified flow fields were applied was verified through benchmarking study with 2-D PORFLOW radionuclide transport model (2DPTM). The flow fields obtained from the hydraulic performance assessment were applied the 2DPTM without any mathematical manipulation.

3.1 Hydraulic model

3.1.1 Hydraulic model development of multi-layer cover system

The conceptual model of the cover and its various components are presented in the Fig. 2. Hydraulically speaking speaking, the conceptual model considers steady state saturated conditions, and all components are considered isotropic and homogeneous porous media. The bottom of the backfill is assumed to be saturated and in direct contact with the top of the vault structure. The geotextiles layers are not considered for the numerical assessment because they only provide structural support during cover construction and serve no hydraulic function. The drains 1 to 3 are 0.1 m in width and represent the discharging drains from each sand layer. This concept allows the assessment of the output flows out of the cover and out of each drain. The waterproof layers are conceptually used to avoid any flow from the drain back to the cover.

The domain considered in the numerical simulation is simplified with a 2-D vertical section approximation based on the fact that the thickness of the cover is several orders of magnitude smaller than its average horizontal length. Fig. 2 also shows the boundary conditions considered for the assessment. The input flow on top of the model is the infiltration rate and no flux boundary conditions can be applied on the vertical edges of the model due to symmetries within the vault. On the bottom surface of the model, a free water surface is assumed arbitrarily, i.e., pressure equal to zero. The number of grids used for this assessment is approximately 2,440 contacting plane-parallel cells (47×52). Hydraulic calculations were performed with the PORFLOW code.

3.1.2 Hydraulic model development of vault system

The vault components are conservatively assumed to be saturated with water as an initial condition. The water flux to be considered as boundary conditions at the top of the vault during the monitoring period (300 years) is determined through the hydraulic performance evaluation of multi-layer cover as described. The net infiltration (precipitation minus evapotranspiration and run-off) as the upper boundary condition of the multi-layer cover system is assumed to be 34.7% of the annual average precipitation in the Wolsong region. The boundary condition was calculated by a water balance simulation considering site-specific data, precipitation, temperature, humidity, wind speed and etc., via HELP code [4]. The water flux as boundary conditions at the top of the vault during post-monitoring is determined with a conservative assumption that the multi-layer cover is instantaneously degraded at 350 years (operation period plus monitoring period). This assumption is conservative in the safety assessment on the near-surface disposal as in Belgium. It is expected that even a degraded cover which is sufficiently thick is capable of protecting the concrete structures for at least a few thousand years against freeze-thaw and wet/dry cycles and to limit water seepage through evapotranspiration [5].

The geometry and the vaious components of the vault considered in the conceptualization are indicated to the Fig. 3. Fig. 7 also presents boundary conditions considered for hydraulic assessment. Entering water flow is imposed at the top of the domain and due to symmetries within the vault, boundary conditions, flux equal to zero boundary conditions are imposed on the vertical edges of the model and at the bottom of the model. The free surface of goundwater is represented by an hydraulic head equals to zero and located 30 cm under the bottom of the slab.

Fig. 7.Conceptual model and hydraulic boundary conditions of vault system.

3.2 Radionuclide transport model

In order to evaluate the integrated performance of 1st stage facility, KORAD have developed and used a simplified 1-D safety calculation model in the performance assessment [6]. This model has advantages to cover many safety calculations at smaller costs than more realistic and complex models and give insights into the radionuclide transport phenomena in a simple and conservative manner. However, simplified models can impose the unnecessary conservatism to performance assessment during the process of conceptualizing the real system and representing the conceptualized model into an 1-D model. In the context of the co-disposal system in Korea this simplifying approach in performance assessment may lead to difficulties with securing enough safety margins for the whole system.

