Training Material for IAEA Advanced Reactor Simulation

PCTRAN

Personal Computer Transient Analyzer

For a Two-loop PWR

And

TRIGA Reactor

For

International Atomic Energy Commission

Workshop on

Nuclear Power Plant Simulator for Education

Politecnico di Milano, Minano, Italy

03-14 October, 2011

By

Dr. Li-Chi Cliff Po

Micro-Simulation Technology

10 Navajo Court

Montville, New Jersey 07045

U.S.A.

Tel 973-263-7327

http://www.microsimtech.com

[email protected]

http://www.microsimtech.com/

ii

Abstract

IAEA has contracted Micro-Simulation Technology since 1996 to prepare a series

of PC-based nuclear power plant simulation software to start its annual

workshop. The original software has been upgraded over the time. This year

(2011) the two-loop PWR model is upgraded to include severe accident features

of core-melt and containment failure. Radiological release source term is

generated for offsite dose projection and consequence study.

The workshop also indicates its interest in experimental pool reactor. Hereby we

present a TRIGA-like model using six delayed neutron groups and eleven decay

gammas in point kinetics equation. Basic concepts of neutron multiplication,

criticality, rod control, feedback and poisoning are introduced. This provides

fundamental understanding of all nuclear reactors.

The work is based on Special Service Agreement BC: Req. 4111, PO 201102741

Personnel No. 080628, dated 15 August 2011.

iii

Overview

The International Atomic Energy Agency (IAEA) is assisting developing countries, by the use of

reactor simulation, to get experience in the operation of nuclear power plants. The principal

objective is to make a "desk top" simulator and a training material available to all Member

States, to assist in their comprehension and training programs for nuclear power. This project

will provide insights and understanding of the designs as well as a clear understanding of the

operational characteristics of the various reactor types. It requires an emphasis on the basic

principles of the operation of each reactor type.

PCTRAN is a reactor transient and accident simulation software program that operates on a

personal computer. Since its first release in 1985, Micro-Simulation Technology has been

constantly upgrading its performance and expanding its capabilities. Numerous versions and

plant models have been installed in countries around the world.

Advancement in modern 32-bit microprocessors and the windows-based graphic user interface

(GUI) has completely revolutionized the simulation technology. It is now possible to automate

the preparation work and actual exercise on a desktop computer. Since 1998, the source code of

PCTRAN has been converted into Microsoft Visual Basic 6.0. Operation of the GUI adheres

strictly to the specifications of the Microsoft Windows environment. Data input/output are in

MS Office’s Access database format. Reports and data can be transferred conveniently through

all Windows-based software products over the entire exercise network.

The plant model in this manual is a generic two-loop PWR with inverted U-bend steam

generators and dry containment system. It could be a Westinghouse, Framatome or KWU design

with thermal output in the neighborhood of 1800 MWt (600 MWe). One loop with the

pressurizer is modeled separately from the other loop. There are a number of PWR plants in the

world belong to this category, e.g. Point Beach, Kewaunee, Prairie Island and Ginna in the US,

Mihama 1 in Japan, Krsko in Slovenia, Angra 1 in Brazil and ChinShan 2 in China.

In this manual the first chapter describes major PWR plant systems simulated by PCTRAN. The

second chapter includes instructions for operating the Windows version. There is an on-line

“Help” button in the menu bar that provides instant instructions. Verification runs are presented

in Chapter 3 for all plant events in a typical PWR Final Safety Analysis Report. Theory and

mathematical models are provided in Chapter 4. The radiological release methods and results

are presented in Chapter 5.

The other subject commissioned by IAEA is introduction of experimental pool reactor. There

are over 200 in the world and over 60 of them belong to General Atomic Company’s TRIGA

reactors. For many member states this type is the only reactor in their country and sole facility

for training, isotope production and research in general. A simulation tool should be useful in

showing concepts such as neutron multiplication, rod control to criticality, feedback, decay heat,

poisoning, etc. TRIGA simulator will be presented in this workshop and documented in

Appendix 1.

iv

Table of Contents

Overview

Part 1 Two-loop PWR

1.0 PWR Plant Systems

1.1 Reactor Power Control

1.3 Pressurizer Water Level Control

1.4 Steam Generator Control

1.5 Reactor Protection System

1.6 Emergency Core Cooling Systems

1.7 Containment System

2.0 PCTRAN 2-loopWindows Operation

2.1 General Description

2.2 Installation

2.3 Help File

2.4 System Operation

2.5 Input Files and Parameters

2.6 Initial Condition Files

2.7 Changing Malfunction Status

2.8 Component Operation

2.9 PostPlot Utility

3.0 PWR Benchmark Analysis

3.1 Normal Operation

3.1.1 Power Reduction to 40%

3.1.2 Normal Reactor Trip

3.2 Transient and Accident Analyses

3.2.1 Uncontrolled Rod Bank Withdrawal

3.2.2 Hot Full Power Rod Drop

3.2.3 Moderator Dilution

3.2.4 Startup of an Inactive RCP

3.2.5 Reduction in Feedwater Enthalpy

3.2.6 Excessive Load Increase

3.2.7 Loss of Reactor Coolant Flow

3.2.8 Turbine Trip

3.2.9 Loss of Normal Feedwater

v

3.2.10 Steam Generator Tube Rupture

3.2.11 Small Break LOCA

3.2.12 Large Break LOCA

3.3 Severe Accidents

3.3.1 TMI-2 Event

3.3.2 Large Break without ECCS

3.3.3 Station Blackout

4.0 Theory and Mathematical Models

4.1 Reactor Core Kinetics

4.2 Reactor Coolant System

4.3 Steam Generator

4.4 Fuel Temperature and Degraded Core


4.6 Containment

5.0 Radiation Monitoring System and Source Term Model

References

Part II Experimental Pool Reactor

1

1.0 PWR Plant Systems

In a PWR's primary coolant system, boiling is suppressed and steam is generated via steam

generators in the secondary coolant loops. A pressurizer is used to maintain the primary coolant

in sub-cooled condition and the pressure close to a constant. Reactor coolant pumps are used to

circulate the primary coolant through steam generators; at which steam is generated at the

secondary side to drive the turbine. The major plant systems are described in this section.

1.1 Reactor Power Control

PWR has sophisticated automatic control systems. The control rod system and soluble boron

control the core neutron flux. The Chemical and Volume Control System (CVCS) control the

primary coolant inventory and water chemistry. On the secondary side, steam output is

controlled by the turbine control valve and steam dump system. The steam generator water level

is controlled by the feedwater system. During the automatic control mode, they work in a

synchronized way so that transition to stabilized conditions will be achieved smoothly.

1.2 Pressurizer Pressure Control

All PWRs are designed to operate close to a constant pressure in the neighborhood of 15 MPa

during power operation. The error between the system pressure and set point goes through a

controller circuit. When the error is too high, the spray is turned on. If the pressure increases

further during a transient, there is relief valves and safety valves set to open to relieve the

pressure. If the pressure decreases and a negative pressure error exists, the proportional heater

turns on and increases linearly to its maximum power. If the discrepancy develops further, the

backup heater turns on. Detail of the heater functions is design specific. The PCTRAN/U model

is generic and thus it is intended for basic principle instruction only.

1.3 Pressurizer Water Level Control

The charging (also called makeup) pump using an error of pressurizer level to the level setpoint

controls pressurizer water level. Depending upon a reactor's design, the level set point may be a

constant or programmed as a function of the unit power. Letdown is turned on when the

pressurizer level exceeds the setpoint. The charging and letdown system also controls the reactor

coolant's chemical composition. Therefore, it is also called the Chemical and Volume Control

System (CVCS). When the pressurizer level is too low, the letdown is isolated and the heaters

are turned off.

1.4 Steam Generator Control

1.4.1 Steam Header Pressure Control

The steam header pressure is controlled at a set pressure by the turbine control (throttle) valve. It

may either be a constant or programmed as a function of the unit power depending upon the

reactor's design. The Steam Dump System controls the turbine bypass valves' opening. At a

2

higher pressure, there are atmospheric dumps and safety valves set to relieve over-pressure in the

steam lines.

Figure 1.1 PCTRAN/U 6.0.1 Windows Mimic

1.4.2 Steam Generator Water Level and Feedwater Control

During normal operation, feedwater pumps provide water to the steam generators. The

feedwater control valve is regulated by the sum of two errors: steam generator water level

relative to the level set point, and feedwater to steam flow mismatch. Through a proportional-

plus-integral controller, the valve regulates the feedwater flow until any transition is stabilized

and the errors diminish.

When the main feedwater pumps are not in service, there are typically turbine and/or motor-

driven auxiliary feedwater pumps. The operators will start them on a low water-level signal or

manually.

3

1.5 Reactor Protection System

Whenever the reactor's operating parameters exceed certain defined safety limits; all control rods

are dropped by gravity into the core to suppress the chain reactor. The following trip functions

are typical for a PWR:

- High reactor pressure and/or pressurizer water level

- High neutron flux

- Over-temperature delta-T

- Over-power delta-T

- High RC outlet temperature

- Low reactor pressure and/or pressurizer water level

- Low SG water level

- Low loop or core flow

- Containment pressure

The over-temperature and over-power delta-T trips are temperature differences between the

reactor coolant inlet and outlet for core DNBR protection.

Liquid boron injection is used to provide negative reactivity if all rod insertion functions fail.


PWR is equipped with redundant trains of ECCS for core heat removal during emergency. They

are generally composed of:

1.6.1 High Pressure Safety Injection (HPSI) System

Consisting of redundant trains of centrifugal pumps that run on emergency diesel power and

operable on high (reactor operating) pressure. It is started on a low reactor pressure and/or low

pressurizer level signal, or high containment pressure signal. The objective is to make up

coolant loss on a small break LOCA beyond the regular makeup (charging) system's capability.

1.6.2 Accumulators (ACC)

Tanks are filled with borate water and pressurized nitrogen. For a LOCA not recoverable by the

HPSI, valves connecting the ACC and the reactor coolant system are opened at about 40 bar (4

MPa). They will be closed when the two side's pressures are equalized so that nitrogen is

prevented from entering the RCS.

1.6.3 Low Pressure Safety Injection (LPSI) System

It consists of redundant trains of centrifugal pumps to be started on Safety Feature Actuation

System (SFAS) signals. Their shutoff head (around 10 - 15 bar) is considerably lower than the

HPSI's. But its flow rate is much greater. It has the capacity to completely refill the reactor

4

vessel following a major LOCA to the point of break. LPSI normally takes its suction from the

Borate Water Storage Tank (BWST). When the water is about exhausted, the operator will

switch the suction from the building sump and run through heat exchangers before injecting back

to the reactor. Note that for some plants the same pumps used for LPSI are used for decay heat

removal during the cooldown period after a normal shutdown. The piping lineup and heat

exchangers belong to the Decay Heat or Residual Heat Removal (RHR) system and thus not part

of the ECCS.

1.7 Containment System

To prevent over-pressure in the containment following a LOCA, PWR is equipped with a

containment spray system and emergency fan coolers. Suction of the spray pumps is from the

Borate Water Storage Tank (BWST). It can also be switched to recirculation mode when water

supply is exhausted. Heat exchangers are then used to remove the heat content inside the

containment to outside ambiance.

Containment is designed to about 4 bar above the atmospheric pressure with a leakage rate in the

order of 1% per day at the design pressure.

5

Figure 1-2 Pressurizer Pressure and Level Control

Σ

PRESSURIZER PRESSURE AND LEVEL CONTROL

PRESSURIZERPRESSURE

1K22 ( 1+ )

T23*S

Σ 1K21 ( 1+ )

T21*S

1

015%

1

0

Σ

T avg

LEVEL PZR %

ERRORLEVEL

K22 = 7% / % LEVELT23 = 720 SEC

POSITION CONTROL

VALVE CHARGING

LETDOWN ISOLATION

PRESSURIZERPRESSUREREFEREMCE

157,2 kg/cm2

K21 = 1Ps / PaT21 = 180 SEC

BACKUPHEATERS(1023 kW)

POWER HEATERS

CONTROL HEATERS

( 377 kW )

SPRAY CONTROL

( 44.2 kg/sec )

POWER RELIEF VALVE 1

( 26.5 kg/sec )

POWER RELIEF VALVE 2

( 26.5 kg/sec )

SAFETY VALVES

( 3 × 47.9 kg/sec )

60%25 ℃

291.7 309.2

15%

1

05%

-0.115×106Pa

-0.17

1

0

-0.104×106Pa

1

0-0.103

0.17 0.515×106Pa

1

0

0.692 ×106Pa

1

0

16.11×106Pa

16.01

17.138 ×106Pa

1

0

-

+

+

+

+

-

6

Figure 1-3 Turbine and Steam Dump Control

309.2

291.7

1 + T12*S

1 + T13*S

Σ

Σ

Σ40%

0

40%

0

1 )

T*S　K( 1 + 　　　

TURBINE AND STEAM DUMP CONTROL

TURBINE LOAD

TURBINE TRIP (0 = NO TRIP, 1 = TRIP )

TEMPERATURE PROGRAM

Tref -

TURBINE VALVE POSITION

+

+

-

Tavg

T12 = 10 SECT13 = 5 SEC

STEAMDUMP

VALVES

SET PRESSURE

T no load

T11 = 30 SECK = 100% / 4.25 kg/cm2

STEAM PRESSURE +RELIEF VALVE OPEN

SAFETY VALVES OPEN

0 100%

℃

2.78

℃

9.12

℃

17.4

8.598

106Pa

9.935

-

7

Figure 1-4 Rod Control

ROD CONTROL

NUCLEAR POWER

-

Σ

℃

309.2

291.7100%

1%

0.17 ℃/%0.83 ℃/%

ΣTref

0

-1%

2

1

0 50 100%

0.55 1.7

72

8 ℃

0.83 2.8

INTEGRAL

INTEGRALREACTIVITYRODS TABLE

T11*S

1 + T11*S

1

1 + T2*S

1

1 + T5*S

1 + T3*S

1 + T4*S

TURBINE LOAD

T avg

+ERRORPOWER

NON LINEAR GAIN

T11 = 40 SEC

TEMPERATURE PROGRAM

T2 = 30 SEC

+

-

-

T3 = 50 SECT4 = 10.1 SEC

T5 = 1 SEC

VARIABLEGAIN

RODS SPEED PROGRAM

ROD POSTION

ROD REACTIVITY

8

Figure 1-5 Main and Auxiliary Feedwater Control

MAIN AND AUXILIARYFEEDWATER CONTROL

50%

0% 100%

1

1 + T30*SΣ

79%

1

1 + T32*S

1 K30(1 )

T31*S

FEEDWATER FLOW

STREAM FLOW

TURBINE LOAD

SG LEVEL PROGRAM

CONSTANT50%

+

-

T30 = 5 sec

Σ

LOW T AVG

( 1/3 LOW LEVEL SG )

( 2 PUMPS )

( 2/3 LOW LEVEL SG )

1 K31(1 )

T33*S

LEVEL SG ( narow range)

SAFETY INJECTION

REACTION TRIP

T avg

MAIN FEEDWATER TRIP

BLACKOUT SIGNAL

FEEDWATER

VALVE POSITION

K31 = 5.0%　VALVE flow/%T33 = 2000 sec

-+

+

FEEDWATER PUMPS TRIP

K30 = 3% full flow/%T31 = 1600 sec

FEEDWATER PUMPS ISOLATION

TURBINE TRIP

MOTOR AUXILIARYFEEDWATER PUMPS

START

TURBINE DRIVENAUXILIARY

FEEDWATER PUMPSTART

295 ℃

10%

10%

Z10Z11

9

2.0 PCTRAN 2-loop PWR Windows Operation

2.1 General Description

The Windows version is a state of the art product taking full advantage of 32-bit PC technology.

The source code is completely re-written using Microsoft Visual Basic 6.0. Operation follows

the Microsoft Windows XP or later operating system’s environment strictly. Data input/out are

in Microsoft Office 2000 or higher Access database files. Reports can be generated by the

program and later accessed by Access.

Since PCTRAN/U 6.0.1 Windows version has used the Super-VGA 1024x768 resolution, to get

the full screen you need to set the monitor resolution to that specification. It can be done by

going to “My computer”, “control panel”, “Display” and “settings” to reset the resolution.

Once initiating by typical Windows Run command or clicking at the PCTRAN icon, the program

banner will appear in front of the mimic. Click the maximize symbol to get the full screen. In

the menu bar, you can click on the “runner” icon to start the run. An alternative way is to click

on the atomic model icon on the lower middle tool bar. The run-speed is immediately to its right

and you can click it for 2, 4, 8 or 16 times fast time. Typically for Windows products, there are

more than one ways to get the same thing done. For transient plotting, you can click the upper

tool bar’s “View” or lower tool bar’s “Plot” to get transient variable plots and pressure/

temperature (P/T) plots. The scale of x-y axes, legend of the curves, and plot titles can all is

changed. All plots can either be printed by a printer or saved as files for later process. Similarly

the output data can be printed as Access reports or saved in database files. Five Access database

files are required: ListData, BackData, OptData, PlotData and DoseData. They are described

bellow:

ListData.mdb is the input file. It contains the following tables:

BasicData Basic plant data

ICControlsData Status of the control buttons of all initial conditions (IC)

ICFanData Status of the fans

ICFanMalfData Status of malfunctions of the fans

ICHXData Status of the heat exchangers

ICHXMalfData Status of the heat exchangers’ malfunction

ICMalfData Status of system malfunctions

ICMalfDataTemp Temporary file for malfunctions

ICPumpData Status of pumps

ICPumpMalfData Status of pump malfunctions

ICThermoData Thermal-hydraulic Initial Conditions

ICTripData Trip status

ICValveData Status of valves

ICValveMalfData Status of valve malfunctions

ListIC List of initial conditions

ListMalf List of malfunctions

10

RadData Radiation parameters

BackData.mdb contains all backtrack conditions for every TimeBackOut interval. It has every

table as the ListData.mdb except BasicData, RadData and ICMalfDataTemp, because they are

not needed. It is only used during a run when back-track may be requested. Its contents will be

erased at completion of a run.

OptData.mdb contains the following tables

PCTRAN Options Everything is pretty straightforward. A few important parameters are:

TimePlotOut = Output time record interval (in seconds) for PlotData recording. A small value

(cannot be smaller than the calculation time step of course) gets better output

resolution, but may results in a huge PlotData file for a long run. A large value

gets coarse resolution but smaller file size. TimePlotOut can be changed

online by going to “Code Control” and “Options”.

TimeBackOut = Time interval for writing a backtrack record. It can also be changed online.

TimeDoseOut = Time interval (in seconds) for writing a DoseData record. This cannot be

edited online. User must edit the database prior to running the code.

The other tables such as Print Format, Print Location and Scaling Method are described in the

table. User needs not to change their contents. In addition, options of x-y coordinates’ maximum

and minimum, scroll time, format of graphic file, time step for calculation and print record, span

of flux/flow map are all saved in the OptData database.

PlotData.mdb stores all the calculated variables. It contains two tables:

ListPlotVariables= List all variable names and their units for plotting. Users should

never change them.

PlotData = Actual data

At end of every run, users will be asked whether the data will be saved. If you want to save the

file, you could choose to save in either Excel or Access format. If Access is chosen, it can be re-

plotted by using the PostPlot.exe utility that coming with PCTRAN. Its function is very similar

to online plotting, but has more features to choose from. Please refer to the section of post-

plotting for complete instructions.

Since PCTRAN/U 6.0 is a Windows product, everything Windows supports will be supported by

PCTRAN. Therefore the printer will not be limited to any specific ones.

11

Figure 2.1 PCTRAN/U 6.0.1 Radiation Monitoring System and Source Term Mimic

12

2.2 Installation

Installation & Quick Run (updated 1/2010)

1) Your computer has to be running the Microsoft Windows XP, Vista or System 7 operating

system. You must have System Administrator's right to register PCTRAN custom-controls

into the Windows System directory.

2) The MS Office 2000 or higher applications Access and Excel must be installed in your

computer.

3) Your monitor should be set to a resolution of SVGA. If not, the full PCTRAN mimic will

not be displayed properly. To reset the monitor, you can go to “My Computer”, “Control

Panel”, “Display”, “Settings” and choose “1024 x 768” for the Desktop Area and a Font Size

of “Normal”.

4) In your CDROM or download zip file, choose the one closest to your plant or interest and

extract its contents to your computer. Then run Setup.exe. The screen display will prompt

you for the succeeding steps. Your computer’s operating system may have Windows dll’s

newer than that to be installed. Click “Yes” to keep your own.

5) You should see “Installation is succeeded”. Sometimes a message “Control olch2x7.ocx does

not register properly” shows up. It is harmless just click “Ignore” and you will get the

success message. Do not abort the installation.

6) The default directory is C:\Program Files\Pctran. You can change it to any location of your

choice. The executable program PCTRAN will be displayed in the Start Menu. You can

make a short cut or copy it to your desktop.

7) After starting PCTRAN, the MST banner will be flashed for a few seconds followed by the

PCTRAN Nuclear Steam Supply System (NSSS) of the plant mimic. There might be prompts

of “There is unsaved plot (or dose) data. Do you want to save it?” Just answer No. You are

ready to run PCTRAN.

8) Click at the Maximize icon in the upper right corner of the Window to get full-screen

display. Then click at the “Code Control” and "Run" button or the "runner" icon to start a

run.

9) Default run is in real-time, i.e. the same speed as the transient time. You can click on the

number 1 right next to the atom icon in the lower status bar to get fast time. Maximum speed

is 16 times faster than real-time.

10) To get a complete tutorial, we suggest you to click on the “Help” button in the menu bar. A

complete sequence of instructions will be displayed by clicking by the >> key.

11) For malfunctions, go to "Code Control" and "Malfunctions". For any of your chosen

malfunction, enter a non-zero fraction, check "Activate" and close the window. After the

NSSS mimic reappears, click at "Run" again to see the effect of the malfunction.

12) The demo kit is full-capability, i.e. it has all the features and capability of the full-functioning

package. The only limit is its runtime is a few hundred seconds.

13) At end of a run, you can either exit or respond “No” and go to the upper left “Restart” button

and choose another IC (initial condition) from the window:

13

2.3 Help File

Software in Windows is usually equipped with a “Help” feature that provides on-line

instructions. They are organized in hyper-linked pages. Keep pressing the >> button, the

complete instructions for Windows operation is provided.

2.4 System Operation

Operation of all PCTRAN/U systems is based on the same user-friendly concept using point-

and-click mouse control in pull-down menus. Shown in the figure is the mimic of the PWR

model for a two-loop PWR of 1800 MWt. Its net electric output is about 600 MW. A single

loop designated as "A" is at the left side and the other loop is designated as "B" at the right side.

