SNAP/RADTRAD 4.0: 

Description of Models

and Methods

Office of Nuclear Regulatory Research

NUREG/CR-7220

SNAP/RADTRAD 4.0:

Description of Models

and Methods

Manuscript Completed: March 2016

Date Published: June 2016

Prepared by: 

W.C. Arcieri, D.L. Mlynarczyk, and L. Larsen

Information Systems Laboratory, Inc.

11140 Rockville Pike, Suite 650

Rockville, MD 20852-3116

Mark Blumberg, NRC Technical Monitor

John Tomon, NRC Contracting Officer’s Representative

Office of Nuclear Regulatory Research

NUREG/CR-7220

 

iii

ABSTRACT

This report documents the models and methods used in the Symbolic Nuclear Analysis 

Package/RADionuclide Transport, Removal And Dose Estimation (SNAP/RADTRAD) code, 

which consists of the SNAP Model Editor graphical user interface (GUI), the SNAP/RADTRAD 

plugin and the RADionuclide Transport, Removal And Dose Estimation analytical code 

(RADTRAD-AC). The SNAP/RADTRAD code was developed for the U.S. Nuclear Regulatory 

Commission (NRC) Office of Nuclear Regulatory Research to estimate transport and removal of 

radionuclides and dose at selected receptors. The SNAP/RADTRAD code is used to estimate 

the radionuclide release from the containment using either the NRC TID-14844 or NUREG-1465 

source terms and assumptions, or a user-specified table. In addition, the code can account for 

a reduction in the quantity of radioactive material released due to containment sprays, natural 

deposition, filters, and other engineered safety features. The code uses a combination of tables 

and numerical models of source term reduction phenomena to determine the time-dependent 

dose at user-specified locations for a given accident scenario. SNAP/RADTRAD can also be 

used to assess occupational radiation exposures, typically in the control room; to estimate site 

boundary doses; and to estimate dose attenuation due to modification of a facility or accident 

sequence.

v

TABLE OF CONTENTS

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

TABLE OF CONTENTS .............................................................................................................v

LIST OF FIGURES ................................................................................................................... vii

LIST OF TABLES......................................................................................................................ix

ACKNOWLEDGMENTS............................................................................................................xi

ABBREVIATIONS ................................................................................................................... xiii

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

2.0 INSTALLATION GUIDE...............................................................................................2-1

2.1 Distribution........................................................................................................2-1

2.2 Hardware and Software Requirements .............................................................2-1

2.3 Installation.........................................................................................................2-2

2.3.1 Installation of AptPlot.............................................................................2-2

2.3.2 Installation of SNAP ..............................................................................2-3

2.3.3 Installation of the RADTRAD-AC ...........................................................2-5

2.3.4 Updates to SNAP, AptPlot and the RADTRAD-AC................................2-5

2.4 Sample Problems..............................................................................................2-6

2.5 Contact Information...........................................................................................2-6

2.6 Code Error and Problem Reporting...................................................................2-6

3.0 MODEL DEVELOPMENT USING SNAP/RADTRAD ...................................................3-1

3.1 Overview of SNAP/RADTRAD ..........................................................................3-1

3.2 The Model Editor User Interface- Model Development .......................................3-2

3.2.1 Overview of Existing Model Features ....................................................3-2

3.2.2 Job Streams and Case Execution in SNAP/RADTRAD...........................3-6

3.2.3 SNAP/RADTRAD Input and Output Files.............................................3-14

3.2.4 AptPlot Plotting Program .....................................................................3-18

3.3 SNAP/RADTRAD Model Development and Modification.................................3-26

3.3.1 Model Editor Menus ............................................................................3-27

3.3.2 Building a SNAP/RADTRAD Model – Component Specification ..........3-30

3.3.3 Building a SNAP/RADTRAD Model – Input Specification ....................3-35

3.3.4 Building a SNAP/RADTRAD Model – Additional Features...................3-45

3.4 SNAP/RADTRAD Input Summary...................................................................3-50

3.4.1 Model Options .....................................................................................3-50
vi

3.4.1.1 Dose Conversion Factors...................................................3-56

3.4.1.2 Adaptive Time Step............................................................3-59

3.4.2 Nuclear Data and Source Scenarios....................................................3-59

3.4.3 Compartments, Pathways, Natural Deposition, Filters and Sprays ......3-65

3.4.4 Dose Locations, Breathing Rates, and Χ/Q Tables..............................3-75

4.0 MODELS USED IN RADTRAD ....................................................................................4-1

4.1 Governing Equations in RADTRAD...................................................................4-1

4.2 Adaptive Time Step Algorithm...........................................................................4-7

4.3 Radionuclide Release Mechanisms ................................................................4-12

4.4 Reactor Coolant System Activity Calculations.................................................4-14

4.5 Removal Models .............................................................................................4-20

4.5.1 Spray Removal Model .........................................................................4-21

4.5.2 Natural Deposition Model ....................................................................4-22

4.5.2.1 Henry’s Correlation ............................................................4-22

4.5.2.2 Powers’ Model ...................................................................4-23

4.5.3 Deposition in Piping Models ................................................................4-27

4.5.3.1 Brockmann Model for Aerosol Removal .............................4-27

4.5.3.2 Bixler Model for Elemental Iodine Removal........................4-31

4.5.3.3 Bixler Model for Organic Iodine Removal ...........................4-31

4.5.4 Filters ..................................................................................................4-32

4.6 Dose Analysis .................................................................................................4-32

4.6.1 Offsite Dose Analysis ..........................................................................4-32

4.6.2 Control Room Dose Analysis...............................................................4-33

5.0 REFERENCES.............................................................................................................5-1
vii

LIST OF FIGURES

Figure 2-1 AptPlot Installation Options window ................................................................. 2-2

Figure 2-2 AptPlot Installation Tool screenshots ............................................................... 2-3

Figure 2-3 SNAP Installation Tool screenshots ................................................................. 2-4

Figure 2-4 Welcome to Model Editor screen ..................................................................... 2-6

Figure 3-1 Opening the Model Editor ................................................................................ 3-3

Figure 3-2 SNAP Model Editor screen .............................................................................. 3-4

Figure 3-3 Illustration of the expand icon .......................................................................... 3-5

Figure 3-4 Illustration of the various icons used to represent a SNAP/RADTRAD 

model............................................................................................................... 3-6

Figure 3-5 Typical job stream in SNAP/RADTRAD ........................................................... 3-7

Figure 3-6 Job stream Property window............................................................................ 3-7

Figure 3-7 Typical root folder settings in SNAP/RADTRAD............................................... 3-8

Figure 3-8 Job stream Property window with an unset root folder ..................................... 3-8

Figure 3-9 Linking the RADTRAD-AC using the SNAP configuration tool ....................... 3-10

Figure 3-10 Saving the RADTRAD-AC using in the SNAP configuration tool .................... 3-11

Figure 3-11 SNAP/RADTRAD job stream and status windows.......................................... 3-12

Figure 3-12 Relationship between job stream steps and code execution .......................... 3-13

Figure 3-13 Drop-down menus for SNAP/RADTRAD output ............................................. 3-14

Figure 3-14 Expanded Output Parameters tab in the Property window ............................. 3-17

Figure 3-15 Expanded NRC Output Flags tab in the Property window .............................. 3-18

Figure 3-16 SNAP/RADTRAD Job Status window with AptPlot icon highlighted ............... 3-18

Figure 3-17 AptPlot startup view ....................................................................................... 3-19

Figure 3-18 Select EXTDATA Channels window for multiple plots .................................... 3-20

Figure 3-19 Control room dose plots for Test23 ................................................................ 3-21

Figure 3-20 AptPlot Axes window ..................................................................................... 3-22

Figure 3-21 AptPlot Set appearance window .................................................................... 3-23

Figure 3-22 AptPlot Graph appearance window................................................................ 3-24

Figure 3-23 Reformatted control room dose plots for Test23 ............................................ 3-26

Figure 3-24 Model Editor tool bar icon description ............................................................ 3-29

Figure 3-25 Navigator window tool bar icon description .................................................... 3-30

Figure 3-26 Navigator window with newly added model components................................ 3-32

Figure 3-27 View / Dock window for 4-node model (unconnected).................................... 3-32

Figure 3-28 View / Dock window for 4-node model (connected)........................................ 3-34

Figure 3-29 Navigator window with all nodes expanded.................................................... 3-35

Figure 3-30 Navigator window with the black bar menu for the engineering units 

selection ........................................................................................................ 3-36

Figure 3-31 Property window with volume entry for Compartment 2 (Containment) .......... 3-36

Figure 3-32 Pathway input windows for sample problem................................................... 3-37

Figure 3-33 X/Q input tables for EAB (left) and LPZ (right)................................................ 3-38

Figure 3-34 SNAP/RADTRAD Edit Total Inventories window editing features................... 3-40

Figure 3-35 Setting the power plant level .......................................................................... 3-40

Figure 3-36 Selecting from available SNAP/RADTRAD inventories .................................. 3-41

Figure 3-37 Edit Total Inventories window Accident Parameters tab................................. 3-42

Figure 3-38 Edit Total Inventories window Adjusted Inventory tab .................................... 3-42

Figure 3-39 Edit Total Inventories window Release Fractions and Timings tab ................. 3-43

Figure 3-40 Edit Total Inventories window Source Term tab ............................................. 3-43

Figure 3-41 Property window for source term iodine chemical form settings ..................... 3-44
viii

Figure 3-42 Model Editor Message window with icons ...................................................... 3-44

Figure 3-43 Example of a SNAP model editor Error Report window.................................. 3-45

Figure 3-44 View / Dock window tool bar icons ................................................................. 3-45

Figure 3-45 Features of the Paste Special window ........................................................... 3-46

Figure 3-46 Zoom and size features.................................................................................. 3-47

Figure 3-47 View / Dock window model canvas ................................................................ 3-48

Figure 3-48 Component Insertion icon feature menus....................................................... 3-48

Figure 3-49 Cylinder drawn using the Annotation features of SNAP.................................. 3-49

Figure 3-50 Property window for the Model Options node................................................. 3-51

Figure 3-51 Setting dose conversion factors in the Model Option Property window........... 3-57

Figure 3-52 Viewing “FGR11&12” Dose Conversion Defaults window .............................. 3-58

Figure 3-53 User-Defined Dose Conversion Factors window ............................................ 3-58

Figure 3-54 RCS Activity Calculator window ..................................................................... 3-60

Figure 3-55 RCS Activity Inputs – PWR window ............................................................... 3-61

Figure 3-56 RCS Activity Inputs – BWR window ............................................................... 3-61

Figure 3-57 Calculate Iodine Activity window .................................................................... 3-62

Figure 3-58 Available pre-defined SNAP/RADTRAD release models................................ 3-63

Figure 3-59 Onsite Χ/Q Table Map window....................................................................... 3-78

Figure 4-1 Schematic of a typical SNAP/RADTRAD dose assessment model .................. 4-2

Figure 4-2 Property widow for the Model Option node..................................................... 4-11

Figure 4-3 Editing Time Step Table window.................................................................... 4-11
ix

LIST OF TABLES

Table 3-1 Files available for viewing using the file viewer in the job status window........ 3-15

Table 3-2 Summary of Model Editor menu commands................................................... 3-27

Table 3-3 Icons used in the View / Dock window ........................................................... 3-33

Table 3-4 Sample problem X/Q values .......................................................................... 3-38

Table 3-5 Summary of SNAP/RADTRAD inputs – General Model Options .................... 3-52

Table 3-6 Summary of SNAP/RADTRAD inputs – Nuclear Data.................................... 3-64

Table 3-7 Summary of SNAP/RADTRAD inputs – Sources............................................ 3-64

Table 3-8 Summary of SNAP/RADTRAD inputs – Compartments ................................. 3-65

Table 3-9 Summary of SNAP/RADTRAD inputs – Pathways ......................................... 3-67

Table 3-10 Summary of SNAP/RADTRAD inputs – Natural Deposition ........................... 3-70

Table 3-11 Summary of SNAP/RADTRAD inputs – Filters............................................... 3-72

Table 3-12 Summary of SNAP/RADTRAD inputs – Sprays ............................................. 3-72

Table 3-13 Summary of SNAP/RADTRAD inputs – Dose Locations ................................ 3-76

Table 3-14 Summary of SNAP/RADTRAD inputs – Χ/Q Tables....................................... 3-77

Table 3-15 Summary of SNAP/RADTRAD inputs – Remaining inputs ............................. 3-78

Table 4-1 Local error solutions for I-131 and I-132........................................................... 4-9

Table 4-2 Chemical element grouping for SNAP/RADTRAD.......................................... 4-12

Table 4-3 Release phase durations for PWRs and BWRs ............................................. 4-14

Table 4-4 Gap release fractions used in SNAP/RADTRAD............................................ 4-14

Table 4-5 SNAP/RADTRAD release fractions to RCS for an REA-CRDA accident ........ 4-15

Table 4-6 Formulations used to determine RCS water radionuclide concentrations 

in PWRs with U-tube steam generators ......................................................... 4-16

Table 4-7 RCS radionuclide concentrations for a reference PWR plant ......................... 4-17

Table 4-8 Formulations used to determine RCS water radionuclide concentrations 

in BWRs......................................................................................................... 4-18

Table 4-9 RCS radionuclide concentrations for a reference BWR plant ......................... 4-19

Table 4-10 Values for coefficients used in the Powers’ spray removal model .................. 4-22

Table 4-11 Correlations of natural deposition decontamination coefficients 

for PWRs DBAs ............................................................................................. 4-24

Table 4-12 Correlations of natural deposition decontamination coefficients 

for BWRs DBAs ............................................................................................. 4-25

Table 4-13 Correlations of natural deposition decontamination coefficients 

for APWR DBAs............................................................................................. 4-26

xi

ACKNOWLEDGMENTS

Many people, both with the U.S. Nuclear Regulatory Commission as well as at contractor 

organizations have contributed to the development of SNAP/RADTRAD. The individual who 

has provided unflagging support for the development of SNAP/RADTRAD over the past several 

years is Mark Blumberg from the Office of Nuclear Reactor Regulation. Mark has been the 

Technical Monitor for the RADTRAD code’s design, computational methods and testing since 

1997. He has also provided much insight into dose analysis for licensing applications 

throughout the code’s conversion to the Java computer programming language and the entire 

SNAP/RADTRAD development process. The agency would like to recognize Chester Gingrich 

from the Office of Nuclear Regulatory Research who was responsible for the initial conversion 

and code programming of RADTRAD into Java. Another individual who is acknowledged is 

Stephen LaVie from the Office of Nuclear Security and Incident Response whose development 

of the RNEditor code is a key element of the source term modeling approach used in 

SNAP/RADTRAD. Finally, the support of John Tomon of the Office of Research who is the 

current Contracting Officer’s Representative and whose patience and guidance is greatly 

appreciated.

In the contractor organizations, the contributions of Ken Jones of Applied Programming 

Technology who, along with his programming staff, develop and maintain the SNAP code are 

greatly appreciated.

xiii

ABBREVIATIONS

APT Applied Programming Technology

AptPlot Applied Programming Technology plotting package

APWR advanced pressurized-water reactor

APWR-DBA advanced pressurized-water reactor design basis accident

Bq Becquerels

BWR boiling-water reactor

BWR-DBA boiling-water reactor design basis accident

BWR-GALE boiling-water reactor gaseous and liquid effluent code

CEDE committed effective dose equivalent

Ci Curies

CRDA control rod drop accident

DCF dose conversion factor

DE dose equivalent

DE I-131 dose equivalent iodine 131

DE Xe-133 dose equivalent xenon 133

DF decontamination factor

DBA-TID design-basis accident based on TID-14844

DBA-AST design-basis accident using NUREG-1465 (Regulatory Guide 1.183) 

models

EAB exclusion area boundary

FGR Federal Guidance Report

FHA fuel handling accident

GUI graphical user interface

HEPA high-efficiency particulate air

LOCA loss-of-coolant accident

LPZ low population zone

Mwt megawatt thermal

NRC U.S. Nuclear Regulatory Commission

ODE ordinary differential equation

PWR pressurized-water reactor

PWR-DBA pressurized-water reactor design basis accident

PWR-GALE pressurized -water reactor gaseous and liquid effluent code

RCS reactor coolant system

RADTRAD RADionuclide Transport, Removal, And Dose Estimation

RAMP Radiation Protection Computer Code Analysis and Maintenance Program

REA rod ejection accident

RG Regulatory Guide

SI International System of Units

SNAP Symbolic Nuclear Analysis Package

Sv Sieverts

TEDE total effective dose equivalent

T/S technical specification

XML extensible markup language

1-1

1.0 INTRODUCTION

The purpose of the Symbolic Nuclear Analysis Package/RADionuclide Transport, Removal and 

Dose Estimation (SNAP/RADTRAD) code is to determine the dose from a release of 

radionuclides during a design basis accident to the exclusion area boundary (EAB), the low 

population zone (LPZ), and the control room and other locations of interest. As radioactive 

material is transported through the containment, the user can account for sprays and natural 

deposition to reduce the quantity of radioactive material. Material can flow between buildings, 

from buildings to the environment, or into control rooms through high-efficiency particulate air 

(HEPA) and charcoal filters, piping, or other connectors. Decay and in-growth of daughters can 

be calculated over time as the material is transported.

The focus of SNAP/RADTRAD is licensing analysis to show compliance with nuclear plant siting 

and control room dose limits for various loss-of-coolant accidents (LOCAs) and non-LOCA 

accidents. The RADTRAD code was originally developed by the Accident Analysis and 

Consequence Assessment Department at Sandia National Laboratories for the U.S. Nuclear 

Regulatory Commission (NRC) in 1997 as documented in NUREG/CR-6604, “RADTRAD: A 

Simplified Model for RADionuclide Transport and Removal and Dose Estimation,” [1]. The code 

was revised to include a Visual Basic graphical user interface (GUI) for user convenience in 

1999, which is described in NUREG/CR-6604, Supplement 1, “RADTRAD: A Simplified Model 

for RADionuclide Transport and Removal and Dose Estimation,” [2]. Finally, NUREG/CR-6604,

Supplement 2, “RADTRAD: A Simplified Model for RADionuclide Transport and Removal and 

Dose Estimation,” [3] was published in 2002 discussing the testing of RADTRAD version 3.03.

The NRC decided to update RADTRAD by converting the code into Java and develop a 

RADTRAD plugin to interface with the SNAP Model Editor GUI. As part of this update to 

RADTRAD, the RADTRAD analytical code (RADTRAD-AC) was separated from SNAP and 

distributed as SNAP/RADTRAD version 4.0. The SNAP Model Editor GUI with the RADTRAD 

plugin is used to develop models and prepare input which is then processed by the RADTRADAC (version 4.5.2). The RADTRAD-AC then calculates the dose and generates the results. 

The combined package is referred to as SNAP/RADTRAD. Use of RADTRAD in the SNAP 

framework allows use of the SNAP features including the Model Editor for developing plant 

models. The Model Editor also provides tools for user input checking, for submitting and 

monitoring calculations, and for running multiple cases. The RADTRAD-AC generates data 

output files suitable for plotting with the Applied Programming Technology plotting package 

(AptPot).

As part of the development of the RADTRAD plugin for SNAP, the user documentation is being 

updated. This report provides the documentation for the use of and the calculation models in 

SNAP/RADTRAD.

2-1

2.0 INSTALLATION GUIDE

This section of the report discusses how to obtain and install SNAP/RADTRAD and the 

RADTRAD-AC codes.

2.1 Distribution

SNAP/RADTRAD is distributed in two parts: the SNAP Model Editor GUI with the RADTRAD 

plugin and the RADTRAD-AC. SNAP with the RADTRAD plugin is used for model development 

and input preparation while the RADTRAD-AC carries out the calculations and generates the 

results. SNAP with the RADTRAD plugin is maintained by Applied Programming Technologies, 

Inc. (APT) and the RADTRAD-AC analytical code is maintained by Information Systems 

Laboratory, Inc.

Directions for obtaining the SNAP Model Editor GUI with the RADTRAD plugin and the 

RADTRAD-AC are available at the Radiation Protection Computer Code Analysis and 

Maintenance Program (RAMP) website (https://www.usnrc-ramp.com). Current version 

information for SNAP with the RADTRAD plugin and RADTRAD-AC are also available at the 

NRC RAMP website. Note that results plotting capability has been built into SNAP/RADTRAD 

using the AptPlot program.

The SNAP Model Editor GUI with the RADTRAD plugin and the AptPlot program is available 

from the APT website (https://www.snaphome.com). The RADTRAD-AC analytical code is 

available from the RAMP website (https://www.usnrc-ramp.com). This code is designed to be 

compatible with the SNAP Model Editor GUI with the RADTRAD plugin.

2.2 Hardware and Software Requirements

The SNAP Model Editor GUI with the RADTRAD plugin and the RADTRAD-AC code 

(SNAP/RADTRAD) can be executed on any computer that supports Java applications. Any of 

the current generation of personal computers that can run the Java runtime environment is 

capable of running SNAP/RADTRAD. For a Windows computer, the Windows operating 

systems that can be used are Vista, Windows 7, Windows 8, and Windows 10. It should be 

noted that the following software is required:

• Java Standard Edition (SE) 6.0 or later. This package is currently available on

http://www.oracle.com/technetwork/java/javase/downloads/index.html.

• SNAP Model Editor GUI with the RADTRAD plugin code maintained by APT.

• RADTRAD-AC packaged separately, and distributed by RAMP.

• AptPlot – plotting package maintained by APT. For further details, see 

https://www.appliedprog.com.

Although not required, the jedit text editing program adds some user conveniences in 

SNAP/RADTRAD. This package is available from www.jedit.org.
2-2

2.3 Installation

Installation of SNAP is very similar to installation of any software package on a Windows 

system. Basically, directory locations on the hard drive to install SNAP are selected. If not 

already accepted earlier, license agreements are then displayed, which the user needs to agree 

to before proceeding. For SNAP and AptPlot, a Java-based installer file named 

Snapinstaller.jar and AptPlotinstaller.jar are provided that guides the installation process of 

SNAP and AptPlot. During the installation process, windows showing installation process and 

user-selectable installation options are displayed.

2.3.1 Installation of AptPlot

To download and install AptPlot select the download AptPlot Installer link (Step 2) on the APT 

website. This will open the AptPlot Installation Option window (Figure 2-1), which provides the 

user with three installation options for installation. The easiest and simplest option is installing 

AptPlot from the internet; however, some users prefer to download the AptPlot Installation Tool

(AptPlotinstaller.jar) to a local directory and then perform the installation from the local directory. 

If installing AptPlot from the local directory you should be able to double-click on the 

AptPlotinstaller.jar file from Windows Explorer to launch the application. If your system does not 

automatically launch jar files in this manner or if you default Java Runtime is earlier than 6.0

follow the directions on the APT website (Step 3) to run the installer.

Figure 2-1 AptPlot Installation Options window

Screenshots of the windows for the AptPlot Installation Tool, Figure 2-2, shows the progress of 

the installation. The location of the installation directory is shown in the Installation Directory

window. The user can change the location although the default location is usually adequate. 

After selecting the installation directory, the Java Runtime Environment License Agreement 

appears which the user must agree to in order for the installation process to proceed forward. 

Once this step is completed, a second license agreement for AptPlot (the GNU General Public 

license) will appear which again the user must agree to in order to continue.
2-3

Figure 2-2 AptPlot Installation Tool screenshots

The user will then be required to select plugins. In the case of AptPlot, the user will select the 

analysis code support (ACS) Plugin and then click on Continue. The installation will proceed to 

completion and the user clicks on Close in the AptPlot Installation Tool window to exit the 

AptPlot installation.

2.3.2 Installation of SNAP

The installation steps for the SNAP are essentially the same as for AptPlot, although the 

windows are somewhat different. The SNAP Installation Tool (Snapinstaller.jar) is downloaded 

from the APT website in a manner similar to that described in Section 2.3.1 above, with the 

exception that the user must first read and accept the Binary Code License Agreement prior to 

downloading SNAP. Once this agreement is accepted a download instructions webpage similar 

to the one described in Section 2.3.1 above opens. Select the download SNAP Installer link 

(Step 2) on the webpage to open the SNAP Installation Option window. The selections on this 

window are identical to those described for Figure 2-1.

Screenshots of the windows for the SNAP Installation Tool, Figure 2-3, shows the progress of 

the installation. The location of the installation directory is shown in the Installation Directory

window. The user can change the location although the default location is usually adequate. 

After selecting the installation directory, the Java Runtime Environment License Agreement 

appears which the user must agree to in order to continue the installation. Once this step is 

completed, a second license agreement for the APT binary code license agreement appears 

which again the user must agree to in order to continue.
2-4

Figure 2-3 SNAP Installation Tool screenshots

The user will then be required to select plugins. In the case of SNAP/RADTRAD, the user will 

select the AVF, ENGTMPL, EXTDATA, RADTRAD, and Uncertainty plugins and then click on 

Continue. The installation will proceed to completion and the user clicks on Close in the SNAP 

Installation Tool window to exit the SNAP installation. If the user wants to know the purpose of 

each plugin, the user can click on each package name and a description will appear on the 

right-hand side of the plugin manager window as illustrated in Figure 2-3.

The installation files are written to the \users\homedir where homedir is the home directory for 

the login ID being used unless you specified a different location. These files are included in the 

snap and .snap directories. The code files are written to the snap directory and files needed to 

use SNAP on a given system are written to .snap directory. For example, the location of the 

root folder on a given computer is written to the .snap directory. The installation files for AptPlot 

are also in \users\homedir in the AptPlot and .aptplot directories. If the user is uncertain of the 

location of the home directory, a command window can be opened by going to Start and typing 

in command in the Search textbox (Windows 7). A command prompt window should appear 

(select Command Prompt from menu above if necessary). Then, type in echo

%USERPROFILE% and your home directory will be displayed.
2-5

2.3.3 Installation of the RADTRAD-AC

The RADTRAD-AC should be installed in the user created radtrad subdirectory under the snap

directory in the \users\homedir. The RADTRAD-AC distribution consists of a group of Java .jar

files that are distributed as a zip file from the NRC RAMP website (https://www.usnrcramp.com/Ramp-Code-Download/2/Code/SNAP%20RADTRAD%20Code). These files are:

• castor-codegen.jar

• castor-core.jar,

• castor-xml.jar,

• castor-xml-schema.jar,

• commons-logging.jar, and

• radtrad.jar.

To install these file, create a subdirectory named radtrad in the directory for SNAP/RADTRAD, 

unzip the files and copy them to that directory. Note: The path to the radtrad.jar file needs to 

be set using the configuration tool (see Section 3.2.2) to the following setting:

$snap\radtrad\radtrad.jar,

If the aforementioned .jar files are copied to a radtrad subdirectory in the SNAP/RADTRAD 

directory, the code should be ready for use. The location of this link within the SNAP framework 

is discussed in Section 2.2.

2.3.4 Updates to SNAP, AptPlot and the RADTRAD-AC

SNAP will automatically make users aware of any available updates to SNAP and its associated 

loaded plugins when the user opens the SNAP Model Editor and the Welcome to Model Editor

screen appears (Figure 2-4).

If the computer has an internet connection, SNAP will compare the currently installed version of 

SNAP and all its associated plugins to the latest versions available on the APT website listed in 

Section 2.1. If there are updates available to either SNAP or any of the loaded plugins the 

Welcome to Model Editor screen will indicate the number of update available to the user. The 

user may perform these updates by logging into the APT website (Section 2.1) to download and 

run the SNAP Installer Tool. The SNAP installer samples the version of SNAP which the user 

has loaded to see what plugins are being used and if they are the latest versions of those 

plugins. The SNAP installer will then ask the user during the installation process to check or 

uncheck the option boxes for the plugins to be installed on the update. The SNAP Installer will 

automatically update these plugins.
2-6

Figure 2-4 Welcome to Model Editor screen

There is no automatic means by which users are notified of updates to AptPlot and the 

RADTRAD-AC. In the case of AptPlot the users can verify the latest version of the code by 

logging into the APT website (Section 2.1) and checking the site for the latest version of the 

AptPlot code. Likewise for the RADTRAD-AC, users can verify the latest version of the code by 

logging into the RAMP website (Section 2.1) and checking the site for the latest version of the 

RADTRAD-AC.

