Assessment study about the risk of Wilks’ formula for uncertainty quantification of design extension condition scenarios in prototype Gen-IV sodium fast reactor

Sensitivity analysis and uncertainty quantification using Wilks’ formula and Monte Carlo for Unprotected Loss of Flow (ULOF) and Unprotected Transient OverPower (UTOP) accidents of prototype Gen-IV sodium-cooled fast reactor were performed. Multi-dimensional analysis for reactor safety for liquid metal reactors code calculations were conducted while simultaneously varying the values of all uncertain parameters according to their distribution using parallel computing platform integrated for uncertainty and sensitivity analysis to obtain uncertainty bands for Figures of Merit (FOM) – coolant, fuel centerline, and cladding temperature at the hottest fuel rod. To specify the uncertainty range of the parameters for each accident scenario, literature survey and expert judgments were consulted. By the sensitivity analysis, the importance ranking of 25 parameters in model identification and ranking table based on phenomena identification and ranking table was identified. Through Monte Carlo calculation, 95% upper limit and 95% confidence level were obtained, and about 2% and 5% under-prediction (risk) of FOM of ULOF and UTOP accidents using Wilks’ formula were confirmed, respectively.     

SARAX程序系统在钠冷快堆瞬态分析中的应用

无保护事故下的瞬态分析是钠冷快堆安全分析的重要内容。基于OECD/NEA发布的MOX-3600和MET-1000基准题,本文利用SARAX程序系统对不同钠冷快堆进行了瞬态计算,分析了堆内各种反应性反馈效应,并计算了无保护失流(ULOF)事故和无保护超功率运行(UTOP)事故下燃料温度和冷却剂温度的变化。计算结果表明：SARAX程序系统在快堆瞬态分析中可给出合理的参数预测结果;ULOF事故对于钠冷快堆是更为严重的事故瞬态,会导致堆内的钠沸腾进而发生严重事故。     

Transmutation of americium in a medium size sodium cooled fast reactor design

We have performed transient analysis of a medium size sodium cooled reactor loaded with different fractions of americium in the fuel. Unprotected Loss of Flow (ULOF) and Unprotected Transient over Power (UTOP) accidents were simulated in a geometrical model of BN600, using safety parameters obtained with the SERPENT Monte Carlo code.     

Safety performance comparation of MOX, nitride and metallic fuel based 25–100 MWe Pb–Bi cooled long life fast reactors without on-site refuelling

In this paper the safety performance of 25–100 MWe Pb–Bi cooled long life fast reactors based on three types of fuels: MOX, nitride and metal is compared and discussed. In the fourth generation NPP paradigm, especially for Pb–Bi cooled fast reactors, inherent safety capability is necessary against some standard accidents such as unprotected loss of flow (ULOF), unprotected rod run-out transient over power (UTOP), unprotected loss of heat sink (ULOHS). Selection of fuel type will have important impact on the overall system safety performance.

The results of safety analysis of long life Pb–Bi cooled fast reactors without on-site fuelling using nitride, MOX and metal fuel have been performed. The reactors show the inherent safety pattern with enough safety margins during ULOF and UTOP accidents. For MOX fuelled reactors, ULOF accident is more severe than UTOP accident while for nitride fuelled cores UTOP accident may push power much higher than that comparable MOX fuelled cores.     

Code development and safety analyses for Pb–Bi-cooled direct contact boiling water fast reactor (PBWFR)

Pb–Bi-cooled direct contact boiling water fast reactor (PBWFR) can produce steam from the direct contact of feed-water and lead bismuth eutectic (LBE) in the chimney of 3 m height, which eliminates the bulky and flimsy steam generators. Moreover, as the coolant LBE is driven by the buoyancy of steam bubbles, the primary pump is not necessary in the reactor. The conceptual design makes the reactor simple, compact and economical. Owing to the large thermal expansion coefficient of LBE and good performance of steam lift pump, the reactor is expected to have good passive safety. A new computer code is developed to investigate the thermal–hydraulic behaviors and safety performance of PBWFR in the present work. Unprotected rod run-out transient over power (UTOP) and unprotected loss of flow (ULOF)/unprotected loss of heat sink (ULOHS) are simulated to test and verify its safety. The results show that PBWFR has very good inherent safety due to the satisfactory neutron and thermal–physical properties of LBE. Cladding materials turn to be the key factor to restrict its safety performance and UTOP is more dangerous for PBWFR. It's suggested that it should appropriately reduce the maximum value of the control rods to mitigate the consequence of UTOP due to good reactivity feedbacks in the core.     