The display also represents the controllable system as small panels with the important equipment

shown as icons (i.e., pumps, valves, and heat exchangers). Selection of the panels and

equipment displayed in the mimic is consistent with the description of plant systems in Section

2.1. The real control room of a nuclear power plant has hundreds if not thousands of instruments

and controls: gauges, displays, strip charts, knobs, switches, dials, push buttons, etc. They are

reduced to absolute minimum in order to fit into a PC's screen. On the other hand, the basic

principle and characteristics of the simulated advance reactor will still be demonstrated by the

selected mimic display. This requires balance in choice, use of common sense and always user-

friendliness in consideration.

For a major system's control where complicated automatic operation logic is involved, e.g., rod

assemblies, pressurizer level and pressure, and steam generator level and pressure, operation is

defaulted to the automatic mode. Anytime if the operator decides to take one of the control

systems into manual operation, just clicks at the corresponding "M" button and a window will

show up. By entering a new set point, activating the manual action and closing the window, the

reactor will then run on the manual mode. These panels are located at the right hand of the

mimic. If you need to change the set point again, click the “A” button and “M” button again to

open the window.

Important components such as the Power-Operated-Relief-Valves (PORV) and safety valves of

the pressurizer and the steam lines, pressurizer spray valve and heaters, Main Steam Isolation

Valves (MSIVs), Turbine Bypass (Steam Dump) Valves, feedwater valves, Reactor Coolant

Pumps, etc. are displayed locally. Their status is indicated by color and can be overridden by the

operator.

Control rod position and motion is displayed by motion of simulated control rods. Pipe breaks

are shown dynamically by flashing sprays at the break location with the leakage flow digitally

displayed.

The system controls for normal operation is:

14

2.4.1 Reactor Control

Pwr Dmd = Power demand (%)

Rate = Ramp rate (%/min)

2.4.2 Steam Generator Control

Turb P = Turbine header pressure (bar)

Tavg = RC Tavg control (C)

SG Lvl = SG narrow range (%)

There are turbine-driven and electric-driven auxiliary feedwater pumps. They will be started on

a low water level signal in the steam generators.

2.4.3 Pressurizer Control

Lvl = Pressurizer water level (%)

Press = RC pressure control (by heaters and spray)

To return to Auto mode, click at "A". The set point field shown in the window will not be used

for auto mode, just activate and close the window it will return to auto operation. The charging

pump and letdown valve is used for actual control of the level. Their status is displayed in the

upper right panel. The operator can override it by using the right mouse button.

2.4.4 RPS and ECCS Manual Control

At the bottom of the mimic, status of the Reactor Protection System (RPS) and Safety Feature

Actuation System (SFAS) is displayed. Reactor will be tripped automatically upon conditions

exceeding any of the RPS set points. The corresponding symbol will turn into red. For example,

if the reactor pressure is below the setpoint for low-pressure trip, 127 bar, the symbol RC P Lo

and the reactor trip button RX T will turn into red. It is followed by all control rods insertion.

The turbine stop valve will be closed and the turbine's color will turn from pink to blue.

Other trips in the panel include:

High reactor pressure (RX P Hi) at 167 bar

Low steam generator level (SGL Lo) at 28%

High steam generator turbine trip (SGL Hi) at 82%

Anticipatory reactor trip at turbine trip (Tb Ant)

The SFAS signal starts HPSI and LPSI. The panel includes the following signals:

- High Reactor Building Pressure (RBP Hi) at 2.6 bar

- (RBP HH was not used for this model)

- Low-low Reactor Pressure (Rx P LL) at 123 bar

15

- (Rx Lo for simultaneous pressurizer low level not used in this model)

The reactor/turbine can also be tripped manually by moving the mouse and clicking at the button.

On the left-hand side, panels for the HPI, ACC and LPI are displayed. Operators can override

the automatic initiations of any ECCS pumps and take manual control.

- HPI and CVCS

Two of the four HPI pumps will start on the SFAS signal, the other two are spares. The

positive displacement pump and the letdown valve are part of the CVCS and controlled by

the pressurizer level control logic.

- Accumulators

Two valves connecting to the accumulators will be opened at RC pressure below 48 bar.

They will be closed when the liquid is exhausted.

- LPI/RHR

Two of the LPI pumps will be started on SFAS signal also, but no flow will be injected

into the RCS until the pressure is below the pump shutoff head at 11.4 bar. A large flow

will be shown and the water level in the Borate Water Storage Tank will start to decrease.

When it is about to be empty, the operator should re-align the suction from the building

sump by clicking at the "Smp" button. Then water will be routed through the heat

exchanger and a heat removal rate will be shown. The same pumps are used for shutdown

cooling by the Residual Heat Removal (RHR) system during normal cooldown. This can

be conducted by clicking at the "SDC" button.

- RB Spray

Reactor Building Spray is started on RB high pressure at 2.6 bar.

- RB Vent

The normal Reactor Building Vent will be closed on SFAS signal for containment isolation

- Fan Coolers

Fan Coolers are started on high RB pressure also. The containment air is routed through

heat exchangers and cooled by external service water to remove the containment heat.

- P/T Saturation Diagram

As a result of the TMI-2 accident, PWR control rooms have been equipped with RC

16

pressure to temperature P/T diagram showing the subcooling margin. Two dots in red and

green in the diagram represent the two hot legs’ pressure and temperature. Their

horizontal distances to the saturation curve show the subcooling margin.

17

2.5 Input Files and Parameters

In this section the PWR PCTRAN model input data are described in detail. Following are

instructions for construction of the basic plant data deck. The user may be required to refer to

Section 5 Mathematical Models for an explanation of some of the input parameters. The input file is

named ListData.mdb. In that there is a BasicData table. It contains the basic plant geometric,

physics, trip set point and other characteristic data. The reactor rated power, reactor coolant pump

heat, decay heat after shutdown, and stored heat from steel piping and uranium oxide are considered.

The pressurizer has heaters, spray, PORV, and safety valves for pressure control. Normal makeup

(charging) and high-pressure injection (safety injection) are available for inventory control. In

addition, the ECCS includes accumulators (Core Flood Tanks) and Low-Pressure Injection. The

steam generator secondary side is normally fed by main feedwater and controlled at a certain level

and pressure. After reactor scram the main feedwater may be lost and the emergency feedwater can

be initiated and controlled at another level while the turbine bypass and atmospheric dump valves

control the steam pressure at staggered set points. In addition, steam safety valves relieve pressure at

even higher set points.

2.5.1 Basic Plant Data

An “Edit” button appears in the main NSSS mimic tool bar for on-line editing of the input data.

Users can edit the BasicData, initial condition ICThermoData and radiation RadData.

Alternatively they can be edited directly by Access. Click the save button to save the changed

entry into the dataset. Click “Save Data Description” then a text file will be saved for printing.

It is very useful for documentation and report. The following is the Basic Data table:

Database: C:\IAEA_2011\PWR_IAEA\ListData.mdb

Table: BasicData

SET: 1

Description: PWR 2-Loop IAEA

POWER 1800 Rated Thermal Power (MW)

P0 155 RCS initial pressure (Bar)

T0 301 RCS initial average temperature (°C)

WRC0 30530 Total core flow rate (t/hr)

TCST 15 RCP coastdown time (sec)

RCP 10 Total RCP heat input (MWt)

APORV 11.8 Area of PORV (cm2) per valve

ASAFT 23 Area of pressurizer safeties (cm2) valves combined

PORV1 165.2 PORV open setpoint (bar)

PORV2 163.2 PORV reseat setpoint (bar)

SAFT1 176 Safety valve open setpoint (bar)

SAFT2 175 Safety valve reseat setpoint (bar)

PHIGH 165.7 High pressure reactor scram setpoint (bar)

TEFW0 60 EFW initiation delay time (sec) after initiation signal (sec)

AL0 0.565 Initial pressurizer level (fraction of full)

PHPI 129.69 HPI auto start setpoint (bar)

PSCRAM 132.2 Low pressure reactor scram setpoint (bar)

TEMP 25 HPI and EFW temperature (°C)

18

PADV 81.8 SG relief valves (atmospheric dump valve) opening pressure

(bar)

ADV 261.09 SG relief valves total capacity( t/hr)

WLD0 13.7 Letdown flow for Chemical & Volume Control System (CVCC)

during normal operation (t/hr)

CHG 30 Charging flow (t/hr)

TRIN 5 Rod insertion minimum time (sec)

TROT 2 Rod withdrawal minimum time (sec)

AKRD 1.333 Reactivity worth of one rod ($)

AKCHG -10 Accumulator/RWST boron activity (pcm/ppm)

GFW 0.5 Feedwater controller constant, a dimensionless number

VSG 565 total SG volume (M3)

TBV 0.4 total TBV flow capacity in fraction of full power steam

HMFW 950 feedwater enthalpy at full power (kJ/kg)

TRXT 99999 reactor trip delay time after turbine trip (sec)

TER1 9.18 maximum Tavg error for steam dump control (°C)

EFW 120 EFW capacity (t/hr) for turbine driven pump

VPRZ 35 pressurizer volume (M3)

VRCS 180 total RCS volume excluding pressurizer (M3)

MSG0 80000 total SG water inventory including steam mass (kg)

TSG0 280 no-load steam generator temperature or RC Tavg (°C)

SSMS 170 reactor vessel stainless steel mass (ton)

UO2MS 56 fuel UO2 mass (ton)

WTR0 114.5 SG tube rupture flow per tube break (t/hr)

PCFT 43 pressure set point for core flood tank initiation (bar)

CFT 60 CFT tank (accumulator) total water capacity (M3)

WCF0 35.3 nominal CFT flow rate at initiation (t/hr)

PLPI 11.36 LPI system initiation pressure (bar)

TAVGL 281 Low Tavg set point for SG isolation (°C)

ULSG 8.535 height of SG U-tubes (M)

HRLV 0.17 pressurizer low level set point for heater shutoff

SPRY 20 PRZ spray flow capacity (t/hr)

PSP1 0.6 PRZ spray initiation error (bar)

PSP2 5 PRZ spray maximum error (bar)

HTR1 270 PRZ proportional heater capacity (KW)

PHTR1 0 proportional heater initiation error ( bar)

PHTR2 -1.1 proportional heater error for full capacity (bar)

PHTRB -1.5 set point for pressure error to turn on backup heater capacity

(bar)

VTAF 90 RCS volume to top of active fuel (M3)

ATAF 7 RCS or core cross section area at top of fuel (M2)

LSG0 11.83 SG wide range level at full power (M)

PSG100 55 Steam generator pressure at 100% power (bar)

HTRB 662 backup heater capacity (KW)

LPSG 2 Number of steam generator loops

GSTM 2 turbine control valve and bypass valve gain constant

TER2 2.78 deadband for Tavg steam dump control for load rejection (°C)

SGHH 82 high-high SG level for turbine trip (%)

ASG1 2.254 SG lower section cross section area (M2)

RLSG 5.1 range for SG narrow range level instrument (M)

SGLL 17 low SG narrow range scram set point (%)

CFTN2 28.227 total nitrogen volume in Core Flood Tanks or accumulators (M3)

PH(1) 0 The head curve for SI pump pressures 1st data point (bar)

PH(2) 34 The head curve for SI pump pressures 2nd data point (bar)

PH(3) 83 The head curve for SI pump pressures 3rd data point (bar)

PH(4) 125 The head curve for SI pump pressures 4th data point (bar)




WH(1) 50 The head curve for SI pump flow 1st data point (t/hr)

WH(2) 45 The head curve for SI pump flow 2nd data point (t/hr)

19

WH(3) 40 The head curve for SI pump flow 3rd data point (t/hr)

WH(4) 35 The head curve for SI pump flow 4th data point (t/hr)




PL(1) 0 The head curve for RHR pump pressures 1st data point (bar)

PL(2) 7 The head curve for RHR pump pressures 2nd data point (bar)

PL(3) 8 The head curve for RHR pump pressures 3rd data point (bar)

PL(4) 8.5 The head curve for RHR pump pressures 4th data point (bar)

PL(5) 8.8 The head curve for RHR pump pressures 5th data point (bar)

PL(6) 9 The head curve for RHR pump pressures 6th data point (bar)

PL(7) 155 The head curve for RHR pump pressures 7th data point (bar)

WL(1) 600 The head curve for RHR pump flow 1st data point (t/hr)

WL(2) 550 The head curve for RHR pump flow 2nd data point (t/hr)

WL(3) 500 The head curve for RHR pump flow 3rd data point (t/hr)

WL(4) 400 The head curve for RHR pump flow 4th data point (t/hr)




PCSP 1.3 containment spray initiation pressure (bar)

GCSP 640 containment spray capacity (t/hr)

USTC 0.01 core uncovery steam cooling effectiveness as fraction of water

cooling

TF0 788.9 average fuel temperature at full power (°C)

PDSN 3.089 containment design pressure (bar)

WSV 2240 main steam safety valve total capacity (t/hr)

PSV 85 main steam safety valve opening press (bar)

TRB0 50 initial containment temperature (°C)

PRB0 1.034 initial containment pressure (bar)

LWRB0 2.8 initial sump water level (M)

ARB 420 sump or containment cross section area (M2)

VRB 40000 containment volume (M3)

PFCL 9.99 High containment pressure set point to start fan cooler (bar)

QCSP0 10 Emergency SI heat exchanger rated capacity (MW)

QCL0 28 Fan cooler capacity (MW)

TDSN 128 containment design temperature (°C)

CRTM 10 containment heat sink concrete mass (ton)

STLM 5 containment heat sink steel mass (ton)

RLK0 0.1 containment leak rate (%/day) at design pressure

PCRT 6.895 RC pressure for break flow changed to non-critical (bar)

RDSP 0.001 Rod speed constant, dimensionless number

QRHR0 10 RHR heat exchanger rate (MW)

TANK0 2600 RWST initial water volume M3

TKMIN 400 RWST water volume to switch to sump M3

PRBH 1.3 High RB press for SI initiation (bar)

LPZL 0.15 Simultaneous low PRZR level with RC press for SI initiation

PSGL 38 Low SG press for SI initiation (bar)

PHPL 128 Simultaneous low RC press with PZR level for SI initiation

(bar)

HCOR 3.67 Fuel length (M)

AFUT 4500 Total core heat transfer area M2

MZRKT 3500 Total mass of fuel channel (Zr) Kg

MZRST 18000 Total mass of fuel cladding (Zr) Kg

MCRT 16214 Total mass of control rods Kg

MVES 3800 Mass of vessel bottom

CNH2B 5 Concentration of H2 in ctmt to start burn (%)

FH2O 0.0533 Fraction of H2O in concrete

FCO2 0.1939 Fraction of CO2 in concrete

FDEC 0.1 Fraction of decomposed concrete gas reacts with corium

WVNT0 10 Containment vent flow at 1 psid (kg/s)

PPMEC 2000 ACC & RWST boron concentration (ppm)

20

2.6 Initial Condition Files

The input parameters in the initial condition (IC) data are in table ICThermoData of Access database

ListData.mdb. The parameters are described as follows:

IC No. 1 for End of Cycle is listed below:

Database: C:\IAEA_2009\PWR2009a\ListData.mdb

Table: ICThermoData

IC: 1

Description: 100% POWER EOC

DT 0.5 Time step size for run (sec)

TINT 0 (run initiation time (sec))

PF 1 Power factor as fraction of rated

ANS 1 Decay heat level as multiplier to American Nuclear

Standard 5.1 decay heat table.

POWR 1 Unit load demand (ULD) set point as fraction of full

power

PWR0 1 Power set point as fraction of full power

TRCPA 99999 Time for left side reactor coolant pump trip (sec)

TRCPB 99999 Time for right side reactor coolant pump trip (sec)

TRKT 99999 (Time to start power ramp (sec))

TRKF 99999 (Time for power ramp is ended (sec))

TTDAFW 999999 (Time for the turbine driven AFW pump to start (sec))

TMDAFW 999999 (Time for the motor driven AFW pump to start (sec))

TCSP 99999 Containment spray initiation time (sec)

TSCRAM 99999 Time for reactor scram (sec)

TFCL 99999 Containment fan cooler initiation time (sec)

TLPI 99999 Low pressure injection initiation time (sec)

TCFT 99999 Core flood tank (accumulator) initiation time (sec)

THPI 99999 High Pressure injection initiation time (sec)

HIFX 1.18 High neutron flux reactor scram set point (fraction of

full power, IC dependent)

WRC1 0.87 Low core flow reactor scram set point (fraction of

full flow, IC dependent)

ALDA 0.405 decay constant, for fast transient 0.405 sec-1, slow

= 0.0767 sec-1

ALIF 0.000021 effective neutron life time (sec)

BETA 0.0075 effective delay neutron fraction

RAMP 10 turbine power demand ramp rate (%/min)

AKMD -0.105 moderator temperature reactivity coefficient ($/°C)

RHSD 8.2 shutdown reactivity ($)

AKDP -0.0021 Doppler (fuel) reactivity coefficient ($/°C)

ITBV 0 (Turbine bypass system control in Tavg/SG pressure

mode)

ICSP 0 (Containment spray system stop/run)

21

IRUN 0 (Initial/snapped IC)

RDPOS 98 rod position % of withdrawn

P 158.2 (RCS pressure (Kg/cm2))

TAVG 309.1 (RCS average temperature (°C))

TM 309.1 (Subcooled RCS temperature (°C))

LEV 0.6195 (Dimensionless RCS inventory)

V 39.6 (Two-phase volume (M3))

VR 260 (Subcooled volume (M3))

W3 -5.748 (Interconnecting flow rate (t/hr))

UC 0.1053 Steam generator heat transfer coefficient at 100%

power

MBK 0 (Integrated break flow in the containment (kg))

FRCL 0 (Clad damage fraction (%))

PSG0 77.14 Steam generator pressure at zero power (bar)

LSGA 11.83 (A SG wide range level (M))

LSGB 11.83 (B SG wide range level (M))

SGCT 41350 (SG mass to level conversion constant ( = MSG0/LSG0))

LSLD 0 (Pressurizer top discharge flow (steam/liquid))

ITDAFW 0 (TD AFW pump not initiated/initiated)

IMDAFW 0 (MD AFW pump not initiated/initiated)

ILEV 0 (Pressurizer not drained/has drained)

ISAT 0 (RCS subcooled/saturated)

ICORE 0 (Reactor at power/tripped)

ILIF 2 Core life beginning/middle/end of cycle

KSGA 1 Number of steam generators at the left hand A-side

IHPI 0 (HPI not initiated/initiated)

IRCA 1 (RCP-A tripped/operating)

IRCB 1 (RCP-B tripped/operating

ICFT 0 (CFT not initiated/initiated

ILPI 0 (LPI not initiated/initiated

ICRT 0 (LOCA flow (critical/non?critical)

X 0.09583 (RCS two-phase volume quality

IMFW 3 (Main feedwater status (on/tripped)

MSGA 82000 (A SG liquid mass (kg))

MSGB 164000 (B SG liquid mass (kg))

PSGA 68.99 (A SG pressure (bar))

PSGB 68.99 (B SG pressure (bar))

XSGA 0.03239 (A SG quality))

XSGB 0.03239 (B SG quality))

PTBVA 69 (A SG pressure (bar))

PTBVB 69 (B turbine bypass controlling pressure (bar))

NSG2A 50 A SG controlling (narrow range level (%)

NSG2B 50 B SG controlling narrow range level (%)

WTBA 0 (A SG turbine flow (t/hr))

WTBB 0 (B SG turbine flow (t/hr))

RHX 0 (Externally inserted rod & boron reactivity ($))

WFWA 1835 (A SG feedwater flow (t/hr))

WFWB 7888 (B SG feedwater flow (t/hr))

WRCA 16520 (RC loop A flow (kt/hr))

WRCB 33030 (RC loop B flow (kt/hr))

WMFW0 5504 (Nominal full power total feedwater flow (t/hr))

LVCR 3.65 (Core water level from bottom of the core (M))

PN2 44.32 (Accumulator nitrogen pressure (bar))

PRB 1.034 (Containment pressure (bar))

22

TRB 50 (Containment temperature (°C))

LWRB 28 (Containment water level (M))

TFSB 789.3 (Submerged fuel average temperature (°C))

TFPK 789.3 (Peak fuel temperature (°C))

QN 1 (Normalized neutron flux)

SUM 0 (integration term in kinetics equation)

WSTA 1835 (A SG steam flow (t/hr))

WSTB 3669 (B SG steam flow (t/hr))

TPCT 326.5 (Peak clad temperature (°C))

VH2O 90 (Total CFT (accumulator) water volume)

VN2 38.23 (total CFT nitrogen volume (M3))

FWERA0 0 (feedwater control valve A error)

FWERB0 0 (feedwater control valve B error)

PERA0 0 (SG A pressure controller error)

PERB0 0 (SG B pressure controller error)

ERL0 0 (pressurizer level controller error)

TimeStep 1 (number of time steps)

LVAP1 -1.2 Break elevation (dimensionless)

PSET1 158.2 (SG header pressure set point, bar)

TKLV 3000 (RWST water inventory, ton)

WCRV 100 (Critical break flow rate, t/hr)

WSTAB 0 SG steam flow cross connect Kg/s

LVAP2 -2 Elv for Przr discharge turn to vapor (dimensionless)

WCRL 100 (Critical break flow rate, t/hr)

PPM 2100 RCS boron concentration (ppm)

PPM0 200 Nominal boron concentration (ppm)

2.7 Changing Malfunction Status

Malfunctions can be turned on by going through “Code Control” and “Malfunctions” in the top

menu bar, or by clicking at the lower left “No Malfunction” status button. The list is then

displayed. After entering the ramp time, delay time and severity, the status should be checked to

"Active" and close the window. The following 18 Malfunctions are displayed:

Malfunction Description Criteria

1 Loss of Coolant Accident (Hot Leg) % of 100 cm^2

2 Loss of Coolant Accident (Cold Leg) % of 100 cm^2

3 Steam Line Break Inside Containment % of 100 cm^2

4 Steam Line Break Outside Containment % of 100 cm^2

5 Spark Presence for Hydrogen Burn (Not Used)

6 Loss of AC Power (Not Used)

7 Loss of Flow (Locked Rotor) (Not Used)

8 Anticipated Transient Without Scram (Not Used)

9 Turbine Trip (Not Used)

10 Steam Generator A Tube Rupture % of 1 full tube rupture

11 Steam Generator B Tube Rupture % of 1 full tube rupture

12 Inadvertent Rod Withdrawal of 1% dk/k withdrawn

23

Malfunction Description Criteria

13 Inadvertent Rod Insertion of 1% dk/k inserted

14 Moderator Dilution of Unborated Injection

15 Load Rejection of Full Load Rejected

16 Containment Failure or spark for H2 detonation % per Day at Design Pressure

17 Fuel Failure at Power % of Fuel Failed

18 Fuel Handling Accident in Containment % of Total

19 Fuel Handling Accdent in Auxiliary Building % of Total

20 Letdown Line Break in Aux Bldg % of Nominal Letdown flow

* No. 18 and 19 are not in the scope of the current project. They are reserved for next phase of work.