2.4 Sample Problems

A set of sample problems for SNAP/RADTRAD are provided on the RAMP website. These 

problems provide a starting point for the user. In addition, there is a Test23 sample problem 

provided with the SNAP installation files from APT. This problem is used to illustrate the use of 

SNAP/RADTRAD in Section 3.0. The user will also find the information on the QuickStart.pdf

file on the RAMP website to be useful.

2.5 Contact Information

Any questions, suggestions, corrections or comments concerning this the code or its 

documentation should be submitted via the SNAP/RADTRAD Support link on the RAMP 

website.

2.6 Code Error and Problem Reporting

While every effort has been made to minimize errors in SNAP/RADTRAD, there may be 

unanticipated circumstances that lead to errors and problems (bugs). To report errors and bugs 
2-7

with the program, first collect as much information as possible about the error or bug. This 

information should include answers to the following questions:

• What version of the SNAP/RADTRAD program are you running? The information for 

SNAP can be found on the screen displayed at startup or by using the Help | About

menu item. Click the Plugins button at the bottom of the popup screen to get the 

information about the SNAP/RADTRAD Plugin.

• What computer operating system is SNAP/RADTRAD being executed on?

• Is the error or bug reproducible?

• What are the steps leading up to the problem?

• What are the exact symptoms (e.g. program crash, error message, etc.)?

• Save the case files and attach them to an issue report.

To report a problem, send a zip file with the case files and answers to the above questions to the

SNAP/RADTRAD Forum webpage under the SNAP/RADTRAD Support link (https://www.usnrcramp.com/content/snapradtrad-support) on the US NRC RAMP website.

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3.0 MODEL DEVELOPMENT USING SNAP/RADTRAD

To run SNAP/RADTRAD will require some familiarity with the overall SNAP approach to 

developing and running models. In this section, the approach to using SNAP to develop, modify 

and execute RADTRAD problems will be discussed. However, SNAP includes many features 

which will not be discussed here. For the interested user, the Symbolic Nuclear Analysis 

Package User's Manual [4] provides more detailed information on the use of SNAP.

3.1 Overview of SNAP/RADTRAD

SNAP is actually a suite of computer applications used to develop, modify, and execute 

computer models principally for thermal hydraulic codes such as the TRAC/RELAP Advanced 

Computational Engine (TRACE) and Reactor Excursion and Leak Analysis Program (RELAP5). 

Of these tools, the Configuration Tool, Model Editor and the Job Status tools are most relevant 

to RADTRAD analysis. The Configuration Tool is used to configure global properties for running 

RADTRAD under SNAP. The Model Editor provides a GUI used to develop RADTRAD models. 

The Job Status tool is used to obtain the job status. Of these tools, the Model Editor is the tool 

used the most as it is the primary tool for developing SNAP/RADTRAD models.

Generally, the approach for developing a new SNAP/RADTRAD model is to define the 

compartments and connections in flow pathways that represent the plant and optionally the 

control room and/or the technical support center being analyzed. Note that flow pathways are 

used to connect components in SNAP/RADTRAD. During the specification of components and 

flow pathways, removal models should be considered and specified for each normal 

compartment as appropriate. For compartments, these removal models include filtration, 

sprays, or natural deposition. The user will need to specify each model required and specify the 

required data using the SNAP Model Editor GUI as a guide.

Once the geometric, flow/leakage and removal information is specified for the compartments 

and flow pathways, a source term is then specified. A comprehensive list of nuclides based on 

International Commission on Radiological Protection (ICRP) Report 38 (ICRP-38) [5] has been 

included in SNAP/RADTRAD. The user will need to decide whether the analysis is either being 

done based on the occurrence of a LOCA by selecting either TID-14844, “Calculation of 

Distance Factors for Power and Test Reactor Sites,” [6] or NUREG-1465, “Accident Source 

Terms for Light-Water Nuclear Power Plants,” [7] and for a non-LOCA where both radionuclides 

from the fuel and the reactor coolant activity may be important contributors and make the 

appropriate selections for the plant being analyzed. A plant power level must be defined to 

obtain the correct source term. The iodine physical form must also be defined as the rate of 

removal and filtration depends on the physical form of iodine.

Parameters related to the dose rate are specified, including Χ/Q data for each receptor location 

and dose conversion factors (DCFs). Default DCFs based on EPA-520/1-88-020, “Limiting 

Values of Radionuclide Intake and Air Concentration and Dose Conversion Factors for 

Inhalation, Submersion, and Ingestion,” Federal Guidance Report No. 11 (FGR 11) [8] and EPA402-R-93-081, “External Exposure to Radionuclides in Air, Water, and Soil,” Federal Guidance 

Report No. 12 (FGR 12) [9] (see Section 4.6) are built into SNAP/RADTRAD. The EAB and the 

LPZ are defined by default in SNAP/RADTRAD. Other dose receptors can be added as 

needed. For each dose receptor that is located in the environment or draws from the 

environment such as a control room, time-dependent Χ/Q and breathing rate values must be 
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specified. For the control room, occupancy factors must also be specified. Note that default 

values for breathing rates are provided which are suitable for most analyses.

SNAP/RADTRAD can be used to develop new models and is backwards compatible to import 

and modify existing RADTRAD version 3.03 and 3.10 models (“*.psf” files). The key aspect of 

model development is the use of compartments and connecting flow pathways to model a 

system. The approach used to prepare this section was to open the SNAP Model Editor GUI 

and start exploring the features for RADTRAD model development. Therefore, the discussion in 

the following sections assumes that the user has SNAP available and open and that the user 

will follow along with the discussion by using the SNAP Model Editor. There is no better way to 

learn how to use the SNAP Model Editor GUI except to actually use it.

3.2 The Model Editor User Interface- Model Development

This subsection describes working within the SNAP/RADTRAD Model Editor to develop and 

modify models.

3.2.1 Overview of Existing Model Features

As noted earlier, the SNAP/RADTRAD Model Editor is the basic tool used to create, modify and 

run input models. To start the Model Editor, navigate to Start->All Programs->SNAP->Model 

Editor, and the Model Editor should start.

To illustrate many of the features in SNAP, the Test 23 sample problem will be used. This 

problem is found in the snap\Samples\RADTRAD\Test23 subdirectory in the snap directory (see 

Section 2.3). It is recommended that a copy of the Test23.med file be placed in the user’s 

working directory, which is the directory where the input and output files will be kept. It is also 

recommended that the user open Test23 and follow along with the presentation in this section.

When the Model Editor is started, a splash screen appears for several seconds and then a 

Welcome to Model Editor screen appears as shown in Figure 3-1 with the Model Editor window 

in the background. Note that if a previous Model Editor session has been exited without first 

closing the model in use then the Restore Session prompt screen will open, as also shown in

Figure 3-1.

Several options are available on the Welcome to Model Editor screen, which are listed below:

• Create A New Model

• Open a Model Document

• Import a New Model

• Start an Empty Session

• SNAP Version Updates

Under each of these items a short description of each option is provided to explain what each

option does.
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Figure 3-1 Opening the Model Editor

Once the SNAP Model Editor is open, the user selects Continue under Open a Model Document

on the Figure 3-1. Navigate to the location of the Test23 subdirectory under the samples 

directory. Click on the file Test23.med. The Model Editor rendering of Test23 will open as 

shown in Figure 3-2. If not, click on the “default view” tab at the bottom of the page to see this 

view. Alternately, the user can click on the Test23.med file in the working directory to start the 

SNAP Model Editor.

Finally, the model can also be opened by selecting File->Open, navigating to the input file (.med

file) of interest, selecting that file and clicking on open, much like any Windows program. Notice 

that there are three separate input sections in the SNAP Model Editor window shown in Figure 

3-2 which are: the Navigator window, the Property window and the View / Dock window where 

the model rendering appears. Also, notice that there are two tabs in the View / Dock window

labeled Default View and Test23 View. In Figure 3-2 the Default View for Test23 is shown 

which gives the model rendering for Test23. The Test23 View provides the job stream view for 

Test23 and the tabs can be clicked-on to show either the modeling rendering or the job stream 

(similar to Microsoft Excel). Job streams will be discussed later in this section. There is also a 

Message window underneath the View / Dock window which lists messages from 

SNAP/RADTRAD.

Before editing, the user should note that each of the windows shown in Figure 3-2 can be 

resized either horizontally or vertically. Resizing is done by hovering the mouse cursor over the 

border between the windows until a double-headed arrow appears. Then the user clicks and 

drags the border to the desired location.
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The user will need to unlock the model by clicking on the Lock ( ) icon shown in Figure 3-2. 

Notice that other icons adjacent to the Lock ( ) icon will change to unlocked ( ) on the toolbar.

Figure 3-2 SNAP Model Editor screen

One powerful feature in SNAP/RADTRAD is the ability to check the model for input errors. To 

illustrate the use of this feature, click on Tools->Check Model to perform a model check. Note 

that the message Note: Model check complete. No errors found in the Message window at the 

bottom of the screen.

The input groups are shown in the Navigator window. Clicking on the Expand ( ) icon will 

expand each group and node, showing the associated input data for that input group and node. 

Figure 3-3 presents an illustration of a node expansion which is obtained by clicking on the

Expand ( ) icon next to Compartments, then clicking on Compartment 1. Note that the 

Compartment 1 input appears in the Property window (lower left). The user should experiment

with other input groups as the approach is the same. Input specification will be presented later

in this section.

Note that the black bar where the input model name appears (Test23.med) contains some 

important features which are summarized in Section 3.4. One of these features is the ability to 

switch units from British to International System of Units (SI). Units switching is done by rightclicking on the black bar, selecting Engineering Units->British to change the units from SI to 

British.
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Figure 3-3 Illustration of the expand icon

Icons are used to represent the various components used in the View / Dock window that 

comprise a typical model. Figure 3-4 presents an illustration of the various icons used.
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Figure 3-4 Illustration of the various icons used to represent a SNAP/RADTRAD 

model

3.2.2 Job Streams and Case Execution in SNAP/RADTRAD

Before continuing the discussion of existing model features and developing a new model, the 

Test23 case will be run to illustrate how cases are run.

Case execution is dependent on the job stream, which may be a source of confusion for new 

SNAP/RADTRAD users. Simply put, job streams are used to pass input and output data from 

one code to another for cases where multiple codes are used. SNAP is used to support a wide 

variety of analysis programs that pass data from one program to another. This feature is less of 

an issue with SNAP/RADTRAD because in most cases, output from SNAP/RADTRAD 

(RADTRAD-AC) is only passed to AptPlot for plotting. For the convenience of the user, a 

default job stream is predefined for all SNAP/RADTRAD cases.

Figure 3-5 presents a typical SNAP/RADTRAD job stream. The default job stream for 

SNAP/RADTRAD shows three steps: 1) input preparation shown in the RADTRAD Model

(Base_Model node), 2) the analytical code execution in the RADTRAD (RADTRAD node)

(middle box in Figure 3-5), and 3) the passing of plot data from SNAP/RADTRAD to AptPlot 

(PlotStep node). The input is passed from the Model Editor (Base_Model node) to the 

RADTRAD-AC (RADTRAD node) and then the plot file data generated by the RADTRAD-AC is 

passed to the AptPlot (PlotStep node).
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Figure 3-5 Typical job stream in SNAP/RADTRAD

As in the case of model input, job streams specification can also be checked. In the case of the 

Test23 problem, expand the Job Stream node in the Navigator window; select Test23 and rightclick, then select Check Stream. An error report window will appear in the Message window 

and in this case, no errors were found.

Part of the job stream input specification is to determine where the RADTRAD-AC output will be 

written. To display the location of the RADTRAD-AC output clicking on the Expand ( ) icon for 

the Job Streams node and select the Test23 job stream to open the Property window as 

illustrated in Figure 3-6.

Figure 3-6 Job stream Property window

The two job stream properties which determine where the output is written are the Root Folder

text box and the Relative Location text box. The SNAP/RADTRAD output is then the Relative 

Folder location appended to the Root Folder location. To review the root folder settings, click on 

the Custom Editors ( ) icon and a window similar to that shown in Figure 3-7 appears. In this 

example, three root folders along with the path locations are shown.
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Figure 3-7 Typical root folder settings in SNAP/RADTRAD

Assuming that the root folder is set to Samples, the path to the output will be 

Samples\RADTRAD or C:\Work\Current\0-RADTRAD\Training\Samples\RADTRAD. In a new 

installation, the root folder is not set. When the root folder is not set, the message No Root 

Folders Available appears in red as shown in Figure 3-8.

Figure 3-8 Job stream Property window with an unset root folder

Setting the root folder requires selecting the Custom Editors ( ) icon under the Root Folder text 

box to open the Edit Calculation Server Root Folders window (Figure 3-7). Click on the New 

( ) icon and navigate to the desired location in the Select Folder Location window. The root 

folder name will change to the last folder name in the directory path.
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The relative location can be reset and should be reset to a name more mnemonic so that the 

SNAP/RADTRAD cases can be tracked. For example, to change the name, highlight the 

Relative Location Name and type in a new name (Sample to Test23). Note that the file location 

is automatically appended.

Note that multiple root folders are allowed which is handy for organizing SNAP/RADTRAD case 

files. To add a root folder, navigate to Tools->Job Status or click on the Job Status ( ) icon and 

expand Local. Right-click on Local and select Root Folders. Click on the New ( ) icon (left on 

Toolbar) and navigate to where you want the root folder (ex. NPP Dose Analysis). The root 

folder path will be created. Also, a path of subdirectories can be specified in the Relative 

Location text box separated by a backslash ( \ ). For example, the relative location can be set to 

RADTRAD\LOCA, so that the path to the output would be snap\Samples\RADTRAD\LOCA

assuming that the root folder is set to Samples.

A couple of points should be noted about root folders. First, the root folder directory needs to 

exist – otherwise you’ll get a warning that the directory doesn’t exist and the root folder will 

not be defined. Second, overlapping paths are not allowed and will generate an error.

Finally, one remaining item should be configured before proceeding to submit the job stream 

for execution. This remaining item is to the link the SNAP Model Editor to the RADTRAD-AC

by navigating to Tools->Configuration Tool to open the SNAP Configuration window and then 

expanding the Applications node by clicking on the Expand ( ) icon. After the Applications

node has been expanded, right click the Applications node to open the drop-down menu as 

shown in Figure 3-9. Select New on the drop-down menu to open the Create Application

window. Enter RADTRAD in the Application Name text box and scroll down to select the 

RADTRAD application and click OK as shown in Figure 3-9.
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Figure 3-9 Linking the RADTRAD-AC using the SNAP configuration tool

The SNAP Configuration window will then change to display the RADTRAD application with 

an error under the Applications node (Figure 3-10). On the right hand side of the SNAP 

Configuration window under the Application Location->Local Location text box click the Select

( ) icon to open Windows File navigator. Navigate to radtrad subdirectory under the snap

directory in the in the user’s home directory as discussed in Section 2.3.3 and select the 

radtrad.jar file for the RADTRAD-AC (not the RADTRAD Plugin). (Note: The file directory 

path should look something like “C:\Users\{User Name}\snap\radtrad\radtrad.jar” and not

“C:\Users\{User Name}\snap\Plugins\radtrad.jar.”) Be sure to save these changes by 

selecting the Save ( ) icon and the Close button on the Save Complete window as shown in 

Figure 3-10. At this point, the user can run Test23.
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Figure 3-10 Saving the RADTRAD-AC using in the SNAP configuration tool

To run the Test23 or any other case, click on Tools->Submit Job. A Submit Job Stream window 

will appear as shown in Figure 3-11. Click on OK and a confirmatory Submit Stream window 

will appear. Finally, click OK and the run will start. The SNAP Job Status window will appear 

which is also shown in Figure 3-11. The SNAP Job Status window, in Figure 3-11 displays a 

completed job stream run.
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Figure 3-11 SNAP/RADTRAD job stream and status windows

The relationship between the SNAP/RADTRAD job stream and the actual case execution is 

shown in Figure 3-12. In the upper left-hand corner, the graphical job stream representation is 

shown. As noted earlier, this representation shows passing input from the Model Editor to the 

RADTRAD-AC and then to AptPlot. The job stream properties are shown in the Navigator

window shown in the upper-right corner of Figure 3-12. The links between the various nodes 

are also shown. In the SNAP Job Status window, the status of each of the job stream steps is 

shown. Again three steps are shown. The user interaction with the SNAP Job Status window 

will be discussed in Section 3.2.3.
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Figure 3-12 Relationship between job stream steps and code execution

Note that the SNAP Job Status window can be accessed from Tools->Job Status in the Model 

Editor for subsequent viewing. A summary of features relevant to SNAP/RADTRAD available in 

the SNAP Job Status window are listed below:

• The Job Console ( ) icon – provides the time step history for the current job.

• The Job Execution ( ) icon – terminates the execution of the current job. This is only

available when the job is running.

• The Job Deletion ( ) icon – removes the current job and files.

• The AptPlot ( ) icon – opens the selected job for plotting in AptPlot.

• The File Viewer ( ) icon – starts the output file viewer.
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3.2.3 SNAP/RADTRAD Input and Output Files

There are a number of files produced that the user should be aware of in SNAP/RADTRAD. 

The main SNAP/RADTRAD interface file is the casename.med file where casename is the 

name of the case being analyzed. The casename.med file contains the data needed to render 

the model in the SNAP Model Editor GUI, the default data used by the code and the userspecified input data. Section 3.4 discusses the actual input that can be specified for a 

SNAP/RADTRAD model.

When a SNAP/RADTRAD case is executed through the RADTRAD-AC, the data flow is not 

directly from the casename.med file. Rather, there are a number of data files that are produced 

by the SNAP/RADTRAD plugin that are read by RADTRAD-AC. These files, which are in 

extensible markup language (XML) format, include DCFs (“*.dfx”), nuclide data (“*.nix”), plant 

information (“*.psx”), release fraction (“*.srx”), and nuclide inventory (“*.icx”) files. Output files 

(.out, .screen and .plot) are produced by the RADTRAD-AC. Log files produced by 

SNAP/RADTRAD are job stream related files (“*.streamlog” and “*.tasklog”). Table 3-1 provides 

a brief description of these files.

When case execution is completed, the SNAP/RADTRAD output can be reviewed by clicking on 

the File Viewer ( ) icon. Note that there is a context in terms of the active job stream step and 

the output that is displayed. If the casename step is highlighted, then the job stream log will be 

available for viewing. If the RADTRAD step is highlighted as shown in the SNAP Job Status

window in Figure 3-13, then the RADTRAD-AC output is available. If the PlotStep is 

highlighted, then the plot file data can be viewed using AptPlot. Figure 3-13 shows a 

screenshot of the drop-down menu cascade from the File Viewer ( ) icon for the RADTRAD job 

step from the SNAP Job Status window.

Figure 3-13 Drop-down menus for SNAP/RADTRAD output
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Table 3-1 Files available for viewing using the file viewer in the job status window

File Name Description

Job Status Window Casename Files

StreamLog - Casename.streamlog a

Output from job stream manager. Provides a highlevel summary of the execution steps for the job 

stream. Typically not reviewed by the 

SNAP/RADTRAD user.

Job Status Window RADTRAD Files

Plot Files->plot - radtrad.plt c Data file for AptPlot from the RADTRAD-AC.

Text Files->input – radtrad.psx b

Plant data input file in XML format. Includes the plantspecific data specified by the user including model 

parameters, information for plant geometry for each 

compartment, information for each flow path, dose 

point information including Χ/Q and breathing rates,

occupancy factors, and information for various 

radionuclide removal models (sprays, natural 

deposition, and filters).

Text Files->nix – radtrad.nix b

Nuclide data information from ICRP-38 in XML format. 

Includes the atomic mass, half-life (s), and branching 

ratios for radionuclide daughters.

Text Files->dfx – radtrad.dfx b

DCF file in XML format based on FGR 11 and 12 (see 

Section 4.6). Includes the organ-specific DCFs. Note 

that only the cloudshine (immersion), the inhaled 

chronic [total effective dose equivalent (TEDE)] and 

thyroid skin DCFs are used to determine dose. 

Organ-specific factors as well as those factors for 

groundshine, inhaled acute and ingestion are not 

used.

Text Files->icx_1 – radtrad_1.icx b

Text Files->icx_2 – radtrad_2.icx b

(etc.)

Initial radionuclide inventory file in XML format.

Duration of source term release and release fractions.

Text Files->srx_1 – radtrad_1.srx b

Text Files->srx_2 – radtrad_2.srx b

(etc.)

Release fraction information file for each radionuclide 

group.

Text Files->output – radtrad.out c Output file from the RADTRAD-AC in the original 

format.

Text Files->NRC-out – radtradNRC.out c Output file from the RADTRAD-AC in the revised NRC 

format.

Text Files->log – radtrad.log a Debug output (usually not referred to by the user).
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Table 3-1 Files available for viewing using the file viewer in the job status window

(cont.)

File Name Description

Text Files->screen – radtrad.screen c Problem time output to show progress of a given 

case.

Text Files->Task Log – RADTRAD_tasklog a

Output from SNAP job steam showing RADTRAD job 

step execution information (usually not referred to by 

the user).

Job Status Window PlotStep Files

PDF Documents – time_pdf – time.pdf c Time step results (usually not referred to by the user).

Text-Files->screen – aptplot.screen Screen output from AptPlot (usually not referred to by 

the user).

Text-Files->Task Log – PlotStep.tasklog

Output from SNAP job steam showing AptPlot job 

step execution information (usually not referred to by 

the user).

a. SNAP/RADTRAD specific output.

b. Input file to the RADTRAD-AC generated by SNAP/RADTRAD plugin.

c. Output file from the RADTRAD-AC.

The files produced by the RADTRAD-AC code, radtrad.out, radtradNRC.out, radtrad.plt, and 

radtrad.screen are the most relevant to the user. The radtrad.out file is basically the original 

(version 3.03/3.10) output file. Major sections of this output file are:

• Input listing – provides a listing of the input in XML format that is used by the 

RADTRAD-AC.

• Input echo – provides an edited input summary of plant description (model), scenario 

(radionuclide source term/DCF) information, compartment/pathway data, Χ/Q, DCF 

and decay data, and other relevant input.

• Breakdown of dose results and nuclide inventory in various compartments at various 

time points generally selected by changes in events (i.e. time at which flow rate 

changes, and time at which Χ/Q changes). Activity balance information is also given.

• I-131 inventory in various compartments as a function of time.

• Cumulative dose results at various dose locations as a function of time.

• Worst two-hour doses at the EAB and the final doses and final doses for the LPZ and 

other dose locations.

The output contents can be controlled from Model Options node by expanding the Output 

Parameters tab in the Property window as shown in Figure 3-14. The main difference in the 

output is generally the editing of results for supplemental time steps when they are used and the 
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model removal/decontamination factors. The Output Parameters flags are discussed in more 

detail in Table 3-5.

Figure 3-14 Expanded Output Parameters tab in the Property window

The radtradNRC.out output file provides a time-dependent summary of activity and dose 

calculations by nuclide. The contents of the radtradNRC.out file are controlled by expanding the 

NRC Output Flags tab under Model Options node in the Property window. See Figure 3-15 for 

the output parameters available. Major sections of this output are:

• Input echo – provides an edited input summary of plant description (model), scenario 

(radionuclide source term/DCF) information, compartment/pathway data, Χ/Q, DCF

and decay data, and other relevant input.

• Output – activity distribution, cumulative and dose difference (delta-dose) for each 

dose component (inhalation, cloudshine, skin, thyroid, and TEDE).

• I-131 inventory in various compartments as a function of time.

• Cumulative dose results at various dose locations as a function of time.

• Worst two-hour doses at the EAB and the final doses and final doses for the LPZ and 

other dose locations.

The NRC Output Flags are discussed in more detail in Table 3-5. The radtrad.screen file lists 

the time step history for a given SNAP/RADTRAD case.
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Figure 3-15 Expanded NRC Output Flags tab in the Property window

3.2.4 AptPlot Plotting Program

A feature of SNAP/RADTRAD is the ability to display plots of dose results. To display a plot, 

click on Plot Files and select plot – radtrad.plt. AptPlot will open. Alternately, click on the 

AptPlot ( ) icon in the SNAP Job Status window and AptPlot will open as illustrated in Figure 3-

16.

Figure 3-16 SNAP/RADTRAD Job Status window with AptPlot icon highlighted
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When AptPlot opens, the windows presented in Figure 3-17 will appear. Dose information by 

dose location (ExclusionAreaBoundary, LowPopulationZone, and ControlRoom spaces omitted)

and dose category (body, cloudshine, skin, tede, and thyroid) for each nuclide separated by 

periods will be presented in the Select EXTDATA Channels window in Figure 3-18. In AptPlot, 

each data set is referred to as a data channel. Test Problem 23 is used to illustrate the features 

of AptPlot and it is suggested that the user open AptPlot for Test Problem 23 and follow the 

discussion below.

Figure 3-17 AptPlot startup view

Basically to make a plot, the user scrolls to the result of interest, highlights that result, clicks on 

the Plot button and the plot will appear. Note that the default time units are in seconds, but that 

can be changed to hours in the drop-down menu next to Time Units text box on the Select 

EXTDATA Channels window (Figure 3-18) prior to actually generating the plot.

AptPlot has many features for generating and formatting plots and the discussion presented 

here is not meant to be exhaustive. A comprehensive help manual can be obtained by selecting 

Help->Help Topics from the top menu. However, some of the more commonly used features 

are illustrated here.

As the user gains familiarity with the naming convention, the filter feature can be used to locate 

specific results of interest by entering the dose location, dose category, and nuclide of interest in 

the Filter text box (Figure 3-18). If the user wants to plot the TEDE dose results for the control 

room, enter the text string ControlRoom.tede* in the Filter text box. Note that the total TEDE 

dose ends with tede (i.e. no nuclide is listed). Also note that the asterisks (wildcard) symbol is 

used to control the list of all items. Wildcards can be embedded in the string (i.e.
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ControlRoom.*.I*) to list the control room dose categories for all iodine nuclides. It is very 

important to note that the case of a character counts in applying filters in AptPlot, otherwise the 

wildcard search feature will not work properly. The spelling of the dataset name in the data 

channel window provides a guide for spelling a channel name.

Figure 3-18 Select EXTDATA Channels window for multiple plots

Multiple data results can be plotted by highlighting the data of interest and clicking the Plot

button. As an example, suppose the user wants to plot the thyroid dose for I-131 through I-135 

for Test Problem 23. The user would enter ControlRoom.thyroid.I* in the Filter text box, then 

select the resulting data channels in the Select EXTDATA Channels window and click on the 

Plot button to make the plot. This string can be shortened to C*R*th*I* as a further example of 

the application of wildcards. To select multiple data channels requires the use of shift-click or 

control-click feature as described below:

• Shift-click – used to select a range of datasets. In this case, click on 

ControlRoom.thyroid.I131. Then hold down the shift key and select 

ControlRoom.thyroid.I135.

• Control-click – used to select multiple datasets one at a time. Hold down the control key 

and click on each dataset, selecting that dataset. Each dataset is highlighted after 

selection.

With either approach, all of the dose datasets will be highlighted as shown in Figure 3-18. Once 

the datasets are highlighted, click on the Plot button and the plot will be generated. The 

resulting plot is shown on Figure 3-19.
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Figure 3-19 Control room dose plots for Test23

Adjustments can be made to the plot by using the plot editing features in AptPlot. These 

features are accessed by selecting Plot in the top menu. A number of features are available, 

but generally Plot->Graph appearance, Plot->Set appearance and Plot->Axis properties provide 

the features needed to edit the plot. Screenshots of each of these windows are shown in 

Figures 3-20 through 3-22. Clicking on the tabs in each window shows various properties and 

features available to the user. A subset of these features is used to edit the plot.

