Accident source term and radiological consequences of a small modular reactor

Accident source term and radiological consequences of a small modular reactor 1 2 first-author https://orcid.org/0000-0001-7044-6807 1 2 1 corresp * wangshaowei@chinansc.cn; * wangshaowei@chinansc.cn; wangshaowei@chinansc.cn 1 1 2 corresp xuchao@chinansc.cn xuchao@chinansc.cn xuchao@chinansc.cn 1 Nuclear and Radiation Safety Center, Ministry of Ecology and Environment, Beijing 102401, China Nuclear and Radiation Safety Center, Ministry of Ecology and Environment, Beijing 102401, China State Environmental Protection Key Laboratory of Nuclear and Radiation Safety Regulatory Simulation and Validation, Beijing 102401, China State Environmental Protection Key Laboratory of Nuclear and Radiation Safety Regulatory Simulation and Validation, Beijing 102401, China Considering the growing global demand for energy and the need for countries to achieve climate goals, there is an increasing global interest in small modular reactors (SMRs) and their applications. Accident source term and radiological consequence evaluations of SMRs are key components of nuclear and radiation safety reviews, which affect the site, exclusion area (EAB), and low population zone (LPZ) outer boundaries. Based on the design characteristics of the SMR and accident analysis results, a theoretical model of a whole-core fuel cladding damage accident was constructed to study the radioactivity released into the environment and its consequences. The accident source term and radiation dose calculation models were established to analyze the released amounts of radionuclides and the total effective dose affecting individuals at the site boundary. The results showed that the amount of radionuclides released into the environment after a whole-core fuel cladding damage accident reached 10 14 Bq, among which the release amount of 133 Xe was the largest. The total effective dose at the site boundary 30 days after the accident was 8.65 mSv. The highest total effective dose affecting individuals occurred to the east-north-east. The results of the accident source term and radiological consequence provide technical support for site boundary dose assessments and reviews of SMRs. Small modular reactor Accident Source term Radiological consequence Total effective dose Introduction 1 Nuclear energy can not only be used to generate electricity but also to convert the heat energy generated by nuclear fission through heat exchange into hot water and steam required for urban heating, achieving clean heating and reducing CO 2 emissions [ 1 1 ]. Compared with large reactors, small modular reactors (SMRs) have a number of advantages, such as a high inherent safety, shorter construction period, lower site restrictions, lower financial risks, a small er environmental impact, and cleaner, lower carbon emissions, which may play a key role in the clean energy transition [ 2 2 - 3 3 2-3 ]. SMRs can fulfil the need for flexible power generation for a wide range of users and applications [ 4 4 - 6 6 4-6 ]. As such, with the increase in people’s living standards, SMRs have attracted increased attention. Several countries are actively developing and deploying SMRs, recognizing their potential for enhancing energy supply security. According to the International Atomic Energy Agency (IAEA) booklet ‘Advances in Small Modular Reactor Technology Developments’ there are more than 70 SMR designs under development for different applications [ 7 7 - 8 8 7-8 ]. For example, four integral pressurized-water SMRs are under development in the USA, namely the NuScale, Westinghouse SMR, SMR-160, and mPower. Additionally, SMRs have been developed by the Russian Federation, such as RITM-200, UNITHERM, VK-300, KARAT-45, KARAT-100, RUTA-70, ELENA, KLT-40S, and RITM-200M, of which KLT-40S has been connected to the grid in May 2020, starting commercial operation. Similarly, a series of SMRs have been developed or constructed in other countries, including China (ACP100, CAP200, DHR400, ACPR50S, HTR-PM, and smTMSR-400), Argentina (CAREM), Japan (DMS, IMR, GTHTR300, and HTTR), and Canada (CANDU SMR, STARCORE, ARC-100, and IMSR). In China, research on nuclear power technology for SMRs has received significant attention. The 14th Five-Year Plan for the National Economic and Social Development of the People's Republic of China and the Outline of 2035 Vision Target proposes to promote the demonstration of advanced reactor types, such as SMRs, 600 MW commercial high-temperature gas-cooled reactors, and offshore floating nuclear power platforms. The ACP100 was developed by the China National Nuclear Corporation (CNNC) for electricity production, heating, and seawater desalination and adopts verified passive safety systems to cope with accident consequences [ 9 9 ]. The CAP200 is a small pressurized water reactor (PWR) with high safety and flexibility developed by the Shanghai Nuclear Engineering Research and Design Institute (SNERDI), which has been designed for nuclear cogeneration and replacement of retired fossil power plants in urban areas [ 10 10 ]. The district heating reactor (DHR400) is a pool-type reactor designed by the CNNC for district heating, seawater desalination, and radioisotope production, operating at a low temperature and atmospheric pressure [ 11 11 ]. The very low possibility of a core meltdown eliminates the likelihood of a large radioactivity release and simplifies the off-site emergency response. The HTR-PM is a commercial demonstration unit partly based on