Pressing the RUN button resumes the run with the selected malfunctions activated.

2.8 Component Operation

All of the components on the two mimic diagrams are functional. Red indicates OPEN or ON,

green indicates CLOSED or OFF.

Pumps are started and stopped by pressing the left mouse button when the cursor is on the pump.

Pumps can be locked or failed to a specific state by pressing the right mouse button when the

cursor is on the pump symbol. When this happens a Red square is placed around the pump. The

pump state can then be set to ON or OFF by operating the pump as discussed above to simulate

control signal failures.

Valves are opened and closed by pressing the left mouse button when the cursor is on the valve.

Valves can be failed to any position from 0-100% open by pressing the right mouse button when

the cursor is on the valve symbol. When this happen a window pops up to allow the user to enter

the failure fraction for the valve. An active valve malfunction is shown by a Red rectangle

around the valve symbol. Three buttons are displayed in the window:

Failure Fraction is the percent of full open at which the valve is failed. The value

can be set to any integer from 0-100.

Status is the current state of the failure. Pressing this button toggles the

state between Inactive and Active.

Close is used to close the equipment failure window to accept the failure

fraction and malfunction state.

A Green box displays a heat exchanger with a Red pipe coil passing through it. Pressing the

right mouse button when the mouse cursor is over the symbol can reduce heat removal by the

24

heat exchanger. Selection of the failure fraction is the same as discussed above for valve

failures. When a heat exchanger malfunction is active a Red box replaces the Green box.

2.9 PostPlot Utility

At completion of a run, the user can get the transient report in text form and the transient

variables in either Excel or Access form. Table 2.1 is the transient report for the tube rupture

event. After saving the plot in Access, the user can use the plotting utility "PostPlot.exe" to

generate pre-achieved data. Just click at PostPlot and open the saved data, the title, variable

selection, scales, range, curve thickness and data interval are all adjustable. There are even

selection of Cartesian and semi-log scales. The latter is appropriate for radiological data since

wide range of variation is expected. This gives great flexibility in output for report preparation.

The user can use query to select the NSSS variables in PlotData.mdb database and radiological

source term in DoseData.mdb database to write reports. A sample one for dose release is

attached.

Table 2.1 "Transient Report" Generated for the SG Tube Rupture Run

Reset to IC #1

000035.0 sec, Safety Relief Valve #0 Position Change: 24%

0354.0 sec, Scram Lo RX Press132.2 kg/cm2

0354.5 sec, Reactor Scram

000354.5 sec, TCV Valve Position Change: 0%

000354.5 sec, Vent Valve Position Change: 0%

000354.5 sec, Turbine trip

000355.0 sec, TBV Valve Position Change: 100%

000355.5 sec, HPI Pump #3 Position Change: 0%




000363.0 sec, HPSI start low RX Press 118.1 kg/cm2


000363.0 sec, HPSI starts

000363.0 sec, RCP-A trip

000363.0 sec, RCP-B trip








25

Table 2.2 PlotData List

ID Label Units Name

1 Time (sec) sec TIME

2 Temperature RCS average (°C) °C TAVG

3 Temperature Hot leg A (°C) °C THA

4 Temperature Hot leg B (°C) °C THB

5 Temperature Cold leg A (°C) °C TCA

6 Temperature Cold leg B (°C) °C TCB

7 Flow Reactor coolant loop A (t/hr) t/hr WRCA

8 Flow Reactor coolant loop B (t/hr) t/hr WRCB

9 Pressure Steam generator A (bar) bar PSGA

10 Pressure Steam generator B (bar) bar PSGB

11 Flow SG A feedwater (t/hr) t/hr WFWA

12 Flow SG B feedwater (t/hr) t/hr WFWB

13 Flow SG A steam (t/hr) t/hr WSTA

14 Flow SG B steam (t/hr) t/hr WSTB

15 Volume RCS liquid (M3) M3 VOL

16 Level Pressurizer (%) % LVPZ

17 Void of RCS (%) % VOID

18 Flow RCS leak (t/hr) t/hr WLR

19 Flow Przr PORV and safeties (t/hr) t/hr WUP

20 Spec Enthalpy Przr top discharge (kJ/kg) kJ/kg HUP

21 Spec Enthalpy RCS leak (kJ/kg) kJ/kg HLW

22 Flow HPI (t/hr) t/hr WHPI

23 Flow Total ECCS (t/hr) t/hr WECS

24 Power Total megawatt thermal (MW) MW QMWT

25 Level SG A wide range (M) M LSGA

26 Level SG B wide range (M) M LSGB

27 Power SG A heat removal (MW) MW QMGA

28 Power SG B heat removal (MW) MW QMGB

29 Level SG A narrow range (%) % NSGA

30 Level SG B narrow range (%) % NSGB

31 Power Turbine load (%) % TBLD

32 Flow SG A tube leak (t/hr) t/hr WTRA

33 Flow SG B tube leak (t/hr) t/hr WTRB

34 Temperature Przr saturation (°C) °C TSAT

35 Power RHR removal rate (MW) MW QRHR

36 Level Core water (M) M LVCR

37 Temp Loop A subcooling margin (°C) °C SCMA

38 Temp Loop B subcooling margin (°C) °C SCMB

26

ID Label Units Name

39 Clad failure (%) % FRCL

40 Press Reactor building (bar) bar PRB

41 Press Partial RB air (bar) bar PRBA

42 Temp Reactor building (°C) °C TRB

43 Level RB sump water (M) M LWRB

44 Ratio Departure from nuclear boiling - DNBR

45 Power Fan cooler heat removal (MW) MW QFCL

46 Flow Total break entering RB (t/hr) t/hr WBK

47 Flow Pressurizer spray (t/hr) t/hr WSPY

48 Flow Containment spray (t/hr) t/hr WCSP

49 Power Pressurizer heater (KW) KW HTR

50 Mass H2 generated by Zr-H2O (kg) kg MH2

51 Concentration RB hydrogen (%) % CNH2

52 Reactivity Soluble boron (%dk/k) %dk/k RHBR

53 Reactivity Mod temperature (%dk/k) %dk/k RHMT

54 Reactivity Fuel (Doppler) (%dk/k) %dk/k RHFL

55 Reactivity Rod (%dk/k) %dk/k RHRD

56 Reactivity Total (%dk/k) %dk/k RH

57 Power Nuclear Flux (%) % PWNT

58 Power Core thermal (%) % PWR

59 Temp Submerged fuel average (°C) °C TFSB

60 Temp Peak fuel (°C) °C TFPK

61 Temp Average fuel (°C) °C TF

62 Temp Peak clad (°C) °C TPCT

63 Flow Accumulator (t/hr) t/hr WCFT

64 Flow Low pressure injection (RHR) (t/hr) t/hr WLPI

65 Flow Charging (t/hr) t/hr WCHG

66 Rad Monitor RB air (CPM) CPM RM1

67 Rad Monitor Steam Line (CPM) CPM RM2

68 Rad Monitor Condenser Off-gas (CPM) CPM RM3

69 Rad Monitor Aux Building Air (CPM) CPM RM4

70 Activity RC Coolant (CPM) CPM RC87

71 Concentration RC I-131 Eq (GBq/cc) GBq/cc RC131

72 Rad Rel Rate RB (GBq/s) GBq/s STRB

73 Rad Rel Rate SG Valves (GBq/s) GBq/s STSG

74 Rad Rel Rate Condenser Off-gas (GBq/s) GBq/s STTB

75 Mass Total Leakage out of RB (kg) Kg RBLK

76 Mass Total Leakage out of SGs (kg) Kg SGLK

77 Dose Rate EAB Thyroid (mSv/hr) mSv/hr DTHY

78 Dose Rate EAB Whole Body (mSv/hr) mSv/hr DWB

79 Press RCS (bar) bar P

27

ID Label Units Name

80 Flow SG A MSV/ADV t/hr WRLA

81 Flow SG B MSV/ADV t/hr WRLB

82 Flow Letdown (t/hr) t/hr WLD

83 Integrated Break Flow (kg) Kg MBK

84 Integrated Break Energy (MJ) MJ EBK

85 RWST Water Volume (M3) M3 TKLV

86 Fraction Zr Oxidation % FRZR

87 Mass of Corium in DW (Kg) Kg MDBR

88 Mass of molten concrete (Kg) Kg MCRT

89 Mass of CCI gases (Kg) Kg MGAS

90 Temp of Debris in Cavity (°C) °C TDBR

91 Temp of Debris in Lower Plenum (°C) °C TSLP

92 Temp of Molten Concrete (°C) °C TCRT

93 Concentration RCS Boron (ppm) ppm PPM

Note: This table is from ListPlotVariables in database PlotData.mdb. It is sorted alphabetically of

the variable names for easy locating. The user can point and click during plotting to get the

curve. In next chapter sample problem runs, user can also use the right hand variable name to

identify and plot the correct curve.

28

3.0 PWR Benchmark Analysis

In order to demonstrate that the PCTRAN simulation software is capable of simulating the PWR

plant operation, two types of runs were conducted. First is to perform normal operation with load

change etc. Second is a set of transient and accident analyses as in the Westinghouse 2-loop

Point Beach FSAR. In this chapter they are described in detail.

3.1 Normal Operation

3.1.1 Load Reduction to 40%

This is a test of the reactor control system for load control. The user can enter a load demand

different from the panel indicated and the reactor will respond to reach the desired load with a

ramp rate RAMP in percent per minute. For example, by clicking at "M" for manual control for

Pwr Dmd in the upper right reactor control panel and entering 40%, the reactor will drop it

power output to 40% at a rate of 10%/min. This will be achieved by precise control of the

turbine control valve. The neutron flux and thermal power follow the turbine load with a

noticeable lag.

The reactor primary pressure after some perturbation returns to the original pressure (about 155

bar) while the secondary pressure rises to a higher value corresponding to the lower power level.

The pressurizer level and reactor coolant Tavg will decrease according to the load program. The

feedwater flow will be run-back to balance the steam flow. The steam generator narrow-range

level returns to the set point of 50% after its initial rise by overfeeding. The rod reactivity is a

result of the rod control system that inserts the assemblies into the core. Feedback from Doppler

and moderator temperature are also presented, they're combined total reactivity controls the

nuclear power in this load reduction process.

Individual plant control systems can be taken into manual by clicking at the "M" button in the

PCTRAN/U's mimic. By entering a set point other than the original value, click at "Inactive" to

change it to "active" and close the window, the system will evolve into a new stabilized status

corresponding to that condition.

For exercises the user should try to change every manual control function and observe the

simulator response. For example, in addition to the power demand setpoint change, the ramp

rate, RAMP, can be altered to 20% per minute, or the pressurizer level to 50%, the SG level to

45%, etc.. The pressurizer heaters can also be set to turn on or off using the equipment

malfunction (right mouse). This is instructive for comprehension of each component's effect to

the whole reactor system.

29

Table Normal Operation and Load Reduction

Run Time = 800 seconds

Initial Condition

(IC #)

Malfunction

(#/%)

Interactive

Control

(panel/%)

Output

Variable

(Name)

Range

(min/max/

unit)

1

None Pwr Dmd/40 TBLD

PWTH

PWNT

THA/THB

TCA/TCB

TFPK

TFSB

TPCT

LVPZ

P

PSGA

NSGA/B

LSGA/B

WSTA/B

WFWA/B

RHDP

RHRD

RHMT

RH

0/120(%)

260/350(C)

0/900 (C)

0/100 (%)

0/200 (bar)

0/100 (%)

0/3000(t/hr)

-100/100

pcm(E-5dk/k)

33

3.1.2 Normal Reactor Trip

The reactor is manually scrammed after full power operation. This transient is to verify that all

control systems work as designed to stabilize at the post-trip hot zero power condition.

In the following plots it is noted the reactor primary pressure drops after the reactor scram. It

recovers to the set point of 155 bar. The loop temperatures and the pressurizer and steam

generator pressures and levels are stabilized at their corresponding post-trip set points in the

control diagrams. The feedwater and steam flow rates are reduced to balance the core decay

heat. Charging and letdown flows are controlled properly to maintain the pressurizer level. The

reactivity feedback and scram (rod) reactivity keeps the core sub-critical with a significantly

margin (about 4% dk/k).

37

3.2 Transient and Accident Analyses

This section demonstrates the response of the PWR plant to each transient provided in the menu.

These sample problems were performed using the default data set (IC#1 etc.) that is the PWR

plant at various power and time-of-life conditions. Input parameters that are important to a

transient will be discussed. In addition to the response of key system parameters, interactive

controls or proper operating procedures to mitigate the accident will be explained.

For each event, a table listing selections of the initial condition, malfunction and other specific

action for conducting the run is provided. The output variables of interest, their range (minimum

and maximum) and run time (time to terminate the run) are included. The figures are labeled

with the figure numbers of the FSAR of Point Beach. Note that the FSAR used British units

while the PCTRAN contract requires SI units. Some of parameters are of the same physical

meaning but with different measurement, e.g. the pressurizer level we use percent, while in

FSAR it is shown in cubic feet. User should be aware that the full volume of the pressurizer is

1500 ft3, thus one could be easily converted to another. For these reasons we did not overlap the

FSAR figures with our benchmark results. The FSAR figures are attached behind each

benchmark analysis for easy comparison.

35

Table 3.1 Transient Benchmark Summary

Event Initial

Condition

Malfunction Interactive

Control

Run Time

(Seconds)

Output

Uncontrolled Rod

Withdrawal (Subcritical)

7 12 (40 sec ramp,

100% failure)

None 60 Neutron Flux, % power, fuel temp, peak clad

temp, average coolant temp.

Uncontrolled Rod

Withdrawal (Fast)

3 12 (100 sec ramp,

100% failure)

None 20 Neutron Flux, pressure, DNBR, average

coolant temp.

Uncontrolled Rod

Withdrawal (Slow)

3 12 (100 sec ramp,

100% failure

None 120 Neutron Flux, pressure, DNBR, average

coolant temp.

Hot Full Power Rod

Drop

1 13 (3 sec ramp,

63% failure)

None 120 Neutron Flux, % power, pressure, average

coolant temp, steam flow

Moderator Dilution 1 14 (500 sec ramp,

50% failure)

None 480 Neutron flux, pressure, DNBR

Loss of Flow – 1 RCP

Trip

3 None Trip 1 pump 30 Loop flow, neutron flux, % power, DNBR

Loss of Flow – 4 RCP

Trip

3 None Trip 2 pumps 100 Loop flow, neutron flux, % power, DNBR

Locked Rotor

3 7 None 20 Loop flow, pressure, DNBR

Startup of Inactive Loop 11 None Start idle RCP 60 Neutron Flux, pressure, average coolant temp

Turbine Trip 1 and 3 None Disable TBV,

trip the turbine

25 Neutron Flux, pressure, average coolant

temp, DNBR, power, pressurizer level

Loss of Feedwater 1 5 Disable TBV, 1

aux feed pump

400 Pressurizer level, average coolant temp, SG

level

Reduction in Feedwater

Enthalpy

1 None Change HMFW

to 900 kJ/kg

100 Power, average coolant temperature,

pressure, DNBR

36

Event Initial

Condition

Malfunction Interactive

Control

Run Time

(Seconds)

Output

Excessive Load Increase 1 and 3 None Set power

demand to

110%

200 Power, average coolant temperature,

pressure, DNBR

Steam Generator Tube

Rupture

1 10 (100% failure) Disable TBV 2000 Pressure, pressurizer level, tube break flow,

safety valve flow

Small Break LOCA 1 2 (20.27, 182.4

cm2 break sizes)

Trip both RC

pumps

1400, 300 RCS volume, pressure, peak clad temp,

pressurizer level, SG pressure and flow

Large Break LOCA 1 2 (2800 cm2

break size)

None 120 Pressure, volume, peak clad temperature

37

3.2.1 Uncontrolled Rod Bank Withdrawal

A rod cluster control assembly (RCCA) withdrawal accident is defined as an uncontrolled

addition of reactivity to the reactor core caused by withdrawal of RCCAs. It results in a power

excursion. Such a transient could be caused by a malfunction of the reactor control or rod

control systems. This could occur with the reactor either subcritical, at hot zero power (HZP), or

at power.

At HZP

Section 14.1.1 of the FSAR describes this incident for the plant. A conservatively low (least

negative) Doppler coefficient and a zero moderator temperature coefficient are assumed. The

zero moderator temperature coefficient yields the highest peak heat flux.

In PCTRAN, selecting an initial condition at HZP and selecting Malfunction #12 for rod

withdrawal run the transient. Alternatively, we may type in a rod demand higher than the current

position and adjust the insertion rate. The plots provided show the results of this transient.

Neutron flux and heat flux respond in a similar manner as seen in the FSAR. Fuel and RCS

average temperature show similar behavior as in the FSAR.

40

Hot Full Power Fast Rod Withdrawal

In the FSAR, the fast withdrawal of a rod at power results in the reactivity insertion of 6 x 10-4

k/sec. This uncontrolled withdrawal results in an increase in core heat flux, which causes

average RCS temperature to increase. The transient is terminated by a reactor trip at 118%

neutron flux.

The case is benchmarked in PCTRAN by selecting a beginning of life full power initial condition

(IC #3). This IC uses a zero moderator coefficient, which was specified in the FSAR.

Malfunction 12 was selected with a ramp time of 100 seconds and a reactivity insertion of 6% to

produce the desired reactivity insertion rate. Neutron flux, RCS pressure, RCS average

temperature, and DNB ratio are plotted for comparison to the FSAR.

Hot Full Power Slow Rod Withdrawal

For this case, a reactivity insertion rate of 2.5 x 10-5

k/sec was specified. In PCTRAN, this is

simulated by selecting Malfunction 12 with a reactivity insertion of .25% over 100 seconds.

Neutron flux, RCS pressure, RCS average temperature, and DNB ratio are plotted for

comparison to the FSAR.

41

0

1 0

2 0

3 0

4 0

5 0

6 0

7 0

8 0

9 0

1 0 0

1 1 0

1 2 0

0 2 4 6 8 1 0

T im e ( s e c )

FS AR Fig ure 14 .1 . 2 -1 U nc ontrolle d F ast R od W ith dra wa l

P C T ra n

2 / 2 6 / 2 0 0 1 2 :3 3 :5 8 P M

P W N T (% d k / k )

1 5 0

1 5 2

1 5 4

1 5 6

1 5 8

1 6 0

0 2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0

T im e ( s e c )

FS AR Fig ure 14 .1 . 2 -1 U nc ontrolle d F ast R od W ith dra wa l

P C T ra n

2 / 2 6 / 2 0 0 1 2 :3 6 :0 3 P M

P (k g / c m 2 )

42

2 9 8

3 0 0

3 0 2

3 0 4

3 0 6

0 2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0

T im e ( s e c )

FS AR Fig ure 14 .1 . 2 -2 U nc ontrolle d F ast R od W ith dra w a l

P C T ra n

2 / 2 6 / 2 0 0 1 2 :4 0 :1 7 P M

T A V G ( ° C )

1 . 4

1 . 6

1 . 8

2 . 0

2 . 2

2 . 4

2 . 6

2 . 8

3 . 0

3 . 2

3 . 4

0 2 4 6 8 1 0 1 2

T im e ( s e c )

FS AR Fig ure 14 .1 . 2 -2 U nc ontrolle d F ast R od W ith dra w a l

P C T ra n

2 / 2 6 / 2 0 0 1 2 :3 8 :5 0 P M

D N B R ( - )

45

0

1 0

2 0

3 0

4 0

5 0

6 0

7 0

8 0

9 0

1 0 0

1 1 0

1 2 0

0 2 0 4 0 6 0 8 0 1 0 0 1 2 0

T im e ( s e c )

FS AR Fig ure 14 .1 . 2 -3 U nc ontrolle d S low R od W ith dra w a l

P C T ra n

2 / 2 6 / 2 0 0 1 2 :4 7 :5 4 P M

P W N T (% d k / k )

1 2 0

1 3 0

1 4 0

1 5 0

1 6 0

1 7 0

0 2 0 4 0 6 0 8 0 1 0 0 1 2 0

T im e ( s e c )

FS AR Fig ure 14 .1 . 2 -3 U nc ontrolle d S low R od W ith dra wa l

P C T ra n

2 / 2 6 / 2 0 0 1 2 :4 8 :4 8 P M

P (k g / c m 2 )

46

2 8 0

2 9 0

3 0 0

3 1 0

3 2 0

0 2 0 4 0 6 0 8 0 1 0 0 1 2 0

T im e ( s e c )


P C T ra n

2 / 2 6 / 2 0 0 1 2 :5 0 :2 3 P M

T A V G ( ° C )

0

1

2

3

4

5

6

0 2 0 4 0 6 0 8 0 1 0 0 1 2 0

T im e ( s e c )


P C T ra n

2 / 2 6 / 2 0 0 1 2 :5 1 :2 7 P M

D N B R ( - )

49

3.2.2 Hot Full Power Rod Drop

Dropping of a full length RCCA occurs when the drive is de-energized. This would cause a

power reduction and an increase in the hot channel factor. If the insertion is not sufficient to trip

the reactor, then a return to full power with the dropped assembly inserted is possible. This

would lead to a reduced safety margin or possibly DNB, depending upon the magnitude of the

resultant hot channel factor. The FSAR states that the DNBR in all credible situations will stay

above 1.30.

In PCTRAN, selecting initial condition #1 and malfunction #13 will initiate this transient. A

ramp time of 3 seconds (rod drop time) and a failure fraction of 63% (0.63% k/k) are specified.

This corresponds to the assumed reactivity insertion rate of 2.1 x 10-3

k for the dropped rod.

The most negative moderator (-0.096 $/C) and Doppler coefficients (-0.003 $/C) are used.

Plots of flux, power, pressure, average temperature, and steam load are provided for comparison

to the FSAR figures. Pressure and temperature response differ slightly from the FSAR. Neutron

flux is in good agreement with the FSAR and matches the power decrease from the dropped rod.

