In the fourth stage (2700–5000 s), the steam generator was isolated from the PRHR system. The PRHR system became stagnated when the primary fluid temperature was in the range of 327.15 K to 458.15 K. In the primary fluid temperature of 473.15 K to 527.15 K, the flow in the PRHR system became steady-state with reverse flow in some PHE branches (Fig. 9), and the reverse flow occurred in the 1#PHE, 4#PHE, 5#PHE and 6#PHE. The flow rates of each branch increased with primary fluid temperature. The flow rates in the reversed PHE branches were basically the same value, while the flow rates in the positive PHE branches were different (Fig. 9).

Thermal stratification effect in the hot and cold ring headers and corresponding Y-junctions was shown in Fig. 10 and Fig. 11, where the temperature contours of the headers and the Y-junctions were plotted for primary fluid temperature of 522.15 K. It was clearly shown in Fig. 10 and Fig. 11 that the layered header model can capture some detail of local flow phenomena in the headers and Y-junctions, such as thermal stratification or local recirculation.

It was observed in the scaled PRHR experiments that the outlet temperatures of the six PHE branches were significantly uneven if the SG branch was not isolated, while the outlet temperatures were nearly equal if the SG branch was isolated. In the numerical simulations, the phenomenon of uneven outlet temperatures of PHE branches were successfully captured in the third stage (600–2700 s in Fig. 12), and the outlet temperatures of PHE branches were nearly equal in the fourth stage (2700–5000 s in Fig. 12). The numerical simulations agreed the experimental data quantitively.

**Fig. 4.** Mass Flow Rate of Each Branch at Different Primary Fluid Temperature.

**Fig. 4.** (*continued*)

**Fig. 4.** (*continued*)

**(o) 533.15K**

**Fig. 4.** (*continued*)

**Fig. 5.** Mass Flow Rate of Each Branch at Primary Fluid Temperature of 327.15 K.

**Fig. 6.** Steady Mass Flow Rate at the Second Stage (PHE 327.15–443.15K, t = 500.0 s).

**Fig. 7.** Steady Mass Flow Rate at the Third Stage (PHE 327.15–383.15 K, t = 2000.0 s).

The uneven outlet temperatures of the PHE branches in the third stage can be explained by the reverse flow in some PHE branches and the thermal stratification effects in the headers. Significant thermal stratification occurred in the third stage, since the fluid from SG branch can flow into the lower part of the cold header or hot header through the low-resistance Y-junctions in the headers. In the fourth stage, since the valves of the SG branch closed, the thermal stratification phenomenon in the headers became insignificant, and the outlet temperatures of PHE branches became the same value.

**Fig. 8.** Steady Mass Flow Rate at the Third Stage (PHE 473.15–533.15 K, t = 2000.0 s).

**Fig. 9.** Steady Mass Flow Rate at the Fourth Stage (PHE 473.15–533.15 K, t = 4000.0 s).

**Fig. 10.** Thermal Stratification of Cold Header and Y-Junction.

**Fig. 11.** Thermal Stratification of Hot Header and Y-Junction.

## **5 Conclusions**

In this paper, a layered RELAP5 model was developed for the PRHR system of a scaled test facility for the NHR-200-II reactor. Numerical simulations were carried for both the PRHR scenario of SG branch isolated and the PRHR scenario of SG branch not isolated. The main conclusions include:

**Fig. 12.** PHE Branch Outlet Temperature Dispersion (PHE 473.15–533.15 K).

fluid temperature was higher than 473.15 K (Fig. 8 and Fig. 9), which was also consistent with the experiment observations.

(3) The uneven outlet temperatures of the PHE branches when the SG branch was not isolated can be explained by the reverse flow in some PHE branches and the thermal stratification effect in the headers. The layered RELAP5 nodalization for the hot and cold headers can be used as a preliminary estimation method of the thermal stratification effect, however, detailed 3-dimensional CFD methodology is still necessary to accurately capture the phenomenon of thermal stratification in the hot and cold headers of the PRHR system.

### **References**

**Open Access** This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

The images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

## **Fatigue Analysis Method of Steel Containment of Floating Nuclear Power Plant**

Mingxuan Liu1, Xinyang Fan1, Danrong Song2, Bin Zheng2, and Meng Zhang1(B)

1 Yantai Research Institute and Graduate School, Harbin Engineering University, Yantai, Shandong, China

<EMAIL_ADDRESS>
2 Nuclear Power Institute of China, Chengdu, Sichuan, China

**Abstract.** Floating nuclear power plant (FNPP) is a movable nuclear power plant built on the floating platform, which can provide clean and stable power for remote coastal areas, and are currently a hot research topic in the field of nuclear power. The steel containment is located in the reactor compartment of the FNPP and it is an important safety guarantee structure. Fatigue and fracture have been an important issue for ship and offshore structures for a long time. Fatigue failure of containment will have serious consequences.

In order to research the fatigue life analysis method of steel containment of the first FNPP in China, the paper adopts miner linear cumulative damage theory and spectral analysis method, based on the American Society of Mechanical Engineers (ASME) standards and relevant standards of China Classification Society (CCS), and uses AQWA to analyze Wave load of FNPP. The hydrodynamic calculation results are imported into finite element model to analyze the structural response of each point of containment, and calibrate the transfer function data of each key point by using the linear system theory and regular wave periodic evaluation method. The fatigue analysis of each point is carried out according to the transfer function and the wave dispersion diagram drawn by the forty years monitoring sea conditions of the working sea area of the FNPP. The result shows that the fatigue life of steel containment is superior and meets the service requirements.

**Keywords:** Floating nuclear power plant · Containment vessel · Fatigue analysis · Transfer function · Regular wave simulation method

## **1 Introduction**

With the continuous adjustment and optimization of China's energy structure and the continuous promotion of the strategy of strengthening the country through the sea, it is increasingly difficult for traditional fossil energy sources as well as emerging energy sources such as wind, wave and solar energy to meet the energy demand brought by the development of coastal oil and gas resources and islands. Offshore floating nuclear power plant refers to a movable floating marine platform equipped with nuclear reactor and power generation system, which is a product of the organic combination of mobile small nuclear power plant technology and ship and marine engineering technology. As early as in the 1970 s, researchers in the United States proposed the idea of floating nuclear power plants [1], and the world's first floating nuclear power plant 'Akademik Lomonossov' was also launched in Russia in 2016 [2]. In floating nuclear power plants, a sealed steel containment structure is usually installed to wrap around the reactor and other auxiliary power generation equipment structures to protect the reactor from normal operation as well as to protect the external environment. Compared to traditional onshore containment, the environment and loads on the small steel containment and support structure of an offshore floating nuclear power plant are very different, especially because the complexity of the marine environment leads to more complex loads on the containment and support structure.

The alternating loads caused by these complex sea conditions may cause fatigue damage to the structure and generate cracks, which in turn threaten the safety of the floating nuclear power plant structure and cause the structure to fracture when the cracks expand to a certain extent, resulting in serious accidents. Floating nuclear power plants. However, there are few studies on the fatigue of floating nuclear power plant containment. Therefore, in order to ensure the operational safety of floating nuclear power plants and protect the surrounding personnel and external environment from nuclear radiation, it is important to carry out research on the fatigue assessment method of floating nuclear power plant steel containment in marine environment to ensure the safe operation of floating nuclear power plants during the design life and reduce economic losses.

The current fatigue assessment methods for marine structures can be divided into, simplified algorithm [4], design wave method [5] and direct calculation of spectral analysis method, among which spectral analysis method has the advantages of high accuracy and can reflect the specific structural details of the ship is widely used in the field of marine engineering, previously Hadi and Yang et al. used spectral analysis method for fatigue reliability analysis of marine platforms [6, 7], Zhang et al. used the spectral analysis method to evaluate the fatigue strength of a small waterline surface catamaran [8]. In contrast, in the study of nuclear power system pressure-bearing equipment, the transient method is usually used to assess its fatigue damage because its stress response time course is easily accessible [9, 10].

In this paper, based on the above research, the fatigue reliability study of a type of floating nuclear power plant containment is carried out by combining the spectral analysis method commonly used in marine engineering with the fatigue strength analysis of floating nuclear power plant containment, while referring to ship-related codes and ASME-related codes [11], using the regular wave simulation method.

### **2 Fatigue Strength Spectrum Analysis Method**

#### **2.1 Spectrum Analysis Method**

The FNPP has a complex working environment and is subjected to the combined action of wind, wave and current. The main part of the fatigue load that causes the fatigue failure of the containment structure of the FNPP is the wave load. The key points of evaluating the fatigue strength of the containment of FNPP are the selection of wave spectrum, the calculation of transfer function and the calculation of fatigue damage.

Spectrum analysis method is a commonly used method in ship and ocean engineering to study load and structural response. Its theoretical basis is the linear system transformation in random process theory. The method firstly obtains the power spectral density function (PSD) of the structural stress response, after that establishes the relationship between the stress response power spectral density function and the rain flow stress range distribution, and then selects a suitable S-N curve and Miner cumulative damage theory to calculate the fatigue damage of the structure (Fig. 1).

**Fig. 1.** Fatigue analysis flow

The FNPP can be regarded as a typical dynamic system in ships and offshore engineering structures. The wave process a acting on the hull is the input of the system, and the alternating stress B caused by the wave action in the structure is the response of the containment. In general, the relationship between the response process of the containment and the wave load input process of the FNPP can be written as:

$$X(t) = L[\eta(t)]\tag{1}$$

where, B represents the operator that transforms C into D. When e is a linear operator, the system is linear.

In the fatigue analysis of ship structure, the calculation of wave load and structural response are based on linear theory. Under this condition, if the wave is a stationary random process, the alternating stress obtained by transformation is also a stationary random process. According to the random process theory, there is the following relationship between the power spectral density functions of two stationary random processes:

$$G\_X(\omega) = |H(\omega)|^2 \cdot G\_\eta(\omega) \tag{2}$$

In function (2), *H*(ω) is a transfer function or frequency response function of linear dynamical system. |*H*(ω)| 2 is response amplitude operator (RAO).

The physical meaning of *H*(ω) is the ratio of the amplitude of the response process to the amplitude of the input process when the linear dynamic system vibrates with a circular frequency of ω.

#### **2.2 Wave Spectrum**

For the spectral analysis method for fatigue assessment of ship structures, since the FNPP is located in a shallow water depth and the wave dispersion diagram is the joint distribution of meaningful wave height and spectral peak period, the improved JONSWAP spectrum is selected for analysis, and its expression is as follows:

$$S(f) = \beta\_I H\_{\frac{1}{\sharp}}^2 T\_P^{-4} f^{-\mathfrak{S}} \exp[-\frac{\mathfrak{S}}{4} (T\_P f)^{-4}] \gamma^{\exp[-(\frac{f}{f\_P} - 1)^2 \int 2\sigma^2]}\tag{3}$$

In function (3):

$$B\_{J} = \frac{0.06238}{0.23 + 0.0336\gamma - 0.185(1.9 + \gamma)^{-1}} [1.094 - 0.01915 \ln \gamma]$$

γ is the crest factor, mean value is 3.3.

σ is the peak shape parameter. When the frequency is on the left side of the maximum value point, it is taken as 0.07, and when the frequency is on the right side of the maximum value point, it is taken as 0.09.

#### **2.3 Regular Wave Simulation Method**

The transfer function is determined by the system through experiments under the action of rule input or random input, or by the system's theoretical analysis of rule input. Based on the regular wave test method in the pool test, we propose the regular wave simulation method, that is, using the wave load calculation program to obtain the response of the ship motion and external hydrodynamic pressure of a series of regular waves arranged according to a certain initial phase interval under the heading angle and circular frequency. The external hydrodynamic pressure and various inertial forces related to the motion of the hull are applied to the finite element model of the hull structure to obtain the stress response. For the stress response of a series of regular waves under the heading angle and circular frequency, the maximum stress response at the point is fitted by Fourier transform, and the stress amplitude of the heading angle and circular frequency can be obtained. The value of the transfer function under the heading angle and circular frequency can be obtained by comparing the obtained stress amplitude with the wave amplitude.

#### **2.4 Fatigue Cumulative Damage Calculation and S-N Curve**

After obtaining the damage caused by each cycle, the selection of a suitable fatigue accumulation damage theory is also one of the core elements of fatigue calculation. The S-N curve and the fatigue cumulative damage analysis method of linear cumulative damage theory are commonly used to evaluate the fatigue of structures in the codes of classification societies of various countries.