the HTR-10 prototype reactor for electricity production designed by Tsinghua University [ 12 12 ]. In December 2021, it was successfully connected to the grid for power generation, making it the world’s first high-temperature gas-cooled reactor pebble bed module, and has achieved the leap from laboratory to engineering applications in China [ 13 13 ]. Furthermore, research on thorium salt reactors was launched by the Shanghai Institute of Applied Physics, Chinese Academy of Sciences (SINAP, CAS) [ 14 14 ]. As a thorium molten salt demonstration reactor, smTMSR-400 will be applied as a high-temperature heat source for electricity generation, aiming to satisfy energy-diversified demands. Although significant advancements have been made in various SMR technologies in recent years, some technical issues, such as defining the source term for SMRs with regard to determining the exclusion area (EAB) and the low population zone (LPZ) outer boundaries as well as developing new code for SMRs, still attract considerable attention. The IAEA has been facilitating Member States to address common technologies and issues of SMRs, and countries around the world are trying to take measures to solve them. During site selection for SMRs, analysis of the accident source term and radiological consequences is key for determining a suitable site, the EAB, and the LPZ outer boundary distance [ 15 15 ]. The lower amount of fuel in the core, improved core cooling features, and resulting elimination of accidents, such as a large break loss-of-coolant accident (LBLOCA), reduce the likelihood of core melting in SMRs, resulting in less accidents and less severe consequences compared with large reactors [ 16 16 ]. The source term of SMRs is smaller than that of large reactors, and the consequences of accidents are of a lower magnitude. In accident analysis, computer codes are usually used to estimate the source term and consequences for nuclear power plants. However, due to the technological differences of SMRs, practical evidence may be required to demonstrate their applicability [ 17 17 - 18 18 17-18 ]. The PAVAN code developed by the Pacific Northwest National Laboratory has been widely used to calculate offsite atmospheric dispersion factors (χ/ Q s) at the EAB and LPZ outer boundary of large light water reactors (LWR). PAVAN is conservative, especially at shorter distances, and overpredicts χ/Qs by two to three orders of magnitude, while ARCON96 overpredicts χ/ Q by one to two orders of magnitude at cumulative frequencies above 95 percent [ 19 19 ]. A comparison of the results of the two codes showed that, within the range of 100–500 m, the χ/ Q s calculated using PAVAN was approximately 6–10 times larger than that calculated by ARCON96 [ 20 20 ]. SMRs have smaller offsite distances to consider in offsite radiological consequence calculations than traditional large LWRs. Therefore, the NuScale SMR uses ARCON96 rather than PAVAN to calculate offsite atmospheric dispersion values [ 21 21 ]. The U.S. Nuclear Regulatory Commission (NRC) completed the review of the NuScale SMR design certification application, released the final safety assessment report in August 2020, and issued the new regulatory guide (RG) 4.28 in August 2021 (Use of ARCON methodology for calculation of accident-related offsite atmospheric dispersion factors). RG 4.28 proposes procedures for using the ARCON code to estimate χ/ Q s at the EAB and the LPZ outer boundary at distances of up to 1,200 m from the nearest edge of a building within the power block area, which provides an important reference for the evaluation of SMR accident source terms and radiological consequences [ 22 22 ]. To date, the selection of accidents for SMRs and the applicability of ARCON for the calculation of off-site χ/ Q s remains the focus of attention. In this study, calculation models of the accident source term, atmospheric dispersion factor, and radiation dose were created for an SMR in China. Then, investigations of the radiological consequences of this SMR were carried out to determine the amount of radioactive substances released as well as the resulting total effective dose. As such, this study provides technical support for dose assessments and reviews at the off-site boundary of SMRs. Accident selection 1 The SMR was an integrated heating reactor with a thermal power of 200 MW. The core contained 57 fuel assemblies with an average fuel enrichment of 3.5 % and a 24-month refueling cycle. It adopted an integrated design with a high inherent safety. The main pipe and pump were cancelled, which eliminated the large and middle break losses of coolant or rod ejection accident as well as accidents related to main pump failure. The boron-free core design reduced the generation of radioactive wastewater. Passive designs, such as secondary passive residual heat removal systems, emergency core cooling systems, and air-cooled containment cooling systems, improved safety. The SMR was equipped with an appropriate control system, protection system, and engineered safety features to minimize the release of radioactive substances into the environment under various operating conditions and protect the public and staff from excessive radiation hazards. The design objective of the SMR was a core damage frequency (CDF) of less than 10 -6 per reactor year and a large release frequency (LRF) of less than 10 -7 per reactor year. The probabilistic safety assessment (PSA) analysis results showed that the LRF was 1.5×10 -8 per reactor year, which was less