Keywords

1 Introduction

China's Advanced Passive Water Reactor (PWR) is an advanced Generation III (G-III) reactor with passive safety features, developed through the introduction and absorption of AP1000 technology (Zheng et al. 2016) to meet the growing electricity demand and to take advantage of the economies of large reactors (Bodansky 2007). The AP1000 developed by Westinghouse is a passive safety pressurized water reactor (Schulz 2006). It is a G-III+ reactor (Saha et al. 2013) that received the design certification from the U.S. Nuclear Regulatory Commission in 2008 (Matzie 2008).

China's National Nuclear Safety Administration illustrated the study requirements for mass and energy release in the case of Design Basic Accident (such as Loss Of Coolant Accident (LOCA) or Main Steam Line Break (MSLB) accidents) in nuclear safety guideline HAD 102/06–2020, The Design of Reactor Containment and Related Systems for Nuclear Power Plant (NNSA 2020). When the MSLB accident happens, the break of the main steam pipe will cause a large amount of high-enthalpy flow to inject into the containment. This large mass and energy leakage would result in a significant increase of pressure in the containment. Then the Passive Core Cooling System (PCCS) works to remove the heat by natural circulation. In order to find the key parameters influencing the transient response of China's large advanced PWR containment and mass- and energy-release into the containment during an MSLB accident, the sensitivity analysis of the MSLB accident with a thermal-hydraulic model is necessary.

Several studies have been performed on uncertainty quantification and sensitivity analysis of the passive safety system of China's advanced PWR or MSLB accident in PWR with passive safety features. Yang Ye et al. performed the Best Estimate Plus Uncertainty (BEPU) analysis in a postulated 2-in. Small Break LOCA (Yang et al. 2020a). Deng Chengcheng et al. carried out best-estimate calculations using RELAP5/MOD3.4 code plus uncertainty quantification and sensitivity analysis of the Small Break LOCA transient for a scaled-down facility-the Advanced Core-cooling Mechanism Experiment (ACME) test facility (Deng et al. 2019). Chang Yuhao et al. performed a BEPU analysis of China's advanced large-scale PWR under the conditions of Large Break LOCA scenarios by employing the RELAP5 code (Chang et al. 2020). Sun Qiuteng et al. performed global sensitivity analysis of the MSLB accident in AP1000 by using sampling methods and surrogate models (Sun et al. 2021). Angelo Lo Nigro et al. performed MSLB coupled 3D NEU-TH sensitivity analysis of the AP1000 plant using RELAP5-3D (Lo Nigro et al. 2002). Yang Ye et al. performed a simulation and uncertainty analysis of MSLB accident on PUMA integral test facility (Yang et al. 2020b).

The sketch of China's Advanced PWR is shown in Fig. 1. In this study, best-estimate calculations using RELAP5 code plus uncertainty quantification and sensitivity analysis of the MSLB transient were carried out for China's Advanced PWR. The important thermal-hydraulic phenomena under MSLB transient were investigated by comparing calculations between China's Advanced PWR and AP1000. Thereafter, the uncertainty quantification process based on Code Scaling, Applicability and Uncertainty (CSAU) methodology was demonstrated, including the selection of input uncertain parameters, the application of Wilks’ statistic method and the uncertainty propagation using the SNAP interface. Lastly, the results of uncertainty quantification and sensitivity analysis were discussed.

Fig. 1.
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The Sketch of China's Advanced PWR (Shi et al. 2021)

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2 RELAP5 Nodalization

The RELAP5 input model for the selected reactor was established based on the technical information obtained from the open literature and design information (Yang et al. 2020a). The selected transient condition is the break of main steam line inside the containment vessel, and the main steam isolation valve is closed within 5s after the break open. In order to simulate the amount of mass and energy released from the break of the secondary loop to the containment, the containment node was set up in the RELAP5 model and connected with the upper cell of In-Containment Refueling Water Storage Tank (IRWST) to form the internal control volume of the containment.

