RASCAL 4.3: Description 

of Models and Methods

Office of Nuclear Regulatory Research

NUREG-1940

Supplement 1
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RASCAL 4.3: Description 

of Models and Methods

Manuscript Completed: February 2015

Date Published: May 2015

Prepared by

J. V. Ramsdell, Jr.1 

G. F. Athey2 

J. P. Rishel3 

1

Ramsdell Environmental Consulting

13106 184th Avenue, NE

Redmond, WA 98052-2103

2

Athey Consulting

P.O. Box 178

Charles Town, WV 25414-0178

3

Pacific Northwest National Laboratory

P.O. Box 999

Richland, WA 99352

John Tomon, RES Technical Monitor/Contracting Officer’s Representative

Anthony Huffert, RES Technical Monitor

Jeff Kowalczik, NSIR Technical Monitor

Office of Nuclear Regulatory Research

NUREG-1940

Supplement 1

iii

ABSTRACT

RASCAL 4.3 contains a number of new features and revision of several old features in response 

to the lessons learned by the U.S. Nuclear Regulatory Commission staff during its response to 

the events at the Fukushima Daiichi nuclear power plants following the March 11, 2011 

earthquake off the coast of Japan and the tsunami that it triggered. This document is a 

supplement to NUREG-1940, “RASCAL 4: Description of Models and Methods,” which is the 

technical basis for the models and methods used in the RASCAL computer code versions 4.0, 

4.1 and 4.2. This supplement contains the technical basis for changes and additions to 

RASCAL implemented in versions RASCAL 4.3 and 4.3.1. Additionally, Appendix A provides 

errata information for NUREG-1940.

RASCAL 4.3 adds a long-term station blackout source term (LTSBO) model based on the 

results of the State-of-the-Art Reactor Consequences Analyses (SOARCA) study. It extends 

the RASCAL domain to 100 miles, increases the allowed calculation duration to 96 hours, and it 

adds a child thyroid dose calculation. RASCAL 4.3 includes new features to acquire 

meteorological data from the Internet, to calculate custom radionuclide inventories for reactor 

cores and spent fuel, to display a radionuclide activity balance within the power plant 

components and atmosphere, and to sort and display the radionuclides released to the 

atmosphere by importance to dose pathways. RASCAL 4.3 also adds the capability to import, 

merge, and export source terms. Improvements include revision of the pressure-hole size 

method of calculating the leak rate from containment and revision of the calculation of spent fuel

source terms.

v

TABLE OF CONTENTS

Section Page

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

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

LIST OF FIGURES ....................................................................................................................ix

LIST OF TABLES.......................................................................................................................xi

ACKNOWLEDGMENTS........................................................................................................... xiii

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

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

2.0 SOURCE TERM CALCULATIONS...............................................................................2-1

2.1 Long-Term Station Blackout (LTSBO)...............................................................2-1

2.1.1 LTSBO and LOCA Source Term Differences.........................................2-4

2.1.2 Calibration of BWR Mark I Suppression Pool Reduction Factors...........2-9

2.2 Loss of Coolant Accident (LOCA) Core Release Fractions .............................2-11

2.3 Core Damage State ........................................................................................2-13

2.4 Coolant Releases............................................................................................2-15

2.5 Pressure-Hole Size Release Model ................................................................2-18

2.6 Containment Radiation Monitor Source Term .................................................2-23

2.7 Effluent Release by Mixtures Source Term .....................................................2-28

2.8 Effluent Release Rate and Concentrations by Radionuclide Source 

Terms ............................................................................................................2-28

2.9 Spent Fuel and Fuel Cycle Facility Accidents..................................................2-29

2.9.1 Drained Spent Fuel Pool (SFP) ...........................................................2-30

2.9.2 Damaged Fuel.....................................................................................2-33

2.10 Uranium Hexafluoride (UF6) Source Terms.....................................................2-35

3.0 TRANSPORT, DISPERSION, AND DOSE CALCULATIONS.......................................3-1

3.1 Transport and Dispersion Calculations..............................................................3-1

3.1.1 Model Grid Dose Consistency ...............................................................3-1

3.1.2 Plume Characterization Output Files .....................................................3-4

3.1.3 Plume Depletion Calculation Correction ................................................3-6

3.2 Child Thyroid Dose Calculations .......................................................................3-6

3.3 Ingestion Dose Coefficients ..............................................................................3-8
vi

3.4 Field Team Dose Estimates ..............................................................................3-8

3.4.1 Projected Direct Reading Dosimeter (DRD) Reading and Doses...........3-9

3.4.2 Post Exposure Dose Estimates ...........................................................3-10

4.0 METEOROLOGICAL DATA ACQUISITION AND PROCESSING.................................4-1

4.1 Meteorological Data..........................................................................................4-1

4.2 Topographic Data .............................................................................................4-1

4.3 Surface Roughness Data..................................................................................4-2

5.0 UPDATED REACTOR CORE AND COOLANT INVENTORY MODELS.......................5-1

5.1 Reactor Core Activity Model..............................................................................5-1

5.2 Model Parameter Estimates..............................................................................5-4

5.3 Comparison with RASCAL 4.2 ..........................................................................5-7

5.4 Model Validation .............................................................................................5-10

5.5 Cooling System Model ....................................................................................5-15

5.6 Inventory Utility: Rx_Inventory_S ....................................................................5-19

5.6.1 Core Inventory Input............................................................................5-20

5.6.2 Cooling and Steam System Input ........................................................5-22

5.6.3 Rx_Inventory_S Model Output.............................................................5-25

5.6.3.1 Core Inventory ...................................................................5-25

5.6.3.2 Coolant Inventory...............................................................5-26

5.6.3.3 Spent Fuel Pool (SFP) Inventory........................................5-29

6.0 ACTIVITY BALANCE....................................................................................................6-1

6.1 Activity Balance File Description .......................................................................6-1

6.2 Generation of the Activity Balance File by RASCAL..........................................6-3

6.3 Activity Balance File Example for BWR LTSBO ................................................6-5

7.0 IMPORTANCE .............................................................................................................7-1

7.1 The Importance Model ......................................................................................7-1

7.2 Importance Results...........................................................................................7-4

8.0 SOURCE TERM IMPORT, EXPORT AND MERGE .....................................................8-1

8.1 Source Term Import Option...............................................................................8-1

8.1.1 CSV File Format....................................................................................8-1

8.1.2 XML File Format....................................................................................8-2

8.2 Import Process..................................................................................................8-4
vii

8.3 Export Process .................................................................................................8-6

8.4 RASCAL 4.3 Source Term Merge/Export Tool..................................................8-6

8.4.1 Load Cases ...........................................................................................8-6

8.4.2 Merge....................................................................................................8-7

8.4.3 Export....................................................................................................8-7

8.4.4 Multi-Unit...............................................................................................8-7

9.0 REFERENCES.............................................................................................................9-1

APPENDIX A NUREG-1940 ERRATA INFORMATION.........................................................A-1

ix

LIST OF FIGURES

Figure Page

Figure 2-1 RASCAL 4.3 radionuclide release timing for a PWR LTSBO accident.............. 2-3

Figure 2-2 RASCAL 4.3 radionuclide release timing for a BWR LTSBO accident.............. 2-4

Figure 2-3 Comparison of release timing for LTSBO and LOCA events for PWRs............ 2-5

Figure 2-4 Comparison of release timing for LTSBO and LOCA events for BWRs............ 2-5

Figure 2-5 Comparison of activity released to the atmosphere in the first 8 h after 

beginning of release for PWR LTSBO and LOCA events................................. 2-6

Figure 2-6 Comparison of activity released to the atmosphere in the first 8 h after 

beginning of release for BWR LTSBO and LOCA events................................. 2-7

Figure 2-7 Kr-85 release rate comparison for a PWR LOCA with a bypass release ........ 2-16

Figure 2-8 Comparison of RASCAL 4.2 (left) and RASCAL 4.3 (right) cloud shine 

dose accumulation......................................................................................... 2-16

Figure 2-9 Initial containment leak rates of representative PWR containment designs 

as a function of effective hole size ................................................................. 2-19

Figure 2-10 Pressure decrease with time for various effective hole sizes for 

representative PWR containment designs ..................................................... 2-20

Figure 2-11 Pressure decrease with time for various effective hole sizes for 

representative BWR containment designs ..................................................... 2-21

Figure 2-12 Pressure decrease with time for various effective hole sizes for 

representative BWR containment designs ..................................................... 2-22

Figure 2-13 RASCAL estimates of 1-percent damage containment radiation monitor 

readings......................................................................................................... 2-24

Figure 3-1 Dose consistency among the eight RASCAL 4.3 computational grids.............. 3-2

Figure 3-2 Maximum doses as a function of distance for a 10° off-cardinal wind 

direction ........................................................................................................... 3-3

Figure 3-3 Cartesian node locations relative to plume centerlines..................................... 3-3

Figure 3-4 Iodine depletion due to dry deposition in RASCAL 4.3 versus RASCAL 4.3.1.. 3-6

Figure 3-5 Scaling factors (thyroid dose/child thyroid dose) for adjusting RASCAL 4.3 

child ................................................................................................................. 3-8

Figure 3-6 RASCAL detailed results for dose and conversion factor estimates ................. 3-9

Figure 4-1 Raster image of the GTOPO30 file used to derive site terrain elevation files 

(*.top) for RASCAL 4.3..................................................................................... 4-2

Figure 4-2 Raster image of the NLCD1992 file used to derive site surface roughness 

files (*.gz0) for RASCAL 4.3............................................................................. 4-3

Figure 5-1 Radionuclide activity as a function of exposure time in fuel batch .................... 5-3

Figure 5-2 Core activity as a function of time during a cycle.............................................. 5-4

Figure 5-3 Comparison of updated model radionuclide inventory with the RASCAL 4.2 

inventory as a function of radionuclide half-life................................................. 5-8

Figure 5-4 Increase in core inventory during the fuel cycle as a function of 

radionuclide half-life......................................................................................... 5-9

Figure 5-5 Radionuclide activity increase during the fuel cycle as a function of 

half-life estimated from end-of-cycle inventory and burnup ............................ 5-10
x

Figure 5-6 Comparison of the updated core inventory estimates with core inventory 

estimates for current generation reactors....................................................... 5-12

Figure 5-7 Comparison of updated core inventory estimates with core inventory 

estimates for new reactors ............................................................................. 5-13

Figure 5-8 Distribution of refueling outage duration in 2011 ............................................ 5-22

Figure 5-9 Steam flow as function of reactor power ........................................................ 5-23

Figure 5-10 Secondary water mass as a function of reactor power for current 

generation and new PWR reactor designs ..................................................... 5-25

Figure 5-11 Sample core_inventory.tmp file...................................................................... 5-26

Figure 5-12 Sample PWR rcs_inventory.tmp file............................................................... 5-28

Figure 5-13 Sample BWR rcs_inventory.tmp file............................................................... 5-29

Figure 5-14 Sample sfpool_inventory.tmp file ................................................................... 5-29

Figure 6-1 Simplified RASCAL LTSBO and LOCA source term model.............................. 6-2

Figure 6-2 User interface presentation of the RASCAL 4.3.1 activity balance 

information....................................................................................................... 6-5

Figure 6-3 RASCAL 4.3.1 Kr-85 activity balance during a BWR Mark III LTSBO event..... 6-6

Figure 6-4 RASCAL 4.3.1 Xe-135 activity balance during a BWR Mark III LTSBO event .. 6-7

Figure 6-5 RASCAL 4.3.1 Cs-137 activity balance during a BWR Mark III LTSBO event .. 6-7

Figure 6-6 RASCAL 4.3.1 I-131 activity balance during a BWR Mark III LTSBO event...... 6-9

Figure 6-7 RASCAL 4.3.1 I-135 activity balance during a BWR Mark III LTSBO event...... 6-9

Figure 7-1 Example of the importance file contextual portion ............................................ 7-4

Figure 7-2 Example of the importance file activity balance portion .................................... 7-5

Figure 7-3 Comparison of MELCOR and RASCAL 4.3.1 source term estimates 

radionuclides.................................................................................................... 7-9

Figure 7-4 Comparison of MELCOR and RASCAL 4.3.1 source term estimates of 

the most important radionuclides contributing to cloud shine dose................. 7-10

Figure 7-5 Comparison of MELCOR and RASCAL 4.3.1 source term estimates of 

the most important radionuclides contributing to inhalation dose.................... 7-10

Figure 8-1 Example of a RASCAL 4.3 CSV format exported atmospheric release 

source term file ................................................................................................ 8-1

Figure 8-2 Example of a RASCAL 4.3 XML format exported atmospheric release 

source term file ................................................................................................ 8-3
xi

LIST OF TABLES

Table Page

Table 2-1 RASCAL 4.3 Default times after LTSBO initiating event to battery 

depletion and the start of release from the reactor ........................................... 2-4

Table 2-2 Activity released to the atmosphere in the PWR events ................................... 2-8

Table 2-3 Activity released to the atmosphere in the BWR events ................................... 2-8

Table 2-4 Comparison of RASCAL dose estimates for LTSBO and LOCA events ........... 2-9

Table 2-5 RASCAL 4.3 and 4.3.1 BWR Mark I suppression pool reduction factors ........ 2-10

Table 2-6 RASCAL 4.3.1 PWR LOCA release phase duration and core release 

fractions ......................................................................................................... 2-12

Table 2-7 RASCAL 4.3.1 BWR LOCA release phase duration and core release 

fractions ......................................................................................................... 2-12

Table 2-8 LTSBO – BWR damage state and effective core recovery times.................... 2-13

Table 2-9 LTSBO – PWR damage state and effective core recovery times.................... 2-14

Table 2-10 LOCA – BWR damage state effective core recovery times ............................ 2-14

Table 2-11 LOCA – PWR damage state effective core recovery times ............................ 2-14

Table 2-12 Comparison of RASCAL 4.2 and RASCAL 4.3 iodine releases for a PWR 

LOCA/bypass accident................................................................................... 2-17

Table 2-13 Containment parameters for four representative PWR containment 

designs .......................................................................................................... 2-19

Table 2-14 Containment parameters for three representative BWR containment 

designs .......................................................................................................... 2-21

Table 2-15 Containment radiation monitor reading interpolation/extrapolation 

parameter values ........................................................................................... 2-26

Table 3-1 Cartesian grid node positions at nominal distance of 1 and 10 miles................ 3-4

Table 3-2 Breathing rates and dose coefficients for use in estimating thyroid doses 

from iodine isotopes inhaled during plume passage......................................... 3-7

Table 3-3 Conversion factor variation with time and distance from the release point...... 3-12

Table 5-1 Production and decay parameters for selected radionuclides .......................... 5-3

Table 5-2 Radionuclide specific core inventory parameters for the updated inventory 

model............................................................................................................... 5-5

Table 5-3 Reactor specific characteristics used to test the updated core inventory 

model............................................................................................................. 5-11

Table 5-4 Statistics of the ratios of the updated core inventory model estimates to the 

FSAR and DCD inventory estimates .............................................................. 5-14

Table 5-5 Statistics of the ratios of the updated core inventory model estimates to the 

FSAR and DCD inventory estimates for radionuclides of interest................... 5-15

Table 5-6 Reactor.tmp file format and contents.............................................................. 5-21

Table 5-7 Fuel management characteristics .................................................................. 5-21

Table 5-8 MELCOR radionuclide classes....................................................................... 5-27

Table 6-1 Locations and transfer pathways for balance activity summaries ..................... 6-1

Table 6-2 Activity balance locations and transfer pathways for reactor accident 

categories ........................................................................................................ 6-3
xii

Table 6-3 Sample of the Balance Summary Available in the User Interface..................... 6-4

Table 7-1 Dose pathway importance following a mid-cycle core melt event with 

containment failure........................................................................................... 7-6

Table 7-2 Radionuclides most important to dose for a BWR Mark III following core 

melt with containment failure............................................................................ 7-7

Table 7-3 Radionuclides most important to dose for a PWR following core melt with 

containment failure........................................................................................... 7-8

Table 8-1 Description of the lines in a RASCAL 4.3 CSV format exported atmospheric 

release source term file.................................................................................... 8-2

Table 8-2 Description of the lines in a RASCAL 4.3 XML format exported atmospheric 

release source term file.................................................................................... 8-4
xiii

ACKNOWLEDGMENTS

The improvements to the RASCAL computer code would not have been possible without the 

guidance, feedback, and help of all the users of the code. Specific contributors to this report 

include all U.S. Nuclear Regulatory Commission (NRC) headquarters and Regional Protective 

Measures Team members, State emergency response personnel, and the NRC’s Office of 

Nuclear Security and Incident Response. The agency would like to thank the NRC staff and 

RASCAL users who have provided comments on their experiences with RASCAL and 

suggestions for RASCAL improvement. The software continues to grow and improve because 

of your efforts and ideas.

xv

ABBREVIATIONS

ABWR advanced boiling-water reactor

ADAMS Agencywide Documents Access and Management System

AP1000 advanced passive reactor

ATD atmospheric transport, dispersion, and deposition

Bq becquerel

BWR boiling-water reactor

CED committed equivalent dose

CEDE committed effective dose equivalent

CF conversion factor

Ci curie

CSV comma separated values

d days

DCD design control document

DRD direct reading dosimeter

ED effective dose

EFPD effective full-power day

EPA U.S. Environmental Protection Agency

EPR Evolutionary Power Reactor

ESBWR economic simplified boiling-water reactor

FDA U.S. Food and Drug Administration

FGR Federal Guidance Report

FSAR final safety analysis report

ft3 cubic feet

gal gallon

gal/d gallons per day

gal/h gallon per hour

GSD geometric standard deviation

GSM geometric standard mean

GWd gigawatt day

h hours

HF hydrogen fluoride

ICRP International Commission on Radiological Protection

in2 square inch

KI potassium iodide

km kilometer

LBLOCA large-break loss-of-coolant accident

LOCA loss-of-coolant accident

LTSBO long-term station blackout

m meters

MELCOR Methods for Estimation of Leakages and Consequences of Releases

mi miles

min minutes
xvi

mph miles per hour

MWd megawatt-day(s)

MWt megawatt thermal

MTU metric ton of uranium

NDFD National Digital Forecast Database

NLCD National Land-Cover Dataset

NRC U.S. Nuclear Regulatory Commission

NWS National Weather Service

ORIGEN_ARP Oak Ridge Isotope Generator_Automatic Rapid Processing

PAGs protective action guidelines

psig pounds per square inch gauge

PWR pressurized-water reactor

RASCAL Radiological Assessment System for Consequence Analysis

RCS reactor coolant system

SBGTS standby gas treatment system

SFP spent fuel pool

SOARCA State-of-the-Art Reactor Consequence Analyses

STDose source term to dose

Sv sievert

TED total effective dose

TEDE total effective dose equivalent

UF6 uranium hexafluoride

UO2F2 uranyl fluoride

US-APWR US-advanced pressurized-water reactor

XML extensible markup language

yr years
1-1

1.0 INTRODUCTION

The Radiological Assessment System for Consequence Analysis (RASCAL) version 4.3 

contains a number of new features and revision of several old features in response to the 

lessons learned by the U.S. Nuclear Regulatory Commission (NRC) staff during its response to 

the events at the Fukushima Daiichi nuclear power plants following the March 11, 2011 

earthquake off the coast of Japan and the tsunami that it triggered. This document is a 

technical supplement to NUREG-1940, “RASCAL 4: Description of Models and Methods.” It is 

one of a set of documents that describe RASCAL [1]. NUREG-1940 (referred to as the 

RASCAL technical document) presents the technical bases for the RASCAL computation codes 

described as RASCAL 4.2.

This supplement describes the changes from RASCAL 4.2 to RASCAL 4.3.1 and provides the 

technical bases for those changes. This supplement has nine sections including an introduction 

to the changes in RASCAL 4.3 and 4.3.1 and one appendix of errata information for NUREG1940. The second section describes the changes and additions to the source term calculations 

(Sections 1, 2, and 3 of NUREG-1940). The third section describes the changes to the 

atmospheric transport, dispersion, and dose calculations (Section 4 of NUREG-1940). Section

four describes the new meteorological data acquisition module. Section five describes a new 

utility tool to create reactor core, coolant, and spent fuel inventories based on specific reactor 

operating practices and most recent outage information. Section six describes a new feature to 

display the radionuclide activity at several locations in a power plant and in the atmosphere and 

activity transfers between locations as a function of time during an accident. Section seven

describes a new calculation which evaluates the importance to dose pathways of radionuclides 

released to the atmosphere. Section eight describes the new source term import option and the 

new Source Term Merge/Export tool. Finally, section nine includes a list of references.

2-1

2.0 SOURCE TERM CALCULATIONS

This section describes the changes to the RASCAL source term module implemented in 

RASCAL 4.3 and RASCAL 4.3.1. The most significant change is the addition of a long-term 

station blackout model (LTSBO). The model, which delays the onset of releases for 48-plus 

hours after the loss of power, is described in Section 2.1. Section 2.2 describes changes to the 

loss-of-coolant (LOCA) model. Section 2.3 describes changes to the option to specify a source 

term based on an estimate of core damage. Section 2.4 describes changes made to the 

treatment of coolant releases. Most notably, the changes to coolant system releases result in 

increased early releases of noble gases and decreased iodine releases for some release 

pathways. Section 2.5 describes revisions to the model used to estimate releases based on 

hole size and containment pressure. RASCAL 4.3 now decreases the containment pressure 

and the leak rate to the atmosphere as a function of time. Section 2.6 describes changes to the 

method for estimating source terms from containment radiation monitor readings. Sections 2.7 

and 2.8 provide additional information about the source term methods using measured effluent 

releases. Section 2.9 contains the discussion of the changes to the calculation for the spent 

fuel source terms. The changes improve the estimates of the at-risk radionuclide inventory in 

these accidents.

Several additions to RASCAL 4.3 related to source terms are described in later sections. 

Section 5 describes a new feature that can be used to estimate custom radionuclide inventories 

in reactor cores, in reactor cooling systems, and in spent fuel. Section 6 describes a new 

feature that provides users with estimates of activity of selected radionuclides in several 

locations within the plant and the activity released to the atmosphere as a function of time. 

Finally, Section 8 describes changes related to the import and export of source terms from 

RASCAL. There is a new feature that allows the import of atmospheric source terms. Also 

described is a new feature which allows the merging of source terms from multiple reactors at a 

single site into a file that can be used by RASCAL to evaluate potential consequences of an 

event involving multiple reactors at the site.

2.1 Long-Term Station Blackout (LTSBO)

One of the first lessons learned in the NRC response to the Fukushima Daiichi accident was 

that RASCAL did not have a readily apparent method for calculating reactor source terms for 

LTSBO events. The RASCAL source term was based on the core damage progression timing 

set forth in NUREG-1465, “Accident Source Terms for Light-Water Nuclear Power Plants,” [2]. 

Although LTSBO events were considered in preparation of NUREG-1465, the release timing set 

forth in Table 3.6 of NUREG-1465 is associated with large-break loss-of-coolant accidents 

(LBLOCAs). LTSBO accidents have a much longer time frame than LOCAs because loss of 

coolant occurs over a period of hours rather than seconds or minutes. A LTSBO release type 

option was added to RASCAL 4.3 to facilitate source term calculations for this type of accident. 

This LTSBO option was updated in RASCAL 4.3.1 by revising the associated in-core release 

fractions for pressurized-water reactors (PWRs) and boiling-water reactors (BWRs).

The LTSBO implementation in RASCAL is based on the LTSBO accident progression as 

described in the following reports:
2-2

• NUREG-1935, Part 1, “State-of-the-Art Reactor Consequence Analyses

(SOARCA) Report” [3],

• NUREG-1935, Part 2, “State-of-the-Art Reactor Consequence Analyses

(SOARCA) Report” [4],

• NUREG/CR-7110, Volume 1, Revision 1, “State-of-the-Art Reactor Consequence 

Analysis Project, Volume 1: Peach Bottom Integrated Analysis” [5], and

• NUREG/CR-7110, Volume 2, Revision 1, “State-of-the-Art Reactor Consequence 

Analysis Project Volume 2: Surrey Bottom Integrated Analysis” [6].

The basic scenario for the LTSBO accident is initiated by an external event that results in a total 

loss of offsite power. The reactor shuts down as expected, but the diesel generators fail to start 

following the earthquakes, so there is no onsite AC power. Reactor cooling is maintained for a 

period of several hours using systems powered by DC power. Ultimately, the onsite batteries 

are depleted; cooling is lost; and reactor coolant system (RCS) coolant gradually boils off. Core 

damage and releases from the core begin when the core is uncovered. The delay between 

depletion of the batteries and the beginning of the releases from the core is several hours.

The releases from the reactor begin once the core starts to uncover. SOARCA terminology 

does not identify specific release phases as gap activity release, early in-vessel release, exvessel release or late in-vessel release. Rather, the SOARCA reports present release fractions 

for radionuclide classes as a function of time. Figure 2-1 shows the SOARCA release fractions 

as implemented in RASCAL for PWRs for 11 radionuclide groups. The initial releases are 

primarily noble gases. The noble gases are followed by the other radionuclides. Figure 2-2 

shows the SOARCA release fractions as implemented in RASCAL for BWRs for the same nine 

radionuclide groups. Only 9 of the 11 groups were used in the SOARCA analyses and those 

9 groups are not exactly the same as those in NUREG-1465. The groups not used are the 

uranium (U) and antimony (Sb) groups. Additionally, the group fuel release fractions do not 

account for decay or ingrowth.
2-3

Figure 2-1 RASCAL 4.3 radionuclide release timing for a PWR LTSBO accident

Time zero in Figures 2-1 and 2-2 is the beginning of release, not the time of the initiating event. 