Some typical AptPlot adjustments are illustrated below:

• Change the x-axis scale from seconds to hours: – Navigate to the Select EXTDATA 

Channel window shown in Figure 3-18 and click on Clear Sets in the lower left-hand 

portion of the screen. Then change the units in the Time Units drop-down menu from 

Seconds to Hours. Confirm that the dose components are highlighted as shown in 

Figure 3-18 using shift-click or control-click. Then, click on Plot and Time (hours) will 

appear on the x-axis.
3-22

• Reset y-axis to logarithmic scale: – Given that the I-131 dose is so dominant, it is hard 

to read the dose contributions from the other iodine nuclides. The y-axis scale can be 

changed to logarithmic by selecting Plot->Axis properties to open the Axes window 

(Figure 3-20). Change the axis setting in Edit text box from X axis to Y axis and click 

on the Main tab if it is not already selected in the Axes window (Figure 3-20). Then 

change the Scale text box from Normal to Logarithmic and click the Apply button to 

change the y-axis to logarithmic.

• Expand y-axis to cover dose range: – The dose range can be expanded by changing 

the Start and Stop values to 0.0001 and 10.0 in the Axes window. The Axes window is

obtained by selecting Plot->Axis properties to open the Axes window (Figure 3-20).

Click on the Main tab if it is not already selected. Change the edit box to Y axis. Then, 

enter 0.0001 in the Start text box and 10.0 in the Stop text box. Then click the Apply

button to apply the change.

Figure 3-20 AptPlot Axes window

• Use scientific notation for the y-axis: – The format for the y-axis labels is set by 

changing the Edit drop-down menu setting in the General section of Figure 3-20. 

Then, set the number format in the Format drop-down menu in the Tick properties

section to Scientific from General. Also set the precision to 0 in the Precision dropdown menu and click the Apply button to reset the format.

• Line colors: – The line colors selected by AptPlot can be hard to see. Each line color 

can be individually adjusted by the user. To adjust a line color select Plot->Set 
3-23

appearance to open the Set appearance window (Figure 3-21). Highlight the dataset 

to be changed in the Data sets section near the top of the Set appearance window

(Figure 3-21). Note that the name of the data contained in a given dataset is identified 

by the String text box in the Legend section in the lower part of the window. Also, note 

that the current color of a particular dataset is shown in the Color drop-down menu in 

the Line Properties section. Using that drop-down menu, select the desired color and 

click on the Apply button. Alternately, to change the color of all lines to black for 

example, highlight all datasets using shift-click or control-click or alternately clicking on 

the All button. Then, select Black in the Color drop-down menu (if it is not already 

selected) and click on the Apply button.

Figure 3-21 AptPlot Set appearance window

• Line symbols: – Symbols for the lines are set from the Main tab in the Set appearance

window (Figure 3-21). To select a symbol for a particular data set, highlight the 

dataset in the Data sets section, then select a symbol type (circle, square, etc.) under 

the Type drop-down menu in the Symbol Properties section. Also, select the desired 

color in the Color drop-down menu and click the Apply button. A symbol will appear 

for each data point and since there are hundreds of data points, a symbol skip will 

have to be set. Select the Symbols tab in the Set appearance window and highlight 

the dataset to be changed. Then, set the Symbol skip to a value like 50 or 75 and click 

on the Apply button. This setting will display a symbol for every 50th or 75th point. 

Repeat these steps for each dataset.
3-24

• Line style: – Line styles (solid, dash, dot-dash, etc.) can be set by selecting the Main

tab in the Set appearance window (Figure 3-21), highlighting the desired data set in 

the Data sets sections and selecting the desired style using the Style drop-down menu 

in the Line Properties section in a manner similar to setting line colors and line 

symbols. Each line is set individually, and then click the Apply button as the settings 

for each dataset are completed.

• Titles and subtitles: – To add a title and subtitle to the plot select Plot->Graph

appearance to open the Graph appearance window (Figure 3-22). In the Main tab 

section enter a title and subtitle as appropriate, then click on the Apply button. The 

title and subtitle will appear. Select the Titles tab and use the sliders to adjust the font 

size for the title and subtitle as desired. Note the font size can be incremented by 

clicking on the channel to the left or right of the slider icon.

Figure 3-22 AptPlot Graph appearance window

Sometimes the legend box overwrites the dose results as in the plot shown in Figure 3-19. In 

order to correct this issue, the plot needs to be shrunk, which will require using several AptPlot 

features. These features are listed below:

• Edit the legend titles: – The title for each legend can be edited. This change is made 

by selecting Plot->Set appearance to open the Set appearance window (Figure 3-21) 

and highlighting the desired data set. Change the title in the String text box in the 

Legend section as appropriate. In this case, the iodine nuclide name is used. Click on 

the Apply button after each title modification is made.
3-25

• Change the font size for the legend: – First, the font size used in legend box will need 

to be reduced, which entails changing the legend title font and the symbol font. To 

change the font size of the legend title, select Plot->Graph appearance to open the 

Graph appearance window (Figure 3-22) and click on the Legends tab. Then, use the 

slider bar to adjust the font size to 75 for example and click on Apply button. The font 

size will change for all datasets. For the symbol size, navigate to the Set appearance

window (Figure 3-21) and select all datasets. Then, change the Size setting in the 

Symbol Properties section to 75 using the slider.

• Change the size of the plot: – The plot overlays a white background which is basically 

set to allow a plot to be printed on 8.5 x 11 paper in landscape mode. So, it is 

desirable to maintain this setting although it can be changed by navigating to View-

>Page setup. However, the approach used here is to shrink the plot by adjusting the 

settings in the Viewport section in the Graph appearance window (Figure 3-22) by 

entering suitable values. In this case, the X max and Y max text box settings are 

changed to 1.0 and 0.8, respectively. These settings permit the legend box to be 

moved to the right-hand side of the plot, and then click on the Apply button. Then, to 

move the legend box, select the Leg. Box tab in the Graph appearance window (Figure 

3-22) and adjust the box location in the X and Y text boxes in the Location section. 

Values of 1.05 and 0.60 will move the legend box to the right-hand side of the plot. 

Another approach is to change the X max text box setting to 1000 which will allow 

sufficient space for the legend box within the plot frame, although it will probably need 

to be moved for aesthetic reasons.

The plot is saved by selecting File->Save and then navigating to the desired directory location, 

entering a suitable name, then click on OK, similar to any Windows program. To access a 

previously saved AptPlot plot, select File->Open, and navigate to the directory location where 

the plot file is saved and select that file. Also, the format and title settings can be saved by 

selecting Plot->Save defaults and overwriting the Defaults.agr file. Note that Plot->Reset 

defaults will reset the defaults to the original settings. Figure 3-23 shows the resulting plot with 

the above modifications.

Note that plots can be generated in a picture format such as “*.png” or “*.jpeg” by navigating to 

File->Print setup. At the top of the Device setup window, change the device to “*.png” for 

example. In the Output section, check that the directory path and filename are suitable. Then, 

click on the Print button and the plot will be saved in “*.png” format using the filename set for the 

plot file.
3-26

Figure 3-23 Reformatted control room dose plots for Test23

For those users who wish to use a spreadsheet for data analysis or for plotting, the dose data 

can be exported. The easiest way is to initiate a new plot session in a comma-delimited format 

that can be read by Microsoft Excel. This feature is accessed from the Select EXTDATA 

Channels window (Figure 3-18). As an example, set up and apply a filter for the I-131 to I-135 

thyroid dose in the control room and select the resulting data channels as done previously. 

Then, highlight the data channels and click on the Export button at the bottom of the window. A 

Save window will appear. Provide a filename, ending the filename with the “*.csv” suffix and 

select comma separated values as the file type (right hand side of the Save window). Then, 

click on Save to write the file. Microsoft Excel will read and organize the dose data by column 

for subsequent use.

3.3 SNAP/RADTRAD Model Development and Modification

Sections 3.1 and 3.2 introduced the SNAP/RADTRAD Model Editor user interface using Test 

Problem 23 as an example. In this section, the details of building a new model are presented. 
3-27

For this illustration, a model consisting of a simple containment compartment, leakage pathway, 

source and an environment compartment will be developed.

3.3.1 Model Editor Menus

The commands available in the Model Editor are typical of Windows programs. Across the top 

of the Model Editor, the File, Edit, Tools, Window, and Help commands are presented. Table 3-

2 describes the commands associated with each of these menu items.

Table 3-2 Summary of Model Editor menu commands

Menu Command Description

File Commands

File->New

Creates a new model. A Select Model Type menu appears with 

available models listed. The SNAP/RADTRAD user picks RADTRAD

and clicks on the OK button.

File->Open

Opens a previously developed model (“*.med” file). The user navigates 

to the directory where the file is located and selects the file to be 

opened similar to any Windows program.

File->Open Recent

Allows the user to open a recently used SNAP/RADTRAD model (or 

AVF file). The user selects the file of interest and it will open in a new 

Model Editor session.

File->Save Saves the current model with the same name as in any Windows 

program.

File->Save As

Saves the file under a new filename. The user navigates to the desired 

directory location and/or updates the filename and clicks the Save

button as in any Windows program.

File->Close Closes the current model. Provides a warning to the user in the case 

of any unsaved changes made to the model.

File->Close All Closes multiple open models. Provides a warning to the user in the 

case of any unsaved changes made to the model.

File->Import

Imports a previously exported RADTRAD model from a set of ASCII or 

XML input files (see Section 3.1). Note that a “*.psf” file is an ASCII file 

from RADTRAD version 3.03 or 3.10 with the same input data as the 

XML formatted “*.psx” files.

File->Export Exports a set of SNAP/RADTRAD XML input files (“*.psx”, “*.nix”, 

“*.srx”, “*.icx”, and “*.dfx”) to a directory selected by the user

File->Exit Exits the Model Editor.
3-28

Table 3-2 Summary of Model Editor menu commands (cont.)

Menu Command Description

Edit Commands

Edit->Undo Reverses previous user inputs to a model similar to most Windows 

program.

Edit->Redo Redoes a previous undo command similar to most Windows program.

Edit->Preferences Allows the user to set various preferences related to fonts, colors, and 

other Model Editor features.

Edit->Plugin Manager

Opens a dialog listing all of the available SNAP plugins. Toggling the 

check-box next to each plugin allows for loading and unloading the 

plugin. This feature is not generally used for SNAP/RADTRAD

because the RADTRAD-AC only uses the RADTRAD Plugin.

Tools Commands

Tools->Check Model Provides a check of the SNAP/RADTRAD input model. This feature is 

very useful for model development in SNAP/RADTRAD.

Tools->Submit Job Submits a model through the job stream and starts the SNAP Job 

Status Tool (see Section 3.2.2).

Tools->Steam Tables Not used in SNAP/RADTRAD.

Tools->Configuration Tool Starts the SNAP/RADTRAD Configuration Tool used to configure 

global properties for running RADTRAD under SNAP

Tools->Job Status Starts the SNAP/RADTRAD SNAP Job Status window (see Section 

3.2.2).

Tools->Model Note Viewer Displays model notes. The user can set up and edit notes as part of 

the model documentation.

Tools->Export to jEdit Exports a model to the jEdit editing program. This feature requires the 

installation of jEdit.

Windows Commands

Windows->Commands Scripting commands window – not used in SNAP/RADTRAD.
3-29

Table 3-2 Summary of Model Editor menu commands (cont.)

Menu Command Description

Help Commands

Help->Contents Link to the SNAP Model Editor manual, which includes information 

about the RADTRAD Plugin.

Help->Check for Updates Checks for updates at the APT, Inc. website. Note that computer 

security settings may inhibit this feature.

Help->Report an Issue

Allows the user to submit Issue Reports on SNAP/RADTRAD directly 

to APT, Inc. Note that issues related to the RADTRAD-AC should be 

reported via the SNAP/RADTRAD Forum webpage under the 

SNAP/RADTRAD Support link on the RAMP website.

Help->About

Provides information on the SNAP Model Editor GUI and Plugin 

version, licensing agreements, and contact information. Note that 

plugin version numbers can be obtained by clicking on the Plugins

button.

Figure 3-24 shows the icon arrangement and function of each icon in the Model Editor. Of 

particular interest is the ability to separate the Navigator, Property, and View / Dock windows 

into separate windows and to also arrange the windows vertically by clicking on the 

Single/Multiple Windows Modes icons shown in Figure 3-24. The remaining icons provide a 

shortcut to some of the menu commands listed in Table 3-2.

Figure 3-24 Model Editor tool bar icon description

Figure 3-25 shows the icon arrangement and the function for each icon in the Navigator window. 

Basically, these tools aid the user in navigating component nodes in the Navigator window and 

multiple models in the SNAP Model Editor GUI.
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Figure 3-25 Navigator window tool bar icon description

3.3.2 Building a SNAP/RADTRAD Model – Component Specification

The first step is to start the SNAP Model Editor and click on Create a New Model in the 

Welcome screen (Figure 3-1). Alternately, a new model in SNAP/RADTRAD can also be 

created by selecting the File->New command as noted in Table 3-2. Select RADTRAD model in 

the Select Model Type screen and notice that the Model Editor opens with no icons in the View / 

Dock window (similar to Figure 3-2). The basic model nodes are shown in the Navigator

window. Expand the Compartment [1] node using the Expand ( ) icon in the Navigator window. 

Highlight (click on) the Compartment 1 (Environment) node, so that data fields for this 

compartment will appear in the Property window. Note that an environment compartment is 

defined by default.

The basic approach to building a SNAP/RADTRAD model is to set up an array of 

compartments, flow pathways and specify key parameters in the various components of the 

model. For sources, compartments, and pathways that ultimately appear in the View / Dock

window, the basic pattern is to highlight (select) the component category (i.e. Source, 

Compartments and Pathways), right-click on the component category, and select New from the 

menu to add a numbered component to that component category. These steps result in a new 

model component being created.

A new compartment is added by right-clicking on the Compartment node in the Navigator

window and selecting New from the drop-down menu that appears. A new compartment 

component Compartment 2 is created. Components are not automatically added to the View / 

Dock window, but must be added by the user. The new component (Compartment 2) is added 

to the View / Dock window by right-clicking on the Compartment 2 and selecting Add to View-

>Default View from the drop-down menu. Compartment 2 now appears in the View / Dock

window.

The new component (Compartment 2) is unnamed. To add a name to the component, type a 

name (i.e. Containment) in the Name text box in the Property window. The name will 

simultaneously appear in both the Navigator and View / Dock windows [Compartment 2 
3-31

(Containment)]. Alternately, newly-defined components can also be dragged from the Navigator

window to the View / Dock window by clicking on the component of interest and dragging it by 

holding the left mouse button down and moving the cursor to the View / Dock window.

The pre-defined Environment compartment is added to the View / Dock window in a manner 

similar to Compartment 2 (Containment) above. Right-click on Compartment 1 (Environment)

and select Add to View->Default View or drag the component by clicking on the Compartment 1 

(Environment) node and dragging it into the View / Dock window. The environment 

compartment will appear in the View / Dock window. Note that two dose locations (EAB and 

LPZ) are automatically specified with the environment compartment.

The next step is to define a flow pathway which is done by right-clicking on the pathway group 

node (Pathways [0]) and selecting New from the drop-down menu that appears. Add Pathway 1

to the View / Dock window by right-clicking on Pathway 1 and then selecting Add to View-

>Default View or drag the component by clicking on the Pathway 1 node and dragging it into the 

View / Dock window. The flow pathway should be named by entering a suitable name in the 

Name text box in the Property window (i.e. Leakage).

Similarly a source can be added by right-clicking on the Sources node in the Navigator window 

(Sources [0]) and selecting New from the drop-down menu that appears. After naming the 

component (i.e. Fuel Release), the component can be added to the View / Dock window in the 

same manner as used above for the compartments and flow pathways.

At this point, the user can see that a pattern is emerging. Each input group has an associated 

group node where components within that group can be defined and added to the Navigator

window. Figure 3-26 displays the Navigator window for the components added in the previous 

steps above. The component nodes that can be added as part of a model are: Sources, 

Compartments, and Pathways. The nodes for Dose Locations, Natural Deposition, Filters, 

Sprays, and Χ/Q Tables are not drawn, but are defined in the same manner as compartments, 

pathways, and sources by right-clicking on the component group node and selecting New from

the drop-down menu that appears.

The user has developed a new model consisting of a source, a compartment representing the 

containment, a leakage pathway and an environment compartment. Also, this new model was 

added to the View / Dock window by either dragging the new component nodes to the View / 

Dock window or right-clicking on the new component nodes, then selecting Add to View-

>Default View. Figure 3-27 shows the View / Dock window with the new model’s components. 

Additionally, once the components are added to the View / Dock window, they can be moved 

around by the user for presentation clarity. Make sure the Selection Tool ( ) icon is activated 

before selecting a component icon to be moved in the View / Dock window. Features common 

to most Windows-based programs are available to aid the user in editing and arranging icons. 

The function of each icon can be determined by hovering the mouse pointer above the icon of 

interest. This action should cause a text pop-up to appear with a short statement of the function 

of that icon. The tools and features most commonly used in SNAP/RADTRAD are illustrated in 

Section 3.3.4.
3-32

Figure 3-26 Navigator window with newly added model components

Figure 3-27 View / Dock window for 4-node model (unconnected)
3-33

Table 3-3 shows all of the icons which are available in the View / Dock window with a 

description of each icon. All of the icons for the compartments, sources and pathways have

connection points for connecting flow pathways and source components to compartment 

components as illustrated in Figure 3-27. The number in the different icons in Figure 3-27 are 

the component numbers (i.e. the number of Compartments, Pathways, and Sources), which are 

generally consecutive in SNAP/RADTRAD models.

One feature that the user should be aware of is the orientation feature for flow pathway icons. 

In Figure 3-27, the orientation is pointing right; however, the orientation can be changed to 

pointing up, pointing down, or pointing left by right-clicking on the flow pathway icon and 

selecting Drawn Orientation from the drop-down menu that appears and then pick the desired 

orientation.

Table 3-3 Icons used in the View / Dock window

View / Dock Window Icons Description

Compartment Icon

Flow pathway connection point indicated by small circles on 

each edge. Small square at the upper-left corner is a source 

connection point.

Source Icon

Small square at the lower edge is a source connection point to a 

compartment.

Flow Pathway Icon

Flow pathway connection point indicated by small circles on 

each side.

Environment Icon

Flow pathway connection point indicated by small circles on 

each edge. Small square at the upper-left corner is a source 

connection point.

Natural Deposition Icon

Icon denoting that natural deposition is active in a component 

(grayed-out indicates inactive).

Filters Icon

Icon denoting that a filter is defined in a component (grayed- out 

indicates no filter).

Sprays Icon

Icon denoting that a spray is defined in a component (grayedout indicates no spray).

The next step is to connect the components using the Connection Tool ( ) icon shown in the 

View / Dock window tool bar (see Section 3.3.4). Connection points for the various icons are 

shown in Figure 3-27. These connection points are indicated by circles and squares on 

periphery of the icons. The first step is to click on the Connection Tool ( ) icon or (cross hairs) 

icon in the View / Dock window tool bar, which activates the connection tool. Then for 
3-34

compartment to flow pathway connections, click on the connection point (circle) on the edge of 

the compartment to be connected and drag holding the left mouse button down to the desired 

connection point (circle) on the flow pathway icon and release the button. The procedure is the 

same for the source to compartment connections except the connection points are denoted by 

squares. Note that square connection points can only be connect to other square connection 

points and likewise circle connection points to only other circle connection points. Figure 3-28

shows the model with the connections made.

Figure 3-28 View / Dock window for 4-node model (connected)

Figure 3-29 shows the expanded node view of the Navigator window corresponding to all the 

components modeled in Figure 3-28. Basically, it is an expanded node view of the schematic 

representation shown in Figure 3-26. Users should get into the habit of naming the various 

components of their models. This practice will help avoid errors, particularly as models get more 

complicated.
3-35

Figure 3-29 Navigator window with all nodes expanded

3.3.3 Building a SNAP/RADTRAD Model – Input Specification

Input specification is the next step in developing a SNAP/RADTRAD model. The Model Editor 

design basically guides the user through the various input parameters required. Clicking on any 

of the defined compartments presents a list of input data that needs to be specified in the 

Property window. Also, an important feature in SNAP/RADTRAD is the ability to check the 

model using the Check Model feature which is found by navigating to Tools->Check Model.

This illustration will start by completing the input for Compartment 2 (Containment) shown in 

Figure 3-28. The volume of this compartment will be set to 2.5E+06 ft3

. Note that the default 

units of the Model Editor are in SI. To switch units to British units, right-click on the black bar in 

the Navigator window, select Engineering Units->British from the drop-down menu to change 

the units. Figure 3-30 shows the location of the black bar and the accompanying drop-down 

menu. Once the desired units are selected, click on the Compartment 2 (Containment) icon in 

the View / Dock window or in the Navigator window to open the Compartment 2 (Containment)

Property window. Enter 2.5E6 in the Volume text box in the Property window. Also check that 

the Compartment Type text box is set to Normal. Other compartment types are discussed in 

Table 3-8. Figure 3-31 shows the Property window with the volume set to 2.5E6. Note that 

deposition, filter, and sprays models are not used.
3-36

Figure 3-30 Navigator window with the black bar menu for the engineering units 

selection

Figure 3-31 Property window with volume entry for Compartment 2 (Containment)

Input for the flow pathway involves a data entry table to capture the time dependence of the 

assumed containment leakage rate of 0.1 percent per day (%/day). The first step is to change 

the Pathway Type text box in the Property window from Piping (default) to Air leakage (typically 

used for containments). Next, specify a leakage rate by clicking on the Custom Editors ( ) icon

adjacent to the Leakage Rate text box to open the Editing Leakage Rate window Figure 3-32. A 

data entry table window will open, which is one of the most common ways to specify input 

entries in SNAP/RADTRAD.
3-37

Figure 3-32 Pathway input windows for sample problem

The user can click on the Add button and add a leakage rate of 0.1 %/day for 0 to 720 h. Two 

rows will be needed in this instance. Users should be aware that there are several ways of 

entering the data using the Custom Editors ( ) icon and the edit table features in 

SNAP/RADTRAD. Some users prefer to set up the number of rows needed for all the data prior 

to entering the time and leakage rate data (e.g. select the Add button twice for this entry). While 

other users prefer to enter one row of data at a time before adding another row to the table. 

When using the second method, users should note that if a cell in an existing row is highlighted 

then the Add button will add the row before the existing row in the table. Likewise if there is no 

cell highlighted in a row and the Add button is selected then the row will appear as the last entry 

row on the table. The user should also note that when new row is added the row will contain 

“Unknown” in the data cells to be entered by the user. To enter data into the newly created cell 

the user should select the cell with the mouse and enter the data. The Tab button on the 

keyboard allows the user to move from cell to cell without selecting the cell with the mouse. 

Data initially entered into a cell will appear in red until the user selects the Enter or the Tab key 

on the keyboard to move to the next cell in the row. Finally, the SNAP Model Editor also allows 

the user to sort data entered out of sequential order by selecting the Sort button on the bottom 

of the Editing Leakage Rate window Figure 3-32. To delete a row, highlight the row to be 

deleted and click on the Remove button.
3-38

The next step is to specify the Χ/Q tables. The Χ/Q values used for this illustration are listed in 

Table 3-4 and the approach is basically the same as that used for the data table entry for the 

flow pathway. The first step is to click on the Expand ( ) icon next to the Χ/Q Tables node in 

the Navigator window, then click on Χ/Q Table 1 (Exclusion Area Boundary) node. In the 

Property window for the Χ/Q Table 1 (Exclusion Area Boundary) click on the Custom Editors ( )

icon adjacent to the X/Q Table text box to open the Editing X/Q Table window Figure 3-33. As 

in the case of the Editing Leakage Rate window described above, the user can enter X/Q values 

from Table 3-4 in the Editing X/Q Table window. Using the Add and Remove buttons, the X/Q 

values for the EAB and LPZ can be completed by the user. Figure 3-33 also shows the 

completed Editing X/Q Table windows.

Table 3-4 Sample problem X/Q values

Time Interval

(h)

Χ/Q Value by Location

(s/m3)

EAB LPZ

0 – 2 1.4E-04 4.5E-05

2 – 8 2.39E-05

8 – 24 1.29E-05

24 – 96 5.49E-06

96 – 720 1.61E-06

Figure 3-33 X/Q input tables for EAB (left) and LPZ (right)

The final item to be completed is the source term specification. The source term specification 

consists of two parts. The first part is to specify the radionuclide inventory in the fuel or reactor 

coolant and the second is the source or release fraction scenario specific to the accident type. 
3-39

Both combine to generate the radionuclide inventory to determine an overall source term. 

Additionally, there is also the setting for core power in the Model Options node that is used to 

determine the radionuclide inventory.

There are two sample default core inventory libraries (PWR and BWR) from Tables 1.4.3.2-2 

and 1.4.3.2-3 of NUREG/CR-6604, which are not editable by the user.

• PWR – normalized Methods for Estimation of Leakages and Consequences of 

Releases (MELCOR) / Accident Consequence Code System (MACCS) sample 3412 

megawatt thermal (Mwt) PWR core inventory (60 nuclides).

• BWR – normalized MELCOR/MACCS sample 3578 Mwt BWR core inventory (60 

nuclides).

To view and access these sample default core inventory libraries in SNAP/RADTRAD, left-click 

on Nuclide Data node in the Navigator window and locate the Total Inventories text box in the 

Property window. Select the Custom Editors ( ) icon adjacent to the Total Inventories text box 

to open the Editing Total Inventories window Figure 3-34. The basic editing features for the Edit 

Total Inventories window are also shown in Figure 3-34. These features can be used to either 

edit an existing file or specify a new inventory file. For example, the PWR inventory file can be 

duplicated by selecting the PWR inventory and then clicking on the Copy Existing File ( ) icon 

which will make a duplicate and append a number to the file that can then be renamed by the 

user. Once a copy is made, the data becomes editable. Nuclides can be added, deleted, and 

rearranged using the Nuclide Editing Tools shown in Figure 3-34. In addition, nuclide files can 

be exported and imported. The user should note that values in the Inventory (Ci) column will 

appear as “Unknown” until the plant power lever is entered as described below.

For this illustration, the generic PWR inventory with a core power level of 3637 Mwt and the 

alternative source term release fractions from Regulatory Guide 1.183 (RG 1.183), “Alternative 

Radiological Source Terms for Evaluating Design Basis Accidents at Nuclear Power Reactors” 

[10] will be demonstrated. The source specification steps are as follows:

• Left-click on the Model Options node in the Navigator window, locate the Plant Power 

Level text box in the Property window and set the plant power level to 3637 as shown 

in Figure 3-35.

• Expand the Sources [1] node and left-click on Source 1 (Fuel Release), locate Source 

Scenarios text box in the Property window and left-click on the Custom Editors ( )

icon. In the Edit Inventory Scenarios window, add a new scenario by clicking on the 

New ( ) icon. When the Select from Total Available Inventories window opens select 

PWR and click the OK button to return to the Edit Inventory Scenarios window as 

shown in Figure 3-36.
3-40

Figure 3-34 SNAP/RADTRAD Edit Total Inventories window editing features

Figure 3-35 Setting the power plant level
3-41

Figure 3-36 Selecting from available SNAP/RADTRAD inventories

• Enter the name PWR Source in the Scenario Name text box on the Edit Inventory 

Scenarios window. Notice that the Active Scenario name changes to PWR Source. 

Under the Accident Parameters tab, pick the DBA AST option under the Accident Type

drop-down menu and select the PWR button under Defaults Type (see Figure 3-37).

• At this point, the user should review the data comprising the source term by clicking on 

each tab in the Edit Total Inventories window and noting the progression of the 

calculations leading to the total source term definition.

• Clicking on the Adjusted Inventory tab will list the core inventory based on the generic 

PWR file as shown in Figure 3-38. Note in Figure 3-38 that there are two columns. 

The column labeled Amount (Ci)/MWth lists the activity in curies (Ci)/MWth and the 

column labeled Inventory lists the total activity in Ci. Note that the inventory is 

calculated using the values in the Amount (Ci)/MWth column and the Plant Power 

Level set previously in the Model Options node.
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Figure 3-37 Edit Total Inventories window Accident Parameters tab

Figure 3-38 Edit Total Inventories window Adjusted Inventory tab

• Clicking on the Release Fractions and Timings tab displays the release fractions from 

Table 2 of RG 1.183 (see Section 4.3 for more details on this tab). The Release 

Durations (hrs) are also listed and are from Table 4 of RG 1.183 as shown on Figure 

3-39.
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Figure 3-39 Edit Total Inventories window Release Fractions and Timings tab

• Finally, clicking on the Source Term tab shows the calculated source term associated 

with the particular nuclide as shown in Figure 3-40. Further discussion of source term 

modeling in SNAP/RADTRAD is presented in Sections 3.4.2.