As shown in Fig. 2, the model mainly focuses on the Reactor Coolant System (RCS), including a Reactor Pressure Vessel (RPV), 4 Cold Legs, 2 Hot Legs, 4 Coolant Pumps, 2 Direct Vessel Injection (DVI) pipes, 2 Steam Generators (SGs) and 1 Pressurizer (PZR). The passive safety system consists of 2 Accumulators (ACCs), 2 Core Makeup Tanks (CMTs), Passive Residue Heat Removal (PRHR) system, Automatic Depressurization System (ADS) and an IRWST. The RPV downcomer is composed of a pair of eight vertical channels, which is connected to 4 cold legs, 2 hot legs, and 2 DVI lines.

Fig. 2.
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RELAP5 Nodalization of MSLB in China’s Advanced PWR

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2.1 Steady-State Results

The MSLB accident is hypothetical, so its initial conditions are set to the normal steady-state operating conditions of the nuclear power plant. After the RELAP5 node modeling is completed, the steady-state calculation of the code is carried out firstly. According to the output file of the RELAP5 code, the model reaches steady-state at about 150 s. The steady-state results are shown in Table 1. Therefore, in the subsequent transient calculation, the steady-state operation phase of 300 s was first set before the opening of the break valve.

2.2 Transient Sequence and Results

The sequence of accidents in the hypothetical scenario is shown in Table 2. In the MSLB accident, there was no coolant leakage in the primary side, and the low setting value of RCS cold leg temperature (Tcl) is triggered to generate the “S” signal, then the reactor is shut down. Therefore, CMT is always in recirculation mode and does not switch to drainage mode. Therefore, ADS1–4 is not enabled. The total amount of mass and energy released depends on the water inventory of SG secondary side and the condensing tank storage of the start-up feed water system.

Table 1. Steady-State Simulation Confirmation (Zheng et al. 2016; Yang et al. 2020a)
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Table 2. Main safety system set points in accident analysis (Deng et al. 2019; Li et al. 2016)
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As shown in Fig. 3 and Fig. 4, compared with the MSLB accident of AP1000 (Westinghouse 2011) (partial data of 600 s after the accident began), APR1400 (Ekariansyah and Sunaryo, 2018), ATLAS (Ha et al. 2014), the PZR pressure (i.e., system pressure) was in good agreement with AP1000 during the blowdown phase. In the passive decay heat removal phase, the pressure of China's Advanced PWR decreases slowly but keeps a downward trend. The CMT maintains a recirculation mode, injecting cooling water into the core in natural circulation. At about 1700 s, the core pressure drops to the ACC injection pressure of 4.83 MPa, and the pressurized nitrogen in ACC injects coolant into the core passively (Fig. 6). Because there was steam loss on the secondary loop in MSLB accident, the RCS integrity was maintained during the accident. Hence, the RPV liquid level remains constant. CMT injection flow rate is lower, but the injection time is logically consistent (Fig. 5).

According to the accident logic, the primary side pressure did not drop to 0.5 MPa, so IRWST was not injected in the MSLB accident. The steel containment vessel has a design pressure of 0.443 MPa and a safety margin of 10%. As shown in Fig. 7, the pressure of the containment vessel rises rapidly when the break is opened in the process of a transient accident. Then the pressure decreases without overpressure due to the cooling of the containment vessel by the thermal components outside the containment vessel (imitating the passive containment cooling system and spray system).

The integral of mass and energy release integral is shown in Fig. 8. Later, as the auxiliary water supply system injected water into the damaged steam generator, steam was continuously released into the containment vessel through the break of main steam line, as shown in the break flow (Fig. 7).

Fig. 3.
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RCS Pressure

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Fig. 4.
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Pressurizer Pressure

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Fig. 5.
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CMT Injection Mass Flow Rate

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Fig. 6.
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ACC Injection Mass Flow Rate

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Fig. 7.
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Containment Pressure

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Fig. 8.
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Mass and Energy Release Amount

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3 Uncertainty and Sensitivity Analysis

Referring to AP600 and AP1000, the MSLB accident scenario is divided into five phases (see Fig. 9): Initial Depressurization, Passive Decay Heat Removal, CMT Draining to ADS Actuation, ADS Blowdown, and IRWST & Sump Injection phase (Wilson et al. 1997). However, in this simulation, only the MSLB accident was set, with no superimposed failure of other systems. Therefore, in the later transient process, it can be seen that there are only Initial Depressurization and Passive Decay Heat Removal phases.