than 10 -7 per reactor year and thus met the probability safety goal of actual elimination. The Safety Review Principles of Small PWR Nuclear Power Plants (Trial) require that the important event sequence of the beyond design-basis accident for small PWR nuclear power plants is analyzed to evaluate whether the safety target is met [ 23 23 ]. In this study, based on the design characteristics and accident analysis results of the SMR, a whole-core fuel cladding damage accident caused by a pipe break was simulated to analyze the accident source term and radiological consequences. Methods and parameters 1 Calculation methods 2 After an accident, the whole-core fuel claddings damage and nuclides are released from the fuel cladding gap and the primary coolant into the containment and subsequently into the environment after a series of removal actions. The process of the accident radiological consequence analysis is shown in Fig. 1 Fig. 1 . For calculation of the radioactivity released into the containment and environment, the nuclides were divided into two categories according to their decay chains: precursor and daughter nuclides. Figure 2 Figure 2 shows several scenarios of the nuclide decay process, where N 1 is the precursor nuclide and N 2 and N 3 are daughter nuclides. In the process of nuclide release from the reactor core into the containment and environment following an accident, the generation and depletion mechanisms of nuclides differ between time periods. The generation of nuclides in the containment atmosphere includes the release of the core fuel cladding gap and primary coolant as well as the decay of the precursor nuclides. The depletion factors to be considered vary between nuclides in the containment atmosphere, and include nuclide decay and containment leakage for inert gases, and nuclide decay, natural removal, and containment leakage for iodine and aerosols, since this would reduce their radioactivity in the containment atmosphere. Furthermore, the nuclides in the environment originate from leakage from the containment. In the analysis of the accident source term, some nuclides, such as 131 I, 132 I, 133 I, 134 I, 135 I, 87 Kr, 88 Kr, 138 Xe, and 136 Cs, were precursor nuclides, and others, such as 85 Kr, 131 Xe m , 133 Xe m , 133 Xe, 135 Xe m , 135 Xe, and 138 Cs, were daughter nuclides. Radioactivity models of the precursor and daughter nuclides were established to calculate their release amounts into the containment and environment. The calculation models of nuclide radioactivity in the containment atmosphere after the accident were as follows [ 24 24 ]: I. The precursor nuclide radioactivity model: <math display="block" id="M1"><mrow><mfrac><mrow><mtext>d</mtext><msub><mi>A</mi><mrow><mi>c</mi><mo>,</mo><mi>i</mi></mrow></msub><mo stretchy="false">(</mo><msub><mi>t</mi><mi>n</mi></msub><mo stretchy="false">)</mo></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac><mo>=</mo><msub><mi>P</mi><mrow><msub><mi>A</mi><mrow><mi>c</mi><mo>,</mo><mi>i</mi></mrow></msub></mrow></msub><msup><mi>e</mi><mrow><mo>−</mo><msub><mi>λ</mi><mi>i</mi></msub><msub><mi>t</mi><mi>n</mi></msub></mrow></msup><mo>−</mo><mo stretchy="false">(</mo><msub><mi>λ</mi><mi>i</mi></msub><mo>+</mo><msub><mi>λ</mi><mrow><mtext>di</mtext></mrow></msub><mtext>+</mtext><msub><mi>λ</mi><mn>0</mn></msub><mo stretchy="false">)</mo><msub><mi>A</mi><mrow><mi>c</mi><mo>,</mo><mi>i</mi></mrow></msub><mo stretchy="false">(</mo><msub><mi>t</mi><mi>n</mi></msub><mo stretchy="false">)</mo></mrow></math> II. The daughter nuclide radioactivity model: <math display="block" id="M2"><mrow><mfrac><mrow><mtext>d</mtext><msub><mi>A</mi><mrow><mi>c</mi><mo>,</mo><mi>j</mi></mrow></msub><mo stretchy="false">(</mo><msub><mi>t</mi><mi>n</mi></msub><mo stretchy="false">)</mo></mrow><mrow><mtext>d</mtext><mi>t</mi></mrow></mfrac><mo>=</mo><msub><mi>P</mi><mrow><msub><mi>A</mi><mrow><mi>c</mi><mo>,</mo><mi>j</mi></mrow></msub></mrow></msub><msup><mi>e</mi><mrow><mo>−</mo><msub><mi>λ</mi><mi>j</mi></msub><msub><mi>t</mi><mi>n</mi></msub></mrow></msup><mo>+</mo><msub><mi>λ</mi><mi>j</mi></msub><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>j</mi><mo>−</mo><mn>1</mn></mrow></munderover><mrow><msub><mi>ξ</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub><msub><mi>A</mi><mrow><mi>c</mi><mo>,</mo><mi>i</mi></mrow></msub><mo stretchy="false">(</mo><msub><mi>t</mi><mi>n</mi></msub><mo stretchy="false">)</mo></mrow></mstyle><mo>−</mo><mrow><mo>(</mo><mrow><msub><mi>λ</mi><mi>j</mi></msub><mo>+</mo><msub><mi>λ</mi><mrow><mtext>dj</mtext></mrow></msub><mo>+</mo><msub><mi>λ</mi><mn>0</mn></msub></mrow><mo>)</mo></mrow><msub><mi>A</mi><mrow><mi>c</mi><mo>,</mo><mi>j</mi></mrow></msub><mo stretchy="false">(</mo><msub><mi>t</mi><mi>n</mi></msub><mo stretchy="false">)</mo><mo>,</mo></mrow></math> where <math id="M3"><mrow><msub><mi>A</mi><mrow><mi>c</mi><mo>,</mo><mi>i</mi></mrow></msub><mo stretchy="false">(</mo><msub><mi>t</mi><mi>n</mi></msub><mo stretchy="false">)</mo></mrow></math> and <math id="M4"><mrow><msub><mi>A</mi><mrow><mi>c</mi><mo>,</mo><mi>j</mi></mrow></msub><mo stretchy="false">(</mo><msub><mi>t</mi><mi>n</mi></msub><mo stretchy="false">)</mo></mrow></math> are the radioactivity of nuclides i and j in the containment, respectively (Bq); <math id="M5"><mrow><msub><mi>P</mi><mrow><msub><mi>A</mi><mrow><mi>c</mi><mo>,</mo><mi>i</mi></mrow></msub></mrow></msub></mrow></math> and <math id="M6"><mrow><msub><mi>P</mi><mrow><msub><mi>A</mi><mrow><mi>c</mi><mo>,</mo><mi>j</mi></mrow></msub></mrow></msub></mrow></math> are