NUREG/IA-0448 

International 

 Agreement Report

Uncertainty Analysis for Maanshan 

LBLOCA by TRACE and DAKOTA

 

Prepared by:

Jong-Rong Wang, Jung-Hua Yang*, Hao-Tzu Lin, Chunkuan Shih*

Institute of Nuclear Energy Research, Atomic Energy Council, R.O.C.

1000, Wenhua Rd., Chiaan Village, Lungtan, Taoyuan, 325, Taiwan

*Institute of Nuclear Engineering and Science, National Tsing Hua University

101 Section 2, Kuang Fu Rd., HsinChu, Taiwan

 

K. Tien, NRC Project Manager 

 

 

Division of Systems Analysis

Office of Nuclear Regulatory Research

U.S. Nuclear Regulatory Commission

Washington, DC 20555-0001

Manuscript Completed: May 2014

Date Published: July 2014

Prepared as part of 

The Agreement on Research Participation and Technical Exchange

Under the Thermal-Hydraulic Code Applications and Maintenance Program (CAMP)

Published by

U.S. Nuclear Regulatory Commission

NUREG/IA-0448 

International 

 Agreement Report

Uncertainty Analysis for Maanshan 

LBLOCA by TRACE and DAKOTA

 

Prepared by:

Jong-Rong Wang, Jung-Hua Yang*, Hao-Tzu Lin, Chunkuan Shih*

Institute of Nuclear Energy Research, Atomic Energy Council, R.O.C.

1000, Wenhua Rd., Chiaan Village, Lungtan, Taoyuan, 325, Taiwan

*Institute of Nuclear Engineering and Science, National Tsing Hua University

101 Section 2, Kuang Fu Rd., HsinChu, Taiwan

 

K. Tien, NRC Project Manager 

 

 

Division of Systems Analysis

Office of Nuclear Regulatory Research

U.S. Nuclear Regulatory Commission

Washington, DC 20555-0001

Manuscript Completed: May 2014

Date Published: July 2014

Prepared as part of 

The Agreement on Research Participation and Technical Exchange

Under the Thermal-Hydraulic Code Applications and Maintenance Program (CAMP)

Published by

U.S. Nuclear Regulatory Commission

iii 

ABSTRACT

This research is focused on the Large Break Loss of Coolant Accident (LBLOCA) analysis of the 

Maanshan power plant by TRACE-DAKOTA code. In the acceptance criteria for Loss of Coolant Accidents 

(LOCAs), there are two accepted analysis methods: conservative methodology and best estimate 

methodology. Compared with conservative methodology, the best estimate and realistic input data with 

uncertainties to quantify the limiting values i.e., Peak Cladding Temperature (PCT) for LOCAs analysis. 

By the conservative methodology, the PCTCM (PCT calculated by conservative methodology) of Maanshan 

power plant LBLOCA calculated is 1228.7K. On the other hand, there are five initial conditions taken into 

account in the uncertainty analysis in this study. In PCT95/95 (PCT of 95/95 confidence level and 

probability) calculation, the PCT95/95 is 1131.1K lower than the PCTCM (1228.7K). In addition, the partial 

rank correlation coefficients between input parameters and PCT indicate that accumulator temperature is 

the most sensitive parameter in this study. 
iv 
v 

FOREWORD

The USNRC (United States Nuclear Regulatory Commission) is developing an advanced thermal 

hydraulic code named TRACE for nuclear power plant safety analysis. The development of TRACE is 

based on TRAC, integrating RELAP5 and other programs. NRC has determined that in the future, TRACE 

will be the main code used in thermal hydraulic safety analysis, and no further development of other 

thermal hydraulic codes such as RELAP5 and TRAC will be continued. A graphic user interface program, 

SNAP (Symbolic Nuclear Analysis Program) which processes inputs and outputs for TRACE is also under 

development. One of the features of TRACE is its capacity to model the reactor vessel with 3-D geometry. 