When the fatigue load spectrum is expressed as a continuous probability density function corresponding to a certain period of time, the fatigue cumulative damage degree can be expressed as

$$D = \int\limits\_{L} \frac{dn}{N} = \int\limits\_{0}^{\infty} \frac{N\_L f\_S(S) dS}{N} = N\_L \int\limits\_{0}^{\infty} \frac{f\_S(S) dS}{N} \tag{4}$$

*S* is the stress range, is the probability density function of the stress range distribution, is the number of cycles required to achieve fatigue failure under a single cyclic load with a stress range of, is the total number of cycles of the internal stress range during the whole time period considered, is the number of cycles of the included stress range, and represents the integral of the whole time interval considered. According to the cumulative damage theory, when the damage degree is accumulated, the fatigue failure of the structure will occur.

The S-N curve is often used to reflect the relationship between the stress range S and the number of cycles required for the structure to achieve fatigue failure under a single cyclic load at the level of the stress range, i.e. the fatigue life n. It is generally obtained by fitting the fatigue test results. A large number of research results show that under a given stress range s, the discrete type of the parameter m is small and can be regarded as a certain value, the fatigue life n and parameter a should be treated as random variables, and it is generally considered that n obeys lognormal distribution. Expressed as

$$NS^m = A\tag{5}$$

Take logarithm on both sides of the equation

$$
\lg N + m \lg S = \lg A \tag{6}
$$

Equation (6) is a commonly used double log-linear model of the S-N curve. The small steel containment material studied in this paper is Steel-SA-738Gr.b. Therefore, the parameters are referred to the appendix of ASME BPVC Volume III [11].

The tensile strength of Steel-SA-738Gr.b is 585-705mpa. According to the S-N curves, the S-N curve of the material can be obtained by interpolation. The curve is transformed into a double logarithmic linear form, taking m = 3 and a = 11.464.

### **3 Containment Fatigue Strength Analysis**

#### **3.1 Hydrodynamic Analysis**

The structural hydrodynamic model is shown in Fig. 2. The right-hand rectangular coordinate system is used. The origin is taken at the intersection of the intersection line of the longitudinal section and the middle transverse section of the platform and the base plane. The X axis is the longitudinal axis, and the point from the tail to the head is positive; Y-axis is the transverse axis, and it is positive from the centerline to the port; The z-axis is the vertical axis, and upward from the base is positive.

For model hydrodynamic analysis, AQWA software is used for hydrodynamic analysis of FNPP. During frequency domain hydrodynamic calculation, the minimum frequency of each wave direction is set at 0.01592 Hz and the maximum frequency is set at 0.27 Hz, with a total of 50 frequency points.

The frequency response curve of the longitudinal bending moment of the middle hull cross-section (x = 0.328 m cross-section) of the reactor bay at 0° wave incidence angle is shown in the following Fig. 3:

**Fig. 2.** Hydrodynamic model of FNPP.

**Fig. 3.** Frequency response curve of longitudinal bending moment (0° wave incidence angle)

Taking 0° wave incidence angle as an example, it can be seen from the calculation results that the peak longitudinal bending moment in the transverse section of the hull in the middle of the stack is about 6.169\*108 N\*m under 0° wave incidence angle and unit wave amplitude, and the corresponding wave frequency is 0.0574 Hz. Another longitudinal bending moment value at the waistline is 3.425\*108 N\*m corresponding to the wave frequency of 0.03147 Hz, and the longitudinal bending moment value is 3.035\*108 N\*m corresponds to a wave frequency of 0.0937 Hz.

#### **3.2 Selection of Fatigue Damage Assessment Points**

The finite element model of the FNPP structure is constructed with shell181 and beam188 elements. The mesh size of the bottom and supporting parts of the containment is 0.1 M, the mesh size of the upper part of the containment is 0.2 m, and the mesh size of the rest parts is 0.8 m. The total number of elements on the ship is about 1.56 million. The finite element model of the containment is shown in Fig. 4.

**Fig. 4.** Structural finite element model.

Since the spectrum analysis method needs to superimpose all working conditions and the number of structural finite element nodes is very large, according to the hydrodynamic calculation results and the longitudinal bending moment diagram, the wave load files of 0.03147 Hz, 0.0574 Hz and 0.0937 Hz in all wave directions are selected to be loaded on the whole ship finite element model of the FNPP without preload and hydrostatic pressure, and the calculation results are obtained. Select the stress concentration node as shown in Table 1:

A local refinement of the grid near the evaluation point of the model is shown in Fig. 5.

#### **3.3 Fatigue Life of Containment**

Wave scatter diagram is a common method to describe the marine environment in ship and ocean engineering. Table 2 shows the monitoring data of the nearby platform in the sea area where the floating nuclear power plant works. In the table, *Hs* denotes the meaningful wave height and *Tp* denotes the spectral peak period.

The long-term distribution of the stress range within the design life of the FNPP containment can be obtained from the short-term distribution combined with the distribution of various sea conditions that may be encountered in operation. In a given sea state, the ship may sail in any course. In the calculation, several courses are divided, and it is assumed that the probability of each course is equal.

The FNPP can set a course every 15° from 0° to 360° in the marine environment. There are 24 courses in total, and the probability of each course angle is 1/24. In order to simplify the calculation, the FNPP, as a symmetrical structure, can simplify the structural response caused by the symmetrical course. Therefore, in the actual calculation, take a course every 15° from 0° to 180°, a total of 13 courses, of which the probability of 0° and 180° is 1/24, and the probability of other courses is 1/12 (Fig. 6).

Therefore, in the regular wave experimental simulation method, AQWA software is used to calculate the response of hull motion and external hydrodynamic pressure

**Fig. 6.** Schematic diagram of wave incidence angle.

of a series of regular waves with unit wave amplitude of 1 at each heading angular circular frequency arranged at a certain initial phase interval, the phase is taken as 0° to 360° with 45° interval, 8 regular waves at each wave direction frequency, and the wave load file is extracted. The wave load is the wave surface pressure, and the wave surface pressure is mapped to the wet surface of the hull to calculate the structural response. The structural response is the response of the structure under the action of unit wave amplitude. The maximum stress value at each calculation point acting on the top of the FNPP containment is extracted and fitted using the fast Fourier transform (Fig. 7), and the stress response transfer function is obtained by dividing the magnitude of the two trigonometric functions.

Since the unit wave amplitude is 1, the fitted resulting amplitude is the stress response transfer function.

**Fig. 7.** Fitted curve of stress response of evaluation point 4 at 0° wave direction 0.26451 Hz.

Under the above conditions, the long-term distribution of the stress range can be expressed as a weighted combination of short-term distributions, and its distribution function is Eq. (7)

$$F\_S(S) = \frac{\sum\_{l=1}^{n\_l} \sum\_{j=1}^{n\_H} v\_{lj} \cdot p\_l \cdot p\_j \cdot F\_{s\theta ij}(S)}{\sum\_{l=1}^{n\_s} \sum\_{j=1}^{n\_H} v\_{lj} \cdot p\_l \cdot p\_j} = \sum\_{l=1}^{n\_s} \sum\_{j=1}^{n\_H} r\_{lj} \cdot p\_l \cdot p\_j \cdot F\_{s\theta ij}(S) \tag{7}$$

In Eq. (7),*nS* is the total number of sea states in the sea state distribution data, *nH* is the total number of divided courses, *pi* is the probability of occurrence of the i-th sea state, which can be obtained according to the frequency of occurrence of each sea state in Table 3;*pj* is the frequency of occurrence of the j-th heading. *vij* is the average zero crossing rate of stress alternating response under the i-th sea state and the j-th heading.*v*0 is the total average zero crossing rate of stress response considering all sea conditions and heading.

$$\nu\_0 = \sum\_{i=1}^{n\_s} \sum\_{j=1}^{n\_H} \nu\_{ij} \cdot p\_i \cdot p\_j \tag{8}$$

**Table 1.** Fatigue damage point calculation number and location.

#### **3.4 Containment Fatigue Life Correction**

In addition to the influence of marine environmental load on the structure, the marine environmental conditions also have a great impact on the fatigue performance of materials, mainly in the form of corrosion. *Fatigue strength guide for hull structures (2021)* of CCS [12] stipulates that for the normal bending stress of hull girder during simplified stress analysis and the hot spot stress under overall load conditions during finite element stress analysis, the corrosion correction factor *fcl* = 1.05;

For the bending normal stress under lateral load in simplified stress analysis and the hot spot stress under local load in finite element stress analysis, the corrosion correction factor *fcl* = 1.1.

In the direct calculation method of fatigue assessment, the fatigue safety factor needs to be superimposed for calculation. In this regard, *GUIDELINES FOR FATIGUE STRENGTH ASSESSMENT OF OFFSHORE ENGINEERING STRUCTURES (2013)* of CCS provides relevant provisions [13].

Fatigue failure criteria can be based on fatigue damage or fatigue life. When based on fatigue damage, the fatigue strength of the calculated point shall meet Eq. (9)

$$D \le \frac{1.0}{S\_{\text{ffg}}} \tag{9}$$

*D*-- Fatigue damage degree;

*Sftg*-- Fatigue strength safety factor.

The fatigue safety factor of the small steel containment of the FNPP is selected by reference to the fixed floating structure. The fatigue damage assessment location is accessible for inspection and maintenance in a dry environment, and the failure consequences are serious. Considering the special nature of the small steel containment of FNPP, we select 5 as the fatigue safety factor. Therefore *D* ≤ 0.2.

See Table 4 for the cumulative fatigue damage degree and the corrected fatigue life of the final six fatigue assessment points of the containment.

*T*1 is fatigue life considering corrosion correction factor/year.

*T*2 is the fatigue life considering the fatigue safety factor and corrosion.

**Table 2.** Wave Dispersion

**Table 3.** Fatigue cumulative damage results.

**Table 4.** Fatigue cumulative damage results after correction.

(a) evaluation point 4 (b) evaluation point 6

**Fig. 8.** Comparison of transfer function results

## **4 Conclusion**

Based on the spectral analysis method and regular wave simulation method, this paper analyzes the small steel containment vessel of FNPP. It is concluded that the maximum fatigue cumulative damage is at No. 8 calculation point, the fatigue cumulative damage degree is 0.1074, and the fatigue life is 74 years. It is located at the bottom support, which meets the design requirements of FNPP. At the same time, the parameters are conservative and the fatigue life is short.

For the regular wave simulation method, take the evaluation point 4 and evaluation point 6 with short fatigue life as an example. Figure 8 shows the transfer function plots of evaluation point 4 and evaluation point 6 at 45° wave direction. The black curve is the simplified theoretical analysis method, and the red curve is the regular wave experimental simulation method. It can be concluded from the figure that the regular wave simulation method has a smoother and more accurate curve, although the calculation is more complex.

## **References**

**Open Access** This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

The images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

## **Correlating IASCC Growth Rate Data to Some Key Parameters for Austenitic Stainless Steels in High Temperature Water**

Caibo Xie, Songhan Nie, Yiqi Tao, and Zhanpeng Lu(B)

Shanghai University, Shanghai, China<EMAIL_ADDRESS>
**Abstract.** Austenitic stainless steels have been widely used for fabricating reactor core-internal components in PWRs due to its high strength, ductility and fracture toughness. The accelerated failure or degradation of austenitic stainless steel represented by IASCC has become one of the key problems affecting the safe and efficient operation of reaction core-internal in PWR nuclear power plants. IASCC is generally divided into three stages: crack initiation, crack propagation and instable fracture. Among the three stages, the crack initiation stage would occupy the major service time, the crack growth stage is featured by quasi-steady crack propagation at a certain rate, and the instable fracture stage should be avoided. Stress intensity factor K at the crack tip is often used to represent the mechanical driving force for SCC as well as IASCC.

In this paper, SCC crack growth rate (CGR) data of austenitic stainless steels irradiated in high temperature water were compiled and reanalyzed to evaluate the influence of key parameters such as radiation dose and mechanical properties on IASCC sensitivity and crack growth rate of these materials in PWR nuclear power plant environment. The CGR-K curves of the irradiated materials were also analyzed. The effects of low, medium and high doses of neutron irradiation are compared, and the analysis process is illustrated with examples. In the research process, abnormal CGR and K of materials under a specific irradiation dose was found, so this phenomenon was analyzed. The CGR data and irradiation dose of austenitic stainless steel in different K range were analyzed. And proposed a way to judge the type of change:type I, type II and type III. Finally, the yield strength of the material under the same irradiation dose was found, and combined with other research data, it was further demonstrated that the neutron irradiation dose had a significant effect on the crack growth rate.

**Keywords:** Austenitic stainless steel · Irradiation assisted stress corrosion cracking · Crack growth rate · High temperature water

## **1 Introduction**

There are pressurized water reactor (PWR), boiling water reactor, heavy water reactor and other types of commercial nuclear power plants. PWR is the most widely used because of its mature technology and rich operation experience, accounting for more than half of the operating nuclear power plants in the world. Prolonged neutron irradiation leads to the changes of mechanical properties due to irradiation induced hardening effect, the changed of local chemical compositions due to radiation-induced segregation effect, the increase of physical defects such as dislocation loops, and the water decomposition due to radiolysis, and finally affects the SCC in high temperature water.