the release rates of nuclides i and j in the reactor core and primary coolant, respectively (Bq/h); <math id="M7"><mrow><msub><mi>λ</mi><mi>i</mi></msub></mrow></math> and <math id="M8"><mrow><msub><mi>λ</mi><mi>j</mi></msub></mrow></math> are the decay constants of nuclides i and j , respectively (h -1 ); <math id="M9"><mrow><msub><mi>λ</mi><mn>0</mn></msub></mrow></math> is the containment leakage rate (h -1 ); <math id="M10"><mrow><msub><mi>λ</mi><mrow><mtext>di</mtext></mrow></msub></mrow></math> and <math id="M11"><mrow><msub><mi>λ</mi><mrow><mtext>dj</mtext></mrow></msub></mrow></math> are the removal constants of nuclides i and j in the containment (h -1 ); <math id="M12"><mrow><msub><mi>ξ</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub></mrow></math> is the branching ratio of nuclide i decaying into nuclide j ; and t n is the time that has passed since the accident (h). The nuclide radioactivity released from the containment into the environment was calculated using the following equations [ 24 24 ]: <math display="block" id="M13"><mrow><msub><mi>A</mi><mrow><mi>e</mi><mo>,</mo><mi>i</mi></mrow></msub><mo stretchy="false">(</mo><msub><mi>t</mi><mtext>n</mtext></msub><mo stretchy="false">)</mo><mo>=</mo><mstyle displaystyle="true"><mrow><msubsup><mo>∫</mo><mrow><msub><mi>t</mi><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub></mrow><mrow><msub><mi>t</mi><mi>n</mi></msub></mrow></msubsup><mrow><msub><mi>λ</mi><mn>0</mn></msub><msub><mi>A</mi><mrow><mi>c</mi><mo>,</mo><mi>i</mi></mrow></msub><mo stretchy="false">(</mo><msub><mi>t</mi><mtext>n</mtext></msub><mo stretchy="false">)</mo><mtext>d</mtext><mi>t</mi></mrow></mrow></mstyle><mo>,</mo></mrow></math> <math display="block" id="M14"><mrow><msub><mi>A</mi><mrow><mi>e</mi><mo>,</mo><mi>j</mi></mrow></msub><mo stretchy="false">(</mo><msub><mi>t</mi><mtext>n</mtext></msub><mo stretchy="false">)</mo><mo>=</mo><mstyle displaystyle="true"><mrow><msubsup><mo>∫</mo><mrow><msub><mi>t</mi><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub></mrow><mrow><msub><mi>t</mi><mi>n</mi></msub></mrow></msubsup><mrow><msub><mi>λ</mi><mn>0</mn></msub><msub><mi>A</mi><mrow><mi>c</mi><mo>,</mo><mi>j</mi></mrow></msub><mo stretchy="false">(</mo><msub><mi>t</mi><mtext>n</mtext></msub><mo stretchy="false">)</mo><mtext>d</mtext><mi>t</mi><mo>,</mo></mrow></mrow></mstyle></mrow></math> where <math id="M15"><mrow><msub><mi>A</mi><mrow><mi>e</mi><mo>,</mo><mi>i</mi></mrow></msub><mo stretchy="false">(</mo><msub><mi>t</mi><mtext>n</mtext></msub><mo stretchy="false">)</mo></mrow></math> and <math id="M16"><mrow><msub><mi>A</mi><mrow><mi>e</mi><mo>,</mo><mi>j</mi></mrow></msub><mo stretchy="false">(</mo><msub><mi>t</mi><mtext>n</mtext></msub><mo stretchy="false">)</mo></mrow></math> are the radioactivity of nuclides i and j in the environment, respectively (Bq). The time that passed since the accident was divided into several time periods ( t n -1 , t n ), and the nuclide radioactivity in each was calculated iteratively. The division of the time steps comprehensively considered factors such as changes in the aerosol removal constant with time, the removal time of iodine, and the time node of nuclide radioactivity output results. The natural removal effects of iodine and aerosols in the containment atmosphere are restricted by the natural removal coefficient and decontamination factor. The calculation model for the nuclide removal time in the containment atmosphere is therefore as follows [ 24 24 ]: <math display="block" id="M17"><mrow><mtable columnalign="left"><mtr columnalign="left"><mtd columnalign="left"><mrow><mi>t</mi><mo>=</mo><msub><mi>t</mi><mn>0</mn></msub><mo>−</mo><mfrac><mrow><mi>ln</mi><mfrac><mn>1</mn><mrow><mi>K</mi><mo>⋅</mo><mi>D</mi><mi>F</mi></mrow></mfrac></mrow><mrow><msub><mi>λ</mi><mtext>d</mtext></msub></mrow></mfrac><mo>,</mo></mrow></mtd><mtd columnalign="left"><mrow><mi>K</mi><mo>=</mo><mfrac><mn>1</mn><mrow><mn>0.5</mn><msub><mi>λ</mi><mtext>d</mtext></msub></mrow></mfrac><mrow><mo>(</mo><mrow><mn>1</mn><mo>-</mo><msup><mtext>e</mtext><mrow><mo>−</mo><mn>0.5</mn><msub><mi>λ</mi><mtext>d</mtext></msub></mrow></msup></mrow><mo>)</mo></mrow></mrow></mtd></mtr></mtable><mo>,</mo></mrow></math> where DF is the maximum decontamination factor of a nuclide; <math id="M18"><mrow><msub><mi>λ</mi><mtext>d</mtext></msub></mrow></math> is the removal constant of a nuclide (h -1 ); and t 0 is the release time of a nuclide from the reactor core and primary coolant into the containment (h). The 95 % χ/Q values for 16 downwind directions and the overall site were calculated using ARCON96 [ 24 24 - 25 25 24-25 ]. However, ACRON96 did not calculate the maximum sector at the 99.5th percentile. Instead, the 99.5th-percentile χ/Q value for each sector was obtained according to the calculation method described in RG 4.28 [ 21 21 ]. First, the percentage of time at which each χ/Q threshold was exceeded was calculated using the following formula: <math display="block" id="M19"><mrow><mi>P</mi><mo>=</mo><mrow><mo>(</mo><mrow><mn>1</mn><mo>−</mo><mfrac><mrow><msub><mi>H</mi><mrow><mtext>avg</mtext></mrow></msub></mrow><mrow><msub><mi>H</mi><mrow><mtext>total</mtext></mrow></msub></mrow></mfrac></mrow><mo>)</mo></mrow><mo>×</mo><mn>100</mn><mo>,</mo></mrow></math> where P is the percentage of time at which each χ/Q threshold is exceeded (%); H total is the total number of hours in the. LOG file for a given averaging interval; and H avg is the number of hours exceeded for