The well-known Wilks’ formula for the one-side tolerance interval is expressed as follows (Wilks 1941):

$$\beta =1-{\gamma }^{N}$$
(1)

To achieve 95% tolerance with 95% confidence (95%/95%), 59 sets of input variables would be sampled according to the Wilks’ formula. The input sets were automatically generated by Design Analysis Kit for Optimization and Terascale Applications (DAKOTA) toolkit using simple random sampling (Adams et al. 2015).

Fig. 9.
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MSLB Transient Scenario (Wilson et al. 1997)

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3.1 Phenomena Identification and Ranking Tables

The initial decompression phase begins at the time of the pipe break and continues until the secondary side of the affected SG (i.e., the SG connected to the steam line of the break) is decompressed to the containment pressure. The reactor is shut down at this stage. The steam line is arranged, so the broken SG initially loss steam through a double-ended pipe break. However, a steam line isolation signal is generated relatively early in this phase to prevent the steam from losing from the turbine side. The behavior at this phase is mainly the discharge of the affected SG into the containment vessel, resulting in supercooling of the RCS due to heat discharge through the pipes of the affected steam generator. It is important to note that this process is asymmetric, with significant differences in heat load and fluid temperature between the affected and unaffected coolant cycles. The primary and secondary side heat transfer of SG plays a dominant role in RCS cooling and is therefore considered to be the primary parameter in this stage. Dominant processes are break flow, SG secondary behavior, RCS loop flow, and asymmetric loop cooldown (Table 3).

When the affected steam generator depresses to containment pressure, the passive residual heat removal phase begins and continues until the CMT recirculation stops (due to the presence of two-phase liquid in the CMT or its inlet line). This stage is characterized by primary path, CMT and PRHR flow driven by natural circulation. The temperature distribution of RCS is asymmetric. The RCS heat source is decay heat and reverses heat transfer generated by an unaffected steam generator. CMT recirculation and PRHR systems are heat traps for RCS. The RCS energy distribution determines the decay heat emission and is therefore considered the most important parameter. Processes important for accurate modeling of this phase are loop asymmetry effects, core heat transfer, SG heat transfer, PRHR heat transfer, and containment shell heat transfer.

3.2 Input Parameters Selection

According to the Phenomena Identification and Ranking Table investigation, the main input parameters related to containment pressure in the MSLB accident can be determined. Under ideal conditions, the distribution of uncertain input parameters is shown in Table 4. Due to the limitation of the RELAP5 model initial conditions, part of the temperature needs to be specified in the form of internal vapor and liquid energy. The final input parameters and their distribution are shown in Table 5.

Table 3. Ranking criteria for the MSLB
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Table 4. Input Parameters under Ideal Condition
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Table 5. Input Parameters with Uncertainty Distribution in RELAP5 Model
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3.3 Uncertainty Results

Figure 10 shows the uncertainty results of the containment pressure, which is also the figure of merit. The uncertainty of the outside temperature of PCCS heat structure directly causes different heat removal from the steel containment shell, which leads to the difference of the pressure and temperature inside the containment. Due to the changes in various input parameters (will be discussed in Sect. 3.4), the maximum containment pressure is 0.3362 MPa, which does not exceed the safety limit-0.443 MPa.

The variation of break mass and energy release is shown in Fig. 11. In the initial depressurization phase, the uncertainty of the break mass and energy release is mainly caused by the uncertainty of the break mass flow. In the passive decay heat removal phase, the uncertainty of the break mass flow, CMT heat removal capacity and PRHR heat removal contributes to the uncertainty of the break mass and energy release. Meanwhile, the maximum mass released to the containment vessel is 4.16 × 105 kg, and the maximum energy released to the containment vessel is 9.74 × 108 kJ.