Accident analysis of lead or lead—bismuth cooled small safe long-life fast reactor using metallic or nitride fuel

Safety analysis of a lead or lead—bismuth cooled small safe long-life fast reactor was performed. It is proposed that the reactor be used in relatively isolated areas, and operated to the end of its life without refueling or fuel shuffling. In the present paper the reactor power and lifetime are set at 150 MWt and 12 years respectively. In order to assume its safety performance, the following accidents without scram were simulated with neutronic-thermal-hydraulic analysis: unprotected loss of flow (ULOF), unprotected rod run-out transient over power (UTOP), simultaneous ULOF and UTOP accidents, and simultaneous ULOF, UTOP and unprotected loss of heat sink (ULOHS) accidents. For each type of accident, four types of long-life small reactor (lead cooled metallic fueled, lead cooled nitride fueled, lead-bismuth cooled metallic fueled, and lead—bismuth cooled nitride fueled) were analyzed. It is shown that all the proposed designs can survive these accidents without requiring help from the operator or active devices.     

Comparative study on safety performance of nitride fueled lead-bismuth cooled fast reactor with various power levels

In the present study safety performance of nitride fueled lead-bismuth cooled fast reactors of several sizes (150 MWt 2500 MWt) but all having maximum burn-up of about 911 % HM are evaluated and compared. Small reactors can be operated up to 12 years, and large reactors(2500MWt) can be operated up to about 4 years without refueling or fuel shuffling. In each reactor excess reactivity is minimized up to below β_eff in order to eliminate super-prompt critical accident. The ULOF and UTOP accident simulation was performed for each design and the results showed that all reactors could survive both accidents passively/inherently. However the temperature margin, especially for cladding, is larger for smaller reactor.     

空间快堆事故工况下温差发电器特性研究

从温差发电器的瞬态导热数学模型出发，研究空间快堆在发生无保护超功率事故(UTOP)与无保护失流事故(ULOF)情况下温差发电器温度和热电转换效率的变化趋势。结果表明，在空间快堆发生事故时，温差发电器的热力学变化足以保证热电装置和空间快堆的安全性。     

Preliminary neutronic and thermal-hydraulic analysis of a 2 MW Thorium-based Molten Salt Reactor with Solid Fuel

The Fluoride-salt-cooled High temperature Reactor (FHR) is an advanced concept combining attractive attributes by adopting low pressure liquid salt, high temperature coated particle fuel and air-Brayton combined cycle. 2 MW Thorium-based Molten Salt Reactor with Solid Fuel (TMSR-SF) designed by Shanghai Institute of Applied Physics (SINAP) as a test reactor is planned to be constructed. In this paper, the preliminary neutronic and thermal-hydraulic analysis of the TMSR-SF is performed. The neutronic investigation is conducted by developing a validated 3-D model for the reactor with MCNP-4C. Core physics parameters of TMSR-SF including the effective multiplication factor, neutron flux distribution, power density distribution, control system worth, reactivity coefficients and kinetics parameters are obtained, which are used as input parameters for the thermal-hydraulic analysis of the TMSR-SF. The FHR Safety Analysis Code (FSAC) is extended to study the safety characteristics of the TMSR-SF by simulating four types of basic transient conditions including the unprotected loss of flow (ULOF), unprotected overcooling (UOC), unprotected transient overpower (UTOP) and the combination of ULOF and UTOP. The results show that the concept design of TMSR-SF is an inherently safe design with no temperature limits exceeded in the analyzed transient conditions.     