IASCC is generally divided into three stages: crack initiation, crack propagation and instable fracture [1]. At the initial stage of crack initiation, the surface of sensitive materials begins to produce microcracks under the coupling effect of environmental and mechanical factors, and these microcracks are invisible under the light microscope. Over time, the microcracks merge with each other to form an initial crack with a length of 10 µm. In the crack growth stage, the crack expands at a certain rate, which is affected by environmental and mechanical factors. The laboratory usually studies the process by introducing the stress intensity factor K at the crack tip. In the instable fracture stage, the crack expands rapidly until the material fracture.

It is well known that SCC of materials in high temperature and high pressure water depends on three factors: materials, environment and relatively high stress is shown in Fig. 1. The key parameters affecting IASCC mainly include the material itself (such as microstructure, microchemistry and yield strength, etc.) and environmental parameters (such as hydrochemistry, irradiation temperature and irradiation dose, etc.). The key parameters such as irradiation temperature and irradiation dose have great influence on the crack growth rate of austenitic stainless steel IASCC. There are also many studies on the influence of material factors such as microstructure, microchemistry and yield strength on IASCC sensitivity of austenitic stainless steel.

**Fig. 1.** The main influencing factors of IASCC

The study of IASCC behavior of austenitic stainless steel needs to pay attention to three stages: crack initiation, crack propagation and instable fracture. The crack propagation stage is the most important. Stress corrosion cracking promoted by irradiation is affected by material itself, medium environment, irradiation temperature and irradiation dose, etc. The research process is complicated and uncertain. The relationship between CGR and K is the key parameter in IASCC process of austenitic stainless steel.

1062 C. Xie et al.

SCC or IASCC is used for the study of materials. There are many types of specimens, such as compact tension (CT) specimen [2], four-point bending specimen [3], round compact tension (RCT) specimen [4] and so on. In this paper, the advantages and disadvantages of sample types are not discussed too much, and only the experimental results are concerned.

## **2 Compiling IASCC Data of Austenitic Stainless Steels in Simulated PWR Primary Water**

Austenitic stainless steels can be divided into many types, among which 304 and 316 based austenitic stainless steel is widely studied, so here only around 304 and 316 based austenitic stainless steel is discussed.

The stress corrosion cracking experiment promoted by neutron irradiation needs special equipment, and the experimental difficulty exists objectively due to the limitation of equipment and other conditions. Radiation doses can range from a few percent of dPa to more than 100 dPa. Experimental data on crack growth rate of 0.06–47.0 dPa austenitic stainless steel were collected in this paper.

The CGR data of irradiated austenitic stainless steel in simulated BWR or PWR environments were obtained from CT samples, RCT samples or four-point bending samples. In the experiment, factors such as irradiation temperature, material type and water environment should be controlled, and the irradiation dose should be reasonably controlled. The CGR data of the sample should be matched with K one by one, and the relation data between CGR and K should be obtained.

Based on 304 and 316 austenitic stainless steel, the materials were irradiated in the light water reactor environment, and the data of researchers were summarized to obtain Fig. 2 [4–12].

Figure 2 is a summary of the relationship between CGR and K of irradiated austenitic stainless steel in a pressurized water reactor environment sorted by irradiation dose. Due to the limitation of experimental data conditions of many researchers, it is difficult to unify the irradiation temperature, which is controlled at 288–340 °C. The influence of irradiation temperature on CGR is very complex and limited by space, so the irradiation temperature will not be discussed too much in this paper. Instead, data analysis and problems will be found dialectically.

The parameter stress intensity factor K is introduced here, which essentially reflects the mechanical changes in the microstructure. Microcracks exist in the microstructure of irradiated austenitic stainless steel. If two cracks have the same strain and stress in a region near the crack tip, then they have the same K. Since the crack tip scale is small, K represents the stress and strain at the crack tip.

As shown in Fig. 2, as a whole from the reference curve, CGR generally shows an increasing trend with the increase of K. However, we found that after data integration, each data was not strictly linear and was greatly affected by the radiation dose.

The CGRs of SCC of unirradiated austenitic stainless steel is lower than that of IASCC of irradiated austenitic stainless steel under the same conditions, and the difference may be several times. Taking the CGRs data of austenitic stainless steel under 3 dpa irradiation dose as an example, the CGR of unirradiated austenitic stainless steel is about 3x10–10 m/s [2–5] while the CGR of irradiated austenitic stainless steel can reach 9x10–10 m/s or 1x10–9 m/s. The difference is about three times. This indicates that neutron irradiation can promote the crack growth rate (CGR) of austenitic stainless steel IASCC to a certain extent. The effect of irradiation dose on CGR of austenitic stainless steel IASCC in PWR is complicated. From the figure, we can roughly divide the radiation dose into low dose, medium dose and high dose. Low radiation dose mainly refers to 0–9 dpa. Under this condition, the change of CGR is not obvious compared with that without radiation. K is mainly between 12 and 20 MPa m0.5. Based on literature review and PWR experience, 3 dpa is the threshold of material irradiation. In the case of 0–3 dpa irradiation dose, the CGR of the material will not change with the increase of the irradiation dose, but still maintain the original growth rate. Under the irradiation dose of 3–9 dpa, irradiation promoted the CGR of austenitic stainless steel. For example, the CGR of 3 dpa was higher than that of 6.3 dpa and 8.0 dpa. K remained in a certain range, while CGR changed abnormally. It is speculated that the CGR is affected by the changes of microstructure defects, dislocation loops and radiation dose.

**Fig. 2.** Relationship between CGR and K of austenitic stainless steel at 0.6–47.0 dpa in pressurized water reactor [4–12]

The radiation dose here refers to the radiation dose of approximately 11.4–25.0 dpa. In the case of medium irradiation dose, CGR and K maintain a positive correlation. At 17.1 and 18.7 dpa, the data are mainly concentrated at the lower left of the figure near the reference curve. At 21.0, 12.9 and 14.0 dpa, the data mainly concentrated in the center of the graph near the curve. Although the data at 11.4, 15.0, and 25.0 dpa are mainly distributed in the upper right of the graph, they generally follow the trend of increasing CGR as K increases. In these data, the phenomenon of 25.0 dpa is worth separate discussion and will be carried out in the future.

High radiation dose refers to radiation dose above approximately 25.0 dpa. As can be seen from the figure, although the CGR of austenitic stainless steel under high irradiation dose is still higher than that of non-irradiated stainless steel, compared with medium irradiation dose, the CGR of austenitic stainless steel is abnormally reduced, mainly between 1x10–11 m/s and 1x10–10 m/s. These results indicate that high irradiation dose is not conducive to the acceleration of the growth rate of austenitic stainless steel IASCC in PWR, but has a certain inhibitory effect.

The relationship between CGR and K of austenitic stainless steel in pressurized water reactor remains relevant, and CGR increases with K in most cases. However, with the increase of irradiation dose, CGR and K of austenitic stainless steel do not increase simultaneously, but atrophy occurs. It may be caused by the excessive damage to the material caused by neutron irradiation.

It is worth noting that although the CGR and K relationship data of irradiated austenitic stainless steel were partially dispersed, CGR and K still showed a positive correlation. It should be pointed out that the 316 based austenitic stainless steel material under the neutron irradiation dose of 25 dpa in Fig. 2 has abnormal conditions. At lower K, that is, when K is less than or equal to 5 MPa m0.5, the CGR of the material is more than 9x10–11 m/s. The appearance of abnormal data points in Fig. 2 caught our attention and thought.

## **3 Effect of Irradiation Dose on SCC Growth Rates**

The CGR of austenitic stainless steel in high temperature water is affected not only by stress intensity factor K, but also by neutron irradiation dose, which is indispensable in the process of stress corrosion cracking promoted by irradiation. In order to study the effect of neutron irradiation dose on CGR of austenitic stainless steel in high temperature water, temperature and K must be controlled within a certain range to make the data reasonable and reliable.

Firstly, the temperature was selected between 335 and 340 °C, which could remove the interference of temperature factors on crack growth rate. Through Fig. 2, we summarized the CGR data of 0.06, 3.0, 8.0, 9.0, 11.4, 12.9, 14.0, 15.0, 17.0, 18.7, 21.0, 32.9, 37.8, 39.0, 47.0 dpa irradiation dose, as shown in Fig. 3 [4–9, 11].

Here we classify K as 5–10 MPa m0.5, 10–15 MPa m0.5, 15–20 MPa m0.5 and 20– 27 MPa m0.5. The CGR and K data of austenitic stainless steel at 335–340 °C were processed to obtain the CGR and neutron irradiation dose of austenitic stainless steel under different normalized K conditions.

When K is normalized to 5–10 MPa m0.5, as shown in Fig. 4 [5–9, 11], the CGR of the material is the highest at 11.4 dpa, close to 1x10–8 m/s. When K is 5–10 MPa m0.5, CGR of all irradiation dose data is greater than 9x10–12 m/s. At 17.1 dpa and 18.7 dpa, the CGR values of the materials are close to each other, basically within the range of 10–11 m/s and 10–9 m/s. At 21.0 dpa, the CGR of the material increased slightly to about 10–9 m/s. CGR at 47 dpa was basically within the data range of 17.1 dpa and 18.7 dpa irradiation dose.

As shown in Fig. 5 [4–9, 11], when K is in the range of 10–15 MPa m0.5, CGR of all data in the figure is greater than 4x10–11 m/s. CGR data under 3.0 dpa were higher than

**Fig. 3.** CGR and K of materials with different neutron irradiation doses at 335–340 °C [4–9, 11]

**Fig. 4.** CGR and neutron irradiation dose of austenitic stainless steel under normalized K 5– 10 MPa m0.5 [5–9, 11]

10–10 m/s. The CGR data range of 12.9 dpa and 14.0 dpa irradiation doses were similar. The CGR at 15.0 dpa was two orders of magnitude higher than that at 12.9 dpa and 14.0 dpa. The CGR data at 21.0 dpa irradiation dose were about 1 order of magnitude higher than those at 12.9 dpaand 14.0 dpa irradiation dose. The CGR data of 21.0 dpa irradiation dose was about 0.1 times that of 15.0 dpa irradiation dose. When the neutron irradiation dose increased from 32.9 dpa to 37.8 dpa and from 37.8 dpa to 47.0 dpa, the CGR data at these three irradiation doses were close to 10–10 m/s (between 5x10–11 m/s and 1x10–10 m/s). The CGR data at these three irradiation doses are not sensitive to the neutron irradiation dose.

**Fig. 5.** CGR and neutron irradiation dose of materials under normalized K 10–15 MPa m0.5 [4–9, 11]

**Fig. 6.** CGR and neutron irradiation dose of materials under normalized K 15–20 MPa m0.5 [4–9, 11]

CGR (3.0 dpa) < CGR(21.0 dpa) < CGR(15.0 dpa) > CGR(12.9 dpa, 14.0 dpa, 32.9 dpa, 37.8 dpa and 47.0 dpa). The peak value of CGR data with neutron irradiation dose of 15 dpa in Fig. 5 has aroused our concern. As for the reason of the peak value? What causes the spike remains to be studied and solved.

As shown in Fig. 6 [4–9, 11], when K is 15–20 MPa m0.5, CGR at 0.06 dpa, a very low irradiation dose, is very low, about 2x10–12 m/s. However, when the irradiation dose reached 3.0 dpa, the CGR data directly reached nearly 10–9, with a significant increase. When the irradiation dose was higher than 8.0 dpa, the CGR of the material increased significantly, and the CGR was greater than 2x10–11 m/s. The CGR data range of 11.4 dpa was close to that of 15.0 dpa, up to about 10–8 m/s. CGR data at 12.9 dpa and 14.0 dpa are close in range, but are still two orders of magnitude lower than CGR data at 11.4 dpa and 15.0 dpa. The CGR data at 21.0 dpa was between 12.9 dpa and 14.0 dpa and 11.4 dpa and 15.0 dpa, with a value of about 10–9 m/s.

On the whole, it shows that when the neutron irradiation dose is greater than or equal to 15 dpa, the crack growth rate decreases with the increase of the dose. At the same time, the irradiation dose of 11.4 dpa and 15.0 dpa showed two similar peak values. Similar to the situation where K is 10–15 m/s as shown in Fig. 5, the phenomenon of peak value arouses concern. The two can be compared and further studied.