50

4 0

5 0

6 0

7 0

8 0

9 0

1 0 0

1 1 0

1 2 0

0 2 0 4 0 6 0 8 0 1 0 0 1 2 0

T im e ( s e c )

FS AR Fig ure 14 .1 . 4 -1 H ot Fu ll P ow er R od D ro p

P C T ra n

2 / 2 8 / 2 0 0 1 1 1 : 4 3 : 5 3 A M

P W N T (% d k / k )

4 0

5 0

6 0

7 0

8 0

9 0

1 0 0

1 1 0

1 2 0

0 2 0 4 0 6 0 8 0 1 0 0 1 2 0

T im e ( s e c )

FS AR Fig ure 14 .1 . 4 -1 H ot Fu ll P ower R od D ro p

P C T ra n

2 / 2 8 / 2 0 0 1 1 1 : 4 5 : 4 6 A M

P W R (% )

51

1 4 0

1 4 2

1 4 4

1 4 6

1 4 8

1 5 0

1 5 2

1 5 4

1 5 6

1 5 8

1 6 0

0 2 0 4 0 6 0 8 0 1 0 0 1 2 0

T im e ( s e c )


P C T ra n

2 / 2 8 / 2 0 0 1 1 1 : 4 6 : 1 9 A M

P (k g / c m 2 )

2 9 0

2 9 2

2 9 4

2 9 6

2 9 8

3 0 0

3 0 2

0 2 0 4 0 6 0 8 0 1 0 0 1 2 0

T im e ( s e c )


P C T ra n

2 / 2 8 / 2 0 0 1 1 1 : 4 7 : 4 1 A M

T A V G ( ° C )

52

0

2 0 0

4 0 0

6 0 0

8 0 0

1 0 0 0

1 2 0 0

1 4 0 0

1 6 0 0

1 8 0 0

2 0 0 0

0 2 0 4 0 6 0 8 0 1 0 0 1 2 0

T im e ( s e c )

FS AR Fig ure 14 .1 . 4 -2 H ot Fu ll P ower R od D ro p

P C T ra n

2 / 2 8 / 2 0 0 1 1 1 : 4 9 : 2 9 A M

W S T A ( t / h r )

W S T B ( t / h r )

55

3.2.3 Moderator Dilution

This event is described in the FSAR as a Chemical and Volume Control System Malfunction. It

is characterized by an inadvertent addition of unborated water into the reactor coolant system via

the reactor makeup portion of the chemical and volume control system. This has the effect of

adding reactivity to the reactor. The assumed reactivity addition rate as stated in the FSAR is 1.5

x 10-5

k/sec. If the reactor is in automatic control, control rods will be inserted in response to

the increase in reactivity. The low insertion limit alarm would alert the operator to initiate re-

boration. Also, it would be necessary to isolate the unborated water source. In manual control,

the power and temperature will until the high pressure scram setpoint is reached in

approximately 90 seconds. The dilution accident in this case is essentially similar to the

uncontrolled rod withdrawal transient. The reactivity rate is less than what was assumed in that

analysis.

In PCTRAN, a moderator dilution transient is initiated by selecting initial condition #1 and

malfunction #14. In order to match the specified reactivity insertion rate, the ramp time was set

to 500 seconds and the failure fraction was set to 50%. This gives a total insertion of 0.75% over

the 500 seconds, which corresponds to 1.5 x 10-5

k/sec. The FSAR states that in manual control

and no operator action, the plant will trip on high pressure. This does not occur in PCTRAN.

Instead, the plant trips on high flux. There are no FSAR figures for comparison. Several

PCTRAN plots are provided to show the response of key parameters to the dilution accident.

56

0

1 0

2 0

3 0

4 0

5 0

6 0

7 0

8 0

9 0

1 0 0

1 1 0

1 2 0

0 2 0 4 0 6 0 8 0 1 0 0 1 2 0 1 4 0 1 6 0 1 8 0 2 0 0 2 2 0 2 4 0

T im e ( s e c )

M o dera to r D ilu tion T ran sient

P C T ra n

3 / 1 / 2 0 0 1 1 0 :2 3 :2 1 A M

P W N T (% d k / k )

1 2 0

1 3 0

1 4 0

1 5 0

1 6 0

1 7 0

1 8 0

0 2 0 4 0 6 0 8 0 1 0 0 1 2 0 1 4 0 1 6 0 1 8 0 2 0 0 2 2 0 2 4 0

T im e ( s e c )


P C T ra n

3 / 1 / 2 0 0 1 1 0 :2 4 :2 7 A M

P (k g / c m 2 )

57

1 . 0

1 . 2

1 . 4

1 . 6

1 . 8

2 . 0

2 . 2

2 . 4

2 . 6

2 . 8

3 . 0

0 2 0 4 0 6 0 8 0 1 0 0 1 2 0 1 4 0 1 6 0 1 8 0 2 0 0 2 2 0 2 4 0

T im e ( s e c )


P C T ra n

3 / 1 / 2 0 0 1 1 0 :2 5 :2 5 A M

D N B R ( - )

58

3.2.4 Startup of Inactive Loop

If the plant is operated with the pump in one loop out of service, there is reverse flow through

that loop. This causes the hot leg temperature to become lower than the cold leg temperature.

The subsequent starting of the loop has the potential to bring in cold water into the core. The

cold water causes a rapid reactivity and power increase. Section 14.1.6 of the FSAR describes

this event. A large negative moderator coefficient is assumed as well as a low Doppler

coefficient. The reactor was assumed to be operating at 10% power, which is the maximum

value with one loop.

The transient was analyzed in PCTRAN by starting with initial condition #1, and resetting the

starting power to 10%. The low flow trip set point was set to 50%, and tripping one RCP.

Resetting the trip set point was necessary so the reactor would not trip with the low flow

condition. Once this transient stabilized, a new initial condition was created at 10% power and

with 1 RCP idle. The hot leg temperature of the idle loop was found to 277.8 C and the cold leg

temperature of the running loop was 279.2 C. This difference of 1.4 C or 2.5 F is less than the

7.4 F difference stated in the FSAR.

The RCP is then restarted and cold water does enter the core, thus raising power. However, the

transient is smaller than described in the FSAR because of the smaller temperature difference.

The response of neutron flux, reactor power, average temperature, and DNBR are shown in the

following plots and are compared to the FSAR.

59

2 8 0

2 8 1

2 8 2

2 8 3

2 4 0 2 6 0 2 8 0 3 0 0

T im e ( s e c )

FS AR Fig ure 14 .1 . 6 -2 S tartup of In ac t ive Loo p

P C T ra n

3 / 1 / 2 0 0 1 3 :3 0 :0 0 P M

T A V G ( ° C )

0

2

4

6

8

1 0

1 2

1 4

1 6

1 8

2 0

2 4 0 2 6 0 2 8 0 3 0 0

T im e ( s e c )


P C T ra n

3 / 1 / 2 0 0 1 3 :3 1 :2 7 P M

P W N T (% d k / k )

60

1 5 2

1 5 3

1 5 4

1 5 5

1 5 6

2 4 0 2 6 0 2 8 0 3 0 0

T im e ( s e c )


P C T ra n

3 / 1 / 2 0 0 1 3 :3 2 :3 0 P M

P (k g / c m 2 )

65

3.2.5 Reduction in Feedwater Enthalpy

The reduction in feedwater enthalpy is another means of increasing core power above full power.

Such increases are attenuated by the thermal capacity in the secondary plant and in the RCS. An

example of this is described in section 14.1.7 of the FSAR as the accidental opening of the low

pressure heater bypass valve which diverts flow around the low pressure feedwater heaters. The

lower feedwater enthalpy will lead to lower inlet temperatures, which, given a negative

moderator coefficient, will result in a power increase.

In PCTRAN, changing the parameter HMFW can simulate a reduction in feedwater enthalpy.

The default value was 950 kJ/kg. This was changed to 900 kJ/kg to give a similar power

response as found in the FSAR. Initial condition #1 was chosen which uses a negative

moderator coefficient. Plots of power, DNBR, pressure, and average temperature are shown on

the following pages. They show good agreement with the FSAR results. The responses of

pressure and temperature are slightly lower than the FSAR.

66

1 0 0

1 0 2

1 0 4

1 0 6

0 2 0 4 0 6 0 8 0 1 0 0

T im e ( s e c )

FS AR Fig ure 14 .1 . 7 -3 R ed uct ion in F eed wate r E n tha lpy

P C T ra n

2 / 2 6 / 2 0 0 1 2 :5 6 :2 2 P M

P W R (% )

1 . 4

1 . 6

1 . 8

2 . 0

0 2 0 4 0 6 0 8 0 1 0 0

T im e ( s e c )


P C T ra n

2 / 2 6 / 2 0 0 1 2 :5 8 :5 1 P M

D N B R ( - )

67

3 0 0 . 0

3 0 0 . 2

3 0 0 . 4

3 0 0 . 6

3 0 0 . 8

3 0 1 . 0

3 0 1 . 2

3 0 1 . 4

3 0 1 . 6

3 0 1 . 8

3 0 2 . 0

0 2 0 4 0 6 0 8 0 1 0 0

T im e ( s e c )


P C T ra n

2 / 2 6 / 2 0 0 1 3 :0 0 :3 6 P M

T A V G ( ° C )

1 5 4 . 0

1 5 4 . 2

1 5 4 . 4

1 5 4 . 6

1 5 4 . 8

1 5 5 . 0

1 5 5 . 2

1 5 5 . 4

1 5 5 . 6

1 5 5 . 8

1 5 6 . 0

0 2 0 4 0 6 0 8 0 1 0 0

T im e ( s e c )

FS AR Fig ure 14 .1 . 7 -4 R ed uct ion in F eed w ate r E n tha lpy

P C T ra n

2 / 2 6 / 2 0 0 1 3 :0 2 :2 2 P M

P (k g / c m 2 )

70

3.2.6 Excessive Load Increase

An excessive load increase incident could result from either an administrative violation such as

excessive loading by the operator or an equipment malfunction in the steam dump control or

turbine speed control. The reactor control system is designed to accommodate a 10 percent step

load increase or a 5 percent per minute ramp load increase (without reactor trip) in the range of

15 to 100 percent of full power. Four cases are discussed in section 14.1.8 of the FSAR, but only

two analyzed here. They are the ones that occur with the reactor in automatic control. The End

of Life (EOL) condition involves running the transient with a large negative moderator

coefficient (maximum feedback). The Beginning of Life (BOL) case uses a zero moderator

coefficient (minimum feedback). Because of the feedback, the reactor responds more quickly to

the increase in demand due to the reduction in core inlet temperature.

The transient is run in PCTRAN by setting the reactor power demand to 110%, with all other

controls in auto. Initial condition #1 is selected for the EOL case and #3 is selected for the BOL

case. No malfunctions are needed for this transient. The responses of power, average

temperature, reactor pressure, and DNBR are consistent with the FSAR.

71

1 0 0

1 0 2

1 0 4

1 0 6

1 0 8

1 1 0

1 1 2

1 1 4

1 1 6

1 1 8

1 2 0

0 2 0 4 0 6 0 8 0 1 0 0 1 2 0 1 4 0 1 6 0 1 8 0 2 0 0

T im e ( s e c )

FS AR Fig ure 14 .1 . 8 -3 10 % Lo ad Inc rea se (EO L )

P C T ra n

2 / 2 6 / 2 0 0 1 3 :1 3 :0 2 P M

P W R (% )

2 9 8

3 0 0

3 0 2

3 0 4

3 0 6

3 0 8

0 2 0 4 0 6 0 8 0 1 0 0 1 2 0 1 4 0 1 6 0 1 8 0 2 0 0

T im e ( s e c )

FS AR Fig ure 14 .1 . 8 -3 10 % Lo ad Inc rea se (EOL )

P C T ra n

2 / 2 6 / 2 0 0 1 3 :1 1 :2 3 P M

T A V G ( ° C )

72

1 5 0

1 5 2

1 5 4

1 5 6

1 5 8

1 6 0

0 2 0 4 0 6 0 8 0 1 0 0 1 2 0 1 4 0 1 6 0 1 8 0 2 0 0

T im e ( s e c )

FS AR Fig ure 14 .1 . 8 -4 10 % Lo ad Inc rea se (EO L )

P C T ra n

2 / 2 6 / 2 0 0 1 3 :1 0 :2 4 P M

P (k g / c m 2 )

1 . 4

1 . 6

1 . 8

2 . 0

0 2 0 4 0 6 0 8 0 1 0 0 1 2 0 1 4 0 1 6 0 1 8 0 2 0 0

T im e ( s e c )

FS AR Fig ure 14 .1 . 8 -4 10 % Lo ad Inc rea se (EOL )

P C T ra n

2 / 2 6 / 2 0 0 1 3 :0 9 :4 6 P M

D N B R ( - )

73

1 0 0

1 0 2

1 0 4

1 0 6

1 0 8

1 1 0

1 1 2

1 1 4

1 1 6

1 1 8

1 2 0

0 2 0 4 0 6 0 8 0 1 0 0 1 2 0 1 4 0 1 6 0 1 8 0 2 0 0

T im e ( s e c )

FS AR Fig ure 14 .1 . 8 -3 10 % Lo ad Inc rea se (BO L )

P C T ra n

2 / 2 6 / 2 0 0 1 3 :0 5 :0 7 P M

P W R (% )

74

2 9 8

3 0 0

3 0 2

3 0 4

3 0 6

3 0 8

0 2 0 4 0 6 0 8 0 1 0 0 1 2 0 1 4 0 1 6 0 1 8 0 2 0 0

T im e ( s e c )

FS AR Fig ure 14 .1 . 8 -3 10 % Lo ad Inc rea se (BOL )

P C T ra n

2 / 2 6 / 2 0 0 1 3 :0 7 :0 5 P M

T A V G ( ° C )

75

1 5 0

1 5 2

1 5 4

1 5 6

1 5 8

1 6 0

0 2 0 4 0 6 0 8 0 1 0 0 1 2 0 1 4 0 1 6 0 1 8 0 2 0 0

T im e ( s e c )

FS AR Fig ure 14 .1 . 8 -4 10 % Lo ad Inc rea se (BO L )

P C T ra n

2 / 2 6 / 2 0 0 1 3 :0 8 :1 0 P M

P (k g / c m 2 )

1 . 4

1 . 6

1 . 8

2 . 0

0 2 0 4 0 6 0 8 0 1 0 0 1 2 0 1 4 0 1 6 0 1 8 0 2 0 0

T im e ( s e c )

FS AR Fig ure 14 .1 . 8 -4 10 % Lo ad Inc rea se (BOL )

P C T ra n

2 / 2 6 / 2 0 0 1 3 :0 9 :0 4 P M

D N B R ( - )

78

3.2.7 Loss Of Reactor Coolant Flow

A loss of coolant flow incident can result from a mechanical or electrical failure in a reactor

coolant pump, or in a fault in the power supply to these pumps. If the reactor is at power, the

immediate effect of loss of coolant flow is a rapid increase in coolant temperature. This increase

could result in departure from nucleate boiling with subsequent fuel damage if the reactor is not

tripped promptly.

Two cases are benchmarked against the FSAR, 1 pump trip and 2 pump trip. In each case, the

core is assumed to be at 102% power with a zero moderator temperature coefficient. The

accident is run in PCTRAN by tripping the RCP on the left for the 1 pump trip case, and by

tripping both the right and the left pump for the 2 pump trip case.

Two additional parameters were set, TCST (RCP coastdown time) and WRC1 (Low flow scram

set point). For the 1 pump case, WRC1 was set to 93.5%. This was necessary because there is

no single loop low flow scram in PCTRAN, but there is one described in the FSAR. It occurs at

90% of nominal flow for the particular loop, but for this analysis, was assumed to occur at 87%.

Assuming 50% flow through each loop, 87% of 50% is about 43.5%. Added to 50% for the

other loop, gives 93.5% of full flow. For the 2 pump case, this value was set to 90%. The pump

coastdown time was set to 15 seconds. This value best fit the results in FSAR Figures 14.1.9-1

and 14.1.9-2. The Excel plots on the next page show good agreement with the FSAR.

The other plots provided can be compared to the FSAR figures for the behavior of neutron flux,

heat flux, and DNB ratio. The PCTRAN results are in good agreement with the FSAR.

Locked Rotor

A locked rotor event is characterized by the instantaneous seizure of a reactor coolant pump

rotor. Flow through the affected reactor coolant loop is rapidly reduced, leading to a reactor trip

on a low flow signal. Before the trip, there is a rapid power and pressure increase. A zero

moderator temperature coefficient was assumed in the analysis.

Malfunction #7 initiates a locked rotor accident. Initial condition #3 was selected for a full

power, zero moderator coefficient simulation. The effect on core flow because of the locked

rotor is shown on the Excel chart. Plots of reactor pressure and DNBR are provided for

comparison to the FSAR figures.

79

Two Loop Operation - 1 Pump Flow Coastdown

FSAR Figure 14.1.9-1

0

0.2

0.4

0.6

0.8

1

1.2

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30

Time (sec)

Co

re F

low

(F

racti

on

of

Init

ial)

Two Loop Operation - 2 Pump Flow Coastdown

FSAR Figure 14.1.9-2

0

0.2

0.4

0.6

0.8

1

1.2

0 10 20 30 40 50 60 70 80 90 100

Time (sec)

Fra

cti

on

of

Init

ial F

low

80

0

2 0

4 0

6 0

8 0

1 0 0

1 2 0

0 1 2 3 4 5 6

T im e ( s e c )

FS AR Fig ure 14 .1 . 9 -3 T wo P ump s Lo ss of Flo w

P C T ra n

2 / 2 6 / 2 0 0 1 3 :1 6 :3 2 P M

P W N T (% d k / k )

0

2 0

4 0

6 0

8 0

1 0 0

1 2 0

0 1 2 3 4 5 6

T im e ( s e c )


P C T ra n

2 / 2 6 / 2 0 0 1 3 :1 7 :3 7 P M

P W R (% )

81

1 . 4

1 . 6

1 . 8

2 . 0

2 . 2

2 . 4

0 1 2 3 4 5 6

T im e ( s e c )


P C T ra n

2 / 2 6 / 2 0 0 1 3 :1 8 :2 2 P M

D N B R ( - )

0

2 0

4 0

6 0

8 0

1 0 0

1 2 0

0 1 2 3 4 5 6

T im e ( s e c )

FS AR Fig ure 14 .1 . 9 -5 One P ump Loss of Flow

P C T ra n

2 / 2 6 / 2 0 0 1 3 :2 0 :2 7 P M

P W N T (% d k / k )

82

0

2 0

4 0

6 0

8 0

1 0 0

1 2 0

0 1 2 3 4 5 6

T im e ( s e c )

FS AR Fig ure 14 .1 . 9 -5 One P ump Loss of Flow

P C T ra n

2 / 2 6 / 2 0 0 1 3 :2 1 :4 9 P M

P W R (% )

1 . 4

1 . 6

1 . 8

2 . 0

2 . 2

2 . 4

0 1 2 3 4 5 6

T im e ( s e c )

FS AR Fig ure 14 .1 . 9 -6 O ne P ump Loss of Flow

P C T ra n

2 / 2 6 / 2 0 0 1 3 :1 9 :1 8 P M

D N B R ( - )

83

Two Loop Operation - Locked Rotor

0

0.2

0.4

0.6

0.8

1

1.2

0 2 4 6 8 10 12 14 16 18 20

Time (sec)

Fra

cti

on

of

Init

ial

Flo

w

Core

Dead Loop

84

1 5 0

1 5 5

1 6 0

1 6 5

0 5 1 0 1 5 2 0

T im e ( s e c )

FS AR Fig ure 14 .1 . 9 -9 Lo cke d R o tor

P C T ra n

2 / 2 6 / 2 0 0 1 3 :2 2 :5 6 P M

P (k g / c m 2 )

1 . 0

1 . 2

1 . 4

1 . 6

1 . 8

2 . 0

2 . 2

2 . 4

2 . 6

2 . 8

3 . 0

0 1 2 3 4 5

T im e ( s e c )

FS AR Fig ure 14 .1 . 9 -1 0 L ock ed R oto r

P C T ra n

2 / 2 6 / 2 0 0 1 3 :2 4 :3 7 P M

D N B R ( - )

94

3.2.8 Turbine Trip

Four cases were analyzed in PWR FSAR for a turbine trip from full power: two for minimum

reactivity feedback and two for maximum feedback (Figs 14.1.10-1 through 14.1.10-8). Figures

14.1.10-1 and 14.1.10-2 show the transient responses for the turbine trip with minimum

reactivity feedback assuming full credit for the pressurizer spray and pressurizer power-operated

relief valves. No credit is taken for the steam dump.

A turbine trip should cause a direct reactor trip. In the FSAR the direct reactor trip is bypassed.

Setting the trip delay time TRXT can simulate this=9999 in the basic input file ICThermoData

table of ListData.mdb. Then the turbine is tripped either by clicking on the button or selecting

Malfunction No. 9 for loss of load. The turbine stop valve will be closed and this causes over-

heating in the primary side. The reactor pressure, pressurizer level and coolant average

temperature increase until the reactor is tripped by high pressure.

Two cases are analyzed: maximum (most negative) feedback moderator temperature reactivity

MTC for IC#1 end-of-life (EOC) and minimum MTC for IC#3 beginning of life (BOC). For

both cases, the reactor trips at 7 seconds due to high RCS pressure. The PCTRAN results for

RCS pressure and temperature, DNBR, and pressurizer level are consistent with the FSAR.

Turbine Trip, Maximum feedback (EOL)


Initial Condition

(IC #)

Malfunction

(#/%)

Interactive

Control

(panel/%)

Output

Variable

(Name)

Range

(min/max/

unit)

1

9 None PWTH

PWNT

THA/THB

TCA/TCB

TAVG

P

DNBR

LVPZ

0/120(%)

260/330C)

100/180 (bar)

1/4

0/100 (%)

95

Turbine Trip, Minimum feedback (BOL)


Initial Condition

(IC #)

Malfunction

(#/%)

Interactive

Control

(panel/%)

Output

Variable

(Name)

Range

(min/max/

unit)

3

9 None PWTH

PWNT

THA/THB

TCA/TCB

TAVG

P

DNBR

LVPZ

0/120(%)

260/330(C)

100/180 (bar)

1/4

0/100 (%)

Two more cases were analyzed in the FSAR: without the pressurizer spray and relief valves.

These could be analyzed by PCTRAN/U by disabling the components interactively on the mimic

screen. Since the outcome for both the maximum and minimum feedback cases are similar to

those with the pressurizer control, they are not presented here.