each χ/Q threshold. A simple linear interpolation could then be used to determine the 99.5th-percentile χ/Q value using the following equation: <math display="block" id="M20"><mrow><mi>y</mi><mo>=</mo><msub><mi>y</mi><mn>1</mn></msub><mo>+</mo><mfrac><mrow><mi>x</mi><mo>−</mo><msub><mi>x</mi><mn>1</mn></msub></mrow><mrow><msub><mi>x</mi><mn>2</mn></msub><mo>−</mo><msub><mi>x</mi><mn>1</mn></msub></mrow></mfrac><mo>⋅</mo><mrow><mo>(</mo><mrow><msub><mi>y</mi><mn>2</mn></msub><mo>−</mo><msub><mi>y</mi><mn>1</mn></msub></mrow><mo>)</mo></mrow></mrow></math> where y is the 99.5th-percentile χ/ Q value (s/m 3 ); y 1 and y 2 are the smaller and greater of the two bounding χ/ Q values, respectively (s/m 3 ); x = 99.5; and x 1 and x 2 are the smaller and greater of the two exceedance frequencies, respectively. The larger of the two χ/ Q values, either the 99.5 % maximum sector value or the 95 % overall site value, were selected to represent the χ/ Q value for the 0–2 h, 2–8 h, 8–24 h, 24–96 h, and 96–720 h time intervals. The individual total effective dose included the inhalation dose from internal exposure, the cloud immersion dose, and the ground deposition dose from external exposure. The following equations were used to calculate the individual total effective doses [ 19 19 ]: <math display="block" id="M21"><mrow><msub><mi>D</mi><mi>a</mi></msub><mo>=</mo><mstyle displaystyle="true"><munder><mo>∑</mo><mi>i</mi></munder><mrow><msub><mrow><mtext>DCF</mtext></mrow><mi>i</mi></msub><msup><mrow/><mi>a</mi></msup><mstyle displaystyle="true"><munder><mo>∑</mo><mi>j</mi></munder><mrow><msub><mi>Q</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub><mo>⋅</mo><mrow><mrow><mo stretchy="false">(</mo><mi>χ</mi></mrow><mo>/</mo><mi>Q</mi></mrow><msub><mo stretchy="false">)</mo><mrow><mi>x</mi><mi>j</mi></mrow></msub></mrow></mstyle></mrow></mstyle><mo>,</mo></mrow></math> <math display="block" id="M22"><mrow><msub><mi>D</mi><mi>g</mi></msub><mo>=</mo><mstyle displaystyle="true"><munder><mo>∑</mo><mi>i</mi></munder><mrow><msub><mrow><mtext>DCF</mtext></mrow><mi>i</mi></msub><msup><mrow/><mi>g</mi></msup><mstyle displaystyle="true"><munder><mo>∑</mo><mi>j</mi></munder><mrow><msub><mi>Q</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub><mo>⋅</mo><msub><mi>ω</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub><mo>⋅</mo><mrow><mo>(</mo><mrow><mn>1</mn><mo>−</mo><msup><mi>e</mi><mrow><mo>−</mo><msub><mi>λ</mi><mi>i</mi></msub><mo>⋅</mo><msub><mi>t</mi><mi>j</mi></msub></mrow></msup></mrow><mo>)</mo></mrow><mo>/</mo><msub><mi>λ</mi><mi>i</mi></msub></mrow></mstyle></mrow></mstyle></mrow></math> <math display="block" id="M23"><mrow><msub><mi>D</mi><mtext>h</mtext></msub><mo>=</mo><mstyle displaystyle="true"><munder><mo>∑</mo><mi>i</mi></munder><mrow><msub><mrow><mtext>DCF</mtext></mrow><mi>i</mi></msub><msup><mrow/><mi>h</mi></msup><mstyle displaystyle="true"><munder><mo>∑</mo><mi>j</mi></munder><mrow><msub><mi>Q</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub><mo>⋅</mo><msub><mrow><mrow><mo>(</mo><mrow><mi>χ</mi><mo>/</mo><mi>Q</mi></mrow><mo>)</mo></mrow></mrow><mrow><mi>x</mi><mi>j</mi></mrow></msub><mo>⋅</mo><mtext>B</mtext><msub><mi>r</mi><mi>j</mi></msub></mrow></mstyle></mrow></mstyle><mo>,</mo></mrow></math> <math display="block" id="M24"><mrow><msub><mi>D</mi><mtext>t</mtext></msub><mo>=</mo><msub><mi>D</mi><mtext>a</mtext></msub><mo>+</mo><msub><mi>D</mi><mtext>g</mtext></msub><mo>+</mo><msub><mi>D</mi><mtext>h</mtext></msub><mo>,</mo></mrow></math> where D a and D g are cloud immersion dose and ground deposition dose from external exposure, respectively (Sv); D h is the inhalation dose from internal exposure (Sv); D t is the individual total effective dose (Sv); Q ij is the amount of nuclide i released into the environment during time interval j (Bq); (χ/Q) xj is the offsite atmospheric dispersion factor at x m from the release point during the time interval j (s/m 3 ); DCF i a is the effective dose conversion factor via cloud immersion of nuclide i (Sv/s)/(Bq/m 3 ); DCF i g is the effective dose conversion factor via ground deposition of nuclide i (Sv/s)/(Bq/m 3 ); DCF i h is the effective dose conversion factor via inhalation of nuclide i (Sv/Bq); ω ij is the ground deposition factor for nuclide i during time interval j (1/m 2 ); λ i is the decay constant for nuclide i (1/s); t j is the release time of the time interval j (s); and Br j is the adult breathing rate during the time interval j (m 3 /s). Main parameters 2 The main assumptions and parameters for the radioactivity and radiation dose calculations after the accident were as follows [ 26 26 , 27 27 , 28 28 , 29 29 , 30 30 ]: · It was assumed that the core was uncovered by a pipe break, all fuel claddings in the reactor core were damaged, and that the containment maintained its integrity. After the accident, nuclides were released from the fuel cladding gap and primary coolant into the containment. The core inventory used to calculate the accident source term was obtained from the end of cycle data ( Table 1 Table 1 ). 