**Fig. 7.** CGR and neutron irradiation dose of materials under normalized K 20–27 MPa m0.5 [5, 6, 8]

As shown in Fig. 7, when K is in the range of 20–27 MPa m0.5, the range of CGR data fluctuates greatly. The main reason is that the CGR data of 0.06 dpa is small and that of 11.4 dpa is large. When the irradiation dose increased from 0.06 dpa to 3.0 dpa, the CGR increased by about 2 steps. From 3.0 dpa to 8.0 dpa, its CGR decreased by more than one order of magnitude, but it was still about four times the CGR data at 0.06 dpa. CGR data at 11.4 dpa fluctuated from 4x10–10 m/s to nearly 10–7 m/s, with a fluctuation range of more than 2 orders of magnitude. Compared with the CGR data at 8.0 dpa, the CGR data at 39.0 dpa was 1.5 or 1.75 times higher, and the CGR data at 47.0 dpa was 2.5 or 0.75 times higher.

1068 C. Xie et al.

Among them, CGR data at 11.4 dpa fluctuated from 4x10–10 m/s to nearly 10–7 m/s, with a fluctuation range of more than 2 orders of magnitude. In the same range of K, why is there such a high CGR data, and why is there such a large fluctuation range of CGR data in the same radiation dose? These questions remain to be explored.

Based on the above data, we propose a method to judge the phase of CGR data varying with neutron irradiation dose.

$$\begin{aligned} \frac{\delta\_{CGR}}{\delta\_{Dose}} &> 0 \text{: type I},\\ \frac{\delta\_{CGR}}{\delta\_{Dose}} &= 0 \text{: type II} \\ \frac{\delta\_{CGR}}{\delta\_{Dose}} &< 0 \text{: type III} \end{aligned}$$

Each type is divided into three categories: type I for increasing, type II for nearly not changing, and type III for decreasing of crack growth rate with increasing dose. There are −S for strongly, −M for moderately, and −W for weakly. As shown in Table 1, the change rate of CGR and irradiation dose in different K ranges is shown.

**Table 1.** Classification of CGR and radiation dose changes in different K ranges

### **4 Verification of Effect of Irradiation Doses on SCC Growth Rate**

Bosch [13] et al. recently studied the correlation between neutron irradiation and mechanical properties of 316 material cold worked processed in pressurized water reactor environment, which provided reference value for our paper. He studied the relationship between neutron irradiation and stress-strain, tensile strength, yield strength and other mechanical properties, and we only take the yield strength related content.

**Fig. 8.** Variation of yield strength of cold worked 316 material with neutron irradiation dose in pressurized water reactor [13]

Figure 8 shows the change of yield strength of 316CW material in PWR environment with neutron irradiation dose under the irradiation temperature of 320–340 °C and the test temperature of yield strength of 300–320 °C.

In Fig. 9 we can see the CGR distribution of 316CW material at 25 dpa. Through the study of Terachi [14] et al., Castano [15] et al., Shoji [16] et al., Toloczko [17] et al. and Donghai Du [18] et al., we can find the CGR situation of 316CW materials without irradiation under different yield strengths of K is 30 MPa m0.5. It can be clearly seen that the CGR of about 800 MPa yield strength is between 10–10 m/s and 10–9 m/s, which is nearly 2 orders of magnitude lower than the CGR after irradiation at the same K. CGR with yield strengths of 500 MPa and more than 200 MPa is between 10–11 m/s and 10–10 m/s, which is nearly 3 orders of magnitude lower than CGR after irradiation.

We can obviously score that the CGR of the cold worked 316 material after neutron precipitation is much higher than that of the cold worked 316 material without neutron irradiation. This shows that neutron irradiation has a great influence on the change of material CGR. In addition, the microstructure defects and dislocations of materials may be increased due to the influence of neutron irradiation on the microstructure and mechanical properties of materials.

**Fig. 9.** CGR and K of 316CW material irradiated at 25.0 dpa, CGR of the material at different yield strengths when K is 30 MPa m0.5 [14–18].

## **5 Conclusions**

The CGR and K relationship data of 304 and 316 austenitic stainless steels under different neutron irradiation doses in high temperature water were summarized. The effect of irradiation dose on the crack propagation rate of irradiated SCC was analyzed and verified:

The CGR and K of austenitic stainless steel under high temperature water environment show positive correlation. The CGR of unirradiated CGR was lower than that of irradiated CGR under the same condition, and the difference was several times. There is a certain degree of dispersion in the relation data between CGR and K.

In the range of different K, the relationship between CGR data and irradiation dose of austenitic stainless steel is different. Peak data points of CGR appear at some irradiation doses, and the specific reasons need to be studied. We propose a classification method for CGR and radiation dose variation trend and apply it to the data presented in this paper.

Finally, the significant effect of neutron irradiation on CGR of austenitic stainless steel was verified based on yield strength.

**Acknowledgments.** This work has been supported by National Science and Technology Major Projects 2019YFB1900905, Natural Science Foundation of China (NSFC No. 51771107), and Independent Research and Development Project of State Key Laboratory of Advanced Special Steel, Shanghai University (SKLASS 2020- Z00).

## **References**

1072 C. Xie et al.

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## **Research on the Optimization of Commercial PWR'S Financial Evaluation Model**

Meifang Bo1, Baojun Zheng2, Shengli Zhang1, Zhengxu Ren3, and Bojie Liu1(B)

 China Nuclear Power Engineering Co., Ltd., Beijing, China<EMAIL_ADDRESS>CHINERGY Co., Ltd., Beijing, China CNNP Rich Energy Co., Ltd., Beijing, China

**Abstract.** Considering industry standards, policies, market environment, actual costs of nuclear power plants (NPPs) and technical characteristics of nuclear power, and combining with industrial circumstances when these industry standards were published, we analyzed the limitations of current commercial PWR's fianancial evaluation methods. Taking HPR1000 as a case study, we deeply estimated the generation cost and cash flow. Moreover, optimization direction of the financial evaluation model after comparative analysis was proposed. This research aims to provide reference to similar NPPs'financial evaluation and basis of investment decision-making for investors, owners and general contractors.

**Keywords:** Commercial PWR · Financial Evaluation · Optimization of Model

## **1 Introduction**

In China, the nuclear power plant (NPP) is regarded as an independent legal entity in the economic evaluation of commercial NPPs, and the on-grid electricity price, an important indicator of the economic feasibility of the NPPs, is calculated on the basis of investment in total capital cost, power generation cost and benchmark internal return rate. The economic evaluation is based on the *Economic Evaluation Guidelines of the Nuclear Power Plant Construction Project* (NB/T20048–2011) (hereinafter referred to as the "NB"), which was released in 2011. Nevertheless, significant changes have taken place in domestic power market policy, actual operating cost of NPPs, the business environment of the external nuclear power market, the safety standards and the technical approach of NPPs since its release 10 years ago. Therefore, the gaps open up the room for research on how can current economic evaluation further contribute to the scientific decision-making in investment, rational resource allocation, and sound development in the whole chain of nuclear power industry.

In addition, the industry standard *NB* focuses on guiding studies on the economic feasibility of NPPs. However, with regard to the commercial NPPs, the shareholders,

Financial support was provided by the R&D project of China Nuclear Power Engineering Co., Ltd (KY22246)

shareholders of listed companies with the long-term development plan at heart in particular, are more concerned about the internal rate of return of all parties involved, while the general contractors pay more attention to the investment of total capital cost per kilowatt and the construction units lay emphasis on whether the project can be approved. The analysis on different schemes can be conducted through scientific economic evaluation, serving as solid data support for all parties, and the results can provide insight in understanding the gap between the theoretical and actual benefits of the project, the allocation options for subsequent development, and the range of maximum total capital cost per kilowatt within the project budget.

## **2 Limitations of the Current Economic Evaluation Model for Pressurized Water NPPs**

On the one hand, *NB* was officially released in 2011, and the calculation parameters, criterion parameter and boundary conditions in its appendix were in consistent with the market environment and industry expectations before finalization. However, the capital cost and expected revenue based on the market environment at that time is vastly different from the current one. On the other hand, *NB* was compiled mainly based on the data of Generation 2+ NPPs that were widely built and operated in China, without taking into account the advanced design, the differences in generation costs between the Generation 2+ and Generation 3 NPPs and the actual cost of NPPs in recent years. Furthermore, the existing *NB* model lacks the in-depth research and analysis on the cash flow planning including financing, loan repayment, and corporate dividend of the whole project, and the evaluation system takes the on-grid electricity price measured by the capital benchmark rate of return as the main indicator, excluding the rate of return of the investment of all parties, which is more closely related to the investors.

## **2.1 The Background of** *NB* **Release**

China's electricity pricing mechanism has undergone a series of changes since the reform and opening up, evidenced by a number of relevant policies implemented, such as the repayment of capital with interest (RCI pricing), "price pegged to the increase in transportation" and "operating price" since 1985. Before 2013, nuclear power on-grid electricity price varies among different generating sets based on compensation costs and reasonable revenue, and against which background the *NB* was compiled and released.

#### **2.2 The Applicable Analysis of** *NB* **to the PWR Reactor Types**

The*NB*regulates that it is suitable for the economic evaluation of PWRs and the economic evaluation of other nuclear facilities could refer to this standard. However, this standard does not clearly indicate the reactor types which are applicable to this standard and there is also no content stating about the relationship between the evolvement of PWR nuclear technology and its applicability to this standard.

The formulation of *NB* is mainly based on the economic parameters and data of the Generation 2+. The effects of technical innovation on economic evaluation methods and parameters are not considered in current *NB*. Therefore, the methods and parameters in this *NB* could not objectively and comprehensively meet the demands of economic evaluation for current PWRs, especially for the third generation PWRs.

### **2.3 Analysis of Macro-economic Environment Change for Nuclear Power Enterprises**

Compared with the year 2011 when the *NB* was published, the market environment regarding the fund cost and expected returns has changed significantly. From 2010 to 2019, the interest rate under macro-economy had been declined obviously. Under the current economic environment, the internal rate of returns for the capital fund could decrease to 7%–8% while the rate of returns for investors could decrease to 6%–7%.

#### **2.4 Analysis of Business Environment Change for Nuclear Power Enterprises**

Compared with the year 2011, the business environment of nuclear enterprises has changed obviously. Due to the higher safety requirement, the project cost of the third generation PWRs has increased. Meanwhile, against the backdrop of benchmark tariff reduction, power market revolution, weakened fiscal and tax support, the nuclear power enterprises are under huge business difficulties. For instance, the power generation capability of some nuclear reactors is compared with their full capacity, posing risks to the business operation of nuclear enterprises. Moreover, with the successive increase of transected electricity, NPPs in certain regions participate in the annual bidding transaction, monthly bidding transaction, straight-powered protocol for large users and trans-provincial and trans-regional power transaction, facing dual pressure from both declined planned electricity and market bidding.

Economic evaluation based on the *NB* would deviate from actual circumstances. The actual operation time of Generation 2+ far exceed 7000 h and operation costs are much higher than the regulations in *NB*, resulting in higher electricity price. Moreover, actual fiscal and tax policies also have minor differences with *NB*. As for the third generation, its economics are facing risks in terms with both power generation and electricity price. Thus, to accurately evaluate the economics of the Generation 3 NPPs, it is imperative to focus on the rationality and accuracy of economic evaluation methods. Under the background of declined interest rate, the return rate could be further decreased. *NB* regulates that the pre-tax benchmark return rate before financing is 7% and the after-tax benchmark return rate after financing is 9%. The above-mentioned return rates could be lowered. Besides, more concentration could be paid to financial internal return rate of investors, which is the core concern of investors. The financial internal return rate of investors is advocated as a core parameter in this study and it could be further optimized to 8%–10%.

#### **2.5 Limitations of Current Financial Evaluation for PWRs**

(1) Economic indicators

Based on the financial evaluation of PWRs with different Under the hypothesis of identical internal return rate, the on-grid electricity price of PWRs with different power show large disparity. Moreover, there is no significantly linear relationship between power generation cost and on-grid electricity. Focusing on the on-grid electricity price and capital internal return rate in economic evaluation would result in the overlook of other economic indicators. Therefore, apart from the internal return rate and on-grid electricity price, we should also concentrate on the power generation cost and payment schedule, achieving more precise and comprehensive economic analysis.

(2) Cost control in the whole life period

According to the feedback from NPPs, the actual operation cost has increased, exceeding the parameters regulated in *NB*. Specifically, cost from uranium mining, conversion and separation is higher than the international market, resulting in high cost of nuclear fuels. The increase of nuclear fuel cost and operation and maintenance cost counteract the advantages of investment decline brought by the batch production of Generation 2+ and design maturation of HPR1000. Therefore, apart from the investment control, we should focus on the cost from the period of both construction and operation. Operation and maintenance cost as well as nuclear fuel cost should be supplemented as auxiliary indicators in the future economic evaluation of PWRs.

