Numerical analysis of thermal process in the near fi eld around vertical disposal of high-level radioactive waste

H.G. Zho, H. Sho, H. Kunz, J. Wng, R. Su, Y.M. Liu

aCNNCKeyLaboratoryonGeologicalDisposalofHigh-levelRadioactiveWaste,BeijingResearchInstituteofUraniumGeology(BRIUG),Beijing,China

bFederalInstituteforGeosciencesandNaturalResources(BGR),Hannover,Germany

Numerical analysis of thermal process in the near fi eld around vertical disposal of high-level radioactive waste

H.G. Zhaoa,*, H. Shaob, H. Kunzb, J. Wanga, R. Sua, Y.M. Liua

aCNNCKeyLaboratoryonGeologicalDisposalofHigh-levelRadioactiveWaste,BeijingResearchInstituteofUraniumGeology(BRIUG),Beijing,China

bFederalInstituteforGeosciencesandNaturalResources(BGR),Hannover,Germany

A R T I C L E I N F O

Articlehistory:

Received 8 May 2013

Received in revised form 2 September 2013

Accepted 10 September 2013

High-level radioactive waste (HLW)

For deep geological disposal of high-level radioactive waste (HLW) in granite, the temperature on the HLW canisters is commonly designed to be lower than 100°C. This criterion dictates the dimension of the repository. Based on the concept of HLW disposal in vertical boreholes, thermal process in the near fi eld (host rock and buffer) surrounding HLW canisters has been simulated by using different methods. The results are drawn as follows: (a) the initial heat power of HLW canisters is the most important and sensitive parameter for evolution of temperature fi eld; (b) the thermal properties and variations of the host rock, the engineered buffer, and possible gaps between canister and buffer and host rock are the additional key factors governing the heat transformation; (c) the gaps width and the fi lling by water or air determine the temperature offsets between them.

? 2013 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting by Elsevier B.V. All rights reserved.

1. Introduction

In most of the concepts for deep geological disposal of highlevel radioactive waste (HLW), which have been proposed by many countries (such as Sweden, Finland, and China), the potential repositories will be built in depths between -300 m and -1000 m under the ground surface. The decay heat emission from the disposed HLW canisters will be transferred to the surrounding buffer and host rock formation, resulting in high temperatures in the near fi eld. The thermal process and the resultant temperature fi eld are determined by the decay heat emission of the HLW, the initial thermal conditions and the thermal properties of the engineered barrier system (EBS) and host rock, possible gaps in the EBS, and the repository layout, etc.

For disposal of HLW in granite formations, the temperature on the canister surface is set to be less than 100°C in the repository (Hokmark and Falth, 2003; Kari, 2006; Zhao et al., 2009). The maximum temperature is a criterion dictating the dimension of a repository. The deep repository will basically contain thousands of heat-generating canisters. In order to keep the canister surface temperatures below that limit, the spacing between nearby canisters cannot be arbitrarily small. On the other hand, that spacing must be kept at a minimum value in order to limit the extension of the repository such that it can be accommodated within the given rock volume. This means that it is necessary to derive reliable relations that shall show how the canister surface temperature depends on the canister power, on the thermal resistance between canister, buffer and host rock, on the canister spacing, and on the thermal properties of the buffer and host rock. Consequently, the studies of thermal conductivity properties and temperature evaluation of repository are necessary for the design of long-term safety of HLW repositories.

2. Concept model of HLW repository

This paper aims to analyze the thermal process in the near fi eld of HLW vertical disposal boreholes, which will be excavated vertically from horizontal tunnels in granite. The vitrif i ed HLW canisters are disposed of in vertical holes in the horizontal tunnels. Fig. 1 shows the principal layout of the repository consisting of four parallel panels. Each panel has a central tunnel area, whose width is 60 m measured from canister centers. In one panel there are 300 tunnel pairs, the length of each tunnel pair is 900 m, and the distance is 9.5 m between each tunnel pair. Each tunnel pair can dispose of 80 canisters, and the distance between canisters is 9.5 m. Totally there are 82,630 canisters (Pan and Qian, 2009). In the designed concept, the repository is set at the depth of -500 m (Zhao et al., 2007, 2009; Zhao, 2013).

Fig.1.Concept design of HLW repository.