1 1 Nuclide 1 1 Radioactivity (Bq) 1 1 Nuclide 1 1 Radioactivity (Bq) 1 1 131 I 1 1 2.1×10 17 1 1 136 Cs 1 1 1.0×10 16 1 1 132 I 1 1 3.1×10 17 1 1 137 Cs 1 1 4.5×10 16 1 1 133 I 1 1 4.4×10 17 1 1 138 Cs 1 1 4.1×10 17 1 1 134 I 1 1 4.9×10 17 1 1 131 Xe m 1 1 2.3×10 15 1 1 135 I 1 1 4.2×10 17 1 1 133 Xe m 1 1 1.4×10 16 1 1 85 Kr m 1 1 5.8×10 16 1 1 133 Xe 1 1 4.4×10 17 1 1 85 Kr 1 1 4.1×10 15 1 1 135 Xe m 1 1 9.1×10 16 1 1 87 Kr 1 1 1.2×10 17 1 1 135 Xe 1 1 1.8×10 17 1 1 88 Kr 1 1 1.5×10 17 1 1 138 Xe 1 1 3.8×10 17 1 1 134 Cs 1 1 4.4×10 16 1 1 - 1 1 - · In the analysis of the radiological consequences of the accident, inert gas, iodine, and Cs released into the environment were considered the key nuclides. The production term of the precursor nuclides was taken into account. · After the accident, the release flow of the primary coolant was constant and the release time was 30 s. The elemental and organic iodine contents in the primary coolant were 97 % and 3 %, respectively. · The radionuclides in the cladding gap of the damaged fuel rods were linearly released into the containment within 30 min after the accident. The radionuclides released from the cladding gap mainly included inert gas, iodine, and alkali metals, and the release proportion was 5 % of the core inventory. The compositions of the particulate, elemental, and organic iodine released from the cladding gap into the containment were 95 %, 4.85 %, and 0.15 %, respectively. · Considering the natural removal of elemental iodine and aerosols in the containment, the decontamination factor limits were 200 and 1000, respectively. The natural removal rates of elemental iodine and aerosols were 1.3 h –1 and 0.1 h –1 , and the corresponding removal times were 4.35 h and 69.34 h, respectively. No deposition, resuspension, or filtration of inert gas was considered due to their inert nature. · Within 24 h after the accident, the leakage rate of the containment was 0.2 % of the containment free volume per day, and the leakage rate was halved after 24 h. · The meteorological data ARCON96 required for χ/ Q calculations, including precipitation, wind direction, wind speed, and cloud cover, were obtained from the annual observation statistics of a site in Heilongjiang, and covered more than 8700 h of data. Atmospheric stability was obtained using meteorological data. The release type was a ground release and the building aera was 0.01 m 2 . · The dose conversion factors were obtained from the GB18871, ICRP71, and federal guidance reports (FGR) No.11 and No.12, and the breath rate from the RG 1.4. The site boundary distance of the SMR was 160 m. According to the safety target of the small PWR, for the important sequence of the beyond design basis accident the individual total effective dose at the site boundary should be less than 10 mSv throughout the entire duration of the accident [ 22 22 ]. Results and discussion 1 Radioactivity released into the environment 2 The nuclide radioactivity released from the primary coolant after the accident was several orders of magnitude smaller than that released from the reactor core fuel cladding gap; therefore, it was negligible. The total radioactivity released into the environment after the accident was 10 14 Bq. Figure 3 Figure 3 shows the change in iodine radioactivity in the environment 30 days after the accident. The radioactivity of various forms of iodine in the environment was closely related to the iodine radioactivity in the cladding gap and containment. Although the particulate iodine in the containment undergoes natural removal over a long period of time, the radioactivity of the particulate iodine released into the environment reached 10 13 Bq after 30 days due to its high proportion in the cladding gap, which was much higher than that of elemental and organic iodine. While the proportion of elemental iodine in the cladding gap was higher than that of organic iodine, elemental iodine is affected by natural removal, such as sedimentation, heat conduction, and water vapor condensation, resulting in a similar release amount of both. There were differences in the release curves of each iodine form. For elemental and particulate iodine, 133 I released the largest amount, reaching 7.42×10 10 Bq and 1.26×10 13 Bq 30 days after the accident, respectively, which resulted from the combined effects of nuclide half-life, initial radioactivity, and natural removal. Regarding organic iodine, 131 I released the largest amount, with a radioactivity of 1.84×10 11 Bq. This was because organic iodine has no natural removal effect and is only affected by self-attenuation and the initial radioactivity. The longer the time after the accident, the more significant the effect of self-attenuation. Among organic iodine nuclides, 131 I has the longest half-life, resulting in a larger release amount compared to other iodine nuclides 30 days after the accident. The radioactivity of Cs released into the environment after the accident is shown in Figure 4 Figure 4 . 138 Cs had the largest initial radioactivity in the fuel cladding gap; therefore, the release amount of 138 Cs was the largest at the initial stage of the accident but, owing to its very short half-life (approximately 32 min) combined with natural removal effects, such as gravity settlement, thermal electrophoresis, and diffusion electrophoresis, the 138 Cs in the containment decayed quickly and was no longer released into the environment a few hours after the accident. In turn, the radioactivity of 134 Cs, 136 Cs, and 137 Cs in the environment gradually increased with time, but the rate of increase gradually slowed. After 30 days, the radioactivity of 134 Cs, 136 Cs, and 137 Cs in the environment reached equilibrium, where the released amounts of 134 Cs and 137 Cs were almost identical, reaching a radioactivity level of 10 12 Bq. The depletion factor of an inert gas is its own decay. At the beginning of the accident, the release amount of 88 Kr was the largest, and the release amounts of 85 Kr m , 87 Kr, and 88 Kr in the environment gradually reached equilibrium with time, whereas the radioactivity of 85 Kr continuously increased and did not reach equilibrium after 30 days ( Fig. 5 Fig. 5 ). 