It can support a more accurate and detailed safety analysis of nuclear power plants. TRACE has a greater 

simulation capability than the other old codes, especially for events like LOCA. 

Taiwan and the United States have signed an agreement on CAMP (Code Applications and Maintenance 

Program) which includes the development and maintenance of TRACE. INER (Institute of Nuclear Energy 

Research, Atomic Energy Council, R.O.C.) is the organization in Taiwan responsible for the application of 

TRACE in thermal hydraulic safety analysis, for recording user’s experiences of it, and providing 

suggestions for its development. To meet this responsibility, the TRACE model of Maanshan NPP has 

been built. In this report, the TRACE model of Maanshan NPP was used to evaluate the Maanshan 

LBLOCA transient. 
vi 
vii 

CONTENTS

Page

ABSTRACT ...................................................................................................................................... iii 

FOREWORD ..................................................................................................................................... v 

CONTENTS..................................................................................................................................... vii 

FIGURES ......................................................................................................................................... ix 

TABLES ........................................................................................................................................... xi 

EXECUTIVE SUMMARY ................................................................................................................. xiii 

ABBREVIATIONS............................................................................................................................ xv

1. INTRODUCTION ...................................................................................................................... 1-1 

2. METHODOLOGY .................................................................................................................... 2-1 

3. MODEL AND ASSUMPTIONS ................................................................................................. 3-1 

3.1 Maanshan TRACE Model ............................................................................................... 3-1 

3.2 LBLOCA Assumptions .................................................................................................... 3-1 

4. RESULTS................................................................................................................................ 4-1 

4.1 Conservative Evaluation................................................................................................. 4-1 

4.2 Best Estimate ................................................................................................................ 4-9 

5. CONCLUSIONS ...................................................................................................................... 5-1 

6. REFERENCES ........................................................................................................................ 6-1 

 
viii 

 

 
ix 

FIGURES

Page 

Figure 1 The procedure of uncertainty analysis ........................................................................ 2-3

Figure 2 PCT distribution and confidence interval .................................................................... 2-4

Figure 3 The LBLOCA TRACE model of Maanshan NPP.......................................................... 3-3

Figure 4 Uncertainty configuration interface ............................................................................. 3-4

Figure 5 The results of power between TRACE and FSAR ....................................................... 4-3

Figure 6 The results of vessel pressure between TRACE and FSAR........................................ 4-4 

Figure 7 The results of break mass flow rate between TRACE and FSAR................................ 4-5

Figure 8 The results of accumulator mass flow rate between TRACE and FSAR .................... 4-6

Figure 9 The results of core inlet flow between TRACE and FSAR .......................................... 4-7

Figure 10 The results of core outlet flow between TRACE and FSAR ........................................ 4-8

Figure 11 The user-defined numeric variables in SNAP ............................................................ 4-11

Figure 12 The PCTs during LBLOCA (included PCTCM and PCTBE)........................................... 4-12

Figure 13 The influences of input parameter for PCT ............................................................... 4-13

Figure 14 The partial rank correlations between input parameters and PCT............................. 4-14

 
x 

 

 
xi 

TABLES 

Page

Table 1 The assumptions of initial input Parameters .................................................................. 3-5

Table 2 The comparison of the steady state data ....................................................................... 4-2 

Table 3 The LBLOCA sequences of TRACE and FSAR.............................................................. 4-2

Table 4 The initial conditions for the uncertainty analysis ........................................................ 4-10 
xii 

 
xiii 

EXECUTIVE SUMMARY

An agreement in 2004 which includes the development and maintenance of TRACE has been signed 

between Taiwan and USA on CAMP. INER is the organization in Taiwan responsible for applying TRACE 

to thermal hydraulic safety analysis in order to provide user s’ experiences and development suggestions. 

To fulfill this responsibility, the TRACE model of Maanshan Nuclear Power Plant (NPP) is developed by 

INER. 