As indicated above, the time from the LTSBO initiating event (initiation of uncovering the core) 

to the beginning of release from the reactor may be several hours. Table 2-1 gives the default 

delay times RASCAL 4.3 assumes for battery depletion and the beginning of release from the 

reactor. The time for the start of the release in Table 2-1 includes the 8-hour heat up time for 

PWRs and the 6-hour heat up time for BWRs from the SOARCA analyses. However, as shown 

by the Fukushima Daiichi reactor operators’ actions, various emergency measures can extend 

these delays.
2-4

Figure 2-2 RASCAL 4.3 radionuclide release timing for a BWR LTSBO accident

Table 2-1 RASCAL 4.3 Default times after LTSBO initiating event to battery depletion 

and the start of release from the reactor

PWR BWR

Battery Depletion 4 h 4 h

Start of Release 12 h 10 h

2.1.1 LTSBO and LOCA Source Term Differences

There are several differences between the LTSBO and LOCA source terms. The difference in 

time delay between the initiating event and the start of release to the atmosphere is the most 

obvious. It has been discussed above. The increased delay for the LTSBO provides time for 

decay and ingrowth of radionuclides. The release fractions and release timing are also different

(see Section 2.2 below).

Figures 2-3 and 2-4 compare the release timing for LTSBOs with the timing for LOCAs for the 

first 12 hours (h) after the beginning of release from the reactor for PWRs and BWRs, 

respectively. These figures clearly show significant differences in the release rates from the 

reactor core for important radionuclide groups such as the iodine, cesium, and tellurium groups.
2-5

Figure 2-3 Comparison of release timing for LTSBO and LOCA events for PWRs

Figure 2-4 Comparison of release timing for LTSBO and LOCA events for BWRs
2-6

Figures 2-5 and 2-6 compare the activity released to the atmosphere and doses from LOCA and 

LTSBO accidents based on RASCAL 4.3.1 calculations for a 3586 megawatts thermal (MWt)

PWR reactor and a 3515 MWt BWR reactor with a Mark II containment. The PWR accident 

release path (Figure 2-5) is an unfiltered ground level (10 m) release via the containment 

leakage pathway without depletion by sprays or filters. The BWR accident release path 

(Figure 2-6) is from the dry well to the atmosphere via the standby gas treatment system 

(SBGTS) with active filters. [Note: It is unlikely that the SBGTS would be available during a 

LTSBO and in this instance the releases of iodine and cesium would increase significantly.] 

Activities and doses are based on the first 8-hour releases. The radionuclides identified in these 

figures provide an indication of which radionuclides are more prevalent in LTSBOs (those above 

the diagonal line) and which are more prevalent in LOCAs (those below the line). Some of the 

extreme differences (e.g., krypton-87 (Kr-87), iodine-134 (I-134), barium-139 (Ba-139), 

lanthanum-142 (La-142), and cesium-138 (Cs-138)) are caused by the delay in the start of the 

LTSBO core damage. Other notable differences (e.g., strontium-89 (Sr-89), Sr-90) are related 

to differences in core release fractions. The differences in core release fractions may well be 

due to the differences in time frames of NUREG-1465 and SOARCA analyses.

Figure 2-5 Comparison of activity released to the atmosphere in the first 8 h after 

beginning of release for PWR LTSBO and LOCA events
2-7

Figure 2-6 Comparison of activity released to the atmosphere in the first 8 h after 

beginning of release for BWR LTSBO and LOCA events

The activity releases to the atmosphere in these events are summarized and compared in 

Tables 2-2 and 2-3. The tables show that the LTSBO events have smaller noble gas releases 

and larger releases of iodines and other particles than the LOCA events. The reduction in noble 

gas releases for LTSBOs is directly related to the delay between the time of reactor shutdown 

and the beginning of core damage. Most of the krypton activity is associated with Kr-87 and Kr88 which have half-lives of less than 3 hours, and about half of the xenon (Xe) activity is 

associated with Xe-135m and Xe-138, which have half-lives of about 15 minutes. The releases 

of iodines and other particles in PWR LTSBO accidents are larger than the releases in LOCAs 

because the LTSBO core release fractions for the iodine and cesium groups are larger than the 

corresponding LOCA core release fractions.
2-8

Table 2-2 Activity released to the atmosphere in the PWR events

Radionuclide

LOCA LTSBO

LTSBO/LOCA Ratio Activity 

(Ci)

Percent 

(%)

Activity 

(Ci)

Percent 

(%)

Noble Gas 9.4E+04 60.3 6.2E+04 44.9 0.66

Iodine 3.6E+04 23.1 4.1E+04 29.7 1.14

Other 2.6E+04 16.6 3.5E+04 25.4 1.36

Total 1.6E+05 1.4E+05 0.88

The BWR event releases more activity to the atmosphere than the PWR event, but because the 

BWR pathway passes through the wet well and is filtered in the SBGTS, almost all of the 

released activity is from the noble gases. A very small fraction of the released activity is from 

the iodines or other particles.

Table 2-3 Activity released to the atmosphere in the BWR events

Radionuclide

LOCA LTSBO

LTSBO/LOCA Ratio Activity 

(Ci)

Percent 

(%)

Activity 

(Ci)

Percent 

(%)

Noble Gas 4.6E+05 100.0 3.9E+05 100.0 0.85

Iodine 1.6E+01 0.0 7.0E+00 0.0 0.44

Other 1.2E+01 0.0 6.1E+00 0.0 0.51

Total 4.6E+05 3.9E+05 0.85

Table 2-4 compares the consequences of these events using RASCAL computational results 

extracted from the Maximum Dose Values table for a receptor at a distance of 2 miles (mi). The 

doses were calculated using RASCAL standard meteorology (4 miles per hour (mph) wind, dose 

(D) stability, no precipitation) and the International Commission on Radiological Protection 

Publication 60 and 72 (ICRP 60/72) dose factors. All doses for the PWR LTSBO event are 

larger than those for the LOCA event. The BWR LTSBO event thyroid doses are also larger 

than the LOCA event thyroid doses. However, the BWR LTSBO event total effective dose (ED)

and cloud shine doses are lower than those for the LOCA event. Factors that contribute to 

these results are:

• The wet well and SBGTS filter significantly reduce the release of iodine

radionuclides and other particles.
2-9

• The elevated release keeps the plume centerline above ground level.

Consequently, the iodines and other particles do not contribute significantly to inhalation doses 

including the thyroid doses.

Table 2-4 Comparison of RASCAL dose estimates for LTSBO and LOCA events

Dose

PWR BWR

LOCA LTSBO Ratio LOCA LTSBO Ratio

Total EDa 6.0E-01 8.7E-01 1.45 2.0E-03 5.5E-03 0.28

Thyroid CEDa 4.5E+00 7.0E+00 1.55 2.1E-03 1.3E-03 0.57

Child Thyroid CEDa 9.1E+00 1.3E+01 1.43 4.0E-03 2.2E-03 0.55

Inhalation CEDa 4.7E-01 6.7E-01 1.43 1.4E-03 ***

Cloud shinea 1.3E-02 1.2E-02 0.92 1.8E-02 5.2E-03 0.29

4-day Ground shinea 1.1E-01 2.0E-01 1.82 *** ***

a rem (roentgen equivalent man)

*** <1.0E-03 rem

2.1.2 Calibration of BWR Mark I Suppression Pool Reduction Factors

Insights gained from ongoing benchmarking studies using the LTSBO feature in RASCAL 4.3 

showed general agreement with the SOARCA analysis for a BWR. Noble gas releases to the 

atmosphere comport with the SOARCA analysis, but the halogen and particulate releases are 

significantly underestimated. The differences in the halogen and particulate releases to the 

atmosphere can be attributed to modeling differences between RASCAL 4.3 and the SOARCA

BWR analysis in the treatment of depletion mechanisms within the suppression pool and late 

revaporization from the reactor pressure vessel directly into the drywell. Late revaporization 

accounts for the bypass of the suppression pool after lower head failure leading to containment 

failure (liner melt through in a Mark I BWR containment).

RASCAL is a fast-running emergency response code that models fission product behavior in 

containment differently than the SOARCA analysis for a LTSBO accident at a Mark I BWR. 

Below is a summary of the major differences between RASCAL and the SOARCA analysis for 

the LTSBO accident sequence:

• RASCAL models holdup of radioactive material in the containment, but it does 

not delay radioactive material movement between the fuel and containment or 

between containment and the atmosphere. Releases through the suppression 

pool are modeled as releases from the containment at the containment leak rate 

with no holdup in the suppression pool.
2-10

• RASCAL models the suppression pool reduction mechanism as a single filter at 

the point of release to the atmosphere, rather than a time-varying depletion 

mechanism in containment. Table 2-5 presents the RASCAL 4.3 suppression

pool reduction factors (saturated and subcooled) which are applied to three 

categories of fission products. The technical basis documents for these 

reduction factors are NUREG-1228, “Source Term Estimation During Incident 

Response to Severe Nuclear Power Plant Accidents,” [7] and NUREG/CR-3727, 

“Fission Product Removal in Engineered Safety Feature (ESF) Systems” [8].

• RASCAL 4.3.1 does not allow the user to switch between the suppression pool 

and drywell during a single calculation. Therefore, the suppression pool release 

path cannot be bypassed once it is selected by the user. In comparison, the 

SOARCA analyses used multiple release paths to model fission product releases 

to the atmosphere.

• RASCAL models fission product deposition in containment as a time-dependent

function but does not account for the revaporization of deposited radionuclides in 

the reactor pressure vessel in the LTSBO sequence. Note that the “LOCA 

(NUREG-1465)” source term option in RASCAL 4.3 incorporates a “late in vessel” 

release which accounts for revaporization and other processes.

Given the variability of suppression pool reduction factors, a series of RASCAL calculations 

were performed to determine the possibility of achieving better agreement with the SOARCA 

results for halogens and particulates using RASCAL v4.3.1 models and modified suppression pool 

reduction factors. Table 2-5 presents the RASCAL 4.3.1 suppression pool factors results of these 

calculations.

Table 2-5 RASCAL 4.3 and 4.3.1 BWR Mark I suppression pool reduction factors

Noble Gases Halogens Other Particles

RASCAL 4.3 Saturated 1.0 0.05 0.05

RASCAL 4.3.1 Saturated 1.0 0.5 0.15

RASCAL 4.3 Subcooled 1.0 0.01 0.01

RASCAL 4.3.1 Subcooled 1.0 0.01 0.01

RASCAL 4.3.1 incorporates saturated suppression pool reduction factors of 1.0 for noble 

gases, 0.5 for halogens, and 0.15 for other particles for the LTSBO scenario at Mark I BWRs 

only, to account for existing differences between RASCAL and SOARCA in modelling fission 

product behavior in the suppression pool and drywell at BWRs with Mark I containments.

These modified RASCAL 4.3.1 suppression pool reduction factors for the LTSBO feature 

account for additional releases from the revaporization of fission products which bypass the 
2-11

suppression pool. This represents an overall “effective” reduction factor for BWRs with a 

Mark I containment, and is not necessarily applicable to other BWR designs. Additionally, 

these modified reduction factors should not be used for the “LOCA (NUREG-1465)” source 

term option in RASCAL 4.3.1, other computer codes, or cited as references for suppression 

pool reduction factors.

2.2 Loss of Coolant Accident (LOCA) Core Release Fractions

NUREG-1465 defines reactor release fractions for BWR and PWR LOCAs for 4 release phases: 

gap activity release, early in-vessel release, ex-vessel release, and late in-vessel release. 

RASCAL 4.3 and earlier versions of the code use the release fractions for the gap release, the 

early in-vessel release, and the ex-vessel release phases to define the release of core activity 

into the containment. These previous versions of the RASCAL computer code do not include 

the late in-vessel release phase. However, RASCAL 4.3.1 includes the activity released from 

the late in-vessel phase in LOCA source terms.

The durations of each phase including the late in-vessel phase are defined in NUREG-1465 

Table 3.6. The late in-vessel release phase commences simultaneously with the occurrence of 

the ex-vessel release phase and extends several hours after the end of the ex-vessel phase

release. Table 3.8, of NUREG-1465, classifies radionuclides into eight radionuclide groups 

based on expected release characteristics. Core release fractions to containment for each 

group by release phase for BWRs and PWRs are listed in Tables 3.12 and 3.13 of 

NUREG-1465.

The only radionuclide groups that have releases during the late in-vessel release phase are the 

halogens (iodine and bromine group), the alkali metals (cesium and rubidium group), and the 

tellurium group (tellurium, antimony, and selenium). In RASCAL 4.3.1 the core release fractions 

for these groups for the ex-vessel phase have been increased to include the portion of the late 

in-vessel release phase that occurs during the time of the ex-vessel release phase, and the late 

in-vessel release fractions have been decreased to account for the activity released during the 

ex-vessel release phase. Tables 2-6 and 2-7 present the core release fractions used by 

RASCAL 4.3.1 for the eight NUREG-1465 groups for PWRs and BWRs respectively. These 

tables include the revised release fractions for the ex-vessel and late in-vessel phases.
2-12

Table 2-6 RASCAL 4.3.1 PWR LOCA release phase duration and core release 

fractions

Cladding Core Melt Ex-Vessel Late In-Vessel

Duration (h) 0.5 1.3 2.0 8.0

Core Release Fraction

Noble Gases (Xe, Kr) 0.05 0.95 0.00 0.00

Halogens (I, Br) 0.05 0.35 0.27 0.08

Alkali Metals (Cs, Rb) 0.05 0.25 0.37 0.08

Tellurium Group (Te, Sb, Se) 0.00 0.05 0.251 0.004

Barium/Strontium Group (Ba, Sr) 0.00 0.02 0.10 0.00

Noble Metals (Ru, Rh, Mo, Tc, Co) 0.00 0.0025 0.0025 0.00

Lanthanides (La, Zr, Cm, Am) 0.00 0.0002 0.005 0.00

Cerium Group (Ce, Pu, Np) 0.00 0.0005 0.005 0.00

Table 2-7 RASCAL 4.3.1 BWR LOCA release phase duration and core release fractions

Cladding Core Melt Ex-Vessel Late In-Vessel

Duration (h) 0.5 1.5 3.0 7.0

Core Release Fraction

Noble Gases (Xe, Kr) 0.05 0.95 0.00 0.00

Halogens (I, Br) 0.05 0.25 0.303 0.007

Alkali Metals (Cs, Rb) 0.05 0.20 0.353 0.007

Tellurium Group (Te, Sb, Se) 0.00 0.05 0.2515 0.0035

Barium/Strontium Group (Ba, Sr) 0.00 0.020 0.10 0.00

Noble Metals (Ru, Rh, Mo, Tc, Co) 0.00 0.0025 0.0025 0.00

Lanthanides (La, Zr, Cm, Am) 0.00 0.0002 0.005 0.00

Cerium Group (Ce, Pu, Np) 0.00 0.0005 0.005 0.00
2-13

Note that in RASCAL 4.3.1, the only groups that have late in-vessel release fractions are the 

halogens (iodine and bromine), the alkali metals (cesium and rubidium), and the tellurium group 

(tellurium, antimony, and selenium). Core release fractions for the other groups are the same in 

RASCAL 4.3.1 as they were in previous versions of the RASCAL computer code.

2.3 Core Damage State

The “core damage state” option from RASCAL 3.0.5 has been moved in RASCAL 4.3. It is now 

an option for both the LTSBO and LOCA source terms. In this current version of the RASCAL 

computer code, the “percent damage” option is essentially equivalent to selecting the “core 

recovered” option and specifying a time that the core is recovered with the exception that the 

“percent damage” option does not require that the user specify a time for the core recovery. 

When the “core damage state” option is selected, RASCAL calculates the duration that the core 

is uncovered and adds the core uncovered duration to the time core is initially uncovered to 

determine when to recover the core.

The relationships among core damage phase, percent damage, and effective time of core 

recovery for LTSBOs and LOCAs for both BWRs and PWRs are based on event progression 

descriptions in NUREG/CR-7110 Volume 1, Revision 1; NUREG-7110 Volume 2, Revision 1; 

and NUREG-1465. Tables 2-8 through 2-11 give the relationships used by RASCAL 4.3.1 in 

estimating effective core recovery times.

Table 2-8 LTSBO – BWR damage state and effective core recovery times

Core Damage Phase Percent Damage

(%)

Core Recovery Time 

(min)a

Cladding Failure 0 to 100 0 to 30b

Core Melt 0 to 100 30 to 120b

Ex-Vessel (Vessel Melt) NA 360c

a. Times are minutes after the start of core damage. The RASCAL interface will convert the relative 

core recovery time to date and time.

b. Linear interpolation of time as function of percent is appropriate.

c. Ex-vessel release is evaluated at a single specific time.
2-14

Table 2-9 LTSBO – PWR damage state and effective core recovery times

Core Damage Phase Percent Damage

(%)

Core Recovery Time 

(min)a

Cladding Failure 0 to 100 0 to 90b

Core Melt 0 to 100 90 to 300c

Ex-Vessel (Vessel Melt) NA 360d

a. Times are minutes after the start of core damage. The RASCAL interface will convert the relative 

core recovery time to date and time.

b. Linear interpolation of time as function of percent is appropriate.

c. Linear interpolation of time as function of percent should be done in two segments. Use segment 1 

for 0 to 75 percent with corresponding times of 90 to 240 minutes, and use segment 2 for 75

percent to 100 percent with corresponding times of 240 to 300 minutes.

d. Ex-vessel release is evaluated at a single specific time.

Table 2-10 LOCA – BWR damage state effective core recovery times

Core Damage Phase Percent Damage

(%)

Core Recovery Time 

(min)a

Cladding Failure 0 to 100 0 to 30b

Core Melt 0 to 100 30 to 120b

Ex-Vessel (Vessel Melt) NA 360c

a. Times are minutes after the start of core damage. The RASCAL interface will convert the relative 

core recovery time to date and time.

b. Linear interpolation of time as function of percent is appropriate.

c. Ex-vessel release is evaluated at a single specific time.

Table 2-11 LOCA – PWR damage state effective core recovery times

Core Damage Phase Percent Damage

(%)

Core Recovery Time 

(min)a

Cladding Failure 0 to 100 0 to 30b

Core Melt 0 to 100 30 to 105b

Ex-Vessel (Vessel Melt) NA 240c

a. Times are minutes after the start of core damage. The RASCAL interface will convert the relative 

core recovery time to date and time.

b. Linear interpolation of time as function of percent is appropriate.

c. Ex-vessel release is evaluated at a single specific time.

Note that no option is provided for percent damage for the ex-vessel release phase. The source 

term for this phase is based on damage that occurs prior to a fixed time in the middle of the 

phase duration.
2-15

2.4 Coolant Releases

In RASCAL 4.2 and earlier versions, activity entering the RCS was mixed in cooling system 

water and released to the environment as the coolant was released. Depending on the rate of 

transfer of activity from the reactor to the RCS and coolant release rate from the RCS, the 

activity in the RCS increased and decreased as the event progressed. Isotopes of noble gases 

and other elements were treated the same.

In RASCAL 4.3, noble gases entering the RCS of a BWR are immediately vented to the 

environment; they do not accumulate in the RCS. This change makes RASCAL consistent with 

BWR designs in which non-condensable gases are stripped from the steam by the air ejectors. 

Other radionuclides are accumulated in the RCS as in previous versions of RASCAL. Noble 

gases entering the primary system of a PWR are accumulated as are other radionuclides, but 

noble gases leaking from the primary system to the secondary system are vented to the 

environment immediately through the air ejectors.

These changes in the treatment of noble gases alter the timing of noble gas releases to the 

environment for those reactor accident release paths that involve the RCS. Noble gases are 

released earlier in the accident sequence in RASCAL 4.3 than they were in previous versions of 

RASCAL. Also, because the noble gases aren’t accumulated in either the BWR or PWR RCS, 

the total noble gas release in RASCAL 4.3 is larger than it is in RASCAL 4.2. Figure 2-7

illustrates the differences in noble gas release for a PWR LOCA with bypass release calculated 

using RASCAL default parameters.

Noble gases are significant contributors to the cloud shine dose. As a result, the change in the 

treatment of noble gas releases is reflected in cloud shine doses. Figure 2-8 shows the 

cumulative cloud shine dose at 1 mile (mi) as a function of time for a PWR LOCA Bypass 

accident for RASCAL 4.2 and RASCAL 4.3. The left panel shows the RASCAL 4.2 dose, and 

the right panel shows the RASCAL 4.3 dose.
2-16

Figure 2-7 Kr-85 release rate comparison for a PWR LOCA with a bypass release

Figure 2-8 Comparison of RASCAL 4.2 (left) and RASCAL 4.3 (right) cloud shine dose 

accumulation

1.E-02

1.E-01

1.E+00

1.E+01

1.E+02

1.E+03

0 1 2 3 4 5 6 7 8

Release Rate (Ci/s)

Time after Beginning of Release (h)

RASCAL 4.2

RASCAL 4.3
2-17

In RASCAL 4.2 there was no decay or ingrowth of activity within the RCS. The treatment of 

activity entering the RCS has been revised in RASCAL 4.3 to include decay and daughter 

ingrowth. This change results in a reduction of release of short-lived radionuclides such as 

I-132, I-133, I-134, and I-135 to the environment compared with previous versions of RASCAL. 

Table 2-12 shows the changes in iodine activity released in the environment for a LOCA/bypass 

accident that is associated with the addition of decay and ingrowth in the RCS. The total iodine 

release in RASCAL 4.3 is reduced to about 75 percent of the RASCAL 4.2 total iodine release.

Table 2-12 Comparison of RASCAL 4.2 and RASCAL 4.3 iodine releases for a PWR 

LOCA/bypass accident

Radionuclide Half Life 

(h)

Dose 

Coefficients

(Sv/Bq)

RASCAL 4.2

(Ci)

RASCAL 4.3

(Ci) Fraction

I-131 193.0 8.89E-09 1.10E+05 1.09E+05 0.991

I-132 2.3 1.03E-10 1.74E+05 1.17E+05 0.673

I-133 20.8 1.58E-09 2.13E+05 1.94E+05 0.912

I-134 0.9 3.55E-11 9.78E+04 2.36E+04 0.241

I-135 6.6 3.32E-10 1.84E+05 1.39E+05 0.757

Total 7.77E+05 5.82E+05 0.749

There are significant reductions in the releases of I-134 and I-132, while the release of I-131 is 

not reduced significantly. Note that the I-131 and I-132 activities in Table 2-6 include ingrowth 

from decay of tellurium parents.

In contrast to the effect of increasing the release of noble gas on the cloud shine dose, the 

decrease in iodine releases from RASCAL 4.2 to RASCAL 4.3 has relatively little effect. The 

thyroid committed effective dose equivalent (CEDE) at 1 mi calculated by RASCAL 4.2 for a 

PWR LOCA/Bypass accident is 141 roentgen equivalent man (rem). The thyroid CEDE at 1 mi 

calculated by RASCAL 4.3 for the same accident is 136 rem. Even though the total iodine 

release decreased by 25 percent, the thyroid CEDE decreased by less than 4 percent. The 

relative insensitivity of the thyroid CEDE to reduction in total iodine released is explained by the 

fact that most of the reduction in the iodine release is associated with radionuclides having 

relatively small dose coefficients. The release of I-131, which has the largest iodine dose 

coefficients, is essentially unchanged from RASCAL 4.2 to RASCAL 4.3.

Daughter ingrowth in the RCS does increase the release of some radionuclides; for example,

the Xe-135m and Xe-135 daughters of I-135. The immediate release of noble gases from the 

steam generator in RASCAL 4.3 increases the noble gas released to the environment by about 

a factor of 2.1. The ingrowth of Xe-135m and Xe-135 from decay of I-135 in the primary and 

secondary systems increases the releases of the radionuclides by approximately an additional 

35 percent and 10 percent, respectively. Noble gases originating in the secondary system from 

ingrowth are immediately vented to the environment.
2-18

2.5 Pressure-Hole Size Release Model

Section 1.5.2 of NUREG-1940 describes the RASCAL option for estimating containment release 

rates based on containment pressure and hole size. As noted at the end of the section, 

RASCAL 4.2 does not calculate the change in containment pressure as gases leave the 

containment; it is up to the user to enter changing containment pressure as the consequence 

assessment proceeds. The algorithm implementing the option to estimate release rates based 

on containment pressure and hole size was revised in RASCAL 4.3. The code adjusts the 

containment pressure to account for the gases leaving the containment. This section describes 

the assumptions and methods RASCAL 4.3 uses in calculating the release rate. Additionally, 

RASCAL 4.3.1 corrects a coding error in the conversion of pressures in the containment 

pressure and hole size method in RASCAL 4.3.

As a starting point for calculating releases from containment pressure and hole size, 

RASCAL 4.3 assumes that the containment pressure prior to the initiating event is equal to 

atmospheric pressure of 14.7 pounds per square inch absolute (psia), with a temperature of

68 degrees Fahrenheit and that the containment atmosphere is essentially dry air. An initial 

hole size and containment pressure should be entered for the time of beginning of release. If 

the hole size is 0.01 square centimeters (cm2

) (0.0015 square inches (in2)) or less, RASCAL

4.3.1 assumes that the containment leak rate is equal to the containment design leak rate. If 

the hole size is 0.01 cm2 or larger, RASCAL uses equation 1-12 from NUREG-1940 to calculate 

the mass flow from the containment to the environment. Note that this equation assumes that 

the area of the hole is small compared to the surface area of the containment and it represents 

steady-state leakage of a non-compressible fluid from a pipe. Conceptually this is not an 

appropriate representation of the containment leak rate under pressure; however, it does 

provide initial leak rate estimates that are not significantly different than those that would be 

obtained from a more representative containment model.