(3) Indicator discordance with practice

In financial evaluation, the table of capital cash flow is formulated based on designated either on-grid electricity price or capital internal return rate. Common practice is to designate capital internal return rate as 9% and evaluate the on-grid electricity price, thus evaluating the feasibility of the on-grid electricity price of specific NPPs. However, investors pay more attention to dividend distribution and there exists large uncertainty with capital internal return rate as the only economic indicator.

## **3 Optimization of Economic Evaluation Model**

In the future, the financial evaluation of NPPs should be transformed from the single indicator to multi indicators. Currently, focusing only on the on-grid electricity price and capital internal return rate would lead to incomplete analysis of economics of NPPs and simultaneously controlling multiple indicators is conducive to achieving comprehensive economic evaluation of NPPs. For instance, cost control should be expanded from construction to the whole life period of NPPs, including operation and maintenance. Table shows advocated multi indicators in future economic evaluation of NPPs (Table 1).

**Table 1.** Proposed multiple indicators for optimized model

## **4 Preliminary Research on the Cost of Power Generation of HPR1000**

Cost of power generation is the basis of on-grid electricity price evaluation. Because the FOAK reactor of HPR1000 has only operated for 2 years, the data for the cost of operation and maintenance is not thorough. Thus, this study only conducts preliminary research on the cost of power generation of HPR1000. Differences of operation and maintenance cost between HPR1000 and the Generation 2+ result from their technical differences.

Cost of materials consumed during operation includes expense from nuclear fuels, chemicals, water and electricity. Water consumption difference between HPR1000 and the Generation 2+ is clear but the quantity of other materials consumed in the operation of HPR1000 is still unclear. Standard of material expenses for HPR1000 should be identified based on the practice of the Generation 2+ and the in-service HPR1000. The cost for each staff of HPR1000 and the Generation 2+ should be the same, but the staff quota of HPR1000 should be modified based on actual situation. Maintenance of NPPs includes general overhaul and routine operation and maintenance. General overhaul planning is related with the type of nuclear reactors. Correspondingly, the expense of general overhaul is also different for each type of reactor. With the progress of science and technology as well as the management of power plants, the repair fee rate should be declined. Boasting with higher design standard, the repair fee rater of HPR1000 could be decreased from 1.35% to 1.2%.

Life period is one of major differences between the Generation 2+ and the HPR1000. The life period of the HPR1000 is 60 years, which mainly influences the design of major equipments. Since the capital cost is low in today's market, a shorter payback period is 1078 M. Bo et al.

conducive to sustainable bonus distribution. Therefore, adopting 20 years as depreciation period is still feasible in the economic evaluation of HPR1000.

Based on the comparative analysis and advanced design concept, we estimated the power generation cost of HPR1000 after optimization of depreciation period and repair fee rate. We estimated the power generation cost and on-grid electricity price based on the total capital cost of 37.75 billion RMB and the capital internal return rate of 9% (Table 2).

**Table 2.** Cost composition of HPR1000

## **5 Financial Evaluation of HPR1000**

Based on the above-mentioned optimization clue, we formulated 8 schemes to analyze the economics of HPR1000 under each condition.

#### **5.1 Scheme Estimation**

(1) Original Scheme (Option 1)

The power generation cost, on-grid electricity price, and the rate of return for all parties were calculated at the total capital cost of 37.75 billion RMB, 1.35% rate of general overhaul cost, depreciation period of 25 years and capital return rate of 9%. The long-term loan is reimbursed by deducted VAT, refunded VAT, depreciation, amortization, and undistributed profits for repayment in order, and cash for circulation will be used to repay short-term loans annually. Dividend will be distributed under the condition of guaranteed loan repayment in the form of cash. The dividend distribution ratio is as follows (Table 3).

**Table 3.** Average dividend distribution ratio of option 1

As seen from the table, in the first five years after the unit is put into commercial operation, the ratio of cash dividends to distributable net profit is 0, suggesting that there will be no dividend in the first 5 years, and the trend continue till the 6th year; from the 6th to 10th years after the operation, the average distribution ratio of annual dividend is 15%, which is still far below the value proposed by the listed company (30%); from the 11th to 15th years, the average distribution ratio of annual dividend is 65%, and the full allocation can't be achieved until 17th year. The dividend distribution is so conservative that the listed company's investment in new projects and its rolling development get impeded.

#### (2) Base Case (Option 2)

The total capital cost, power generation cost, and investment return of all parties were retrodicted with 1.35% general overhaul rate, depreciation period of 25 years, capital return rate of 9%, and the on-grid electricity price, which was calculated according to that of the benchmark local thermal power desulfurization and denitrification. The arrangement of cash flow and dividend is similar to the Option 1 in nature with comparable annual dividend distribution ratio.

#### (3) General overhaul Scheme (Option 3)

The total capital cost, power generation cost, investment return of all parties were retrodicted with 1.2% general overhaul rate, adjusted from 1.35% according to the estimated quota of annual overhaul expense and fixed assets, depreciation period of 25 years, capital return rate of 9%, and the on-grid electricity price calculated according to that of benchmark local thermal power desulfurization and denitrification. The arrangement of cash flow and dividend is similar to the previous case in nature with comparable annual dividend distribution ratio.

(4) Depreciation Scheme (Option 4)

The total capital cost, power generation cost, investment return of all parties were retrodicted with 1.2% general overhaul rate, depreciation period of 20 years, capital return rate of 9%, and the on-grid electricity price calculated according to that of benchmark local thermal power desulfurization and denitrification. The arrangement of cash flow and dividend is similar to the previous case in nature with comparable annual dividend distribution ratio.

(5) Rate of return Scheme I (Option 5)

The option 5 is to adjust the order of cash flow, the dividend distribution and repayment scheme. The total capital cost and power generation cost were retrodicted with 8% of capital return rate and 9% of return rate of all parties, considering low loan interest rate for the rolling development of the company. Combining the study of the dividend distribution of the listed companies with the research on the dividend of NPPs, the arrangement of cash flow is as follows.

Cash dividends for shareholders are guaranteed at a certain amount, and the rest is repaid to long-term loans in the order of deducted VAT, refunded VAT, depreciation, amortization, and undistributed profits remained after dividend. The short-term loan will be used to compensate for the long-term loan that could not be covered by dividend and repayment. The corresponding dividend distribution plan is that there will be no dividend in the first two years after commercial operation, 860 million RMB per year from the 3rd to 7th year, 1.2 billion RMB per year from the 8th to12th year, and full percent of the profit from the 13th year onwards through the subsequent operation.

(6) Rate of return Scheme II (Option 6)

The dividend distribution and loan repayment scheme is adjusted in option six, while other parameters remain the same as Option 4. The total capital cost and power generation cost were retrodicted with 8% of capital return rate and 10% of return rate of all parties. The slight changes in the cash flow and the corresponding dividend distribution can be found in comparison with Option 5. There will be no dividend in the first two years after commercial operation, 1.08 billion RMB per year from the 3rd to 7th year, 1.66 billion RMB per year from the 8th to 12th year, and full percent of the profit from the 13th year onwards through the subsequent operation.

(7) Rate of Return Scheme III (Option 7)

The dividend distribution and loan repayment scheme is adjusted in option seven, while other parameters remain the same as Option 4. The total capital cost and power generation cost were retrodicted with 7% of capital return rate and 9% of return rate for shareholders. The slight changes in the cash flow and the corresponding dividend distribution can be found in comparison with Option 5. There will be no dividend in the first two years after commercial operation, 1.03 billion RMB per year from the 3rd to 7th year, 1.4 billion RMB per year from the 8th to 12th year, and full percent of the profit from the 13th year onwards through the subsequent operation.

#### (8) Rate of Return Scheme IV (Option 8)

The dividend distribution and loan repayment scheme is adjusted in option eight, while other parameters remain the same as Option 4. The total capital cost and power generation cost were retrodicted with 7% of capital return rate and 10% of return rate for shareholders. The slight changes in the cash flow and the corresponding dividend distribution can be found in comparison with Option 5. There will be no dividend in the first two years after commercial operation, 1.31 billion RMB per year from the 3rd to 7th year, 1.6 billion RMB per year from the 8th to 12th year, and full percent of the profit from the 13th year onwards through the subsequent operation.

#### **5.2 Results and Comparative Analysis**

(1) Estimation results

Table 4 shows the results of power generation cost and its composition for each scheme while Table 5 demonstrates main indicators.

**Table 4.** Estimation of power generation cost

(*continued*)

**Table 4.** (*continued*)

**Table 5.** Estimation of main indicators

#### (2) Comparative Analysis

Based on the results of the above options, it can be concluded that the rate of return of shareholders from all parties and the total capital cost per kilowatt increase by modification of power generation cost of the base case in the model and optimization of cash flow with current low interest rate under the condition that the on-grid electricity price and energy being the same, i.e. the same revenue from electricity sales.

The model enables shareholders to prepare for the rolling development of the company and invest in new projects from a long-term perspective. In addition, as the total capital cost of projects gradually increase, the general contractor can better allocate its resources against background of mounting investment in the Generation 3 NPPs by diverting premium resources to design, construction and procurement, which will in turn benefit the owner. The optimization that attaches more importance to the whole life cost of the project rather than limited to the investment in the total capital cost can be more conducive to the sustainable development of the entire nuclear power industry.

It can be concluded that the yield of the plant can be further increased with the same construction investment. Meanwhile, the project can endure higher construction investment under the condition of the same or even higher yield, urging relevant units to apply higher safety standards to improve the safety and reliability of the plant. Based on the current market environment and operating practice of dividend strategy of groups including China National Nuclear Corporation (CNNC), it is recommended that Option 6 can generate stable shareholder yield and total capital cost per kilowatt. Finally, the risk resisting capability of nuclear units is lifted.

## **6 Conclusions**

Considering the current market and the experience practice of in-service NPPs, we optimized the economic evaluation model of NPPs. Since in listed nuclear power companies, investors pay more attention to dividends and the long-term development of the company, the optimized capital internal return rate, internal return rate of investors and total capital cost could be obtained via optimized capital flow and bonus allocation. This research provides viable investment strategies for decision makers.

The flexible arrangement of cash flows and allocating bonus to investors in priority would significantly enhance the debt risk compared with the baseline scenario. Moreover, if the interest rate increases with the change of financial market, the debt rate of the proposed scenarios would increase, posing debt risks to the project. However, the asset liability under current circumstances could meet the requirements. It is noted that our research is based on the current market environment and the variance of power market and financial market would influence the results of optimization.

### **References**

1084 M. Bo et al.

**Open Access** This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

The images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

## **Design of Radioactive Waste Classification and Detection System for Nuclear Facility Decommissioning**

Kang Chang1(B) , Guangming Cheng2, Jinwei Zeng2, Wenzhang Xie1, Chenyu Shan1, Qingxin Lei1, Jia Huang1, Feng Liu1, Xiajie Liu1, and Li Li1

1 China Nuclear Power Technology Research Institute Co., Ltd., Shenzhen, China<EMAIL_ADDRESS>
2 Guangxi Fangchenggang Nuclear Power Co., Ltd., Fangchenggang, China

**Abstract.** The most important indicator of the radioactive waste classification and detection system is its identifiable minimum activity of low level radioactive waste, that is, the lower detection limit. In order to design a low level and very low level waste classification and detection system that can perform large-scale and rapid measurement, and explore the influence of various factors on the low limit of detection, this paper establishes the layout model of the detection unit of the classification detection system by Monte Carlo method to simulate the number of NaI crystals, the density of the detected object, the distance between the detection crystal and the detected object, the distance between the adjacent measured waste and the measurement time, etc. Meanwhile this paper analyzes the characteristics of the low limit of detection, and performs operations research analysis based on the principle of being able to detect radioactive waste with specific activity of not less than 0.1 Bq·g−1, maximizing the shielding effect and optimizing the shielding weight, and designs a low level and very low level waste classification and detection system that can measure radioactive waste which density is not less than 0.25 g/cm3 and which specific activity is not less than 0.1 Bq·g−1.

**Keywords:** Monte carlo · Low limit of detection · Radioactive waste · Classification

## **1 Introduction**

During the decommissioning of nuclear facilities, a large amount of radioactive waste will be generated, covering different types of waste such as medium, low and very low level radioactive and clearance level waste. According to Chinese current radioactive waste classification standard, different types of radioactive waste need to adopt different disposal methods. Timely and accurate classification of decommissioned nuclear facilities is one of the key links in radioactive waste management, and it is also an important means to minimize waste and reduce disposal and supervision costs [1–5].