Figure 3-40 Edit Total Inventories window Source Term tab

The final step for the source term specification is to set the source term fraction and the iodine 

chemical forms to the RG 1.183 (NUREG-1465) values. The user sets the source term fraction
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by entering the value of 1 in the Source Term Fraction text box of the Property window for 

Source 1 (Fuel Release) as shown in Figure 3-41. The iodine chemical form is set by using the 

drop-down menu associated with the Iodine Physical Form text box in the Property window for 

Source 1 (Fuel Release) as shown in Figure 3-41. The aerosol, elemental and organic iodine 

fractions are listed but are not editable (grayed-out).

Figure 3-41 Property window for source term iodine chemical form settings

The user can now run a model check by navigating to Tools->Check Model and looking for the 

notes in the Message window in the lower part of the Model Editor indicating that no errors were 

found as shown in Figure 3-42. There are three icons to the right of the message window used 

to copy or delete messages.

Figure 3-42 Model Editor Message window with icons

If an error is detected, an Error Report window appears listing the errors and warning messages 

as shown in the example Error Report window shown in Figure 3-43. The error messages, 

which are generally self-explanatory, provide a guide of what needs to be fixed. Note that there 

are other classifications of messages (Notes, Alerts, Warnings, and Errors). Generally, SNAP 

displays messages in these different classifications automatically. The goal for model 

development is to have no errors or warnings generated by the SNAP Model Editor. Users 

should note that models may execute with warnings detected by the Model Editor, but they will 
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not execute with errors. Once error checking is complete and no errors or warnings exist in the 

model, the user can run the case as described in Section 3.2.2 (Tools->Submit Job).

Figure 3-43 Example of a SNAP model editor Error Report window

3.3.4 Building a SNAP/RADTRAD Model – Additional Features

There are a number of features and icons in the View / Dock window, as shown in Figure 3-44, 

that the SNAP/RADTRAD user should become familiar with for general model building. These 

features include the Cut ( ), Copy ( ) and Paste ( ) icons which are used by selecting the 

icon (Compartment, Pathway, etc.) in the View / Dock window to be cut or copied, then clicking 

on the Cut ( ) or Copy ( ) icon and pasting it in the View / Dock window.

Figure 3-44 View / Dock window tool bar icons

The Paste Special ( ) icon allows the user to paste multiple copies or to control component 

renumbering. The features of the Paste Special ( ) icon are shown in Figure 3-45. The utility 

of this tool is to maintain unique component numbers in the copy and paste process. To 

duplicate a component using the Copy ( ) icon and Paste Special ( ) icon, confirm the 
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Selection Tool ( ) icon is activated (Figure 3-44) and then click on the component to be 

duplicated. Click on Paste Special ( ) icon and confirm that the numbering offset is selected, a

value of 1 for the offset is fine. Then click on the OK button and the component will be 

duplicated.

Figure 3-45 Features of the Paste Special window

The Selection Tool ( ) icon, as the name implies, allow the selection of icons for copying. This 

tool needs to be activated as shown in Figure 3-44 to allow components to be selected or 

moved. A component is moved by clicking on the component and holding the left mouse button 

down while dragging the component to the desired location. The Find Component ( ) icon is 

used to find a component and it is usually used for large models with tens or hundreds of 

components and is typically not needed for SNAP/RADTRAD models.

Another very useful feature of SNAP/RADTRAD is the ability to group components (rubber band 

selection) and move them as a unit. The Group ( ) and Ungroup ( ) icons appear inactive 

(grayed out) until a group of components are defined. To define a component group, click the 

mouse button in an empty area of the View / Dock window, then drag the cursor around the 

group of components to be grouped (rubber banded) together. The Group ( ) icon, shown in 

Figure 3-44, will now become active. Click the Group ( ) icon to group the components 

together and note that the Ungroup ( ) icon the View / Dock window tool bar will become 

active. Clicking on the Ungroup ( ) icon ungroups the components in the previously defined 

group.

The Zoom ( ) icon is used to zoom in on sections of a model. Clicking on the Zoom ( ) icon 

and then clicking on the background of the View / Dock window will magnify the components. 

Additionally, some useful zoom and sizing features are available when the Selection Tool ( ) 

icon is activated by right-clicking on the View / Dock window background and clicking on Zoom 

in the drop-down menu. Alternately these features are available while the Zoom ( ) icon is 

active by right-clicking on the View / Dock window background. Both methods open the Zoom 

and Size window shown in Figure 3-46
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Figure 3-46 Zoom and size features

When the Zoom tab is activated, the zoom level can be set to any desired value by either using 

the slider or entering a number in the percent value in the text box. Note that clicking on the red

arrow ( ) displays a drop-down list of preset values from which the user may make a suitable 

selection. When the Canvas Size tab is active, the width and height of the canvas can be set. 

The canvas is the portion of the View / Dock window surrounded by a thin border on two sides 

(bottom and right sides) and the scaling ruler on the remaining two sides of a model as 

illustrated in Figure 3-47. All component icons are rendered on the canvas and for larger 

models, sometimes the canvas borders cannot be seen. The Zoom ( ) icon can be used to 

shrink the model and bring the borders into view. Also, if the canvas is larger than the model, 

clicking on the Trim Excess button will shrink the canvas area to fit the model.

In some SNAP models, the scale of icons is of interest to get a sense of perspective particularly 

for models where plant components are represented. Generally, SNAP/RADTRAD models are 

represented in a manner similar to a block diagram; however, a plant representation can be 

drawn using the Component Insertion ( ) icon on Figure 3-44.

SNAP/RADTRAD provides the feature of scaling meshes with some of the drawing features 

available using the Component Insertion ( ) icon. The Component Insertion ( ) icon allows the 

insertion of various components and basic drawing shapes into a model representation. Figure 

3-48 displays the Component Insertion ( ) icon menus illustrating the available features. These 

menus are accessed by clicking on the drop-down arrow.

The features that would be most used in developing a SNAP/RADTRAD model would be the 

Compartments, Sources and Pathways Insertions. These three features make it easy to build a 

model by navigating the menus to the component of interest, clicking on that component, then 

moving the cursor to the View / Dock window and clicking again. This approach provides an 

alternative and is quicker than the approach involving right-clicking on the desired nodes in the 

Navigator window described earlier.
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Figure 3-47 View / Dock window model canvas

Figure 3-48 Component Insertion icon feature menus

The other feature that is useful is the ability to annotate a model using the Annotation feature. 

This Annotation feature allows the user to draw basic shapes and to add descriptive text. The 

basic approach is to navigate to the annotation feature of interest, select that feature and then 

click on the View / Dock window which will draw the selected icon.

As an example, to draw an ellipse, navigate to Annotation->Ellipse, click on Ellipse in the menu, 

then move the cursor to the View / Dock window and click in that window to draw the selected 
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shape. Right-clicking on the shape activates a menu that allows various drawing rendering 

features to be set. These features are typical of Windows-based drawing programs and are not 

discussed in detail.

The drawing features combined with scaling may be of interest to some users with an artistic 

tendency. When a new model is initiated, default values are set for the dimensions of the 

canvas which are a height of 850 pixels and a width of 1100 pixels. These values can be 

checked in the Canvas Size tab in the Zoom and Size window. Additionally, the user can enter 

custom values for the height and width by typing them and selecting the Enter key on the 

keyboard. The default scaling is 20 pixels per meter with a width scale factor of 1.0 which can 

be checked by clicking on the Scaling tab in the Zoom and Size window which is shown in 

Figure 3-46. Dividing the pixel values by the scaling factor yields a height of 42.5 meters and a 

width of 55 meters. Note that the ruler at the edge of the canvas shows these dimensions. 

Actually, units are immaterial in this context as the dimensions can be expressed in yards, feet 

or any other units. The scaling factor is actually the number of pixels per some unit of length.

Once a suitable scaling is set, scaled drawings representing plant components can be made 

using the annotation features discussed above. A sample is shown in Figure 3-49 in which a 

cylinder is scaled to be 100 feet in diameter and 100 feet high.

Figure 3-49 Cylinder drawn using the Annotation features of SNAP

It is noted that, in general, the icons used to represent various components in a 

SNAP/RADTRAD model are adequate for model presentation. These features are illustrated for 

those users who may want to explore and use these features for additional model annotation.
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3.4 SNAP/RADTRAD Input Summary

Up to this point, the user has seen the various approaches to specifying input in 

SNAP/RADTRAD. The first step is to define a component (compartment, flow pathway, dose 

location, etc. using the right-click and left-click sequences shown earlier) and then specifying the 

actual input parameters using drop-down menus, text boxes, and input tables. However, up to 

this point, many of the available input parameters have not been discussed.

Tables 3-5 through 3-15 present a summary of all of the inputs that can be specified in a 

SNAP/RADTRAD model. The organization of the tables follows the group node organization in 

the Navigator window. Summary explanations of the input requirements are provided. In 

addition, screenshots are provided to help orient the user and to provide context with the input. 

Comments are also provided to aid the user in specifying input.

SNAP/RADTRAD input is largely self-explanatory given that the user has some dose analysis 

background. However, the user should be aware of the relationships among some of the group 

nodes from an input specification perspective. These relationships are as follows:

• general model options (Table 3-5);

• nuclide data and sources for specifying source terms (Tables 3-6 and 3-7);

• compartments, pathways, natural deposition, filters and sprays (Tables 3-8 through 3-

12);

• dose locations (including breathing rates), and Χ/Q tables (Tables 3-13 and 3-14); and

• remaining inputs (Table 3-15).

The relationships will become obvious as the user works with the SNAP Model Editor. 

Sometimes the relationship is “one way.” As an example, the user can tell which Χ/Q table is 

linked to a particular dose location by clicking on one of the Dose Location nodes. However, if 

the user clicks on a particular Χ/Q Table node, the associated dose location is not readily 

identified. Hence, it is important to name the various model components to keep track of 

associations.

3.4.1 Model Options

Model options are applied to the overall problem and the use of the default values should be 

acceptable for most problems, but should be checked by the user. Table 3-5 lists the available 

inputs for the Model Options node in SNAP/RADTRAD (Figure 3-50). Some general comments 

on model options are listed below:

• Plant Power Level needs to be specified as it is used to determine the overall inventory 

in the source term calculation.

• Either Decay or Decay with daughter production should be used for most problems.

• The Onset of Gap Release and the Start of Accident. Note that the values of the 

Onset of Gap Release and the Start of the Accident should remain at 0.0. If values 

greater than 0.0 are used, the problem time is advanced by the specified time value. 
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Therefore, specifying a value greater than 0.0 causes the lookup values for timedependent data such as Χ/Q to be later than it should be. This issue will be addressed 

in future versions of the RADTRAD-AC. An Adaptive Time Step algorithm and a 

Default with Error Calculation options have been added to SNAP/RADTRAD.

• Options are provided to reduce the volume of output in the Output Parameters and 

NRC Output Flags Property window if the user desires to reduce the volume of output

data.

Figure 3-50 Property window for the Model Options node
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Table 3-5 Summary of SNAP/RADTRAD inputs – General Model Options

Input Description

Model Options – General

Title

Problem title (optional), specified by user. Typically, it is a good idea to 

name the problem particularly since multiple models can be accessed 

in a single SNAP Model Editor session.

Description Problem description (optional), specified by user. It is a good idea to 

provide a short problem description for the record.

Plant Power Level Core power level in MW(th) (required).

Decay

Select one of the following options:

• Decay and daughtering (default)

• No decay or daughtering

• Decay, no daughtering

Onset of Gap Release

Specify the time that the gap release from the fuel starts in hours 

(required). The default is 0.0 hours which is recommended for most 

SNAP/RADTRAD models.

Start of Accident

Specify the time that the accident starts in hours (required). This 

parameter is only significant if radionuclide decay is being calculated. 

The default is 0.0 hours which is recommended for most 

SNAP/RADTRAD models.

Accident Duration Specify the time the accident ends in hours (required). The default is 

720 hours which is recommended for most SNAP/RADTRAD models.

Dose Conversion Type

Select one of the following options for DCFs:

• User defined

• FGR 11 & 12 (default)

Generally, the default FGR 11&12 DCFs should be used.

Dose Conversions Values for FGR 11 & 12 can be displayed. If user-defined is selected, 

then user can input DCFs.

Time Step Algorithm

Two algorithms are available for controlling the time step:

• Adaptive

• Default

• Default with Error Calculation

The Default time step algorithm is the original RADTRAD (version 3.10) 

algorithm implemented with the matrix exponential method [11] (see 

Section 4.1). The Adaptive and the Default with Error Calculation time 

step algorithms were introduced with the RADTRAD-AC (version 4.5.0)

and are discussed in Section 4.2.
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Table 3-5 Summary of SNAP/RADTRAD inputs – General Model Options (cont.)

Input Description

Time Step Table

Specified by user. This option allows the user to specify time steps for 

finer time step resolution for the default time step algorithm and also 

used to control the generation of output. If this option is not used,

SNAP/RADTRAD generates time-dependent output at each time point 

where there is a change in the time-dependent input data such as Χ/Q, 

filtration efficiency, etc. The appropriate time step size is dependent on 

how quickly radioactivity is added or removed from the system being 

modelled. If the default time step algorithm is used the user should 

manually adjust the time step size to make sure the results are 

independent of the time step size. Finally, the user should note that 

entering values in this table will override the Adaptive time step 

algorithm if the minimum and maximum time step size are equal (see 

Section 4.2).

Use Full Time Step

(if Time Step Algorithm is

Adaptive)

When Adaptive time stepping is enabled, a full step solution is 

compared to a two half step solution to determine the error. The two 

half step solution is generally more accurate and is used by default. If 

Use Full Time Step is set to True, then the full step solution is used. 

Note that this option is valid if Adaptive time stepping is used or if 

Default with Error Calculation is turned on and the default value is set 

to True.

Plot All Points

When the Adaptive time stepping or Default with Error Calculation

options are enabled, time steps will be repeated in order to calculate 

error. By default, repeated time steps are not plotted. If Plot All Points

is enabled, set to True, then these points are written to the plot file. 

The default value is set to False.

Max Error

(if Time Step Algorithm is

Adaptive)

When Adaptive time stepping is enabled, this option indicates the error 

threshold used for Adaptive time stepping to determine when time step 

needs to be cut. This value is the fractional error and the default value 

is set to 1E-03.

Model Options – Output Parameters

The following output parameter flags only affect the casename.out output file.

Dose/Activity Output Units

This flag option determines whether the RADTRAD output text files are 

generated in Curies and Rem based units [traditional RADTRAD units] 

or SI units (MBq, mSv). The default units are Curies and Rem.

Echo Model Definition

The flag options are either True or False and specified by the user. If 

set to False, the edited summary of the input is suppressed. The 

default value is set to True.

Show Event

This option determines whether the code should write output at each 

time interval. The flag options are either True or False and specified by 

the user. The default value is set to True.
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Table 3-5 Summary of SNAP/RADTRAD inputs – General Model Options (cont.)

Input Description

Show Step

This option displays each time interval given by the time step control 

input on the output. The flag options are either True or False and 

specified by the user. The user should set this flag to True to get the 

output for all time steps. The default value is set to True.

Show Model

This displays the model output at each time interval in the output. The 

flag options are either True or False and specified by the user. The 

default value is set to True.

Model Options – NRC Output Flags

The available flags that control the generation of output to the NRC-formatted output file. 

Note that the bulk of the output is generated for the Delta Dose and Cumulative Dose 

results.

Input Echo

This option defines whether the input model will be echoed to the NRC 

output file. The flag options are either True or False and the default 

value is set to True.

General Input Parameters

This option defines whether general input parameters are written to the 

NRC output file. These parameters include the number of 

compartments, pathways, dose locations, and nuclides. The problem 

start and end time are also included in the parameters under this 

option. The flag options are either True or False and the default value 

is set to True.

Source Term Parameters

This option defines whether the source term parameters, as specified 

in the inputs, are written to the NRC output file. These parameters 

include the plant power level, inventory power, the consideration for 

radioactive decay and daughter production, start time of the release, 

and the delay time for the release if applicable. The iodine chemical 

fractions, nuclide group release fractions and timings, and nuclide 

inventory file are also included in the parameters under this option. 

The flag options are either True or False and the default value is set to 

True.

Dose Conversion Factor 

Data

This option defines whether the DCFs, as specified in the inputs, are 

written to the NRC output file. These include the nuclide DCFs and 

decay constants. The flag options are either True or False and the 

default value is set to True.

Compartment Data

This option defines whether compartment data parameters, as 

specified in the inputs, are written to the NRC output file. These 

parameters include the number of compartments and the specific data 

for each compartment such as the number, name, volume, type, dose 

location, radionuclide removal features (sprays, recirculation filters, and 

natural deposition), source input and output from the compartment, and 

flow path connections. The flag options are either True or False and 

the default value is set to True.
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Table 3-5 Summary of SNAP/RADTRAD inputs – General Model Options (cont.)

Input Description

Flow Path Data

This option defines whether flow pathway data parameters, as 

specified in the inputs, are written to the NRC output file. These 

parameters include the number of pathways and the specific data for 

each pathway such as the number, name, to compartment, from 

compartment, nuclide transfer mechanism, and output mode. The flag 

options are either True or False and the default value is set to True.

Dose Location Data

This option defines whether dose location data parameters, as 

specified in the inputs, are written to the NRC output file. These 

parameters include the number of dose locations and the specific data 

for each dose location such as the name (EAB, LPZ, and control 

room), Χ/Q data, breathing rate data, and occupancy factor data. The 

flag options are either True or False and the default value is set to 

True.

Activity Distribution Results

This option defines whether activity distribution results at the end of 

each time step are written to the NRC output file. These results include 

the radionuclide, the group number, and the activity (Ci) in each 

compartment of the model at the end of the time step. The flag options 

are either True or False and the default value is set to True.

Delta Dose Results

This option defines whether delta dose results at the end of each time 

step are written to the NRC output file. These results include the 

change in doses (inhalation, cloudshine, skin, thyroid, and TEDE) for 

each radionuclide at the dose locations (EAB, LPZ, and control room) 

from the previous time step to end of the next time step. The flag 

options are either True or False and the default value is set to True.

Cumulative Dose Results

This option defines whether cumulative dose results at the end of each 

time step are written to the NRC output file. These results include the 

integrated doses (inhalation, cloudshine, skin, thyroid, and TEDE) for 

each radionuclide and dose location at the end of the time step. The 

flag options are either True or False and the default value is set to 

True.

I-131 Activity Summary

This option defines whether an I-131 activity summary table is written 

to the NRC output file. The results are a table of the I-131 activity (Ci) 

in each compartment at the end of each time step. The flag options 

are either True or False and the default value is set to True.

Cumulative Dose Summary

This option defines whether the cumulative dose summary table is 

written to the NRC output file. The results are a table of the cumulative 

thyroid, skin, TEDE and whole body doses at each dose location (EAB, 

LPZ, and control room) at the end of each time step. The flag options 

are either True or False and the default value is set to True.
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Table 3-5 Summary of SNAP/RADTRAD inputs – General Model Options (cont.)

Input Description

Lines Per Page

This option specifies the maximum number of lines per page in the 

NRC output before inserting a page break. The user can adjust this 

value with the default value set at 55 lines per page.

Cut-off Value

This option specifies the cut-off value for table data. The nuclide 

summary tables written at each time step will use this value to 

determine which nuclides are written: at least one column for the 

nuclide must have a value greater than the cut-off, or it will not be 

written for that time step. The default value is set at 1.0E-04.

Model Options – Diagnostic Flags

Level – xxx

These flags are used for generating additional output for code 

debugging using write statements contained in the code subroutines. 

Increasing the flag value from zero to five will increase the information 

provided. Higher values indicate a greater amount of output, with a 

value of zero disabling the diagnostic. The default values for these 

Diagnostic Flags are set to zero. These flags are not generally used 

for SNAP/RADTRAD analyses. Some additional information regarding 

these flags can be found in Section 4.2.3 of NUREG/CR-6604.

3.4.1.1 Dose Conversion Factors

The DCFs are also managed under the Model Options node and relate concentration and dose 

to organs by nuclide. There are two modes of DCF management, FGR 11&12 (default) and 

User Defined DCFs. The user can select the either of these two options by selecting the dropdown menu button next to the Dose Conversion Type text box as shown in Figure 3-51.
3-57

Figure 3-51 Setting dose conversion factors in the Model Option Property window

When set to FGR 11&12 (default) option, the RADTRAD plugin automatically matches the 

nuclides in active scenario inventories (see Section 3.3.3) against an extensive database of 

DCF values taken from the reference data in FGR 11 and FGR 12. Additionally the user can 

view these DCFs by selecting the View ( ) icon next to the Dose Conversion text box to open 

the Viewing “FGR11&12” Dose Conversion Defaults window as shown in Figure 3-52. The user 

should note that icons on the tool bar in Figure 3-52 are “greyed” out indicating that these icons 

are not active with this option and that the user cannot change the FGR 11 and FGR 12 DCF 

values. Additionally, the user should note that the RADTRAD plugin flags an error when the 

source inventory contains nuclides that are not in the DCF file (nuclides in the DCF file that are 

not in a source inventory are not listed as an error). When exporting models, the RADTRAD 

plugin will only write the DCFs for nuclides found in the active source scenario inventory (in the 

order defined in the inventory). This helps to preserve the RADTRAD requirement of equivalent 

nuclides in the DCFs and the source inventory.
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Figure 3-52 Viewing “FGR11&12” Dose Conversion Defaults window

When the user selects the User Defined option, the icon next to the Dose Conversion text box 

changes from the View ( ) icon to the Custom Editors ( ) icon. The user can select the 

Custom Editors ( ) icon to open the User-Defined Dose Conversion Factors window as shown 

in Figure 3-53.

Figure 3-53 User-Defined Dose Conversion Factors window

As noted in Figure 3-53, the icons on the tool bar are active with this option indicating that these 

icons can be used to change the DCF values. The names and functions of these icons on the 

tool bar are the same as those in Figure 3-34, with the exception of the Import ( ) icon. The 

Import ( ) icon on Figure 3-53 provides a drop-down menu option in which the user can select 

either the FGR11&12 or Import from file option. The Import from file option will open a typical 

Windows file navigator window to allow the user to search for a specific file (the default file type 

option is “*.dfx” and “*.inp”). As shown in Figure 3-53 the DCFs are listed in a table format with 
3-59

one nuclide per row. Additionally, nuclides that are not present in a source inventory are 

highlighted with a blue background and nuclides listed in a source inventory that are not 

represented in the DCFs are displayed with DCF values listed as <unset>. For additional 

information on DCFs usage in the dose analysis see Section 4.6.

3.4.1.2 Adaptive Time Step

Generally, the Default time step algorithm is adequate for most RADTRAD calculations. If the 

user wants to determine if there are time step sensitivities then two options are available:

1. Default with Error Calculation, and

2. Adaptive time step.

Error in the dose calculation can be determined by selecting the Default with Error Calculation

option. The results can be view using the AptPlot program. Search for error or error.scaled to 

see the error results. To use the adaptive time step algorithm, select Adaptive in the Time Step

option from the drop-down menu.

The Adaptive time step algorithm is new in SNAP/RADTRAD and it is considered to be 

experimental. Use of this algorithm adds a significant amount of running time to the problem. It 

is suggested that the user set up the problem using the Default time step algorithm option and 

check for any time step sensitivities using the Default with Error Calculation or Adaptive time 

step algorithm option. For additional information on the Adaptive time step algorithm see 

Section 4.2.

3.4.2 Nuclear Data and Source Scenarios

The source term specification was introduced in Section 3.3.3. However, a new feature that has 

been added to SNAP/RADTRAD is the ability to consider the reactor coolant system (RCS) 

activity for either a PWR or BWR. The user can access the RCS Activity Calculator window, 

Figure 3-54, by clicking on the Nuclide Data node in the Navigator window, and then selecting

the Custom Editors ( ) icon for Total Inventories text box in the Property window to open the 

Edit Total Inventories window. Then select the Open RCS Activity Calculator ( ) icon on the 

Edit Total Inventories window as shown in Figure 3-34. The user has the option to enter RCS

activity or to allow SNAP/RADTRAD to calculate the RCS activity. Formulations for the 

calculation of RCS activity are presented in Section 4.4. Figure 3-54 displays the RCS Activity 

Calculator window where the user can select from either BWR or PWR.

The user will note that the RCS Activity Calculator window in Figure 3-54 is an input 

specification window where parameters need to be specified to determine the RCS activity. 

There are two options available to calculate RCS activity.

1. The user can input the RCS specific activity (μCi/g) in the Activity column (Figure 3-54)

and then add the effect of iodine spiking by checking either the Use pre-incident spike or 

the Use co-incident spike box. If the user checks the Use co-incident spike box, then the 

Calculate Appearance button on Figure 3-54 will become active. Note that the coincident spike model is not available for BWRs.

2. The user can also have SNAP/RADTRAD calculate the equilibrium Technical

Specification (T/S) Limit RCS activity (without spiking) and add the effect of a preincident or co-incident spike to the total RCS activity.
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In Figure 3-54, the user will note the Activity column is editable so that the user can input the 

known radionuclide specific activity, the RCS mass in kilograms and the RCS inventory will be 

calculated. Generally, the radionuclide specific activities based upon one percent fuel defects 

are presented in Chapter 11 of the Final Safety Evaluation Report for a given plant. Once the 

radionuclide specific activity is entered, the user has the option to calculate the iodine and 

xenon equilibrium activities from the specified equilibrium activity for the dose equivalent iodine 

131 (DE I-131) or the dose equivalent xenon 133 (DE Xe-133) from the facility’s technical 

specification (T/S) equilibrium specific activity. These calculations are done by checking or 

unchecking the appropriate boxes on the RCS Activity Calculator window. Note that the 

calculations are completed using the user-specified radionuclide specific activity (μCi/g).

Additionally, after selecting either the BWR or the PWR option on Figure 3-54, when the user 

selects the Calculate Activity button on Figure 3-54 either Figure 3-55 or 3-56 will open 

respectively. In either instance, the user inputs the required data and clicks the OK button to 

complete the calculation. Note that for the BWR, the user can apply the calculation to either 

steam or liquid (Calculate activity in steam or liquid?) by clicking on the radio button for either 

the Steam activity or Liquid activity option shown in Figure 3-56.

Figure 3-54 RCS Activity Calculator window
3-61

Figure 3-55 RCS Activity Inputs – PWR window

Figure 3-56 RCS Activity Inputs – BWR window

To apply pre-incident or co-incident spiking to either user-supplied or code-calculated RCS 

radionuclide specific activities, the appropriate box is checked on the RCS Activity Calculator

window (Figure 3-54) and the required input supplied. For the pre-incident spike, which is 

applicable to either PWRs or BWRs, the user checks the Use pre-incident spike box and 

supplies the T/S spike activity.

To use the co-incident spike, which is applicable only to PWRs, the user can select either user 

defined values by inputting the iodine appearance rate data into table in the Iodine Appearance 

Rate section of Figure 3-54 or choose to have the code calculate the iodine appearance rate by 

selecting the Calculate Appearance button. Note that the iodine appearance rate Ci/hr column 

is editable so that the user can enter appropriate values of the iodine appearance rate.

When the user clicks the Calculate Appearance button the Calculate Iodine Appearance window 

as shown in Figure 3-57 will open. The user will provide the required inputs and click the OK
3-62

button which will update the iodine appearance rate values in the table in the Iodine Appearance 

Rate section of Figure 3-54.

Figure 3-57 Calculate Iodine Activity window

Once the RCS activity calculations are complete, the user clicks on the OK button on the RCS 

Activity Calculator window (Figure 3-54) and the total RCS activity is automatically transferred 

from the RCS activity calculator to the Inventory (Ci) column in the Edit Total Inventories window 

(Figure 3-34) and the specific inventory amount is back-calculated from the core power. Note 

that a new file is created each time the RCS activity calculator is invoked. These files are 

automatically named, but the user can rename them using the Name text box in the Edit Total 

Inventories window (Figure 3-34). Finally the models used to compute the RCS activity are 

discussed in Section 4.4 and an example showing the detailed use of the RCS Activity 

Calculator, in a SNAP/RADTRAD model, is demonstrated in the draft SNAP/RADTRAD 

Workbook (available at the RAMP website (https://www.usnrc-ramp.com).