When RASCAL 4.3 determines that the release rate is to be calculated by the containment 

pressure and hole size method, it checks to see if the increase in containment temperature is 

sufficient to account for the increase in containment pressure. If it is, RASCAL 4.3 assumes 

that the containment atmosphere consists of essentially dry air, and uses the density of dry air 

in the calculation of containment leak rate. If the increase in temperature is not sufficient to 

account for the increase in containment pressure, RASCAL 4.3 assumes that the increase in 

pressure is the result of a major leak in the RCS. In this case, RASCAL 4.3 calculates the 

containment atmosphere density assuming that the water in the RCS has been drained to 

containment and has evaporated. RASCAL 4.3 also adds the activity in the RCS to the activity 

in containment.

RASCAL 4.3.1 calculates the initial leak rate based on containment size, hole size, and 

containment pressure. Table 2-13 lists reactor and containment parameters of four 

representative PWR reactor containment designs. The equivalent design hole is a hole that 

would give the design leak rate at the design pressure assuming the RASCAL 4.3.1 pressure 

hole model. Figure 2-9 shows the initial containment leak rates as a function of effective hole 

size for the representative PWR containment designs, assuming that the containment is initially 

at design pressure. The equivalent design holes in Table 2-13 may be estimated directly from 
2-19

Figure 2-9. Containment design parameters, with the exception of the equivalent design hole 

size (Table 2-13), are included for each reactor in the United States RASCAL facility database

file. The containment design parameters are listed under the reactor parameters portion of the 

user interface case summary. Note that the term effective hole size is used because the hole in 

the model is assumed to be circular in shape, but the actual hole shape during an event may not 

be circular. Additionally, the leak rate may be smaller than the design leak rate if the pressure is 

less than the design pressure.

Table 2-13 Containment parameters for four representative PWR containment designs

PWR

Containment 

Type

Rated 

Power

Containment 

Volume

Design 

Pressure

Design 

Leak 

Rate

Equivalent 

Design 

Hole

(MWt) (ft3) (psig) (%/day) (cm2)

Braidwood Unit 1 Dry Ambient 3586 2.90E+06 61 0.1 0.1

Watts Bar Unit 1 Ice Condenser 3459 9.20E+05 15 0.5 0.5

Prairie Island Unit 1 Dry Ambient 1677 1.30E+06 41 0.5 0.3

Beaver Valley Unit 1 Subatmospheric 2900 1.80E+06 54 0.1 0.07

Figure 2-9 Initial containment leak rates of representative PWR containment designs 

as a function of effective hole size
2-20

As the containment leaks to the environment RASCAL 4.3.1 updates the containment pressure 

and leak rate to account for the decrease in mass of the containment atmosphere. Figure 2-10

shows the decrease in containment pressure for each of the four representative reactors. In 

each case the initial pressure is the containment design pressure.

Figure 2-10 Pressure decrease with time for various effective hole sizes for 

representative PWR containment designs

Table 2-14 lists reactor and containment parameters of three representative BWR reactor 

containment designs. Figure 2-11 shows the initial containment leak rates as a function of 

effective hole size for the representative BWRs containment designs, assuming that the 
2-21

containment is initially at design pressure. Figure 2-12 shows the decrease in containment 

pressure for each of the four representative reactors. In each case the initial pressure is the 

containment design pressure.

Table 2-14 Containment parameters for three representative BWR containment 

designs

BWR

Containment 

Type

Rated 

Power

Containment 

Volume

Design 

Pressure

Design 

Leak 

Rate

Equivalent 

Design Hole

(MWt) (ft3) (psig) (%/day) (cm2)

Quad Cities Unit 1 Mark I 2957 2.70E+05 56 0.5 0.1

LaSalle Unit 1 Mark II 3546 3.74E+05 45 0.5 0.15

Perry Unit 1 Mark III 3758 1.08E+06 15 0.2 0.2

Figure 2-11 Pressure decrease with time for various effective hole sizes for 

representative BWR containment designs
2-22

Figure 2-12 Pressure decrease with time for various effective hole sizes for 

representative BWR containment designs

In reality, the pressure should decrease to atmospheric pressure. However, RASCAL assumes 

that the containment pressure will only decrease to a pressure that is one percent above 

atmospheric pressure. This 1 percent residual pressure differential is used to provide leakage 

to the environment through the open hole. If containment integrity is reestablished, the leak rate 

may be reset to the original leak rate by resetting the hole size.

In calculating the release through a hole, RASCAL updates the containment pressure and leak 

rate every 15 minutes using the leak rate at the beginning of the 15 minute period. This 

procedure causes an overestimation of the release rate in the early release periods if the leak 
2-23

rates are high. If the release period is long enough, the overestimation of release rates will be 

followed by period of underestimated release rates that will ultimately compensate for the 

overestimated early releases. The magnitude of the overestimation of early release rates is a 

function of the hole size.

At this point, it should be noted that the RASCAL 4.3 approach to estimating releases via the 

containment pressure-hole size release path does not consider all of the factors that may alter 

the release rate through the hole. For example, the approach does not consider any decrease 

in pressure that may be associated with condensation of the reactor coolant or a decrease in 

temperature of the containment atmosphere. These factors are likely to reduce the containment 

atmosphere pressure and the release rate. Similarly, RASCAL 4.3 does not consider any 

potential heating of the containment atmosphere by the reactor. Heating of the containment 

atmosphere could increase the containment pressure and release rate.

RASCAL does not include any of the physics that would be required to predict increases in 

containment pressure as an event progresses. It is up to the user to enter containment 

pressures as they increase. It is also important to enter containment pressures as the 

pressures decrease because estimates of hole size are likely to be crude at best. RASCAL 

reinitializes its pressure calculation each time a containment pressure is entered.

If the leak rate from containment is small (design leak rate or less), containment pressures may 

be entered less frequently than when the leak rate is large. If there isn’t containment damage or 

venting, it is likely to be sufficient to enter the containment pressure every hour or two. When 

there is venting or containment damage, pressures should be entered more frequently.

2.6 Containment Radiation Monitor Source Term

Section 1.2.4 of NUREG-1940 describes the RASCAL option for estimating source terms using 

containment radiation monitor readings. The containment radiation monitor source term 

calculation in RASCAL 4.3 is based on Method A.4 of NUREG/BR-0150, “Response Technical 

Manual (RTM)-96” [9]. Figures A-5 through A-12 of NUREG/BR-0150 show estimates of 

containment monitor readings for core damage states ranging from 1 to 100 percent for invessel core melt, gap releases, and coolant releases for PWR and BWR reactors for 1 and 

24 hours after reactor shutdown. Figures 1-1 through 1-5 in NUREG-1940 are based on these 

figures in NUREG/BR-0150.

The RASCAL implementation of the method described in NUREG/BR-0150 scales the 

containment monitor reading entered by the user to account for the difference between the 

3,000 MWt reactor power used to produce the figure and the actual reactor power. 

Equation 1-4 of NUREG-1940 is used to calculate this scaled containment monitor value. This 

method of scaling the containment monitor reading based upon reactor power is not part of 

Method A.4 of NUREG/BR-0150. This scaling of the containment radiation monitor reading to 

reactor power has been deleted from RASCAL 4.3.1. The effect of deleting this scaling of the 

containment radiation monitor reading to reactor power has resulted in a source term that is 

more sensitive to differences in reactor designs in RASCAL 4.3.1.
2-24

RASCAL 4.3.1 also includes a revision to the procedure for interpolation/extrapolation of the 

damage ranges as a function of the time after reactor shutdown. Although the interpolation is 

not explicitly discussed in NUREG/BR-0150, it is based on the data in Figures A-5 through A-12

of NUREG/BR-0150.

The RASCAL 4.3 interpolation/extrapolation procedure is as follows:

• For times between shutdown and the containment radiation monitor reading of 

zero to 1 hour, the containment radiation monitor reading corresponding to 

1-percent damage is equal to the monitor reading shown in NUREG/BR-0150

figures for 1 hour.

• For times greater than 24 hours, the containment radiation monitor reading 

corresponding to 1-percent damage is equal to the containment radiation monitor 

reading shown in NUREG/BR-0150 figures for 24 hours.

• For times between 1 and 24 hours, the containment radiation monitor reading 

corresponding to 1-percent damage is estimated by linear interpolation between 

the monitor readings shown in NUREG/BR-0150 figures for 1 hour and 24 hours.

The solid blue line in Figure 2-13 shows the RASCAL 4.3 estimates of the 1-percent damage 

containment radiation monitor reading for a PWR reactor with cladding failure.

Figure 2-13 RASCAL estimates of 1-percent damage containment radiation monitor 

readings
2-25

As indicated in Figure 2-13, the RASCAL 4.3 interpolation/extrapolation procedure provides

reasonable estimates of the containment radiation monitor readings associated with 1-percent 

damage for times between shutdown and 24 hours. However as indicated in Figure 2-13, for 

times longer than 24 hours, the RASCAL 4.3 interpolation/extrapolation procedure is likely to 

overestimate the 1-percent damage containment radiation monitor reading. This overestimate 

occurs because the activity associated with one percent damage will continue to decrease 

because of radioactive decay.

RASCAL 4.3 calculates the percentage of damage associated with the actual containment 

radiation monitor reading by dividing actual containment radiation monitor reading by the 

estimated monitor reading for 1-percent core damage. Consequently, an overestimate of the 

1-percent damage containment radiation monitor reading will result in an underestimate of the 

reactor damage and ultimately potential radiation doses. Additionally, if this procedure were 

revised to include timeframes greater than 24 hours, the extrapolation of the linear decrease 

(Figure 2-13 dashed blue line) leads to a zero monitor reading at about 48 hours and unreal 

negative values for times greater than 48 hours. Therefore, the RASCAL 4.3 

interpolation/extrapolation procedure needed to be revised to adequately address scenarios in 

which the time between reactor shutdown and damage may be significantly longer than 

24 hours (e.g., Fukushima Units 2 and 3).

In RASCAL 4.3.1, an exponential decay function was fitted to the 1 hour and 24 hour 1-percent 

damage containment monitor readings as an alternative to the RASCAL 4.3 linear 

interpolation/extrapolation procedure. In this RASCAL 4.3.1 method, the 1 hour and 24 hour 

1-percent damage containment radiation monitor readings would be used to estimate the 

parameters a and b in Equation 2-1:

1% MMMM = aaee−bbbb (2-1)

where

1% MR = one percent damage containment monitor reading entered in (R/h)

t = time between reactor shutdown and the monitor reading (h), and

a and b = derived from the 1 hour and 24 hour 1-percent damage containment 

radiation monitor readings included with Method A-4 of NUREG/BR-0150 

(listed in Table 2-15).
2-26

Table 2-15 Containment radiation monitor reading interpolation/extrapolation 

parameter values

Reactor Type Path Condition a b

PWR no spray Normal Coolant 1.11E-02 1.00E-01

PWR no spray Spiked Coolant 5.48E-01 9.22E-02

PWR no spray Cladding Failure 6.08E+02 2.94E-02

PWR no spray Core Melt 5.86E+03 4.48E-02

PWR spray Normal Coolant 6.52E-03 8.25E-02

PWR spray Spiked Coolant 2.21E-02 1.00E-01

PWR spray Cladding Failure 1.41E+02 8.14E-02

PWR spray Core Melt 2.51E+03 8.86E-02

BWR Mark I&II dry well, no spray Normal Coolant 1.11E-03 1.00E-01

BWR Mark I&II dry well, no spray Spiked Coolant 1.00E-01 1.05E-01

BWR Mark I&II dry well, no spray Cladding Failure 1.16E+03 5.65E-02

BWR Mark I&II dry well, no spray Core Melt 1.05E+04 5.23E-02

BWR Mark I&II dry well with spray Normal Coolant 1.05E-04 5.23E-02

BWR Mark I&II dry well with spray Spiked Coolant 3.37E-03 1.18E-01

BWR Mark I&II dry well with spray Cladding Failure 2.74E+02 9.22E-02

BWR Mark I&II dry well with spray Core Melt 4.72E+03 9.36E-02

BWR Mark I&II wet well Normal Coolant 1.00E-05 0.00E+00

BWR Mark I&II wet well Spiked Coolant 1.00E-03 0.00E+00

BWR Mark I&II wet well Cladding Failure 1.09E+02 9.97E-02

BWR Mark I&II wet well Core Melt 1.98E+03 9.55E-02
2-27

Reactor Type Path Condition a b

BWR Mark III dry well, no spray Normal Coolant 4.56E-04 1.30E-01

BWR Mark III dry well, no spray Spiked Coolant 1.57E-02 1.15E-01

BWR Mark III dry well, no spray Cladding Failure 2.17E+02 1.33E-01

BWR Mark III dry well, no spray Core Melt 1.86E+03 3.53E-02

BWR Mark III dry well with spray Normal Coolant 3.18E-05 5.75E-02

BWR Mark III dry well with spray Spiked Coolant 4.38E-04 9.04E-02

BWR Mark III dry well with spray Cladding Failure 4.40E+01 7.10E-02

BWR Mark III dry well with spray Core Melt 7.62E+02 8.46E-02

BWR Mark III wet well Normal Coolant 1.05E-04 5.23E-02

BWR Mark III wet well Spiked Coolant 1.04E-03 3.98E-02

BWR Mark III wet well Cladding Failure 2.63E+02 9.04E-02

BWR Mark III wet well Core Melt 4.85E+03 7.51E-02

The RASCAL 4.3.1 curve, the orange line in Figure 2-13, demonstrates the predicted 1-percent

damage containment radiation monitor readings for cladding failure in a PWR. This procedure

provides 1-percent damage containment radiation monitor damage estimates that are about the 

same as the RASCAL 4.3 one percent damage containment radiation monitor damage

estimates for timeframes up to 24 hours. For timeframes greater than 24 hours, this procedure

provides 1-percent damage containment radiation monitor damage readings that continue to 

decrease, but do not become zero. Additionally, as indicated in Figure 2-13, the 1-percent 

damage containment radiation monitor readings at 48 hours is about twice as large as the 

RASCAL 4.3 method. Finally, if the RASCAL 4.3.1 method is extended to estimate the 

1-percent damage containment radiation monitor readings at 96 hours, the value increases by 

about a factor of 8 over the RASCAL 4.3 method.

It is important to note that containment radiation monitor readings may be used to track 

increasing reactor damage by entering a sequence of containment radiation monitor readings. 

However, RASCAL will not reduce the damage estimate if one or more of the containment 

radiation monitor readings indicate that damage is not as great as indicated by a previous 

containment radiation monitor reading. RASCAL always uses the highest damage estimate 

when damage is estimated from containment radiation monitor readings.
2-28

2.7 Effluent Release by Mixtures Source Term

There have not been any changes to the effluent release by mixtures source terms in 

RASCAL 4.3 or RASCAL 4.3.1. However, there have been a number of questions related to 

these methods that indicate that additional discussion is warranted.

When using this option in RASCAL to calculate a source term the user assumes full 

responsibility for specifying the monitored mixture source term. RASCAL assumes that the 

monitor mixture data are the independent measurements of noble gases, iodine concentrations, 

and particles. RASCAL assumes that the monitored mixture particles consist of cesium iodide 

(CsI) and, given this assumption, the activity in particles would be more than 99.5 percent if the 

monitor reading were taken in the first hour after reactor shutdown. Section 1.2.8 of 

NUREG-1940 discusses the particle radionuclide composition. RASCAL adds the iodine in the 

particles to the iodine release rate specified by the user to get a total iodine release for use in 

determining potential consequences in the environment. If the monitors that give the estimates 

of iodine and particle release rates are in the same release path, it is likely that the iodine in the 

particles contributes to both the iodine release rate and the particle release rate. As a result, 

these monitor readings are independent and the total iodine release would be likely to be 

overestimated by as much as a factor of two.

When the iodine and particle release rates are from a monitor or monitors in the same release 

path, it is appropriate to use one release rate or the other. If near-term consequences 

(e.g., doses from plume passage) are of most interest, the larger of the release rates should be 

used. This is because the iodine release is likely to be more important than the cesium release. 

If long-term consequences (e.g., future land use) are of most interest, the particle release rate 

should be used because the cesium releases are likely to be more important. When in doubt of 

which reading to use, the user should refer to the importance output described in Section 7 of 

this supplement to determine which monitor reading to use.

2.8 Effluent Release Rate and Concentrations by Radionuclide

Source Terms

There have not been any changes to the calculation of effluent release rate or concentration 

release rate methods of calculating source terms in RASCAL 4.3 or RASCAL 4.3.1. However, 

there have been a number of questions related to these methods that indicate that additional 

discussion is warranted.

When either of these two methods is selected, the user assumes full responsibility specifying 

the release rate. RASCAL neither evaluates the source term to determine whether it is 

reasonable or not, nor does the code adjust the source term for radioactive decay or daughter 

ingrowth, although decay and ingrowth are included in calculations once radionuclides are 

released to the atmosphere. RASCAL does not adjust the source term for depletion in the 

release path; therefore there is no reduction for deposition or filters.

If the source term entered by the user includes radionuclides that have daughters, which are not 

included in the source term entered by the user, RASCAL will add the daughter to the list of 
2-29

radionuclides released. The release rates for daughters added by RASCAL will be zero, but 

RASCAL will grow in the daughters in the environment. As a result, the daughters will be 

included in the importance calculation.

2.9 Spent Fuel and Fuel Cycle Facility Accidents

RASCAL 4.3 features an increase in the modularization of the computer code to enhance the 

maintainability of the code. This increase includes the separation of the calculation of the spent 

fuel pool (SFP) and fuel cycle facility source terms from the calculation of the reactor source 

terms. The RASCAL 4.3 code package now has three source term modules; one for calculating 

reactor source terms, one for calculating spent fuel source terms, and one for calculating fuelcycle facility source terms.

There are two components to the RASCAL 4.3 spent fuel accident source term calculation. The 

first is the calculation of the at-risk radionuclide inventory, and the second is the calculation of 

the portion of the at-risk radionuclide inventory that is released to the environment. The 

changes to the spent fuel accident source term calculation in RASCAL 4.3 are in the 

determination of the at-risk radionuclide inventory in the spent fuel. There have not been any 

significant changes in the calculation of the spent fuel or fuel cycle facility source terms related 

to release paths.

RASCAL 4.3 has two methods of estimating reactor fuel radionuclide inventories. The default 

method, based on average reactor power and end-of-life fuel burnup is described in 

Section 1.1.1 of NUREG-1940. A new method, referred to as the custom fuel option, was 

added in RASCAL 4.3. This method is described in detail in Section 5 of this supplement. The 

method tracks fuel batches through the reactor. Radionuclides build into the fuel in each as the 

batch is exposed and decay during reactor outages. When an outage occurs, each batch of fuel 

in the reactor has its own radionuclide inventory. The reactor core inventory is the sum of the 

inventories of the individual batches. The inventory in the assemblies in a batch of fully custom 

spent fuel is similar to the inventory in the assemblies calculated from the default inventory. The 

inventories of short-lived radionuclides (e.g., I-131) in assemblies of custom fuel at the end of its 

first or second cycle are similar to the inventories in assemblies using the default method 

because they are primarily functions of reactor power. In contrast, the assembly inventories of 

long-lived radionuclides (e.g., Cs-137) are significantly lower when the custom fuel option is 

used than they are when the assembly inventory is calculated using the default method. The 

difference in assembly inventories for long-lived radionuclides between the methods can be a 

factor of six or more.

RASCAL 4.3 revised the calculation of the at-risk inventory for fuel damaged underwater to 

include consideration of the fraction of fuel rods damaged in damaged fuel assemblies. 

RASCAL 4.3.1 corrects an error in the calculation of spent fuel inventories used when the spent 

fuel is uncovered. Also, the code has an enforced delay after reactor shutdown before spent 

fuel damage can occur. The delay is 1 day for BWRs and 3 days for PWRs. These delays 

account for the time from reactor shutdown until fuel is relocated into the SFP. RASAL 4.3 

included this time delay for the spent fuel damaged underwater option. RASCAL 4.3.1 adds this 

feature for the spent fuel uncovered option.
2-30

2.9.1 Drained Spent Fuel Pool (SFP)

The at-risk radionuclide inventory when the fuel in the SFP is uncovered is a function of the 

number, age, and burnup of the fuel assemblies in the pool at the time the pool is drained. 

RASCAL 4.3 calculates the at-risk radionuclide inventory starting with the fuel from the most 

recent refueling outage. If the SFP is drained during a refueling outage, there may be a full core 

of recently exposed fuel in the pool. If there is, then RASCAL 4.3 calculates the radionuclide

inventory for each batch of fuel in the core offload. Otherwise, RASCAL 4.3 only calculates the 

inventory for the oldest batch of fuel in the reactor at the last refueling. The radionuclide

inventories of fuel in the SFP from previous refueling are calculated assuming that one batch of 

fuel is removed from the reactor at each refueling and the time between refueling is equal to the 

plant refueling cycle.

There may also be fuel in the SFP from other reactors. This is likely to be the case when 

reactors share a common SFP. RASCAL 4.3 includes an option to add the inventory of 

radionuclides in spent fuel from a second reactor to the SFP at-risk radionuclide inventory in the 

event of a drained pool. The basic assumptions for the spent fuel from the other reactor are as 

follows:

1. The other reactor is the same type as the first reactor and is operated in the 

same manner (e.g., both reactors are PWRs, have the same fuel management, 

and have the same spent fuel burnup).

2. The spent fuel from the other reactor has full burnup.

3. The ages of the spent fuel batches increase from the youngest to oldest in 

increments of the fuel cycle length.

Under these assumptions, the radionuclide inventory in a batch of fuel at the other reactor at the 

time of shutdown will be the same as the inventory of full cycle fuel from the first reactor.

RASCAL 4.3 has two methods for calculating the at-risk inventories for uncovered SFP events. 

These two methods are the default fuel inventory and the custom fuel inventory method, which 

are both described in the paragraphs below.

Default Fuel Inventory - The following procedure is used by RASCAL 4.3 to calculate the at-risk 

inventory in a SFP for uncovered fuel events when the default core inventory method is 

selected.

1. The inventory of a batch of fuel is calculated from the core inventory by dividing 

the inventory of each radionuclide by the number of batches of fuel in a full core. 

RASCAL 4.3 assumes that there are 3 batches of fuel in the core when using the 

default fuel inventory.

2. If there is fuel from another reactor in the SFP, an initial batch inventory for the 

other reactor fuel is defined to be the same as the batch inventory calculated in 

step 1.
2-31

3. The reactor batch inventory defined in step 1 is decayed to account for the time 

delay between reactor shutdown and the time of the event.

4. The decayed reactor inventory is added to the SFP inventory. If there has been 

a full core offload at the time of the event, the inventory added to the SFP is 

increased to include all batches from the core. All batches are assumed to have 

the same inventory.

5. If there are batches of fuel in the SFP from the previous reactor refueling

outages, the batch inventory in step 3 is decayed to account for the refueling 

interval (typically 18 to 24 months).

6. Add the decayed inventory to the SFP inventory.

7. Repeat steps 5 and 6 for all batches of fuel from previous refueling outages of 

the reactor.

8. If there is fuel from another reactor in the SFP, decay the batch inventory from 

step 2 to account for the time between the event and the most recent refueling of 

the other reactor.

9. Add the decayed inventory for the other reactor fuel batch to the SFP inventory.

10. If there are additional batches of fuel from the other reactor, decay the batch 

inventory for the other reactor to account for the refueling interval of the other 

reactor. The refueling interval for the other reactor is assumed to be the same as 

the refueling interval for the primary reactor.

11. Add the decayed inventory for the other reactor fuel batch to the SFP inventory.

12. Repeat steps 10 and 11 until inventories for all of the other reactor fuel batches 

have been added to the SFP inventory.

When steps 1 through 12 have been completed, the RASCAL 4.3 calculated default fuel 

inventory is the SFP at-risk inventory for the event.

Custom Fuel Inventory - A reactor inventory base file must exist before the custom fuel 

inventory option can be selected. RASCAL 4.3 contains an additional tool to “Create Reactor 

Inventory Base File” on the RASCAL 4.3 main menu screen. This tool is used to enter the 

information on reactor operations and refueling that is needed for calculating custom fuel 

inventories.

The method for calculating the at-risk inventory for fuel uncovered events when the custom fuel 

option is selected is similar to the method used with default fuel inventories. The differences are 

primarily in the definition of the batch inventories for the most recent offload from the primary 

reactor. The following procedure is used by RASCAL 4.3 to calculate the at-risk inventory in a 

SFP for uncovered fuel events when the custom inventory option is selected:
2-32

1. The batch inventories for batches currently offloaded from the reactor are read 

from an inventory file (sfpool_inventory.tmp) created for the event. The file 

contains batch inventories for all fuel batches in core at the time of shutdown. All 

activities are in becquerel (Bq). If the full core offload option is selected, all 

batches of fuel are offloaded. If the full core offload option is not selected, only 

the batch of fully spent fuel is offloaded. The radionuclide activities in the 

offloaded batches are converted to curies (Ci) and added to the SFP activity. 

Note that the inventory for each batch of fuel will be different.

2. If there is fuel from previous refueling outages of the reactor in the SFP, an initial 

batch inventory for the previous fuel batches is defined to be the same as the 

inventory for the fully spent fuel most recently offloaded from the primary reactor.

3. If there is fuel from another reactor in the SFP, the activity inventory for a batch 

of fuel from the other reactor is defined to be the same as the inventory for the 

fully spent fuel from the primary reactor.