The main objective of this study is to develop an advanced 2-D safety calculation model named 2DGTM in order to reduce the unnecessary conservatism included in the simplified 1-D model and facilitate the use of probability to treat uncertainty in performance assessment. GoldSim code matches these intents soundly because it is a graphics based object-oriented computer program designed to carry out dynamic, probabilistic simulations and contains contaminant and radionuclide transport modules which approximate contaminant or radionuclide transport processes semi-analytically using pipe elements or numerically using networks of mixing cells. In addition, a system level code the GoldSim has high level of scalability which is the ability to handle growing amount of work in a capable manner [7]. In particular, the GoldSim code with cell networks provides a potential for 2-D radionuclide transport modeling desired in this study. Networks of cell pathways with advective or diffusive connections can be created manually but this procedure is cumbersome and time-consuming if the network contains a large number of cells. GoldSim provide a special element to automate the creation of large cell networks. The “Cell Net Generator” discretizes a rectangular or cylindrical region of space and creates a twodimensional array of cell elements including any necessary advective or diffusive mass flux links between them.

The radionuclide transfer boundary conditions used in the study are shown in Fig. 8. A zero concentration boundary condition is applied at the upper surface 30 cm above the top slab because diffusion is the dominant transfer mechanism of radionuclides. Zero flux boundary conditions are applied to the vertical edges of the model. A zero concentration boundary condition is applied to the bottom free surface representing total and immediate dilution of radionuclides in the groundwater.

Fig. 8.Radionuclide transfer boundary conditions considered inperformance assessment.

As in the hydraulic performance assessment, the geometrical representation is two-dimensional and corresponds to a transverse half-cross section in the middle of the vault. The domain of radionuclide transport is constructed through overlapping the material zones considering various components of the vault and flow velocity zones obtained from the PORFLOW water flow simulation. The defined domain is presented in the Fig. 9. The grid carried out for this assessment is a 2D structured grid and contains 1560 planeparallel cells (40 x 39).

Fig. 9.Zone definition of the 2-D GoldSim radionuclide transport model in the vault system (not to scale).

3.3 Modeling parameters

The radioactivity in Becquerel per waste package is assumed as presented in the Table 1. The source term used in this study is representative of potential releases of radionuclides from various forms under the identified range of environmental conditions. The source term was derived from the concentrated liquid waste. The concentrated liquid waste in terms of its density and porosity properties is the closest to the average characteristics of all waste streams to be disposed. It is assumed to be solidified with cementitious materials in 200 L steel drum.

Table 1.Values of activity per waste package

Fig. 10.Field of hydraulic head H (m) and distribution (not at scale) of the water flux (L/m2/yr) within the cover of the KORAD reference concept.

The hydraulic properties of the disposal cover materials used for the reference case are presented in Table 2. The hydraulic properties are obtained from an ONDRAF/NIRAS document [5]. To manage uncertainties imposed in the hydraulic properties and recharge rate, sensitivity cases considered as altered situations also are defined and calculated in this study.

Table 2.Hydraulic properties considered for the cover [5]

The site specific annual maximal rainfall (years 2010-2013) is 1445 L/m2/yr (or mm/yr) and the portion of the infiltration in the ground, after evapotranspiration and direct run-off, is 34.7% given through HELP code simulation. Based on this data, the infiltration rate (IR) in the cover is IR=1445×0.347≒500 L/m2/yr after closure.

Hydraulic and transport parameters of the components of the vault system are given by Table 3 and Table 4. For confining concretes of the vault (bottom slab, shaping concrete, wall, filling concrete, biological slab, top slab and etc.) values are obtained from KORAD data for intact concrete. The values of the hydraulic dispersive parameters such as ground, backfill, draining concrete, drain, waterproof material and waste package, are obtained from the design data of Centre de l’Aube (CSA), Andra. As the Table 4 shows, for all selected radionuclides, all values of the distribution coefficient and retardation coefficients taken in the components of the vault arise from KORAD data.