Regardless of whether fuel or RCS activity is used, it is the total inventory that is the basis for 

the source term calculation accessed from the Source Scenarios text box, in the Property

window, once a new source model is initiated. Recall from earlier discussions that part of the 

specification of a new source scenario is the appropriate nuclide inventory either from the 

reactor fuel, RCS or other source. Once that step is completed, an appropriate release model is 

specified from the available pre-defined release models listed under the Accident Parameters

tab on the Edit Inventory Scenario window as shown in Figure 3-58. Alternately, the user has 

the option of setting release fractions and a release time under the Release Fractions and 

Timings tab. For releases of radionuclides from the reactor coolant, the release rate is usually 

controlled using the flow pathway leak or flow rate from the compartment where the reactor 

coolant is released. Accordingly, using a user-specified release fraction of 1.0 for noble gases, 

halogens, and alkali metals and a release duration of 1.0E-04 hours for the gap release as a 

surrogate should suffice. Note that the initial inventory prior to the application of release 

fractions appears under the Adjusted Inventory tab while the Source Term tab lists the actual 

releases to be used in the model after multiplication by the release fractions.

• For the Use Total Inventory option, user-defined release data are entered under the 

Release Fractions and Timings tab.
3-63

• For DBA-TID and DBA-AST options, the release fractions are listed under the Release 

Fractions and Timings tab. The basis for the values for these options is presented in 

Section 4.3.

• For the Gap Release, rod ejection accidents-control rod drop accidents (REA-CRDA), 

and fuel handling accidents (FHA) options, the default release fractions are set under 

the Accident Parameters tab as each accident is selected. The release fractions for 

the relevant nuclide groups are set to 1 under the Release Fractions and Timings tab.

Tables 3-6 and 3-7 list the available inputs for the Nuclear Data and Source nodes in 

SNAP/RADTRAD.

Figure 3-58 Available pre-defined SNAP/RADTRAD release models
3-64

Table 3-6 Summary of SNAP/RADTRAD inputs – Nuclear Data

Input Description

Nuclide Model

Select one of the following options:

• ICRP-38 definitions (default)

• User Defined

It is recommended that the ICRP-38 data be used.

Note that if the User-Defined option is selected and new nuclide 

definitions are specified and then the user switches to the ICRP-38

option, the new nuclide definitions are deleted. References in the Total 

Inventories or the Sources to those nuclide definitions will be set to 

“<not defined>.”

Nuclides

Specified by user when the User Defined option is chosen in the 

Nuclide Model input. Note that the nuclide definitions can be reviewed 

by selecting Custom Editors ( ) icon. This will open the Nuclide 

Definitions window, which contains the nuclide name, atomic mass,

and half-life on the left-hand side. When a user clicks on a nuclide on 

the left-hand side the daughter nuclides and its associated branching 

ratios will be displayed on the right-hand side of the window.

Total Inventories

Used to develop radionuclide inventories in the fuel or in the RCS. 

This input works in conjunction with the Sources node to develop a 

source term. The two sample default core inventories for a PWR and 

BWR from RADTRAD 3.03 are included in the SNAP Model Editor. 

Core inventories can also be specified by the user. Section 3.3.3 and 

Figures 3-34 through 3-40 provide more detailed instructions on how to 

use these inputs.

Table 3-7 Summary of SNAP/RADTRAD inputs – Sources

Input Description

Name Specified by user for the source (optional).

Component Number

Multiple sources can be used in a model and the SNAP/RADTRAD 

Model Editor assigns the number. These numbers must begin with 

number 1 and increase sequentially for each additional source. 

Description Specified by user (optional).

Source Scenarios

Various source (release) scenarios are available to the users which are 

linked to the Nuclide Data definition. Source scenarios include LOCA 

DBAs and non-LOCA DBAs such as FHA, CRDA or REA, and Gap 

releases. Additionally, scenarios involving RCS activity, such as steam 

generator tube ruptures and main steam line breaks can also be 

defined. Section 3.4.2 and Figures 3-54 through 3-58 provide more 

detailed instructions on how to use this input to model these scenarios.
3-65

Table 3-7 Summary of SNAP/RADTRAD inputs – Sources (cont.)

Input Description

Source Term Fractions

User defined value which is the fraction of the inventory being released 

by the source. Multiple sources referencing the same inventory can 

divide the source term between them through this value.

Iodine Physical Form

Specified the fraction of iodine that is in elemental, organic or 

particulate chemical form. Predefined fractions are listed below and 

are user-selectable from the drop-down menu.

• TID-14844 – 0.05 aerosol (particulate), 0.91 (elemental), and 

0.04 (organic)

• NUREG–1465 – 0.95 aerosol (particulate), 0.0485 

(elemental), and 1.5E-03 (organic).

• User Defined

Note that if one of the predefined fraction options is selected, the 

above fractions appear in the Aerosol Fraction, Elemental Fraction or 

Organic Fraction text boxes. These fields are greyed-out and are not 

editable. Selecting the user-defined option from the iodine physical 

form drop-down menu allows the user to specify the aerosol, 

elemental, and organic fractions.

Compartments Links the release scenario to a given compartment. Works in 

conjunction with the compartment specification.

3.4.3 Compartments, Pathways, Natural Deposition, Filters and Sprays

Section 3.3.2 presented the approach for defining compartments and pathways and connecting 

these two components. Once an initial model is developed, completing the model is a matter of 

input specification. Input specification is done by left clicking on the Expand ( ) icon (if it is not 

already expanded) of the associated component (Compartments, Pathways, Natural Deposition, 

Filters and Sprays) in the Navigator window, and completing the input specification fields of the 

Property window for that component. The input specification fields for the components in the 

Property window consist of input text boxes, drop-down menus or input tables that are accessed 

by the Custom Editors ( ) icon. Tables 3-8 through 3-12 list the available inputs for the 

Compartments, Pathways, Natural Deposition, Filters and Sprays in SNAP/RADTRAD.

Table 3-8 Summary of SNAP/RADTRAD inputs – Compartments

Input Description

Name Specified by user (optional).

Component Number

Multiple compartments can be used in a model and the 

SNAP/RADTRAD Model Editor assigns the number. These numbers 

must begin with number 1 and increase sequentially for each additional 

component.
3-66

Table 3-8 Summary of SNAP/RADTRAD inputs – Compartments (cont.)

Input Description

Description Specified by user (optional).

Type

The user can select from the following options:

• Control Room Dose – This option is used for a control room

compartment which enables a dose location to be associated 

with the compartment.

• Environment – This option couples radionuclide release points 

and dose locations through the specification of Χ/Q.

• Normal – A general compartment type that can be 

interconnected to other compartments. Removal by sprays, 

natural deposition and filtration can be modeled in these 

compartments.

• Normal Dose – This option is similar to the Normal 

compartment except that a dose location can be specified 

within the compartment.

Note that an Environment compartment is defined by default in 

SNAP/RADTRAD. Additional compartments are specified by the user.

Output Level Detail

Sets the detail level used to output compartment data (nuclide activity 

and decontamination for the compartment) during model execution. 

The user can select from the following options:

• No additional detail (default)

• Full edit at time steps

• Full edit at end of problem only.

When set to Full edit at time steps, the editing of nuclide activity and 

decontamination for the compartment are printed to the output. These 

details may be printed at every time step or only once, at the end of the 

problem.

Volume

Specified by user (ft3 or m3 depending on user-specified units 

selection). Units switching is done by right-clicking on the black bar of 

the Navigator window and selecting Engineering Units and British or SI 

units. 

Deposition

Works in conjunction with the Natural Deposition node summarized in 

Table 3-10. Used in Normal and Normal Dose compartments as 

appropriate.

Filter

Works in conjunction with the Filter node summarized in Table 3-11. 

Used in Normal, Normal Dose and Control Room Dose compartments 

as appropriate.

Spray Works in conjunction with the Spray node summarized in Table 3-12. 

Used in Normal and Normal Dose compartments as appropriate.
3-67

Table 3-9 Summary of SNAP/RADTRAD inputs – Pathways

Input Description

Name Specified by user (optional).

Component Number

Multiple pathways can be used in a model and the SNAP/RADTRAD 

Model Editor assigns the number. These numbers must begin with 

number 1 and increase sequentially for each additional component.

Description Specified by user (optional).

From Compartment Lists the upstream compartment in this pathway.

To Compartment Lists the downstream compartment in this pathway.

Pathway Type

The method by which radionuclides are transported and deposited 

through the pathway. The user can select from the following options:

• Piping (default) – transport in volumetric flow with a 

decontamination factor.

• Filtered pathway – transport in volumetric flow through filters 

with a specified efficiency.

• Generic – transport in volumetric flow with a decontamination 

factor (replaces legacy suppression pool mechanism). Allows 

for the user to independently specify the decontamination

factors for aerosols (particulate), elemental iodine, organic 

iodine, and noble gases.

• Air leakage – transport in volumetric percent (%/day). This is 

the typical path used for containment leakage.

• Generic w/non-Iodine aerosols – transport is the same as the 

Generic option above without Iodine particulate.

Printout Level Detail

Determines what additional pathway details are written to the output 

file. The user can select from the following options:

• None (default) – writes no extra details.

• Transport Each Time Step – writes information about the 

transport for each group (noble gas, elemental, organic, and 

aerosol (particulate)) at each time step.

• Nuclide and Transport Each Time Step – same as the option 

above, but includes information about each transported 

nuclide.

• Nuclide and Transport at End Only – same as the option 

above, but only written out at the end of the calculation.
3-68

Table 3-9 Summary of SNAP/RADTRAD inputs – Pathways (cont.)

Input Description

Aerosol Removal Model

(if pathway type is Piping)

Specifies how aerosols (particulates) are deposited in the pipe. The 

user can select from the following options:

• No aerosol removal (default) – aerosol removal is not 

modeled in the pipe.

• User Defined Decontamination Factors – if the user selects 

this option the Aerosol DF text box appears below this option. 

Select the Custom Editors ( ) icon for this text box to open 

the Editing Aerosol DF window. The user enters timedependent decontamination factors and flow rates (ft3/min or 

m3/s) in the data entry table (see Section 3.3.3 for details 

regarding data entry using the Custom Editors ( ) icon and 

the edit table features in SNAP/RADTRAD).

• Brockmann-Bixler Model – If the user selects this option the

following additional input text boxes appear below this option 

with user-specified values to be entered:

 pipe volume (ft3 or m3)

 pipe surface area (ft2 or m2)

 pipe angle (degrees)

 pipe temperature (°F or °C)

 pipe pressure (psi or kPa)

 pipe aerosol settling velocity (ft/min or m/s)

 pipe aerosol flow rates are entered by selecting 

the Custom Editors ( ) icon to open the Editing 

Pipe Aerosol Flow Rates window. Enter the flow 

rates (ft/min or m/s) as a function of time in the

data entry table.

Note that addition guidance and information on these inputs is 

available by clicking on the Help ( ) icon and Section 4.5.3.

Elemental Iodine Removal 

Model

(if pathway type is Piping)

Determines how elemental iodine is deposited in the pipe. The user 

can select from the following options:

• None (default) – elemental iodine removal is not modeled in 

the pipe.

• Enter DFs and Flow Rates – if the user selects this option the

removal rate is defined as a function of flow rate and DFs over 

time. When this option is selected the Elemental Iodine DF

text box appears below this option. Select the Custom Editors

( ) icon for this text box to open the Editing Elemental Iodine 

DF window. The user enters time-dependent DFs and flow 

rates (ft3/min or m3/s) in the data entry table.

• Enter Deposition Velocity – If the user selects this option the 

Elemental Iodine Deposition Velocity text box appears below 

this option. The user enters iodine the deposition velocity 

(ft/min or m/s).
3-69

Table 3-9 Summary of SNAP/RADTRAD inputs – Pathways (cont.)

Input Description

Organic Iodine Removal 

Model

(if pathway type is Piping)

Determines how organic iodine is deposited in the pipe. The user can 

select from the following options:

• None (default) – elemental iodine removal is not modeled in 

the pipe.

• Enter DFs and Flow Rates – if the user selects this option the

removal rate is defined as a function of flow rate and DFs over 

time. When this option is selected the Organic Iodine DF text 

box appears below this option. Select the Custom Editors 

( ) icon for this text box to open the Editing Organic Iodine 

DF window. The user enters time-dependent DFs and flow 

rates (ft3/min or m3/s) in the data entry table.

• Enter Deposition Velocity – If the user selects this option the 

Organic Iodine Deposition Velocity text box appears below 

this option. The user enters iodine the deposition velocity 

(ft/min or m/s).

Note: The NRC does not credit organic deposition in design basis 

calculations. 

Filter

(if pathway type is Filter 

Pathway)

Specifies the air filter removing radionuclides from transport in the 

pathway. Use the Select ( ) icon to open the Select from Filters

window to link to one of the available filter models or creates a filter 

component.

Aerosol DF

(if pathway type is Generic 

or Generic w/non-Iodine 

Aerosols)

Select the Custom Editors ( ) icon for this text box to open the Editing 

Aerosol DF window. Enter the time-dependent DFs and flow rates

(ft3/min or m3/s) in the data entry table.

Elemental Iodine DF

(if pathway type is Generic 

or Generic w/non-Iodine 

Aerosols)

Select the Custom Editors ( ) icon for this text box to open the Editing 

Elemental Iodine DF window. Enter the time-dependent DFs and flow 

rates (ft3/min or m3/s) in the data entry table.

Organic Iodine DF

(if pathway type is Generic 

or Generic w/non-Iodine 

Aerosols)

Select the Custom Editors ( ) icon for this text box to open the Editing 

Organic Iodine DF window. Enter the time-dependent DFs and flow 

rates (ft3/min or m3/s) in the data entry table.

Note: The NRC does not credit organic deposition in design basis 

calculations.

Noble Gas Flow Rates

(if pathway type is Generic 

or Generic w/non-Iodine 

Aerosols)

Select the Custom Editors ( ) icon for this text box to open the Editing 

Noble Gas Flow Rates window. Enter the time-dependent flow rates

(ft3/min or m3/s) in the data entry table.

Leakage Rate

(if pathway type is Air 

leakage)

Select the Custom Editors ( ) icon for this text box to open the Editing 

Leakage Rate window. Enter the time-dependent flow leakage rates

(%/day) in the data entry table.
3-70

Table 3-10 Summary of SNAP/RADTRAD inputs – Natural Deposition

Input Description

Name Specified by user (optional).

Component Number

Multiple natural deposition models can be used in a model and 

the SNAP/RADTRAD Model Editor assigns the number. These 

numbers must begin with number 1 and increase sequentially for 

each additional component.

Description Specified by user (optional).

Aerosol Deposition Model

Specifies the method by which the deposition removes 

radionuclides from the compartment. The user can select from 

the following options:

• None (default) –no deposition is modelled.

• User Defined Coefficients – deposition is determined 

from user-specified removal rate coefficients over time.

• Henry’s Model Coefficients – uses Henry’s model for 

natural deposition. User specifies compartment height 

and particle density over time. See Section 4.5.2.1 for 

more model details and references.

• Powers’ Deposition Model – the Powers’ model for 

natural deposition, calculated based on an uncertainty 

percentile associated with a reactor and accident type. 

This model is only for large buildings, and is not valid for 

deposition in passages such as pipes. See Section 

4.5.2.2 for more model details and references.

Aerosol Removal Coefficients

(if Aerosol Deposition Model is 

User Defined Coefficients)

Defines the aerosol (particulate) radionuclide removal as a 

function of time. Select the Custom Editors ( ) icon for this text 

box to open the Editing Aerosol Removal Coefficients window. 

Enter the time-dependent removal coefficients (1/hour) in the

data entry table.

Henry Deposition Table Data

(if Aerosol Deposition Model is 

Henry’s Model Coefficients)

The table is used by the code to determine the particle deposition 

rate from the compartment height and particle density over time. 

Select the Custom Editors ( ) icon for this text box to open the 

Editing Henry’s Deposition Table Data window. Enter the timedependent height (ft or m) and particle density (lb/ft3 or g/cm3) in 

the data entry table.
3-71

Table 3-10 Summary of SNAP/RADTRAD inputs – Natural Deposition (cont.)

Input Description

Powers Accident Model Type

(if Aerosol Deposition Model is 

Powers Deposition Model)

Sets the model of decontamination based on the type of reactor 

and accident. Select the accident type using the drop-down 

menu.

• PWR-DBA

• BWR-DBA

• APWR-DBA

Power’s Model Percentile

(if Aerosol Deposition Model is 

Powers Deposition Model)

Sets the uncertainty percentile for the Powers model for natural 

deposition. Select the accident type using the drop-down menu.

• 10%

• 50%

• 90%

Note: The 10% deposition model yields the most conservative 

aerosol removal coefficients.

Elemental Deposition Model Type

Determines the method by which the deposition removes 

elemental iodine from the compartment. The user can select 

from the following options:

• None (default) –no decontamination is modelled.

• User Defined Coefficients – decontamination is specified 

as a function of removal coefficients over time. When 

this option is selected the Elemental Iodine Removal 

Coefficient text box appears below this option.

Elemental Iodine Removal 

Coefficient

(if Elemental Deposition Model 

Type is User Defined Coefficients)

Defines the elemental iodine radionuclide removal as a function 

of time. The removal coefficient is defined as the fraction of the 

total elemental iodine mass inserted into the containment 

removed per second. Select the Custom Editors ( ) icon for this 

text box to open the Editing Elemental Iodine Removal 

Coefficient window. The user enters time-dependent elemental 

iodine removal coefficients (1/hour) in the data entry table.
3-72

Table 3-11 Summary of SNAP/RADTRAD inputs – Filters

Input Description

Name Specified by user (optional).

Component Number

Multiple filters can be used in a model and the SNAP/RADTRAD 

Model Editor assigns the number. These numbers must begin 

with number 1 and increase sequentially for each additional 

component.

Description Specified by user (optional).

Filter Table

The removal efficiency of filters and flow rate through the filters 

as a function of time. Select the Custom Editors ( ) icon for this 

text box to open the Editing Filter Table window. Each row 

defines time dependent filter flows (ft3/min or m3/s) and 

efficiencies (%) for:

• aerosol (particulate)

• elemental iodine

• organic iodine filtration

There is no noble gas efficiency as it is assumed that the noble 

gases are not filtered. The efficiencies will change in a stepwise 

fashion at each specified time.

Table 3-12 Summary of SNAP/RADTRAD inputs – Sprays

Input Description

Name Specified by user (optional).

Component Number

Multiple spray models can be used in a model and the 

SNAP/RADTRAD Model Editor assigns the number. These 

numbers must begin with number 1 and increase sequentially 

for each additional component. 

Description Specified by user (optional).
3-73

Table 3-12 Summary of SNAP/RADTRAD inputs – Sprays (cont.)

Input Description

Aerosol Removal Model

Determines the method by which the spray removes aerosol 

(particulate) radionuclides from the compartment. The user can 

select from the following options:

• None (default) – aerosols are not removed from the 

compartment.

• User Defined Coefficient Table – allows the user to 

specify the aerosols removal rate coefficient over time. 

When this option is selected the Aerosol Removal 

Coefficients, Aerosol DF Limit Enabled, Aerosol DF 

Limit, Aerosol Lambda/10 DF Limit Enabled, and the 

Aerosol Lambda/10 DF Limit text boxes appear below 

this option.

• Powers’ Model – the aerosol removal rate is 

determined using by the Powers and Burson model, 

which takes into account sprayed and non-sprayed 

volume, deposition percentile, and spray flux ratio and 

height over time. When this option is selected the 

Powers Model Spray Table, Powers Model Spray Ratio

and the Powers Model Percentile text boxes appear 

below this option. See Section 4.5.1 for more details.

Aerosol Removal Coefficients

(if Aerosol Removal Model type is

User Defined Coefficient Table)

Select the Custom Editors ( ) icon for this text box to open the 

Editing Aerosol Removal Coefficients window. The user enters 

time-dependent aerosol removal coefficients (1/hour) in the data 

entry table.

Aerosol DF Limit Enabled

(if Aerosol Removal Model is User 

Defined Coefficient Table)

The user selects from either True or False. If True is selected, 

the Aerosol DF Limit text box appears below this option.

Aerosol DF Limit

(if Aerosol Removal Model is User 

Defined Coefficient Table)

The user enters a DF value to limit the amount of aerosol 

removal. Once this DF is reached in the compartment the 

aerosol lambda or removal coefficient is automatically set to 

zero. The DF value must be 1.0 or greater and the default value 

is 1.0E+06.

Aerosol DF Limit, Aerosol 

Lambda/10 DF Limit Enabled

(if Aerosol Removal Model is User 

Defined Coefficient Table)

The user selects from either True or False. If True is selected, 

the Aerosol Lambda/10DF Limit text box appears below this 

option.

Aerosol Lambda/10 DF Limit

(if Aerosol Removal Model is the 

Powers Model)

The user enters a DF value to limit the amount of aerosol 

removal. Once this DF is reached in the compartment the 

aerosol lambda or removal coefficient is automatically set to 

1/10th its original value. The DF value must be 1.0 or greater

and the default value is 50.
3-74

Table 3-12 Summary of SNAP/RADTRAD inputs – Sprays (cont.)

Input Description

Powers Model Spray Table

(if Aerosol Removal Model is the 

Powers Model)

Specified as a function of spray flux and the fall height of the 

spray droplets (typically the distance between the spray headers 

and the containment floor). Select the Custom Editors ( ) icon 

for this text box to open the Editing Powers Model Spray Table

window. Enter the time-dependent spray flux (cfm/ft2 or

(m3/s)/m2) and spray height (ft or m). Unit switching is done by 

right-clicking on the black bar of the Navigator window and 

selecting Engineering Units and choosing either British or SI 

units.

The spray flux and height are discussed in NUREG/CR-5966, “A 

Simplified Model of Aerosol Removal by Containment Sprays” 

[12].

The Powers’ model is valid in the spray flux ratio range 1.0E-05 

to 2.5E-03 m3/s-m2 (0.002 and 0.5 cfm/ft2) and a range of spray 

fall heights between 5 to 50 m (16.4 and 164 ft).

Powers Model Spray Ratio

(if Aerosol Removal Model is the 

Powers Model)

The ratio of unsprayed to sprayed volume in the compartment. 

This is typically zero, as the unsprayed volume is often modeled 

as a separate compartment. Good mixing is assumed for any 

ratio above zero; if good mixing is not available, the sprayed and 

unsprayed compartments should be modeled separately.

Powers Model Percentile

(if Aerosol Removal Model is the 

Powers Model)

The percentile model used in the calculation. Select the percent 

using the drop-down menu.

• 10%

• 50%

• 90%

Note: the 10% model yields the most conservative aerosol 

removal coefficients.

Elemental Iodine Removal Model

Determines the method by which the spray removes aerosol 

(particulate) radionuclides from the compartment. The user can 

select from the following options:

• None (default) – elemental iodine is not removed from 

the compartment.

• User Defined Coefficient Table – elemental iodine is

removed using user-specific removal rate coefficients

input by the user. When this option is selected the 

Elemental Iodine Removal Coefficients, Elemental-I DF 

Limit Enabled, and Elemental-I DF Limit text boxes 

appear below this option.

Elemental Iodine Removal 

Coefficients

(if Elemental Iodine Removal Model 

is the User Defined Coefficients)

Defines the elemental iodine radionuclide removal coefficients 

used to determine the elemental iodine removal rate as a 

function of time. Select the Custom Editors ( ) icon for this text 

box to open the Editing Elemental Iodine Removal Coefficients

window. The user enters time-dependent elemental iodine

removal coefficients (1/hour) in the data entry table.
3-75

Table 3-12 Summary of SNAP/RADTRAD inputs – Sprays (cont.)

Input Description

Elemental-I DF Limit Enabled

(if Elemental Iodine Removal Model 

is the User Defined Coefficients)

The user selects from either True or False. If True is selected, 

the Elemental-I DF Limit text box appears below this option.

Elemental-I DF Limit

(if Elemental Iodine Removal Model 

is the User Defined Coefficients)

The user enters a DF value to limit the amount of elemental 

removal. Once this DF is reached in the compartment the 

elemental lambda or removal coefficient is automatically set to 

zero. The DF value must be 1.0 or greater and the default value 

is 20.

Organic Iodine Removal Model

Determines the method by which the spray removes organic 

iodine from the compartment. The user can select from the 

following options:

• None (default) – organic iodine is not removed from the 

compartment.

• User Defined Coefficient Table – organic iodine is

removed using user-specified removal rate coefficients

as an organic removal coefficient over time. When this 

option is selected the Organic Iodine Removal 

Coefficients text box appear below this option.

Organic Iodine Removal 

Coefficients

(if Organic Iodine Removal Model 

is the User Defined Coefficients)

Defines the organic iodine radionuclide removal as a function of 

time. Select the Custom Editors ( ) icon for this text box to 

open the Editing Organic Iodine Removal Coefficients window. 

The user enters time-dependent elemental iodine removal 

coefficients (1/hour) in the data entry table.

Note: The NRC does not credit organic deposition in design 

basis calculations.

3.4.4 Dose Locations, Breathing Rates, and Χ/Q Tables

Section 3.3.3 demonstrates the general approach for defining dose locations, breathing rates, 

and Χ/Q tables. Generally, the default breathing rates are used for most analyses and are 

entered under the Dose Locations node in the Property window. The values for Χ/Q are 

specified through the use of data entry tables as illustrated in Section 3.3.3 (Figure 3-33). 

Tables 3-13 and 3-14 list the available inputs for the Dose Locations and Χ/Q Tables nodes in 

SNAP/RADTRAD.
3-76

Table 3-13 Summary of SNAP/RADTRAD inputs – Dose Locations

Input Description

Name

The EAB or LPZ dose location names are set by 

SNAP/RADTRAD. Other dose location names (i.e. control 

room) are created by the user.

Description

The EAB or LPZ dose location descriptions are set by 

SNAP/RADTRAD. Other dose location descriptions (i.e. control 

room) must be created manually by the user.

Component Number

Multiple dose locations can be used in a model and the 

SNAP/RADTRAD Model Editor assigns the number. These 

numbers must begin with number 1 and increase sequentially 

for each additional component.

Breathing Rates

Defines the breathing rates at the dose locations as a function 

of time. Select the Custom Editors ( ) icon for this text box to 

open the Editing Breathing Rates window. The user can then, if 

necessary, select the default breathing rates by left clicking the 

Default button and choosing between either the EAB/LPZ or 

Control Room options. The default breathing rates for each are 

listed below:

• EAB/LPZ

Time

(h)

Breathing 

Rates

(m3/s)

0.0 3.5E-04

8.0 1.8E-04

24.0 2.3E-04

• Control Room

Time

(h)

Breathing 

Rates

(m3/s)

0.0 3.5E-04

Additionally the user can enter time-dependent breathing rates 

(ft3/min or m3/s) in the data entry table.

Χ/Q Table

Specifies the Χ/Q table to be used with this dose location. Use 

the Select ( ) icon to open the Select from Χ/Q Tables window 

to link to one of the available Χ/Q Tables.

Occupancy Factors

Specifies the occupancy factors table to be used with the 

control room (or the technical support center) dose location. 

Use the Custom Editors ( ) icon to open the Editing 

Occupancy Factors window. The user can then use the provide 

time dependent occupancy factors for the dose location. 

Occupancy factors may only be input for the control room 

compartment.
3-77

Table 3-14 Summary of SNAP/RADTRAD inputs – Χ/Q Tables

Input Description

Name

X/Q values are specified for the EAB and LPZ dose locations by 

default in SNAP/RADTRAD. Users must specify X/Q data for 

the EAB and LPZ. X/Q data for additional dose locations can be 

specified by the user (optional).

Component Number

The EAB is set to Χ/Q Table 1 and LPZ is set to Χ/Q Table 2 by 

SNAP/RADTRAD. User-specified X/Q tables are automatically 

numbered by SNAP/RADTRAD.

Description Specified by user (optional).