4. The activity in the SFP is decayed to account for the time between reactor 

shutdown and the event.

5. The previous fuel batch inventory from step 2 is decayed to account for the time 

between the next to last refueling and the time of the event and added to the SFP

inventory.

6. The previous fuel batch inventory from step 5 is decayed to account for the 

refueling cycle time and added to the SFP inventory.

7. Step 6 is repeated until the inventories for all previous batches of fuel have been 

added to the SFP.

8. Inventories for batches of fuel from the other reactor are added to the SFP in the 

same manner used in the default fuel inventory calculation.

When steps one through eight have been completed, the RASCAL 4.3 calculated custom fuel 

inventory is the SFP at-risk inventory for the event.

It is important for the user to understand that, the start time from when the fuel is uncovered to 

the time that runaway cladding oxidation (a.k.a., a zirconium fire) (if one occurs) is highly 

dependent on the age of the fuel, its storage configuration relative to other ‘hot’ fuel, the size 

and location of any leakage in the SFP, etc. RASCAL users should select parameter values for 

these calculations in consultation with subject matter experts. Additionally, RASCAL users 

should realize that several RASCAL cases may need to be run in order to produce a reasonable 

range of possible outcomes.

Under very challenging conditions (e.g., co-located, recently offloaded fuel with a large leak), 

the time can be on the order of a couple of hours. While, under other conditions, the time can 

be very long (e.g., days) or even infinite (in the case of the fuel being air cooled). Some sample 

times can be taken from the SFP study documented in the enclosure to SECY-13-0112, 
2-33

“Consequence Study of a Beyond-Design-Basis Earthquake Affecting the Spent Fuel Pool for a 

U.S. Mark 1 Boiling-Water Reactor” [10]. Specifically, Table 27 presents Methods for Estimation 

of Leakages and Consequences of Releases (MELCOR)-derived timings for a BWR Mark 1 

SFP with fuel in a 1x4 pattern, for several different combinations of time since discharge, 

leakage size, and mitigation effects. The delta-times from the start of fuel becoming uncovered 

to the time the hottest assemblies experience a gap release (a precursor to potential runaway 

cladding oxidation) range from 3 to 22 hours. Table 50 of that study provides additional times 

for more limiting conditions associated with hot fuel being co-located, but the same general 

range of timings applies.

In the unlikely event that a runaway cladding oxidation occurs, RASCAL 4.3 assumes that if the 

runaway cladding oxidation occurs; radioactive materials may be released from the fuel using 

the release fractions in Section 5 (Table 5-1). The model assumes that clad burning will not 

start earlier than 2 hours after the fuel is uncovered and that it takes 24 hours for the releases 

specified in Section 5 (Table 5.1) for clad burning to occur. Thus, 1/96 of the total release 

fraction listed in Section 5 (Table 5-1) will occur during each 15-minute time step. The release 

from the fuel terminates when the fuel is recovered or is otherwise cooled by sprays or steam 

cooling. Additionally, there is no reduction factor other than radioactive decay, which results in 

a conservative estimate of accident consequences.

2.9.2 Damaged Fuel

The at-risk radionuclide inventory in a damaged spent fuel accident is limited to the radionuclide

inventories in the damaged fuel assemblies. RASCAL 4.3 calculates the at-risk radionuclide

inventory in the damaged fuel assemblies based on the burnup of the damaged fuel assemblies 

and the time since the irradiation of the fuel. Similar to the SFP uncovered event, RASCAL 4.3 

has two methods for calculating the at-risk inventories for the damaged spent fuel accidents. 

These two methods are the default fuel inventory and the custom fuel inventory method, which 

are both described in the paragraphs below.

In each method, the default time since exposure is based on technical specifications for each 

reactor type related to the minimum time between shutdown and removing the reactor head. 

The actual time between reactor shutdown and fuel damage is likely to be longer than the 

minimum and may be significantly longer if the damage occurs during reracking of the fuel or 

movement of fuel assemblies to dry cask storage.

Default Fuel Inventory - The following procedure is used by RASCAL 4.3 to calculate the at-risk 

inventory in fuel-damaged underwater events when the default core inventory method is 

selected. This method is based on extremely limited data; therefore, this method provides 

uncertain input to consequence assessments.

1. RASCAL calculates the inventory for a fuel assembly from, the normalized core 

inventory in Table 1-1 of NUREG-1940 adjusted for burnup as described in 

NUREG-1940 Section 1.1.1, the average reactor power, and the number of fuel 

assemblies in core. The burnup, average reactor power and the number of 

assemblies in core are obtained from the RASCAL facility database. RASCAL 
2-34

users may adjust the reactor power and burnup when the plant is selected in the 

user interface.

2. The assembly inventory is multiplied by the number of damaged assemblies and 

the fraction of rods damaged (new in RASCAL 4.3.1) to obtain the at-risk 

inventory for the damaged fuel event. The number of damaged assemblies and 

fraction of rod damaged are specified by users in the Source Term Pool 

Storage-Damaged Assembly Underwater data entry screen in the user interface.

3. The at-risk inventory is adjusted for delay between reactor shutdown and fuel 

damage.

This procedure assumes that all damaged fuel assemblies have the same inventory, both 

initially and after decay and the inventory is an end-of-cycle, core average inventory. These 

assumptions can lead to significant errors in the at-risk inventory if the fuel assemblies are from 

different fuel batches within the same offload, or they are from batches off loaded from different 

refueling outages. There can also be a significant error if damage only occurs to a single fuel 

assembly and the assembly is from a fuel batch that has not been exposed for three full cycles. 

In this latter case, the at-risk inventory of long-lived isotopes such as cesium-137 (Cs-137) and 

strontium-90 (Sr-90) can be overestimated by a factor of five or more.

Custom Fuel Inventory - A reactor inventory base file must exist before the custom fuel 

inventory option can be selected. The following procedure is used to calculate the at-risk 

inventory in fuel-damaged underwater events with custom fuel inventories. The method is 

based on limited data; therefore, this method provides uncertain input to consequence

assessments.

1. RASCAL reads a batch inventory from an inventory file (sfpool_inventory.tmp) 

created for the event and converts the inventory from Bq to Ci. The file contains 

batch inventories for all batches in the reactor at shutdown. The inventory that is 

read is determined by the “number of days fuel assemblies were exposed in the 

reactor” which is entered by the user in the Source Term Pool Storage-Damaged 

Assembly Underwater data entry screen in the user interface.

2. An assembly inventory is created by dividing the batch inventory by the number 

of assemblies in a batch (number of assemblies in core/number of batches in 

core).

3. An initial at-risk inventory is calculated from the assembly inventory by 

multiplying the assembly inventory by the number of assemblies damaged and 

the fraction of rods damaged.

4. The initial at-risk inventory is adjusted to account for decay between the time of 

reactor shutdown and time of the fuel damage event.

This procedure assumes that all damaged fuel assemblies have the same inventory, both 

initially and after decay. It does not assume that the assemblies have a core average inventory 
2-35

or that the assemblies have been exposed for more than one cycle. These assumptions can 

lead to significant errors in the at-risk inventory if the fuel assemblies are from different fuel 

batches within the same offload, or they are from batches offloaded from different refueling 

outages.

2.10 Uranium Hexafluoride (UF6) Source Terms

There have not been any changes to the calculation of uranium hexafluoride (UF6) source terms 

in RASCAL 4.3 or RASCAL 4.3.1. However, there have been questions related to these 

calculation methods that indicate that additional discussion is warranted.

Specifically, the questions pertain to several cases in which the UF6 release rate inside a 

building was varied without what was considered an appropriate variation in the RASCAL 

results. The RASCAL results did not change as expected because the total UF6 inventory 

specified by the RASCAL user was of a sufficiently small amount that the UF6 release to the 

building terminated well before the release from the building (to the environment) terminated. 

All of the values in the Maximum Dose Values table for UF6 releases are values based on 

integration over the full calculation period. These maximum values in the table reflect the total 

release from the building (to the environment) not the UF6 release rate into the building. In 

these situations the total UF6 releases to the building and the total uranyl fluoride (UO2F2) and 

hydrogen fluoride (HF) releases from the building are the same for all practical purposes. 

Conversely, if the total inventory specified by the RASCAL user had been much larger or much 

smaller, the RASCAL results would have changed as expected.

3-1

3.0 TRANSPORT, DISPERSION, AND DOSE CALCULATIONS

This section describes the changes to the atmospheric transport and dispersion calculations 

and the dose calculations implemented in RASCAL 4.3. RASCAL 4.3 adds a fourth model 

domain for puff (far field) dispersion and deposition calculations. RASCAL 4.3.1 adds two new 

output files, and corrects an error in calculation of depletion in the plume (near field) deposition 

calculations.

3.1 Transport and Dispersion Calculations

The general features of the atmospheric transport and dispersion calculations and dose 

calculations have not changed in RASCAL 4.3. However, in response to staff requests arising 

from the Fukushima Daiichi accident, RASCAL 4.3 has added a fourth Cartesian computational 

grid which increases the RASCAL 4.3 domain from a 50-mile (mi) (80 kilometer (km)) radius to a 

100-mi (160 km) radius. The 100-mi grid has 5-mi (8 km) spacing between computational 

nodes. The default close-in polar grid associated with the 100-mi Cartesian grid extends to 

10 mi just as it does with the 50-mi Cartesian grid.

In conjunction with the addition of the 100-mi grid, RASCAL 4.3 includes updated topographic 

and surface roughness data files for all grids. The data in the topographic data files, which are 

used in modification of wind fields, were extracted from U.S. Geological Survey digital elevation 

data. The terrain elevation values in the file are spatial averages of elevations at nine locations 

within 1 mi of the nominal grid location. The data in the surface roughness, which are used in 

the modification of wind fields and in the transport and dispersion calculations, are based on 

land use data extracted from the National Land Cover Data set. The surface roughness lengths 

were estimated from land use data. The surface roughness estimates are also 9-point spatial 

averages centered on the node position with about 100 ft spacing between points. The surface 

roughness length for overwater locations have been set to a value of 0.001 meters (m). The 

topographic and surface roughness files are described more fully in Section 4.

3.1.1 Model Grid Dose Consistency

Figure 3-1 shows the consistency in dose calculations for the eight model grids (4 polar and 

4 Cartesian). The calculations were made with a cardinal wind direction (90 degrees, 

180 degrees, 270 degrees, or 360 degrees), a 4 mi/h wind speed and D class stability.

A cardinal wind direction should be used when testing model calculations with a constant wind 

direction because the centerline of the plume passes directly over computational nodes in these 

directions. When an off-cardinal wind direction is used, the plume centerline does not 

necessarily pass directly over the computational nodes on the Cartesian grid. In fact, for most 

wind directions, the plume centerline passes between Cartesian grid nodes. Near the release 

point where the plume is narrow, the grid spacing is large compared to the plume width. As a 

result, the doses shown on the Maximum Dose Values table and in the Detailed Results for the 

Cartesian grid may be significantly lower than centerline doses. These points are illustrated in 

Figure 3-2.
3-2

The only difference in the RASCAL 4.3 input values for the calculations leading to Figures 3-1 

and 3-2 is the wind direction. A cardinal wind direction was used for the calculations for 

Figure 3-1 and a wind direction 10 degrees off a cardinal direction was used for the calculations 

for Figure 3-2. Note that the largest deviation in doses is for doses calculated on the Cartesian 

grid at distances less than the minimum distance shown for the Cartesian grid in the Maximum 

Dose Values table. Note also that the doses are correct for the nodes but the nodes are not on 

the plume centerline.

Figure 3-1 Dose consistency among the eight RASCAL 4.3 computational grids
3-3

Figure 3-2 Maximum doses as a function of distance for a 10° off-cardinal wind 

direction

Figure 3-3 illustrates plume centerlines relative to Cartesian grid node locations for nodes at 

nominal distances of 1 and 10 mi on the 10-mi grid.

Figure 3-3 Cartesian node locations relative to plume centerlines

With a wind direction of 270 degrees (west wind), a plume centerline would pass directly over 

nodes at both nominal distances at 90 degrees (east). With a wind direction of 280 degrees, the 

plume centerline would pass between nodes at both distances.

Table 3-1 lists the actual direction and distance from the release point for the nodes shown in 

Figure 3-3. At the 1-mi distance, there is a 10-degree separation between the plume centerline 
3-4

(100 degrees) and the closest computational node; at the 10-mi distance the separation is only 

1.3 degrees. As a result, the dose calculated for the node closest to the plume centerline at 

1 mi is about a factor of 20 lower than the centerline dose, while the dose calculated for the 

node closest to the plume centerline at 10 mi is only about 15 percent lower that the centerline 

dose.

Table 3-1 Cartesian grid node positions at nominal distance of 1 and 10 miles

Direction Distance (mi) Direction Distance

090° 1.0 090° 10.0

116.6° 1.12 092.9° 10.01

135° 1.41 095.7° 10.05

098.5° 10.11

101.3° 10.20

As mentioned above, the doses calculated for the nodes are correct; they are just not on the 

plume centerline. When real meteorological data are used and the wind direction varies in time 

and space, the footprint of the plume is spread out and the centerline/off-centerline distinction 

becomes less significant. Ultimately, over a period of hours, the doses calculated for the 

Cartesian grid give a better picture of the plume footprint than the doses on the polar (close-in) 

grid. The limitations associated with the node spacing can be minimized by using the 

appropriate grid. For example, for doses at distances of about 10 mi, use the 10-mi grid or the 

25-mi grid. Do not use the doses from the 100-mi grid. The doses calculated for the 100-mi 

grid are correct, but they do not provide the optimum spatial resolution in doses near 10 mi.

3.1.2 Plume Characterization Output Files

The two additional output files created by RASCAL 4.3.1 are Plume_Char.tmp and 

Puff_Char.tmp. These files contain intermediate computational results related to the plume. 

The information may be used to check model dispersion and dose calculations, or it may be 

used to track plume positions with time.

Plume_Char.tmp contains nine lines for each time step. The first of these lines gives the time 

(hours (h)) since the beginning of release, the release height (m), the wind direction (10

degrees) and wind speed (meters per second (m/s)), stability class, mixing layer depth (m), 

precipitation class, turbulence parameters (m/s), deposition velocities (m/s), and washout 

coefficients (1/h). These parameters apply to all arcs on the polar grid. The next eight lines 

give the plume characteristics. There is one line for each arc. Each line has the following 

information:

• arc number
3-5

• distance (m)

• plume height (m)

• horizontal and vertical dispersion parameters (m)

• vertical reflection term

• fraction of iodine remaining in the plume

• fraction of other depositing material remaining in the plume

In RASCAL, puff positions are tracked on a 21 node by 21 node Cartesian grid. The 

Puff_Char.tmp file starts with a line that gives the node spacing for the domain in use, and the 

release point location. In RASCAL 4.3.1, the release location is always 11.0. The puff 

information is presented in blocks by time. The first line of each block is the elapsed time in

hours since the beginning of the release to the atmosphere. Blocks of data are written at 

15 minute intervals. The remaining lines in each block give the puff information starting with the 

most recently released puff and continuing in order of increasing puff age. The order of puff 

information is:

• puff number (the youngest puff has the largest number)

• puff age (h)

• puff location (x, y) (Puffs are tracked after they leave the domain and when the 

puff gets far enough out of the domain, the puff is deleted. The remaining puffs 

are not renumbered as puffs are deleted)

• plume height (m)

• horizontal and vertical dispersion parameters (m)

• vertical reflection term (Note that this term is not the same term used for plumes

and it is a factor of two less that the plume vertical reflection term)

• deposition velocity for iodine (m/s)

• deposition velocity for other depositing material (m/s)

• washout coefficient for iodine (1/h)

• washout coefficient for other depositing material (1/h)

• fraction of iodine remaining in the puff

• fraction of other depositing material remaining in the puff
3-6

3.1.3 Plume Depletion Calculation Correction

The new plume characteristics file revealed a variability in plume depletion fractions that was 

not readily apparent in the normal plume model output. This evaluation of the variability led to

the discovery of coding error in calculation of plume depletion associated with dry deposition. 

The error resulted in small overestimates of dry deposition and underestimates of material 

remaining in the plume. Figure 3-4 shows an example of the fraction of iodine remaining in the 

plume model in RASCAL 4.3 (original code – red curve) and the revised model in RASCAL 

4.3.1 (revised code – blue curve). In the RASCAL 4.3 code, approximately 89 percent of the 

iodine would remain in the plume at 10 km (6.2); 11 percent of the iodine would have deposited 

by 10 km. In the RASCAL 4.3.1 revised code, about 92 percent of the iodine remains in the 

plume at 10 km; only about 8 percent of the iodine would deposit by 10 km.

Figure 3-4 Iodine depletion due to dry deposition in RASCAL 4.3 versus RASCAL 4.3.1

3.2 Child Thyroid Dose Calculations

The U.S. Environmental Protection Agency (EPA) has released a draft Protective Action Guide 

(PAG) manual for interim use and public comment [11]. Section 2.3 of the draft PAG manual 

considers the protective actions during the early phases of a radiological incident. Specifically,

it deals with the administration of potassium iodide (KI). Table of 2-1 of the PAG manual 

suggests administration of KI when the projected dose to the child thyroid from exposure to 

iodine exceeds 5 rem. Calculation of the child thyroid dose has been added to RASCAL 4.3 to 

allow evaluation of recommendations for administration of KI. The draft PAG manual also 
3-7

discusses U.S. Food and Drug Administration (FDA) recommendations for administration of KI 

to adults [12] and [13]. The child thyroid doses are calculated when the Federal Guidance 

Report Number 13 (FGR 13) [14] International Commission on Radiological Protection 

(ICRP) 72 dose coefficients are selected. The child thyroid dose is not calculated when FGR 11 

[15] ICRP-26/30 dose coefficients are selected.

RASCAL 4.3 child thyroid dose coefficients are based on the dose coefficients for a 1-year old 

child in file FGR13INH.HDB included with FGR13PAK [16]. For consistent treatment of iodine 

the child dose coefficients in RASCAL 4.3 are weighted averages assuming that of the iodine in 

the atmosphere 25 percent is associated with particles, 30 percent is associated with reactive 

gases (e.g., iodine (I2)), and 45 percent is associated with nonreactive gases (e.g., methyl iodide 

(CH3I)).

The child thyroid doses calculated by RASCAL 4.3 in the Source Term to Dose (STDose) and 

Field Measurement to Dose modules are based only on exposure to iodine isotopes for 

consistency with the EPA PAG definition. In contrast, the adult thyroid doses calculated by 

RASCAL are based on exposure to all radionuclides.

As mentioned above, FDA recommendations for administration of KI are based on age. The 

only factors in the thyroid dose calculation that are functions of age are the breathing rate and 

dose coefficients. Table 3-2 lists the light-activity breathing rates and the composite thyroid 

dose coefficients for the iodine isotopes that are typically associated with reactor accidents.

Table 3-2 Breathing rates and dose coefficients for use in estimating thyroid doses 

from iodine isotopes inhaled during plume passage

Age

Breathing 

Rate Dose Coefficients (Sv/Bq)

(m/s) I-131 I-132 I-133 I-134 I-135

100 d 5.28E-05 2.52E-06 3.40E-08 6.78E-07 7.02E-09 1.39E-07

1 y 9.72E-05 2.47E-06 3.03E-08 6.12E-07 6.24E-09 1.24E-07

5 y 1.58E-04 1.40E-06 1.57E-08 3.18E-07 3.23E-09 6.43E-08

10 y 3.11E-04 7.10E-07 7.02E-09 1.42E-07 1.44E-09 2.88E-08

15 y 3.83E-04 4.59E-07 4.53E-09 9.09E-08 9.30E-10 1.85E-08

20 y 4.17E-04 2.93E-07 2.87E-09 5.70E-08 5.90E-10 1.17E-08

The values in Table 3-2 may be used to scale the RASCAL 4.3 dose estimates for a 1-year old 

child to estimates of thyroid doses from iodine for children of other ages and for adults (20 yr). 

Figure 3-5, which is based on the data in Table 3-2, shows appropriate scaling factors. 

According to the FDA, there is generally little value in use of KI for adults over the age of 40.
3-8

Figure 3-5 Scaling factors (thyroid dose/child thyroid dose) for adjusting RASCAL 4.3 

child

3.3 Ingestion Dose Coefficients

Ingestion dose coefficients have been added to the radionuclide database in RASCAL 4.3. The 

database includes ingestion dose coefficients from both FGR No 11 and FGR No.13. The 

FGR 13 ingestion dose coefficients are for adults. These dose coefficients are not used in any 

dose calculations in RASCAL 4.3. They are used to establish relative importance of 

radionuclides in the source term to potential doses via the food pathway. The importance model 

and calculation are discussed in Section 7.

3.4 Field Team Dose Estimates

During the course of an event, field teams may be exposed to the plume for short durations.

RASCAL 4.2 included a calculation that; (1) estimated external and total doses for field teams 

prior to exposure, and (2) provided conversion factors that may be used to estimate total dose 

from the readings of direct reading dosimeters after exposure.

The dose estimates and conversion factors are found in the detailed results portion of the 

RASCAL output when either the External Gamma Exposure Rate or the External Gamma + 

Beta Exposure Rate result type is selected. Generally, the dose estimates and conversion 

factors should be obtained from the Cartesian grid to ensure that they appropriately account for 

the plume transit time. To view the dose and conversion factor estimates, place the cursor over 

the field team location on a dose footprint and left click to display the dose rate versus time plot 

0.0

0.2

0.4

0.6

0.8

1.0

1.2

100 d 1 yr 5 yr 10 yr 15 yr 20 yr

Thyroid Dose / Child Thyroid Dose

Age

I-131

I-132

I-133

I-134

I-135
3-9

for the location (Figure 3-6). The doses and conversion factors are found in the table on the 

right side of the screen.

Figure 3-6 RASCAL detailed results for dose and conversion factor estimates

3.4.1 Projected Direct Reading Dosimeter (DRD) Reading and Doses

The estimated direct reading dosimeter (DRD) reading for a field team at the time and location 

selected is based on the gamma or gamma + beta exposure rates assuming a 15-minute

exposure period. The calculation of these exposure rates is discussed in Section 4 of NUREG1940.

The estimated total external and internal dose at the time and location selected for a field team 

that has not taken KI is the sum of the ground shine, cloud shine, and inhalation CEDE 

assuming a 15 minute exposure period. Calculation of these dose rates are described in 

Sections 4.9.1, 4.9.2 and 4.9.3 of NUREG-1940, “RASCAL 4: Description of Models and 

Methods.”

The estimated total dose for a field team that has taken KI is lower than the estimated total 

because KI effectively blocks iodine absorption by the thyroid. RASCAL 4.3 calculated the 

correction to the total dose to account for the effect of KI as

∆DDKKKK = 0.9 × 0.03 × DD hyy (3-1)

where
3-10

∆DKI = dose reduction due to administration of KI (mrem),

0.9 = effectiveness of KI in reducing the thyroid dose,

0.03 = thyroid weighting factor in calculation of the inhalation CEDE, and

Dthy = thyroid dose (mrem).

Calculation of the thyroid dose is discussed in Section 4.9.1 of NUREG-1940. The total dose 

estimate for field teams that have taken KI is then calculated by subtracting the KI dose 

reduction from the dose estimate for field teams that did not take KI.

As stated above, the projected DRD readings and doses are for a 15-minute exposure period. If 

the expected duration of the field team exposure is less than or greater than 15 minutes, the 

projected DRD reading and doses may be adjusted using the ratio of the expected exposure 

duration to 15 minutes. However, if the expected exposure duration is significantly longer than 

15 minutes, this adjustment procedure should not be used. Instead, the DRD readings and 

doses should be estimated by adding the projected DRD readings and doses for successive 15-

minute periods within the exposure period.

3.4.2 Post Exposure Dose Estimates

The projected DRD readings and doses discussed above are all dependent on the accuracy of 

the source term, release path, meteorological conditions, plume location and transit time, and 

field team exposure time and location. There is a reasonable likelihood that actual DRD 

readings and doses will differ from the projected values. As soon as DRD readings are 

available they should be used instead of the projected values. RASCAL 4.3 estimates 

conversion factors (CFs) that may be used to estimate total dose commitment (external dose +

internal dose) from DRD readings. The CF is found at the bottom of the table that presents the 

projected DRD readings and doses described above.

There are two CFs, one for field teams that have not taken KI and the other for field teams that 

have taken KI. For field teams that have not taken KI, the CF is calculated as

CCCC = DDgggg + DDcc + DDiiiih

DD DDpp

(3-2)

where

CF = CF for field teams that have not taken KI (mrem/mR),

Dgs = projected ground shine dose (mrem),

Dcs = projected cloud shine dose (mrem),

Dinh = projected inhalation CEDE (mrem), and

DRDp = projected DRD reading (mR).

Given the actual DRD reading and the CF, the total dose may be estimated by the user as:

DD = CCCC × DD DDaa (3-3)

where
3-11

D = the estimated external + internal dose (mrem)

DRDa = the actual dosimeter reading (mR)

The dose calculation for field teams that have taken KI is similar to the calculation for teams that 

have not taken KI. The first step is to calculate a CF. In this case, RASCAL 4.3 calculates the 

conversion factor as

CCCCKKKK = DDgggg + DDcc + DDiiiih − ∆DDKKKK

DD DDpp

(3-4)

where

CFKI = CF for field teams that have taken KI (mrem/mR), and

∆DKI = dose reduction associated with KI (mrem).