96

FSAR Section 14.1.10 (Turbine Trip w/o Bypass EOL, Auto Control, PCTRAN U2LP Results)

0

20

40

60

80

100

120

0 5 10 15 20 25 30

Time (sec)

Po

we

r (%

)

PWNT

PWR


260

270

280

290

300

310

320

330

0 5 10 15 20 25 30

Time (sec)

Te

mp

era

ture

(d

eg

C)

TAVG

THA

THB

TCA

TCB

97


100

110

120

130

140

150

160

170

180

0 5 10 15 20 25 30

Time (sec)

Pre

ss

ure

(k

g/c

m^

2)

RCS Pressure (P)


0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 5 10 15 20 25 30

Time (sec)

DN

BR

DNBR

98


0

10

20

30

40

50

60

70

80

90

0 5 10 15 20 25 30

Time (sec)

Pre

ss

uri

ze

r L

ev

el

(%)

LVPZ

99

FSAR Section 14.1.10 (Turbine Trip w/o Bypass BOL, Auto Control, PCTRAN U2LP Results)

0

20

40

60

80

100

120

0 5 10 15 20 25 30

Time (sec)

Po

we

r (%

)

PWNT

PWR


260

270

280

290

300

310

320

330

0 5 10 15 20 25 30

Time (sec)

Te

mp

era

ture

(d

eg

C)

TAVG

THA

THB

TCA

TCB

100


100

110

120

130

140

150

160

170

180

0 5 10 15 20 25 30

Time (sec)

Pre

ss

ure

(k

g/c

m^

2)

RCS Pressure (P)


0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 5 10 15 20 25 30

Time (sec)

DN

BR

DNBR

101


0

10

20

30

40

50

60

70

80

90

100

0 5 10 15 20 25 30

Time (sec)

Pre

ss

uri

ze

r L

ev

el

(%)

LVPZ

106

3.2.9 Loss of Normal Feedwater

A loss of feedwater transient can be initiated by tripping all main feedwater pumps, closing all

feedwater valves, or from the malfunction list. All would result in a reactor trip on high RCS

pressure or low SG level. RCS temperature and pressurizer level will increase due to a reduction

of heat transfer until a secondary heat sink is established. This is established by the Emergency

Feedwater (EFW) automatically starting on low SG level, or by manually clicking on the EFW

pumps.

FSAR section 14.1.11 describes a loss of feedwater event with the turbine bypass valves not

available. Also, only one motor driven auxiliary feedwater pump is available, with a flow rate of

200 gpm. In PCTRAN, selecting malfunction #5 and manually disabling the turbine bypass

valve simulate the transient. The EFW flow rate for the turbine-driven pump was set to 90 t/hr,

which corresponds to 400 gpm. This pump, as well as one motor driven pump, was disabled so

there was only one motor driven pump available.

The PCTRAN results show that the low SG level set point of 17% is reached in approximately

80 seconds after the trip of the feedwater pumps. Pressurizer level and average temperature

increase as expected.

107

2 9 0

2 9 2

2 9 4

2 9 6

2 9 8

3 0 0

3 0 2

3 0 4

3 0 6

3 0 8

3 1 0

0 1 0 0 2 0 0 3 0 0 4 0 0

T im e ( s e c )

FS AR Fig ure 14 .1 . 11 -1 L oss o f N o rmal Fee dw ater

P C T ra n

2 / 2 6 / 2 0 0 1 3 :2 6 :5 0 P M

T A V G ( ° C )

3 0

4 0

5 0

6 0

7 0

8 0

9 0

0 1 0 0 2 0 0 3 0 0 4 0 0

T im e ( s e c )


P C T ra n

2 / 2 6 / 2 0 0 1 3 :2 8 :2 2 P M

L V P Z (% )

108

0

1 0

2 0

3 0

0 1 0 0 2 0 0 3 0 0 4 0 0

T im e ( s e c )


P C T ra n

2 / 2 6 / 2 0 0 1 3 :3 0 :0 9 P M

L S G A (M )

110


This accident, as described in section 14.2.4 of the FSAR, is initiated by a complete rupture of a

single steam generator tube which will result in a loss of reactor coolant to the secondary side.

The loss of inventory will cause RCS pressure and pressurizer level to decrease. Continued loss

of inventory leads to a reactor trip on low pressurizer level. Safety injection soon follows the

reactor trip in order to maintain pressurizer level. The safety injection signal terminates normal

feedwater and initiates auxiliary feedwater addition. The plant trip automatically shuts off steam

supply to the turbine and if outside power is available, the steam dump valves open permitting

steam dump to the condenser. In the event of station blackout, the steam dump valves close to

protect the condenser. The steam generator pressure would rapidly increase resulting in steam

discharge to the atmosphere through the steam generator safety valves. The accident is assumed

to take place with one percent defective fuel rods.

In PCTRAN, a SG tube rupture event is initiated by selecting malfunction #10 for an A-side

break. A failure fraction of 100% is chosen. In addition, the turbine bypass valve is prevented to

open by selecting its malfunction to 0% open. There are no plots in the FSAR for this transient.

However, the FSAR states that approximately 70,000 lbs of coolant is transferred to the

secondary side during the first 30 minutes of the transient. It is assumed that the accident is

terminated after 30 minutes by operator action. This number compares favorably to the

PCTRAN results. The amount of coolant transferred to the SG was calculated by summing the

values of the variable WTRA, which is the tube break flow. The calculation gave a value of

69,700 lbs. Plots of reactor pressure, pressurizer level, tube leak rate, and safety valve flow rate

are provided.

111

9 0

1 0 0

1 1 0

1 2 0

1 3 0

1 4 0

1 5 0

1 6 0

0 2 0 0 4 0 0 6 0 0 8 0 0 1 0 0 0 1 2 0 0 1 4 0 0 1 6 0 0 1 8 0 0 2 0 0 0

T im e ( s e c )

S tea m Gen era tor T ube R up ture

P C T ra n

2 / 2 8 / 2 0 0 1 1 :2 1 :1 4 P M

P (k g / c m 2 )

0

1 0

2 0

3 0

4 0

5 0

6 0

7 0

8 0

9 0

1 0 0

0 2 0 0 4 0 0 6 0 0 8 0 0 1 0 0 0 1 2 0 0 1 4 0 0 1 6 0 0 1 8 0 0 2 0 0 0

T im e ( s e c )


P C T ra n

2 / 2 8 / 2 0 0 1 1 :2 2 :3 7 P M

L V P Z (% )

112

0

1 0

2 0

3 0

4 0

5 0

6 0

7 0

8 0

9 0

1 0 0

1 1 0

1 2 0

1 3 0

1 4 0

0 2 0 0 4 0 0 6 0 0 8 0 0 1 0 0 0 1 2 0 0 1 4 0 0 1 6 0 0 1 8 0 0 2 0 0 0

T im e ( s e c )


P C T ra n

2 / 2 8 / 2 0 0 1 1 :2 3 :3 5 P M

W T R A ( t / h r)

0

1 0

2 0

3 0

4 0

5 0

6 0

7 0

8 0

9 0

1 0 0

1 1 0

1 2 0

1 3 0

1 4 0

0 2 0 0 4 0 0 6 0 0 8 0 0 1 0 0 0 1 2 0 0 1 4 0 0 1 6 0 0 1 8 0 0 2 0 0 0

T im e ( s e c )


P C T ra n

2 / 2 8 / 2 0 0 1 1 :2 4 :1 1 P M

W R L A ( t / h r )

113

3.2.11 Small Break LOCA

As contrast with the large breaks, the blowdown phase of the small break occurs over a longer

time period. Core recovery and long term recirculation then follow a gradual blowdown. FSAR

Section 14.3.2 analyzed a spectrum of 2 to 6 inch small breaks. A small break was simulated by

entering 182.4% of Malfunction 2 for a 6-inch (182.4-cm2) break. The RCS pressure and RCS

water volume are compared with Figs. 14.3.2-23 and 14.3.2-27. Note the 2 charging pumps’

head curve is given by Fig. 14.3.2-19 (for Case 1- 2 Pumps; all lines delivering) and translated

into the PCTRAN database Basic Data table WHI and PHI entries with proper unit conversion.

A comparison of the PCTRAN results for RCS pressure to the FSAR Figure 14.3.2-27 shows a

fairly close agreement. A comparison of the PCTRAN results for Volume of water in the RCS to

FSAR Figure 14.3.2-23 also shows consistent results. The PCTRAN plots show the top of the

core becomes uncovered after 50 seconds and the ECCS completes covers the core at around 185

seconds. This is consistent with the FSAR plots, however PCTRAN uncovers the core slightly

earlier than the FSAR. This is probably due to the uncertainty of the core and RCS volumes

used in the FSAR analysis.

The 2-inch break was also analyzed with PCTRAN. The 2-inch break was simulated by entering

20.27% of Malfunction 2 (20.27-cm2) . The RCS pressure and RCS water volume are compared

with Figs. 14.3.2-20 and 14.3.2-24. As with the 6-inch break discussed previously, the 2

charging pumps’ head curve, given by Fig. 14.3.2-19 (for Case 1- 2 Pumps; all lines delivering),

is used for the analysis. A comparison of the PCTRAN results for RCS pressure and volume

with the FSAR results (FSAR Figures 14.3.2-20 and 14.3.2-24) shows the PCTRAN results to be

consistent with the FSAR.

114

Small Break LOCA (6 in.)


Initial Condition

(IC #)

Malfunction

(#/%)

Interactive

Control

(panel/%)

Output

Variable

(Name)

Range

(min/max/

unit)

1 2/182.4% Trip both RC

pumps

TFPK

TFSB

TPCT

LVPZ

P

PSGA/B

NSGA/B

LSGA/B

WSTA/B

WFWA/B

WRCA/B

FRCL

LVCR

LWRB

PRB

PRBA

TRB

WHPI

WCFT

WLPI

WLR

HLW

VOL

0/900 (C)

0/900 (C)

0/900 (C)

0/100 (%)

0/200 (bar)

0/100 (kg/cm2)

0/100 (%)

0/20 (M)

0/3000 (t/hr)

0/4000 (t/hr)

0/50 (Kt/h)

0/100 (%)

0/5 (M)

0/10 (M)

0/2 (kg/cm2)

0/2 (kg/cm2)

0-200 (C)

0-200(t/hr)

0/200 (t/hr)

0/200 (t/hr)

0/1500(t/hr)

0/3000 (Kj/kg)

0/180 (m3)

115

Small Break LOCA (2 in.)


Initial Condition

(IC #)

Malfunction

(#/%)

Interactive

Control

(panel/%)

Output

Variable

(Name)

Range

(min/max/

unit)

1 2/20.27% Trip both RC

pumps

TFPK

TFSB

TPCT

LVPZ

P

PSGA/B

NSGA/B

LSGA/B

WSTA/B

WFWA/B

WRCA/B

FRCL

LVCR

LWRB

PRB

PRBA

TRB

WHPI

WCFT

WLPI

WLR

HLW

VOL

0/900 (C)

0/900 (C)

0/900 (C)

0/100 (%)

0/200 (bar)

0/100 (kg/cm2)

0/100 (%)

0/20 (M)

0/3000 (t/hr)

0/4000 (t/hr)

0/50 (Kt/h)

0/100 (%)

0/5 (M)

0/10 (M)

0/2 (kg/cm2)

0/2 (kg/cm2)

0-200 (C)

0-200(t/hr)

0/200 (t/hr)

0/200 (t/hr)

0/1500(t/hr)

0/3000 (Kj/kg)

0/180 (m3)

116

FSAR Section 14.3.2 (6 in Small Break LOCA, PCTRAN U2LP Results)

0

20

40

60

80

100

120

140

160

180

0 50 100 150 200 250 300 350

Time (sec)

Pre

ss

ure

(k

g/c

m^

2)

RCS Pressure (P)


0

20

40

60

80

100

120

140

160

180

0 50 100 150 200 250 300 350

Time (sec)

Vo

lum

e (

m^

3)

RCS Volume (VOL)

117


0

100

200

300

400

500

600

700

800

900

0 50 100 150 200 250 300 350

Time (sec)

Te

mp

era

ture

(d

eg

C)

TFSB

TFPK

TF

TPCT


0

10

20

30

40

50

60

0 50 100 150 200 250 300 350

Time (sec)

Pre

ss

uri

ze

r L

ev

el

(%)

LVPZ

118


0

10

20

30

40

50

60

0 50 100 150 200 250 300 350

Time (sec)

Pre

ss

ure

(k

g/c

m^

2)

PSGA

PSGB


0

10

20

30

40

50

60

0 50 100 150 200 250 300 350

Time (sec)

Ste

am

Ge

ne

rato

r L

ev

el

(%

)

NSGA

NSGB

119


11.65

11.7

11.75

11.8

11.85

11.9

11.95

12

12.05

0 50 100 150 200 250 300 350

Time (sec)

Ste

am

Ge

ne

rato

r L

ev

el

(m

)

LSGA

LSGB


0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 50 100 150 200 250 300 350

Time (sec)

Flo

w (

t/h

r)

WSTA

WSTB

120


0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 50 100 150 200 250 300 350

Time (sec)

Flo

w (

t/h

r)

WFWA

WFWB


0

2

4

6

8

10

12

14

16

18

0 50 100 150 200 250 300 350

Time (sec)

Flo

w (

Kt/

hr)

WRCA

WRCB

121


0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 50 100 150 200 250 300 350

Time (sec)

Cla

d F

ail

ure

(%

)

FRCL


0

0.5

1

1.5

2

2.5

3

3.5

4

0 50 100 150 200 250 300 350

Time (sec)

Le

ve

l in

Co

re (

M)

LVCR

122


0

1

2

3

4

5

6

7

0 50 100 150 200 250 300 350

Time (sec)

Wa

ter

Le

ve

l in

Re

ac

tor

Bu

ild

ing

(M

)

LWRB


0

0.5

1

1.5

2

2.5

0 50 100 150 200 250 300 350

Time (sec)

Pre

ss

ure

(k

g/c

m^

2)

PRB

PRBA

123


0

20

40

60

80

100

120

0 50 100 150 200 250 300 350

Time (sec)

Te

mp

era

ture

(d

eg

C)

TRB


0

200

400

600

800

1000

1200

0 50 100 150 200 250 300 350

Time (sec)

Flo

w (

t/h

r)

WHPI

WCFT

WLPI

124


0

1000

2000

3000

4000

5000

6000

0 50 100 150 200 250 300 350

Time (sec)

Bre

ak

Flo

w (

t/h

r)

WLR


0

500

1000

1500

2000

2500

3000

0 50 100 150 200 250 300 350

Time (sec)

Bre

ak

En

tha

lpy

(k

J/k

g)

HLW

128


0

20

40

60

80

100

120

140

160

180

0 200 400 600 800 1000 1200 1400 1600

Time (sec)

Pre

ss

ure

(k

g/c

m^

2)

RCS Pressure (P)


0

20

40

60

80

100

120

140

160

180

0 200 400 600 800 1000 1200 1400 1600

Time (sec)

Vo

lum

e (

m^

3)

RCS Volume (VOL)

129


0

100

200

300

400

500

600

700

800

900

0 200 400 600 800 1000 1200 1400 1600

Time (sec)

Te

mp

era

ture

(d

eg

C)

TFSB

TFPK

TF

TPCT


0

20

40

60

80

100

120

0 200 400 600 800 1000 1200 1400 1600

Time (sec)

Pre

ss

uri

ze

r L

ev

el

(%)

LVPZ

130


0

10

20

30

40

50

60

70

0 200 400 600 800 1000 1200 1400 1600

Time (sec)

Pre

ss

ure

(k

g/c

m^

2)

PSGA

PSGB


0

10

20

30

40

50

60

0 200 400 600 800 1000 1200 1400 1600

Time (sec)

Ste

am

Ge

ne

rato

r L

ev

el

(%

)

NSGA

NSGB

131


11.4

11.6

11.8

12

12.2

12.4

12.6

12.8

13

13.2

13.4

0 200 400 600 800 1000 1200 1400 1600

Time (sec)

Ste

am

Ge

ne

rato

r L

ev

el

(m

)

LSGA

LSGB


0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 200 400 600 800 1000 1200 1400 1600

Time (sec)

Flo

w (

t/h

r)

WSTA

WSTB

132


0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 200 400 600 800 1000 1200 1400 1600

Time (sec)

Flo

w (

t/h

r)

WFWA

WFWB


0

2

4

6

8

10

12

14

16

18

0 200 400 600 800 1000 1200 1400 1600

Time (sec)

Flo

w (

Kt/

hr)

WRCA

WRCB

133


0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 200 400 600 800 1000 1200 1400 1600

Time (sec)

Cla

d F

ail

ure

(%

)

FRCL


0

0.5

1

1.5

2

2.5

3

3.5

4

0 200 400 600 800 1000 1200 1400 1600

Time (sec)

Le

ve

l in

Co

re (

M)

LVCR

134


0

2

4

6

8

10

12

14

0 200 400 600 800 1000 1200 1400 1600

Time (sec)

Wa

ter

Le

ve

l in

Re

ac

tor

Bu

ild

ing

(M

)

LWRB


0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 200 400 600 800 1000 1200 1400 1600

Time (sec)

Pre

ss

ure

(k

g/c

m^

2)

PRB

PRBA

135


0

10

20

30

40

50

60

70

80

0 200 400 600 800 1000 1200 1400 1600

Time (sec)

Te

mp

era

ture

(d

eg

C)

TRB


-50

0

50

100

150

200

250

300

350

400

450

500

0 200 400 600 800 1000 1200 1400 1600

Time (sec)

Flo

w (

t/h

r)

WHPI

WCFT

WLPI

136


0

100

200

300

400

500

600

700

800

0 200 400 600 800 1000 1200 1400 1600

Time (sec)

Bre

ak

Flo

w (

t/h

r)

WLR


500

700

900

1100

1300

1500

1700

0 200 400 600 800 1000 1200 1400 1600

Time (sec)

Bre

ak

En

tha

lpy

(k

J/k

g)

HLW

139

3.2.12 Large Break LOCA

In the FSAR, large break LOCAs of 0.5 ft2, 3 ft

2, and 6 ft

2 sizes are discussed. A double-ended

break of the cold leg is also discussed. In PCTRAN benchmarking was done with just the 3 ft2

break size.

Choosing malfunction #2 simulated a cold leg break size of 3.0 ft2. A break size of 2800 cm

2

was entered. The simulation was run with initial condition #1. Clad temperature starts to

increase 20 seconds into the accident and peaks at about 450 C. This is less than the reported

value of 1700 F found in the FSAR. Reactor pressure, RCS volume, and peak clad temperature

are graphed over the first several seconds of the accident.

140

5 0

6 0

7 0

8 0

9 0

1 0 0

1 1 0

1 2 0

1 3 0

1 4 0

1 5 0

1 6 0

1 7 0

1 8 0

1 9 0

2 0 0

0 2 0 4 0 6 0 8 0 1 0 0 1 2 0

T im e ( s e c )

FS AR Fig ure 14 .3 . 2 -3 La rge Brea k L OCA (3 sq . ft. )

P C T ra n

3 / 1 / 2 0 0 1 1 1 :1 1 :1 5 A M

V O L ( M 3 )

0

1 0

2 0

3 0

4 0

5 0

6 0

7 0

8 0

9 0

1 0 0

1 1 0

1 2 0

1 3 0

1 4 0

1 5 0

1 6 0

0 2 0 4 0 6 0 8 0 1 0 0 1 2 0

T im e ( s e c )

FS AR Fig ure 14 .3 . 2 -1 3 L arg e Bre ak LO CA (3 sq. ft . )

P C T ra n

3 / 1 / 2 0 0 1 1 1 :0 8 :2 3 A M

P (k g / c m 2 )

141

0

1 0 0

2 0 0

3 0 0

4 0 0

5 0 0

0 2 0 4 0 6 0 8 0 1 0 0 1 2 0

T im e ( s e c )

FS AR Fig ure 14 .3 . 2 -1 7 L arg e Bre ak LOCA (3 sq. ft . )

P C T ra n

3 / 1 / 2 0 0 1 1 1 :1 2 :1 6 A M

T P C T (° C )

145

3.4 Severe Accidents

Accidents beyond design basis, i.e. multiple failure of equipment or human error exceeds

licensed criteria result in core-melt and/or containment failure. Three cases are analyzed here.

The first is the March 29, 1929 event at Three Mile Island in Pennsylvania, USA and other two

are hypothetical ones.

3.3.1 TMI Accident Scenario

TMI-2 Accident scenario is reproduced here. For the following sequence of events:

1. loss of the condensate pump leading to loss of both main feedwater pumps.

2. Both sides’ AFW isolation valves are tagged out of service so that AFW is never

available.

3. After the SG’s are boiled dry and the primary pressure increases to lift the PORV, it stays

open despite the pressure drops below the reseat set point.

4. Continued two-phase discharge through the PORV elevates the indicated pressurizer

level at a high level. The operator turns off the HPI pumps.

5. Bulk boiling takes place in the reactor core. It is witnessed by diminishing sub-cooling

margin and a void in the reactor vessel head.

6. After the core is uncovered, the clad temperature increases rapidly and reacts with steam

to generate hydrogen.

7. Hydrogen is released through the stuck-open PORV and ruptured coolant drain tank. Its

concentration is observed in the containment.

Run Time = 10,000 seconds

Initial

Condition (IC

#)

Malfunction and

Interactive Control

Output

Variable

(Name)

Range

(min/max/

unit)

1

1. Disable both AFW

isolation valves

(MF=100%)

Trip the condensate

pump after steady state

operation at 100 %

power.

2. After reactor trip by

low SG level in about

50 seconds, observe SG

level goes down to dry

in about 3000 seconds.

3. When the RC

TBLD

PWTH

PWNT

THA/THB

TCA/TCB

TFPK

TFSB

TPCT

LVPZ

P

PSGA

NSGA/B

LSGA/B

CNH2

0/120(%)

260/350(C)

0/900 (C)

0/100 (%)

0/200 (bar)

0/100 (%)

0/10 (/%)

146

pressure increases to lift

the PORV, use

malfunction to lock the

valve open at 100%.

4. When the RC

pressure drops to initiate

the HPI, observe the

pressurizer level goes

up to full (100%).

5. Disable both HPI

pumps and trip both RC

pumps on vibration

caused by RC

saturation.

6. Observe the reactor

head becomes voiding,

then core uncovered.

7.Observe hydrogen

generation when the

peak clad temperature

exceeds 1000 C.

8. When the

containment hydrogen

concentration exceeds

5%, it burns.