85 Kr released from the fuel cladding gap decayed slowly in the containment atmosphere owing to its long half-life (10.72 years) and was gradually released into the environment; therefore, its release amount was the largest among krypton nuclides. Regarding xenon nuclides, 133 Xe released the highest amount, with a radioactivity of 10 14 Bq in the environment ( Fig. 6 Fig. 6 ). The released amounts of 135 Xe m , 135 Xe, and 138 Xe reached a steady state and 133 Xe m tended to be balanced, while those of 131 Xe m and 133 Xe continued to increase after the accident. This was mainly because the half-life of 131 Xe m and 133 Xe is 11.84 days and 5.25 days, respectively, which is longer than that of other xenon nuclides. The time required for inert gases released into the environment to reach equilibrium is proportional to their half-life; the longer the half-life of the nuclide, the longer it takes for radioactivity to reach equilibrium. Radiation dose at the site boundary 2 The 99.5th-percentile χ/ Q values for the 16 downwind directions and the 95th-percentile χ/ Q values for the overall site at different time periods after the accident were obtained ( Fig. 7 Fig. 7 ). The maximum value of the 99.5th-percentile χ/ Q for the 16 downwind directions appeared in the east-north-east (ENE) and northeast (NE) directions, and the χ/ Q values decreased with time. In the 0–2 h and 2–8 h time intervals, the 95th-percentile χ/ Q values for the overall site were less than the maximum values of the 99.5th-percentile χ/Q for the 16 downwind directions, while the 95th-percentile χ/ Q values for the overall site in the 8–24 h, 24–96 h, and 96–720 h time intervals were significantly greater than the maximum values of the 99.5th-percentile χ/Q for the 16 downwind directions. The individual total effective doses (adults) at the site boundaries are shown in Fig. 8 Fig. 8 . Of the 16 downwind directions, the ENE direction received the largest radiation dose, followed by the NE direction. The individual total effective doses calculated using the 99.5th-percentile χ/ Q values for the 16 downwind directions were lower than those calculated using the 95th-percentile χ/ Q values for the overall site. According to the larger χ/ Q value of the 99.5-percent maximum sector value and the 95-percent overall site value for each time interval, the total effective dose at the site boundary was 8.65 mSv. The inhalation dose from internal exposure was the main contributor to the individual total effective dose, accounting for 88.5 %, followed by the cloud immersion dose from external exposure, which accounted for 8.7 %, while the contribution of the ground deposition dose from external exposure was small, accounting for only 2.8 %. The dose resulting from ground deposition had a long-term effect. After accidents where nuclides are released into the environment within a short time span, the ground deposition dose from external exposure can be ignored. For example, the NuScale SMR does not consider the ground deposition dose for the analysis of radiological consequences in fuel handling accident. The χ/ Q value and nuclide radioactivity released into the environment at different time periods after the accident jointly affected the individual total effective dose. At the 0–2 h time point, the cumulative release amount of nuclides in the environment was small, even though the χ/ Q value of the ENE direction was higher than that of the overall site. At the 2–8 h time point, the χ/ Q values of the ENE and NE direction were similar to that of the overall site. After 8 h, the χ/ Q value of the ENE direction was lower than that of the overall site, the nuclides in the containment were continuously released into the environment, especially those with a long half-life, and the release amount gradually increased with time. Therefore, after the accident the individual total effective dose calculated by the 95th-percentile χ/ Q value for the overall site was higher than that calculated by the 99.5th-percentile χ/ Q values for the 16 downwind directions. Uncertainty in the calculation results 2 Uncertainty in calculation results is an unavoidable problem in nuclear and radiation safety analyses [ 31 31 , 32 32 , 33 33 , 34 34 ]. In general, the sources of uncertainty in accident radiological consequences include: 1) uncertainties in the models of radiological consequences, 2) uncertainties from parameters such as experimental and empirical data, and 3) uncertainties caused by human factors. The uncertainties caused by models mainly refer to the radioactivity model of nuclides in the containment and environment, the atmospheric dispersion factor, and the radiation dose models. Herein, the accident source term model was verified using the recognized TACTIII and TITAN 5 computer codes. The results showed that the relative deviation of nuclide radioactivity in the environment calculated by the established model and TACT III was within ± 5%, and that of the nuclide effective removal time in containment calculated by the established model and TITAN 5 was less than 1 % [ 23 23 ]. The main reason for the differences in the nuclide radioactivity released into the environment was the fact that the nuclide decay constants used in the established calculation model were obtained from the radioisotope manual, which differs from