These maximum values could be referred to new reactor containment design with proper scaling analysis.

3.4 Sensitivity Analysis

The importance of the input variables to the safety parameters can be quantified by the spearman rank correlation coefficient:

$$Spearman={r}_{s}=\frac{{\sum }_{i=1}^{n}\left[\left({R}_{i}-\frac{1}{n}{\sum }_{i=1}^{n}{R}_{i}\right)\left({Q}_{i}-\frac{1}{n}{\sum }_{i=1}^{n}{Q}_{i}\right)\right]}{\sqrt{{\sum }_{i=1}^{n}{\left({R}_{i}-\frac{1}{n}{\sum }_{i=1}^{n}{R}_{i}\right)}^{2}}\sqrt{{\sum }_{i=1}^{n}{\left({Q}_{i}-\frac{1}{n}{\sum }_{i=1}^{n}{Q}_{i}\right)}^{2}}}$$
(2)

The correlation coefficient ranges from −1 to + 1. Positive and negative signs indicate positive and negative correlations, and the magnitude of the value indicates the strength of the correlation. Figure 12 shows the spearman rank correlation coefficients. The statistical significance of parameters is taken into account when its absolute value is greater than 0.2.

Fig. 10.
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Uncertainty Results of Containment Pressure

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Fig. 11.
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Uncertainty Results of Break Mass and Energy Release

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Fig. 12.
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Sensitivity Analysis Results: 34 Input Parameters to Containment Pressure

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The main findings are given below:

  1. 1.

    Thermal Conductivity of PRHR Material: The thermal conductivity of PRHR material is negatively correlated with the containment pressure. With the thermal conductivity of PRHR material increasing, the heat is removed more, then the containment pressure decreases to a lower value. In the accident transient, the thermal conductivity of PRHR material determines the heat removed from the RCS.

  2. 2.

    PZR Liquid Internal Energy: The PZR liquid internal energy has a positive correlation with the containment pressure. With the PZR liquid internal energy increases, the more heat is removed, the higher the containment pressure would be. The PZR is connected to the RCS hot leg, and its temperature will affect the coolant temperature of the whole primary system. After the MSLB accident occurred, due to the instantaneous increase of the secondary side flow and the supercooling of the primary side, the low setting value of RCS cold leg temperature (Tcl) is triggered to generate “S” signal. When the primary coolant temperature increases, the “S” signal would be delayed, resulting in more core heat being released to the primary coolant, then to the heat sink (SG), and finally to the containment, resulting in increasing containment pressure.

  3. 3.

    Broken SG 2nd Side Temperature: The broken SG 2nd side temperature negatively correlates with the containment pressure. With the broken SG 2nd side temperature increases, the SG water is flashing earlier and remove RCS heat earlier, tripped the “S” signal earlier. Therefore, the core generates less decay power, and the containment pressure decreases.

4 Conclusions

The simulation and analyzation of China’s Advanced PWR MSLB accident were conducted by RELAP5 code. The uncertainty and sensitivity analysis were performed, and the spearman rank correlation coefficient evaluated the importance of each input parameter on the object safety parameter, i.e., the figure of merit.

By comparing the code simulation results and the available test results, it is observed that the code can reasonably predict the important thermal-hydraulic phenomenon for China’s Advanced PWR MSLB accident. The maximum containment pressure did not reach the design limit pressure during the overall uncertainty analysis. This indicates the passive safety system was put into operation by pre-set logic during the entire accident transient, ensuring effective heat removal from the core. The passive safety system can assure the safety of the core and containment in the MSLB accident.

According to the spearman rank correlation coefficient, the most influential variable for the maximum containment pressure is the RCS temperature. It means that the RCS temperature has an essential effect on the initial energy stored in RCS coolant. The uncertainty of parameters such as thermal conductivity of PRHR material and broken SG 2nd side temperature also significantly impact the maximum containment pressure.