3. Concept model of EBS

In the designed concept, vitrif i ed HLW will be conf i ned in low carbon–steel canisters. The cylindrical canisters have a size of 820 mm in diameter and 1790 mm in length. They will be disposed of in vertical boreholes with a diameter of 1920 mm and 4310 mm in length. The space between canister and borehole wall will be backf i lled with compacted bentonite, and the thickness of bentonite between canister and host rock is 500 mm. Fig. 2 shows schematically the EBS concept for the HLW disposal in vertical boreholes. The previous studies of EBS concept and performance assessment show that the bentonite thickness between 350 mm and 700 mm has the similar function to retard nuclides transportation under the condition of the canister being destroyed (Lennart, 2002). Considering manufacturing and installation tolerances, a clearance (gap) ofr= 5 mm between the canister and the buffer andr= 40 mm between the buffer and the rock wall are assumed to exist (Table 1 and Fig. 2). So the remaining bentonite thickness between the canister and the host rock is 500 mm. The inner gap between the canister and buffer will probably stay dry for a while due to the high temperature at the canister surface. In contrast, the outer gap between the buffer and rock will be fi lled with water in a relatively short time due to the connection with the saturated host rock. Initially during installation the outer gap is artif i cially wetted (Kunz et al., 2006, 2009, 2011; Zhao et al., 2009).

4. Decay heat of HLW

The decay heat is a strongly decreasing phenomenon, for example, the decay heat is only a half of the total amount after 50 years. Fig. 3 shows decay power of vitrif i ed HLW, which is based on the ORIGEN2 and ORIGEN-S calculations. Reasonable decay heat level is reached in 30–50 years cooling time depending on the burn-up value of the fuel (Heikki, 2005). The decay power is presented by a sum of exponential terms:

Table1Parameters of the designed EBS.

Fig.2.Concept model of EBS.

whereP1is the power at the fi rst timet1(t1= 10 years is chosen for vitrif i ed HLW),tiis the random time point during the long-term disposal phase, andaiis a coeff i cient corresponding to the actual time pointti. Hereaitakes different values for fuel of different ages for a selected time period of 10–10,000 years.

Fig.3.Decay power of vitrif i ed HLW (reprocessing products of 1 ton PWR spent fuel with burn-up 40 MWd/(kgU)).

5. Thermal properties of host rock and buffer materials

The initial rock temperature in a potential repository is taken from in situ measurement in the borehole at preselected Beishan area.

The thermal conductivities of the host rock and buffer materials are determined on the core samples drilled from the Beishan granite and the compacted Gaomiaozi bentonite which is being investigated as a buffer material. According to the concept design of the canister, the canister material is low carbon–steel. Its thermal conductivity is constant generally under the condition of low and intermediate temperature. A very low effective conductivity of air gap between canister and bentonite is assumed to be 0.094 W/(m K). The effective conductivity of 40 mm water-f i lled gap between bentonite and rock must be relatively higher and takes a value of 0.62 W/(m K). But before water saturation, the effective conductivity of the outer gap is assumed to be lower, only 0.28 W/(m K). The thermal properties of the rock and buffer materials are used in analyses and summarized in Table 2 (Zhao et al., 2009; Kunz et al., 2013; Zhao, 2013).

6. Thermal analysis of the single vitrif i ed HLW canister

6.1.Governingequations

Thermal conduction analysis concerning canister optimization and layout studies of the deep repository have been performed by numerical calculation using computing code ANSYS which was chosen because of its high pre- and post-processing capability, a feature important in studies involving a great deal of variations and sensitivity analysis.

The thermal governing equation is

where cv= ρc is the volumetric heat capacity of the material, λ is the heat conductivity of the material,Tis the temperature of a unit volume center,tis the time, and Φ is the decay heat generation. To make two-dimensional (2D) analysis possible, an axisymmetric model was formed around an individual canister in a vertical borehole. The effect of the tunnel was not considered in analysis. Eq. (2) was formulated for 2D axisymmetric analysis. Fully implicit scheme was applied to make it possible to use longer time steps. The numerical modeling supposes the heat fl ux through the air gap by conductivity in the gap and radiation on the gap surface, and the convection was neglected for the gap because of its minor effect. Interfaces between different materials were handled by applying the heat fl ux continuity equation (Eq. (3)) over the interfaces. Thecalculations were made assuming that each material is homogeneous.

Table2Thermal properties used in analyses.

where λcan, λairand λbenare the conductivity values of the canister (low carbon–steel), air and bentonite, respectively. Eq. (3) is effective if the air gap width in comparison with the thickness of the bentonite is small. The numerical calculations were performed iteratively for the whole simulation duration.

6.2.Boundarytemperatureconditions

To handle the temperatures on the model boundaries, two alternatives can be taken into account. The edges very far from the canister can be chosen to avoid heat pulse ref l ection from the edge. This makes the model larger. The other possibility is to calculate the temperatures on the boundaries from the analytical solution. The latter was applied throughout the numerical analysis.

6.3.Analysisofsinglevitrif i edHLWcanister

The temperature on the canister surface is very signif i cant in the analysis. First of all, the temperature of host rock, rock surface of tunnel and different interfaces of EBS, was calculated by use of analytical method. Secondly, the thermal conductivity properties of single canister system were calculated by numerical method. The gaps around the canister were considered in the two analysis methods. The verif i cation is based on the comparison of the results obtained above. The line source model was corrected in the analytical method, and the maximum surface temperature from numerical calculation was adopted to verify the accuracy of the analytical line heat source model.