According to the user manual, TRACE is the product of a long term effort to combine the capabilities of the 

NRC’s four main systems codes (TRAC-P, TRAC-B, RELAP5 and RAMONA) into one modernized 

computational tool.NRC has ensured that TRACE will be the main code used in thermal hydraulic safety 

analysis in the future without further development of other thermal hydraulic codes, such as RELAP5 and 

TRAC. Besides, the 3-D geometry model of reactor vessel, which is one of the representative features of 

TRACE, can support a more accurate and detailed safety analysis of NPPs. On the whole TRACE 

provides greater simulation capability than the previous codes, especially for events like LOCA.

Maanshan NPP operated by Taiwan Power Company (TPC) is the only Westinghouse-PWR in Taiwan. 

The rated core thermal power is 2775 MW. The reactor coolant system has three loops, each of which 

includes a reactor coolant pump and a steam generator. The pressurizer is connected to the hot-leg piping 

in loop 2. The main components of LBLOCA model include the pressure vessel, pressurizer, steam 

generators, steam piping in the secondary side (including four sets of steam dump and vent valves), 

steam dump system, accumulators, and safety injection of emergency core cooling system (ECCS). The 

pressure vessel is divided into 12 levels in the axial direction, two rings in the radial direction (internal and 

external rings) and six equal azimuthally sectors in the “θ” direction. The control rod conduit connects the 

12th and 7th layers of the vessel from end to end. The fuel region is between the third and sixth layers, 

and heat conductors are added onto these structures to simulate the reactor core. 

There are two tasks in this study, conservative evaluate and best estimate plus uncertainty for Maanshan 

LBLOCA analysis. The analysis results of conservative methodology are verified against the Final Safety 

Analysis Report (FSAR). For a LOCA analysis, the important parameters are peak cladding temperature 

(PCT). By coupling with DAKOTA, the input parameters with uncertainties of Maanshan model were 

generated randomly based on specified PDFs. Because the required minimum number of TRACE runs is 

dependent of the values of confidence level and probability, Wilks’ formula was employed to determinate 

the minimum number of runs. Since the value of PCT is the safety criterion to ensure the integrity of fuel 

assemblies for LOCAs, the minimum number of 59 was used to generate the maximum bound of PCT 
xiv 

which achieve 95/95 criterion. 

In the conservative evaluation, analytical results indicate that the Maanshan TRACE model predicts the 

behavior of important plant parameters in consistent trends with the FSAR data and the PCTCM of 

Maanshan LBLOCA calculated is 1228.7K. On the other hand, the maximum value of PCT is 1158.4 K 

from the 59 trials of best estimate plus uncertainty. In PCT of 95/95 confidence level and probability 

calculation, the mean value (PCTmean) and standard deviation () of the 59 trial are 1022.8 K and 65.8 

K respectively. The PCT95/95 is 1131.1K lower than the PCTCM and limited valve (1477K). Compared to 

conservative methodology, the best estimate plus uncertainty provides a greater safety margin for the PCT 

evaluation. 

In addition, correlations between input parameters and PCTs are calculated for sensitivity study and 

ranking to investigate what input parameters dominate the contribution of uncertain distribution of PCT. 

The partial rank correlation between input parameters and PCT indicates that accumulator temperature is 

the most sensitive parameter. 

 
xv 

ABBREVIATIONS

BAF Bottom of the Active Fuel 

CAMP Code Applications and Maintenance Program 

DBA Design Basis Accidents 

ECCS Emergency Core Cooling System 

FSAR Final Safety Analysis Report 

HHSI High Head Safety Injection 

INER Institute of Nuclear Energy Research Atomic Energy Council, R.O.C. 