When using physical measurement techniques such as radiation detection to classify radioactive waste, especially when classifying clearance level waste (EW), very low-level waste (VLLW) and low-level waste (LLW), due to the very low level of radioactivity of the first two types of waste, the low limit of detection of instrument used has higher requirements. Therefore, this paper refers to other classification detection devices (e.g. box-type waste detecting device and waste barrel gamma scanning device) and uses Monte Carlo calculation software to simulate the low limit of detection of the module of a low-very low radioactive waste classification detection system, and studies relationship between the different detection crystal volume and crystal arrangement, different measurement time, different shielding thickness around the detection crystal, the distance between the detection crystal and the upper surface of the waste, and the density with the low limit of detection, and optimizes the detection module of the low-very low radioactive waste classification detection system.

**Fig. 1.** Box-type waste detecting device and waste barrel gamma scannig device

## **2 Materials and Methods**

#### **2.1 Detector Source Response Coefficient**

The detector source response coefficient K of the classification detection system is an important design parameter of the detector, that is, the counting rate generated by the radioactive source per unit specific activity in the measurement chamber of the classification detection system in the detector. In the development phase, we uses the F8 counting card in the MCNP program and SCORE card in the FLUKA program to simulate the calculation to obtain the pulse count rate produced in the detector in the measurement chamber of the specific activity of the waste in the detector. Detector source response coefficient.

$$K = \text{TallyF}\_{FB} \times V \times 1 \tag{1}$$

where *K* is the detector source response coefficient of the classification detection system, cps·Bq−1·m−3; *TallyF8* is counting rate (energy range of 100 keV ~ 3 meV), cps; *V* is the volume of waste to be measured in the simulation calculation, m3; *I* is the decay branch ratio of gamma rays produced by radionuclides in the waste to be measured.

#### **2.2 Minimum Detectable Concentration**

Minimum detectable concentration (MinDC, MDC) [4–6] represents the minimum activity concentration value that the classified detection system can analyze for specific nuclides in the measured waste. It is an important indicator of the sensitivity of the classification detection system when it is applied in a given situation. The premise that the waste to be tested can be reliably detected is that the activity concentration of the waste to be measured is greater than the minimum detectable concentration.

$$M\_{ln}DC = \frac{2.706 \left/ t + 4.65 \sqrt{l\_b/t}}{K} \tag{2}$$

where: *MinDC* is the minimum detectable concentration, Bq·m−3; *lb* is the environmental background count rate, cps; *t* is the given measurement time, s.

#### **2.3 Model of Simulation**

As shown in Fig. 2, this paper establishes the detection module model in the abovementioned radioactive waste classification detection system in the Monte Carlo simulation software MCNP and FLUKA. In the calculation model, the size of a single NaI crystal is 40 cm × 10 cm × 5 cm; the size of the waste detection box ( stainless steel) is 65 cm × 65 cm × 10 cm; the radioactive source term is divided into two parts. One is the environmental background, and it is considered that the environmental dose rate in the working area of the detection system is the upper limit of the white area's dose rate, and it is equivalent to a uniform spherical shell surrounding the whole detection device. The spherical shell is a source of air uniformly distributed with Cs-137 sources. The other part is the radioactive waste contained in the detection box, which is set as a cuboid source in the simulation.

**Fig. 2.** Lay-out of the detectors and waste box

## **3 Results and Discussion**

#### **3.1 Effect of Crystal Arrangement on the Low Limit of Detection**

According to the Nuclear Safety Guidelines HAD401/04 "Radioactive Waste Classification", the level of Cs-137 control is 0.1 Bq·g−1, that is, the classification detection system for requirements of Cs-137.

Usually, the larger the crystal volume or the number of crystals are, the smaller the low limit of detection is. However, due to the high volume NaI crystal price, this paper selects several different NaI detection crystal arrangement and quantity as shown in Fig. 1 to simulate the detection of the lower limit change, in order to choose the most costeffective crystal arrangement and quantity. As shown in Fig. 3(a), when the background count rate is 5 cps·cm−3 and when the detection time is 30 s, no detection scheme can meet 0.1 Bq·g−1; when the detection time is 60 s, at least 4 NaI detection crystals should be selected to meet 0.1 Bq·g−1; as shown in Fig. 3(b), when the background count rate is 0.5 cps·cm−3, there is no limit to the number of NaI detection crystal blocks; in Fig. 3(a)(b), it shows that the detection efficiency of the 8 NaI crystal tiling type is better than the detection efficiency of the two-layer superposition form, mainly because the gamma ray energy is low, and the radiation energy can be deposited by selecting one layer of crystal, and the two-layer superposition form increases the lower limit of background influence detection caused by the crystal itself.

**Fig. 3.** Difference in the mdc with the volume of NAI crystals in different environment background

#### **3.2 Effect of Average Distance Between Detector and Waste Upper Surface on Low Limit of Detection**

In the actual measurement process of the radioactive waste classification detection system, the average distance between the detector and the waste surface is required to be adjustable, so as to avoid the overflow of the waste to be detected and the detector can achieve the best detection effect, so different source distances are used to simulate the change of the low limit of detection. As shown in Fig. 4, it can be seen that the low limit of detection increases as the average distance between the detector and the upper surface of the waste increases. Figure 4(a), when the NaI background count rate is 5 cps;cm−3 and when the measurement time is 60 s, the average distance between the NaI detector and the upper surface of the waste should not exceed 10 cm, even if the measurement time is relaxed to 120 s, the average distance should not exceed 20 cm. And when the NaI background count rate is 0.5 cps;cm−3, the average distance between the NaI detector and the upper surface of the waste should not exceed 50 cm.

#### **3.3 Influence of the Density of Waste to be Measured on the Low Limit of Detection**

In addition, the types of waste of the decommissioning of nuclear facilities are various and the density varies greatly, including metal materials such as steam generators in nuclear power plant, waste gas masks, and radioactive medical waste. In order to explore the impact of waste density on the low limit of detection and avoid discomfort to the detection system due to excessive or small waste density, different waste densities are used to simulate changes in the low limit of detection.

As shown in Fig. 5, under the same measurement conditions, the low limit of detection decreases with increasing waste density. Figure 5(a) when the measurement time is 60 s, if the NaI background count rate is 5 cps·cm−3, the waste density should not be less than 0.25g·cm−3. Figure 5(b) when NaI background count rate is 0.5 cps·cm−3 there are no restrictions on waste density.

#### **3.4 Effect of Shielding on the Low Limit of Detection**

The background count rate in the NaI detection crystal mainly comes from the noise of the NaI crystal, the environmental background of the area where the detection system is located, and the adjacent waste box to be tested. From the above analysis, it can be seen that the background count rate of different levels also has an important impact on the detection lower limit, so shielding must be set around the detector. Since the noise of the NaI crystal itself cannot be eliminated by shielding, and the background count rate in the NaI detection crystal with different intervals of the waste box to be detected is not shielded. The result is shown in Table 1. The environmental background is much lower than the influence of the adjacent waste box to be detected on the background of the NaI detection crystal, so the following only simulates the waste box to be detected at different intervals, changes in the lower limit of detection under different shielding thicknesses.

**Fig. 4.** Difference in the mdc with the average distance between the detector and the upper surface of waste in different environment backgrounds

**Fig. 5.** Difference in the mdc with the density of waste in different environment backgrounds

As shown in Fig. 6(a), when the spacing between adjacent waste boxes is 1 m, the thickness of the shielding lead layer is 2 cm and 4 cm, respectively, the background count rate can be reduced to 5 cps;cm−3 and 0.5 cps;cm−3 as shown in Fig. 6(a) and (b), when the spacing between adjacent waste boxes is 1.5 m or more, the background count rate can be reduced to 5 cps;cm−3 and 0.5 cps;cm−3 when the thickness of the shielding lead layer is 1 cm and 3 cm, respectively. As shown in Table 2, for a conservative estimate, when the distance between adjacent waste boxes is selected for 1 m, the background count rate is reduced to 5 cps;cm−3 and 0.5 cps;cm−3, respectively. The weight of lead shielding is about 139.3 kg and 303.1 kg, because the aging lead used for shielding is expensive, so it is proposed to use 2 cm thickness lead shielding.

**Table 1.** Background count rate in NAI without sheilding

**Fig. 6.** Difference in the MDC with the distance between adjacent wastes to be detected

**Table 2.** Parameters after shielding

## **4 Conclusions**

In this paper,Monte Carlo softwareMCNP and FLUKA are used to simulate the influence of the number of NaI crystals, the composition of the measured object, the distance between the detection crystal and the measured object, and the measurement time on the lower limit of detection. The results show that:

1) In the case of the same arrangement method, the lower limit of detection varies with the increase in the number of detected crystals; the low limit of detection of the tiling type is better than the two-layer superposition form; it is expected to use 8 NaI crystal tiling type arrangement method in engineering.

Taking into account the weight and shielding effect of lead shielding, it is proposed to use 2 cm thickness lead shielding to reduce the background count rate to 5 cps·cm−3 below, at the same time, the average distance between the NaI detector and the upper surface of the waste should be controlled at 20 cm, and the waste density should be controlled not less than 0.25 g·cm−3.

**Fig. 7.** Device schematic

Based on the above research contents, this paper designs the device as shown in the Fig. 7. The conveyor transports the detection cassettes containing the radioactive waste into the detection chamber with shielding and collimation through the pedrail. The source-less efficiency and energy spectrum analysis program completes the calibration and measurement of the waste, according to which the radioactive of the waste is judged and classified, and the transmission device is controlled to continue to move.

## **References**

**Open Access** This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

The images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

## **Hot-Pressing Sintering and Analytical Characterization of Coated Particle-Dispersed Fuel Pellets**

Wentao Liu1,2(B) , Zongyi Shao1,2, Ying Meng2, Zongshu Li1,2, and Zheng Sui1,2

1 CNNC Key Laboratory of Fabrication Technology of Reactor Irradiation Special Target, Baotou 014035, China<EMAIL_ADDRESS>2 China North Nuclear Fuel Co., Ltd., Baotou 014035, China

**Abstract.** Coated particle-dispersed fuel pellets have the characteristics of high thermal conductivity and multilayer protection against fission products, which are an important component of ATF fuel. In this paper, by carrying out research on the dressing process of TRISO particles, it is realized that SiC powder completely encapsulates TRISO particles. The hot-pressing sintering method was used to study the influence of different sintering aids, different hot-pressing sintering holding time, different hot-pressing sintering temperature, different hot-pressing sintering pressure and different powder particle size on the density of pellets. The power with a particle size of 10nm is sintered at 3% sintering aid, 1690 °C, 1.5h holding time, 80 MPa vacuum hot pressing, and a full ceramic micro-encapsulated fuel core with a relative density of 95% or more is prepared, and the internal particle structure is complete.

**Keywords:** Coated particle-dispersed fuel pellets · TRISO · Hot press sintering

## **1 Introduction**

The purpose of research and development of advanced reactor systems is to meet the economic, environmental and social development needs of the 21st century. Its technical goals involve four aspects: sustainability, economy, safety and reliability, nuclear nonproliferation and physical protection. Specifically, it contains eight technical goals, covering various technical directions related to the design and implementation of reactors, energy conversion systems and fuel cycle facilities.

The nuclear fuel element is the core component of the reactor, and its advanced nature and safety are the important basis for the advanced nature and safety of the reactor. ATF (Accident Tolerant Fuel) fuel that can tolerate accidents to a certain extent and has inherent safety, is an important development direction in the field of nuclear fuel in the world. As an important part of ATF, the coated particle-dispersed fuel obtained from TRISO particle-dispersed silicon carbide matrix is aimed at the weakness of the traditional UO2-Zr alloy fuel system, and combines the mature TRISO (Tri-Structural Isotropic) particles with the tolerance of fission products. As well as the advantages of good thermal performance and thermal stability of SiC matrix, it is a more promising development direction in advanced accident-resistant nuclear fuel.

The coated particle-dispersed fuel is based on a fuel pellet with three-dimensionally isotropic TRISO-coated particles embedded in a SiC matrix. The structure of the pellets and the internal TRISO particles is shown in Fig. 1. Such pellets feature high thermal conductivity, multiple layers of protection against cracking products, and high burnup, which facilitates normal and transient operability of the reactor.

**Fig. 1.** Schematic diagram of TRISO particle and coated particle dispersion fuel

After the concept of coated particle dispersion fuel in which TRISO particles are dispersed in a silicon carbide matrix was proposed, researchers from the United States, South Korea and other countries have conducted in-depth research in this direction, and prepared products with good thermal conductivity. All-ceramic microencapsulated die with uniform phase distribution.

In this paper, the effect of binder on the dressing of TRISO granules and the effect of pre-compression molding pressure on the green density were studied through mixing, molding and hot-pressing sintering experiments. After the SiC matrix and TRISO particles were uniformly mixed and molded, the effects of different sintering aid contents, different hot-pressing holding times, different hot-pressing sintering temperatures, different hot-pressing sintering pressures, and different powder particle sizes on the properties of pellets were studied.