WHPI

WUP

HUP

PRB

LRB

TRB

0-100 (t/hr)

-100/100

0-4000 (KJ/Kg)

0-10 (kgf/cm2)

0-15 (M)

(0-100) (C)

The following mimic shows at 3770 seconds into the transient, the SG’s are empty, one PORV

stuck open, the pressurizer level stays high so that HPSI pumps are tripped, and a bubble is

formed in the vessel head. When the clad temperature exceeds 1000ºC, metal-water reaction

generates a large amount of hydrogen. If there is a spark when the concentration is above 5%, it

may burn. We simulate this by setting MF5 to activate a spark and burn. Sudden containment

pressure and temperature spikes with big noise correspond to hydrogen burns. The subsequent

transient plots successfully reproduce the TMI sequence. We simulate this by changing the

containment background color into red and orange.

152

3.3.2 Large Break without ECCS

A 2000 cm2 cold leg severe accident case was run by disabling the accumulators, HPI and LPI

pumps. The core was rapidly exposed and start to melt, collapsed and melt through the vessel

bottom. The containment pressure surged briefly when the vessel failed. Hydrogen

concentration in the containment built up but it did not explode because elevated containment

pressure that raised the detonation concentration. In the dose mimic the red area under the melt

corium in the reactor cavity floor symbolizes corium-concrete-interaction (CCI) with aerosol

generation in the containment. At this point should we further select Malfunction 14 for

containment failure and type in a large failure fraction (the containment vessel is designed to

leak less than 1% per day at design pressure), a large release rate will be presented in the

containment mimic with elevated site boundary doses. The source term can be saved into

DoseData.mdb file for RadPuff offsite dose projection. All important severe accident

phenomena are reproduced in this case.

154

3.3.3 Station Blackout

A station blackout loses both offsite AC and onsite diesel power. Only turbine-driven AFW

pump is operating to provide feedwater to the steam generators. Here it is also assumed not

available. Only DC-operated pressurizer and SG PORV’s are operating to relieve pressure.

In the following transient figures, the steam generators are boiled dry following loss of all

feedwater. The primary coolant pressure increases to cycle the pressurizer PORV. When the

pressurizer level reaches the top, discharge turns into two-phase that ruptures the drain tank and

pressurizes the containment. Continued coolant loss exposes the core to melt and vessel failure.

159

4.0 Theory and Mathematical Models

The basic PCTRAN mathematical model [1,2,3,4] was selected for the framework of the PWR

project. The following sections describe the basic theory and thermal hydraulic models in detail.

A reduced-node approach (compared to the full-scope simulator) was used to model the primary

coolant system. For PWRs, a non-equilibrium pressurizer model handles its normal controls by

the spray, heater and relief valves. It also allows sudden changes and extreme conditions such as

"water solid" in the pressurizer and two-phase in the reactor core. The steam generators are

modeled as homogeneous equilibrium two-phase volumes. Heat transfer from the primary to the

secondary is treated rigorously during both forced and natural circulation.

A point kinetics model for reactor power calculation and has added a containment model. By

including fuel and containment condition simulation in addition to the original NSSS model,

PCTRAN/U is a complete nuclear plant simulator.

In PCTRAN/U, the loop flow model was revised to accommodate individual pump trip and

possible reversed flows. Modeling of the major plant control systems and improved heat transfer

correlation for the steam generators are included.

The fluid discharge rate from a break uses typical critical flow models. A mechanistic model of

the coolant flow covering both forced and natural circulation provides temperature distribution in

the primary coolant.

The containment conditions are calculated based on a homogeneous equilibrium model with

participation of non-condensable air and hydrogen. During a severe accident with the core being

exposed to steam for extended period of time, the core may become overheated. Zirconium in

the cladding may react with steam and hydrogen will be generated. Simulation of clad failure

and hydrogen content in the containment will be included in PCTRAN/U.

The mass and energy balance equations with co-relations in momentum and heat transfer are

solved for all control volumes simultaneously. Transient progress is handled by using Euler

integration over every time step increment. Key plant parameters are then displayed graphically

on a mimic.

160

4.1 Reactor Core Kinetics

A point kinetics model with one delayed neutron group and reactivity control from external

sources (e.g. control rods and boron injection) and feedback from moderator temperature,

Doppler and void was formulated. The point-kinetics equation is expressed by

(1)

(2)

where

n = neutron density

= reactivity

= delayed neutron fraction

= neutron life time

= decay constant

C = precursor concentration

Define

For the conventional unit of dollars for reactivity, R(t) is controlled externally by the control

rod's worth and boron concentration, and feedback by moderator and fuel temperatures, and

voids, i.e.

R(t) = Rex(t) + RM(t) + RD(t) + RV(t)

RM(t) = KM (Tavg(t) - Tavg(0))

RD(t) = KD (TF(t) - TF(0))

Cndt

dn

Cndt

dC

)()(

ttR

161

RV(t) = KV * VOID

Where RM, RD and RV are the reactivity coefficients for moderator temperature, fuel temperature

(Doppler) and void respectively. TF is fuel average temperature and VOID is a system-wise void

fraction defined in latter sections. In PCTRAN/U, a forward finite difference method is used to

solve Equations (1) and (2). A time step in the order of 0.001 seconds is required to achieve

numerical stability.

For one-group of delayed neutrons, the decay constant should be used between 0.0767 sec-1

and

0.405 sec-1

. In particular, =0.0767 sec-1

being appropriate for very slowly varying neutron

densities and =0.405-1

being suitable during very rapid changes.

Typical reactivity coefficients are used in the database for the generic model of each plant type.

During a power excursion, the user can set the reactivity worth corresponding to rod movements.

After a reactor trip or the core is shutdown to subcriticality by boron injection, the ANS 5.1 [5]

will be used for decay heat input.

162

4.2 Reactor Coolant System

The basic thermal hydraulics of the mathematical model is first-principle in mass and energy

balance. This ensures credible and realistic simulations. Instead of modeling numerous control

volumes around the coolant loop as most transient analysis codes did, a fluid boundary is

introduced that separates saturated two-phase fluid from subcooled liquid. For a PWR's primary

side, the former is initially the pressurizer and the latter is the rest of the RCS. During a

transient, the boundary is allowed to move upward or downward. Extreme and complicated

phenomena such as two-phase in the coolant loops, core uncovery, and even water-solid

conditions can be reproduced. For a BWR, the reactor core and steam dome form the two-phase

saturated region, while fluid in the remainder lower plenum and recirculation loops belongs to

the subcooled region.

The basic model is composed of two inter connected volumes. The upper two-phase volume,

with total volume V2, consists of a vapor space, which occupies a fraction of V2, and a

saturated liquid space. They are treated separately:

a. Saturated Two-Phase Volume

The specific enthalpies and volumes of liquid and vapor are denoted as hf, hg and vf and vg,

respectively. The quality, x, and mixture average enthalpy hm are related by:

/vg

x = (1)

/vg + ( 1 - )/vf

hm = x hg + ( 1- x ) hf (2)

The flow discharge leaving the two-phase volume is denoted with flow rate W22 and enthalpy

h22. W12 and h12 in Figure 3.1 correspondingly express the inter-connecting flow. Then the

conservation of mass requires:

dM2

= W12 - W22 (3)

dt

For conservation of energy, we shall model the nuclear core heat being generated in this volume

163

Figure 4.1 – PCTRAN Schematic

164

dU

= W12 h12 - W22 h22 (4)

dt

Where U is the total internal energy in this volume, and is expressed by:

U = M2 ( hm - P vm ) (5)

Where M2 is the total mass, P is the system pressure, and vm is the average specific volume.

Note that there is no elevation assumed in this model, therefore the upper two-phase region and

the lower subcooled region have the same pressure. There is no friction loss along the flow paths

either; thus the inter-connecting flow W12 is modeled for balancing the mass between the two

volumes only. Substituting (5) and (3) into (4) we obtain:

dhm 1 dP

= [W12(h12 – hm) – W22 (h22 - hm ) + V2 ___ ]

dt M2 dt (6)

From Equation (2), its derivative with respect to time is:

dhm (hm)x dP (hm)p dx

= + _____ ___

dt p dt x dt

(7)

Equate Equation (6) and (7), we obtain:

dt

dxh

dt

dP

dP

dhx

dP

dhx fg

fg

)1(

165

dx dhg dhf V2 dP

hfg + [ x ( ) +( 1 - x) ]

dt dP dP M2 dt

1

= [W12 (h12 - hm ) - W22 (h22 - hm )] (8)

M2

This equation is in the form of a first order linear differential equation of x and P. In order to

solve both, another equation is required. It is found in the equation of state of the system:

V2 = M2 [ xg v + (1-x) vf ]

= V2 (x, P, M2 )

= constant

Thus

(9)

By rearranging the terms and substituting (3) for dm2/dt, we have:

dt

dM

M

V

dt

dP

P

V

dt

dx

x

V

dt

dV

PxxMMP

2

,2

2

,

2

,

22

0

)1()1( 2

22

dt

dMvxxv

dt

dP

dP

dvx

dP

dvxM

dt

dxvvM fg

fg

fg

166

= ( W22 - W12 ) [ x vg + ( 1- x) vf ] (10)

Equations(8) and (10) are simultaneously existing and thus readily solvable for x and P if the

surge line condition W12 and h12 is known. It should be noted that saturation is maintained all

the time during transient and the derivatives of h and v with respect to P are evaluated along the

saturation lines.

dt

dP

dP

dvx

dP

dvxM

dt

dxvM

fg

fg

)1(22

167

b. The Subcooled Liquid Region

Assuming that the ECCS injection flow is the only flow into this region and the LOCA break

flow Wok is the net loss, conservation of mass and energy balance equations in the subcooled

region results in

(11)

where hs, the specific enthalpy for the subcooled liquid, is a function of the system pressure and

the liquid temperature T

hs = hs ( P, T ) (12)

Substituting (12) into (11) we have:

(13)

Similarly the equation of state for subcooled liquid is expressed by:

V1 = M1 vs ( P, T ) = constant

Thus

0dt

dV

dt

dM

M

V

dt

dV S

MS

11

1

11

1S

The conservation of mass requires:

LR12EC1 WWW

dt

dM

SGCssLRLRsECEC

s QQdt

dPVhhWhhWhhW

dt

dhM

112121 )(

SGCs1212sLRLRsECEC

P

s

1

T

s

11 QQhhW)hh(WhhWdt

dT

T

hM

dt

dP

P

hMV

168

By rearranging these three equations, we have:

(14)

Equation (13) and (14) are linear simultaneous equations for P and T, and are also solvable for a

given set of inter-connecting flow W12 and enthalpy h12. For the enthalpy, we have made a

simple assumption that it is the upstream enthalpy, i.e. when the flow is going upward, it is set

equal to hs, and when W12 is in the opposite direction, it is set equal to hf, the saturated liquid

enthalpy in the upper volume. Having derived Equations (8), (10), (13) and (14), they are in the

format of:

. .

A x + BP = C W12 + M

. .

D x + EP = F W12 + N

. .

J P + KT = L W12 + Q

. .

G P + HT = I W12 + R

. . .

These first order linear simultaneous equations are easily de-coupled for dx/dt, dP/dt, dT/dt, and

W12.

Direct integration will result in the transient variables of P, x, and T. The quality x is then

converted to the system level or void fraction.

The Euler integration method is chosen for numerical integration. A correction to the slope of a

variable is introduced if the Euler convergence is checked to become unstable.

LR12ECs

P

s1

T

s1 WWWv

dt

dT

T

vM

dt

dP

P

vM

169

4.3 Break Discharge Model

If a break is within the subcooled region and the water level is above the break, the choking

orifice flow by Zaloudek [6] will be

If the break is located in the saturated region's liquid phase, Moody's liquid critical flow [7] will

be used. If it is located in the vapor phase, the vapor critical flow will be used.

4.4 Reactor Coolant Flow Model

PCTRAN/U uses a semi-empirical method for reactor coolant flow that encompasses both forced

and natural circulation conditions. For forced circulation when the reactor coolant pumps are on,

full (volumetric) rated flow is assumed. In the event that the pumps remain operating while the

system is flashing, the volume occupied by the void reduces the flow. Once the pumps are

tripped, the flow coasts down exponentially until stable natural circulation is established.

The reactor hot and cold leg temperatures for a PWR are calculated by the heat balance from the

reactor core and removal rate by the steam generators at a given loop flow rate

.

Where Tavg is the RC average temperature

2

2

TTT

TTT

CW

QT

AvgC

AvgH

pRC

SG

2/1

1 81.02

sat

f

c

LR PPv

gAW

170

4.5 Steam Generator

For a PWR, a steam generator's secondary side is modeled as a separate saturated two-phase

volume in thermal contact with the primary. To accommodate asymmetric events, a second

steam generator has also been included. For PWR plants with more than two steam generators,

the steam generators are lumped into two loops.

Total heat flux is given by:

Q = uw Aw (Tavg - TSG )

where

uw = heat transfer coefficient (KW/m2/hr)

Tavg = reactor primary coolant average temperature (C)

Tsg = SG secondary saturated temperature (C)

Aw = wet tube surface area (m2)

The wet surface area is a constant if all tube bundles are submerged under the SG water level.

This is true for most operating conditions. During a loss of feedwater event, heat transfer will be

significantly retarded if the SG water level falls below the top of tube bundles, it is modeled by

proportion to the water level height.

The simplified heat transfer equation is a good approximation to the rigorous log-mean

expression. From the primary to the secondary side, the overall heat transfer coefficient is

related to the individual ones by:

where u1 and u2 are heat transfer coefficients for the reactor coolant to the wall and wall to

secondary coolant respectively, and k is heat conductance of the metal and d is the thickness.

During transients u1 is related to the primary coolant flow according to the Dittus-Boetler

correlation:

21

111

uk

d

uuw

171

u1 WRC 0.8

= _______

u10 WRC00.8

Similarly, we shall use the average of the steam and feedwater flows to represent secondary

flow:

During a primary coolant pump trip, the reduced flow rate affects the primary side heat transfer

coefficient, which in turn affect the overall heat transfer rate. Similarly secondary side feedwater

pump loss or turbine trip will affect the heat transfer also. However, even if the forced flow is

completely ceased, natural circulation will proceed. This revised model presents a rigorous

calculation of heat transfer rate for all possible conditions in the reactor coolant system.

4.7 Emergency Core Cooling System

A PWR's HPSI and LPSI are modeled as simple flow injections into the RCS. Flows are

functions of the back-pressure of the reactor coolant according to the corresponding pump's head

curve. Similarly are the RCIC, HPCI, HPCS, LPCI and LPCS of a BWR. Generally a spray

system has somewhat different effect from an injection system. It is more effective in pressure

reduction to the control volume it sprays into. On the other hand, an injection stream tends not to

mix with the fluid in the control volume it enters into completely. It is mostly for coolant

makeup and has a delayed effect in affecting the other thermodynamics parameters such as

pressure and temperature. These have been considered in the PCTRAN/U ECCS models.

The accumulator tanks are filled with nitrogen gas. The adiabatic expansion equation

PV1.3

= constant

is used for calculating the gas transient pressure.

4.8 Containment

A dry containment model was used for PWRs. A simple mass and energy balance in a

8.0

8.0

020

2

2 FW

STMFW

W

WW

u

u

172

homogeneous and enclosed compartment was assumed. The total mass in the compartment

before the LOCA blowdown is the sum of air, vapor and liquid, i.e.:

MT = Ma + Mg + Mf

where

MT = Total mass

Ma = Air mass

Mg = Vapor mass

Mf = Liquid mass

At a given compartment temperature T and pressure P, the total pressure is:

P = Pa + Pw

where

Pa = Partial pressure of air

Pw = Partial pressure of vapor

= Psat (T)

assuming 100% humidity, then

where

V = Total compartment volume

a

aw

a

wg

w

g

wf

w

f

TR

PALVM

Pv

ALVM

Pv

ALM

173

Lw = Water level in compartment

A = Cross section area of the compartment

Ra = Gas constant for air

T = Absolute temperature

The ideal gas law has been used. The initial total energy in the compartment is:

U = Mf hf(Pw) + Mg hg(Pw) + Ma Cv T

In the following time increment, a net blowdown water mass Mw with specific enthalpy hb is

introduced into the compartment. More generally, a net increment of non-condensable air at

temperature T1 and energy input U through a heat exchange process is also introduced into this

compartment. Then the new mass and energy balance is:

Ma' = Ma + Ma

Mw' = Mw + Mw

U' = U + Mw hw + Ma Cv T1 + U

Since the compartment is confined to a constant volume, the new specific volume of water is:

vw' = V

Mw'

The new equilibrium temperature and pressure after blowdown, T' and P', and the vapor quality

x' are related by:

vw' = x' vg' (Pw') + (1 - x') vf' (Pw')

Pw' = Psat(T')

The average water specific enthalpy is given by

hw' = x' hg' + (1 - x') hf'

From above

174

vw' - vf'

x’ = _______

vg' - vf'

The new total internal energy is also given by

U' = Ma' Cv T' + Mw' hw'

By equating the two equations of U', the only unknown is T', the new compartment temperature.

It can be solved by the Newton iteration method.

After it is solved, the steam table and the specific volumes give the new vapor partial pressure

for vapor and liquid at that pressure can be found. Then the new water level is related to liquid

mass by:

Lw' = V (1 - x') vf'

A [x' vg' + (1 - x') vf']

The new partial air pressure is then given by:

Pa' = Ma' Ra T

V - A Lw'

Finally, the new total pressure is

P' = Pa' + Pw'

4.9 Severe Accident Degraded Core Model

A simplified model accounting for the temperatures of fuel and cladding has been constructed in

PCTRAN. This model can simulate: 1) thermal power transmitted into the coolant in contrast to

nuclear power generated by the core during normal operation; and, 2) fuel and cladding heatup

during accident conditions. Core thermal power QMWT is represented by

175

QMWT = UF * (TF - Tavg)

Where TF is the known average fuel temperature at 100% rated power. The heat transfer

coefficient UF is then calculated such that the core thermal power is equal to the neutron power

from the kinetics equation at steady state.

Transient fuel temperature will be calculated by the imbalance between nuclear power and

thermal power. When the PCTRAN calculated core water level is below the top of the fuel,

temperature of the exposed sector of fuel rod will increase because steam cooling is much less

effective than liquid contact at the fuel surface.

Peak clad temperature is a major concern for reactor safety analysis. It is generally designed not

to exceed 1000C. Beyond that water-zirconium reaction becomes possible. The chemical

reaction is in the form of [ref 22]

Zr + 2 H2O -> ZrO2 + 2 H2 + ΔQ1

'The reaction rate is temperature-dependent, and given by

K1 = 3300 exp (-22900/T) (kg/M2)2/sec, T in Kelvin

ΔQ1 = 6.5E6 J/Kg-Zr

If there is oxygen present, oxidation may also take place. The equations are:

Zr + O2 -> ZrO2 + ΔQ2

K2 = 52.67 exp (-17597 /T) (kg/M2)2/sec, T in Kelvin

ΔQ2 = 4.1E6 J/Kg-Zr

Hydrogen generation is modeled in PCTRAN. The heat and hydrogen generation will contribute

to the reactor vessel and containment condition calculations.

This simplified model will show a rise in peak fuel temperature and clad temperature when the

core is uncovered and lowering, and a gradual decrease in temperature when ECCS refills the

176

core. When the core is completely reflooded, the cladding temperature will be the same as the

water temperature.

From the calculated peak clad temperature and reactor coolant condition, there are published

relations for estimating the extent of core damage. In the USNRC's "Severe Reactor Accident

Incident Response Training Manual" [17], there is possible core damage as function of core

temperature and percent of fuel rods with ruptured cladding vs. maximum core exit temperature

(Figs.5.5 and 5.6). In PCTRAN, the calculated peak cladding temperature, TPCL, was assumed

as the maximum core exit temperature, and the correlation was incorporated in tabulated form

for estimate of the percent of fuel rods with failed cladding, FRCL.

This calculation must be used with caution and may be considered as only gross indicators of

core damage conditions. Great uncertainties exist as phenomena of severe accidents, and fuel

damage are still under intensive research. However, for an emergency exercise, the calculated

extent of core damage may serve as an estimate of fission gas and core radioactivity release

source term. Combined with the calculated coolant discharge in the containment, containment

dose rate can be estimated. Furthermore, PCTRAN also generates leakage rates through the

containment. Therefore, radioactivity release outside the containment and offsite dose can be

estimated according to dispersion models.

A severe accident is defined as beyond design-basis with significant core damage and

containment failure. A borderline is usually set in probability safety assessment (PSA) Division

2 for top of the fuel (TAF) uncovery, and Division 3 for fission product relocation. Our previous

models have actually covered core heatup and hydrogen generation by metal-water reaction. The

current addition is concentrated in core-melt.

The core is modeled into six vertical nodes. Each one will generate a portion of the decay heat.

When the boundary heat removal rate is less than the core heat, the core node is heated up to the

point of melting. Molten fuel may collapse into the bottom of the vessel. The vessel lower head

177

may then heat up to the melting point, too. The molten debris may drop into the containment

cavity floor. During the fuel damage process, first the fission gas in the clad may leak out. Later

if the fuel and cladding continue their degradation, fuel isotopes will release also. In addition to

iodine and noble gases, there are alkali metals, tellurium, barium, cerium, lanthanides, etc. The

elevated concentration of these radioactive isotopes would find their ways through the vessel

break, relief valves, and containment leakage into the environment.

In conducting a test run, you can initiate a large break LOCA, e.g. 2000 cm2 hot leg break for

the PWR or recirculation line break for the BWR. With automated initiation of ECCS, the core

will soon be reflooded and no significant clad damage is expected. So we purposely disable all

ECCS trains. The water level in the vessel then drops rapidly and soon exposes the fuel. You

should click the “View” button in the top menu bar and choose “Dose mimic”.

178

Figure Percent of Fuel Rods with Ruptured Cladding vs. .Maximum Core Exit Thermocouple

Temperature

179

Core-Concrete Interaction Model

In the event that the molten core heats up the vessel bottom and melts through it, the debris falls

into the reactor cavity (drywell pedestal for BWR). It is called corium as the metal interacts with

concrete and form a slump. At lower temperatures, degassing of concrete occurs and both steam

180

and carbon dioxide can be released. At higher temperatures concrete can also be melt and mixed

with metals. Since concrete is normally formed by Ca, Fe, Si, Al, Na, Mg, Mn, Cr, etc. with

variable compositions. Typical fractions are:

Mass fraction of

concrete Component

0.3288 CaO

0.357 SiO2

0.067 Al2O3

0.0533 H2O

0.1939 CO2

The most important reactions are:

Fe + CO2 -> FeO + CO + Q1

Fe + H2O-> FeO + H2 + Q2

Ni + H2O -> NiO + H2 + Q3

Zr + H2O -> ZrO2 + H2 + Q4

2 Cr + 3 H2O -> Cr 2O3 + 3 H2 + Q5

Where Q1 = -337 Joule/gm

Q2 = 22.3 Joule/gm

Q3 = 22.3 Joule/gm

Q4= 7760 Joule/gm

Q5 = 7760 Joule/gm

Each reaction rate is temperature-dependent and given by the parabolic law:

K = R5 exp (-G/T) (kg/M2)2/sec, T in Kelvin

181

To keep track of every reaction is too tedious for a simplified code. Therefore we lump all them

together into a single form similar to the above Zr-H2O or Zr-O2 equations. Leaving the reaction

rate and exothermal heat as typical values for adjustment.