LBLOCA Large Break Loss of Coolant Accident 

LHSI Low Head Safety Injection 

LOCA Loss of Coolant Accident 

NPP Nuclear Power Plant 

NRC Nuclear Regulatory Commission 

PCT Peak Cladding Temperature 

PDF Probability Distribution Functions 

PWR Pressurized Water Reactor 

RCP Reactor Coolant Pumps 

RCS Reactor Coolant System 

SI Safety Injection 

SNAP Symbolic Nuclear Analysis Package 

TAF Top of the Active Fuel 

TPC Taiwan Power Company 

TRACE TRAC/RELAP Advanced Computational Engine 

US United States 

 
xvi 

 

 
1-1 

1. INTRODUCTION

The Loss of Coolant Accident (LOCA) is one of the most important Design Basis Accidents (DBA). In light 

water reactors, the severity of a LOCA will limit how high the reactor power can operate. Recently, the 

trend of nuclear reactor safety analysis reveals an increasing interest to substitute best estimate for 

conservative methodologies which may apply conservative codes or the combination of best-estimate 

codes and conservative initial and boundary conditions to achieve the safety margins and regulate the 

licensing and operations of nuclear reactors [1]. Compared with conservative methodologies, the 

methodologies of best estimate plus uncertainty adopt best estimate codes and realistic input data with 

uncertainties to quantify the limiting values i.e., PCT for LOCAs. The methodologies of best estimate are 

divided into two approaches which evaluate the problems based on either propagation of input 

uncertainties or extrapolation of output uncertainties. For the propagation of input uncertainties, the 

uncertainty effects are involved by identifying the uncertain input parameters with specified Probability 

Distribution Functions (PDFs) followed by sample runs. For the extrapolation of output uncertainties, 

uncertainty is determined by the comparison between numerical results and experimental data. The 

uncertainty attributes have been divided for convenience into different categories: (1) initial conditions 

uncertainty, (2) power distribution uncertainty, (3) global model uncertainty, and (4) local model 

uncertainty. This study is focused on the initial conditions uncertainty analysis, which includes the RCS 

conditions and ECCS fluid conditions (i.e., pressurizer pressure, RCS average temperature, safety 

injection temperature, accumulator volume, accumulator water temperature, and accumulator pressure). 

 
1-2 

 
2-1 

2. METHODOLOGY 

There are two tasks in this study, conservative evaluate and best estimate plus uncertainty for Maanshan 

LBLOCA analysis. The analysis results of conservative methodology are verified against the Final Safety 

Analysis Report (FSAR). For a LOCA analysis, the important parameters are peak cladding temperature 

(PCT). As defined by the 10CFR50.46 regulation, the PCT does not exceed 1477.6K (2200). The 

detail criteria for the LOCA analysis are described in Appendix K of 10CFR50, as follows: 

A. The calculated peak fuel element clad temperature is below the requirement of 2200. 

B. The amount of fuel element cladding that reacts chemically with water or steam does not exceed 

1% of the total amount of Zircaloy in the reactor. 

C. The clad temperature transient is terminated at a time when the core geometry is still amenable 

to cooling. The localized cladding oxidation limits of 17% are not exceeded during or after 

quenching. 

D. The core remains amenable to cooling during and after the break. 

E. The core temperature is reduced and decay heat is removed for an extended period of time, as 

required by the long-lived radioactivity remaining in the core. 

Figure 1 shows the best estimate plus uncertainty methodology of LBLOCA in this study. By coupling with 

DAKOTA, the input parameters with uncertainties of Maanshan model were generated randomly based on 

specified PDFs. Because the required minimum number of TRACE runs is dependent of the values of 

confidence level and probability, Wilks’ formula [2] was employed to determinate the minimum number of 

runs. The correlations between number of code runs, confidence level, and probability of Wilks’ formula 

are defined: 

1െα୬ ൒ β Eg. 1 

where  is probability,  is the confidence level, and n denotes the number of code runs. 

