高放射核废处置库温度场的分布线热源解析模型
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摘要
针对高放射核废地质处置库的KBS–3v布置模式,提出一种三维瞬态温度场预测的核废罐分布线热源解析模型(模型Ⅰ),并通过算例,与现有的核废罐分布点热源解析模型(模型Ⅱ)、处置巷道分布线热源解析模型(模型Ⅲ)、处置区分布平面热源解析模型(模型Ⅳ)进行对比,并分析温度场的分布特征和时变规律。研究发现:对于围岩,模型Ⅰ的温度解与其他3种解析模型的解在核废罐附近有些差别,但随着与核废罐距离的增加和核废罐放热功率的衰减,这4种不同解析模型的解趋于相等;对于回填膨润土,模型Ⅰ的最高温度增量比模型Ⅱ的最高温度增量小27%,比模型Ⅲ的最高温度增量大7%,比模型Ⅳ的最高温度增量大16%;根据模型Ⅰ,核废罐附近围岩的温度在100a内迅速升高,且在100～700a内始终比初始温度高30℃以上,但随着核废罐放热功率的衰减而相应地减小;回填膨润土的温度和温度变化率都随着核废罐间距的减小而增大,并且核废罐间距越小,敏感度越大。模型Ⅰ在几何上比其他3种模型更符合实际情况,因此计算结果也更为合理。
With regard to a KBS-3 v schemed geological repository for disposal of high level nuclear waste,a canister distributed line heat source analytical model(model Ⅰ) is developed for the prediction to the 3 D transient temperature field,and sample calculation analyses are conducted. The objectives are to compare with three other analytical models in the literature,i.e. the canister distributed point heat source analytical model(model Ⅱ),the drift distributed line heat source analytical model(model Ⅲ),and the zone areal heat source analytical model(model Ⅳ),and to analyze the spatial distribution patterns and temporal variation features of the temperature field,and to study the influences of the spacing of the waste canisters on the temperature rise of the bentonite backfill. The calculations indicate:for the surrounding rocks,there are some differences in the vicinity of the canisters between the temperature solutions from model Ⅰ and the three other analytical models,but with the increase of distances from the canisters and the attenuation of heat power of the canisters,such differences of temperature solution from the four different analytical models tend to diminish correspondingly;for the bentonite backfill,the peak temperature increment from model Ⅰ is 27% smaller than model Ⅱ,7% larger than model Ⅲ,16% larger than model Ⅳ;according to model Ⅰ,the temperature in the vicinity of the canisters increases drastically within the initial 100 years,and exceeds over 30 degrees Celsius based on the virgin rock temperature during 100 th to 700 th year,but later decreases as the heat power of the canisters attenuates; both the temperature and its rate of variation in the bentonite backfill increase if the spacing between the canisters is reduced,and so does the sensitivity. Model I is geometrically more consistent with reality,thus the calculation results are more rational,than the other three existing models.
With regard to a KBS-3 v schemed geological repository for disposal of high level nuclear waste,a canister distributed line heat source analytical model(model Ⅰ) is developed for the prediction to the 3 D transient temperature field,and sample calculation analyses are conducted. The objectives are to compare with three other analytical models in the literature,i.e. the canister distributed point heat source analytical model(model Ⅱ),the drift distributed line heat source analytical model(model Ⅲ),and the zone areal heat source analytical model(model Ⅳ),and to analyze the spatial distribution patterns and temporal variation features of the temperature field,and to study the influences of the spacing of the waste canisters on the temperature rise of the bentonite backfill. The calculations indicate:for the surrounding rocks,there are some differences in the vicinity of the canisters between the temperature solutions from model Ⅰ and the three other analytical models,but with the increase of distances from the canisters and the attenuation of heat power of the canisters,such differences of temperature solution from the four different analytical models tend to diminish correspondingly;for the bentonite backfill,the peak temperature increment from model Ⅰ is 27% smaller than model Ⅱ,7% larger than model Ⅲ,16% larger than model Ⅳ;according to model Ⅰ,the temperature in the vicinity of the canisters increases drastically within the initial 100 years,and exceeds over 30 degrees Celsius based on the virgin rock temperature during 100 th to 700 th year,but later decreases as the heat power of the canisters attenuates; both the temperature and its rate of variation in the bentonite backfill increase if the spacing between the canisters is reduced,and so does the sensitivity. Model I is geometrically more consistent with reality,thus the calculation results are more rational,than the other three existing models.
引文
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[13]CLAESSON J,PROBERT T.Thermo-elastic stress due to a rectangular heat source in a semi-infinite medium.Presentation of an analytical solution[J].Engineering Geology,1996,49(3):223-229.