Given the actual DRD reading and this CF, the total dose may be estimated by the user as

DDKKKK = CCCCKKKK × DD DDaa (3-5)

where

DKI = estimated external + internal dose (mrem) for those who have taken KI.

Doses calculated in this manner will be consistent with the DRD reading. However, the doses 

may still be in error because the CF is based on the radionuclide mix assumed in calculating the 

projected DRD readings and doses.

Table 3-3 shows an example of the variation in the CFs as a function of time after the beginning 

of release and distance from release point at the center of the plume. The example is based on 

a LOCA with containment bypass. The variations in CFs seen in the table are the result of 

variation in source term radionuclide mix with time, the transit time from the release point to the 

receptor, and the changes in radionuclide mix in the plume caused by decay and deposition 

between the release point and the receptor. The variation of the conversion factors across the 

plume at any given time and distance is small compared to the variations with time and 

distance. There is no need to correct the doses estimated from actual DRD readings for 

exposure time unless the exposure time significantly exceeds 15 minutes. If the exposure time 

significantly exceeds 15 minutes, consideration should be given to calculating conversion 

factors for successive 15 minute intervals during the exposure period and using an average 

conversion factor to estimate doses. It may be appropriate to weight the interval conversion 

factors by the projected DRD for the interval in the averaging process.
3-12

Table 3-3 Conversion factor variation with time and distance from the release point

Conversion Factors

(CF)

Time after 

LOCA (h)

Distance 

(mi) Without KI With KI

2

1.0 1.0 1.0

2.0 1.0 1.0

3.0 1.0 1.0

5.0 1.0 1.0

10.0 1.1 1.1

3

1.0 1.6 1.3

2.0 1.5 1.3

3.0 1.3 1.2

5.0 1.1 1.0

10.0 1.1 1.0

4

1.0 2.1 1.7

2.0 2.2 1.8

3.0 2.4 1.8

5.0 2.3 1.7

10.0 1.1 1.0

8

1.0 2.2 1.7

2.0 2.6 2.0

3.0 3.2 2.4

5.0 4.3 3.1

10.0 5.3 3.7
4-1

4.0 METEOROLOGICAL DATA ACQUISITION AND PROCESSING

A new utility to download meteorology data from the Internet, called MetFetch, has been 

developed to allow RASCAL 4.3 users to process and download model-ready observations 

(*.obs) and forecasts (*.fcs) from the Internet for direct use in a RASCAL 4.3 calculation. This 

section describes the MetFetch program, the meteorological data available to download, and 

the topographic data that are used in RASCAL 4.3 to process the meteorological data.

4.1 Meteorological Data

Observations and forecasts are available for approximately 2500 station locations and include 

primary National Weather Service (NWS) and Federal Aviation Administration (FAA) stations 

located throughout the United States and its territories. Observations are obtained through the 

NWS Western Regional Headquarters Web server; forecasts are obtained through the NWS 

National Digital Forecast Database (NDFD) [17]. Since MetFetch downloads observations and 

forecasts from remote servers, an Internet connection is required to use this utility.

4.2 Topographic Data

RASCAL gridded terrain files (*.top) have been derived for each site in the RASCAL facility 

database using elevation data from a Global Digital Elevation Model (GTOPO30) file [18].

A RASCAL terrain *.top file contains four terrain grids with 22 points in the X and Y directions, at

grid spacings of 10.0, 5.0, 2.5, and 1.0 mi, respectively.

GTOPO30 is a digital elevation model (DEM) covering the full extent of the globe, with a native 

horizontal resolution of 30-arc seconds (approximately 1 kilometer); these data were developed 

by the U.S. Geological Survey’s Earth Resources Observation and Science (EROS) Data 

Center in 1996 using a variety of data sources. Figure 4-1 is a raster image of the GTOPO30 

file used to derive site terrain files for RASCAL. Darker shades of gray represent lower terrain

and lighter shades of gray represent higher terrain. Oceans are colored white.
4-2

Figure 4-1 Raster image of the GTOPO30 file used to derive site terrain elevation files 

(*.top) for RASCAL 4.3

4.3 Surface Roughness Data

RASCAL gridded surface roughness files (*.gz0) have been derived for each site in the 

RASCAL facility database using land use/land cover data from the National Land Cover Dataset 

1992 (NLCD1992) file [19]. A RASCAL roughness *.gz0 file contains four surface roughness 

grids with 21 points in the X and Y directions, at grid spacings of 10.0, 5.0, 2.5, and 1.0 mi, 

respectively.

The NLCD1992 file utilizes a 21-class land cover classification scheme that has been applied to 

the continental United States at a spatial resolution of 30 m. NLCD92 is based primarily on the 

classification of Landsat Thematic Mapper circa 1990’s satellite data. Other ancillary data 

sources used to generate these data included topography, census, and agricultural statistics, 

soil characteristics, and other types of land cover and wetland maps.

A lookup table from the EPA AERSURFACE User’s Guide [20] is then used to convert the 

21 land-cover codes to corresponding surface roughness values. Figure 4-2 is a raster image 

of the NLCD1992 file used to derive site surface roughness values for RASCAL. Each color 

represents an NLCD class code and has a corresponding surface roughness value.
4-3

Figure 4-2 Raster image of the NLCD1992 file used to derive site surface roughness 

files (*.gz0) for RASCAL 4.3

5-1

5.0 UPDATED REACTOR CORE AND COOLANT INVENTORY 

MODELS

RASCAL 4.2 and earlier versions of RASCAL have used in their source term calculations 

reactor core inventories based on an assumed power level of 3,479 MWt and fuel burnup of 

38,585 megawatt days per metric ton of uranium (MWd/MTU). Similarly, earlier versions of 

RASCAL used tabled values of reactor coolant radionuclide concentrations which were scaled 

up and down based on reactor power.

RASCAL 4.3 uses these same assumptions for its default reactor radionuclide inventories.

However, RASCAL 4.3 also has an option to estimate reactor core and coolant radionuclide

inventories at the time of an accident using reactor specific information on reactor operations 

prior to the accident. This option is implemented in a new feature that is bundled with RASCAL 

4.3 and may be called from the RASCAL 4.3 user interface. This section describes the updated 

inventory models and utility code implementing them. Sections 5.1 through 5.4 deal with the 

reactor core inventory; Section 5.5 deals with the reactor coolant inventory. Section 5.6 

addresses the input to and output from the code, Rx_Inventory_S, which implements the 

updated RASCAL 4.3 inventory model.

5.1 Reactor Core Activity Model

Production rate P’i of a radionuclide i [(Bq/MWt)/d] is a function of reactor type (BWR or PWR)

and is independent of burnup. This is a reasonably good assumption for most radionuclides. 

Production of the actinides increases with burnup, so RASCAL assumes a production rate that 

is an average for peak rod burnup of 42 Gigawatt day/metric ton of uranium (GWd/MTU) for a 

BWR and 62 GWd/MTU for a PWR.

Given constant reactor power, the rate of change of activity of a radionuclide as a function of 

time is given by

ddAAii(tt)

dd = PPii

′ − λλiiAAii( ) (5-1)

where

Ai(t) = total core activity of radionuclide i in Bq/MWt at time t

P’I = production rate of radionuclide i in (Bq/MWt)/d in the core

λi = decay constant for radionuclide i

Solving this equation, the activity at time t is given by:

AAii (tt) = PPii

′

λλii

× [1.0 − exp(−λλiitt)] (5-2)

Routine reactor operation involves alternating periods when the reactor is at power and when it 

is shutdown for refueling or maintenance. While the reactor is shutdown, the activity in the core 

decreases due to radioactive decay. During refueling a portion of the irradiated fuel, typically 

one-third, is replaced by fresh fuel which has no fission product activity. The fission product 

activity in the remaining fuel decays during the refueling outage, so that there is less activity 
5-2

when the reactor restarts than there was when it shutdown. As a result, the activity of each 

radionuclide at restart cannot be calculated directly from Equation (5-2). The activity remaining 

at the time of restart is calculated as:

AAii(ttrr ) = AAii(tt ss)exp[−λλii(ttrr − tt )] (5-3)

where

trs = time of restart,

tsd = time of shutdown.

To calculate activity Ai(trs) after restart, it is necessary to first determine an effective reactor 

operation exposure time that would result in Ai

(trs). The effective reactor operation time, teffi, is 

calculated as:

tteeeeee = − 1

λλii

ln �1 − AAii(ttrr )λλii

PPii

� (5-4)

Finally, the activity during the second and subsequent fuel cycles is calculated using Equation

(5-2) replacing t, the time since the start of initial exposure, with;

ttii = tteeeeee + (tt − ttrr ) (5-5)

Note that after the initial exposure period, the time used for the calculation of activity becomes a 

function of the radionuclide.

Figure 5-1 shows the activity for selected radionuclides in a fuel batch as a function of time from 

initial exposure to final discharge for a typical reactor with a 540 d fuel cycle assuming a 30 d 

refueling outage during which one-third of the fuel in the core is replaced. Table 5-1 gives the

production and decay parameters for the selected radionuclides. The production parameters 

are core-average numbers. For individual fuel batches, the parameters must be divided by the 

number of cycles that fuel remains in the core.

The iodine-131 (I-131) and I-133 activities in Figure 5-1 clearly show the refueling outages. 

These radionuclides also show that the activity level for short-lived radionuclides is reasonably 

constant throughout the fuel life. The activity decreases significantly during refueling outages, 

but quickly returns to the equilibrium level when the reactor restarts. In contrast, the activities of 

long-lived radionuclides such as cesium-137 (Cs-137) and plutonium (Pu-240) continue to 

increase throughout the fuel life. The activity does not decrease significantly during refueling 

outages and does not reach equilibrium. Assuming three-cycle operation for a typical reactor, 

Figure 5-2 shows the variation in core activity during a cycle for a mature reactor core (core with 

fuel in first, second, and third cycles). For short-lived radionuclides, the activity increases from 

zero to equilibrium, while for long-lived radionuclides, the activity level increases by a factor of 

two from beginning of cycle to end of cycle. About one half of the core activity of long-lived 

isotopes is in the spent fuel at the end of the cycle.
5-3

Figure 5-1 Radionuclide activity as a function of exposure time in fuel batch

Table 5-1 Production and decay parameters for selected radionuclides

Radionuclide Half Life Decay Constant Production Rate

(d) (1/d) (Bq/MWt)/d

I-133 8.67E-01 7.99E-01 1.62E+15

I-131 8.04E+00 8.62E-02 8.46E+13

Sr-89 5.05E+01 1.37E-02 1.26E+13

Ce-144 2.84E+02 2.44E-03 3.46E+12

Cs-134 7.53E+02 9.21E-04 3.25E+11

Cs-137 1.10E+04 6.30E-05 1.25E+11

Pu-240 2.39E+06 2.90E-07 4.67E+08
5-4

Figure 5-2 Core activity as a function of time during a cycle

5.2 Model Parameter Estimates

The updated core inventory model has a set of parameters that relate to reactor operation, and 

another set of parameters that are radionuclide specific. The reactor related parameters are the 

number of fuel cycles, the length of fuel cycle, the average duration in days of a refueling 

outage, the date of the beginning of the last cycle, the length of the last refueling outage, the 

amount of uranium in core (MTU) and the reactor power (MWt). Information on reactor 

operations and fuel is generally available in Chapters 4, 7 and 15 of reactor final safety analysis 

reports (FSARs).

The radionuclide specific parameters are the half-life and production rate of each radionuclide. 

NUREG/CR-6703, “Environmental Effects of Extending Fuel Burnup Above 60 GWd/MTU” [21],

lists the most important radionuclides in terms of dose. The half-lives of these radionuclides are 

listed in DCFPAK 3.02. Appendix E of NUREG/CR-6703 lists core-average activity for 

important radionuclides for PWRs and BWRs for peak rod burnups ranging from 22 GWd/MTU 

to 75 GWd/MTU based on a series of Oak Ridge Isotope Generator_Automatic Rapid 

Processing (ORIGEN_ARP) calculations. The radionuclide production constant values can be 

calculated from the data in NUREG/CR-6703 Appendix E by solving Eq (2) for P’i given reactor 

power of 28.3 MWt/MTU for PWRs and 22.22 MWt/MTU for BWRs used in the ORIGEN_ARP

calculations. Table 5-2 lists the radionuclide specific parameter values for the updated model.
5-5

Table 5-2 Radionuclide specific core inventory parameters for the updated inventory

model

Radionuclide Half-life 

(d)

Decay Constant

(1/d)

RASCAL 4.3 Model Production

BWR

(Bq/MWt)/d

PWR

(Bq/MWt)/d

H-3 4.51E+03 1.54E-04 5.770E+08 5.811E+08

Co-58 7.08E+01 9.79E-03 1.500E+11 1.401E+11

Co-60 1.92E+03 3.61E-04 9.716E+09 1.045E+10

Kr-85m 1.87E-01 3.71E+00 8.925E+14 8.291E+14

Kr-85 3.91E+03 1.77E-04 1.146E+10 1.110E+10

Kr-87 5.30E-02 1.31E+01 6.298E+15 5.846E+15

Kr-88 1.18E-01 5.87E+00 3.913E+15 3.622E+15

Rb-86 1.87E+01 3.71E-02 8.925E+10 9.817E+10

Sr-89 5.05E+01 1.37E-02 1.263E+13 1.169E+13

Sr-90 1.06E+04 6.54E-05 9.395E+10 9.053E+10

Sr-91 3.96E-01 1.75E+00 2.052E+15 1.908E+15

Sr-92 1.13E-01 6.13E+00 7.674E+15 7.229E+15

Y-90 2.67E+00 2.60E-01 4.796E+13 4.224E+13

Y-91 5.85E+01 1.18E-02 1.418E+13 1.336E+13

Y-92 1.48E-01 4.68E+00 5.902E+15 7.108E+11

Y-93 4.21E-01 1.65E+00 1.586E+15 1.513E+15

Zr-95 6.40E+01 1.08E-02 1.835E+13 1.789E+13

Zr-97 7.04E-01 9.85E-01 1.639E+15 1.606E+15

Nb-95 3.52E+01 1.97E-02 3.363E+13 3.284E+13

Mo-99 2.75E+00 2.52E-01 4.663E+14 4.596E+14

Tc-99m 2.51E-01 2.76E+00 4.518E+15 4.498E+15

Ru-103 3.93E+01 1.76E-02 2.774E+13 2.873E+13

Ru-105 1.85E-01 3.75E+00 4.047E+15 4.336E+15

Ru-106 3.68E+02 1.88E-03 1.331E+12 1.446E+12

Rh-105 1.47E+00 4.72E-01 4.860E+14 5.132E+14

Sb-125 1.01E+03 6.86E-04 1.321E+10 1.408E+09

Sb-127 3.85E+00 1.80E-01 1.527E+13 1.597E+13

Te-127m 1.09E+02 6.36E-03 9.172E+10 9.562E+10

Te-127 3.90E-01 1.78E+00 1.492E+14 1.561E+14

Te-129m 3.36E+01 2.06E-02 1.253E+12 1.276E+12
5-6

Radionuclide Half-life 

(d)

Decay Constant

(1/d)

RASCAL 4.3 Model Production

BWR

(Bq/MWt)/d

PWR

(Bq/MWt)/d

Te-129 4.83E-02 1.44E+01 4.301E+15 4.371E+15

Te-131m 1.25E+00 5.55E-01 1.077E+14 1.102E+14

Te-132 3.26E+00 2.13E-01 2.995E+14 2.975E+14

I-131 8.04E+00 8.62E-02 8.458E+13 8.484E+13

I-132 9.58E-02 7.24E+00 1.037E+16 1.035E+16

I-133 8.67E-01 7.99E-01 1.617E+15 1.599E+15

I-134 3.65E-02 1.90E+01 4.239E+16 4.184E+16

I-135 2.75E-01 2.52E+00 4.866E+15 4.827E+15

Xe-133 5.25E+00 1.32E-01 2.638E+14 2.659E+14

Xe-135 3.79E-01 1.83E+00 1.486E+15 1.228E+15

Cs-134 7.53E+02 9.21E-04 3.254E+11 3.592E+11

Cs-136 1.31E+01 5.29E-02 4.929E+12 4.908E+12

Cs-137 1.10E+04 6.30E-05 1.249E+11 1.247E+11

Ba-139 5.74E-02 1.21E+01 2.152E+16 2.108E+16

Ba-140 1.27E+01 5.46E-02 9.727E+13 9.595E+13

La-140 1.68E+00 4.13E-01 7.734E+14 7.552E+14

La-141 1.64E-01 4.23E+00 6.867E+15 6.713E+15

La-142 6.42E-02 1.08E+01 1.713E+16 1.673E+16

Ce-141 3.25E+01 2.13E-02 3.489E+13 3.444E+13

Ce-143 1.38E+00 5.02E-01 7.607E+14 7.383E+14

Ce-144 2.84E+02 2.44E-03 3.464E+12 3.406E+12

Pr-143 1.36E+01 5.10E-02 7.535E+13 7.366E+13

Nd-147 1.10E+01 6.30E-02 4.169E+13 4.130E+13

Np-239 2.36E+00 2.94E-01 5.598E+15 6.030E+15

Pu-238 3.20E+04 2.17E-05 4.020E+09 4.517E+09

Pu-239 8.78E+06 7.89E-08 2.991E+08 2.816E+08

Pu-240 2.39E+06 2.90E-07 4.670E+08 4.372E+08

Pu-241 5.26E+03 1.32E-04 1.440E+11 1.419E+11

Am-241 1.58E+05 4.39E-06 2.343E+08 1.946E+08

Am-242 6.68E-01 1.04E+00 1.604E+14 1.577E+14

Cm-242 1.63E+02 4.25E-03 4.336E+11 4.315E+11

Cm-244 6.61E+03 1.05E-04 3.689E+09 6.095E+09
5-7

5.3 Comparison with RASCAL 4.2

RASCAL 4.2 core inventory estimates are based on the result of an ORIGEN_ARP calculation 

made in December 2003. Full details of the ORIGEN_ARP calculations are not available. 

However, notes accompanying the inventory data indicate that the calculations were made for 

reactor power of 3,479 MWt with a burnup of 38,585 MWd /MTU and 17,850 MWd/assembly for 

a reactor with 193 fuel assemblies. These values give a reactor fuel load of about 89.3 MTU 

and a 0.463 MTU/assembly. Although the reactor design is not specified in the notes 

accompanying the ORIGEN_ARP results, the fuel characteristics listed above are consistent 

with a late generation Westinghouse PWR (possibly Sequoyah Unit 1 or 2).

Table 1-1 of NUREG-1940 lists the core inventory assumed in RASCAL 4.2 normalized to a 

reactor power of 3,479 MWt. The radionuclide activity used in RASCAL 4.2 is the normalized 

activity multiplied by the thermal power of the reactor being modeled. An additional adjustment 

is made for activities of radionuclides having half-lives longer than 1 year. The activities of the 

long-lived radionuclides are scaled up by the ratio of the core-average fuel burnup (MWd/MTU) 

to 38,585 MWd/MTU.

Figure 5-3 shows the ratio of the normalized RASCAL 4.3 core activity to normalized 

RASCAL 4.2 core activity as a function of radionuclide half-life for the radionuclides common to 

both models. Ratios larger than 1.0 indicate that the RASCAL 4.3 model predicts larger 

inventory values as compared to RASCAL 4.2. For most radionuclides, the normalized activity 

calculated with the RASCAL 4.3 model is nearly the same as the activity in RASCAL 4.2. 

Radionuclides with significantly increased activity are identified in the Figure 5-3. The RASCAL 

4.3 model includes eight radionuclides not included in RASCAL 4.2. Those radionuclides are 

cobalt-58 (Co-58), Co-60, plutonium-238 (Pu-238), Pu-239, Pu-240, americium-241 (Am-241), 

Am-242, and curium-244 (Cm-244). There are also four radionuclides that were included in the 

RASCAL 4.2 inventory that are not included in the RASCAL 4.3 model inventory. Those 

radionuclides are krypton-83m (Kr-83m), antimony-129 (Sb-129), xenon-133m (Xe-133m), and 

Xe-138. A fifth radionuclide, Xe-135m, is not included in the RASCAL 4.3 inventory production 

model; however, it may be included in equilibrium with I-135 which is included in the model.
5-8

Figure 5-3 Comparison of updated model radionuclide inventory with the RASCAL 4.2 

inventory as a function of radionuclide half-life

The RASCAL 4.3 custom fuel inventory utility provides a convenient method of obtaining the 

core inventory for a specific time in the fuel cycle. The inventory is calculated from the date of 

last startup and the time in question and the duration of the last outage. Figure 5-4 shows the 

variation in activity from early cycle (1 month after startup) to the end of cycle (18 months after 

startup) as a function of radionuclide half-life. Time in cycle is important for radionuclides with 

half-lives of about 50 days and longer. For some important radionuclides (e.g., Cs-134 and 

Cs−137), the activity in the core can increase by almost a factor of two during the cycle. The 

two radionuclides that show significantly larger increases than expected given their half-lives are 

praseodymium-144 (Pr-144) (half-life = 0.012 d) and tellurium-125m (Te-125m) (half-life = 58 d). 

These radionuclides are short-lived daughters of longer lived parents (cerium-144 (Ce-144) and 

Sb-125).

0.5

1.0

1.5

2.0

2.5

1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05

Core Inventory Ratio (R43/R42)

Half Life (d)

Cs-136

Y-90

Y-92

Rb-86

Cm-242
5-9

Figure 5-4 Increase in core inventory during the fuel cycle as a function of 

radionuclide half-life

By default, RASCAL 4.3, RASCAL 4.2 and earlier versions use end-of-cycle inventories. 

However, because they adjust the inventory of long-lived radionuclides for burnup, they can 

approximate early-cycle inventories using the average burnup value for the fuel in the reactor on 

the user interface screen used to select the plant location. The average burnup at the beginning 

of a cycle is approximately one-half of the burnup at the end of cycle (for three cycle fuel 

management). For four-cycle fuel management, the burnup at the beginning of cycle is about 

60 percent of the end-of-cycle burnup. Figure 5-5 shows the approximate increase in activity 

during the fuel cycle as a function of half-life that would be estimated by RASCAL 4.2 and 

RASCAL 4.3 from the default inventory using the average burnup. Comparing Figures 5-4 and 

5-5, it is clear that the approximate method based on adjustment of the default end-of-cycle 

inventory gives reasonable results for most radionuclides. However, it does not properly 

account for the increase in Pr-144 and Te-125m. The choice between using a custom inventory

or a burnup adjusted end-of-cycle inventory may be reasonably made based on the availability 

of information at the time of an event, refueling dates, etc., or average core burnup.
5-10

Figure 5-5 Radionuclide activity increase during the fuel cycle as a function of half-life 

estimated from end-of-cycle inventory and burnup

5.4 Model Validation

The updated core inventory model has been used to estimate core inventories for five current 

generation reactor types and four new generation reactor types. In each case, the reactor 

specific parameters have been selected to match the conditions used to estimate the core 

inventories in the current generation reactor FSARs and the new reactor design control 

documents (DCDs). Table 5-3 lists the reactor specific model parameters for each reactor type 

modeled. For each type, the fuel load and reactor power were matched to the data in the FSAR 

or DCD [22, 23, 24, and 25], when available. When the data were not available, data were 

obtained from the reactor characteristics in NUREG/CR-6703. Except for the Evolutionary 

Power Reactor (EPR), the number of cycles and cycle exposure (effective full power days 

(EFPD)) were adjusted until the updated core inventory model gave fuel burnup consistent with 

the burnup used for the FSAR or DCD core inventory. The DCD core inventory for the EPR is a 

composite based on a set of burnups ranging from 5 to 62 GWD/MTU. The core inventory in 

the EPR DCD is the maximum activity for each radionuclide from the set of burnups.

Figures 5-6 and 5-7 compare the updated core inventory model estimates of core activity with 

core activity estimates included in FSARs and DCDs. Core estimates for six types of current 

generation U.S. reactors are compared in Figure 5-6. These comparisons indicate that the 

updated core inventory model provides reasonable core inventory estimates for the current fleet 

of U.S. reactors. Similarly, the comparisons of the updated model core inventory estimates with 
5-11

DCD core inventories for new generation reactors shown in Figure 5-7 indicate that the model 

also provides reasonable core inventory estimates for new reactors.

Table 5-3 Reactor specific characteristics used to test the updated core inventory 

model

Reactor

Type

Number 

of 

Cycles

Cycle 

Exposure 

(EFPD)

Fuel load

(MTU)

Power

(MWt)

Core Ave 

Burnup

(GWd/MTU)

Max 

Burnup

(GWd/MTU)

W 2-loop 3 460 46.1 1783 35.59 53.40

W 4-loop 3 509 104.3 4100 40.00 59.99

CE 3 535 95.5 3507 39.65 60.00

B&W 3 480 2568 2619 28.47 42.71

GE 3 3 670 150 3016 24.20 32.2

GE 4 3 487 104.3 3499 23.82 35.01

AP1000 3 506 84.8 3468 41.36 62.00

ESBWR 3 639 160 4590 35.00 51.03

US-APWR 3 730 138.7 4540 34.76 54.99

EPR 3 517 128.9 4590 41.30 61.98

Assuming that the FSAR and DCD core inventories are the true inventories, the ratio of model 

inventory estimates to the FSAR and DCD values should be approximately log-normal 

distributed. If the model is unbiased, the geometric mean and median ratios should be 1.00. 

The geometric standard deviation (GSD) characterizes the scatter of the estimates. A GSD of 

1.0 would indicate a perfect model. Otherwise, about 68 percent of the ratios would fall in the 

range between 1/GSD and GSD, and about 95.5 percent of the ratios would fall in the range 

between 1/(2×GSD) and 2×GSD.