Transient analyses for accelerator driven system PDS-XADS using the extended SIMMER-III code

Transient analyses for Preliminary Design Studies of an Experimental Accelerator Driven System (PDS-XADS) were performed with the reactor safety analysis code SIMMER-III, which was originally developed for the safety assessment of sodium-cooled fast reactors and recently extended by the authors so as to describe the XADS specifics such as subcritical core, strong external neutron source and lead–bismuth–eutectic (LBE) coolant. As transient scenarios, the following cases were analyzed in accordance with the PDS-XADS program: spurious beam trip (BT), unprotected beam overpower (UBOP), unprotected transient overpower (UTOP), unprotected loss of flow (ULOF) and unprotected blockage (UBL) in a single fuel assembly. In addition, to cover some core-melt situations and investigate the potential for recriticalities, so-called snap-shot analyses with ad hoc postulated severe blockage conditions were also investigated.The simulation results for BT and UBOP showed that immediate fuel damage might not take place under short-time beam interruption or a 100% increase of the external neutron source. Concerning UTOP, it was found that a reactivity jump of 1 $ would not lead to damage of the fuel and the cladding. The ULOF simulation showed that the remaining natural convection of the coolant would prevent the cladding from disruptions. In the simulation of UBL in a single fuel assembly, it was shown that no cladding failure might be expected, due to the radial heat transfer and the coolant flow in the hexcan gap. Under an artificial suppression of the radial heat transfer for this UBL case, a pin failure occurred in the simulation but subsequent fuel sweep-out into the upper plenum region would bring a reactivity reduction and no power excursion. The severe accident simulations starting from postulated blockage above an already disrupted core showed that a severe recriticality could be avoided by the fuel sweep-out into the dummy-assembly or hexcan gap regions.The present simulation results showed that the current PDS-XADS design has a remarkable resistance against severe transient scenarios even in core-degradation conditions.     

Fundamental safety strategy against severe accidents on prototype sodium-cooled fast reactor

The accident categories of severe accidents (SAs) for prototype sodium-cooled fast reactor (SFR) which need proper measures were investigated through the internal event probabilistic risk assessment (PRA) and event tree analysis for the external event and six accident categories, unprotected loss of flow (ULOF), unprotected transient over power (UTOP), unprotected loss of heat sink (ULOHS), loss of reactor sodium level (LORL), protected loss of heat sink (PLOHS) and station blackout (SBO), were identified. Fundamental safety strategy against these accidents is studied and clearly stated considering the characteristics and existing accident measures of prototype SFR, and concrete measures based on this safety strategy are investigated and organized. The sufficiency of these SA measures is confirmed by comparing the evaluated core damage frequency (CDF) and containment failure frequency (CFF) to the target value, 1×10^?5 and 1×10^?6 per plant operating year, respectively, which were selected based on the IAEA's safety target. However, the target value of CDF and CFF should be satisfied considering all the SAs caused by both internal and external events. External event PRA for prototype SFR is now under evaluation and we set out to satisfy the target value of CDF and CFF considering both internal and external events.     

先进空间快堆安全特性分析

以200kW空间快堆RAPID－L为对象，建立瞬态分析模型，分析了在无保护超功率事故UTOP和无保护失流事故ULOF下的瞬态特性。计算结果表明:快速型锂膨胀模块（LEM）可以随着冷却剂温度变化自动快速的响应，能够在不停堆的情况下保证反应堆的安全，因此，RAPID－L具有固有安全特性。     

Study of the Self-Controllability for the Fast Reactor Core with High-Thermal-Conductivity Fuel

The tolerance capability against ATWS for the FBR core with metallic fuel can be improved by employing a fuel with high thermal conductivity (HTC fuel) instead of the conventional metallic fuel, UPu-Zr. To investigate the self-controllability for the HTC-fueled core with U-Pu-Al alloy fuel, having one order of magnitude higher thermal conductivity than that of the U-Pu-Zr, the core employing the U-Pu-Al fuel was evaluated against ULOF and UTOP. Based on the systematic calculation, it was found that the larger temperature margin between the steady state and ULOF/UTOP conditions caused the excellent tolerance capability against ULOF and UTOP for the HTC-fueled core compared with that for the Zralloy-fueled core. Also, the conditions of the core reactivity coefficients required for neither fuel melting nor coolant boiling were investigated by using a “self-controllability map” consisting of effective fuel and coolant reactivities. As a result, the self-controllable region was found to be expanded especially for UTOP in the case of the HTC-fueled core.     