Since the value of PCT is the safety criterion to ensure the integrity of fuel assemblies for LOCAs, the 

minimum number of 59 was used to generate the maximum bound of PCT which achieve 95/95 

criterion. 

Assuming the PDF of PCT is a normal distribution, this research used the mean value and standard 

deviation of the 59 trial to calculate the PCT which cover 95 % area of the PCT distribution (Fig. 2), 

which is calculated by Eq. 2. 
2-2 

PCTଽହ/ଽହ ൌ PCT୫ୣୟ୬ ൅ 1.645σ Eq. 2 

where PCTmean is the mean value of PCT,  is the standard deviation of PCT. 

All TRACE runs were defined and executed through SNAP job streams [3-4], and TRACE calculation 

results were read by AptPlot script. The data interactions and communications between TRACE and 

DAKOTA [5-6] were controlled by SNAP. Finally, correlations between input parameters and PCTs are 

calculated for sensitivity study and ranking to investigate what input parameters dominate the contribution 

of uncertain distribution of PCT. 

 
2-3 

Figure 1 The procedure of uncertainty analysis 
2-4 

Figure 2 PCT distribution and confidence interval 
3-1 

3. MODEL AND ASSUMPTIONS 

3.1 Maanshan TRACE Model 

Figure 3 shows the TRACE model of Maanshan NPP. The rated core thermal power is 2775 MW. It is a 

three-loop model, and each loop has a feedwater control system. The main structure of this model 

includes the pressure vessel, pressurizer, steam generators, steam piping at the secondary side, the 

accumulators, and safety injection of ECCS. The pressure vessels are cylindrical, and are divided into 12 

levels in the axial direction, two rings in the radial direction (internal and external rings) and six equal 

azimuthally sectors in the “” direction. The control rod conduit connects the 12th and 7th layers of the 

vessel. The fuel region is between the third and sixth layers, and heat conductors are added onto these 

structures to simulate the reactor core. In this LOCA study, a LBLOCA is defined as a rupture in cold-leg 

with a total cross sectional area. The break was located in loop 1, which is one of the two loops that don’t 

have a pressurizer. In addition, this TRACE model uses the “point kinetic” method to calculate the core 

power. The decay heat power model is based on the 1973 ANS proposed Standard. 

In best estimate plus uncertainty analysis, the setting of input uncertainties and the execution of 

uncertainty analysis was performed via SNAP. The built-in graphical user interface of uncertainty 

configuration shown in Figure 4 provides several tabs to define the number of samples, variables, and 

PDFs. The version of code in this study is TRACE V5.0p3 under SNAP V2.2.1. 

3.2 LBLOCA Assumptions

In LBLOCA analysis, it usually adopts conservative assumptions or limited value for initial conditions and 

boundary conditions. By the conservative assumptions, it must be assumed that the reactor has been 

operating continuously at a power level at least 1.02 times the licensed power level. Table 1 shows the 

assumptions of initial input parameters in this study. It’s assumed the pipe break occurred in RCS at 0s. 

Since the loss of off-site power is assumed, the Reactor Coolant Pumps (RCPs) trip at the inception of 

the accident. After break occurred, the reactor trip signal subsequently occurs when the pressurizer low 

pressure trip setpoint is reached. Also, low pressure caused the ECCS injecting water to RCS cold-leg 

and preventing excessive clad temperatures. A safety injection signal is generated when the appropriate 

setpoint is reached (1715 psia) and delay time is 27 sec. As single failure assumed, there are only one 

Low Pressure Head Injection (LHSI) pump and one High Head Safety Injection (HHSI) pump operate in 

this LBLOCA analysis. When the RCS pressure decreased below 615 psia, accumulator injection started. 

Cold water in the accumulator was expelled into the reactor coolant system by nitrogen gas. Continued 
3-2 

operation of the ECCS pumps supplies water during long term cooling, the core temperatures have been 

reduced and prevent the fuel cladding damage. 