Tables 5-4 and 5-5 present model statistics for each reactor type and average statistics for the 

nine reactor types. Based on these estimates, it is reasonable to conclude that the updated

core inventory model is unbiased with a GSD of about 1.3. About 70 percent of the ratios would 

be expected to fall within the range 0.8 to 1.3 and about 95 percent of the values would be in 

the range of 0.4 to 2.6. Table 5-5 presents the ratios for 6 radionuclides of interest. There is 

considerably more scatter at this level of detail. Since the updated model provides consistent 

inventory estimates given the input, the scatter may, in large part, be due to the modeling 

assumptions that were made in estimating the core inventories for the FSARs and DCDs. The 

variation in ratios for curium-242 (Cm-242) is a case in point. Estimates of the core inventory of 

actinides have increased in recent years. Thus, the variation in ratios for Cm-242m inventory 

estimates may be associated with the age of the FSAR/DCD core inventory estimate.
5-12

Figure 5-6 Comparison of the updated core inventory estimates with core inventory 

estimates for current generation reactors

1.E+16

1.E+17

1.E+18

1.E+19

1.E+20

1.E+16 1.E+17 1.E+18 1.E+19 1.E+20

Updated Model (Bq)

Westinghouse 2-Loop (Bq)

1.E+16

1.E+17

1.E+18

1.E+19

1.E+20

1E+16 1E+17 1E+18 1E+19 1E+20

Updated Model (Bq)

Westinghouse 4-Loop (Bq) 

1.E+16

1.E+17

1.E+18

1.E+19

1.E+20

1.E+16 1.E+17 1.E+18 1.E+19 1.E+20

Updated Model (Bq)

Combustion Engineering (Bq)

1.E+16

1.E+17

1.E+18

1.E+19

1.E+20

1.E+16 1.E+18 1.E+20

Updated Model (Bq)

Babcock & Wilcox (Bq)

1.E+16

1.E+17

1.E+18

1.E+19

1.E+20

1.E+16 1.E+17 1.E+18 1.E+19 1.E+20

Updated Model (Bq)

General Electric III (Bq)

1.E+16

1.E+17

1.E+18

1.E+19

1.E+20

1.E+16 1.E+17 1.E+18 1.E+19 1.E+20

Updated Model (Bq)

General Electric IV (Bq)
5-13

Figure 5-7 Comparison of updated core inventory estimates with core inventory 

estimates for new reactors

1.E+16

1.E+17

1.E+18

1.E+19

1.E+20

1.E+16 1.E+17 1.E+18 1.E+19 1.E+20

Updated Model (Bq)

AP1000 (Bq)

1.E+16

1.E+17

1.E+18

1.E+19

1.E+20

1.E+16 1.E+17 1.E+18 1.E+19 1.E+20

Updated Model (Bq)

ESBWR (Bq)

1.E+16

1.E+17

1.E+18

1.E+19

1.E+20

1.E+16 1.E+17 1.E+18 1.E+19 1.E+20 1.E+21

Updated Model (Bq)

US-APWR (Bq)

1.E+16

1.E+17

1.E+18

1.E+19

1.E+20

1.E+16 1.E+17 1.E+18 1.E+19 1.E+20 1.E+21

Updated Model (Bq)

EPR (Bq)
5-14

Table 5-4 Statistics of the ratios of the updated core inventory model estimates to the 

FSAR and DCD inventory estimates

Reactor Type n median GSM GSD

W 2-loop 57 0.990 0.172 1.287

W 4-loop 33 0.997 0.179 1.170

CE 62 0.919 0.918 1.411

B&W 57 0.965 0.994 1.186

GE 3 59 0.989 0.920 1.351

GE 4 59 0.995 1.028 1.264

AP1000 57 0.947 1.007 1.271

ESBWR 59 0.980 1.006 1.231

US-APWR 58 0.825 0.849 1.317

EPR 58 0.797 0.712 1.435

Average 0.940 0.954 1.292

Standard Deviation 0.073 0.108 0.088
5-15

Table 5-5 Statistics of the ratios of the updated core inventory model estimates to the 

FSAR and DCD inventory estimates for radionuclides of interest

Reactor Type I-131 Sr-89 Sr-90 Cs-134 Cs-137 Cm-242

W 2-loop 0.994 0.852 1.180 1.249 1.203 3.038

W 4-loop 1.004 0.838 0.997 1.102 1.027 --

CE 0.995 0.647 0.610 0.889 1.094 1.687

B&W 0.970 0.839 1.077 1.229 1.094 1.639

GE 3 0.979 1.004 0.640 0.596 0.611 1.004

GE 4 0.997 0.950 0.682 1.05 0.700 1.004

AP1000 0.957 0.786 0.992 1.069 1.005 2.923

ESBWR 0.961 0.975 0.988 0.866 0.872 1.800

US-APWR 0.822 0.626 0.900 0.805 0.781 1.849

EPR 0.861 0.656 0.660 0.425 0.614 0.914

Average 0.954 0.817 0.873 0.928 0.854 1.863

St. Dev. 0.062 0.138 0.207 0.267 0.217 0.727

5.5 Cooling System Model

The starting point for the updated coolant inventory model is a variant of Equation 5-1, which 

was the starting point for the core inventory model. It is:

ddCCii(tt)

dd = SSii

′

(tt)

MM − (λλii+ + ii) × CCii(tt) (5-6)

where

Ci(t) = coolant concentration of radionuclide i (Bq/kg) at time t,

S’i

(t) = appearance rate of radionuclide i in (Bq/h) in the coolant,

M = total mass of coolant (kg),

λi = decay constant (h-1

) for radionuclide i,

Ri = combined removal rate (h-1

) for radionuclide i for all of the processes other

than decay that remove radionuclides from the coolant.

The appearance rate of activity in the reactor coolant should be related to the core activity 

inventory. As seen in the previous section, except for short-lived radionuclides at reactor 

startup, the core inventory of a radionuclide tends to be nearly constant for periods of a few 
5-16

days. The removal rate for radionuclides in a reactor coolant system is typically of the order of 

1 per hour. As a result, it is reasonable to assume that under normal operating conditions, the 

radionuclide activity in coolant is in equilibrium with the core activity and dCi (t)/dt = 0.0. Thus, 

the activity concentration in the primary coolant can be calculated as:

CCii(tt) = SSii

′

(tt)

[MM × (λλii + ii)] (5-7)

The following develops this model for BWR and PWR reactors. The development is based on 

the procedures for estimating reactor coolant activity set forth in NUREG-0016 [26], NUREG0017 [27], and ANSI/ANS-18.1-1999 [28]. These documents provide coolant inventories for 

three reference reactors: a BWR, a PWR with U-tube steam generators, and a PWR with oncethrough steam generators. They also provide details related to the calculation of the removal 

rates for each reactor type. Unfortunately, the documents do not provide any information 

related to estimating the radionuclide appearance rates.

Assuming that as a practical matter it is not realistic to try to characterize the cause of variations 

in appearance rate as either variations in fraction of fuel defects or variations in escape 

coefficients, the RASCAL 4.3 coolant inventory model assumes:

SSii

′

(tt) = AAii(tt) × EEEEii (5-8)

where

Ai

(t) = core inventory of radionuclide i (Bq),

Esi = escape rate coefficient.

The Rx_Inventory_S code calculates Ai

(t), and default values of Esi for various reactor types are 

included in data statements in the code. For daughter radionuclides, the appearance rate S’i(t) 

has an additional term to represent ingrowth in the reactor cooling system. This ingrowth term 

is shown in Equation 5-9:

SSii

′

(tt) = AAii(tt) × EEEEii + AAcccc(tt) × λλ × BB (5-9)

where

Acj(t) = activity of the parent in the coolant,

λj = decay constant for the parent,

BFj = fraction of disintegrations of the parent j that yield daughter i.

There is also activity in the coolant that does not come from the reactor core. There are 

corrosion products that are not a function of fuel defects. ANSI/ANS-18.1 and new reactor 

DCDs list and provide estimates of coolant concentrations for chromium-58 (Cr-58), Cr-60,

zirconium-95 (Zr-95) and Zr-97 and a number of other activation products. The only activation 

products in the reactor coolant system (RCS) other than the isotopes of Cr and Zr that might 
5-17

contribute significantly to radiological doses are sodium-24 (Na-24), manganese-54 (Mn-54), 

Mn-56, copper-64 (Cu-64) and silver-110m (Ag-110m). Appearance rates for these 

radionuclides are included in the inventory calculation module as appropriate for each reactor 

type.

For the purpose of estimating coolant activity, a BWR reactor coolant system has two flow 

paths. The first path is through the reactor water cleanup system, and the second path is the 

steam flow path through the turbine. Thus, the removal rate for most radionuclides for a BWR 

reactor is given by Equation 5-10 (these variable symbols are used in ANSI/ANS-18.1):

ii = ( × NN ii) + ( × NN ii × NN ii × NN ii)

WW (5-10)

where

Ri = removal rate of the radionuclide i from the RCS (h-1

),

FA = flow through the purification system cation demineralizer (kg/h),

NAi = fraction of radionuclide i removed in the RCS cleanup system,

FS = steam flow rate (kg/h),

NSi = ratio of concentration radionuclide i in reactor steam to the concentration in 

reactor water,

NCi = ratio of condensate demineralizer flow rate to the total steam flow rate,

NBi = fraction of radionuclide i removed by the condensate demineralizers,

WP = weight of water in the RCS (kg).

For the 3.4E+03 MWt reference reactor in ANSI/ANS-18.1, the mass of coolant in the reactor 

coolant system is 1.7E+05 kg, the reactor cleanup system flow is 5.76E+04 kg/h, the steam flow 

is 6.84E+06 kg/h, and 100 percent of the steam flow passes through the condensate 

demineralizer.

PWRs are divided into two classes based on steam generator design, U-tube steam generators 

and once-through steam generators. However, the same basic equations apply to both classes; 

the difference between the classes is captured in the model parameter values. There are two 

flow paths for water passing through the reactor, a path through the steam generator (primary 

side) and a path though the reactor cleanup system. The steam driving the turbine is in a 

separate path. This path includes the steam generator (secondary side), the turbines, the 

condenser, and a condensate cleanup system. Activity in the primary coolant (primary side 

water) comes directly from the reactor. It is removed by the reactor water cleanup system. 

Activity in the secondary side steam and condensate comes from primary to secondary leakage 

in the steam generator. It is removed by the condensate cleanup system. Equation 5-7 applies 

separately to the primary and secondary side. Equation 5-9 defines the appearance rate on the 

primary side. A similar equation is used to define the appearance rate on the secondary side. 

ii( ) = CCii(tt) × LL × CC (tt) × λλ × BB (5-11)

Where
5-18

si(t) = secondary side appearance rate (Bq/h),

Ci(t) = concentration in the primary coolant (Bq/g),

L = primary to secondary leak rate (gal/h),

Cj

(t) = concentration of the parent in the secondary coolant (Bq/g),

λj = decay constant of the parent (h-1

),

BFj = fraction of disintegrations of parent j that yield daughter i.

ANSI/ANS-18.1 secondary coolant inventories are based on a primary to secondary leak rate of 

1.4E+00 kg/h (75 lbs/d). This value is used to estimate realistic secondary side inventories in 

the Advanced Passive Reactor (AP1000), EPR and US-Advanced Pressurized-Water Reactor 

(US-APWR) DCDs. Design-basis secondary side coolant inventories for these reactors are 

based on significantly larger primary to secondary leak rates (e.g., 4.9E+05 gal/h for the 

AP1000).

The ANSI/ANS-18.1 PWR model for removal of activity in primary side coolant consists of a 

purification demineralizer followed by a cation demineralizer. Treated water is stored in a 

purification system tank where it may be degassed. A portion of the flow may be diverted to the 

boron recovery system. Using the nomenclature of ANSI/ANS-18.1, the removal rate for 

primary side coolant noble gas activity is:

= [ + ( − ) × YY]

WW (5-12)

where

R = removal rate (h-1

),

FB = RCS flow to the boron recovery system (kg/h),

FD = flow through the purification demineralizer (kg/h),

Y = fraction of noble gases removed by degassing,

WP = mass of the primary coolant (kg).

The removal rate is for other radionuclides, except H3, is:

= �( × NN ii) + (1 − NN ii) × � + ( × NN ii)��

WW (5-13)

where

R = removal rate (h-1

),

FD = flow through the purification demineralizer (kg/h),

NBi = fraction of activity of radionuclide i removed in the purification 

demineralizer,

FB = RCS flow to the boron recovery system (kg/h),

FA = flow through the cation demineralizer (kg/h),

NAi = fraction of activity of radionuclide i removed in the cation demineralizer.

The ANSI/ANS-18.1 model does not include a removal mechanism for H3 other than decay.
5-19

On the secondary side, noble gases are assumed to transfer to the steam immediately and to 

be effectively removed by the condenser offgas system. Therefore, the concentration of noble 

gases in the condensate is assumed to be 0.0 and the concentration in steam is calculated as:

CCii(tt) = ii(t) (5-14)

where

Ci(t) = concentration of radionuclide i at time (t) (μCi/g),

si(t) = rate of introduction of radionuclide i at time (t) (Ci/s),

FS = steam flow (kg/h).

Equation 5-15 is used to calculate the secondary side concentrations of H3 and other nuclides. 

For these radionuclides, the secondary side removal rate is calculated as:

ii = [( × NN ) + (NN ii × × NN × NNNNii)]

WW (5-15)

where

FBD = steam generator blowdown flow (kg/h),

NBD = fraction of blowdown removed from secondary side,

NSi = ratio radionuclide i concentration in steam to that steam generator,

FS = steam flow (kg/h),

NC = fraction of steam flow passing through condensate demineralizer,

NXi = fraction of radionuclide i removed by condensate demineralizer.

The Rx_Inventory_S code includes default values for R and NS for various reactor types in data 

statements. The default values are based on the ANSI/ANS-18.1 model. They were calculated 

for each reactor type using the RCS parameters given in reference documents. The flows and 

cleanup fractions for current-generation light water reactors are based on the BWR and PWR 

reference reactors in ANSI/ANS-18.1. The flows and cleanup fractions for new reactor designs 

are based on reactor characteristics as set forth in Section 11.1 of the reactor DCD. Where the 

DCD includes design basis and realistic characteristics, the default values of R are based on the 

realistic values.

Default escape coefficients have also been calculated for each reactor type using the published 

primary coolant concentrations and RCS parameters. These coefficients, which are applied to 

individual radionuclides in the core, have units of fraction of a core activity per hour. They are 

included in data statements in the Rx_Inventory_S code.

5.6 Inventory Utility: Rx_Inventory_S

The inventory model Rx_Inventory_S uses two input files. One of the input files contains the 

radionuclide decay and production data. It is named Coreinventory.dat. The other input file 

contains user inputs related to the reactor and cooling system. It is named Reactor.tmp. This 
5-20

file has two parts. The first section (first seven lines) provides information about the reactor: its 

power, how it is operated, and the date of the last refueling outage. This information is used to 

calculate the core inventory. The second section provides information on the cooling and steam 

systems. There is one line in this section for BWRs and two lines for PWRs. Table 5-6 lists the 

format content of each of the lines in the Reactor.tmp file.

5.6.1 Core Inventory Input

The first line of the Reactor.tmp file is used to identify the information in the file. This line is 

copied to the output files. The next six lines contain the data used to run the core inventory 

model. Each of the remaining lines starts with a key word or phrase that identifies the 

information in the record. The keyword is followed by the input.

The second line identifies the reactor type. The core inventory model recognizes seven reactor 

types and selects the PWR or BWR radionuclide production parameters based on reactor type. 

The reactor types are: BWR, Advanced Boiling-Water Reactor (ABWR), Economic Simplified 

Boiling-Water Reactor (ESBWR), PWR, US-APWR, EPR, and AP1000.

The third line lists the reactor power (MWt) and core uranium load (MTU). The characteristics of 

U.S. reactors, including rated power and fuel load, are listed in Appendix A of NUREG/CR-6703. 

However, power uprates since 1997 may have resulted in changes to characteristics of these 

reactors. The results of power uprates are listed on the NRC Web site at: 

http://www.nrc.gov/reactors/operating/licensing/power-uprates/status-power-apps.html.

The fourth line in this section lists the fuel management practices for the reactor the first entry is 

a key to typical management styles. Table 5-7 gives the number of cycles that fuel remains in 

the core and the cycle duration represented by each key number. The second entry in this line 

is the cycle of the oldest batch of fuel in the core. In general, it should be equal to the number 

of cycles. This entry may be less than the number of cycles when the reactor is just starting up. 

If the entry is greater than the number of cycles, the model will assume that it is equal to the 

number of cycles. The final entry is the length in days of a typical refueling outage. Figure 5-8

shows the distribution of the duration of refueling outages in days for the 60 U.S. reactors that 

refueled in 2011.
5-21

Table 5-6 Reactor.tmp file format and contents

Line Format Variables and Keywords Notes

1 a80 header

2 a20, 1x, a6 reactor type BWR, ABWR, ESBWR, PWR, 

AP1000, US-APWR, or EPR

3 a20, 2f10.0 reactor power (MWt), total uranium 

(MTU)

4 a20, 3i5 fuel management type, cycle, normal 

refueling outage (d)

5 a20, 4i5 month, day, year, duration End of last refueling outage, 

outage duration (d)

6 a20, 3i5 month, day, year Date of initiating event 

7 a20, 1x, a10 status

Status at time of initiating 

event: normal operation, 

shutdown, low power

BWR

8 a20, 4f9.0

total coolant mass (kg), steam flow 

(kg/h), condensate cleanup flow 

fraction 

WP, FS, NC

PWR

8 a20, 5f10.0 primary coolant mass (kg) WP

9 a20, 6f9.0

steam generator type, primary to 

secondary leak rate, total secondary 

coolant mass (kg), steam flow (kg/h) 

SG_type (‘U-Tube’ or ‘OnceThrough’), L, WS, FS

Table 5-7 Fuel management characteristics

Key Number of Cycles Cycle Duration (d)

1 2 730

2 3 547

3 3 730

4 4 365

5 3 365
5-22

Outage durations ranged from 25 to 183 d with a median duration of 41 d and a mean duration 

of 55 d. The longer duration outages generally indicate major reactor maintenance activities 

took place in addition to refueling.

Figure 5-8 Distribution of refueling outage duration in 2011

The last three lines in this section are related to the most recent fuel cycle. The fifth line in the 

first section contains the date that the reactor restarted after the last refueling outage and the 

duration of the outage. The date that U.S reactor restarted after the last refueling outage can be 

found by searching the daily status reports. These reports are found at: 

http://www.nrc.gov/reading-rm/doc-collections/event-status/reactor-status/.

Recent status reports only list the status of the reactor as percent of rated power. Status 

reports more than 28-days old include additional information such as the reason for an outage.

The sixth line contains the date for which the core inventory is to be calculated. Typically this 

line would contain the date of the event.

The last line of this section is the status of the reactor at the time of the event. The status is not 

used in the current model. However, future model development will include source term 

estimates for low-power events and events that occur when the reactor is shutdown.

5.6.2 Cooling and Steam System Input

The second section of the Reactor.tmp file contains information related to the reactor cooling 

system. The contents of this section are determined by reactor type (BWR or PWR). Table 5-6
5-23

lists the input for the two basic reactor types. The variable names in this section of the input file 

are the same as the names used in ANSI/ANS-18.1. For BWRs (current generation, ABWR, 

and ESBWR) the input is the mass of water in the reactor cooling system, the steam flow and 

the fraction of the condensate that returns through a cleanup system. This information is input 

in a single line in the file.

The mass of water in the coolant system is included in the RASCAL 4.3 facility database. The 

steam flow may be obtained from the plant FSAR or DCD. If it isn’t readily available, the steam 

flow may be estimated from reactor thermal and electrical power. Figure 5-9 shows the 

relationship between design-basis steam flow and design-basis thermal power for current 

generation and new nuclear power plant designs.

Figure 5-9 Steam flow as function of reactor power

To a very good approximation, the steam flow may be estimated from the thermal power using:

= 2000 (kkkk⁄h)

MM

× PP (5-16)

where

FS = steam flow (kg/h),

P = reactor power (MWt).

This relationship is based on the design values of power and steam flow; however, RASCAL 4.3 

also uses the relationship to estimate steam flow at lower power levels when the reactor is 

operating at less than design power.

2.E+06

3.E+06

4.E+06

5.E+06

6.E+06

7.E+06

8.E+06

9.E+06

1.E+07

1000 1500 2000 2500 3000 3500 4000 4500 5000

Steam Flow (kg/h)

Reactor Power (MWt)

BWR

PWR
5-24

The ANSI/ANS-18.1 gives a nominal value of 1.0 for the ratio of condensate demineralizer flow 

to steam flow (NC) for BWR reactors. It also has a note that the reference plant is assumed to 

be a “non-pumped forward drained plant,” and states that for a “pumped forward plant” the value 

of NC should be consistent with the plant design values. The value of NC for most of the BWR 

plants reviewed was 1.0. However, three plants had NC values in the range of 0.65 to 0.67. 

Lower values of NC result in larger coolant inventories. If the specific BWR reactor being 

modeled does not have a condensate cleanup system, the condensate cleanup fraction should 

be set to zero.

For PWRs (current generation, AP1000, US-APWR, or EPR), the cooling system information is 

included in two lines in the file. The first line contains the mass of water on the primary cooling 

side. The second line lists the steam generator type (U-tube or once-through), the primary to 

secondary leak rate, the mass of water in the secondary side, and the steam flow. Most PWRs 

use U-tube steam generators. Babcock and Wilcox (B&W) reactors are the exception; they use 

once-through steam generators (B&W reactors in the United States are: Crystal River Unit 3; 

Oconee Units 1, 2, and 3; Arkansas Unit 1; Three Mile Island Unit 1; and Davis-Besse Unit 1).

The RASCAL 4.3 facility database includes the primary system water mass and the steam 

generator type for U.S. reactors. The primary to secondary leak rate is a design value that 

should be available from the plant FSAR or DCD. A primary to secondary leak rate of 75 lb/d 

(1.4E+00 kg/h) is assumed in ANSI/ANS-18.1. The AP1000 DCD assumes a primary to 

secondary leak rate of 500 gal/d (approximately 4000 lb/d) for design-basis calculations and a 

primary to secondary leak rate of 75 lb/d (9 gal/d) as a realistic value. Given no better 

information, the primary to secondary leak rate might be estimated as the difference between 

the primary makeup flow and the primary letdown flow. The mass of the secondary side water 

should be available from design documents such as the FSAR and DCD. If it is not readily 

available from a design document, the secondary water mass may be estimated from the 

reactor design power. Figure 5-10 shows the relationship between secondary water mass and 

reactor power for current generation and new power plant designs.
5-25

Figure 5-10 Secondary water mass as a function of reactor power for current 

generation and new PWR reactor designs

When necessary, RASCAL 4.3 estimates the secondary water mass for PWR using:

WW = 85.7 × PP − 1.24E + 05 (5-17)

where

WS = secondary water mass (kg),

P = reactor design power (MWt).

RASCAL 4.3 estimates the steam flow on the secondary side using Equation 5-16.

5.6.3 Rx_Inventory_S Model Output

The Rx_Inventory_S program generates four output files. Three of these files provided 

inventories for the core, the coolant, and spent fuel pool (SFP). The remaining file is a debug 

file that contains intermediate computational results. This section describes the inventory files.

5.6.3.1 Core Inventory

The core inventory file (core_inventory.tmp) is intended for use by the reactor accident source 

term module. Figure 5-11 presents a portion of a core inventory file. The first line states that 

the file is a reactor core inventory. The next seven lines echo the user input used to calculate 

the inventory. These lines are followed by the year and day of the year for which the core 

0.0E+00

5.0E+04

1.0E+05

1.5E+05

2.0E+05

2.5E+05

3.0E+05

3.5E+05

1000 1500 2000 2500 3000 3500 4000 4500 5000

Secondary Coolant (kg)

Power (MWt)
5-26

inventory was calculated, the core-average burnup of the fuel, and the number of radionuclides 

in the inventory. There are other radionuclides in the inventory, but the radionuclides in this file 

contribute most to potential offsite consequences. The remainder of the file is a listing of the 

activity (Bq) of the radionuclide inventory.

Reactor core inventory estimates

ANSI/ANS-18.1 Reference BWR

Reactor Type BWR 

Reactor Parameters 3400.0 140.3

Fuel Management 2 3 60

Last Startup Date 3 24 2010 60

Shutdown Date 5 28 2011

Reactor Status Operating 

Exposure date, year= 2011 day= 148

Core average burnup, GWd/MTU 2.314E+01

Total radionuclides = 67

Nuclide Bq 

H-3 1.65E+15

Co-58 5.16E+16

Co-60 2.48E+16

Kr-85m 8.19E+17

Kr-85 3.23E+16

Kr-87 1.64E+18

Kr-88 2.26E+18

Rb-86 8.19E+15

Rb-88 2.26E+18

Sr-89 3.12E+18

Sr-90 2.82E+17

Sr-91 3.99E+18

Sr-92 4.25E+18

Figure 5-11 Sample core_inventory.tmp file

5.6.3.2 Coolant Inventory

Cooling system inventory estimates are stored in the file rcs_inventory.tmp. This file lists the 

inventories that would be used to estimate source terms for releases of coolant to the 

environment that do not involve damage to the reactor core, e.g., steam generator tube 

ruptures. Again, the first line of the file describes the contents of the file and the following three 

lines for a PWR (two lines for a BWR) list the reactor parameter inputs provided by the user. 