## **2 Materials and Methods**

#### **2.1 Materials**

The TRISO particles used in the study are fuel particles with spherical UO2 as the core. The outer layer of the core is sequentially coated with loose pyrolytic carbon, inner dense pyrolytic carbon, silicon carbide and outer dense pyrolytic carbon. The SiC powder used is β phase and its purity is greater than 99.9%. The particle size distribution of the raw material powder is relatively uniform, but the deviation between the median value and the average value is small, and the powder particle size as a whole presents a normal distribution centered on the median value.

Due to the poor sintering performance of SiC powder, in the process of preparing by NITE liquid phase sintering method, adding a small amount of sintering aid for cosintering can improve the sintering performance of the material to a certain extent.  After ball milling, the powder is dried, crushed and sieved; the sieved mixed powder is evenly wrapped on the surface of the TRISO particles; the TRISO particles after uniformly wrapping the base powder and the base powder are mixed uniformly according to a certain volume ratio, and then pre-compressed and formed; finally Vacuum hot pressing sintering, heating rate 10 °C·min-1, sintering temperature 1650 ~ 1750 °C, 1 ~ 2.5 h holding time, 65 ~ 90 MPa.

## **3 Results and Discussion**

## **3.1 Influence of Binder on Dressing Effect of TRISO Particles**

In order to improve the compatibility of SiC and TRISO particles during the green forming process of the coated particle-dispersed fuel pellets, and at the same time prevent the TRISO particles from contacting each other, it is necessary to coat a layer of SiC on the surface of the TRISO particles.

Due to the large difference in particle size between TRISO particles and SiC powder, it is difficult for SiC to directly coat the surface of TRISO particles without binder, as shown in Fig. 2(a). After investigation and test, use glycerol as binder, absolute ethanol as diluent, configure 10% glycerol-absolute ethanol as binder, and use glue tip dropper to evenly wrap the surface of TRISO particles with a layer of adhesive. Then, it is dispersed into the matrix powder (SiC + sintering aid) to realize the bonding of a layer of matrix powder on the surface of the TRISO particles. As shown in Fig. 2(b), the surface of the TRISO particles is completely covered and the dressing effect is good.

**Fig. 2.** Mixture macro effect diagram:(a) The effect of dressing without binder.(b) The effect of dressing without binder

#### **3.2 Influence of Pre-press Forming Pressure on Green Density**

The weight of the TRISO particles and the SiC powder after adding the sintering aid are calculated and weighed according to the volume fraction, and the ingredients are mixed, and then loaded into the pre-compression mold, and the floating female mold is pre-compressed using a micro-controlled pressure testing machine to determine the molding pressure and raw material. The relationship between blank density and TRISO particle integrity is shown in Fig. 3. It can be seen from Fig. 3 that the higher the pressing pressure, the higher the green density of the pellets. The higher the green density, the better the density of pellets after sintering, so the molding pressure should be raised as high as possible. It was observed in the experiment that when the pressure was lower than 2.0 KN, the TRISO particles were not damaged, and when the pressure reached 2.5 KN, the surface layer of some TRISO particles appeared to fall off, and there was abnormal noise during the pressing process.

**Fig. 3.** Variation curve of green density with pressure

#### **3.3 Effects of Different Hot Pressing Sintering Processes on the Properties of Pellets**

Table 1 shows the density changes of pellet fuel pellets covered by pressureless sintering under different additions of sintering aids. When the addition of sintering aids is less than 3wt%, the density of pellets increases with the addition of sintering aids., when the addition amount of sintering aid is greater than 3wt%, the increase in the density of pellets is no longer obvious.

Table 2 shows the change results of the density and phase of the pellets at different hot pressing sintering temperatures. It can be seen from the results that as the sintering temperature increases, the density of the pellets increases, and the β-SiC in the pellets will be partially converted into α -SiC, when the sintering temperature is higher than 1710 °C, obvious α-SiC diffraction peaks appear in the pellet phase.

**Table 1.** Effect of Sintering Aid Additives on the Density of Pellets

**Table 2.** Influence of sintering temperature on the density and phase of pellets

Table 3 shows the change results of the density of pellets under different hot pressing and holding time. With the prolongation of holding time, the diffraction peak of α-SiC phase in the pellets gradually increased; when the holding time was 1h, the inner and outer layers of the pellets appeared Phenomenon, the pellets are not burned through, and after the holding time exceeds 2h, the density of the pellets does not increase significantly.

**Table 3.** The effect of holding time on the density of pellets

Table 4 is divided into the change results of the density of pellets under different hot-pressing pressures. The analysis results show that with the increase of hot-pressing pressure, the density of pellets gradually increases. When the hot-pressing pressure is in the range of 75 ~ 80 MPa, the The increase in density decreases. When the hot pressing pressure reaches 90 MPa, the punch on the die breaks.

**Table 4.** The effect of sintering pressure on the density of pellets

Table 5 shows the experimental results of SiC powder with different particle sizes. It can be seen from the results that with the decrease of powder particle size, the density of pellets gradually increases.

**Table 5.** Effect of Powder Particle Size on Pellets Density

#### **3.4 Performance Characterization of Coated Particle-Dispersed Fuel Pellets**

Using SiC matrix powder with a particle size of 10nm, vacuum hot-pressing sintering at 3wt% sintering aid addition, 1690 °C hot-pressing sintering temperature, 1.5 h holding time, and 80 MPa hot-pressing sintering pressure, the obtained all-ceramic micro-encapsulated dispersed fuel pellets were prepared. The real thing is shown in Fig. 4.

**Fig. 4.** Coated particle dispersion fuel pellets

The SEM of the SiC matrix is shown in Fig. 5, the second phase composed of sintering aids exists inside the SiC matrix, and the distribution is uniform. The metallographic photos of TRISO particles can clearly see that the outer layer of the particles has 4 layers of cladding layers, the particle structure is complete, and there is no damage during the molding and sintering process. After core sintering, the thickness and element distribution of each layer of TRISO particles are still comparable to those of the original particles, and the thickness of the outer dense pyrolytic carbon layer is 19 μm.

**Fig. 5.** SEM image of coated particle-dispersed fuel pellets

It can be seen from Fig. 6(a) that the thermal diffusivity of the coated particledispersed fuel core gradually decreases with the increase of temperature, and the thermal diffusivity at each temperature point is lower than that of the base SiC. The addition of TRISO particles reduces the core to a certain extent. The thermal diffusivity is still significantly higher than that of the traditional UO2 fuel core. It can be seen from Fig. 6(b)that the thermal expansion coefficient of the fuel core increases gradually with the increase of temperature, and the change trend is linear. As the content of TRISO particles increases, the thermal expansion coefficient of the core decreases slightly. In the range of 0 – 1000 °C, the thermal expansion coefficient of the coated particle-dispersed fuel core is significantly lower than that of the traditional UO2 core.

**Fig. 6.** Thermophysical properties vary with temperature:(a) Thermal diffusivity. (b) Thermal expansion coefficient

## **4 Conclusions**

## **References**

**Open Access** This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

The images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

## **Study on Capiliary Characteristics of Stainless Steel Wire Mesh Wick of Alkali Metal Heat Pipe**

Yiru Zhu, Luteng Zhang(B) , Zhiguo Xi, Zaiyong Ma, Wan Sun, Longxiang Zhu, and Liangming Pan

> Chongqing University, Chongqing, China<EMAIL_ADDRESS>
**Abstract.** The capillary characteristics of the wicks are of great significance to the normal operation of the heat pipe,and this study carried out the wick experiment of vertical reel stainless steel wire mesh in liquid sodium working medium and the visual observation experiment of sodium film in the wire mesh wick. The experimental results show that when the temperature of liquid sodium is about 400 °C, the capillary phenomenon of stainless steel wire mesh occurs more obviously, and after 450 °C, the evaporation of sodium is gradually obvious and accompanied by the mass fluctuation of the wire mesh wick. The visual observation experiment of sodium liquid film in the wire mesh found that the wetting and transition point of sodium on the surface of the stainless steel wire mesh was about 410 °C, which was a good verification of the occurrence of the more obvious capillary phenomenon of the wick at about 400 °C.

**Keywords:** Alakali metal heat pipe · Wick · Capillary characteristics · Contact angle

## **1 Introduction**

Heat pipe is an efficient heat transfer component that uses working medium to transfer heat at different parts of the phase change. The heat pipe principle was first proposed by Gaugler [1] in 1944. In 1965, Cotter [2] first proposed a relatively complete theory of thermal management. Because of their superiority, Heat pipes are also used for cooling abyssal sea reactors and abyssal sea reactors. However, the heat transfer capacity of the heat pipe is limited by its own heat transfer limit. When the heat transfer limit of the heat pipe occurs, the heat of the reactor core cannot be exported in time, which leads to a reactor safety accident. The capillary limit is due to the fact that the capillary indenter produced by the evaporation and condensation sections of the heat pipe is not enough to overcome the pressure drop caused by the return of the working medium. The working fluid cannot flow back to the evaporation section normally. It will cause the evaporation section to dry up, and cause the wall temperature of the evaporation section to rise rapidly, and even burnout the heat pipe wall. Since the heat pipes are all operating at high temperatures in the heat pipe cooling reactor. The heat pipes must use high temperature heat pipes. The working medium of high-temperature heat pipes is generally lithium, sodium, potassium and other alkali metals, so high-temperature heat pipes are often referred to as alkali metal heat pipes. Because of the high viscosity and density of alkali metals, a greater driving force is required in the reflux of the wick. Therefore, exploring the capillary force of the high-temperature heat pipe wick can guide the selection of the operating conditions of the heat pipe, so as to avoid the occurrence of the capillary limit of the high-temperature heat pipe and ensure the safety of the operation of the space reactor.

The most commonly used methods for testing capillary characteristics in the wick are the bubble method [3] and the capillary rising method. Shufeng Huang [4] tested the capillary characteristics of a new type of stainless steel fiber-powder composite wick with the capillary rise method and compared it with a composite wick with a single structure and other structures. Guanghan Huang [5] used an infrared camera to set up a capillary rise rate test device that measured the capillary characteristics of the axial channel wick of the alkaline corrosion treatment. Yong Tang [6] used an infrared camera combined with capillary rise method to measure the capillary performance of the sintered groove composite wick, sintered wick and groove wick with ethanol as the working medium. The results show that the sintered powder wick has better capillary characteristics than the single structure wick. Heng Tang [7] measured the capillary characteristics of a new micro-V-shaped channel wick using the capillary ascending method and acetone as the working medium. Daxiang Deng [8] used a new infrared thermal imaging method to test the capillary characteristics of the sintered groove wick with ethanol as the working medium. Daxiang Deng [9] also tested the capillary characteristics of the micro-Vchannel wick with ethanol and acetone for the working medium. Li [10] calculated the capillary characteristics of different porosity wicks in acetone using the mass change curve assessment recorded by the electronic balance.

Most of the above scholars are experiments on the capillary characteristics of sintered wicks, groove wicks and composite wicks with ethanol and acetone as working medium. Due to the reactive chemical properties of the alkali metal working medium, there are fewer test experiments for the capillary core performance of alkali metal heat pipes. In this paper, 304 stainless steel is used as the material of the wire mesh wick, sodium is used as the working medium, and the capillary characteristics of the wire mesh wick is studied by the capillary rising method, and the capillary characteristics of the sodium heat pipe are preliminarily explored. The sodium film in the screen was photographed, and the spread of liquid sodium at different temperatures on the stainless steel wire mesh was obtained, and the law of the capillary ability of the wire mesh wick changed with temperature was verified.

### **2 Experimental Methods and Principles**

#### **2.1 Experiment on Capillary Ability of the Wire Mesh Wick**

The capillary ability experiment of the wick is measured by the capillary rise method and the quality change process of the wick is recorded with an electronic balance. Figure 1 shows the entire experimental setup and schematic. The experimental principle is that when the wire mesh wick sample is extended into a stainless steel test tube containing liquid sodium, the liquid sodium will be sucked into the wick due to the influence of

**Fig. 1.** Capillary ability test equipment diagram

capillary force and can reach a certain height. When the rise of sodium in the wire mesh wick reaches stability, the following relationship is satisfied:

$$h = \frac{2\sigma\cos\theta}{\rho g r\_p} = \frac{2\sigma}{\rho g r\_{\text{eff}}}\tag{1}$$

wherein θ is the contact angle between sodium and the wire mesh wick, the σ is the surface tension of liquid sodium, *rp* is the liquid sodium density, *reff* is the effective capillary radius of the wick, and rp is the pore radius. The experimental equipment includes glove box, well-type heating furnace, electronic balance and so on. The glove box provides an inert gas environment with its own dehydration and deaeration functions, which can avoid the contamination of the sodium working medium by oxygen and water vapor during the experiment. Both the well furnace and the electronic balance are placed inside the glove box in the argon atmosphere. The electronic balance has a maximum range of 220 g, an accuracy of 0.2 mg, and can be connected to the computer segment to output real-time quality changes. The test tube contains a K-type thermocouple for internal liquid sodium temperature measurement, and the XSR21A series paperless recorder is used to implement the output temperature data, and the paperless recorder error is 0.2%· F, which F is the set range.