 
3-3 

Figure 3 The LBLOCA TRACE model of Maanshan NPP 

 
3-4 

Figure 4 Uncertainty configuration interface 

 
3-5 

Table 1 The assumptions of initial input Parameters 

Input Parameters Value 

Licensed Core Power 102% of 2275MWt 

Thermal Design Flow ( kg/s/loop) 4331.8 

Vessel Average Temperature (K) 584.5 

Initial RCS Pressure (MPa) 15.858 

Low Pressurizer Pressure Reactor Trip 

Setpoint (MPa) 

12.824 

Low Pressurizer Pressure SI Setpoint (MPa) 11.824 

Safety Injection Initiation Delay time with loss 

of offsite power(sec) 

27 

Accumlator Water Volume (m3

/tank) 27.89 

Accumlator Tank Volume (m3/tank) 41.06 

Minimum Accumlator Gas Pressure (MPa) 4.42 

Accumlator Water Temperature (K) 310.9 

Nominal RWST Water Temperature (K) 302.6 
3-6 

 
4-1 

4. RESULTS

4.1 Conservative Evaluation 

In TRACE, steady-state initialization was performed. The parameters’ results such as the power, the 

pressure of the pressurizer, the Tavg temperature, and the RCS flow rate are compared with FSAR data. 

Table 2 shows the comparison between the steady-state results of the TRACE and FSAR. The results are 

clearly mutually quite consistent. Following the steady-state initialization, the LBLOCA transient predicted 

results are compared with the FSAR data. Table 3 presents the sequence of LBLOCA and the timings of 

the LBLOCA predicted by TRACE. The sequence of TRACE arose from the actuation of the related control 

system, which in turn had to be actuated by physical parameter signals. If the parameters predicted by 

TRACE differ from the FSAR data, then the event sequences will also be difference. Such deviations can 

be observed in the comparisons of transient event analyses. 

Figure 5 plots the power curve that calculated from TRACE in the case of LBLOCA, and then compares 

with the FSAR data. In TRACE, the core power can be calculated using the built-in point kinetics model, 

and the power calculated includes decay heat. It displays that the power curve of TRACE is almost the 

same as those of FSAR data. Figure 6 compares the pressures of the vessel and suggests that the 

pressure calculated by TRACE approximately follows the trend of the FSAR data. Figure 7 compares the 

break mass flow rate of cold-leg pipe. It reveals that break mass flow rate predicted by TRACE agrees 

closely with the results of the FSAR data. Figure 8 shows the comparisons of accumulator mass flow rate 

of intact loops between TRACE model and FSAR data. Figure 9 compares the core inlet flow rate, 

revealing that the flow rate calculated by TRACE is in agreement with the FSAR data except for the period 

between 6 and 18 sec. It reveals that the flow rate calculated by TRACE is slightly lower between 6 and 

18 sec. Figure 10 plots the results for core outlet flow rate. The difference results of core outlet flow before 

6 sec are consideration of the nature flow in TRACE. Analytical results indicate that the Maanshan 

TRACE model predicts the behaviors of important plant parameters in consistent trends with the FSAR 

data. The PCTCM of TRACE calculated by conservative method was 1228.7K (1752). 

 
4-2 

Table 2 The comparison of the steady state data 

Parameter FSAR TRACE Error (%) 

Power (MWt) 

Tavg * (K) 

Pressurizer pressure (MPa) 

Loop Flow (kg/sec) 

2830 

584.5 

15.858 

4331.8

2830 

584.53 

15.859 

4347 

0 

0.0001 

0.0001 

0.0035 

*Tavg = (Hot-leg temperature +Cold-leg temperature)/2 

Table 3 The LBLOCA sequences of TRACE and FSAR 

LBLOCA FSAR (sec) TRACE (sec) 