The next four lines list the RCS parameters that vary by radionuclide. These parameters, which 

are included in Rx_Inventory_S data statements, are listed by the MELCOR radionuclide

classes plus a class for tritium. The MELCOR classes are listed in Table 5-8.
5-27

Table 5-8 MELCOR radionuclide classes

MELCOR 

Class 

Number

Radionuclide Class

1 noble gases (Xe)

2 cesium (Cs)

3 barium (Ba)

4 iodine (I)

5 tellurium (Te) 

6 ruthenium (Ru) 

7 molybdenum (Mo)

8 cerium (Ce)

9 lanthanum (La)

10 uranium (U)

11 cadmium (Cd)

12 tin (Sn)

16 cesium iodide (CsI)

Many of the parameter values in each of these lines are the same because the parameter 

values in the reference documents are generally only given for four radionuclide classes, noble 

gases, I, Cs and rubidium (Rb), and other radionuclides. The escape rates are in fraction of 

core activity per hour, the primary and secondary cleanup values are removal rates per hour, 

and carry over is the fraction of activity in the secondary water that carries over into the steam. 

The remainder of the file presents the RCS inventory estimates. Figure 5-12 presents a portion 

of a PWR rcs_inventory.tmp file. Each radionuclide is followed by its estimated concentrations 

(Bq/g) in the primary coolant, the secondary water, and in the steam.
5-28

Cooling system inventory estimates

ANSI Reference PWR

RCS Primary Param 2.50E+05

RCS Secondary Param U-Tube 1.40E+00 2.05E+05 6.84E+06

Escape Rates 7.00E-08 2.00E-10 5.00E-10 1.00E-08 5.00E-10 5.00E-10 

5.00E-10 5.00E-10 5.00E-10 5.00E-10 5.00E-10 0.00E+00

Primary Cleanup 9.20E-04 3.71E-02 6.61E-02 6.66E-02 6.61E-02 6.61E-02 

6.61E-02 6.61E-02 6.61E-02 6.61E-02 6.61E-02 0.00E+00

Carry Over 1.00E+00 5.00E-03 5.00E-03 1.00E-02 5.00E-03 5.00E-03 5.00E03 5.00E-03 5.00E-03 5.00E-03 5.00E-03 1.00E+00

Secondary Cleanup 0.00E+00 1.67E-01 1.67E-01 1.67E-01 1.67E-01 1.67E-01 

1.67E-01 1.67E-01 1.67E-01 1.67E-01 1.67E-01 0.00E+00

Coolant inventory concentrations in Bq/g 

 Primary Secondary Steam

H-3 3.70E+04 3.95E+04 3.95E+04

Co-58 2.89E+01 1.18E-03 1.18E-05

Co-60 1.76E+01 7.18E-04 7.18E-06

Kr-85m 1.37E+03 0.00E+00 2.81E-04

Kr-85 1.04E+04 0.00E+00 2.13E-03

Kr-87 7.80E+02 0.00E+00 1.60E-04

Kr-88 2.39E+03 0.00E+00 4.89E-04

Rb-86 1.86E-01 7.55E-06 3.78E-08

Rb-88 7.09E-01 1.94E-06 9.70E-09

Sr-89 8.68E+01 3.54E-03 1.77E-05

Sr-90 9.10E+00 3.72E-04 1.86E-06

Sr-91 5.33E+01 1.52E-03 7.59E-06

Sr-92 2.49E+01 4.03E-04 2.01E-06

Figure 5-12 Sample PWR rcs_inventory.tmp file

The BWR rcs_inventory.tmp file is similar to the PWR rcs_inventory.tmp file with minor 

exceptions. There is only one line of RCS parameter values in the user input; the secondary 

water cleanup removal rates are replaced by removal rates for a condensate cleanup system; 

and radionuclide concentrations are only provided for water and steam. Figure 5-13 presents a 

portion of a BWR rcs_inventory.tmp file.
5-29

Cooling system inventory estimates

ANSI/ANS-18.1 Reference BWR 

RCS Parameters 1.70E+05 6.84E+06 1.00E+00

Escape Rates 3.00E-07 1.00E-10 2.00E-10 2.00E-08 2.00E-10 2.00E-10 

2.00E-10 2.00E-10 2.00E-10 2.00E-10 2.00E-10 0.00E+00

Primary Cleanup 0.00E+00 1.71E-01 3.08E-01 3.08E-01 3.08E-01 3.08E-01 

3.08E-01 3.08E-01 3.08E-01 3.08E-01 3.08E-01 0.00E+00

Carry Over 1.00E+00 2.00E-02 1.00E-03 2.00E-02 1.00E-03 1.00E-03 

1.00E-03 1.00E-03 1.00E-03 1.00E-03 1.00E-03 1.00E+00

Condensate Cleanup 0.00E+00 1.97E-02 3.55E-02 7.11E-01 3.55E-02 3.55E02 3.55E-02 3.55E-02 3.55E-02 3.55E-02 3.55E-02 0.00E+00

Coolant inventory concentrations in Bq/g 

 Water Steam

H-3 3.70E+02 3.70E+02

Co-58 5.96E+00 1.19E-01

Co-60 2.86E+00 5.72E-02

Kr-85m 0.00E+00 3.59E+01

Kr-85 0.00E+00 1.42E+00

Kr-87 0.00E+00 7.18E+01

Kr-88 0.00E+00 9.93E+01

Rb-86 2.50E-02 5.01E-04

Rb-88 5.29E-01 1.06E-02

Sr-89 1.07E+01 1.07E-02

Sr-90 9.66E-01 9.66E-04

Sr-91 1.13E+01 1.13E-02

Figure 5-13 Sample BWR rcs_inventory.tmp file

5.6.3.3 Spent Fuel Pool (SFP) Inventory

Figure 5-14 presents a portion of the third output file for the spent-fuel inventory estimates. It 

contains the inventory for each batch of fuel in the reactor at the time of shutdown. The first line 

of the file indicates the file content, and the second line is the header provided by the user. The 

third line gives the date for which the inventories have been calculated. Generally this should 

be the date that the reactor was shutdown. The next three lines provide batch specific 

information. The first of these lines lists the number of full-power exposure days for the fuel in 

each batch. The second lists the metric tons of uranium in each batch, and the third line lists 

the burnup of each batch. The remainder of the file contains inventory information.

spent fuel batch inventory estimates

ANSI/ANS-18.1 Reference BWR 

Exposure date, year= 2011 day= 148

Days 487 974 1404

MTUs 4.677E+01 4.677E+01 4.677E+01

GWd/MTU 1.180E+01 2.360E+01 3.402E+01

Nuclide Bq Bq Bq 

H-3 2.72E+14 5.57E+14 8.18E+14

Co-58 1.71E+16 1.72E+16 1.72E+16

Co-60 4.39E+15 8.51E+15 1.19E+16

Kr-85m 2.73E+17 2.73E+17 2.73E+17

Kr-85 5.38E+15 1.09E+16 1.60E+16

Kr-87 5.46E+17 5.46E+17 5.46E+17

Kr-88 7.55E+17 7.55E+17 7.55E+17

Rb-86 2.73E+15 2.73E+15 2.73E+15

Rb-88 0.00E+00 0.00E+00 0.00E+00

Figure 5-14 Sample sfpool_inventory.tmp file

6-1

6.0 ACTIVITY BALANCE

The RASCAL 4.3 source term calculations track radionuclide activity in the fuel, as it passes 

through the plant, and as it enters the environment. The details of these calculations have been 

available in files used to track program execution and troubleshoot problems. However, these 

files have not been available to the RASCAL users in previous versions of the code. RASCAL

4.3 makes this information available to users by creating an activity balance file and displaying 

the contents through the user interface.

6.1 Activity Balance File Description

The activity balance file tracks activity for selected radionuclides and radionuclide groups from 

the reactor fuel (Rx Core) and reactor coolant system (RCS) through various pathways to the 

environment. The activity balance file lists, for each time step, the activity in five locations [e.g.,

Rx Core, RCS, steam generators (SG), Containment (Cont), and environment (Env)] and its 

movement through nine pathways. The locations and transfer pathways are listed in Table 6-1. 

In the activity balance file terminology, the containment refers to the entire release pathway 

between the reactor fuel and the free atmosphere.

Table 6-1 Locations and transfer pathways for balance activity summaries

Col Name Activity Balance File Locations and Transfer Pathways

1 Rx Core Activity in the reactor fuel

2 Rx-RCS Activity transferred from the reactor fuel to primary coolant

3 Rx-Cont Activity transferred from the reactor fuel to containment

4 Rx-Env Activity transferred from the reactor fuel to the environment

5 RCS Activity in the primary coolant

6 RCS-Cont Activity transferred from primary coolant to containment

7 RCS-SG Activity transferred from primary to secondary coolant (steam 

generators) 

8 RCS-Env Activity transferred from primary coolant to the environment

9 SG Activity in the secondary coolant (steam generators)

10 SG-Cont Activity transferred from secondary coolant (steam generators) to 

containment

11 SG-Env Activity transferred from secondary coolant (steam generators) to the 

environment

12 Cont Activity in containment (Dry well for BWR)

13 Cont-Env Activity transferred from containment to the environment

14 Env Total activity released to the environment (cumulative from start of 

release)
6-2

Although depletion processes and decay are included in RASCAL 4.3, the activity removed from 

consideration by these processes is not tracked in the activity balance file. However, the activity 

listed in the activity balance file for the Rx Core, RCS, SG, and Cont does reflect the reduction 

in activity by depletion and decay. The activity released to the Env reflects the reduction in 

activity prior to release to the environment, but it does not reflect decay or ingrowth in the 

environment. Depletion of activity within the plant may be estimated from the initial activity in 

the fuel, the activity remaining in the fuel, the activity in the release path, and the activity 

released to the free atmosphere.

The activity balance file data are particularly useful in developing an understanding of how the 

RASCAL source term model works. For LTSBO and LOCA events, the RASCAL source term 

model may be represented as three boxes—reactor, containment, and atmosphere—as shown 

in Figure 6-1. The reactor box includes calculation of the initial reactor fuel inventory, decay of 

radionuclides in the fuel, and release of radionuclides from the fuel. The containment box may 

include a portion of the reactor vessel and various pipes and ducts in addition to the 

containment building. In RASCAL, the containment building is characterized by a single volume 

(free volume of the containment building for PWRs, and drywell plus wetwell volume for BWRs). 

When radionuclides are released from the fuel, they are assumed to become uniformly mixed 

within the containment instantaneously.

Figure 6-1 Simplified RASCAL LTSBO and LOCA source term model

RASCAL has three mechanisms for depleting activity between the reactor fuel and the free 

atmosphere. The radionuclide activity is modified by decay and ingrowth between the time of 

reactor shutdown and ultimate release to the atmosphere. While radionuclides are in 

containment, they are assumed to gradually deposit on surfaces as a function of time. The

radionuclides may also be washed out by sprays, if sprays are activated. Finally, radionuclides 

may be removed from the containment atmosphere by the action of filters as the containment 

atmosphere is released to the atmosphere outside (environment) of containment. In RASCAL 

BWR wetwell suppression pools are modeled as filters. These reduction mechanisms are 

functions of flow out of the containment. The details of the depletion mechanisms are found in 

sections 1.3, 1.4, and 1.6 in NUREG-1940.
6-3

6.2 Generation of the Activity Balance File by RASCAL

RASCAL 4.3.1 creates an activity balance file for source terms types based on reactor 

conditions. These source terms types include LTSBO, LOCA, Coolant Release, Containment 

Radiation Monitor, Coolant Sample and Containment Air Sample. A file is created for source 

terms based on monitored release pathways, but the file is empty. Table 6-2 lists the activity 

locations and transfers tracked in the activity balance file for each source type and release path.

Table 6-2 Activity balance locations and transfer pathways for reactor accident 

categories

Source Term Type Release 

Pathways Activity Locations and Transfers

PWR Events

LTSBO

Cont Leak Rx Core, Rx-Cont, RCS, RCS-Cont, Cont, Cont-Env, 

Env

SGTR Rx Core, Rx-RCS, RCS, RCS-SG, SG, SG-Env, Env 

Bypass Rx Core, Rx-RCS, RCS, RCS-Env, Env

LBLOCA

Cont Leak Rx Core, Rx-Cont, RCS, RCS-Cont, Cont, Cont-Env, 

Env

SGTR Rx Core, Rx-RCS, RCS, RCS-SG, SG, SG-Env, Env 

Bypass Rx Core, Rx-RCS,RCS, RCS-Env, Env

Coolant Release

Cont Leak NA

SGTR RCS, RCS-SG, SG, SG-Env, Env

Bypass RCS, RCS-Env, Env

BWR Events

LTSBO

Wetwell Rx Core, Rx-Cont, RCS, RCS-Cont, Cont, Cont-Env, 

Env

Drywell Rx Core, Rx-Cont, Cont, Cont-Env, Env

Bypass Rx Core, Rx-RCS, RCS, RCS-Env, Env

LBLOCA

Wetwell Rx Core, Rx-Cont, RCS, RCS-Cont, Cont, Cont-Env, 

Env

Drywell Rx Core, Rx-Cont, RCS, RCS-Cont, Cont, Cont-Env, 

Env

Bypass Rx Core, Rx-RCS, RCS, RCS-Env, Env

Coolant Release

Wetwell NA

Drywell NA

Bypass RCS, RCS-Env, Env
6-4

The activity balance file includes separate tables for 12 activity groups and radionuclides. In 

each table, the activity for each location and transfer is presented as a function of time. The 

initial time is the time of reactor shutdown. The second time is the time that the release starts 

(t = 0), and the remaining times are at 900 second (s) intervals following the beginning of 

release. These features are shown in Table 6-3 and represent data from a portion of the activity 

balance file for a PWR LOCA as it is displayed in the user interface. The activity shown is “total 

activity” in curies (Ci). The first column is the time of the activity balance. The shutdown and 

the release start time (Rel Start) rows give the activity balance at the time of reactor shutdown 

and the beginning of release from the Rx Core. At these two times all of the activity is in the 

Rx Core. If the event involved release of activity from the RCS, the activity in the RCS would 

also be shown. The activities shown in the Rx Core, Cont, and Env columns are the activities at 

the end of the period. They account for decay and depletion. The activity in the Env column is 

the total activity released to the atmosphere. The activity balance file does not reflect the decay 

that takes place in the atmosphere. Decay in the atmosphere and on the ground is calculated in 

the RASCAL transport and diffusion models. The activities shown in the Rx-Cont and Cont-Env 

columns are the activities transferred during the time period.

The activity balance information may be accessed from the user interface using the View 

Balance button on the Source Term Tab. Figure 6-2 shows how the activity balance file 

information is presented through the RASCAL 4.3.1 user interface.

Table 6-3 Sample of the Balance Summary Available in the User Interface

Time Step Period

(h)

Activity (Ci)

Rx Core Rx-Cont Cont Cont-Env Env

Shutdown 7.07E+09 0.00E+00 0.00E+00 0.00E+00 0.00E+00

Release Start Time 

(Rel Start) 7.07E+09 0.00E+00 0.00E+00 0.00E+00 0.00E+00

0.25 6.97E+09 3.63E+07 2.86E+07 3.21E+02 3.21E+02

0.50 6.87E+09 3.42E+07 4.97E+07 5.51E+02 8.72E+02

0.75 6.66E+09 1.42E+08 1.61E+08 1.75E+03 2.63E+03

1.00 6.46E+09 1.34E+08 2.55E+08 2.74E+03 5.37E+03

1.25 6.27E+09 1.30E+08 3.37E+08 3.60E+03 8.97E+03
6-5

Figure 6-2 User interface presentation of the RASCAL 4.3.1 activity balance 

information

6.3 Activity Balance File Example for BWR LTSBO

Figures 6-3 through 6-7 illustrate the movement of five radionuclides from a RASCAL 4.3.1 

activity balance file for an unmitigated BWR LTSBO scenario described in NUREG/CR-7110 

Volume 1, Revision 1, “State-of-the-Art Reactor Consequence Analysis Project, Volume 1: 

Peach Bottom Integrated Analysis”. The radionuclides presented in the figures are in order of 

increasing complexity of the source term model with respect to depletion mechanisms.

Figure 6-3 depicts the plot of the RASCAL 4.3.1 krypton-85 (Kr-85) activity balance file for the 

unmitigated BWR LTSBO scenario. Kr-85 is inert noble gas that does not deplete by natural 

deposition, sprays, or the action of filters. Additionally, given the half-life of Kr-85 and the time 

frame of the scenario, Kr-85 decay can be neglected. Figure 6-3 shows the Kr-85 in the fuel 

(blue line) from the time of the initiating event until fuel damage begins at about 9 hours. At this 

point, almost all of the Kr-85 activity moves from the fuel to containment (orange line) over a 

period of about 2 hours. During this period of time and the next few hours the Kr-85 activity 

slowly leaks to the atmosphere (green line). Finally, at approximately 20 hours the containment 

fails and most of the Kr-85 activity remaining in the containment is released to the free 

atmosphere.
6-6

Figure 6-3 RASCAL 4.3.1 Kr-85 activity balance during a BWR Mark III LTSBO event

Figure 6-4 depicts the plot of the RASCAL 4.3.1 xenon-135 (Xe-135) activity balance file for the 

unmitigated BWR LTSBO scenario. Like Kr-85, Xe-135 is also a noble gas that is not depleted 

by natural deposition, sprays, or the action of filters. However unlike Kr-85, Xe-135 experiences 

significant ingrowth from iodine-135 (I-135) and decay during the BWR LTSBO event. The 

ingrowth and decay of Xe-135 can be seen by comparing the activity balance file plot for Xe-135 

shown in Figure 6-4 with the activity balance file plot for Kr-85 shown in Figure 6-3. The 

ingrowth of Xe-135 is clearly seen in Figure 6-4 in the increase in Xe-135 activity in the fuel 

(blue line) for the period between the reactor shutdown and the beginning fuel damage (9 

hours). Additionally, the continued ingrowth of the Xe-135 in the fuel is clearly indicated by its 

persistence at greater than 24 hours after the initiating event. The decay of Xe-135 is indicated

in the release path depletion (gray line) between 9 and 20 hours. This depletion reduces the 

fraction of Xe-135 release to the free atmosphere to about 50 percent of the Xe-135 in the fuel 

at the beginning of fuel damage.

Figure 6-5 depicts the plot of the RASCAL 4.3.1 cesium-137 (Cs-137) activity balance file for the 

unmitigated BWR LTSBO scenario. The decay of Cs-137 can be ignored because it has a long 

half-life. Additionally, the BWR LTSBO scenario does not include the use of containment sprays 

or filtration by the SBGTS. Consequently, the only depletion mechanism applied to activity prior 

to release to the free atmosphere are the natural deposition of Cs-137 particles in the release 

path and scrubbing as the Cs-137 particles pass through the wetwell suppression pool.
6-7

Figure 6-4 RASCAL 4.3.1 Xe-135 activity balance during a BWR Mark III LTSBO event

Figure 6-5 RASCAL 4.3.1 Cs-137 activity balance during a BWR Mark III LTSBO event
6-8

There is a significant difference between the Cs-137 activity balance file plot (Figure 6-5) and

the activity balance file plots for Kr-85 and Xe-135 (Figure 6-3 and 6-4). Almost all of the activity 

released from the fuel is depleted in the release path (orange line). As a result, the activity 

released to the atmosphere and available for later release is a small value compared to the 

activity initially in the fuel (blue line) and the depleted activity (gray line). In fact, the activity 

available for release to the free atmosphere is the small difference between two large numbers. 

This fact has significant consequences related to the accuracy and precision of the estimates of 

activity released to the free atmosphere.

Assuming that the initial Cs-137 activity in the fuel is well-known compared to the activity 

depleted in the release path, a small change in the calculated value of depleted activity will 

result in a relatively large change in activity released to the free atmosphere. For example, 

changing the fraction of activity depleted from 99.9 percent of the initial activity to 99.0 percent 

would increase the activity released to the free atmosphere by an order of magnitude.

The practical implication of the sensitivity of activity release to the atmosphere to changes in 

depletion is that large differences can be expected in Cs-137 source term estimates of various 

models as a result of small differences in representations of depletion processes within the 

models. It seems unlikely that the models used to represent the depletion processes in 

RASCAL and other consequence assessment models warrant precision greater than 2 

significant figures.

Figures 6-6 and 6-7 depict the plots of the RASCAL 4.3.1 activity balances for I-131 and I-135, 

respectively. The radionuclides decay, as well as deposit, in the release path. Both 

radionuclides show the dominance of depletion in the activity balance.
6-9

Figure 6-6 RASCAL 4.3.1 I-131 activity balance during a BWR Mark III LTSBO event

Figure 6-7 RASCAL 4.3.1 I-135 activity balance during a BWR Mark III LTSBO event

7-1

7.0 IMPORTANCE

During the emergency response to the Fukushima Daiichi accident, there were frequent 

requests to identify a limited number of radionuclides that were the most important contributors 

to doses. RASCAL 4.3 includes a feature to process the total radionuclide activity released to 

the environment in the course of an event and evaluate the relative importance of the 

radionuclides to five dose measures and rank the radionuclides in order of importance. The 

order of importance is a function of the time step as well as the dose calculated. The 

importance utility calculates importance at the end of the release and at seven additional time

steps ranging from 1 day (d) to 10 years (yr). The results of the importance calculation are 

available through the user interface.

7.1 The Importance Model

The importance model assumes that the importance of radionuclides can be determined from 

pseudo dose calculations that are based on the dose calculation methods described in 

NUREG-1940. The pseudo doses calculated in RASCAL 4.3.1 are for the submersion (cloud 

shine), inhalation, ground shine, and ingestion pathways, and for total effective dose equivalent 

(TEDE).

The pseudo dose for a radionuclide i for cloud submersion during plume passage is defined as:

ppDDii(tt) = QQii(tt) × DD ii (7-1)

where

pDi(t) = the pseudo dose from radionuclide i at time t = 0,

Qi(t) = total activity release of radionuclide i decayed to the release time,

DCi = submersion dose coefficient for radionuclide i.

After plume passage, the cloud submersion pseudo dose is calculated as:

ppDDii(tt) = QQii(tt) × DD ii × ddddii × rr ii(tt) (7-2)

where

dvi = deposition velocity for radionuclide i, (0.0 m/s for noble gases, 0.003 m/s for 

iodines, and 0.001 m/s for other radionuclides),

rsi(t) = resuspension factor for time t after the end of release (NUREG-1940 

Section 7).

Similar equations define the pseudo doses for the inhalation, ground shine, and ingestion 

pathways. The pseudo doses for the inhalation pathway during plume passage are calculated 

by:
7-2

pp ii(tt) = QQii(tt) × vv × DD ii (7-3)

where

vb = breathing rate (m/s),

DCi = inhalation dose coefficient for radionuclide i.

After plume passage the inhalation pseudo dose is calculated as:

pp ii(tt) = QQii(tt) × ddddii × rr ii(tt) × vv × DD ii (7-4)

The pseudo doses for the ground shine pathway are calculated by:

pp ii(tt) = QQii(tt) × DD ii × ddddii × wwww(tt) (7-5)

where

DCi = ground shine dose coefficient for radionuclide i,

wx(t) = weathering factor for ground.

RASCAL 4.3 calculates a pseudo TEDE dose potential. It is the sum of the pseudo doses for 

the submersion, inhalation, and ground shine pathways.

Finally, the ingestion pathway pseudo dose is calculated as:

pp ii(tt) = QQii(tt) × DD ii × ddddii × wwwwww (tt) (7-6)

where

DCi = ingestion dose coefficient for radionuclide i,

wxlv(t) = weathering factor for leafy vegetables.

The importance of radionuclide i to each of the dose pathways at time t is calculated as:

IIii(tt) = pp ii(tt)

∑ pp ii(tt) ii

(7-7)

where

Ii(t) = importance of radionuclide i and the summation over all radionuclides 

releases.

The sum of pseudo doses of all radionuclides is referred to as the dose potential for the 

pathway.
7-3

Note that RASCAL 4.3 uses the dose coefficient for the submersion, inhalation, and ground

shine pathways that were selected in the user interface, either FGR 11 and FGR 12 [29] dose 

coefficients or FGR 13 dose coefficients. The FGR 13 dose coefficients are for an adult.

The importance of each radionuclide in the source term includes the contributions to the pseudo 

dose from all daughters. When a parent radionuclide and a daughter radionuclide are both 

explicitly included in the source term, they are treated separately. The importance of the parent 

will include contributions from daughter activity that grows in after release. It will not include 

contributions from the explicit daughter activity that is included in the source term. By the same 

token, the importance of the explicit daughter will only be based on the activity i in the source 

term and the activity of any additional daughters that grow in after release. It will not include 

any contribution of the daughter that grows in from the explicit parent.

The ingestion pathway is generally not treated in RASCAL 4.3 because it is of secondary 

importance in emergency response. Ingestion pathway doses can be minimized by monitoring 

and interdiction. However, there may be some delay between plume passage and the start of 

effective monitoring and interdiction. The ingestion pathway importance calculation in RASCAL 

4.3 is meant to provide a quick, if gross, indication of those radionuclides that might contribute 

most to ingestion doses.

The ingestion importance calculation assumes that the likely early ingestion pathway is via 

consumption of leafy vegetables. Activity is deposited on the vegetables during plume passage 

and is removed from the leaves by various environmental processes until the vegetables are 

harvested. These processes are represented by weathering function in Equation 7-8. The 

weathering function is defined as:

wwwwww (tt) = ee −ln(2)×14 (7-8)

where

14 = effective half-life of the weathering process, which is assumed to end after 

183 d (6 months).