In the core Zr-water reaction calculation, cylindrical geometry has been used for vertical tube

bundle configuration. For CCI it is instead a semi-hemisphere configuration to represent the

slump pile of debris. The top hemisphere interacts with atmosphere above, and the bottom flat

surface interacts with concrete floor. A red slab represents the molten pool of concrete in the

mimic display. Following are dose mimics for BWR and PWR plants respectively.

The concrete penetration depth is limited by the corium temperature decrease during a transient.

As soon as the corium temperature is reduced to below the reaction threshold temperature, the

reaction is stopped. Another limit is the total amount of core mass. As soon as the whole core

dropped into the containment has completely reacted with concrete, no further actions are

possible. Whichever comes first will stop further propagation of CCI. Heat generation by CCI is

182

not explicitly displayed or tracked as an output variable, since there is no way to be verified or

benchmarked against experimental or other code predictions.

There are specific input data entries, intermediate data for restart, and output variables for the

core-melt model. Input is already included at the end of Basic Data table. Intermediate data are

in Table ICCoreData. They are usually not required for running a case. But for debugging

purpose following is a list for its description:

PCMELT / PCTRAN common

variables

Name in PCMELT Description Unit Type PCMELT

input/output

AFUN Heat transfer area of node m2 Real*8,parameter -

AFUT Total core heat transfer area m2 Real*8,parameter -

COOLTR Total heat transfer from core (last step) kJ Real*8 output

DWHT Heat transfer from debris in lower DW kJ Real*8 output

QH2 Total oxidation energy kJ Real*8 output

LFUN Length of node m Real*8,parameter -

LFUT Total lenght of fuel element m Real*8,parameter -

MCRT Total mass of control rods kg Real*8,parameter -

MH2T Total mass of H2 kg Real*8 output

MNODSUH Total node mass ratio (1 to0) Real*8 output

MUO2T Total mass of UO2 kg Real*8,parameter -

MVES Mass of vessel bottom kg Real*8,parameter -

MZRKT Total mass of fuel channel (Zr) kg Real*8,parameter -

MZRST Total mass of fuel cladding (Zr) kg Real*8,parameter -

NDS Number of core nodes Integer, parameter

PCMELT PCMELT code in operation (1 = yes) Integer, parameter

SCLADFAIL Damaged cladding rate (0 to 1) Real*8 output

TTN Node average temperature °C Real*8 output

TVES Temperature of reactor vessel bottom °C Real*8

VAL Core plate rupture (0 to 1) Integer

VESBK Reactor vessel rupture (0 to 1) Integer

183

5.0 Radiation Monitoring System and Source Term Model

The first barrier is the fuel pellet. After a reactor reaches full power, the fuel elements undergoes

thermal expansion and gaseous fission products will find their way through cracks to the gap

between the pellet and cladding. Noble and volatile fission product gases are typical for the

isotopes of iodine, cesium and tellurium.

The second barrier to release is fuel cladding or pins, prevents the fission products from entering

the reactor coolant. Currently all light water reactor fuel designs are limited to less than 0.1%

failure rate over the in-core time of the fuel pins.

The third barrier is the containment. The design leakage rate is 0.1% per day at design pressure.

Sump recirculation following a large break LOCA provides a leakage path through the Auxiliary

Building. Following is a list of the possible pathways:

- Radio-nuclide Transport From the Fuel Pallets Into the Gap

- Radio-nuclide Transport From the Fuel cladding into the Coolant

- Loss of Coolant Accident Transport from the Coolant to the Containment

- Containment design basis leakage and failed-to-closed isolation valves

- Routine Effluent Releases for Condenser

- Steam line Safety and PORV release to the Atmosphere

- Letdown line and ECCS Recirculation from the RB sump into the Auxiliary Building

- Auxiliary Building vent

For TCP's Third NPP PWR, being a pressurized water reactor, the following model governs

fission product transport.

184

5.1 Radiological Dose Release (Source Term) Calculation Model for PWR

1. Fission Product Inventory

The radiation sources associated with a gap-activity-release accident are based on the assumption

that the fission products in the space between the fuel pellets and the cladding of all fuel rods in

the core are released as a result of cladding failure. The gap activities were determined using the

model of Regulatory Guide 1.25. Specifically, 10% of the iodine and 10% of the noble gas

activity (except Kr-85 which is 30%).

2. Activities in the Reactor Coolant and Secondary System

The reactor coolant equilibrium activities are based on less than 1% failed fuel. Table 11.1-2

provides the concentrations and is reproduced as Table __. The steam generator blow-down

before converting into steam and entering the turbine treats the radioactive material and chemical

impurities

The secondary system activity used in the analysis of accidents is based upon the following

assumptions:

- Design basis 1.0 gal/min primary-to-secondary leak rate

- Total steam generator blowdown rate of 238 gpm

- Operation of the 50% flow condensate polishing demineralizers

The SG activities are for a typical PWR plant.

During normal operation, production of the fission products and their removal reach an

equilibrium value. That must be under a Technical Specification limit typically about 0.1% of

the fuel gap content. For a design basis LOCA, RG 1.4 and TID-14844 specifically requires

50% of iodine is released from the core, and of which 50% is plated out in the containment. So

there is 25% stay in the coolant. For noble gases 100% is released. Then the coolant

concentration for each isotope is increased by the given factor. The original equilibrium

concentration becomes negligibly small relative to the design base source term.

Where

Ci = Isotope concentration (Ci/gm)

ff = Fuel or clad failure fraction

RC

i

iM

FPffC

185

FPi = Fuel or clad isotope inventory (Ci)

3. Transient Calculation Methodology of Activity

For an isotope's concentration in the reactor coolant during a transient, it follows the following

differential equation:

tCM

M

WPM

dt

tdCiRC

RC

LDiiRC

i

Where

i = 0.693/ Half life of the isotope (1/sec)

WLD = Letdown flow rate (gm/sec)

At steady state there is no additional fuel of clad failure, ff = 0, then the production rate Pi is given

by

Equilibrium Production rate for isotope i (Ci/sec) = (D + WLD/ MRCS ) MRCS Ci (0)

After reactor trip, letdown is isolated and the leakage rate is the steam generator tube leak rate. The

above differential equation can be solved either analytically or numerically.

4. Iodine Spike Factor

Following either a pre-accident transient or an accident-induced depressurization event,

additional fission product leaks out the existing cladding seams into the reactor coolant. Increased

reactor iodine concentration is called “spike”. The Standard Review Plan requires a conservative

spiking factor up to 500 times of normal equilibrium value to be used. Westinghouse has used both

the 500 value as a conservative upper value and a more realistic value of 60 in its steam generator

tube rupture (STGR) analysis. This rate should be applied to the production rate Pi above.

5. Flashing

Liquid discharge to a lower pressure environment will turn into steam following isenthalpic

expansion. Radioactive iodine associated with steam would have a change to release in the

subsequent process. Those staying in the liquid will not be released. The flashing fraction is given

by the isenthalpic expansion equation:

186

HLiq (Pi) = x hg + ( 1 - x ) h f

Where x is the quality or flashing mass fraction of liquid with enthalpy hLiq at high pressure that

would evaporate into steam at a lower pressure. ). hf and hg are the specific enthalpy of liquid and

steam respectively at the discharge point. For loss of coolant in the containment, flashing is

considered in the calculation. The factors can also be input in the database.

6. Partition Factor

Quantity of isotope in the gas phase as a fraction of the total (liquid and gas) is defined as partition

factor. For noble gases all are released so the PF is always one. For iodine Westinghouse used 0.01

in the steam generator and 0.0075 in condenser for initial condition. During a tube rupture event the

factor is 0.1 in the faulted SG (Table 15.1-5). For a steam line break 1.0 was assumed in the faulted

SG (Table 15.1-3).

7. Containment spray for iodine removal after a major LOCA

Containment spray has significant effect in removing elemental and particulate iodine. It has

little effect to organic iodine. When the spray is on, concentration in the sprayed region in the

containment will be determined by

Ci (t) = Ci (0) exp ( - t )

Where the spray removal constant, , for each form of iodine depends upon the spray droplet

size. In FSAR Table 15.6-10, the constant is 23.1/hr for elemental iodine and 0.45/hr for

particulate. When the concentration is reduced to a given level, defined as dose reduction factor,

equilibrium is assumed. There will be no further reduction. In the same table the reduction

factor (RF) for both elemental and particulate iodine is 100 (i.e. 1/100 times reduction).

8. Fan Coolers

Fan cooler operating in the containment mixes atmosphere between sprayed and unsprayed

regions. The concentrations in the sprayed region Cs(t) and unsprayed region Cu(t) are given by

)()()(

tCV

QtC

V

Q

dt

tdCu

s

s

S

i

s

)()()(

tCV

QtC

V

Q

dt

tdCu

u

s

u

u

Where Q is the fan cooler volumetric flow rate (33,000 ft3/min), Vs and Vu are sprayed and

187

unsprayed volume respectively in the containment. The sprayed fraction is 81% in Table 15.6-

10. The average concentration in then given by

)()()( tCV

VtC

V

VtC u

us

s

9. Iodine plate-out in the steam lines and condensers

User has control for the plate-out, which is a fraction of iodine stayed on the surface of the

release pathway. For example, 50% is assumed instantly released and of which 50% is plated

out in the inner surface of the containment in TID 14844. So the total release in the containment

is 25% of the total core inventory.

The change of RCS concentration is equal to the difference between the production rate and the

removal rate. After a reactor scram, the production rate is increased by the spike factor. The

letdown flow is typically isolated. And the removal rate is governed by the steam generator tube

leakage flow WTR

Change in Concentration = Spike factor x Eq. Production Rate – MRCS WTRCi(t)

There are additional variations in modeling the spiking factor. For instance, the isotope

concentration can be instantly multiplied by the factor in some analyses, while the activity release

rate is multiplied and a differential equation is solved in others. The equilibrium release rate is that

equal to the production which is the sum of decay and the Letdown system removal rate. The latter

method is obviously more rigorous and chosen for our calculation

188

Table 1

PWR NPPS Fission Product Inventory

________________________________________________________________

Isotope Core Inventory Fraction in Gap Inventory

(Ci) Gap (Ci)

_______________________________________________________________

I-131 8.0E7 0.10 8.0E6

I-132 1.2E8 0.10 1.2E7

I-133 1.7E8 0.10 1.7E7

I-134 1.8E8 0.10 1.8E7

I-135 1.5E8 0.10 1.5E7

Kr-83M 9.9E6 0.10 9.9E5

Kr-85M 2.2E7 0.10 2.2E6

Kr-85 5.2E5 0.30 1.6E5

Kr-87 4.1E7 0.10 4.1E6

Kr-88 5.8E7 0.10 5.8E6

Kr-89 7.2E7 0.10 7.2E6

Xe-131M 5.6E5 0.10 5.6E4

Xe-133M 2.3E7 0.10 2.3E6

Xe-133 1.6E8 0.10 1.6E7

Xe-135M 3.3E7 0.10 3.3E6

Xe-135 3.4E7 0.10 3.4E6

Xe-138 1.4E8 0.10 1.4E7

1) Based on a typical PWR plant data.

2) I -127 and I-129 inventory are in Kg and have no

contribution to the thyroid dose. They are not included.

189

Table 2

PWR NPPS Design Reactor Coolant and SG Secondary Equilibrium

Activities

____________________________________________

Isotope RC Activity SG 2nd Activity

(Ci/gm) (Ci/gm)

____________________________________________

I-131 2.3E+0 4.79E-3

I-132 2.8E+0 3.11E-3

I-133 3.7E+0 7.10E-3

I-134 5.9E-1 3.70E-4

I-135 2.1E+0 3.39E-3

Kr-83M 4.6E-1 2.01E-5

Kr-85M 2.0E+1 8.84E-5

Kr-85 7.7E+0 3.44E-4

Kr-87 1.3E+0 5.61E-5

Kr-88 3.7E+0 1.63E-4

Kr-89 1.1E-1 2.69E-6

Xe-131M 2.1E+0 9.37E-5

Xe-133M 1.7E+1 7.58E-4

Xe-133 2.6E+2 1.16E-2

Xe-135M 4.7E-1 1.80E-5

Xe-135 7.2E-1 3.20E-4

Xe-137 1.8E-1 4.78E-6

Xe-138 6.6E-1 2.49E-5

____________________________________________

1) The RC activities are based on a typical PWR plant. 2) The SG activities are based on a typical PWR plant. 3) Xe-137 activity is presented in RC and SG but no value shown

in core and gap inventory.

4) Other isotopes, e.g. Rb, Mo, Tc, Ru, Ag, Te and Tc in Table 11.1-2 are not included here because they do not contribute to

offsite dose calculation.

190

Table 3

Isotope Data for Dose Calculation

____________________________________________________

Isotope Half Live Avg Gamma Thyroid DCF

(hour) (Mev) (Rem/Ci)

____________________________________________________

I-131 193.2 0.381 1.49E6

I-132 2.3 2.333 1.43E4

I-133 21.0 0.608 2.69E5

I-134 0.9 2.529 3.73E4

I-135 6.7 1.635 5.60E4

Kr-83M 1.86 0.002 0

Kr-85M 4.48 0.159 0

Kr-85 93995 0.002 0

Kr-87 1.27 0.793 0

Kr-88 2.8 1.95 0

Xe-131M 285.6 0.02 0

Xe-133M 54.0 0.0416 0

Xe-133 127.0 0.0454 0

Xe-135M 0.3 0.432 0

Xe-135 9.15 0.247 0

Xe-138 0.3 1.183 0

Based on a typical PWR plant

Thyroid dose conversion factor from RG 1.109 Rev.1

191

5.2 Input Parameters for Dose Calculation

The radiological dose calculation's input file is stored in this Access database table RadData.

Each data entry is a "field" in data tables. During development some of the parameters may be

dropped or new ones may be added. The current parameters are defined as follows:

Database: C:\IAEA_2009\PWR2009\ListData.mdb

Table: RadData

ID: 1

Description: Corrected inventory

PLORB 0.4 Plate-out or partition factor in the Reactor Building

PLOSG 0.1 Plate-out or partition factor in the steam generator

PLOTB 1 Plate-out or partition factor in the Turbine

PLOAX 1 Plate-out or partition factor in the Auxiliary

building

DRFRB 1 Dose reduction factor in the Reactor Building

DRFSG 1 Dose reduction factor in the steam generator

DRFTB 1 Dose reduction factor in the turbine

DRFAX 1 Dose reduction factor in the Auxiliary building

FLSRB 0.3 Flashing factor in the Reactor Building

FLSSG 1 Flashing factor in the primary containment

FLSTB 1 Flashing factor in the Turbine Building

FLSAX 1 Flashing factor in the Auxiliary building

FANCR 17 FAN CIRCULATION RATE (M3/SEC)

FSPRY 0.81 FRACTION OF CONTAIMENT SPRAYED AREA TO TOTAL

GPRL 0.01 FRACTION OF GAP RELEASE

DCFE 0.01 Saturated decontamination factor for elemental iodine,

i.e. fraction of the maximum value at which spray will no longer reduce the

isotope concentration.

DCFP 0.01 Saturated decontamination factor for particulate

iodine

DCFO 0.92 Saturated decontamination factor for organic iodine

SPIKEI 500 Iodine spike factor after reactor scram and

depressurization

SPIKEN 6 Noble gas spike factor

BRTH 0.000347 Breathing rate (M3/sec)

XOQEAB 0.0013 X/Q at exclusion area boundary (sec/M3)

XOQLPZ 0.00038 X/Q at low population zone (sec/M3)

WAUX 1 (Reference Auxiliary building vent flow rate (M3/sec))

WOG 0.1 Off-gas flow rate (M3/s)

SGTL 0.2 Nominal SG tube leak rate during operation (kg/s)

VAX 50 Auxiliary building volume (m3)

VCDS 10 Reference condenser hotwell volume (M3)

AUX 1 Aux Bldg fuel handling accident source term multiplier

RMB1 0.0011 containment monitor background reading (mSv/h)

RMB2 0.022 Steam line N16 background reading (mSv/h)

RMB3 0.033 Turbine building background reading (mSv/h)

RMB4 0.044 Aux Bldg background reading (mSv/h)

RC87N 5000 RC87N (mSv/h)

FRCE 0.94 fraction of elemental iodine

FRCP 0.05 fraction of particulate iodine

FRCO 0.01 fraction of organic iodine

192

SPRE 10 spray constant for elemental iodine (1/sec)

SPRP 3.6 spray constant for particulate iodine (1/sec)

SPRO 0.2 spray constant for organic iodine (1/sec)

5.3 Radiological Consequences

The dose model is tested for the FSAR events. Note there are many uncertainties in attempting

to reproduce the methodology, for instance, the method of treating iodine spike and definition of

fuel failure/damage. Unlike thermal hydraulics in transient calculation, for which better

agreement is achievable, radiological methodology is traditionally more mechanistic. In general,

in benchmarking any dose assessment models, order of magnitude consistency is more important

than numerical agreement. Usually within a factor of two is accepted as very good agreement.

5.3.1 Loss of Coolant Accident

Although for all design basis accidents the reactor is designed to limit the fuel damage below 1%

and oxidation below 17% according to 10CFR50.46, TID14844 requires 100% release of the

core noble gas and 25% of iodine to demonstrate adequacy of the ECCS. In PCTRAN model we

input FRCL=100% in MF17 for fuel damage, PLRB =0.5 for instant plate-out and DRRB =0.5

for dose reduction factor for the noble gases to achieve the 25% release rate. Of the iodine fission

product released to the containment, 91% is in the form of elemental iodine, 5% is in particulate,

and 4% in organic. Consistent with Table 15.6-10 assumptions, the building leakage rate is 0.1%

per day at design pressure. The iodine remove constant in sprayed region SPRE=23.1/hr for

elemental and SPRP = 0.45/hr for particulate iodine respectively. Apparently there is no spray

reduction for organic iodine. The iodine decontamination factor in sprayed region is 100, i.e.

when dose reduction reaches 1/100; there will be no further reduction. We also assumed the

flashing fraction in the reactor building is 0.4 according to isentropic expansion of pressurized

water to containment pressure.

The ESF leakage calculation is equivalent to the Auxiliary Building leakage pathway calculation

in PCTRAN. File DOSEDATA.MDB records data summary for every TimeDoseOut seconds in

PCTRAN Options table of database OptData.mdb. The larger the output interval set by the user,

the more data intervals the computer's memory can hold for a long run. PCTRAN radiation dose

and source term calculation is presented in file DOSEDATA.MDB. There are reports on the

source term and Post-Accident Sampling System (PASS) for coolant and reactor building air

concentration data.

Radioactive halogen such as isotopes of iodine exists in the primary coolant water and

containment vapor. Only that in the vapor may be released through open vents or leak path.

When the containment spray is turned on, a significant fraction is removed depending upon the

droplet size. The containment filtration system or Standby Gas Treatment System may also

remove a significant fraction. The radioactivity release rate is given by:

ACTi = CNi * ( WLKG + WLKA ) * (1 - EFF)

193

Where EFF is the filter efficiency. Unit conversion is not shown in these equations but has been

properly taken care of in the code. ACT is in Ci/Hr. Integrated over time is the integrated

activity.

The standard method from Reg. Guide 1.3 will be used for dose calculation. For thyroid dose at

site boundary, it is given by

DTHY = BRTH * ( X/Q ) x CONV( Ii ) * ACT ( Ii )

Where Ii represents the ith isotope of iodine, and CONV are the dose rate conversion factors,

which are also listed in Table 6.2. The calculated dose rate is in Rem/Hr.

For whole body dose rate, it is given by:

DWB = 0.247 (X/Q) EGi * Ai

Where EGi is the average gamma energy in MeV per disintegration for the ith isotope, Both

halogen and noble gases are included. They are also listed in Table 6.2 and were input to the

code.

The radiological consequences were reevaluated using the assumptions of Regulatory Guide 1.3.

It resulted in the offsite thyroid and whole body at Exclusion Area Boundary (EAB) in 2 hours

and Low Population Zone (LPZ) in 30 days. For practical use of a simulator, 30 days is too long

and thus not discussed. These doses should be below the guidelines of 10CFR100, which set the

limits at 300 Rem for thyroid and 25 Rem whole body respectively.

194

Output Parameters

RM1 = Containment Air Radiation Monitor (CPM)

RM2 = Steam Line Radiation Rad Monitor (CPM)

RM3 = Condenser Off-gas Rad Monitor (CPM)

RM4 = Aux Building Air Rad Monitor (CPM)

KR87= Rx Water Kr87 Equivalent Concentration (Ci/gm)

I131= Rx Water I131 Equivalent Concentration (Ci/gm)

STRB= Rx Bldg Rad (I & NG) Release Rate(Ci/s)

STSG= SG Atmospheric relief & Safety Valves Rad Release Rate (Ci/s)

STTB= Condenser Off-gas Rad Rel Rate (Ci/s)

RBLK= Total Leakage out of Reactor Bldg (Kg)

SGLK= Total Leakage out of SGs (Kg)

DTHY= EAB Thyroid Dose Rate (mSv/h)

DWB = EAB Whole Body Dose Rate (mSv/h)

It is noted that the 2-hr thyroid dose at EAB, 22.9 Rem, is nominal for a typical PWR plant. Note

that the flashing factor of 0.4 and apparently none was assumed in the FSAR, the agreement

assures that the calculation model is validated.

195

5.3.2 Steam Line Break Outside Containment

FSAR Section 15.1.5 described the dose consequence for a large steam line break outside the

containment. There is a pre-existing tube leak rate of 1 gpm between the SG primary and

secondary. The steam line break results in SG secondary coolant released directly into the

atmosphere. The iodine-spiking factor can be assumed either as 60 for a pre-accident spike or as

high as 500 for accident induced spike. In Table 15.1-3 the reactor coolant concentration is based

upon pre-existing iodine spike of 60 micro-Curies/gram I-131 dose equivalent. The partition

factor was assumed as the maximum value 1.0 in the FSAR so that all iodine was released. The

two intact steam generators were used to control cool down the plant following the steam line

break. Time to isolate the defective steam generator is 30 minutes. Steam and radioactive

material release through the SG relief and safety valves are included in the model calculation, but

it forms a relatively small part of the total dose. User should pay attention to the data input of

the iodine spiking factor, the partition factor, the plate-out factor and reduction factor, if any.