X/Q Table

Select the Custom Editors ( ) icon for this text box to open the 

Editing X/Q Tables window. The user enters time-dependent 

X/Q values (s/m3) in the data entry table.

One item of note is the link between the dose location and Χ/Q table. Like most of the functions 

in the SNAP Model Editor there is a couple of different ways to create the link between the dose 

location and the Χ/Q table. The easiest way to establish this link is by clicking on the main Χ/Q 

Tables [2] node in the Navigator window to view the Property window for this node. In the 

Property window select the Custom Editors ( ) icon to the right of the Onsite Χ/Q Tables text 

box to open the Onsite Χ/Q Table Map window (Figure 3-59). Alternatively, the user can also 

open the Onsite Χ/Q Table Map window by opening the Property window for the environment 

compartment and select the Custom Editors ( ) icon to the right of the Onsite Χ/Q Tables text 

box.

The Onsite Χ/Q Table Map window will appear and the user can link the Χ/Q table and dose 

location. In the Onsite Χ/Q Table Map window (Figure 3-59), the provided row headers list each 

of the pathways which are entering the environment. These are annotated further by the 

Release to Environment label to the left of the rows. Column headers in the Onsite Χ/Q Table 

Map window represent the pathways out of the environment. These are annotated by an Intake 

from Environment label placed above the table. Each column represents an exhaust while 

every row represents an inflow. To map an X/Q table, click within a cell to enable the Select ( ) 

icon. Click the Select ( ) icon to open the Select from X/Q Tables window; use this window to 

select the X/Q Table mapped to the inflow and exhaust. Users should note that 

SNAP/RADTRAD does not allow X/Q tables to be defined for exhaust from the control room to 

the environment. The remaining nodes under the Navigator window are listed and described in 

Table 3-15.
3-78

Figure 3-59 Onsite Χ/Q Table Map window

Table 3-15 Summary of SNAP/RADTRAD inputs – Remaining inputs

Input Description

Connections

Connections among compartments (paths), dose locations, and source connections can be specified. 

Usually, drag and drop is used. Note that connections between compartments cannot be created by 

the Navigator window. A pathway needs to be defined and then the connection needs to be made 

using the Connection Tool ( ) icon in the View / Dock window (see Section 3.3.2).

Job Streams

Name

The name for this job stream. This will be used to generate the 

relative path for the tasks that make up this stream. The default 

value for the name is Simple_Stream and it is recommended 

that SNAP/RADTRAD users change this to a unique name that 

is identifiable to the model (see Section 3.2.2).

Description Specified by user (optional).
3-79

Table 3-15 Summary of SNAP/RADTRAD inputs – Remaining inputs (cont.)

Input Description

Stream Type

Defines the type of calculation that may be implemented through 

this job stream. The user can select from the following options:

• Basic Job Stream (default) – a simple job stream.

• Numeric Combination – builds a set of input models by 

modifying one or more shared numeric variables. Each 

selected shared numeric will either iterate through a list 

of predefined values or increment from a start value to 

an end value.

• Tabular Parametric – the parametric case takes the 

form of a table of shared variable values.

• Dakota Uncertainty – uncertainty support for the 

Dakota toolkit.

SNAP/RADTRAD user should use the default value.

File Groups

Typically, the File Groups text box is not used in 

SNAP/RADTRAD. Defines groups of input sources and forces 

files inside file sets to be associated one-to-one with other file 

sets or parametric model node outputs.

Platform The platform that this stream will be submitted to by default. 

The default value for SNAP/RADTRAD is Local.

Root Folder

The calculation server folder where the job stream is executed

(see Section 3.2.2). Select the Custom Editors ( ) icon for this 

text box to open the Edit Calculation Server Root Folders

window.

Relative Location

The relative location of this stream in relation to the selected 

staging location. The staging location is where intermediate 

files, such as the stream definition, will be stored while a job 

stream is running (see Section 3.4.2 of reference [4] for more 

details).

Log Level

Typically, the Log Level text box is not changed from the default 

value (Information) in SNAP/RADTRAD. Defines the current log 

level for messages produced by this stream. 

View in Job Status

This property determines whether the SNAP Job Status window 

will be opened to view the status of this stream after submission. 

The default value for SNAP/RADTRAD is Yes.
3-80

Table 3-15 Summary of SNAP/RADTRAD inputs – Remaining inputs (cont.)

Input Description

Linear Execution

Job Streams using Linear Execution are executed one task at a 

time, prioritized by their Step Number. In a normal (non-linear) 

Job Stream, tasks will be executed as soon as their 

dependencies are available (i.e. up-stream tasks are complete) 

up to the maximum number allowed by the platform. This option 

should only be used in situations where the stream must 

execute one task at a time and each task must complete before 

another can be executed.

In most cases, including SNAP/RADTRAD, this value should be 

left at its default value (No).

Numerics

The SNAP user-defined Numerics feature is designed to allow properties of a model to be modified 

and/or calculated outside the normal input for the model. A user may create real, integer, Boolean, 

string, and table variables, as well and functions. Typically, the Numerics node is not used in 

SNAP/RADTRAD. See Section 2.5 of reference [4] for more details about User-Defined Numerics in 

other SNAP applications.

Views

The user can specify multiple views so that various model icons can be seen. Usually, one view 

(Default View) is sufficient for SNAP/RADTRAD models. The Property window for the Default View

node values can be modified by the user as needed, but typically the default values for the text boxes 

will be sufficient for most models. Section 3.3.4 describes some of the options associated with the 

Default View node Property window text boxes. The user can select the Help ( ) icon for each 

Default View node Property window text box to obtain more information on each one.
4-1

4.0 MODELS USED IN RADTRAD

The radiological consequences of an accident in a nuclear reactor depend upon the quantity of 

the radioactive material that escapes to the environment or enters into the control room. 

SNAP/RADTRAD is designed to calculate doses at offsite locations, such as the EAB, LPZ and 

in the control room. Source term models from TID-14844 or from NUREG-1465 are 

incorporated into SNAP/RADTRAD to describe fission product release from the fuel to the 

containment. Models for natural deposition within a compartment and engineered removal 

mechanisms, such as sprays and filters are available in the code. Flow between compartments 

is modeled and HEPA and charcoal filters can be included in the flow paths for radionuclide 

removal due to filtration. Leakage to the environment can also be modeled and doses 

calculated to various points in the environment, such as the EAB and LPZ. After transporting 

the nuclides to different locations, SNAP/RADTRAD calculates the dose at user-specified 

locations. Note that much of the discussion in this section is based on the original RADTRAD 

documentation in NUREG/CR-6604 and its two supplements.

4.1 Governing Equations in RADTRAD

The basic RADTRAD-AC model is a multi-compartment model where each compartment 

represents a portion of the plant being analyzed. Generally, the containment volume(s), 

environment, and control room(s) are modeled as compartments. Figure 4-1 presents a 

diagram illustrating a typical SNAP/RADTRAD model. This figure shows a two-volume 

containment connected to the environment. A two-volume containment compartment may be 

used to represent the sprayed and unsprayed portions of the containment. A control room is 

shown which contains ventilation intakes from the environment through two filtered flow 

pathways, one recirculating and one that intakes directly from the environment. Recirculating 

filtered flow paths are typically used to reduce the airborne radionuclide concentration in the 

control room. An unfiltered intake to the control room from the environment representing in

leakage is also represented. The control room ventilation discharges back to the environment. 

Dashed lines denote connections with transfer rates of zero and are shown for completeness 

(e.g. no backflow from the control room or environment to the containment).

The governing equations in the RADTRAD-AC are balanced first-order linear differential 

equations relating the release of radionuclides typically from the reactor core to a given 

compartment to the removal of radionuclides within a given compartment and the transfer of 

radionuclides among compartments. Within each compartment except the environment, the 

radionuclides that are airborne within that compartment are assumed to be uniformly distributed 

or mixed. The environment compartment is where the EAB and LPZ dose points are located. 

In many cases, the control room ventilation system draws suction from the environment. Note 

that coupling of transfer pathways from the containment to the EAB, LPZ and control room 

intakes is done using Χ/Q values. The Χ/Q values relate the amount of radionuclide released to 

the environment to the dispersed radionuclide concentration at a particular location in the 

environment. Since each Χ/Q value is associated with a release point and an intake location, 

the radionuclide inventory is not uniformly distributed in the environment compartment.
4-2

Figure 4-1 Schematic of a typical SNAP/RADTRAD dose assessment model

The equations used to calculate the quantity of radionuclide in each compartment can be 

presented concisely in terms of the Λkk,jj

ii coefficients. However, it is important to note that 

multiple factors contribute to each of these transfer and removal rate coefficients. After 

presenting the concise form of the transport equations, the specific terms included in the Λkk,jj

ii

coefficients will be presented.

In developing equations representing the system shown in Figure 4-1, the quantity within each 

compartment or transferred from compartment is expressed in terms of the number of atoms in 

a chemical element group presented in Section 4.3 (Table 4-2). The quantity can also be 

expressed in terms of radionuclide inventory for each nuclide. In the equations below, the term 

species can refer to a radionuclide or chemical element.
4-3

Referring to Figure 4-1, the rate of change of the number of atoms in compartment 1 (upper left) 

is determined from Equation (4-1):

ddNN1

ii

dddd = RR1

ii − Λ1,1ii NN1ii + Λ1,2ii NN2ii + Λ1,3ii NN3ii + Λ1,4ii NN4ii (4-1)

where

RR1

ii = the source release rate of species i in compartment 1 in atoms/s

Λ1,1

ii = the removal rate of species i within compartment 1 in 1/s

NN1

ii = the inventory of species i in compartment 1 in atoms

Λ1,2

ii = the transfer rate of species i from compartment 2 to compartment 1 in 1/s

NN2

ii = the inventory of species i in compartment 2 in atoms

Λ1,3

ii = the transfer rate of species i from compartment 3 to compartment 1 in 1/s

NN3

ii = the inventory of species i in compartment 3 in atoms

Λ1,4

ii = the transfer rate of species i from compartment 4 to compartment 1 in 1/s

NN4

ii = the inventory of species i in compartment 4 in atoms.

The rate of change of the number of atoms in compartment 2 is given by Equation (4-2):

ddNN2

ii

dddd = RR2

ii − Λ2,2ii NN2ii + Λ2,1ii NN1ii + Λ2,3ii NN3ii + Λ2,4ii NN4ii (4-2)

where:

RR2

ii = the source release rate of species i in compartment 2 in atoms/s

Λ2,2

ii = the removal rate of species i within compartment 2 in 1/s

Λ2,1

ii = the transfer rate of species i from compartment 1 to compartment 2 in 1/s

Λ2,3

ii = the transfer rate of species i from compartment 3 to compartment 2 in 1/s

Λ2,4

ii = the transfer rate of species i from compartment 4 to compartment 2 in 1/s.

The rate of change in the number of atoms in compartment 3 is given by Equation (4-3):

ddNN3

ii

dddd = RR3

ii − Λ3,3ii NN3ii + Λ3,1ii NN1ii + Λ3,2ii NN3ii + Λ3,4ii NN4ii (4-3)

where:

RR3

ii = the source release rate of species i in compartment 3 in atoms/s

Λ3,3

ii = the removal rate of species i within compartment 3 in 1/s

Λ3,1

ii = the transfer rate of species i from compartment 1 to compartment 3 in 1/s

Λ3,2

ii = the transfer rate of species i from compartment 2 to compartment 3 in 1/s

Λ3,4

ii = the transfer rate of species i from compartment 4 to compartment 3 in 1/s.

The rate of change of the number of atoms in compartment 4 is given by Equation (4-4):

ddNN4

ii

dddd = RR4

ii − Λ4,4ii NN4ii + Λ4,1ii NN1ii + Λ4,2ii NN2ii + Λ4,3ii NN3ii (4-4)

where:

RR4

ii = the source release rate of species i in compartment 4 in atoms/s
4-4

Λ4,4

ii = the removal rate of species i within compartment 4 in 1/s

Λ4,1

ii = the transfer rate of species i from compartment 1 to compartment 4 in 1/s

Λ4,2

ii = the transfer rate of species i from compartment 2 to compartment 4 in 1/s

Λ4,3

ii = the transfer rate of species i from compartment 3 to compartment 4 in 1/s.

More generally, the rate of change of the number of atoms in the kth compartment in a set of n 

interconnected compartment is given by Equation (4-5) below:

ddNNkk

ii

dddd = RRkk

ii − �λλjj,jj

ii NNkk

ii

nn

jj=1

+ � λλkk,jj

ii NNjjii

nn

jj=1,jj≠kk

(4-5)

In Equation (4-5), RRkk

ii is the source release rate of species i in compartment k in atoms/s. The 

first summation represents the removal terms from compartment k due either to removal within 

the compartment or transfer to another compartment. The second summation represents 

transfer from compartment j to compartment k. The general matrix formulation of transport 

Equation (4-5) is represented in Equation (4-6).

⎝

⎜⎜

⎛

NṄ

1

ii

NṄ

2

ii

NṄ

3

ii

⋮

NṄ

nn

ii⎠

⎟⎟

⎞ =

⎝

⎜⎜

⎛

RR1

ii

RR2

ii

RR3

ii

⋮

RRnn

ii ⎠

⎟⎟

⎞

+

⎝

⎜

⎜

⎛

−Λ1,1

ii Λ1,2ii Λ1,3ii ... Λ1,nn ii

Λ2,1

ii −Λ2,2ii Λ2,3ii ... Λ2,nn ii

Λ3,1

ii Λ3,2ii ⋱ ... Λ3,nn ii

⋮ ⋮ ⋮ ... ⋮

Λnn,1

ii Λnn,2ii Λnn,3ii ... −Λnn,nn ii ⎠

⎟

⎟

⎞

⎝

⎜⎜

⎛

NN1

ii

NN2

ii

NN3

ii

⋮

NNnn

ii⎠

⎟⎟

⎞

(4-6)

Note that the time derivative is represented by NṄ

jj

ii

. The Λ coefficient matrix is a transfer matrix 

where the diagonal terms are the removal coefficients applicable to a given compartment j

(hence the – sign) and the off-diagonal terms are transfer coefficients relating the transfer of 

material from various compartments to compartment j.

Off-diagonal transfer terms are calculated as f/V where f is the flow rate out of a compartment 

(volume units/s) and V is the compartment volume, yielding units of 1/s. This ratio is multiplied 

by the radionuclide inventory in the upstream connecting compartment to provide a source to 

the connecting downstream compartment. Diagonal terms or removal terms are more complex 

because of the various removal processes that are modeled in the RADTRAD-AC. However, 

the idea is the same in that a removal coefficient expressed in units of 1/s is multiplied by the 

radionuclide inventory to yield a removal rate. The terms included in the diagonal removal 

coefficients and the off-diagonal transfer coefficients are shown below (Equation 4-7) with 

details on the calculation of removal coefficients provided in Section 4.5.

The terms included in the diagonal removal coefficients each have unit of 1/s and are:

Λjj,jj

ii = λλjj,ssssssii + λλjj,ddddii + λλjj,ff ffffii +� λλkk,jjii nn

kk=1

kk≠jj

(4-7)

where:

λλjj,ssssss

ii = the spray removal coefficient in 1/s

λλjj,dddd

ii = the natural deposition removal rate in 1/s
4-5

λλjj,ff ffff

ii = the filtered removal rated within compartment in 1/s

λλkk,jj

ii = the removal rate from compartment j toward compartment k in 1/s.

The removal rate λλkk,jj

ii includes a few different types of transfer between compartments as shown 

in Equation (4-8).

λλkk,jj

ii = λλkk,jj, ll ii + λλkk,jj,ff ffffii + ffkk,jj

VVjj

(4-8)

where:

λλkk,jj, ll ii = the transfer via leakage paths in 1/s

λλkk,jj,ff ffff

ii = the transfer through a filtered path in 1/s

ffkk,jj = the flow in m3

/s from j to k through a path with a DF

VVjj = the volume of compartment j in m3

.

The removal terms from Equation (4-8) are related to the off-diagonal transfer terms in Equation

(4-6). However not all of the nuclide leaving compartment j necessarily reaches compartment k. 

The filtered flow and the DF related flow terms require an additional coefficient that indicates the 

fraction of the nuclide that was removed in transit. The terms in the off-diagonal transfer 

coefficients are shown in Equation (4-9).

Λjj,kk

ii = λλjj,kk, ll ii + �1 − ηηjj,kk

ii

100� λλjj,kk,ff ffff

ii + � 1

DDDD� ffjj,kk

ii

VVkk

(4-9)

where:

ηηjj,kk

ii = the percent efficiency of the filter in the path from compartment k to j

DDDD = the nondimensional DF for path with flow fromcompartment k to j.

Equation (4-6) is solved in the RADTRAD-AC using a matrix exponential method based on work 

done in references [11] and [13]. Matrix exponential methods are used to solve systems of 

linear differential equations of the form NṄ = RR + ΛNN subject to an initial condition N0. The units 

of the solution variable are expressed in atoms. This quantity can be converted to other units 

such as grams or Becquerels (Bq). Section 4.6 discusses how dose is calculated from the 

number of atoms.

Note that radionuclide decay is not explicitly included in Equation (4-6). Rather, decay is 

accounted for in the RADTRAD-AC by dividing the solution of the differential equations into two 

parts: (1) radioactive decay and daughter in-growth, and (2) radionuclide transport. Inclusion of 

radioactive decay and daughter in-growth modeling with Equation (4-4) significantly increases 

the size of the linear system as well as the computational load to solve the system. The

separation of these calculations was used to overcome the limitations of personal computers 

available at the time the original version of the RADTRAD-AC was developed and has been 

retained to the present time.

Radioactive decay and daughter production occur within a compartment, so no 

intercompartmental transfer needs to be considered. The equations that are solved for these 

processes at each time step are shown in Equation (4-10).
4-6

ddNNjj

ii

dddd = � λλννββνν

ii nn−1

νν=1

NNjj

νν + λλdddddd dd

ii NNjj

ii (4-10)

where:

ββνν

ii = the fraction of nuclide νν that decays to nuclide ii (dimensionless)

λλνν = the decay rate associated with ββνν

ii in 1/s

NNjj

νν = the quantity of nuclide νν in compartment jj

λλdddddd dd

ii = the rate of decay of nuclide ii in 1/s.

The decay and transport calculations are performed alternately. That is, the code begins its

integration over a time step by analyzing the effect of radioactive decay and daughter in-growth 

on the inventory of all compartments using Equation (4-10). After updating the inventory, the 

code calculates the effect of radionuclide transport between compartments during that same 

time step using Equation (4-6). This process of alternating between radioactive decay and 

daughter in-growth and radionuclide transport continues until the specified end time is reached. 

In calculations where radioactive decay is not modeled, the solution algorithm is simplified to the 

single step of calculating radionuclide transport.

During the course of its numerical integration, the code keeps track of the quantity of each 

nuclide at each location. Locations include not only compartment volumes, but surfaces and 

filters as well. By tracking the radionuclides in this manner, conservation of mass can be 

verified.

The analytical solution of a matrix equation in the form Ṅ = ΛN + R is N(t) = N(0)eAt - A-1(eAt -1)R 

from Equation 3.7 and 3.8 of reference [13], can be confirmed by substituting the solution into 

the matrix equation. Numerical solution of the transport equations is accomplished by 

constructing the solution as a Taylor series expansion of the analytical matric exponential 

solution in terms of t (specifically the eAt term which is the only time dependent term) and 

truncating the series when the estimated relative error is less than 1E-08. One advantage of 

this approach is its capacity to obtain good solutions over large time intervals. The key 

assumption is that there is no change in any phenomenon during a time step, i.e., that the 

coefficients in the ordinary differential equations (ODEs) are constant.

Without this assumption, the method would not apply. In order to accommodate this 

assumption, the code synchronizes time steps with the user-supplied phenomena in order to 

capture changes in the coefficients. Another advantage of this approach is that it is very fast 

and extremely robust. The algorithm is essentially identical to the one described in reference 

[13]. A useful discussion of matrix exponential methods and how they are solved is given in 

reference [14].

The assumption that all nuclides can be grouped according to their chemical and transport 

similarities is also applied in the solution. Thus, four transport groups were used: noble gases, 

elemental iodine, organic iodine, and aerosols. Note that the aerosol transport group includes 

all radionuclides assumed to be aerosol as listed in Section 4.3. These transport groups 

interact with their surroundings differently, but all components of any one group act the same. 

This implies that all xenon and krypton isotopes will transport identically and that cesium, 

barium, and all other aerosol isotopes will transport identically. The user specifies the fractions 

for the released iodine and thus partitions the iodine within the latter three groups.
4-7

4.2 Adaptive Time Step Algorithm

The RADTRAD-AC includes a default algorithm for selecting time step size that is fast and has 

proven to produce good results for typical models. However, the default time step algorithm 

does not perform error checking to verify that a solution has converged. The Adaptive Time 

Step option increases the computational cost significantly, but allows the RADTRAD-AC to 

estimate error and adjust the time step size keeping the error within a specified limit. For many 

models, the Adaptive Time Step option will not change results significantly because the default 

time step algorithm is adequate to achieve convergence.

As discussed above, a single system of coupled ODEs that simultaneously represents all of the 

phenomena considered by the RADTRAD-AC is defined. Computation time can be reduced by 

dividing the calculations into two parts: (1) transport and (2) radioactive decay. The 

fundamental premise behind this approach is that during a time step of small enough duration, 

ignoring the interdependence of the two components of the calculations results in negligible 

error. That is, numerically solving the transport equations defining transfer of material between 

compartments during a time step can be solved numerically, without taking account of the 

radioactive decay and in-growth occurring over that period, will have a negligible impact on the 

transport solution. Likewise, solving the radioactive decay and in-growth equations during a 

time step, without considering the simultaneous phenomenon of transport between 

compartments, will have a negligible impact on the decay and in- growth results. Reducing the 

time step size reduces the error that results from separately calculating transport and 

radioactive decay, and the RADTRAD-AC automatically reduces the default time step size when 

decay is active. If the user is concerned with this approach, adaptive time step control can be 

enabled to assure that the error introduced by this assumption is small.

The purpose of an adaptive time step algorithm is to actively choose the time step size in order 

to keep the solution error below a specified limit. The exact error is not known, so error must be 

estimated. The error estimate is then used to decide if the time step is too large (or too small) 

and adjust the time step size accordingly. The adaptive time step algorithm involves the 

following steps:

1. The error is estimated at each time step by calculating two solutions for the next time 

step, with one solution being more accurate. The magnitude of the difference between 

the solutions is used to estimate the error. The errors range from 0, if there is no error,

to a maximum error of 1. The error is scaled in order to reduce the number of time steps 

taken in regions where the solution is not changing significantly. The scaled error is also 

limited to the range 0 to 1.

2. The scaled error is compared to the user specified maximum error and the following 

steps are taken depending on the magnitude of the error:

a. If the error value is above the maximum error value (0.001 by default, but can be 

set by the user), then the time step size is cut in half and the calculation is 

repeated.

b. If the error value is between the maximum error and 1/10 the maximum error, the 

time step size is kept.

c. If the error is below 1/10 the maximum error the time step size is doubled starting 

with the next time step.
4-8

This algorithm works without modifications as long as error decreases as the time step size 

decreases and the time step size stay above the minimum time step size. Modifications to this 

logic to address special cases are discussed later in this section.

The governing equations for the RADTRAD-AC are defined and solved in terms of the 

radionuclide inventory (atoms) in each compartment. However, the key results are the dose to 

hypothetical individuals located at specified locations. The dose values were used in calculating 

an error estimate since they are the primary values of interest. Additionally, the dose values are 

included in the plot file which makes it easier to understand the adaptive time step controller 

behavior and diagnose problems.

The ODE solves for NNjj

ii

( mm), which is the number or atoms of nuclide i in compartment at time tm

(the time at time step m). Based on the nuclide quantities, dose values are calculated at each 

dose location specified in the model. Two different dose pathways are modeled, cloudshine and 

inhalation, to calculate dose to the skin, thyroid, and TEDE. These doses are referred to as 

‘dose categories’ for the remainder of this section. The dose that is calculated can be 

represented as a function of time by a vector DDkk( mm), where the kk index represents the different 

dose categories. A separate error is calculated for each category, and the largest of these is 

recorded as the error.

To estimate the error at each time step m, two solutions are calculated for time tm+1 = tm + Δt

starting from the base solution point NNjj

ii

( mm), with associated dose represented as Dk,B (dose for 

category kk at the base point):

1. The first solution at time tm+1 is calculated by advancing the ODE solver by a full time 

step of size Δt. The associated dose is represented as Dk,S1 (solution 1 dose for category 

kk).

2. The second solution for time tm+1 is calculated by advancing the ODE solver by two half 

time steps (i.e. time steps of size Δt/2). The associated dose is represented as Dk,S2

(solution 2 dose for category kk).

In order to estimate the error, it is useful to define a measure of magnitude for the dose vector. 

The most obvious choice is the Euclidean length, which gives an overall measure of the 

magnitude of the dose vector. The magnitude (or norm) of the dose vector will be represented 

as ‖D‖.

To estimate the local error for dose category kk, the magnitude of the difference between the two 

solutions ‖Dk,S2 ─ Dk,S1‖ is compared to the magnitude of the change in the solution over the time 

step. The magnitude of the change in the dose over the current time step for solution 1 and 2 is 

‖Dk,S1 ─ Dk,B‖ and ‖Dk,S2 ─ Dk,B‖ respectively. To characterize the change in the magnitude, the 

two values are averaged (‖Dk,S1 ─ Dk,B‖ + ‖Dk,S2 ─ Dk,B‖)/2. A slightly modified version of the 

following formula is used in Equation (4-11) to calculate a local error:

eeeeeeeeee = 2�DDkk,SS2 − DDkk,SS1�

�DDkk,SS1 − DDkk,BB� + �DDkk,SS2 − DDkk,BB� (4-11)

If we consider that the points Dk,B, Dk,S1, and Dk,S2 form a triangle, and that the error above is the 

magnitude (or length) of one side of the triangle compared to the average magnitude of the two 
4-9

remaining sides, it can be shown that the range of values for the error is 0 to 2. A value of 0 

occurs if the dose solutions Dk,S1 and Dk,S2 are identical, in which case the numerator is 0. The 

range 0 to 1 seems to be a more natural choice for specifying an allowable error fraction, so the 

error equation was modified slightly by dropping the factor of 2, resulting in Equation (4-12) for 

local error:

ll llllll eeeeeeeeee = �DDkk,SS2 − DDkk,SS1�

�DDkk,SS1 − DDkk,BB� + �DDkk,SS2 − DDkk,BB� (4-12)

To provide an example of how Equation (4-12) works, the error will be calculated for a set of two 

nuclides (I-131 and I-132). Table 4-1 represents the values for I-131 and I-132 at the base step 

and after solution 1 and solution 2 are calculated.

Table 4-1 Local error solutions for I-131 and I-132

Solution Step

I-131 Dose

(rem)

I-132 Dose

(rem)

Magnitude

(I-1312 + I-1322)0.5

(rem)

DB (20 h) 0.75 0.00130

DS1 (24 h) 0.92 0.00153

DS2 (24 h) 0.90 0.00150

DS1 – DB 0.17 0.00023 0.17000016

DS2 – DB 0.15 0.0002 0.15000013

DS1 – DS2 0.02 0.00003 0.020000002

Note that the change in the dose value (0.17) over a solution step for I-131 (Dk,S1 ─ Dk,B) is much 

larger than the change in the dose value of 0.00023 for I-132. This is reflected in the magnitude 

of the dose vector since the value is very close to the I-131 value of 0.17 rem. In the error 

calculation below the small tail value is dropped. In general, it is the dose channels with the 

largest change in dose over a time step that dominates the error calculation. Over this time 

step, the local error is calculated by Equation (4-13).

ll llllll eeeeeeeeee = 0.02

(0.17 + 0.15) = 0.0625 (4-13)

The default threshold for error is 0.001, so the local error exceeds the default threshold by an 

order of magnitude.

In test simulations it was found that the RADTRAD-AC required very small time steps to limit 

error despite the fact that the rate of dose increase was very small over the first few seconds in 

these cases. In order to avoid taking an excessive number of time steps over a time period 

when the changes in dose were small, the error is scaled in proportion to how quickly the dose 

is increasing compared to a more global measure of the rate of change in dose.