Break began 

Reactor scram setpoint reached 

SI signal generated 

Accumulators Injection 

Start of Pumped SI 

Accumulators empty 

0.0 

0.50 

1.4 

15.0 

28.4 

52.1 

0.0 

0.50 

1.5 

14.2 

28.5 

59.5 

 
4-3 

0 5 10 15 20 25 30 35

Time (sec)

0

0.2

0.4

0.6

0.8

1

1.2

Power (nomalized)

FSAR

TRACE

Figure 5 The results of power between TRACE and FSAR 
4-4 

0 5 10 15 20 25 30 35

Time (sec)

0

4

8

12

16

20

Pressure (MPa)

FSAR

TRACE

Figure 6 The results of vessel pressure between TRACE and FSAR 
4-5 

0 5 10 15 20 25 30 35

Time (sec)

0

10000

20000

30000

Flow rate (kg/sec)

FSAR

TRACE

Figure 7 The results of break mass flow rate between TRACE and FSAR 
4-6 

0 5 10 15 20 25 30 35

Time (sec)

0

500

1000

1500

2000

2500

Flow rate (kg/sec)

FSAR

TRACE

Figure 8 The results of accumulator mass flow rate between TRACE and FSAR 
4-7 

0 5 10 15 20 25 30 35

Time (sec)

-8000

-4000

0

4000

8000

12000

16000

Flow rate (kg/sec)

FSAR

TRACE

Figure 9 The results of core inlet flow between TRACE and FSAR 
4-8 

0 5 10 15 20 25 30 35

Time (sec)

-4000

0

4000

8000

12000

16000

Flow rate (kg/sec)

FSAR

TRACE

Figure 10 The results of core outlet flow between TRACE and FSAR 
4-9 

4.2 Best Estimate

In best estimate plus uncertainty of LBLOCA analysis, several plant parameters were considered in the 

uncertainty quantified. These include RCS conditions and ECCS fluid conditions. Table 4 lists the 5 

parameters (i.e., pressurizer pressure, safety injection temperature, accumulator volume, accumulator 

water temperature, and accumulator pressure) taken into account in this uncertainty analysis, which are 

defined as the SNAP user-defined numeric variables (see Figure 11 ) and linked with uncertainty 

configuration to generate TRACE input files. In particular, the statistical theory predicts that 59 

calculations are required to simultaneously bind the 95th percentile of one parameters (PCT) with a 

95-percent confidence level. Figure 12 shows the PCTs calculated by conservative methodology and best 

estimate methodology during LBLOCA. By the conservative methodology, the PCTCM of Maanshan power 

plant LBLOCA calculated is 1228.7K. On the other hand, the maximum value of PCT is 1158.4 K from the 

59 trials of best estimate. In PCT of 95/95 confidence level and probability calculation, the mean value 

(PCTmean) and standard deviation () of the 59 trial are 1022.8 K and 65.8 K respectively. From the Eq. 

2, the PCT95/95 is 1131.1K lower than the PCTCM and limited valve (1477K). Compared to conservative 

methodology, the best estimate provides a greater safety margin for the PCT evaluation. 

In addition, correlations between input parameters and PCTs are calculated for sensitivity study and 

ranking to investigate what input parameters dominate the contribution of uncertain distribution of PCT. 

The DAKOTA toolkit was applied for the sampling of input parameters and the calculation of correlations 

and ranking of input parameters. The coefficients are obtained by Pearson’s correlation shown in Eq. 3. 

r ൌ ∑ ሺ୶౟ି୶തሻሺ୷౟ି୷ഥሻ ౤

౟సభ

ට∑ ሺ୶౟ି୶തሻమ ∑ ሺ୷౟ି୷ഥሻ ౤ మ ౟సభ ౤

౟సభ

 Eq. 3 

where r is the Pearson’s correlation coefficient, n is the number of samples, and x and y denote two 

quantities. 

The influence and partial rank correlation between input parameters and PCT are shown in Figure 13-14, 

and the results indicate that accumulator temperature is the most sensitive parameter. 