Comparative study of unprotected loss of flow accident analysis of 1000 MWe and 500 MWe Fast Breeder Reactor Metal (FBR-M) cores and their inherent safety

Unprotected loss of flow (ULOF) analysis of metal (U–Pu–6% Zr) fuelled 500 MWe and 1000 MWe pool type FBR are studied to verify the passive shutdown capability and its inherent safety parameters. Study is also made with uncertainties (typically 20%) on the sensitive feedback parameters such as core radial expansion feedback and sodium void reactivity effect. Inference of the study is, nominal transient behavior of both 500 MWe and 1000 MWe core are benign under unprotected loss of flow accident (ULOFA) and the transient power reduces to natural circulation based Safety Grade Decay Heat Removal (SGDHR) system capacity before the initiation of boiling. Sensitivity analysis of 500 MWe shows that the reactor goes to sub-critical and the transient power reduces to SGDHR system capacity before the boiling initiation. In the sensitivity analysis of 1000 MWe core, initiation of voiding and fuel melting occurs. But, with 80% core radial expansion reactivity feedback and nominal sodium expansion reactivity feedback, the reactor was maintained substantially sub-critical even beyond when net power crosses the SGDHR system capacity. From the study, it is concluded that if the sodium void reactivity is limited (4.6 $) then the inherent safety of 1000 MWe design is assured, even with 20% uncertainty on the sensitive parameters.     

Feasibility study of nitride fuel core and recycle system toward self-consistent nuclear energy system

A concept of nitride core and recycling system in relation to SCNES⁽¹⁾ has been investigated and it has been found that the safety of intact core is enhanced by zero burnup reactivity and negative feedback at ULOF (Unprotected Loss of Flow) and ULOHS (Unprotected Loss of Heat Sink). The self-actuating modules are examined so as to eliminate recriticality of degraded core. The nitride core can employ transuranics-added fuels and burn long life radioactive fission products after isotope-separation of FPs. The enrichment of ¹⁵N and the laser isotope separation seem to need about 2.4% of produced electric energy in the preliminary evaluation.     

Amorphization and recrystallization of the ABO3 oxides

Single crystals of the ABO₃ phases CaTiO₃, SrTiO₃, BaTiO₃, LiNbO₃, KNbO₃, LiTaO₃, and KTaO₃ were irradiated by 800 keV Kr⁺, Xe⁺, or Ne⁺ ions over the temperature range from 20 to 1100 K. The critical amorphization temperature, T_c, above which radiation-induced amorphization does not occur varied from approximately 450 K for the titanate compositions to more than 850 K for the tantalates. While the absolute ranking of increasing critical amorphization temperatures could not be explained by any simple physical parameter associated with the ABO₃ oxides, within each chemical group defined by the B-site cation (i.e., within the titanates, niobates, and tantalates), T_c tends to increase with increasing mass of the A-site cation. T_c was lower for the Ne⁺ irradiations as compared to Kr⁺, but it was approximately the same for the irradiations with Kr⁺ or Xe⁺. Thermal recrystallization experiments were performed on the ion-beam-amorphized thin sections in situ in the transmission electron microscope (TEM). In the high vacuum environment of the microscope, the titanates recrystallized epitaxially from the thick areas of the TEM specimens at temperatures of 800–850 K. The niobates and tantalates did not recrystallize epitaxially, but instead, new crystals nucleated and grew in the amorphous region in the temperature range 825–925 K. These new crystallites apparently retain some ‘memory' of the original crystal orientation prior to ion-beam amorphization.     

The prospect of mox fuel based PbBi cooled small nuclear power reactors

Safety performance of MOX fuel based PbBi cooled small fast power reactors has been analyzed and discussed. Though the thermal conductivity of MOX fuel is not large relative to that of nitride or metal fuel, but by proper combination of relatively small power density and relatively large natural circulation it can compensate fuel temperature decrease with coolant temperature increase smartly during unprotected loss of flow accident. Under such condition, accident analysis discussed in this paper show that under unprotected total loss of flow (ULOF) accident the reactor can survive inherently using combination of reactivity feedback. For unprotected rod run out transient over power (UTOP) accident the MOX reactor can overcome external reactivity by smaller power increase compared to that of nitride fueled reactors case. In this case doppler feedback plays much more important role compared to radial expansion component. So the MOX fueled small power reactors discussed here can survive both UTOP and ULOF accident with still enough temperature margin.     