Table 3.Hydraulic and transport parameters taken into account in the various components of the vault

Table 4.Values of the distribution coefficient Kd and retardation coefficient R taken into account in the various components of the vault for the selected radionuclides

Sensitivity analysis has performed to understand how the system works and which parameters have a strong influence on results and which are less relevant. For post-monitoring period, three sets of hydraulic parameter variation of confining concrete are determined with the data of the vault and waste package considered at CSA, Andra and Wolsong silo-type disposal facility, KORAD. The sensitivity cases for post-monitoring period are determined by using the hydraulic conductivity data corresponding to two different states of concrete degradation; degraded concrete and fully degraded as shown in the Table 5.

Table 5.Sensitivity cases in radionuclides transport evaluation

 

4. Results and discussion

4.1 Hydraulic performance of multi-layer cover and vault

4.1.1 Multi-layer cover

The hydraulic performance assessment indicators are water fluxes in L/m2/yr, through different surfaces, from a layer to another, into the drains, and out of the backfill. Fig. 6 shows the hydraulic heads field and some associated streamlines and the distribution of the water flux within the cover during the monitoring phase in the reference case of the clay hydraulic conductivity 10-9 m/s. These results show that around 43% of the water entering into the layer n°1 of sand goes out through the drain n°1. This is due to the hydraulic conductivities contrasts between the gravel and the layer n°1 of sand which promotes the discharging of the water flow through the drain n°1. An even higher contrast effect of hydraulic conductivities, more than 5 orders of magnitude, exists between the layer n°2 of sand and the clay. Almost 100% of the water flow entering in the layer n°2 of sand goes out of the model through the drain n°2, thanks to the hydraulic conductivity contrast between the sand and the clay. Only 0.01% of the rainfall recharge is infiltrating into the clay, crossing the layer n°3 of sand and the backfill. Thus, the drain n°3 doesn’t discharge any water from the cover during monitoring phase and conceptually have a temporary function to drain the water before the completion of the multi-layer cover. The water flow infiltrating to the storage vault is 0.05 L/m2/yr and almost 100% of the rainfall recharge is discharged through the drains.

To analyze sensitivity cases related to the cover properties and the recharge flow, three sensitivities cases were considered. One sensitivity case is defined by multiplying the reference recharge by 2 and the amount of increases from 500 L/m2/yr to 1000 L/m2/yr. The other two sensitivities are defined considering the cover properties: one with a hydraulic conductivity of the clay equal to 10-8 m/s and the other equal to 10-7 m/s.

The Table 6 shows the sensitivity results as well as the reference case for comparison. The sensitivity analysis shows that the hydraulic behaviors of the sensitivity cases are very similar in comparison to the reference case. The hydraulic conductivity contrasts between sand draining layer and the other layers, especially the clay layer, promote the discharge of the water flow through drain n°1 and n°2. Most of the water flux is discharged through the drains. The drain n°2, at the top of the clay layer, is still the most efficient of the three drains. The water flow infiltrating into the storage vault is still very low. The highest infiltration rate of all the assessed sensitivities is 5 L/m2/yr, for a clay layer with a hydraulic conductivity of 10-7 m/s.

Table 6.Water flux results (L/m2/yr) of hydraulicperformance assessment of the final cover system according to change of rainfall recharge and hydraulic conductivity of clay layer (Kclay)

Concerning the sensitivity to the infiltration rate, a water flux of 0.1 L/m2/yr is reaching the storage vault, representing 0.01% of the infiltration rate. Concerning the sensitivity to the clay layer hydraulic properties, a hydraulic conductivity of the clay equal to 10-8 m/s increases the infiltration rate by an order of magnitude from the reference case 0.05 L/m2/yr to 0.5 L/m2/yr and for the clay of 10-7 m/s, the infiltration rate increases by two orders of magnitude from the reference case to 5 L/m2/yr.

These results are in line with the theoretical fact that as saturated conditions are assumed, and given the specific boundary conditions, water flux inside the model are linearly dependent on the infiltration rate and hydraulic conductivities.