Fig. 4 shows the geometry of the model area for numerical analysis. Table 3 presents additional parameters for numerical analysis and for the line heat source model. The gap between bentonite and host rock is fi lled with water in vertical disposal model. Since the conductivity of water is lower than that of the rock, the maximum value of 40 mm for the width of the water gap was chosen. The test was geometrically identical to an actual HLW canister and EBS

model.

The decay power of vitrif i ed HLW was presented by a fi tting function as described in Fig. 3. The decay heat (559 W) of a single vitrif i ed HLW canister at disposal is reached after 30 years pre-cooling when the 40 MWd/(kgU) burn-up spent fuel has been reprocessed. The initial temperature (19°C) of canister is not an essential parameter, since it reaches the stationary temperature during only several days.

Fig.4.(a) Grid and material types (canister red, inner air gap Cambridge blue, bentonite yellow, outer water gap blue, backf i ll light yellow and rock sky blue) and (b) example of temperature distribution after 1.125 years when the maximum temperature of 64.965°C (numerical analysis) is encountered.

Fig. 4 illustrates the grid and material types and temperature distribution after 1.125 years. In the model there are 28,960 fi nite elements. The canister was assumed to be homogeneous with uniform power generation over its volume, and the contents of canister was not modeled, since the low carbon–steel has a very high thermal conductivity (51.6 W/(m K)) causing nearly uniform temperature distribution on the external surface of the canister. Fig. 4b shows that the temperature distribution pattern is symmetrical with the horizontal plane passing through the middle of the canister. Thus different heights of the buffer above and below thecanister and different conductivities of the tunnel backf i ll material show a minor effect. The line heat source model may thus estimate successfully the temperature in the middle height of the canister, where the maximum temperature is encountered.

Fig. 5 shows heat fl ux distributions after 1.125 and 10 years. The maximum heat fl ux is reached, 352.59 W/m2and 285.22 W/m2respectively, at the corners of the canister since the space angle to the bentonite direction is largest. The temperature deviation is the highest in outwards direction, which can be also seen from Fig. 4b. Thermal fl ux φ0at the middle height of the canister is about 79% of the average heat fl ux φmeanon the canister surface.

Fig. 6 shows temperature history of different parts on single canister surface, and the maximum temperature happens at the middle height of the canister. Fig. 7 shows a detailed temperature prof i le in radial direction at the middle height of the canister after 1.125 years. The maximum temperatureTrock+ ΔTwater+ ΔTben+ ΔTairgap=T0is formed from different parts: 32.37°C + 2.0°C + 22.3°C + 8.2°C = 64.965°C. In case of several canisters the shape of the near-f i eld temperature prof i le in Fig. 6 remains practically unchanged. It is only elevated to higher level of about 5–20°C depending on the spacing between canister and tunnel and disposing rate.

Fig. 8 indicates that the analytical and numerical solutions give accurately the same temperature histories (Trock) on the rock wall. This proves that for the analytical solution using effective canister height, only rock material and several canisters can be superposed even if they were very close to each other. In practice, the distance between canisters is more than several meters. The analytical solution (k= φ0/φmean= 1) gives a higher temperature (7.9°C) than the numerical solution on the canister surface. The analytical solution is corrected to give equal canister temperature history to the numerical solution (Fig. 9), when a value ofk= 0.79 is chosen. According to numerical analysis (Fig. 5), the heat fl ux φ0at the middle height of the canister is 79% of the average heat fl ux φmeancorresponding to a value ofk= 0.79. The value ofk= 0.79 isused in the following analytical analysis to obtain correct canister temperature.

Table3Initial data for the line source analysis (vitrif i ed HLW).

Fig.5.Heat fl ux distribution along canister external surface between center of lower and upper lids after 1.125 and 10 years.

Fig.6.Temperature history of different parts on single canister surface.

Fig.7.Radial temperature prof i le at the middle height of the canister after 1.125 years, when the maximum temperature of 64.965°C (numerical analysis) is encountered.k= φ0/φmean= 1.

Fig.8.Temperature history on the single canister surface and the wall of the deposition hole.k= φ0/φmean= 1.

The temperature distribution and evolution around single HLW canister had similar characteristics when the gap between rock and buffer was fi lled with air in comparison with water fi lling. The maximum temperature 66.75°C was reached at the middle height of the canister surface after 0.796 year when the outer gap was fi lled with air. The analytical solution was corrected to give equal canister temperature history to the numerical solution, when a value ofk= 0.79 was chosen.

Table4Estimated temperature difference of gaps.