[14]ZENG H Y,DIAO N R,FANG Z H.A finite line-source model for boreholes in geothermal heat exchangers[J].Heat Transfer-Asian Research,2002,31(7):558-567.
[15]CARSLAW H S,JAWGER J C.Conduction of heat in solids[M].Oxford:Clarendon Press,1959:353.
[16]Swedish Nuclear Fuel and Waste Management Company(SKB).Design,production and initial state of the canister[R].Stockholm:Swedish Nuclear Fuel and Waste Management Company,2000.
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[18]Swedish Nuclear Fuel and Waste Management Company(SKB).Long-term safety for the final repository for spent nuclear fuel at Forsmark:main report of the SR-Site project[R].Stockholm:Swedish Nuclear Fuel and Waste Management Company,2011.
[2]MIN K B,LEE J,STEPHANSSON O.Implications of thermallyinduced fracture slip and permeability change on the long-term performance of a deep geological repository[J].International Journal of Rock Mechanics and Mining Sciences,2013,61(1):275-288.
[3]张勇,项彦勇.饱和稀疏裂隙岩体三维水流-传热过程中位移和应力的一种半解析计算方法[J].岩土力学,2016,37(12):3 481-3 490.(ZHANG Yong,XIANG Yanyong.A semi-analytical method for calculation of three-dimensional water flow and heat transfer in single-fracture rock with distributed heat sources[J].Rock and Soil Mechanics,2016,37(12):3 481-3 490.(in Chinese))
[4]ZHENG L,RUTQVIST J,BIRKHOLZER J T,et al.On the impact of temperatures up to 200℃in clay repositories with bentonite engineer barrier systems:A study with coupled thermal,hydrological,chemical and mechanical modeling[J].Engineering Geology,2015,197:278-295.
[5]王青海,刘艳,司高华,等.高放废物包装容器材料腐蚀研究进展[J].腐蚀与防护,2011,32(1):40-44.(WANG Qinghai,LIU Yan,SI Gaohua,et al.Research progress of container materials for high level radioactive waste[J].Corrosion and Protection,2011,32(1):40-44.(in Chinese))
[6]Swedish Nuclear Fuel and Waste Management Company(SKB).Heat propagation in and around the deep repository[R].Stockholm:Swedish Nuclear Fuel and Waste Management Company,1999.
[7]RUTQVIST J,BARR D,BIRKHOLZER J T,et al.A comparative simulation study of coupled THM processes and their effect on fractured rock permeability around nuclear waste repositories[J].Environmental Geology,2009,57(6):1 347-1 360.
[8]RUTQVIST J,ZHENG L,CHEN F,et al.Modeling of coupled thermo-hydro-mechanical processes with links to geochemistry associated with bentonite-backfilled repository tunnels in clay formations[J].Rock Mechanics and Rock Engineering,2014,47(1):167-186.
[9]HAUKWA C B,WU Y S,BODVARSSON G S.Thermal loading studies using the Yucca Mountain unsaturated zone model[J].Journal of Contaminant Hydrology,1999,38(1/3):217-255.
[10]DOUGHTY C.Investigation of conceptual and numerical approaches for evaluating moisture,gas,chemical,and heat transport in fractured unsaturated rock[J].Journal of Contaminant Hydrology,1998,38(1/3):69-106.
[11]LI J,YIM M S,MCNELIS D.A simplified methodology for nuclear waste repository thermal analysis[J].Annals of Nuclear Energy,2011,38(2/3):243-253.
[12]H?KMARK H,CLAESSON J.Use of an analytical solution for calculating temperatures in repository host rock[J].Engineering Geology,2005,81(3):353-364.
[13]CLAESSON J,PROBERT T.Thermo-elastic stress due to a rectangular heat source in a semi-infinite medium.Presentation of an analytical solution[J].Engineering Geology,1996,49(3):223-229.
[14]ZENG H Y,DIAO N R,FANG Z H.A finite line-source model for boreholes in geothermal heat exchangers[J].Heat Transfer-Asian Research,2002,31(7):558-567.
[15]CARSLAW H S,JAWGER J C.Conduction of heat in solids[M].Oxford:Clarendon Press,1959:353.
[16]Swedish Nuclear Fuel and Waste Management Company(SKB).Design,production and initial state of the canister[R].Stockholm:Swedish Nuclear Fuel and Waste Management Company,2000.
[17]Swedish Nuclear Fuel and Waste Management Company(SKB).Background report:SR 97 Processes in the repository evolution[R].Stockholm:Swedish Nuclear Fuel and Waste Management Company,1999.
[18]Swedish Nuclear Fuel and Waste Management Company(SKB).Long-term safety for the final repository for spent nuclear fuel at Forsmark:main report of the SR-Site project[R].Stockholm:Swedish Nuclear Fuel and Waste Management Company,2011.