4.1.2 Vault

Fig. 11 presents the relation between hydraulic conductivity contrast and infiltrated water into the vault. Almost all of the entering flow by-pass the vault and is drained by the backfill because of an important contrast of permeability between surrounding backfill and confining concrete, i.e. the contrast factor 5.0×108 in operating phase, 3.3×106 in temporary phase and monitoring phase, and 2.0×103~6.7×104 in post-monitoring phase and the infiltrated water is obviously proportional to the contrast factor in the range of the solid line box whatever the hydraulic boundary on the top of the backfill.

Fig. 11.Relation between hydraulic conductivity contrast and infiltrated water into the vault.

Fig. 12 and Fig. 13 show the fields of hydraulic head and associated pathways and the distribution of water within the vault according to the evolution of the confining concrete. As with the infiltrated water, the field configuration doesn’t vary with the hydraulic boundary condition since the configuration only depends on the contrast factors within the vault.

Fig. 12.Field of hydraulic head H (m) according to the evolution of the concrete.

Fig. 13.Water fluxes getting into or out the vault according to the evolution of the concrete.

For the intact concrete, the very low quantity of water (7.3×10-6 ~ 1.1×10-3% of infiltration rate through the multilayer cover) that will infiltrate through the vault is mainly drained by drain network at the bottom (62%) and the other quantity goes to groundwater through the wall (36%) and bottom slab (2%). These low quantities of water within the vaults lead to diffusion-dominant transfer of solute. For the degraded concrete, only 0.16% of infiltration gets into the vault and this quantity leads to diffusive transfer of solute everywhere in the vault the same as the case of sound concrete.

However, diffusion is not the dominant transfer phenomena with the fully degraded concrete. Fully degraded concrete causes 5% of infiltration water to enter the vault due to reduction of the contrast between the backfill and confining concrete compared to degraded concrete. In this hydraulic context the convection becomes main transfer process almost everywhere in the vault except in the bottom slab. Diffusion is still dominant only in the bottom slab.

The hydraulic conductivity of crushed concrete equal to 10-4 m/s of the altered waste package and is higher than 10-5 m/s of the surrounding backfill. Due to the effect of drastic decrease of the permeability contrast between confining concrete and backfill, 96% of the top water flow gets into the vault, mainly through the top slab and also through the wall and 80% of the amount of infiltrated water in the vault goes to groundwater table through the bottom slab. In this hydraulic context convection is dominant everywhere.

Note that such hydraulic conductivity of the crushed concrete is highly unrealistic in normal evolution and is applied for altered situations such as earthquake situation causing through-going cracks [8] but not used in the radionuclide transfer calculations of this study.

The hydraulic performance assessment in this study indicates two important facts that the water flow configurations strongly depends on the permeability contrasts between the confining concrete and other components and don’t vary according to the IR boundary conditions. These results imply that the infiltrated water into the vault can be easily estimated without further calculations.

4.2 Radionuclide transport results

Results of solute transport, in terms of evolution of instantaneous molar flux of selected radionuclides, are presented below for several cases determined in the Table 5.

In order to identify influence of location of the waste package in the vault on molar flux coming out the waste package, location sensitivity(LS) calculation is performed by 2DGTM. Results of GoldSim are presented together with results of 2DPTM in Fig. 14 to benchmark the accuracy of 2DGTM. Fig. 14 highlights the instantaneous normed molar flux of 99Tc, a mobile radionuclide with long halflife, coming out the waste package according to its location within the vault.

Fig. 14.Instantaneous normed molar flux coming out of 6 waste packages located in the vault: 99Tc.

These results present two behaviors according to the location of the package. “Closeness” of waste packages located at edges (location number 2, 4, 5, 6) with filling concrete and draining concrete of the vault leads to a continuous release from these waste packages by implementation of a gradient of concentration between packages and concrete. For waste packages located in the center of the vault (location number 1, 3), a fast homogenization of the concentration between waste packages and the filling concrete leads to sharp attenuation of solute diffusion of these parcel towards the release.