the nuclide data of the TACT III database, such as the decay constant of 138 Xe. The relative deviation of the calculation results was within ± 0.05 % when using the same nuclide decay constants. The atmospheric dispersion factor was calculated using ARCON96, which was based on field measurements obtained at seven reactor sites. The diffusion coefficients were revised and the dispersion algorithms improved the model performance, resulting in higher prediction accuracy [ 21 21 , 25 25 ]. The individual total effective dose calculation model was verified through analysis of radiological consequences of fuel handling accident at the NuScale SMR. The individual total effective dose calculated by the established model was 5.4 mSv and that in NuScale final safety analysis report was 5.5 mSv, which proves the accuracy of the radiation dose model. The parameter values used in the accident radiological consequence analysis were collected from internationally recognized and widely used literature, such as the International Commission on Radiological Protection reports, federal guidance reports from the Environmental Protection Agency, and Nuclear Regulatory Commission regulatory guides. To analyze the changes in nuclide radioactivity in the reactor core, the uncertainties in power (1 %) and fuel management plan changes (4 %) were considered for the core inventory based on existing nuclide presence data. Meteorological data were provided by a small modular reactor designer. Uncertainties caused by human factors usually result from the user's inexperience in model and calculation processes, inaccurate division of time nodes, and calculation input data errors. These uncertainties were controlled for through independent recalculation conducted by different professionals. Conclusion 1 The flexibility of the SMR design not only offers advanced nuclear technology for the production of electricity but also generates heat and clean water to meet the biggest human needs globally. Countries around the world are researching and developing SMRs, and NuScale received the first SMR design approval from the U.S. NRC in 2020. Similarly, China is currently engaged in designing and researching a series of SMRs, such as the ACP100, CAP200, DHR400, and ACPR50S. Based on the design characteristics of an SMR in China, a whole-core fuel cladding damage accident was studied, and models of the accident source term and radiological consequences were established to analyze the radiation dose at the site boundary. The results can be summarized as such: (1) The radioactivity released into the environment 30 days after the accident reached 10 14 Bq, of which 133 Xe released the largest amount, thus making it a nuclide of particular concern. (2) Affected by the initial radiological activity in the fuel rod, nuclide half-life, and natural removal in the containment, the radioactivity changes in the various nuclides in the environment differed. The radioactivity of 131 I (elemental and organic iodine), 85 Kr, 131 Xe m , and 133 Xe released into the environment within 30 days after the accident continuously increased, whereas that of other nuclides reached equilibrium. (3) After the accident, the χ/ Q value decreased with time. The 95th-percentile χ/ Q values for the overall site were lower than the maximum values of the 99.5th-percentile χ/ Q for the 16 downwind directions at 0–2 h and 2–8 h after the accident; in turn, in the later time intervals the 95th-percentile χ/ Q values for the overall site were greater than the 99.5th-percentile χ/ Q values for the 16 downwind directions. (4) Both χ/ Q and the release of radioactivity into the environment affected the individual total effective dose. Compared to the 99.5th-percentile χ/ Q values for the 16 downwind directions, the individual total effective dose calculated using the 95th-percentile χ/ Q values for the overall site was higher. 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Tech. 25 ( S1 ), S010602 ( 2014 ). doi: 10.13538/j.1001-8042/nst.25.S010602 http://doi.org/10.13538/j.1001-8042/nst.25.S010602 Evaluations of fission product reduction strategies for severe accident management in CANDU6 Methodology and conceptualization by Hai-Ying Chen and Fu-Dong Liu. Investigation was carried out by Fu-Dong Liu and Chao Xu. Calculations were run by Hai-Ying Chen, Yi-Chuan Wang, and Qiao-Feng Liu. Data collection and analysis were conducted by Hai-Ying Chen, Shaowei Wang, and Yi-Chuan Wang. The original draft was written by Hai-Ying Chen, Shao-Wei Wang, and Chao Xu. All authors reviewed and commented on previous versions of the manuscript. All authors read and agreed to the published version of the manuscript. 10.1007/s41365-023-01192-5 2022-11-10 2022-12-21 2023-01-10 2023-03-27 2023-04-20 © China Science Publishing & Media Ltd. (Science Press), Shanghai Institute of Applied Physics, the Chinese Academy of Sciences, ChineseNuclear Society and Springer Nature Singapore Pte Ltd. 2023 This is a post-peer-review, pre-copyedit version of an article published in Nuclear Science and Techniques. The final authenticated version is available online at: http://dx.doi.org/10.1007/s41365-023-01192-5 http://dx.doi.org/10.1007/s41365-023-01192-5 . Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. 2023 The data that support the findings of this study are openly available in Science Data Bank at https://doi.org/10.57760/sciencedb.j00186.00041 and http://resolve.pid21.cn/31253.11. sciencedb.j00186.00041. Data availability Nuclear Science and Techniques 3 34