An error scaling factor is calculated using the following steps:
4-10

1. The local rate of change for the dose is characterized by taking the change in dose (rem) 

over the time step (i.e. ‖Dk,S2 ─ Dk,B‖) and dividing this by the time step size Δt. This 

gives a local rate of change d‖D‖/dt.

2. Two more global rate of change values are then calculated:

a. One global estimate of d‖D‖/dt is calculated by taking a time step of the default 

time step size. The error may be large for this time step, but the rate of change 

in dose provides a general estimate of how rapidly the dose is expected to 

increase over time steps of the default size. The calculation is only performed 

over the first 1/10 of the simulation because early on, this is the best estimate 

that can be obtained of the rate of change in dose. Later in the simulation, the 

calculated dose provides a reasonable estimate.

b. The value d‖D‖ = ‖Dk,S ─ Dk,B‖ is integrated (i.e. summed over the time steps) 

and divided by the total simulation time DT. This basically gives a rate at which 

dose would have to increase over the whole simulation to get the current dose 

magnitude.

3. The scaling factor is calculated by dividing the local rate of change by the maximum of 

the two global rate estimates from step 2. If the local dose is changing at a very slow 

rate compared to the global measure, then the error is of less concern since the error is 

small in comparison to time when dose is increasing rapidly. If the scaling factor 

exceeds 1, it is set to 1.

4. The scaled error is calculated by multiplying the error by the scaling factor. The scaled 

error can then be used to decide if the time step size needs to be cut, held constant, or 

increased.

In some cases, it may be desirable to directly control the time step size even if the adaptive time 

step algorithm is used. This can be done by opening the Property window for the Model 

Options node and then left-clicking on the Custom Editors ( ) icon for the Time Step Table text 

box to open the Editing Time Step Table window as shown in Figure 4-2. The user can then 

use the Add button to add rows to the table and specify a time step table with the minimum and 

maximum time step size set to the same value as shown in Figure 4-3. This will override the 

adaptive time step algorithm.
4-11

Figure 4-2 Property widow for the Model Option node

Figure 4-3 Editing Time Step Table window

In test cases, it was found that the reported error was always large over the first few time steps. 

To stabilize the simulation, a few time steps are taken at the minimum time step size. The 

adaptive time step logic is interrupted occasionally over the first 1/10 of the simulation to take a 

step of the default size in order to calculate a scaling factor. In some cases the error may 

increase as the time step size is decreased due to round off error or due to instability of the 
4-12

numerical algorithm (which can happen if the time step size is too large). The adaptive time 

step algorithm tracks the error vs. time step size. If it detects a region where the error increases 

as the time step size decreases, the algorithm just uses a default time step for a few steps and 

returns control to the adaptive time step logic. In some cases the adaptive time step algorithm 

cuts the time step until the minimum time step size is reached. The adaptive time stepper will 

count how many steps it remains at the minimum time step size. If more than a few time steps 

are taken at the minimum time step, a time step of the default size is requested. This approach 

is used to keep the adaptive time algorithm from performing calculations for long periods at the 

minimum time step size.

4.3 Radionuclide Release Mechanisms

A large number of radionuclides in various chemical forms are generated in the fuel as the 

reactor operates. The nuclides which are generated are categorized into chemical groups in 

order to make the problem more tractable. Table 4-2 lists the chemical grouping used in 

SNAP/RADTRAD. Note that the chemical grouping was revised from RADTRAD version 3.03 

because of the addition of the ICRP-38 nuclide set by combining strontium and barium into a 

single group and adding the other chemical elements as Group 9. Since SNAP/RADTRAD 

treats all nuclides that are in Groups 3 and above as aerosols, there was no internal coding 

changes needed. A representative nuclide is used to identify each chemical group. The tenth 

group for non-radioactive aerosols is retained in SNAP/RADTRAD.

Table 4-2 Chemical element grouping for SNAP/RADTRAD

Group 

Number Group Name

RG 1.183 

Chemical 

Grouping

Additional Nuclides

1 Noble Gases Kr, Xe H (H-3), Ne, Ar, Rn, N, O

2 Halogens I Br

3 Alkali Metals Cs, Rb

4 Tellurium Group Te, Sb Se

5

Barium, Strontium 

(Alkaline Earth 

Metals)

Sr, Ba Sr, Ba

6 Noble Metals Ru, Rh, Mo, 

Tc, Co Pd

7 Cerium Group Ce, Pu, Np

8 Lanthanides

La, Zr, Nd, 

Nb, Pr, Y, Cm, 

Am

Eu, Pm, Sm

9 Others

Ac, Ag, Al, As, At, Au, Be, Bi, Bk, C, Ca, Cd,

Cf, Cl, Cr, Cu, Dy, Er, Es, F, Fe, Fm, Fr, Ga, 

Gd, Ge, Hf, Hg, Ho, In, Ir, K, Lu, Md, Mg, Mn,

Na, Ni, Os, P, Pa, Pb, Po, Pt, Ra, Re, S, Sc, 

Si, Sn, Ta, Tb, Th, Ti, Tl, Tm, U, V, W, Yb, Zn

10 Non-Radioactive 

Aerosols No change F, Cl a

a. F and Cl (halogens) are included in Group 10 since they likely do not behave like iodine.
4-13

The iodine group is further subdivided into three physical forms, which are elemental, organic 

and aerosols. The fraction of each form depends on the source term model used. The 

radionuclide inventory for the fuel for all radionuclides of interest in dose analysis on a per Mwt 

basis for PWR and BWR plants is included in SNAP/RADTRAD.

Two models available in SNAP/RADTRAD in which to model the release from the fuel are the 

TID-14844 model and the NUREG-1465 model. The TID-14844 model, which is generally 

applied to LOCA analysis, is based on the assumption that 100 percent of the noble gas 

radionuclides and 50 percent of the iodine radionuclides are available for release to the 

containment. The iodine release is reduced by a factor of 2 to account for deposition within the 

containment so that 25 percent of the iodine remains airborne in the containment based on the 

assumptions in Regulatory Guide 1.3 (RG 1.3), Revision 2, “Assumptions used for Evaluating

the Potential Radiological Consequences of a Loss of Coolant Accidents for Boiling Water

Reactors,” [15] and Regulatory Guide 1.4 (RG 1.4), Revision 2, “Assumptions used for 

evaluating the Potential Radiological Consequences of a Loss of Coolant Accidents for 

Pressurized Water Reactors” [16]. No adjustment is made for the noble gases since 

radionuclides in this group are inert. The release is assumed to be instantaneous (a puff 

release) and is assumed to occur at the beginning of the accident (t=0). The fractions for the 

physical form of iodine used in the TID-14844 model are: elemental – 0.91, organic – 0.04, and 

aerosol – 0.05.

An alternative release model was developed in NUREG-1465 for LOCA analysis that 

considered the results of severe accident research conducted by the NRC. In this model, the 

release from the fuel is subdivided into the Gap release and the Early In-vessel release. 

Radionuclides that have accumulated in the gap between the fuel pellet and the cladding that is 

released when cladding failure commences is the Gap release. The Early In-vessel release 

occurs as fuel rod temperatures increase driving the volatile nuclides, such as iodine from the 

fuel pellet into the vessel through the failed cladding. The release fractions for the Gap and 

Early In-vessel releases are summarized below:

• Noble gases – 0.05 for the Gap release and 0.95 for the Early In-vessel releases.

• Iodine – 0.05 for the Gap release for both PWR and BWR. For Early In-vessel, the 

iodine release fraction is 0.35 for PWR and 0.25 for BWR.

• Cesium – 0.05 for the Gap release for both PWR and BWR. For Early In-vessel, the 

cesium release fraction is 0.25 for PWR and 0.2 for BWR.

• Remaining groups – 0.05 and less.

The fractions for the physical form of iodine used in the NUREG-1465 model are: elemental –

0.0485, organic – 0.0015, and aerosol – 0.95.

Release phase duration is considered in NUREG-1465 in contrast to the instantaneous release 

model used in TID-14844. The release phase durations from Table 3-6 of NUREG-1465 are 

listed in Table 4-3. Additionally, the radionuclides for each phase are assumed to be uniformly 

released over the time period corresponding to that phase.
4-14

Table 4-3 Release phase durations for PWRs and BWRs

Release Phase

Duration (h)

PWR BWR

Gap 0.5 0.5

Early In-Vessel 1.3 1.5

Note that Gap release fraction models are available in SNAP/RADTRAD. The two models 

which are available are based on Table 3 of RG 1.183 and Regulatory Guide 1.25 (RG 1.25), 

“Assumptions Used for Evaluating the Potential Radiological Consequences of a Fuel Handling 

Accident in the Fuel Handling and Storage Facility for Boiling and Pressurized Water Reactors,”

[17]. The Gap release fractions used are listed in Table 4-4.

Table 4-4 Gap release fractions used in SNAP/RADTRAD

Radionuclide RG 1.25 RG 1.183

I-131 0.12 a 0.08

Kr-85 0.3 0.1

Other Noble Gases 0.1 0.05

Other Iodines 0.1 0.05

Alkali Metals 0.0 0.12

a. The value in RG 1.25 is 0.1 and this value was increased by 20 percent to account for 

the use of extended burnup fuel, per NUREG/CR-5009, “Assessment of the Use of 

Extended Burnup Fuel in Light Water Power Reactors,” [18].

The FHA also requires several other input parameters including the number of fuel rods or 

assemblies in the core, the number of fuel rods or assemblies damaged, the fraction of fuel rods 

or assemblies damaged, the radial peaking factor for the damaged assemblies, the pool iodine

DF and the decay period. The pool iodine DF is set to a default value of 200 which is from 

Appendix B of RG 1.183 for water pool depths of 23 feet or greater and the decay time, 

essentially the time since plant shutdown. Note that the decay calculation carried out by the 

SNAP/RADTRAD Model Editor input for the fuel handling accident does not include 

contributions from daughter products.

4.4 Reactor Coolant System Activity Calculations

Models for specifying the release during a FHA, a REA, and CRDA have also been incorporated 

into SNAP/RADTRAD. The models generally follow those specified in RG 1.183. For the FHA, 

the user-selectable Gap release fractions are based on either RG 1.25 or RG 1.183 as listed in 

Table 4-4. In addition, relevant plant parameters (number of rods or assemblies in the core, 

number of rods or assemblies damaged, fraction of fuel rods or assemblies damaged, radial 

peaking factor, pool iodine DF, and decay period) for modeling a FHA can be specified by the 

user. Similarly, for the REA-CRDA, a release model based on RG 1.183 is available in 
4-15

SNAP/RADTRAD. The release fractions used are listed in Table 4-5. Also, the relevant plant 

parameters for cladding breach, fuel melt fraction and radial peaking factor can be set by the 

user in SNAP/RADTRAD.

Table 4-5 SNAP/RADTRAD release fractions to RCS for an REA-CRDA accident

Radionuclide Gap Release Melt Release

Noble Gas 0.1 1.0

Iodine 0.1 0.5

Alkali Metals 0.0 0.0

It should be noted that the release assumptions used in SNAP/RADTRAD can be confirmed 

through the SNAP Model Editor by defining a source, then reviewing the nuclide definitions for 

that source. This approach is better because the user can confirm the values actually used in 

the SNAP/RADTRAD calculations. The ability to calculate the RCS activity, consider 

equilibrium activities based on DE I-131 and DE Xe-133 and iodine spiking has been 

incorporated into SNAP/RADTRAD.

The RCS activity calculator, described in Section 3.4.2, determines the RCS concentrations 

using formulations based on the NUREG-0017, Revision 1, “Calculation of Releases of 

Radioactive Materials in Gaseous and Liquid Effluents from Pressurized Water Reactors (PWRGALE Code),” [19], NUREG-0016, Revision 1, “Calculation of Releases of Radioactive Materials 

in Gaseous and Liquid Effluents from Boiling Water Reactors (BWR-GALE Code),” [20], and the 

ANSI/ANS-18.1-1999, “Radioactive Source Term for Normal Operation of Light Water 

Reactors,” [21]. The formulations used are basically correlations correcting for plant-to-plant 

variations in power, system fluid and steam mass and flow rates and other plant-specific 

parameters applied to a reference PWR or BWR plant. The RCS activity calculations performed 

in SNAP/RADTRAD are similar to, but basically a subset of those performed by the PWR and 

BWR Gale codes.

Table 4-6 presents the formulae used by the SNAP/RADTRAD RCS activity calculator for the 

reference PWR plant to calculate coolant concentration adjustment factors for the radionuclide 

concentration in the RCS. Note that these formulations are applicable to plants with U-tube 

steam generators. The adjustment factors presented in Table 4-6 are multiplied by the 

reference PWR radionuclide concentrations given in Table 4-7 to obtain the RCS concentration 

(μCi/g).
4-16

Table 4-6 Formulations used to determine RCS water radionuclide concentrations in 

PWRs with U-tube steam generators

Element Class Adjustment Factor Formula a

Noble Gases = �

162 ∙ PP

WW � ∙ �

0.0009 + λλ

RR + λλ �

Halogens = �

162 ∙ PP

WW � ∙ �

0.067 + λλ

RR + λλ �

Cs, Rb = �

162 ∙ PP

WW � ∙ �

0.037 + λλ

RR + λλ �

where:

R = the removal rate - reactor coolant 1/h

λ = the radionuclide decay constant in 1/h

P = the core power in Mwt

WP = the mass of reactor coolant system water lbm

Formulas for the removal rate (R) are presented below b

Noble Gases RR = FF + ( − FF) ∙ YY

WW

Halogens & Cs, Rb RR = ∙ NN + (1 − NN ) ∙ ( FF + FF ∙ NN )

WW

where:

FD = the removal rate in the reactor coolant in 1/h

NB = the fraction of material removed in passing through the purification

demineralizer

FB = the reactor coolant letdown flow in 1/h

FA = the flow through the purification system cation demineralizer

NA = the fraction of material removed in passing through the cation 

demineralizer

Y = the ratio of the total amount of noble gases routed to gaseous 

radwaste from the purification system to the total amount routed 

from the primary coolant system (not including the boron recovery 

system)

a. The adjustment factor formula is from Table 2-7 of reference [19].

b. The formulas for the removal rates (R) are from Table 2-6 of reference [19] and Table 9 of 

reference [21]. The values for the constants are from a reference PWR described in Table 2-4 of 

reference [19] and Table 2 of reference [21]. The PWR-GALE code calculates the removal rates 

(R) for these nuclides for PWRs other than the reference PWR plant described in Table 2-4 of 

reference [19] and Table 2 of reference [21].
4-17

Table 4-7 RCS radionuclide concentrations for a reference PWR plant

Radionuclide Concentration

(μCi/g) a Radionuclide Concentration(μCi/g) a

Kr-83m b 0.0E+00 I-131 2.0E-03

Kr-85 4.3E-01 I-132 6.0E-02

Kr-85m 1.6E-02 I-133 2.6E-02

Kr-87 1.7E-02 I-134 1.0E-01

Kr-88 1.8E-02 I-135 5.5E-02

Xe-131m 7.3E-01 Cs-134 3.7E-05

Xe-133 2.9E-02 Cs-136 8.7E-04

Xe-133m 7.0E-02 Cs-137 5.3E-05

Xe-135 6.7E-02 Rb-86 b 0.0E+00

Xe-135m 1.3E-01

Xe-138 6.1E-02

a. The radionuclide concentrations are from Table 6 of reference [21].

b. The radionuclide concentration is not from Table 6 of reference [21].

Table 4-8 presents the formulae used by the SNAP/RADTRAD RCS activity calculator for the 

reference BWR plant to calculate coolant concentration adjustment factors for the radionuclide 

concentration in the RCS water and steam. The adjustment factors presented in Table 4-8 are 

multiplied by the reference BWR radionuclide concentrations given in Table 4-9 to obtain the 

RCS concentration (μCi/g) for either the RCS water or steam.
4-18

Table 4-8 Formulations used to determine RCS water radionuclide concentrations in 

BWRs

Element Class Adjustment Factor Formula

Noble Gases a 1.0

Halogens = �

112 ∙ PP

WW � ∙ �

1.01 + λλ

RR + λλ �

Cs, Rb = �

112 ∙ PP

WW � ∙ �

0.19 + λλ

RR + λλ �

where:

R = the removal rate - reactor coolant 1/h

λ = the radionuclide decay constant in 1/h

P = the core power in Mwt

WP = the mass of RCS water lbm

Formulas for the removal rate (R) are presented below b

Noble Gases 1.0

Halogens & Cs, Rb RR = FF ∙ NN + NNNN ∙ FF ∙ NN ∙ NN

WW

where:

FA = the water cleanup demineralizer flow rate in lb/h

NA = the reactor water cleanup demineralizer DFs

NC = the ratio of condensate demineralizer flow rate to steam flow rate

FS = the steam flow rate in lb/h

NS = the ratio of radionuclide concentration in reactor steam to the 

concentration in reactor water

NB = the condensate demineralizer DF

a. The adjustment factor formulas are from Table 2-5 of reference [20] and Table 10 of reference 

[21].

b. The formulas for the removal rates (R) are from Table 2-4 of reference [20] and Table 8 of 

reference [21]. The values for the constants are from a reference BWR described in Table 2-3 of 

reference [20] and Table 1 of reference [21]. The BWR-GALE code calculates the removal rates 

(R) for these nuclides for BWRs other than the reference BWR plant described in Table 2-3 of 

reference [20] and Table 1 of reference [21].
4-19

Table 4-9 RCS radionuclide concentrations for a reference BWR plant

Radionuclide

Liquid

Concentration

(μCi/g) a

Steam

Concentration

(μCi/g) a

Radionuclide

Liquid

Concentration

(μCi/g) a

Steam

Concentration

(μCi/g) a

Kr-83m 0.0E+00 5.9E-04 I-131 2.2E-03 4.4E-05

Kr-85 0.0E+00 4.0E-06 I-132 2.2E-02 4.4E-04

Kr-85m 0.0E+00 1.0E-03 I-133 1.5E-02 3.0E-04

Kr-87 0.0E+00 3.3E-03 I-134 4.3E-02 8.6E-04

Kr-88 0.0E+00 3.3E-03 I-135 2.2E-02 4.4E-04

Xe-131m 0.0E+00 3.3E-06 Cs-134 3.0E-05 3.0E-08

Xe-133 0.0E+00 1.4E-03 Cs-136 2.0E-05 2.0E-08

Xe-133m 0.0E+00 4.9E-05 Cs-137 8.0E-05 8.0E-08

Xe-135 0.0E+00 3.8E-03 Rb-86 b 0.0E+00 0.0E+00

Xe-135m 0.0E+00 4.4E-03

Xe-138 0.0E+00 1.5E-02

a. The radionuclide concentrations are from Table 5 of reference [21].

b. The radionuclide concentration is not from Table 5 of reference [21].

T/S equilibrium activity based on DE I-131 and DE Xe-133 are determined from the DCFs and 

the RCS concentration. Equations (4-14) and (4-15) show the formulation used

DDDD II 131 = ∑ii ii ∙ DD DDii

DD DDII 131 (4-14)

DDDD XX 133 = ∑ii ii ∙ DD DDii

DD DDXX 133

(4-15)

where:

DCFi = the DCF for each iodine or xenon nuclide. [The thyroid DCF (Sieverts 

(Sv)/Bq) is used for iodine nuclides and the whole body DCF (Sv-m3

/Bq-s) 

is used for xenon nuclides.]

DCFI 131 = the I-131 thyroid DCF (Sv/Bq)

DCFXe 133 = the Xe-133 whole body DCF (Sv-m3/Bq-s)

Ci = the i-th radionuclide concentration in μCi/g.

The actual equilibrium factor is calculated from the user-specified value of DE I-131 (typically 1 

μCi/g) divided by DE I-131. This factor is multiplied by the RCS activity to obtain the equilibrium 

activity based on DE I-131. The approach is the same for Xe-133 except that Xe-133 factors 

are applied. The calculation is performed separately for liquid and steam in BWRs.
4-20

The pre-incident spike activity is computed from the user-specified spike activity (typically 60 

μCi/g) divided by DE I-131 and then multiplied by the RCS activity. The calculation is performed 

separately for liquid and steam in BWRs.

Co-incident spiking is somewhat more complicated as the iodine appearance rate must be 

determined. The appearance factor in units of Ci/h is computed as shown in Equation (4-16)

= �MMMM ∙

1 − 1⁄DDDD

WW + WW � ∙ SS ∙ �

3600

1 6 � ∙ WW ∙ (4-16)

where:

MLD = the normal letdown flow rate in gpm (converted to g/s in above equation)

DF = the mixed bed demineralizer DF

WP = the mass of RCS T/S leakage rate in gpm (converted to g/s in above 

equation)

λ = the decay constant in 1/s

SpM = the iodine spike multiplier

EFI = the equilibrium factor for iodine in μCi/g.

The total iodine appearance for co-incident spiking is computed by multiplying the appearance 

rate by the spike duration in hours to obtain the total iodine appearance. The iodine 

appearance is added to the equilibrium activity to obtain the total RCS activity for iodine. Note 

that co-incident spiking only applies to PWRs.

One item that should be noted is that there are several formulations for the calculation of the 

RCS inventory, including ANSI/ANS-18.1-1999, the PWR-GALE Code and the BWR-GALE 

Code. The current status of ANSI/ANS-18.1-1999 is that it has been administratively withdrawn 

because it was neither reaffirmed nor updated during a 10 year period. The American Nuclear 

Society has formed a Working Group in calendar year 2014 and are now updating ANSI/ANS18.1-1999.

4.5 Removal Models

Models for radionuclide removal from the compartment atmosphere including sprays, natural 

deposition, leakage, and filters are included in SNAP/RADTRAD. The removal coefficients for 

the various removal mechanisms are equivalent. For example, filtration is expressed in terms of 

efficiencies, and natural deposition in terms of removal coefficients. These are related to each 

other as well as to DFs. The DF is defined as the ratio of the total material (aerosol or 

elemental iodine) subjected to a removal process to the total aerosol material that remains 

airborne. Equation (4-17) shows the relationship between the DF and the removal coefficient, λ.

dd

dddd = λλ (4-17)

The average DF is related to the mass fraction, mf, remaining in the volume as shown in 

Equation (4-18).

mmff = MM( )

MM(0) = 1DDDD = ee−(λλ ) (4-18)

where:
4-21

MM( ) = the mass of aerosol as a function of time (t) in a compartment

MM(0) = the total mass subjected to removal in a compartment.

The DF is also related to the removal efficiency, η, as shown in Equation (4-19).

DDDD = 1

1 − ηη (4-19)

4.5.1 Spray Removal Model

The spray removal mechanism in SNAP/RADTRAD can be modeled using either the Powers’

model, as described in NUREG/CR-5966, for aerosol removal or through the specification of 

user-defined removal coefficients. As the Powers’ model is only applicable to aerosols, the 

SNAP/RADTRAD user will still need to specify removal coefficients for elemental and organic 

iodine.

The extent to which sprays will decontaminate an aerosol-laden atmosphere depends on the 

number of spray droplets falling through the atmosphere and the distance they fall. The water 

flux into the containment atmosphere is time dependent and the fall distance is dependent upon 

the containment design. The Powers’ model is based on a correlation that determines the 

removal coefficient for an aerosol considering the spray water flux, Q (m3

∙H2O/m2∙s) and the fall 

height of the spray droplets H (m) and considers uncertainty in the various parameters affecting 

spray removal. Since the model was developed from an uncertainty study, the user specifies a 

percentile. The “best estimate” value is associated with the 50th percentile, or median values; 

the lower bound is associated with the 10th percentile; and the reasonable upper bound, or 

largest DF, with the 90th percentile. The model was developed using values of 0.001, 0.1 and

0.25 cm3 H2O/cm2 s for the spray water flux, Q, and fall heights of 500, 853, 1000, 1584, 2000, 

3000, 4000, and 5000 cm. The aerosol removal coefficient is dependent on the fraction of the 

aerosol suspended in the atmosphere, mf, which is defined as the aerosol mass in the 

atmosphere of a compartment at a given time, t, divided by the total aerosol mass released into 

the compartment atmosphere until this time. The model includes the effect of the unsprayed 

portions of the containment by incorporating the assumption that the circulation in the 

compartment is rapid compared with the removal rate. Equation (4-20) specifies the aerosol 

removal coefficient (λλjj,ssssss

ii ) at any time in units of 1/s.

λλjj,ssssss

ii = 1

3600 (1 − αα)

( − bb ll gg10 QQ) ��1 − mmff

0.9

� + �

mmff

0.9

� �

(4-20)

× [exp ( + lnQQ + HH + DD QQ2HH + QQ HH2 + QQ + GG QQ2HH2)]

The values for the constants A, B, C, D, E, F, G, a, b, and c in Table 4-10 are from Section 7 of 

NUREG/CR-5966. The parameter α is the ratio of the compartment volume not exposed to 

sprays to the compartment volume exposed to sprays (unsprayed volume/sprayed volume). If 

the assumption that the circulation is rapid compared with the removal rate is not valid, then the 

user can split the compartment into two separate compartments and model the flow from the 

unsprayed portions to the sprayed portions as a convective flow. In this case α would be zero 

for the compartment containing the sprays.
4-22

Table 4-10 Values for coefficients used in the Powers’ spray removal model

Constant

Value

10th Percentile 50th Percentile 90th Percentile

A 5.5750 6.83707 7.10927

B 0.94362 1.0074 0.92549

C 0.0 -2.4045E-05 0.0

D -6.9821E-03 -4.1731E-03 -8.0868E-04

E -7.327E-07 9.006E-08 0.0

F 0.0 -1.2478 0.0

G 3.555E-06 0.0 0.0

a 0.1108 0.1815 0.3751

b -0.00201 -0.01153 0.00648

c 0.8945 0.5843 0.2786

This expression was originally developed for a puff release of aerosols into a system. In those 

cases where there is a continuing release, the size distribution will continually be renewed by 

the injected particulate. The model has been extended for this case by setting coefficients A

through G to zero. This makes the model assume that the size distribution has not changed in 

time and that most of the material suspended is fresh material provided by the source. The 

aerosols removed by the sprays are collected in the sump.

4.5.2 Natural Deposition Model

Natural deposition in SNAP/RADTRAD can be modeled using either Henry’s correlation or 

Powers’ model for aerosol removal due to natural deposition or through the specification of 

user-defined removal coefficients. As Henry’s correlation and Powers’ model are only 

applicable to aerosols, the SNAP/RADTRAD user will still need to specify removal coefficients 

for elemental iodine.

4.5.2.1 Henry’s Correlation

The correlation developed by Henry, described in reference [22], is based upon observation of 

experiments concerned with aerosol decontamination. The form of Equation (4-21) is based 

upon the consideration that sedimentation was the dominant phenomenon observed, and the 

coefficients were determined from experimental data from liquid metal reactor tests.

λλ = 1 �

h

h � � ρρPPρρPP

� (ρρAA)KK (4-21)

where:

h = 5.0 m, as determined from the ABCOVE test AB5

h = the user-provided fall height in m

ρρPP = the user-provided particle density in kg/m3
4-23

ρρPP = the theoretical sodium oxide particle density of 2270 kg/m, as determined 

from the ABCOVE test AB5

ρρAA = the aerosol mass in the volume.

The coefficients that best fit the data are:

where:

ρρAA ≥ 6.0E − 05 kk �

mm3 then 1 = 0.0220 and kk = 0.60

ρρAA < 6.0E − 05 kk �

mm3 then 1 = 0.0016 and kk = 0.33.

Henry’s correlation input can be modified to account for the influence of aerosol shape and 

moisture on the particle density by using Equation (4-22)

ρρPP = ααρρTT + (1 − αα)ρρww (4-22)

where:

αα = the ratio of the effective aerosol particle density to theoretical density

ρρTT = the theoretical density in kg/m3

ρρww = the density of water in kg/m3

.

In many cases the aerosol has only 20 percent of its theoretical density, so that in a high steam 

environment its effective density would be closer to that of water. This correlation is 

implemented in SNAP/RADTRAD.