Fig.9.Numerically and analytically calculated radial temperature prof i les in the middle of the canister after 1.125 years, when the maximum temperature of 64.965°C is encountered.k= 0.79.

6.4.Estimateoftemperaturedifferenceofgapsaroundcanister

The effective conductivities of gaps have been translated into approximate maximum temperature offset, assuming that the initial disposal decay heat was 559.7 W and 350.7 W, respectively, when the vitrif i ed HLW had been cooled down for 30 years and 50 years. The estimate regarded the conditions about 5 years after deposition, i.e. when the power has decreased by about 12% of the initial heat of the HLW canister. Table 4 shows the temperature difference at 5 years after the disposal of vitrif i ed HLW in the borehole. The heat emissivity from the canister, bentonite and host rock surface was estimated at ε = 0.8 (Zhao et al., 2009) by using the effective conductivity values of different gaps given above.

The study shows that the most important and sensitive inf l uence factor on temperature difference between gaps is the canister initial decay heat. The higher the initial decay heat is, the larger the gaps temperature difference is. The temperature offset between canister and bentonite is less than 10°C, and the higher the inner gap is, the larger the temperature offset between the canister and bentonite is. When the gap between the bentonite and the host rock is fi lled with water, the gap’s temperature offsets is small, but it will be 1–3°C higher when the gap is fi lled with air.

7. Conclusions

(1) The factors that affect the maximum temperature on the canister surface include the initial power of the canister, the material thermal properties of the EBS, the gaps around the canister in the EBS, the initial ground temperature and thermal properties of the host rock, and the repository layout, etc.

(2) The most important and sensitive parameter is the initial disposal power of the canister.

(3) The two key factors that affect the maximum temperature on the canister surface are the material parameter’s uncertainty and nature variability of the host rock and the EBS, and the gaps around the canister in the EBS.

(4) The temperature offset between the canister and bentonite is not more than 10°C, and the bigger the inner gap is, the larger the temperature offset between the canister and bentonite is. When the gap between the bentonite and the host rock is fi lled with water, the gap’s temperature offset is small, but it will be 1–3°C higher when the gaps is fi lled with air.

Heikki R. Disposal canister for spent nuclear fuel – design report. Technical Report Posiva 2005-02; 2005, Eurajoki, Finland.

Hokmark H, Falth B. Thermal dimensioning of the deep repository. SKB TR-03-09; 2003, Sweden.

Kari I. Thermal analysis of repository for spent EPR-type fuel. Technical Report Posiva 2005-06; 2006, Eurajoki, Finland.

Kunz H, Zhao HG, Nowak T, Shao H, Br?uer V. A comprehensive solution for THMC-coupled processed in the fi eld of nuclear waste disposal – application of the numerical tools GINA/RockFLow to the Chinese Beishan site. In: GeoProc 2006; 2006.

Kunz H, Zhao HG, Nowak T, Shao H, Wang J. Comparative coupled THM modeling of Chinese HLW disposal concept – Geosys/Rockf l ow and ANSYS. In: SinoRock 2009; 2009.

Kunz H, Zhao HG, Shao H, Hesser J, Wang J, Br?uer V. Optimization of a boreholetunnel concept design for HLW disposal in granite using a 3D coupled THM modelling. In: IRSM 2011; 2011.

Kunz H, Zhao HG, Shao H, Zaretzki B. 3D numerical model evaluation of packer tests for hydraulic characterization of fractured rock. In: SinoRock 2013; 2013. p. 479–84.

Lennart A. Criticality safety calculations of storage canisters. SKB Technical Report TR-02-17; 2002, Stockholm, Sweden.

Pan ZQ, Qian QH. Strategy study of the high level radioactive waste disposal. Beijing: Atomic Energy Press; 2009 [in Chinese].

Zhao HG, Wang J, Liu YM. A study of the thermal conductivity property of the highlevel radioactive waste repository: the case of Beishanpreselected site, Gansu Province. Earth Science Frontiers 2009;16(Supp.):186.

Zhao HG, Wang J, Yang CH, Chen WM, Su R. Preliminary discussion on depth for high-lever radioactive waste repository in Jiujing block, Beishan area, Gansu Province. Chinese Journal of Rock Mechanics and Engineering 2007;26(Suppl. 2):3966–73 [in Chinese].

Zhao HG. Thermal conductivity property of the HLW horizontal disposal. In: The 4th East Asia Forum on Radioactive Waste Management (EAFORM); 2013. p. 152–60.

*Corresponding author. Tel.: +86 13521800390.

E-mailaddress:hgz72@sohu.com (H.G. Zhao).

Peer review under responsibility of Institute of Rock and Soil Mechanics, Chinese Academy of Sciences.

Vertical disposal

Engineered barrier system (EBS)

Thermal conductivity properties