#### **2.2 Sodium Membrane Spreading Observation Experiment**

The spreading observation experiment of liquid sodium on the surface of stainless steel wire mesh is based on a heating stage and a microscope, and the experimental equipment diagram is shown in Fig. 2. The hot stage contains platinum electric heating material and crucibles inside and can be heated at a maximum heating temperature of up to 1500 °C. Cold water circulation devices and inert gas runners are provided around the hot stage. Cooling circulation units are used to cool hot stage materials, and inert gases can reduce air pollution to sodium during experiments. The microscope has a maximum magnification of 1000X and can observe samples in the micron range.

**Fig. 2.** Hot stage experimental equipment diagram

During the experiment, argon gas is continuously pumped in the crucible of the hot stage, and then the sodium block is placed inside the crucible of the hot stage, and then the cleaned stainless steel wire mesh is covered on the surface of the sodium block. Close the hot stage cover and place under the microscope and select multiples of the microscope objective, focusing until the mesh structure is clearly visible. Then turn on the chiller and turn on the heating to photograph the screen at the set temperature.

## **3 Analysis of Experimental Processes and Results**

The experiment adopted 800 mesh 304 stainless steel wire mesh wick as the material, and it was fixed by three-layer rolling. The wick was cleaned in absolute ethanol and acetone successively using an ultrasonic cleaner. Samples of the cleaned wick was sent to the inside of the glove box through the glove box transition chamber. Removed the sodium from the kerosene in the glove box and cut off the surface oxide layer of sodium with a knife. Weigh 120 g of sodium on a balance and place in a stainless steel test tube. The balance indication was adjusted and zeroed, and the wick was weighed and fixed with a hook under the balance, resulting in an initial mass of 44.847 g. The tube clamping height was adjusted by the motor, and the initial liquid sodium infiltration depth was calculated to be about 1.2 cm. The experimental heating temperature program was set to rise first and then fall. When the water content and oxygen content in the gloves dropped below 0.5 ppm and 1 ppm, respectively, and the balance indication was no longer significantly changed, the well furnace was opened and the experiment began. The experimental results of the 800 mesh 3-layer wire mesh aspiration core are shown in Fig. 3.

As can be seen from the Fig. 3, the mass of the wick remains essentially unchanged when heated to 300 °C at the initial temperature. At 300 °C, the stepper motor is driven to move the wick sample downward so that it comes into contact with the liquid sodium, so there is a turning point of mass degradation at 300 °C. In the temperature range of 300–400 °C, the mass of the wick increases only slightly, and is accompanied by small mass fluctuations, and the analysis may be due to the combined effect of sodium flow and sodium evaporation. After the temperature reaches 400 °C, the mass of the wick as shown in Fig. 3 increases significantly and basically reaches the initial level. When

**Fig. 3.** 800 mesh wick experimental result diagram

heated from 400 °C to 450 °C, the mass of the wick changes are small and there are no significant mass fluctuations. When the liquid sodium temperature reaches 450 °C, the evaporation of metallic sodium is significantly enhanced, which directly leads to significant fluctuations in the quality of the wick in the range of temperature 450 °C to 650 °C. When heated to around 520 °C at 450 °C, the mass of the wick increases slightly. Bader [11] shows that the contact angle of sodium on the 304 stainless steel wire varies with temperature as shown in Fig. 4, which shows that sodium has a wetting transition point near about 400 °C. Therefore, the quality of the wick changes significantly at 400 °C in the experiment, because the contact angle of liquid sodium on the surface of stainless steel is suddenly reduced, so that the capillary ability of the wick is enhanced. The experimental results are basically consistent with the results of the contact angle change given in the literature. And after 500 °C, the liquid sodium and stainless steel have basically been completely wet, the mass change of the wick is not as obvious as when it is 400 °C, and the violent sodium evaporation phenomenon makes the quality of the wick fluctuate greatly.

However, during heating from 520 °C to 650 °C, the quality of the wick decreases slightly. However, in the cooling stage after 650 °C, due to the increase in surface tension of liquid sodium, the capillary effect is enhanced, the suction effect of the wick on sodium is enhanced, the quality of the wick continues to rise, and the quality of the wick reaches stability after the cooling reaches 400 °C. Figure 5 shows the results of the wick, which shows that the sample has been basically completely infiltrated at the end of the experiment, and the highest infiltration height of sodium measured with a ruler is about 15 cm, and the final wick weighing mass has reached 49.378 g.

**Fig. 4.** The contact angle between liquid sodium and stainless steel changes with temperature

**Fig. 5.** wire mesh wick sodium aspiration experimental result diagram.

The results of the wire mesh wick sodium liquid film observation experiment are shown in the following figure. Figure 6 shows the microstructure diagram of the wick in the initial state, and the surface of the wire mesh shows a silvery-white luster. At a heating temperature of 400 °C, the wire mesh surface loses its original luster, producing yellow and green corrosive products. One of the corrosion products contains a Cr2O3 oxide layer on the surface of stainless steel that reacts with sodium to form a NaCrO2 ternary oxide. At this time, a clear metallic luster appears inside the wire mesh, and liquid sodium begins to be gradually sucked onto the surface of the wire mesh wick Fig. 7.

When the heating temperature reaches 500 °C, liquid sodium is sucked onto the surface of the wire mesh due to capillary force, and the experimental results are shown in Fig. 8. When the heating temperature reaches 550 °C, the objective lens is contaminated

**Fig. 6.** Mesh structure diagram in the initial state

with sodium vapor due to the evaporation of sodium, resulting in a decrease in the brightness of the picture as shown in Fig. 9. At 600 °C, due to the evaporation of sodium, the reason for the reduction of the sodium film inside the wire mesh and the reason why the sodium vapor covers the lens cannot be observed significantly metallic. The observation experiment of sodium film spreading in the wire mesh is a good verification of the results of the increase of the capillary capacity of the 800 mesh wire mesh wick with the increase of temperature, and the increase of sodium suction of the wick leads to the increase of its own quality. During the experiment, a momentary temperature transition point was captured, it was about 410 °C. Since the argon gas flow has been passed through during the experimental process, the temperature on the surface of the wire mesh will be slightly lower than the temperature of the heating wire, so the temperature transition point should be before 410 °C.

**Fig. 7.** Spread of sodium film in the wick at 400 °C

**Fig. 8.** Spread of sodium film in the wick at 500 °C

**Fig. 9.** Spread of sodium film in the wick at 600 °C

## **4 Conclusion**

In the capillary ability experiment of the wick, when heated from 300 °C to 450 °C, the quality of the wick increased to a certain extent, and the increase of sodium vapor after 450 °C made the quality of the suction core fluctuate significantly. In the temperature range of 520–650 °C, the quality of the wick is slightly reduced. The magnitude of the fluctuations also increases as the temperature increases. And in the process of cooling down by 650 °C for the first time, with the increase of the surface tension of liquid sodium, the wick has a significant increase in mass. Before and after the experiment, the sodium infiltration height of the 800-mesh wick increased from 1.2 cm to 15 cm, and the mass increased from 44.847 g to 49.378 g. The observation experiment of the spread of sodium film in the wire mesh proved that when near 410 °C, there is a transition point of liquid sodium and stainless steel wetting, and the capillary ability increases more obviously, and more sodium is sucked on the suction core, which is mutually verified with a strong growth when the quality of the wick is about 400 °C in the capillary experiment. And at 500 °C, liquid sodium has good wetting properties on the surface of 1112 Y. Zhu et al.

stainless steel wire mesh, and liquid sodium has been better spread on the surface of the wire mesh wick.

**Acknowledgement.** The authors appreciate the support of National Natural Science Foundation of China (No.11905021), the Project of Science and Technology on Reactor System Design Technology Laboratory (Contract No. HT-KFKT-24–2021002), the Project of Nuclear Power Technology Innovation Center of Science Technology and Industry for National Defense(HDLCXZX-2021-ZH-036), and Operation Fundation of Key Laboratory of Nuclear Reactor System Design Technology of Nuclear Power Institute of China.

## **References**

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## **Analytical Method Research of Source Term for Steam Generator Tube Rupture Accident of Small Modular Reactor**

Ming-ming Xia(B) , Jun-long Wang, Jian-ping Zhu, Chao Tian, and Jia-jia Liu

Science and Technology on Reactor System Design Technology Laboratory, Nuclear Power Institute of China, Chengdu, Sicuan, China

<EMAIL_ADDRESS>
**Abstract.** Based on the full reference to the existing engineering practice and safety review experience, and considering the actual design characteristics of the small modular reactor ACP100, a set of source term analysis method suitable for ACP100 of the steam generator tube rupture (SGTR) accident is proposed, and the source term analysis and consequence evaluation of ACP100 SGTR accident was carried out using this method. The analysis shows that the radiological consequences of the accident source term calculated by this method meet the acceptance criteria of small modular reactor. The analysis results of this article can provide support for the follow-up review of accident source term of ACP100.

**Keywords:** Small modular reactor · SGTR · Source term analysis method

## **1 Introduction**

The steam generator tube rupture (SGTR) is one of the design basis accidents with high frequency and great impact during the life of the pressurized water reactor nuclear power plant, and it is also the focus of domestic nuclear safety supervision and review agencies. After SGTR, the water and steam in secondary coolant were radioactively polluted due to the release of primary coolant containing radionuclides to the secondary coolant through the break in the tube of steam generator. The radioactively polluted secondary coolant steam is released to the environment through the condenser extraction or the safety valve of the steam generator, resulting in radioactive contamination of the environment [1]. Therefore, it is great significance to carry out the SGTR source term analysis conservatively and reasonably.

This study fully investigates the SGTR source term analysis methods of M310 and Hualong 1 (ACP1000). By comparing the design differences of M310, ACP1000 and ACP100, according to the calculation assumptions and parameters of M310 and ACP1000, combined with the design characteristics of ACP100, proposed the SGTR source term analysis method of ACP100, and an ACP100 nuclear power unit SGTR source term analysis and radiological consequence evaluation are carried out using this method.

## **2 Calculation Assumptions and Parameters**

In this study, the calculation assumptions and parameters of M310, ACP1000 and ACP100 regarding the primary coolant activity and the iodine carryover coefficient in the steam generator were compared and analyzed.

## **2.1 Primary Coolant Activity**

In the accident condition, the primary coolant activity will have an activity peak phenomenon. At this time, the primary coolant activity is in a transient value, and transient assumptions is related with steady state value before the accident.

## **2.1.1 Primary Coolant Activity in Steady State**

SGTR source term analysis of M310, the primary coolant activity in steady state is normalized at 4.44 GBq/t in I-131 equivalent, it is the maximum value of 200 reactor-year operations in a French nuclear power plant [2]. This value is not conservative enough to be lower than the operating limit of primary coolant activity [3]. SGTR source term analysis of ACP1000, the primary coolant activity in steady state is normalized at 37 GBq/t DE I-131, it is assumed that the fuel element cladding failure rate is 0.25%. This value corresponds to the technical specification the maximum radioactivity limit condition is conservative enough [4]. Therefore, ACP100 refers to assumption of ACP1000, and the primary coolant activity in steady stat is assumed that the fuel element cladding failure rate is 0.25%, and the calculation results are normalized at 7.4 GBq/t DE I-131, as shown in Table 1.

## **2.2 Primary Coolant Activity in Transient State**

## **2.2.1 Primary Coolant Noble-Gas Activity in Transient State**

Primary coolant noble-gas activity in transient state of M310 and ACP1000 are the steady state value multiplied by the crest factor, the crest factor is taken from the operating experience of the French nuclear power station. The main factors affecting the crest factor are the reactor power and operating pressure. M310, ACP1000 and ACP100 have different reactor power, but the fuel assemblies used are of the same type, the mechanism of fission products released from damaged fuel rods to the primary coolant is the same, and the primary coolant system pressure is similar, so the primary coolant noble-gas activity in transient state calculation of ACP100 can use the same crest factor as that of M310 and ACP1000. The crest factor is shown in Table 1.

### **2.2.2 Primary Coolant Iodine Activity in Transient State**