 
4-10 

Table 4 The initial conditions for the uncertainty analysis 

Input parameters Nominal 

values 

Uncertainty 

range 

PDFs 

Pressurizer pressure 15.513 (MPa) [-3.45, +3.45] 

Uniform 

distribution 

Accumulator pressure 4.482 (MPa) [-1.25, +1.25] 

Accumulator volume 28.32 (m3

) [-0.43, +0.43] 

Accumulator temperature 

Safety injection temperature 

311 (K) 

303(K) 

[0, +27.78] 

[-20, +19.45] 

Note: normal distributions are sampled over ±4σ

 
4-11 

Figure 11 The user-defined numeric variables in SNAP 
4-12 

Figure 12 The PCTs during LBLOCA (included PCTCM and PCTBE) 
4-13 

Figure 13 The influences of input parameter for PCT 
4-14 

Figure 14 The partial rank correlations between input parameters and PCT

‐0.15

‐0.1

‐0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

ACC  temperature ACC  pressure ACC  volume PZR  pressure SI  temperature
5-1 

5. CONCLUSIONS

In this study, the LBLOCA analysis results of conservative methodology are verified against the FSAR 

data. The analysis results indicate the Maanshan TRACE model could predict the behaviors of important 

plant parameters (i.e., power, break flow rate, vessel pressure, accumulate flow rate, core inlet flow rate, 

and core outlet flow rate) in consistent trends with the Maashan FSAR data. 

In best estimate plus uncertainty of LBLOCA analysis, five plant parameters were considered in the 

uncertainty quantified and taken into account in this uncertainty analysis. Since the value of PCT is the 

safety criterion to ensure the integrity of fuel assemblies for LOCAs, the minimum number of 59 was used 

to generate the maximum bound of PCT95/95 which achieve 95/95 criterion. The PCTs by conservative 

method and best estimate plus uncertainty calculation are 1228.7 K (PCTCM) and 1131.1 K (PCT95/95) 

respectively. The mean value and standard deviation of the 59 trial by TRACE-DAKOTA are 1022.8 K 

(PCTmean) and 65.8 K () respectively, and the maximum value of PCT is 1158.4 K. Compared to 

conservative methodology, the best estimate plus uncertainty provides a greater safety margin for the PCT 

evaluation. In addition, the partial rank correlation coefficients between input parameters and PCT indicate 

that accumulator temperature is the most sensitive parameter in this study. 

 
5-2 
6-1 

6. REFERENCES

1. Jaeger, W., et al., “On the uncertainty and sensitivity analysis of experiments with 

supercritical water with TRACE and SUSA,” ICONE-18, Xi’an, China, May 17-21, 2010, 

paper ID: 29044 

2. Wilks, S. S., “Statistical prediction with special reference to the problem of tolerance limits,” 

Annals of Mathematical Statistics, Vol. 13, 400, 1942. 

3. US Nuclear Regulatory Commission (USNRC), TRACE V5.0 User Manual, 2007. 

4. APT, 2007. Symbolic Nuclear Analysis Package (SNAP). User’s Manual. Report, Applied 

Programming Technology (APT), Inc. 

5. Gingrich, C. “Recent developments in SNAP and SNAP uncertainty analysis capabilities,” 

presentation slides, CAMP 2011 spring meeting, Bariloche, Argentina, 2011 

6. Jaeger, W., et al., “Uncertainty and sensitivity study with TRACE-DAKOTA and 

TRACE-SUSA: a comparison based on NUPEC BFBT experimental data,” presentation 

slides, CAMP 2012 spring meeting, Ljubljana, Slovenia, May 30-June 1, 2012. 




UNITED STATES

NUCLEAR REGULATORY COMMISSION

WASHINGTON, DC 20555-0001

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NUREG/IA-0448 Uncertainty Analysis for Maanshan LBLOCA by TRACE and DAKOTA