4.5.2.2 Powers’ Model

The Powers’ model for aerosol removal due to natural deposition, in NUREG/CR-6604, is based 

on the observation of a self-preserving aerosol size distribution as a key component in 

predicting aerosol behavior. Powers included the effects due to turbulence and to the multiple 

aerosol releases specified in NUREG-1465. The modified model was then compared with a 

series of CONTAIN computer code cases to verify the aging and aerosol size distributions due 

to the multiple sources. To account for the uncertainties, a large number of calculations were 

performed with the modified mechanistic model, with specific values for the type of reactor 

containment, reactor power, and the source term release phase, while varying the values of the 

uncertainty parameters. Typical uncertainty parameters were the containment pressure during 

the various release phases, the floor and wall surface areas, the zirconium inventory, the ratio of 

containment volume to thermal power, and the properties of the concrete. In all, over 20 

parameters that were related to the phenomena were varied. Equation (4-23) shows the 

governing equation used in Powers’ model

ddDDDDii( )

dddd = λλdddd ,II(PP h, )DDDDii( ) (4-23)

where:

DDDDii( ) = the DF for the i

th class of radioactive aerosol at time t where i indicates 

the phase at which the material was released into the containment:

during the Gap or Early In-vessel phases
4-24

λλdddd ,II(PP h, ) = the decontamination coefficient at time t and power Pth for phase I

PP h = the thermal power of the reactor.

The decontamination coefficient should be weighted by each chemical group release rate as 

was done by Powers. However, SNAP/RADTRAD does not maintain the necessary weighting 

factors; hence a single chemical release rate based on iodine was used for the weighting 

coefficients.

The decontamination coefficient, λ, was solved over the various release time intervals and for 

the different types of reactors and various operating power levels using a Monte-Carlo 

uncertainty analysis. The results of these analyses are tabulated in Tables 4-11 and 4-12, for 

PWRs and BWRs, and are presented in terms of percentile DFs, λdep(N%,Pth). Since the model 

was developed from an uncertainty study, the user specifies a percentile, N%. The best 

estimate value is associated with the 50th percentile, or median values; the lower bound is 

associated with the 10th percentile; and the reasonable upper bound, or largest DF, with the 90th

percentile.

Table 4-11 Correlations of natural deposition decontamination coefficients for PWRs

DBAs

Release Phase Time Interval (s) Correlations (h-1)

Gap 0 – 1800

(0 – 0.5 h)

λdep (90) = 0.0365 + 3.580E-06 P(Mwt)

λdep (50) = 0.0268 + 3.475E-06 P(Mwt)

λdep (10) = 0.0182 + 3.260E-06 P(Mwt)

Gap 1800 – 6480

(0.5 – 2.0 h)

λdep (90) = 0.1036 [1 - exp (-2.239 P(Mwt)/1000)]

λdep (50) = 0.0820 [1 - exp (-1.159 P(Mwt)/1000)]

λdep (10) = 0.0645 [1 - exp (-0.938 P(Mwt)/1000)]

Early

In-Vessel

1800 – 6480

(0.5 – 1.8 h)

λdep (90) = 0.0522 [1 - exp (-2.458 P(Mwt)/1000)]

λdep (50) = 0.0417 [1 - exp (-1.258 P(Mwt)/1000)]

λdep (10) = 0.0326 [1 - exp (-0.910 P(Mwt)/1000)]

Gap + Early

In-Vessel

6480 – 13,680

(1.8 – 3.8 h)

λdep (90) = 0.421 [1 - exp (-2.530 P(Mwt)/1000)]

λdep (50) = 0.196 [1 - exp (-1.040 P(Mwt)/1000)]

λdep (10) = 0.094 [I - exp (-0.869 P(Mwt)/1000)]

Gap + Early

In-Vessel

13,680 – 49,680

(3.8 – 13.8 h)

λdep (90) = 0.1920 - 1.35E-06 P(Mwt)

λdep (50) = 0.1382 + 6.85E-06 P(Mwt)

λdep (10) = 0.0811 + 10.15E-06 P(Mwt)

Gap + Early

In-Vessel

49,680 – 80,000

(13.8 – 22.22 h)

λdep (90) = 0.1010

λdep (50) = 0.0912

λdep (10) = 0.0860 [1 - exp (-2.384 P(Mwt)/1000)]
4-25

Table 4-12 Correlations of natural deposition decontamination coefficients for BWRs

DBAs

Release Phase Time Interval (s) Correlations (h-1)

Gap 0 – 1800

(0 – 0.5 h)

λdep (90) = 2.903 [exp(-1060/P(Mwt)]

λdep (50) = 2.252 [exp(-1977/P(Mwt)]

λdep (10) = 1.285 [exp(-2199/P(Mwt)]

Gap 1800 – 7200

(0.5 – 2.0 h)

λdep (90) = 1.809 [exp(-777/P(Mwt)]

λdep (50) = 1.722 [exp(-1777/P(Mwt)]

λdep (10) = 1.161 [exp(-2274/P(Mwt)]

Early

In-Vessel

1800 – 7200

(0.5 – 2.0 h)

λdep (90) = 0.746 [exp(-626/P(Mwt)]

λdep (50) = 0.752 [exp(-1565/P(Mwt)]

λdep (10) = 0.520 [exp(-2173/P(Mwt)]

Gap + Early

In-Vessel

7200 – 18,000

(2.0 – 5.0 h)

λdep (90) = 1.959 [exp(-548/P(Mwt)]

λdep (50) = 1.811 [exp(-1107/P(Mwt)]

λdep (10) = 1.551 [exp(-1507/P(Mwt)]

Gap + Early

In-Vessel

18,000 – 30,000

(5.0 – 8.33 h)

λdep (90) = 1.533 [exp(-573/P(Mwt)]

λdep (50) = 1.317 [exp(-1225/P(Mwt)]

λdep (10) = 0.836 [exp(-1051/P(Mwt)]

Gap + Early

In-Vessel

30,000 – 43,200

(8.33 – 12.0 h)

λdep (90) = 1.524 [exp(-647/P(Mwt)]

λdep (50) = 1.339 [exp(-1474/P(Mwt)]

λdep (10) = 0.780 [exp(-1316/P(Mwt)]

Gap + Early

In-Vessel

43,200 – 70,000

(12.0 – 19.4 h)

λdep (90) = 1.564 [exp(-717/P(Mwt)]

λdep (50) = 1.373 [exp(-1634/P(Mwt)]

λdep (10) = 0.778 [exp(-1548/P(Mwt)]

Gap + Early

In-Vessel

70,000 – 86,400

(19.4 – 24.0 h)

λdep (90) = 1.562 [exp(-719/P(Mwt)]

λdep (50) = 1.441 [exp(-1785/P(Mwt)]

λdep (10) = 0.780 [exp(-1686/P(Mwt)]

Equations (4-24), (4-25) and (4-26) determine the current decontamination coefficient, λnet, from 

the sum of the coefficients for each phase weighted by the iodine release rate, SI2,I, for phase I.

λλnn = ln{[DDDD( + ∆ )⁄DDDD( )]}

∆ (4-24)

where:

(4-25)
4-26

DDDDII = �exp�λλdddd ,II(NN%, PP h) �

4

II=1

(4-26)

Table 4-13 also provides the decontamination coefficients for a DBA in an advanced 

pressurized-water reactor (APWR) design. These values are based upon work by Powers, 

which found that the CONTAIN-related calculation results were correlated with values in the 

table. These correlations do not vary with reactor thermal power; hence an approximation is 

used when the user selects a PWR design with a different power level.

Table 4-13 Correlations of natural deposition decontamination coefficients for APWR 

DBAs

Release Phase Time Interval (s) Correlations (h-1)

Gap 0 – 1800

(0 – 0.5 h)

λdep (90) = 0.466

λdep (50) = 0.233

λdep (10) = 0.029

Gap 1800 – 6480

(0.5 – 1.8 h)

λdep (90) = 0.872

λdep (50) = 0.487

λdep (10) = 0.160

Early

In-Vessel

1800 – 6480

(0.5 – 1.8 h)

λdep (90) = 0.393

λdep (50) = 0.240

λdep (10) = 0.100

Gap + Early

In-Vessel

6480 – 13,680

(1.8 – 3.8 h)

λdep (90) = 1.210

λdep (50) = 0.980

λdep (10) = 0.731

Gap + Early

In-Vessel

13,680 – 49,680

(3.8 – 13.8 h)

λdep (90) = 0.594

λdep (50) = 0.397

λdep (10) = 0.245

Gap + Early

In-Vessel

49,680 – 86,400

(13.8 – 24.0 h)

λdep (90) = 0.598

λdep (50) = 0.327

λdep (10) = 0.107

The approximation used assumes that the significant difference between the PWR and the 

APWR design, in terms of natural deposition, is that the wall cooling enhances the phoretic 

deposition. Therefore, the difference in decontamination coefficient at 1800 Mwt represents this 

phoretic deposition and is then scaled by the power ratio. Equation (4-27) represents the final 

approximation used

λλdddd ( _PP h) = λλdddd (PP _PP h) + �λλdddd ( _1800) − λλdddd (PP _1800)� PP h

1800 (4-27)
4-27

where:

λλdddd ( _PP h) = the decontamination coefficient from the APWR at the power level 

indicated (Pth =1800 or design power)

λλdddd (PP _PP h) = the decontamination coefficient from the PWR DBA calculation for the 

power level indicated (Pth =1800 or design power).

4.5.3 Deposition in Piping Models

At the discretion of the user, piping can be modeled as a transfer pathway where deposition can 

occur. A model is available for the removal of fission products during transport through pipes. 

Alternatively, the user may specify DFs and volumetric flow rates as a function of time. Noble 

gases are assumed not to interact with the piping and are transmitted without any depletion. 

The models chosen do not have documented limitations; however, the assumption is made that 

only primary deposition phenomena are being modeled. Scenarios in which supersaturated 

conditions occur, or in which very high or very low velocities are found, may give unrealistic 

results.

The models that are available in SNAP/RADTRAD for piping deposition include the Brockmann 

model for aerosol removal, the Bixler model for elemental iodine removal, and the Bixler model 

for organic iodine removal.

4.5.3.1 Brockmann Model for Aerosol Removal

The Brockmann model described in reference [23] is used to determine the amount of aerosol 

deposition that occurs in pipe bends and due to settling, turbulent inertia and diffusion. The 

mean particle diameter, dp, used in the Brockmann model is assumed to be 1 μ with an average 

particle density, ρp, of 1000 kg/m3

. The temperature, pressure, open volume, and other 

parameters are provided by the user. Particles will settle due to gravitational force and deposit 

on the horizontally projecting lower surface of the flow path during transport. This turbulent flow 

deposition efficiency, ηg, is modeled in Equation (4-28).

ηηgg = 1 − exp�−UUgg ss⁄ππ � (4-28)

UUgg = ττ

ττ = ss ∙ dd2ρρ ⁄18μμ

ss = 1.0 + 2.0

mm

dd �1.257 + 0.4ee−0.55dd ⁄mm � (dd dd dd )

where:

UUgg = the gravitational deposition velocity in m/s

τ = the particle relaxation time in s

Q = the user provided gas flow in m3/s

ss = the user provided total pipe surface area in m2

μ = the viscosity of air, 1.93E-05 Pa-s
4-28

mfp = the particle mean free path in cm

g = the gravitational acceleration in m/s2.

For instances of laminar flow, described in reference [24] the deposition efficiency is described 

by Equation (4-29).

ηηgg = 1 − 2

ππ �2εε�1 − εε2⁄3 − εε1⁄3�1 − εε2⁄3 + arcsin�εε1⁄3� (4-29)

where:

ε = 0.75ZZ − 0.75 UUgg

UU DD

and

L = the horizontal pipe length (As/π D) in m

As = the user provided total pipe surface area in m2

D = the pipe diameter (4 Vol/As) in m

Ug = the gravitational deposition velocity in m/s

U = the linear velocity (Q/As) in m/s

Q = the user provided gas flow in m3/s.

The laminar and turbulent settling efficiencies are equivalent for Reynolds Number between 500 

and 2300.

If the flow is turbulent, then turbulence in the central core can propel a particle into the laminar 

sublayer. If the particle inertia is high, then it will penetrate the sublayer and be collected on the 

wall. There have been experiments, reference [25], on inertial deposition velocity and 

Brockmann has modeled the turbulent deposition efficiency, ηturb, as shown in Equation (4-30).

ηη tt tt = 1 − exp(−UU ss⁄QQ) (4-30)

where:

UU = 0.01988UU RR 1⁄8 ⁄

Re = ρρ UU ddHH⁄μμ

and

UU = the turbulent inertial deposition velocity in m/s

UU = the air velocity in m/s

ddHH = the hydraulic diameter in m (4 Vol/As)

ρρ = the density of air in kg/m3

.

When the flow in the pipe is slower as described in Equation (4-31), then the turbulent velocity is 

calculated using Equation (4-32).
4-29

ττUU

ddHH

RR 3⁄4 < 326.3 (4-31)

UU = 1.861E − 07 �

ττUU

ddHH

�

2

UU RR 11⁄8 (4-32)

Small particles undergoing Brownian diffusion will diffuse from areas of high concentration to 

those of low concentration. Since the wall acts like a sink for these particles, there is net 

diffusion from the bulk to the wall. This phenomenon has been analyzed in reference [26] and 

the diffusional deposition efficiency is modeled as shown in Equation (4-33).

ηηdd = 1 − exp�−UUdd ss⁄QQ� (4-33)

where:

UUdd = the diffusion velocity in m/s

ss = the user provided total pipe surface area in m2

Q = the user provided gas flow in m3/s.

In cases of laminar flow, this efficiency is modeled as shown in Equation (4-34).

ηηdd = 2.56ζζ2⁄3 − 1.2ζζ − 0.177ζζ4⁄3 (4-34)

where:

ζ = the dimensionless diffusion parameter � ssDDdd ⁄QQddHH�

and

ss = the user provided total pipe surface area in m2

DDdd = the particle diffusion coefficient in m2

/s

Q = the user provided gas flow in m3/s

ddHH = the hydraulic diameter in m [see Equation (4-30)].

The particle diffusion coefficient is computed as shown in Equation (4-35) in units of cm2

/s units 

which is converted in the code to units of m2

/s.

DDdd = 1.38E − 16 TTgg × � ss

3 ππ μμ dd � (4-35)

where:

slip = 1.0 + 2.0 mm

dd �1.257 + 0.4ee−0.55dd ⁄mm � [see Equation (4-28)]

and
4-30

Tg = the gas temperature in °K

1.38E-16 = Boltzmann constant in g cm2

/s2 °K

μ = the viscosity of the gas in g/cm s

dp = the particle diameter in cm.

When the flow is slow or the pipe length is large such that ζ > 0.02, then the diffusional 

deposition efficiency is modeled as shown in Equation (4-36).

ηηdd = 0.819 exp (−3.657 ζζ) + 0.097 exp(−22.3 ζζ) + 0.032 exp (−57 ζζ) (4-36)

In cases of turbulent flow, the diffusional efficiency, from reference [27], is modeled as shown in 

Equation (4-37).

ηηdd = 1 − exp �−ζζ2⁄3 0.0187 RR 13⁄24 �

ddHH

�

1⁄3

� (4-37)

where:

ζ = the dimensionless diffusion parameter [see Equation (4-34)]

Re = ρρ UU ddHH⁄μμ [see Equation (4-30)]

L = the path length in m ( ss⁄ππddHH)

ss = the user provided total pipe surface area in m2

ddHH = the hydraulic diameter in m [see Equation (4-30)].

When the direction of gas flow is diverted in a bend, an aerosol particle may deviate from the 

gas flow due to its inertia and deposit on the wall. The efficiency of an aerosol particle in a bend 

is modeled as shown in Equation (4-38).

ηη = ττUU φφ

ddHH

(4-38)

where:

τ = the particle relaxation time in s [see Equation (4-28)]

UU = the air velocity in m/s

φ = the user-provided sum of the angles the flow has been diverted in radians

ddHH = the hydraulic diameter in m [see Equation (4-30)].

When the flow is turbulent, the efficiency of an aerosol particle in a bend, from reference [28], is 

modeled as shown in Equation (4-39).

ηη = 1.0 − exp

(−2.83 ττ UU φφ)

ddHH

(4-39)

where:

τ = the particle relaxation time in s [see Equation (4-28)]
4-31

UU = the air velocity in m/s

ddHH = the hydraulic diameter in m [see Equation (4-30)].

In cases of laminar flow, the efficiency of an aerosol particle in a bend is modeled as shown in 

Equation (4-40).

ηη = �1.0 + � ττ UU

0.171ddHH

�

PP1

�

−PP2

(4-40)

where:

PP1 = 0.452 � ττ UUaaaaaa

0.171 ddHH

� + 2.242

PP2 = 

2 φφ

ππ

Therefore, the total aerosol deposition efficiency is modeled as model as shown in Equation (4-

41).

ηηTT = 1.0 − �1.0 − ηηgg�(1.0 − ηη tt tt)�1.0 − ηηdd �(1.0 − ηη ) (4-41)

4.5.3.2 Bixler Model for Elemental Iodine Removal

The equation for the Bixler model for elemental iodine removal in pipes is given by Equation (4-

42).

ηη = 1 − exp �

− SSUU

100QQ � � (4-42)

where:

UU = ee2809⁄TT−12.5

and

T = the gas temperature in °K.

4.5.3.3 Bixler Model for Organic Iodine Removal

The equation for the Bixler model for organic iodine removal in pipes is given by Equation (4-

43).

ηηoo = 1 − exp �

− SSUUoo

100QQ � � (4-43)

where:

UUoo = ee2809⁄TT−19.30

and
4-32

T = the gas temperature in °K.

Note: Organic iodine removal is not credited in design basis calculations.

4.5.4 Filters

Heating, ventilation, and air conditioning (HVAC) system filter efficiency can be input by the user 

for the different nuclide groups as a function of time. The filter efficiency is specified as the 

fraction of material passing through the filter that is trapped on the filter media. This efficiency, 

expressed in terms of a decontamination coefficient as shown in Equation (4-44).

λλff ffff = �

ηηff ffff

100 � � λλjj,kk,ff ffff

ii (4-44)

where:

λλjj,kk,ff ffff

ii = the volume-normalized flow rate from compartment through the filter in in 

1/s.

4.6 Dose Analysis

Doses in the environment, within a control room, or within a given volume due to inhalation and 

whole body immersion can be computed in SNAP/RADTRAD. The models used are presented 

in the following sections and, as discussed in Section 3.4.1.1, the user can either choose the 

FGR 11 & 12 (default) or a user defined set of DCFs.

4.6.1 Offsite Dose Analysis

The dose to an individual at the EAB and the LPZ in the environment compartment is calculated 

in SNAP/RADTRAD. The dose due to cloudshine (immersion) for each nuclide, n, is calculated 

using Equation (4-45).

DD ,nn

ee = nn �

χχ

QQ� �DD DD ,nn (4-45)

where:

DD ,nn

ee = the air immersion (cloudshine) dose due to nuclide n in the environment 

compartment in Sv

nn = the integrated release of nuclide n in Bq

�

χχ

QQ� � = the user-provided atmospheric dilution factor in s/m3

DD DD ,nn = the FGR 11 & 12 air immersion (cloudshine) DCF for nuclide n in

Sv-m3

/Bq-s.

The activity is related to the number of atoms of nuclide, n, as shown in Equation (4-46).

nn = λλnnNNnn (4-46)

where:

λλnn = the radiological decay constant for nuclide n in 1/s.
4-33

The thyroid and committed effective dose equivalent (CEDE) doses due to inhalation from each 

nuclide, n, are calculated using Equation (4-47).

DDii,nn

ee = nn �

χχ

QQ� � ∗ DD DD ,nn (4-47)

where:

DDii,nn

ee = the inhalation dose commitment due to nuclide n in the environment 

compartment in Sv

nn = the integrated release of nuclide n in Bq

�

χχ

QQ� � = the user-provided atmospheric dilution factor in s/m3

BR = the user-provided breathing rate in m3/s

DD DDii,nn = the FGR 11 & 12 inhalation DCF for nuclide n in Sv/Bq for the CEDE or 

thyroid.

The TEDE is calculated as the sum of the CEDE and the immersion or cloudshine dose. Note 

that the conversion factor of 100 Rem = 1 Sv is applied to all the dose equations to obtain the 

dose in units of Rem. The total dose over the entire problem time is computed as the sum of 

the contributions over each time interval and each nuclide.

4.6.2 Control Room Dose Analysis

The dose to an individual in a control room is calculated from the time-integrated concentration 

of radionuclides in the control room compartment. The dose to the individual due to air 

immersion (cloudshine) in the control room is calculated using Equation (4-48).

DD ,nn

CCCC = �

DD DD ,nn

GGFF

� OO � nn( )dddd (4-48)

where:

DDii,nn

ee = air immersion (cloudshine) dose due to nuclide n in the control room 

compartment in Sv

DD DD ,nn = the FGR 11 & 12 air immersion (cloudshine) DCF for nuclide n in

Sv-m3

/Bq-s

OF = the user-provided control room occupancy factor

nn( ) = the instantaneous concentration of radionuclide n in the control room in 

Bq (s)

GGFF = the Murphy-Campe geometric factor, given in reference [29], which is 

relates the dose from an infinite cloud to the dose from a cloud of 

volume, V, in 1/m3

. This factor is defined in Equation (4-49).

GGFF = 351.6

VV0.338 (4-49)

The thyroid and CEDE doses (inhalation dose) to an individual in the control room are

calculated using Equation (4-50).
4-34

DDii,nn

CCCC = ∙ OO ∙ DD DD � nn( )dddd (4-50)

where:

DDii,nn

CCCC = the inhalation dose commitment due to nuclide n in the control room in 

Sv

BR = the user-provided breathing rate in m3/s

OF = the user-provided control room occupancy factor

DD DDii,nn = the FGR 11 & 12 inhalation DCF for nuclide n in Sv/Bq

nn(ττ) = the instantaneous concentration of radionuclide n in the control room.

The TEDE dose is calculated as the sum of the CEDE dose and the immersion or cloudshine 

dose. The total dose over the entire problem time is computed as the sum of the contributions 

over each time interval and each nuclide.
5-1

5.0 REFERENCES

[1] NUREG/CR-6604, “RADTRAD: A Simplified Model for RADionuclide Transport and 

Removal and Dose Estimation,” U.S. Nuclear Regulatory Commission, Washington, DC, 

December 1997.

[2] NUREG/CR-6604, Supplement 1, “RADTRAD: A Simplified Model for RADionuclide 

Transport and Removal and Dose Estimation,” U.S. Nuclear Regulatory Commission,

Washington, DC, June 1999.

[3] NUREG/CR-6604, Supplement 2, “RADTRAD: A Simplified Model for RADionuclide 

Transport and Removal and Dose Estimation,” U.S. Nuclear Regulatory Commission,

Washington, DC, October 2002.

[4] SNAP Manual, Version 2.2.1, “Symbolic Nuclear Analysis Package (SNAP) User's 

Manual,” Applied Programming Technology, Inc., Bloomsburg, PA, October 2012.

[5] ICRP Publication 38, “Radionuclide Transformations – Energy and Intensity of 

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[6] TID-14844, “Calculation of Distance Factors for Power and Test Reactor Sites,” U.S. 

Atomic Energy Commission, Washington, DC, March 1962.

[7] NUREG-1465, “Accident Source Terms for Light-Water Nuclear Power Plants,” U.S. 

Nuclear Regulatory Commission, Washington, DC, February 1995.

[8] EPA-520/1-88-020, “Limiting Values of Radionuclide Intake and Air Concentration and 

Dose Conversion Factors for Inhalation, Submersion, and Ingestion,” Federal Guidance 

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1988.

[9] EPA-402-R-93-081, “External Exposure to Radionuclides in Air, Water, and Soil,” 

Federal Guidance Report No. 12, U.S. Environmental Protection Agency, Washington, 

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[10] Regulatory Guide 1.183, “Alternative Radiological Source Terms for Evaluating Design 

Basis Accidents at Nuclear Power Reactors,” U.S. Nuclear Regulatory Commission, 

Washington, DC, July 2000.

[11] Lee, C.E. and Wilson, B.C., “A Conservative Variational Method for Multicomponent 

Concentration Time Dependent Diffusion,” Journal of Computational Physics, Vol. 60 (1), 

August 1985, p. 1-22.

[12] NUREG/CR-5966, “A Simplified Model of Aerosol Removal by Containment Sprays,” 

U.S. Nuclear Regulatory Commission, Washington, DC, June 1993.

[13] Washington, K.E., “A Reflected Kinetics Model for Nuclear Space Reactor Kinetics and 

Control Scoping Calculations,” Texas A&M University, College Station, TX, May 1986.
5-2

[14] Birchall, A. and James, A.C., “A Microcomputer Algorithm for Solving First-Order 

Compartmental Models Involving Recycling,” Health Physics, Vol. 56 (6), June 1989, p. 

857-858.

[15] Regulatory Guide 1.3, Revision 2, “Assumptions used for Evaluating the Potential 

Radiological Consequences of a Loss of Coolant Accidents for Boiling Water Reactors,” 

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[16] Regulatory Guide 1.4, Revision 2, “Assumptions used for Evaluating the Potential 

Radiological Consequences of a Loss of Coolant Accidents for Pressurized Water 

Reactors,” U.S. Nuclear Regulatory Commission, Washington, DC, June 1974.

[17] Regulatory Guide 1.25, “Assumptions Used for Evaluating the Potential Radiological

Consequences of a Fuel Handling Accident in the Fuel Handling and Storage Facility for

Boiling and Pressurized Water Reactors,” U.S. Nuclear Regulatory Commission, 

Washington, DC, March 1972.

[18] NUREG/CR-5009, “Assessment of the Use of Extended Burnup Fuel in Light Water 

Power Reactors,” U.S. Nuclear Regulatory Commission, Washington, DC, February

1988.

[19] NUREG-0017, Revision 1, “Calculation of Releases of Radioactive Materials in 

Gaseous and Liquid Effluents from Pressurized Water Reactors (PWR-GALE Code),”

U.S. Nuclear Regulatory Commission, Washington, DC, April 1985.

[20] NUREG-0016, Revision 1, “Calculation of Releases of Radioactive Materials in 

Gaseous and Liquid Effluents from Boiling Water Reactors (BWR-GALE Code),” U.S. 

Nuclear Regulatory Commission, Washington, DC, January 1979.

[21] ANSI/ANS-18.1-1999, “Radioactive Source Term for Normal Operation of Light Water 

Reactors,” American Nuclear Society, La Grange Park, IL, September 1999.

[22] Fauske & Associates, Inc., “FAI Aerosol Correlation, An Industry Degraded Core 

Rulemaking (IDCOR) Program Report,” Fauske & Associates, Inc., Bethesda, MD, 1984.

[23] Brockmann, J.E., “Sampling and Transport of Aerosols,” Aerosol Measurement: 

Principles, Techniques, and Applications, Third Edition, John Wiley & Sons, Hoboken, 

NJ, September 2011.

[24] Fuchs, N.A., “The Mechanics of Aerosols,” Macmillan Company, New York, NY, 1964.

[25] Liu, B.Y.H. and Agarwal, J.K., “Experimental Observation of Aerosol Deposition in 

Turbulent Flow,” Journal of Aerosol Science, Vol. 5 (2), March 1974, p 145–148.

[26] Gormley, P.G. and Kennedy, M., “Diffusion from a Stream Flowing Through a Cylindrical 

Tube,” Proceedings of the Royal Irish Academy, Vol. 52-A (1948 - 1950), p 163–169.

[27] Friendlander, S.K., “Smoke, Dust, and Haze: Fundamentals of Aerosol Behavior,” Wiley, 

New York, NY, 1977.
5-3

[28] Pui, D.Y.H., Romay-Novas, F. and Liu, B.Y.H., “Experimental Study of Particle 

Deposition in Bends of Circular Cross Section,” Aerosol Science and Technology, Vol. 7 

(3), February 1987, p 301–315.

[29] Murphy, K.G. and Campe, K.M., “Nuclear Power Plant Control Room Ventilation System 

Design for Meeting General Criterion 19, 13th AEC Air Cleaning Conference,” U.S. 

Atomic Energy Commission, Washington, DC, August 1974.





NUREG/CR-7220 SNAP/RADTRAD 4.0: Description of Models and Methods