Fig. 15 presents the results of solute transport for 99Tc in terms of instantaneous and cumulated normed molar flux coming out through different surfaces for LS case. During the operating period, when water flow is the most important, most of the 99Tc activity released by the vault is collected by the drain. The hydraulic role of drain is assessed for the transport of radionuclides by advection. During this phase, transport by advection via the drain is characterized by faster kinetics than the transport by diffusion through confining concretes. In transient cover phase and monitoring phase, reduction of flow coming into the vault leads to a limitation of advective transport within the vaults towards the drain; molar flux coming out of top and bottom slab are higher than those coming out of the drain. Solute transfer towards the groundwater is managed by the bottom slab and the wall.

Fig. 15.Instantaneous and cumulated normed molar flux coming out through different surfaces for the location sensitivity case: 99Tc.

The transport evaluations for the other radionuclides are not presented in this paper but they were performed in the LS case and their results lead to the following topics. Before 350 years, sorbing radionuclides in concrete and waste packages such as 14C, 137Cs, 59Ni, 63Ni, 94Nb and 90Sr show negligible molar flux coming out of bottom slab and top slab less than 10-12 mol/yr, as well as intermediate components. For radionuclides characterized by short half-life less than 5 years, such as 55Fe, 58Co, 60Co and 144Ce, total quantity of radionuclide has decreased within the vault.

Comparing 2DGTM and 2DPTM, the radionuclide releases from the waste packages located at the vault edges show similar results while the waste packages located in the center have difference in reaching time to homogenization as shown in Fig. 14. However, considering the total release of all waste packages, these differences of waste packages located in the center are relatively very small and don’t affect overall performance of the vault as shown in Fig. 15.

For the sensitivity analysis, two cases for the hydraulic conductivity of confining concrete and three cases for IR boundary are determined in order to cover the wide range of hydraulic parameter variation. Three kinds of radionuclides, 99Tc, 14C, and 59Ni, are selected to assess the effect of retardation according to the degree of sorption. Fig. 16, Fig. 17, and Fig. 18 present the results of the sensitivity calculations. Note that the instantaneous molar fluxes in the figures are considered as a main indicator in this performance assessment and are summarized into follow pathways: top slab, bottom slab, wall, and groundwater table. Note that the radionuclides drained through the drain system are assumed that all of them are released to the groundwater table without any evacuation process due to the failure of the separated water collecting system during the post- monitoring period.

Fig. 16.Results of radionuclide transfer evaluation in case of IR 1 L/m2/yr (monitoring) and 100 L/m2/yr(post-monitoring).

Fig. 17.Results of radionuclide transfer evaluation in case of IR 25 L/m2/yr (monitoring) and 250 L/m2/yr(post-monitoring).

Fig. 18.Results of radionuclide transfer evaluation in case of IR 50 L/m2/yr (monitoring) and 500 L/m2/yr (post-monitoring).

For the degraded concrete (DC) case, the total accumulated molar flux of 99Tc drained to the final outlet, groundwater table, increases according to the increase of the IR. The main reason of this result is due to the growth in bypass flow rinsing 99Tc molar flux getting out by the cover and wall through the surrounding backfill. For degraded concrete, diffusive transfer into the vault is still dominant and solute transfer towards the groundwater table is managed by the bottom Slab and by the wall.

For the fully degraded concrete (FDC), the transfer behavior of 99Tc getting out the vault becomes more complex than the degraded concrete. In this hydraulic context, the diffusive transfer and the convective transfer are co-dominant in the vault. The permeability of the filling concrete favors the drainage of the infiltrated water to the draining concrete. The rate of IR increase is consequently correlated to the increase of the total accumulated molar flux and maximum molar flux released from vault to the groundwater table.