Adjustment of these data input will affect the overall accumulated dose at site boundary.

In Table 15.1-3 the "Fuel defects is" 1% and "failed fuel" is also 1%. It is not clear what is the

difference between the two terms' definition. The activity release to reactor coolant from failed

fuel and available for release for both noble gases and iodine are 1% of core gap inventory.

According to Table 15.0-7, the gap inventory of I-131 is 8.0E6 Ci. Thus the I-131 concentration

in 1.8E8 grams of reactor coolant should be

I-131 concentration = 0.01 x 8E6 /1.8E8 x 1.E6 = 444 uCi

Disregarding the contribution from other iodine isotopes I-132, 133, 134 and 135, the pre-

existing iodine spike dose equivalent is greater than that shown in the same table - 60 uCi/gm.

Typically in other Westinghouse's documentation, either a factor of 60 or 500 should be used.


FSAR described the dose consequence for a double-ended SG tube rupture event. There is a pre-

existing tube leak rate of 1 gpm total between the SG primary and secondary. It is evenly

distributed into the 3 steam generators. After a double-ended break in one of the steam

generators, the break rate there suddenly increased to about 500 gpm (70 lb/sec) according to

Fig. 15.6-4I. NSSS thermal hydraulics simulation has already been discussed in Chapter 4 of this

report. The dose consequence is discussed here.

The ruptured SG secondary coolant is released directly into the atmosphere with a higher

partition factor of 0.1. The iodine-spiking factor can be assumed either as 60 for a pre-accident

spike or as high as 500 for accident induced spike. The partition factor was assumed as the

normal low value of 1/100 in the intact steam generators. The intact steam generator is used to

control cool down the plant following the steam line break. Steam and radioactive material

release through the SG relief and safety valves are included in the model calculation, but it forms

a relatively small part of the total dose. The adjustable factors in the input are iodine spiking

factor, partition factor, plate-out factor and reduction factor. Adjustment of these data input will

196

affect the model projected dose rate and accumulated dose at site boundary.

5.3.4 Letdown Line Break

The dose consequence of an un-isolated letdown line break in the Auxiliary Building was

described in Section 15.6.2 of FSAR. The leak rate is about 140 gpm and lasts about 30 minutes.

The reactor coolant concentration is based upon pre-existing iodine spike of 60 micro-

Curies/gram I-131 dose equivalent. The total iodine equivalent available for release is thus

60x10-6

x 140 /7.4805 x 62.4 x 453.6 x 30 = 948 Curies

In our benchmark analysis MF 20 is introduced with 100% magnitude so that the leak rate is

WLD0=23.7 t/hr (6.58 kg/s) which is comparable to the FSAR letdown leakage rate of 140 gpm

(9 kg/sec). In Table 15.6-13 the iodine release rate is 20%, so we set the plate-out or partition

factor PLOAX=0.2 in file RAD.DAT. In order to get 60 uCi/gm I-131 dose equivalent

concentration, the gap release fraction, GPFR is set to 0.01. All leakage flow flashes into steam

in the Auxiliary Building and no further reduction is assumed. The leak is isolated in 30 minutes

so that the integrated dose will not increase after that. The calculated doses at site boundary are

shown in the following table. They are consistent with the FSAR Table 15.6-14.

197

References

1. L. C. Pwu (Po), 'A Faster-Than-Realtime Computer Code for Loss-of-Coolant and

Feedwater Transient Prediction', ANS Transactions, Volume 39, 1981. pp 1056-1057.

2. L. C. Pwu (Po), 'A Fast Running Transient Program for Light Water Reactors',

Proceedings of International Nuclear Power Plant Thermal Hydraulics and Operations

Topical Meeting, Taipei, Taiwan. ANS Publication, October 22, 1984. Paper L8.

3. L. C. Po, “Analysis of the Rancho Seco Overcooling Event Using PCTRAN, ” Nuclear

Science & Engineering, 98, 154-161 (1988).

4. L. C. Po “IAEA Activities in Advanced Reactor Simulation,” paper S1, the Fifth

International Topical Meeting on Nuclear Thermal Hydraulics, Operations and Safety

(NUTHOS-5), April 14-18, 1997, Beijing, China.

5. David L. Hetrick, "Dynamics of Nuclear Reactors", University of Chicago Press, p 27.

6. American Nuclear Standard 5.1, 1979. Decay Heat Table.

7. L. S. Tong and J. D. Young, 'A Phenomenogical Transition and Film Boiling Heat

Transfer Correlation'. Proc. Fifth International Heat Transfer Conference, Tokyo. (1974).

8. F. J. Moody, 'Maximum Flow Rate of a Single Component, Two-Phase Mixture',

Transactions of ASME, Ser C, 87 (1965). pp. 134-142.

9. R. T. Lahey, Jr. and F. J. Moody, 'The Thermal-Hydraulics of a Boiling Water Nuclear

Reactor', ANS (1979). p. 202.

10. USNRC NUREG-1210, "Pilot Program: NRC Severe Reactor Accident Incident

Response Training Manual". February, 1987.

11. "Assumptions Used for Evaluating the Potential Radiological Consequences of a Loss of

Coolant Accident for BWRs", Regulatory Guide 1.3.

12. Regulatory Guide 1.109, "Calculation of Annual Doses to Man from Routine Releases of

Reactor Effluent for the Purpose of Evaluating Compliance with 10CFR50, Appendix I".

13. "Source Term Estimation during Accident Response to Severe Nuclear Power Plant

Accidents", NUREG 1228.

198

Appendix A TRIGA -Experimental Pool Reactor Simulator

1.0 Overview and Specifications

Micro-Simulation Technology (MST) has prepared a experimental pool reactor simulator for

educational purpose. Following are features and capabilities:

1. The software will simulate a water moderated and cooled pool type reactor using a point

kinetics model with 6 delayed neutron groups. The model will include simulation of the

Iodine 135 – Xenon 135 fission product poison decay chain with adjustable “fast time”

capability (to establish steady state iodine and xenon levels as well as for student

demonstration). An instructor adjustable neutron source will be provided to permit

observation of sub-critical multiplication during the simulated approach to criticality.

2. The input parameter to the point kinetics reactor model will be the core average reactivity

computed from the following:

a. An instructor adjustable base reactivity value;

b. Simulated control rod position;

c. Local (e.g. in-core) moderator density and voids;

d. Fuel centerline temperature (Doppler);

e. Xenon-135 Level.

3. A simplified reactor thermal-hydraulic model will be provided which computes fuel

centerline temperature (for Doppler reactivity feedback) as well as in-core moderator

temperature and density. The bulk (e.g. pool) temperature will be computed as well. The

pool surface will be assumed to be at normal atmospheric pressure at all times, and bulk

boiling of the pool will not be assumed. Simulation of core void will be limited to that void

produced by sub-cooled and nucleate boiling within the core; transition and bulk boiling will

not be simulated.

4. An instructor interface will be provided with the following capabilities:

a. The ability to “Freeze” and “Resume” the real-time simulation at any time;

b. The ability to “Snap” the existing simulator condition to multiple hard-disk files for later

use as an initial condition(s);

c. The ability to “Reset” the simulator to a previously stored initial condition;

d. The ability to run the entire simulation in “slow time” (to permit observation of fast

transients);

e. The ability to run the Iodine 135 – Xenon 135 decay chain in “fast time” (to permit

observation of Xenon transients);

f. The ability to change key reactor parameters including:

- Doppler coefficient;

- Moderator temperature coefficient’

- Basic core reactivity

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- Neutron lifetime

- Decay neutron precursor fractions

- Delayed neutron precursor decay constants

- Control rod worth

- Initial pool water temperature

- Neutron source strength

- Control rod speed

Note that, in general, these parameters must be set with the simulated control rods fully

inserted into the core in order to avoid unrealistic neutron flux transients.

g. A plotting package which permits viewing of key parameters on a “strip chart” display as

well as the ability to transfer stored plot data to an ExcelTM

spreadsheet.

5. A “virtual” control panel graphic display will be provided with the following capability:

a. Display of critical reactor parameters including:

- bulk pool temperature

- local in-core moderator temperature

- source range monitor counts and rector period

- intermediate / power range monitor neutron flux and period

- core average reactivity

- control rod positions

b. The ability to insert and withdraw control rods at a fixed speed (adjustable via the

instructor interface as previously described);

c. The ability to manually “scram” the reactor.

6. The simulated source range monitor will have a short period trip; the intermediate / power

range monitor will have a high flux level as well as a short period trip. The set points for

these trips will be adjustable via the instructor interface. A short period or high flux level trip

will result in an automatic “scram” of the reactor.

7. User-level documentation for the simulator software will be provided.

In this documentation, the first chapter describes point kinetics and solution technique of the

experimental pool reactor. The second chapter includes instructions for operating the Windows

version. Sample runs of reactor startup to critical, shutdown and xenon effect, etc are in the final

chapter.

200

2. Experimental Pool Reactor Description

We chose a TRIGA type experimental pool reactor for the simulator model. It has a rated power

of 250 KW with neutron flux in the order of 1013

n/cm2/sec. The fuel is in cylindrical shape.

Uranium-zirconium hydride UZRH of 19% enriched U-235 is the fissile material in the fuel

assemblies. Water used for cooling is always in atmospheric pressure. The control rods contain

boron are used for neutron absorption. Combined they have the function of power regulation,

chemical shim and safety shutdown. Graphite is used for moderation.

There is a heat exchanger for heat removal during power operation. During source range and

intermediate range operation with little core heat, the heat exchanger pumps could be shut off.

The pool is maintained borated. A tank containing borate acid concentration higher than the

pool’s is used for increase the pool concentration. Another tank with pure water is used for de-

boration. By opening or closing the corresponding valves and pumps the operator can adjust the

boron concentration. It is a slower process than using the rods.

During power operation, the clad temperature may approach boiling temperature of water.

Localized or nucleate boiling may take place that reduces the average water density in the core.

This effect is considered in addition to Doppler (fuel temperature) and boron reactivity in the

neutronics calculation.

Transient Output Variables

ID Label Units Name

1 Time (sec) sec TIME

2 Temp pool water in (°C) °C TPLIn

3 Temp pool water (°C) °C TPLOut

4 Level pool water (M) M LPOOL

5 Temp peak clad (°C) °C TPCT

6 Temp HX 2nd (°C) °C TCROut

7 Temp fuel center line (°C) °C TFPK

8 Flow pool water M3/h WPOOL

9 Flow HX 2nd (M3/h) M3/h WCRC

10 Flow makeup (M3/h) M3/h WMU

11 Power heat exchanger (W) W QHX

12 Rod position (%) % RDPOS

13 Reactivity boron (%dk/k) %dk/k RHBR

14 Reactivity Doppler (%dk/k) %dk/k RHDP

15 Reactivity rod (%dk/k) %dk/k RHRD

16 Reactivity total (%dk/k) %dk/k RH

17 Reactivity Xe-135 (%dk/k) %dk/k RHXE

18 Reactivity Sm-149 (%dk/k) %dk/k RHSM

19 K-infinity Kinf

201

ID Label Units Name

20 K-effective Keff

21 Concentration boron (ppm) ppm CNBR

22 Neutron flux (n/cm2/s) n/cm2/s NFLX

23 Neutron period (sec) sec NPRD

24 Power core (W) W QCOR

25 Power decay heat (W) W QDCH

26 Void in core (%) % VOID

27 Power rated (%) % QPWR

28 Fission power (W) W QFIS

Please note for neutron flux the unit is in E6 n/cm2/s so that not too many zeroes shown on semi-

log scale.

The TRAIGA reactor is modeled for PCTRAN RxPool simulation code. It is hereby upgraded in

the current release:

1. Data for two reactor sizes are provided: in BasicData table of ListData.mdb database,

Record 1 is rated 1 MW full power of flux 3E13 n/cm2/sec and Record 2 rated 250

KW and 1E13 n/cm2/sec.

2. Typically for a TRIGA reactor, there are 4 control rods for transient, safeguard, shim

(control) and regulator respectively.

3. The pool water is not borated. However the mechanism of adding boric acid into the

pool and deboration by pure water is maintained.

4. The heat exchanger is not operating during startup. It can be turned on anytime when

the pool water becomes hot.

5. In the initial condition list IC2 is a common shutdown condition. The operator should

set the rod position demand somewhere around 85% with a rod speed about 20%/min

in the beginning of startup. This would take a little over 4 minutes to the power range.

6. During rod pulling the effective reactivity k-eff will increase. When it approaches 1.0

(critical) the neutron flux will move into the intermediate range. Soon it moves into

the power range and the fuel starts to heat up.

7. When the fission power approaches the rated full power the operator should set the

rod demand slightly higher with a much lesser rod speed (e.g. 1%/min) until the rated

power is reached. Then the speed should be set back to zero to stop its movement.

8. The high flux trip (FXPR) is set at 105% of the rated flux.

Anytime during this process by clicking “Restart” and “Save an IC” the condition can be saved

for reuse. The following figure shows the 1 MW plant at full power condition. The rods are

pulled to about 87.3%. It was save as IC9.

The following diagram is the TRIGA reactor at full power condition. Note the fuel centerline

temperature is about 308ºC. Full power is 1 MW with flux near 3.0E13 n/cm2/sec. The water

temperature is still near room temperature of 25ºC. It will heat up until the heat exchanger is

202

initiated. Also plotted are transient curves of the reactivity k-inf and k-eff, neutron flux, decay

heat and total power. The first 200 seconds the decay heat is dying down. One could wait the

decay heat dropping down to very low level for startup, too.

204

(flux in million neutrons/cm2/sec => full power = 3E13 n/cm2/sec)

205

Should we choose another TRIGA rated at 250 KW, startup from the same IC2 shutdown

condition will reach full power in a similar fashion. Following figure shows the 250 KW plant at

full power condition. The rods are pulled to about 87.7%.

206

3.0 Sample Runs

Six initial conditions are saved as “protected” set that ranging from full power to intermediate

range and shutdown conditions. At any time during a run the user can save additional IC’s with

index higher than 6.

In the panel the reactivity and thermal-hydraulics variables are displayed in the panel. To pull

the rods, user can use the scroll bar to set a demand of withdraw percent and the rate in % per

minute. If the rate is too fast, it will be witnessed by the shortening of the reactor period (i.e. e-

fold multiplication factor). If the period is shorter than the scram set point of power range,

intermediate range or source range respectively, the reactor will scram. For power range and

intermediate range, there are also high flux scrams. So during the period of intermediate range

on route to power range, the user should reset the monitor to power range by clicking the top

button. Otherwise the high flux scram in the intermediate range would scram the reactor.

At any time during startup, the operator should watch the neutron period closely against the short

period scram. If it is getting close, he or she should reduce the rod speed or stop all together.

If the reactor is scrammed and the operator decides to start it up by pooling the rods, the scram

button will be cleared as soon as the rod position is greater than 1%.

Case 1 Reactor scram form 100% power

By choosing one of the full power conditions, the operator should check the core neutronics and

thermal-hydraulic condition. By pressing the Scram button the control rods will be inserted by

gravity and the reactor becomes subcritical. There is decay heat from the core slowly decreasing

with time. Feedback by Iodine and Xenon buildup will be indicated. It is relatively slow so fast-

time should be used for observation this effect. There is a dedicated time-time multiple for this

purpose. The indicated time post shutdown is displayed by its side. In reactor power plant

where neutron flux is at much higher level (> 1E18 n/cm2/sec), xenon buildup is much more

obvious than the pool reactor (flux level in 1E13 n/cm2/sec). It will reach a peak in about 11

hours. So immediate after a shutdown, restart should be conducted either soon after or deferred

for about a day or more. Otherwise this Xenon poisoning effect would make restart difficult.

Case 2 Startup from a subcritical condition

Starting from one of shutdown conditions, the operator should set the rod demand in staggered

steps with corresponding rate. The rate can start from larger increment, e.g. 10%, 20%, 30% to

40% with withdrawing rate at 10% per minute. Watch the neutron period decreases while the

flux increases to higher decades. If the period gets close to the short-period scram, the rate

should be reduced. Watch over the k-infinity and k-effective, too. When K-eff becomes 1, it is

defined as “critical”. The neutron period decreases rapidly. The operator should reduce the rod

moving rate to its minimum – 1%/min or zero to hold it for a while before further movement.

The on-line plotting can be used for trending.

Case 3 Variations of neutron source, Doppler and Moderator temperature coefficients

207

The source term is a user input imbedded in ICThermoData table. It varies from 1 to 1E6 n/sec.

If the number is too low it would be difficult to startup. Since just by delayed neutrons from last

operation, it is not sufficient to multiply to full criticality. On the other hand, a strong neutron

source in the order of 1E6 n/sec it will be relatively easy to reach full power.

4.0 Theory and Solution Technique

4.1 Six-group Point Kinetics Model

A point kinetics model with six delayed neutron groups and reactivity control from

external sources and feedback was formulated. They are expressed by

where

n = neutron density

= reactivity = (k -1 ) / k

k = effective multiplication factor

i = delayed neutron fraction for the ith group

ι = neutron life time

i = decay constant for the ith group

Ci = precursor concentration

S = neutron source

The six-group point kinetics equations are solved by finite difference method in the

program. Reactivity is controlled by rod movement and boron concentration adjustment.

Its feedback in moderator density and fuel temperature (Doppler) effects are described

below:

4.2 Core Reactivity Corrections of Point Kinetics Model

The reactivity corrections in the model are calculated as:

K∞ = K∞0 (1 – ∆KB /K∞

0) (1 – ∆KDOP /K∞

0) (1 – ∆KXe /K∞

0)(1 – ∆KSm /K∞

0)

SCndt

dnii

i

6

1

iiii Cn

dt

dC

208

Where

K∞ = the corrected K∞ of core.

K∞0 = the uncorrected K∞

0 of fuels (combination results of rod controlled and

uncontrolled K∞0) in the core.

∆KB = the reactivity correction of core due to boron.

∆KDOP = the reactivity correction of fuel temperature in the core.

∆KXe = the reactivity correction of core due to Xenon-135.

∆KSm = the reactivity correction of core due to Samarium-149.

The uncorrected K∞0 of fuels in the core is retrieved from the following formula:

K∞u = A1 + A2 * ρ + A3 * ρ

2 + A4 * ρ

3 ---uncontrolled core fuel K∞

K∞c = A5 + A6 * ρ + A7 * ρ

2 + A8 * ρ

3 ---controlled core fuel K∞

K∞0 = K∞

u + frod * (K∞

c - K∞

u)

Where

ρ is the moderator density of core (gm/cm3).

frod is the fuel rod controlled fraction in the core.

The Global Core reactivity ∆KCore of the core is calculated as:

KEFF = K∞ /KEIGEN

∆KCore = 1 - 1/KEFF

Where

KEIGEN is the core eigenvalue; the critical value in the core analysis calculation.

Neutron density is directly proportional to the fission power. Remainder of the core power is

provided by fission product decay heat. It is given by an eleven group equation:

t

j

i

DHjeEQ

11

1

209

Where

Ej = amplitude of j-th term

λj = decay constant of j-th term

t = elapsed time since shutdown

Concentration of each decay group γj is represented by

The total power in the core is given by

Where Ef is about 0.93, i.e. fission heat is about 93% of total core power.

4.3 Pool Cooling System

PCTRAN/PoolRx uses a semi-empirical method to model the circulating pool cooling system.

The circulating suction and discharge temperature are given by:

Where QHX is the heat removal rate by the heat exchanger. At steady state it is equal to core

power QCore. TH and T C are the pool outlet and inlet temperature respectively. The heat

exchanger secondary side outlet and inlet temperatures tH and t C are related by:

Standard method of number of heat transfer unit (NTU) is used to determine the heat exchanger

efficiency.

Cmin = min (Wsf Cp, WscCp)

CpW

QTT

HX

HXCH

CpW

Qtt

Sec

HXCH

11

1

0 )()(i

jjfEtnPtP

)()()(

tnEtdt

tdjjj

j

210

CR = Cmin / Cmax

NTU = UA / Cmin

EFF = 2 / (1 + CR + Sqr(1 + CR * CR) * ((1 + Exp(-NTU * Sqr(1 + CR * CR))) _

/ (1 - Exp(-NTU * Sqr(1 + CR * CR)))))

The heat transfer efficiency is then given by

K = Eff * Cmin

The heat transfer rate is

QHX = K ( TH - tC )

The normal log-mean temperature method is used for its heat transfer rate. The heat transfer rate

is given by the log-mean temperature times the heat transfer coefficient:

Where

u = heat transfer coefficient (KW/m2/hr)

A = heat exchanger tube area (m2)

In transient, the bulk pool water temperature is given by:

HXCore

pool

waterp QQdt

dTMC ,

4.3 Boron Concentration

Boron is used to fine-tune reactivity and core power. Its concentration is given by

CC

HH

CCHH

HX

tT

tT

tTtTuAQ

ln

211

outoutinin CWCW

dt

MCd

outoutinin CWCWdt

dCM

dt

dMC

Mdt

dMCCWCW

dt

dCoutoutinin

M

tWWCCWCWCC outinoutoutinin 0

4.4 Fuel and Clad Temperatures

A mechanistic model accounting for the temperatures of fuel and cladding has been constructed

in PCTRAN/SFP. This model can simulate thermal power transmitted into the coolant in

contrast to nuclear power generated by the fuel during startup and power operation. Fuel thermal

heat transfer is described by

QF-CL = UF Afuel (TF – TCL)

QCL-Water = UCL AClad (TCL – T Water)

Where TF is the average fuel temperature, TCL the average clad temperature and Twater water

temperature. The heat transfer coefficient U is established at steady state full power.

In a pool reactor, the bulk of water is maintained near or slightly above the room temperature. If

the clad surface is heated to above saturated temperature of water, i.e. 100°C, localized

subcooled boiling may take place. The empirical correlation by Thom (J.R. S. Thom et al, Proc.

Instn. Mech. Engrs. 226, 1966) was used to calculate the void production rate. It affects the local

water density; that in turn feedback to the kinetics of neutron density calculation.

Transient fuel temperature will be calculated by the imbalance between power deposited in the

fuel and heat sink.

CLFCoreF

FPF QQdt

dTCM

212

Where MF is mass of fuel in the core, Cp is its specific heat and T the temperature in average. Q

is the power with subscript Core representing the core power and F-CL for heat transfer from the

fuel to cladding.

Training Material for IAEA Advanced Reactor Simulation

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