ULOF and UTOP Analyses of a Large Metal Fuel FBR Core Using a Detailed Calculation System

ULOF and UTOP analyses of a large metal fuel FBR core (1,500 MWe, averaged discharge burnup: 150 GWd/t) are conducted. The effect of core radial expansion is considered as the major negative feedback during the transient. A detailed analysis system is used, in which a transient core thermal-hydraulic code is coupled with three dimensional core radial deformation and reactivity feedback calculation codes, in order to calculate the radial expansion feedback. In ULOF analysis, the pump flow halving time is assumed to be 10 s, which is reasonably long and effective in avoiding too large power to flow ratio. The reactivity insertion during UTOP is set to be 34¢, based on the control rod reactivity design. As the analysis results, it is found that the core shows benign responses to both events, owing largely to the radial expansion feedback. No significant coolant boiling or fuel failure is predicted. The response during ULOF is compared to that of an oxide fuel core of similar design, and it is confirmed that the negative Doppler effect associated with the fuel temperature rise plays the major role in the quick power decrease.     

Thermodynamic studies on Cs4U5O17(s) and Cs2U2O7(s) by emf and calorimetric measurements

The oxygen potentials over the phase field: Cs₄U₅O₁₇(s)+Cs₂U₂O₇(s)+Cs₂U₄O₁₂(s) was determined by measuring the emf values between 1048 and 1206 K using a solid oxide electrolyte galvanic cell. The oxygen potential existing over the phase field for a given temperature can be represented by: Δμ(O₂) (kJ/mol) (±0.5)=−272.0+0.207T (K). The differential thermal analysis showed that Cs₄U₅O₁₇(s) is stable in air up to 1273 K. The molar Gibbs energy formation of Cs₄U₅O₁₇(s) was calculated from the above oxygen potentials and can be given by, Δ_fG⁰ (kJ/mol)±6=−7729+1.681T (K). The enthalpy measurements on Cs₄U₅O₁₇(s) and Cs₂U₂O₇(s) were carried out from 368.3 to 905 K and 430 to 852 K respectively, using a high temperature Calvet calorimeter. The enthalpy increments, (H⁰_T−H⁰₂₉₈), in J/mol for Cs₄U₅O₁₇(s) and Cs₂U₂O₇(s) can be represented by, H⁰_T−H⁰_298.15 (Cs₄U₅O₁₇) kJ/mol±0.9=−188.221+0.518T (K)+0.433×10⁻³T² (K)−2.052×10⁻⁵T³ (K) (368 to 905 K) and H⁰_T−H⁰_298.15 (Cs₂U₂O₇) kJ/mol±0.5=−164.210+0.390T (K)+0.104×10⁻⁴T² (K)+0.140×10⁵(1/T (K)) (411 to 860 K). The thermal properties of Cs₄U₅O₁₇(s) and Cs₂U₂O₇(s) were derived from the experimental values. The enthalpy of formation of (Cs₄U₅O₁₇, s) at 298.15 K was calculated by the second law method and is: Δ_fH⁰_298.15=−7645.0±4.2 kJ/mol.     

钠冷快堆反应性意外引入事故时停堆保护研究

在反应堆系统中,当反应堆处于异常工况时,如果运行参数超出保护限值,则由保护系统触发相关保护动作,以保证反应堆的状态符合事故验收准则的要求。本文将通过Simulink建立钠冷快堆主要系统模型,在发生反应性意外引入事故时,借鉴快堆事故分析中预期瞬态无停堆保护（ATWS）的分析方法,基于相应保护参数的测量误差和数据处理过程对反应堆一回路的保护参数及其整定值进行研究,并确保钠冷快堆的状态在整个反应性引入事故过程中符合钠冷快堆的事故验收准则。仿真结果表明,当发生补偿棒失控提升5 s和10 s时,目前的堆芯出口钠温、功率、功率流量比等保护参数的整定值、信号测量延迟及落棒时间可取其他值。当补偿棒失控提升15 s时,只要保证保护参数整定值、相应参数的信号测量延迟及落棒时间能使反应堆在36.45 s前进入深度次临界都是可以的。