The differences between DC case and FDC case arise from permeability contrasts of the confining concretes. In DC case, the diffusive transfer from the outlet surfaces is dominant everywhere in the vault and the IR variation only affects the draining solutes through the surrounding backfill. In FDC case, the percentage of IR entering into the vault increases due to the smaller permeability contrast than DC and it leads to the faster release of solute into the groundwater by advective transfer to the drain. In addition, most of the initial inventory of 99Tc is not decayed because of the characteristics of non-sorbing and long-lived radionuclides and is released to the groundwater table in every sensitivity case. The different permeability contrasts affect on the releasing duration and maximum flux rate.

The results of 14C and 59Ni show similar behavior of evolution of the instantaneous molar flux getting out the vault with 99Tc according to changes in IR and permeability contrast but they have the adsorption property on the confining concrete and shorter half-life compared to the 99Tc. These differences cause slower advective transfer by retardation effect and lead to a noticeable amount of decay. When comparing the results obtained for DC case and FDC case, in the former case the decay amount of 14C and 59Ni are about 15% and 10% respectively of initial inventory each and their decay ratios are not influenced by IR variation in the system but in the latter case the decay amount of the two radionuclides vary from 14% to 10% and from 9% to 3% respectively according to the change of IR.

In the framework of the defined benchmark, the conducted radionuclide transport calculations allow to point out that 2DGTM and 2DPTM are similar considering maximum value and overall long-term behavior of radionuclides. Although the configurations of the output fluxes at intermediate components are somewhat different between 2DGTM and 2DPTM, the final output fluxes to groundwater table are very similar. In fact, the differences are expected. The 2DGTM is developed according to the strategy with 2DPTM has features of the coarse grid and simplified flow field data. The refinement of the calculation time step and of the mesh cell size is of importance. It is well known that the finer the calculation time step and the mesh size cell are, the more accurate the computed transport calculation is. However, when comparing the results obtained for the sensitivity analysis on the grid performance, the error made due to the spatial and time discretization has much smaller effect on the results of 2DGTM than the other parameter errors at the given refinement level. This fact points out that it is a reasonable to be assumed that the grid spacing is sufficiently fine to obtain an accurate solution for this performance assessment.

The simplification of flow field data applied for 2DGTM can cause relatively larger discrepancy with 2DPTM than the refinement of the time step and the mesh cell size. Especially, in case of FDC in which the convection and diffusion are co-dominant, the detailed velocity profiles inside the storage vault are as important as the diffusion-relate parameters. Therefore the 2DGTM with the representative flow velocity for each defined zone by average scheme can results in the larger discrepancy with 2DPTM. The Fig. 16 to 18 indicate that the more the IR is, the larger the effect of simplification is. However, it is expected that this problem can be resolved with cautious approach to abstracting the flow field from the PORFLOW hydraulic performance assessment.

 

5. Conclusion

Although the results obtained from the 2DGTM overall well matched to the 2DPTM, to make sure the feasibility of 2DGTM further verification should be required. For example, solubility limit and mechanical dispersivity were not considered in this study. The somewhat unrealistic treatments of them were introduced in an conservative manner. As in this study, further verification studies are needed to assess the realistic performance of the desired disposal system.

This paper describes development of the 2DGTM which has been done with GoldSim code. 2DGTM uses more precise 2D geometry and flow field data abstracted from PORFLOW hydraulic performance evaluation. The conducted radionuclide transport calculations allows to point out that if the calculation results are lightly dependent on the numerical methods used and on time stepping and space meshing, it can be reduced as low as wanted by increasing time and space refinement. The 2DGTM have the outstanding merit in view of computation time. With this advantage, the 2DGTM provides the better understanding of the radionuclide transfer behavior than conventional radionuclide transport models which are subject to overestimate or ignore some physical processes. The accuracy of the 2DGTM was verified by the benchmark study with 2DPTM in this study. These two advantages of 2DGTM allow us to calculate a large number of sensitivity cases in performance assessment at low cost and help to determine the parameter importance. In the view point of design study, the results of performance assessment are ultimately used to derive the design requirements of desired system and feedback to the pre-determined design. In addition, probabilistic performance assessment with 2DGTM would be conducted to help the project team to better understand system behavior and to guide research and development work.