There are many factors that are important in calculating ingestion pathway doses that are not 

included in RASCAL 4.3. Among these factors are the variation of interception fractions of 

various types of leafy vegetables and the removal of activity from leaf surfaces by handling, 

washing, and food preparation. Age is another important factor that is not considered in 

RASCAL importance calculations. The dose coefficient and the consumption are both functions 

of age. Neither the variation of the dose coefficient with age nor the variation of consumption 

with age is treated in the calculation of the pseudo doses used to determine relative importance. 

As a result, caution should be used in the interpretation and extrapolation of the ingestion 

importance numbers.
7-4

7.2 Importance Results

The importance calculation results are presented in two parts. The first part establishes a 

context for interpretation of the radionuclide specific importance values. This context is 

important because all importance values are normalized to give a total importance of 1.00. The 

contextual information in the first part of the results shows the change in TEDE dose potential 

with time and the change with time of the relative contributions of the submersion, inhalation, 

and ground shine pathways to TEDE. Figure 7-1 shows an example of the contextual portion of 

the importance results file.

Relative Importance of TEDE

Days 0. 1. 7. 30. 183. 365. 1825. 3650.

rTEDE 1.0E+00 5.0E-07 2.9E-07 1.1E-07 6.1E-08 4.9E-08 1.5E-08 7.5E-09

Relative Importance of Pathways to TEDE

Days 0. 1. 7. 30. 183. 365. 1825. 3650.

cs 3.4E-02 4.2E-04 2.8E-04 5.7E-05 3.0E-07 2.4E-07 9.2E-08 8.8E-08

inh 9.7E-01 3.9E-02 3.9E-02 1.4E-02 8.9E-05 7.4E-05 5.1E-05 7.5E-05

gs 8.5E-07 9.6E-01 9.6E-01 9.9E-01 1.0E+00 1.0E+00 1.0E+00 1.0E+00

Figure 7-1 Example of the importance file contextual portion

The rTEDE row clearly shows that the dose potential during plume passage (t = 0) is orders of 

magnitude larger than the potential following plume passage. Similarly, the cloud shine (cs), 

inhalation (inh), and ground shine (gs) rows show that inhalation is the dominant pathway during 

plume passage and that ground shine is the dominant pathway following plume passage.

The second portion of the importance results file shows the importance of specific radionuclides. 

Figure 7-2 shows a portion of the activity balance file that presents the importance of specific 

radionuclides for a PWR LOCA event.
7-5

Cumulative Importance to dose at t = 1. days

 Cloudshine Inhalation Groundshine Ingestion TEDE 

 1 I-132 0.21 Sr-90 0.23 I-132 0.21 I-131 0.30 I-132 0.20 1

 2 La-140 0.41 Pu-241 0.36 La-140 0.39 Cs-134 0.51 La-140 0.38 2

 3 Cs-134 0.54 I-131 0.47 Cs-134 0.52 Te-132 0.61 Cs-134 0.50 3

 4 I-133 0.61 Sr-89 0.56 I-133 0.59 Cs-137* 0.71 I-133 0.58 4

 5 Te-132 0.68 Cm-242 0.65 Te-132 0.67 Ba-140 0.78 Te-132 0.65 5

Cumulative Importance to dose at t = 7. days

 Cloudshine Inhalation Groundshine Ingestion TEDE 

 1 La-140 0.44 Sr-90 0.27 La-140 0.41 Cs-134 0.29 La-140 0.40 1

 2 Cs-134 0.65 Pu-241 0.41 Cs-134 0.62 I-131 0.54 Cs-134 0.60 2

 3 Cs-136 0.73 Sr-89 0.52 Cs-136 0.70 Cs-137* 0.68 Cs-136 0.68 3

 4 I-131 0.79 Cm-242 0.61 I-131 0.76 Ba-140 0.75 I-131 0.74 4

 5 Cs-137* 0.84 Cs-134 0.70 Cs-137* 0.82 Sr-90 0.81 Cs-137* 0.79 5

Cumulative Importance to dose at t = 30. days

 Cloudshine Inhalation Groundshine Ingestion TEDE 

 1 Cs-134 0.56 Sr-90 0.32 Cs-134 0.54 Cs-134 0.47 Cs-134 0.53 1

 2 Cs-137* 0.70 Pu-241 0.50 Cs-137* 0.68 Cs-137* 0.69 Cs-137* 0.68 2

 3 La-140 0.81 Cs-134 0.60 La-140 0.78 Sr-90 0.79 La-140 0.77 3

 4 Cs-136 0.87 Cm-242 0.71 Cs-136 0.84 I-131 0.85 Cs-136 0.83 4

 5 Ba-140 0.90 Sr-89 0.79 Ba-140 0.87 Sr-89 0.90 Ba-140 0.86 5

Cumulative Importance to dose at t = 183. days

 Cloudshine Inhalation Groundshine Ingestion TEDE 

 1 Cs-134 0.76 Sr-90 0.41 Cs-134 0.75 Cs-134 0.53 Cs-134 0.75 1

 2 Cs-137* 0.98 Pu-241 0.62 Cs-137* 0.97 Cs-137* 0.83 Cs-137* 0.97 2

 3 Zr-95 0.99 Cs-134 0.74 Y-90 0.98 Sr-90 0.96 Y-90 0.98 3

 4 Nb-95 0.99 Cm-242 0.81 Zr-95 0.98 Ce-144* 0.97 Zr-95 0.98 4

 5 Ru-106* 1.00 Ce-144* 0.88 Sr-89 0.99 Y-90 0.98 Sr-89 0.99 5

Figure 7-2 Example of the importance file activity balance portion

The example only shows the five most important radionuclides for four time periods. The file 

lists the importance of all radionuclides (typically 70 to 80) for eight time periods. The time 

periods not shown in the figure are 0 d (end of model run), 3.65E+02 d (1 yr), 1.825E+03 d 

(5 yr), and 3.65E+03 d (10 yr). For each time period and pathway, the radionuclides are listed 

in order of decreasing importance. The number following the radionuclide is the fraction of dose 

potential contributed by that radionuclide and the radionuclides that are above it in the list.

The importance lists in Figure 7-2 illustrate two features that are common to most importance 

lists. The first is that the most important radionuclides are different for different dose pathways 

and the most important radionuclides change with increasing time after the release. The 

second is that the number of radionuclides that contribute significantly to dose potential 

decreases with increasing time. These points are clearly illustrated in the ground shine 

importance lists by comparing the lists for 1 and 183 d. The two most important radionuclides 

for ground shine at day 1 contribute about 39 percent of the dose potential. Neither radionuclide

is in the top 5 list for 183 d. Further, the top 2 radionuclides at day 183 contribute about 

97 percent of the dose potential.

Table 7-1 summarizes the variation in pathway importance for representative BWRs and PWRs

as a function of time after the end of release assuming a mid-cycle core melt event with 

containment failure. The 0 day entries include the dose potential from plume passage. 

Inhalation is the most important pathway during plume passage followed by cloud shine. During 

plume passage, ground shine is typically insignificant. After plume passage, ground shine is the 

dominant dose pathway, inhalation is a secondary pathway, and cloud shine is insignificant. 

The numbers in parentheses are the pathway fraction of the total dose potential.
7-6

Table 7-1 Dose pathway importance following a mid-cycle core melt event with 

containment failure

Most Important Least Important

BWR 

Mark 

III

LTSBO

0 days Inhalation (0.97) Cloud shine (0.029) Ground shine (< 0.001)

1 day Ground shine (0.94) Inhalation (0.055) Cloud shine (< 0.001)

7 days Ground shine (0.94) Inhalation (0.057) Cloud shine (< 0.001)

30 days Ground shine (0.99) Inhalation (0.01) Cloud shine (< 0.001)

6 months Ground shine (1.00) Inhalation (<0.001) Cloud shine (< 0.001)

BWR 

Mark

III

LOCA

0 days Inhalation (0.96) Cloud shine (0.036) Ground shine (< 0.001)

1 day Ground shine (0.94) Inhalation (0.062) Cloud shine (< 0.001)

7 days Ground shine (0.94) Inhalation (0.058) Cloud shine (< 0.001)

30 days Ground shine (0.98) Inhalation (0.016) Cloud shine (< 0.001)

6 months Ground shine (1.00) Inhalation (<0.001) Cloud shine (< 0.001)

PWR LTSBO

0 days Inhalation ((0.98) Cloud shine (0.021) Ground shine (< 0.001)

1 day Ground shine (0.92) Inhalation (0.081) Cloud shine (< 0.001)

7 days Ground shine (0.91) Inhalation (0.092) Cloud shine (< 0.001)

30 days Ground shine (0.98) Inhalation (0.022) Cloud shine (< 0.001)

6 months Ground shine (1.00) Inhalation (<0.001) Cloud shine (< 0.001)

PWR LOCA

0 days Inhalation (0.97) Cloud shine (0.027) Ground shine (< 0.001)

1 day Ground shine (0.94) Inhalation (0.064) Cloud shine (< 0.001)

7 days Ground shine (0.94) Inhalation (0.059) Cloud shine (< 0.001)

30 days Ground shine (0.99) Inhalation (0.014) Cloud shine (< 0.001)

6 months Ground shine (1.00) Inhalation (<0.001) Cloud shine (< 0.001)

Table 7-2 lists the 5 radionuclides with the greatest dose potential for the three important dose 

pathways following a mid-cycle core-melt accident with loss of containment at a typical BWR 

reactor with the Mark III containment. Table 7-3 provides the same information for a typical 

PWR reactor. The numbers in parentheses following the pathway are the relative pathway 

importance. For each pathway, the radionuclides are listed in order of decreasing importance. 

The number in parentheses following the radionuclide is the cumulative importance of the 

radionuclide plus the importance of the more important radionuclides in the pathway (i.e. the 

radionuclides listed above).
7-7

Table 7-2 Radionuclides most important to dose for a BWR Mark III following core 

melt with containment failure

Event Time Pathway

BWR 

Mark III 0 days

Cloud shine 

(0.029)

Inhalation 

(0.97)

Ground shine 

(<0.001)

Xe-133 (0.55) I-131 (0.70) I-132 (0.30)

I-132 ( 0.68) I-133 (0.77) I-131 (0.45)

LTSBO Xe-135 (0.81) Cs.137* (0.83) I-133 (0.57)

I-131 (0.87) Cs-134 (0.87) Te-132 (0.66)

I-133 (0.92) Te-132 (0.91) Cs-134 (0.74)

BWR 

Mark III 0 days

Cloud shine 

(0.036)

Inhalation 

(0.97)

Ground shine 

(<0.001)

Xe-133 (0.56) I-131 (0.31) I-132 (0.24)

Xe-135 (0.73) Cs-137* (0.42) La-140 (0.48)

LOCA I-132 (0.84) Pu-241 (0.52) Cs-134 (0.60)

La-140 (0.88) Cs-134 (0.60) Te-132 (0.67)

I-131 (0.91) Sr-90 (0.68) Cs-136 (0.72)

BWR 

Mark III 1 day

Cloud shine 

(<0.001)

Inhalation 

(0.056)

Ground shine 

(0.94)

I-132 (0.26) I-131 (0.48) I-132 (0.26)

I-131 (0.44) Cs-137* (0.62) I-131 (0.44)

LTSBO Cs-134 (0.55) Cs-134 (0.72) Cs-134 (0.55)

Te-132 (0..64) Ru-106* (0.79) Te-132 (0.64)

La-140 (0.72) Te-132 (0.85) La-140 (0.71)

BWR 

Mark III 1 day

Cloud shine 

(<0.001)

Inhalation 

(0.062)

Ground shine 

(0.94)

La-140 (0.36) Cs-137* (0.15) LA-140 (0.33)

I-132 (0.53) Pu-241 (0.28) I-132 (0.51)

LOCA Cs-134 (0.67) I-131 (0.41) Cs-134 (0.64)

Cs-136 (0.73) Cs-134 (0.52) Te-132 (0.70)

Te-132 (0.78) Sr-90 (0.62) Cs-136 (0.76)
7-8

Table 7-3 Radionuclides most important to dose for a PWR following core melt with 

containment failure

Event Time Pathway

PWR 0 days

Cloud shine 

(0.021)

Inhalation 

(0.98)

Ground shine 

(<0.001)

Xe-133 (0.61) I-131 (0.33) I-132 (0.32)

I-132 (0.81) Pu-241 (0.59) La-140 (0.47)

LTSBO I-131 (0.85) Cs-137* (0.68) Cs-134 (0.59)

La-140 (0.88) Cs-134 (0.75) Te-132 (0.68)

Cs-134 (0.91) Ce-144* (0.81) I-131 (0.75)

PWR 0 days

Cloud shine 

(0.0271)

Inhalation 

(0.97)

Ground shine 

(<0.001)

Xe-133 (0.71) I-131 (0.35 La-140 (0.34)

I-132 (0.79) Cs-137* (0.49 Cs-134 (0.50)

LOCA La-140 (0.86) Cs-134 (0.59) I-132 (0.66)

I-131 (0.90) Pu-241 (0.67) Cs-136 (0.73)

Cs-134 (0.93) Cm-242 (0.74) I-131 (0.80)

PWR 1 day

Cloud shine 

(<0.001)

Inhalation 

(0.081)

Ground shine 

(0.92)

I-132 (0.25) Pu-241 (0.35) I-132 (0.25)

La-140 (0.46) I-131 (0.48) La-140 (0.44)

LTSBO Cs-134 (0.61) Cs-137* (0.60) Cs-134 (0.58)

Te-132 (0.69) Cs-134 (0.69) Te-132 (0.67)

I-131 (0.76) Ce-144* (0.78) I-131 (0.75)

PWR 1 day

Cloud shine 

(<0.001)

Inhalation 

(0.064)

Ground shine 

(0.94)

La-140 (0.41) Cs-137* (0.18) La-140 (0.38)

Cs-134 (0.58) I-131 (0.33) Cs-134 (0.56

LOCA I-132 (0.70) Cs-134 (0.46) I-132 (0.67)

Cs-136 (0.77) Pu-241 (0.58) Cs-136 (0.75)

I-131 (0.83) Cm-242 (0.68) I-131 (0.81)

Importance is particularly useful as a tool to allow users to focus on the radionuclides that are 

most significant to dose. As seen in Tables 7-2 and 7-3, a small number of radionuclides 

contribute almost all of the dose potential for each pathway. The remaining radionuclides 

contribute very little to dose potential. However, they may be a distraction. To illustrate this 

point, consider the unmitigated BWR LTSBO scenario described in NUREG/CR-7110 Volume 1, 

Revision 1. Figure 7-3 compares the source term calculated by RASCAL 4.3.1 for the scenario 

with the MELCOR source term for the 61 radionuclides that are common to the two source 

terms. (Note: The MELCOR source term activities have been adjusted for decay from the 

initiating event to the time of release.) Figure 7-4 shows the same comparison for the 
7-9

17 radionuclides that contribute the most to the cloud shine dose pathway. The 

44 radionuclides not shown in Figure 7-4, but which appear in Figure 7-3, combined contribute

less than 0.5 percent to the total cloud shine dose pathway dose potential. The 0 days in the 

Figure title indicates that the activities are at the end of the model run. Figure 7-5 compares 

activities for the 19 radionuclides most important to the inhalation pathway dose potential. The 

42 radionuclides not shown in Figure 7-5 but which appear in Figure 7-3, combined contribute 

less than 0.5 percent to the total inhalation pathway dose potential.

Figure 7-3 Comparison of MELCOR and RASCAL 4.3.1 source term estimates 

radionuclides
7-10

Figure 7-4 Comparison of MELCOR and RASCAL 4.3.1 source term estimates of the 

most important radionuclides contributing to cloud shine dose

Figure 7-5 Comparison of MELCOR and RASCAL 4.3.1 source term estimates of the 

most important radionuclides contributing to inhalation dose
8-1

8.0 SOURCE TERM IMPORT, EXPORT AND MERGE

RASCAL 4 has always included a function to export the atmospheric source term to an external 

file. Early versions supported only the comma-separated values (CSV) format. RASCAL 4.3 

introduces several new features related to handling the atmospheric source terms. The first 

feature is the option to export this source term in an extensible markup language (XML) format 

and to apply an importance filter. The second feature added is the capability to import an 

atmospheric source term to be used with the RASCAL atmospheric transport, dispersion, and 

deposition (ATD) models bypassing the RASCAL internal source term model. Finally, 

RASCAL 4.3 includes a new tool to export and merge source terms. When combined, these 

features and the new tool give RASCAL 4.3 the capability to provide support for multi-unit 

releases.

The following sections describe the formats of the CSV and XML files, the export and import 

processes, and the capabilities of the merge/export tool.

8.1 Source Term Import Option

RASCAL 4.3 accepts imported source terms in either CSV or XML format. RASCAL 4.3 also 

creates exported atmospheric source terms in these formats. The export can be done from 

within the Source Term to Dose (STDose) model or using the Source Term Merge/Export tool.

8.1.1 CSV File Format

The CSV format is a commonly used way to move data between programs. It is a useful format 

as it is in plain-text form and can be edited by a variety of applications. It is also directly 

supported by the Excel spreadsheet software. This allows a user to modify a source term 

generated by the RASCAL source term models to make adjustments for processes not modeled 

by RASCAL. The file can then be imported and used as the basis for a model run using the 

RASCAL ATD models. Figure 8-1 illustrates a sample of an exported RASCAL 4.3 atmospheric

release source term file in the CSV format.

Creator, RASCAL v4.3.0 Source Term

File_Created, 2013/09/15 09:47

Site_Name, Arkansas - Unit 1

Release_Latitude, 35.310000

Release_Longitude, -93.231390

UTC_Offset, -6

Release_Height, 10.0 m

Case_Title, Basic 2 nuclide

Case_Runtime, 2013/09/15 09:46

Case_Desc, 

Activity_Units, Ci

Other_Info, Importance filter, None

Interval,2013/09/15,2013/09/15,2013/09/15,2013/09/15,2013/09/15

Start,00:00,00:15,00:30,00:45,01:00

Cs-137,3.00E-01,3.00E-01,3.00E-01,3.00E-01,0.00E+00

I-131,1.11E+00,1.11E+00,1.11E+00,1.11E+00,0.00E+00

Figure 8-1 Example of a RASCAL 4.3 CSV format exported atmospheric release 

source term file
8-2

Table 8-1 presents a description of the lines in the exported atmospheric source term in the 

RASCAL 4.3 CSV file. Keywords start each line and must appear exactly as shown. The 

description indicates what follows the comma after the keyword. In some cases (e.g., time 

steps) there will be multiple items separated by commas. The table also indicates whether a 

line is required for import to RASCAL.

Table 8-1 Description of the lines in a RASCAL 4.3 CSV format exported atmospheric 

release source term file

Keyword Description of values after keyword Requirement for 

import file

Creator Model name and version; result type Optional

File_Created Date and time the export file was created Optional

Site_Name Name of the location Optional

Release_Latitude Latitude in decimal degrees of the model 

release point. Optional

Release_Longitude Longitude in decimal degrees of the model 

release point. Optional

UTC_Offset Hours from UTC Optional

Release_Height Release height and units Recommended

Case_Title Title given to the modeling run Optional

Case_Runtime When the modeling run occurred Optional

Activity_Units Units for the reported activities Recommended

Other_Info Status of the importance filter option Optional

Interval The dates of each time step, separated by 

commas Required

Start The times of each time step, separated by 

commas. Must be exactly 15 minutes apart Required

The above is followed by a line for each radionuclide in the 

release consisting of the radionuclide name, a comma, and the 

activity for that radionuclide for each time step (separated by 

commas)

Required

All the above elements are part of the exported CSV file. Only the last three are required for an 

import file. Note that the time step for RASCAL 4.3 atmospheric source terms is 15 minutes.

8.1.2 XML File Format

The XML format is used to create documents that are readable by both humans and computers.

It is useful to create a structured file that can be validated easily. This format is included in 

RASCAL 4.3 as part of the effort to standardize information exchange formats. Figure 8-2 

illustrates a sample of an exported atmospheric release source term file in the XML format.
8-3

<?xml version="1.0" encoding="utf-8"?>

<!--RASCAL atmospheric source term XML export file-->

<Atmospheric_SourceTerm>

<EventLocation Name="Arkansas - Unit 1" Latitude="35.31" Longitude="-93.23139" 

Elevation="103" UTC_Offset="-6" TimeType="Local 24 hour clock"/>

<Creator ModelName="RASCAL 4.3" CaseName="Basic 2 nuclide" ModelRunTimeStamp="2013-

09-15T09:46:00" Description="" CreationDate="2013-09-15" CreationTime="09:47:14" 

Analyst_Name="Dose Analyst" OtherInfo="Importance filter: None"/>

<ReleasePoint Name="Release Point 1" Release_Height="10" Release_Height_Units="m" 

Start_Date="2013-09-15" Start_Time="00:00:00" End_Date="2013-09-15" 

End_Time="04:00:00" Activity_Units="Ci">

<Release_Step Nuclide_Count="2" Step_Sequence_Number="1" Start_Date="2013-09-15" 

Start_Time="00:00:00">

<Activity_Release Nuclide_Name="Cs-137" Released_Amount="3.00E-01"/>

<Activity_Release Nuclide_Name="I-131" Released_Amount="1.11E+00"/>

</Release_Step>

...... repeats for each time step

<Release_Step Nuclide_Count="2" Step_Sequence_Number="5" Start_Date="2013-09-15" 

Start_Time="01:00:00">

<Activity_Release Nuclide_Name="Cs-137" Released_Amount="0.00E+00"/>

<Activity_Release Nuclide_Name="I-131" Released_Amount="0.00E+00"/>

</Release_Step>

</ReleasePoint>

</Atmospheric_SourceTerm>

Figure 8-2 Example of a RASCAL 4.3 XML format exported atmospheric release 

source term file

Table 8-2 presents a description of the lines in the exported atmospheric release source term in 

the RASCAL 4.3 XML file.
8-4

Table 8-2 Description of the lines in a RASCAL 4.3 XML format exported atmospheric 

release source term file

Line or Element Description

Line 1 Standard XML file header

Line 2 Comment

Deposition_Sourceterm Main element of the file; indicates that it is deposited material 

(not an atmospheric release)

EventLocation

Contains the following attributes describing the release point:

Name

Latitude (degrees; negative is South)

Longitude (degrees; negative is West)

Elevation (meters)

UTC_Offset (hours from Greenwich)

TimeType (always = Local 24 hour clock)

Creator

Contains the following attributes describing the tool creating 

the file:

ModelName

CaseName

ModelRunTimeStamp (when the model was run)

CreationDate (when this file was created)

CreationTime (when this file was created)

Analyst_Name

OtherInfo (importance filter information)

Release_Point

Contains the following attributes describing the location of the 

release being reported;

Name

Release_Height

Release_Height_Units

Start_Date

Start_Time

End_Date

End_Time

Activity_Units

Release_Step

Repeats for 15 minute time step of the STDose time 

dependent source term

Nuclide_Count – how many radionuclides released

Step_Sequence_Number – from 1 to N, when N = number 

time steps

Start_Date

Start_Time

Activity_Release

There will be one element for each radionuclide in the 

release step.

Nuclide_Name

Released_Amount

8.2 Import Process

The atmospheric source term import option is available in the STDose model for all event types. 
8-5

When an atmospheric source term is imported, RASCAL 4.3 obtains the time-dependent 

atmospheric source term and release height from the imported file. The RASCAL 4.3 modules 

that would normally calculate the source term and release information are bypassed.

Following is a list of how the import process handles inputs:

• No checking is done to make sure the site name or the geographic coordinates in 

the import file match the location specified in the STDose model. Any import file 

can be used for any site selected.

• The import file release height will be used if available. If the release height 

and/or units is missing or unrecognized, a release height of 10 meters (m) will be 

used.

• If the activity units are missing or unrecognized a default unit of curies (Ci) will be 

used.

• The time step must be exactly 15 minutes. The import process is aborted if a 

nonstandard time step is detected.

• Radionuclide names must be formatted as used by RASCAL. For example “Kr85” [krypton-85] is made up of the following: first letter capitalized, following 

letters not capitalized; a dash followed by the numerals. Finally, any trailing 

characters such as ‘m’ or ‘*’. The import process checks the radionuclide name 

against the names in the RASCAL radionuclide database. It will recognize 

radionuclides for which RASCAL includes implicit daughters and will add the * 

(e.g., Cs-137 will be converted to Cs-137* for RASCAL use). Records containing 

unrecognized radionuclide names will be ignored but the import process will not 

be aborted.

• Up to 120 radionuclides can be in the import file. The import process will abort if 

there are 121 or more radionuclides.

• The import file can span more than 96 hours but only the first 96 hours of data 

will be imported. This matches the maximum 96-hour calculation duration of the 

STDose model.

• For the XML format, the file is validated against the schema (XSD). Failure to 

validate results in the import aborting.

RASCAL 4.3.1 expands the import function to build in missing daughters. For example, assume 

the source term was filtered on export to include only the top five contributors to dose and was 

then imported back into RASCAL. In RASCAL 4.3 an error might have been generated as 

some daughters needed by the ATD models may have been removed by the filtering process.

An upgrade to RASCAL 4.3.1 detects those missing daughters and adds them when needed so 

that the import process can complete.
8-6

8.3 Export Process

The atmospheric source term export option is available for all STDose model event types. It is 

accessed from the Release vs. Time screen from the Source Term tab on the main STDose 

display.

The exported file can be in either CSV or XML format. Section 8.1 provides a description of the 

formats. There are two options that impact the formatting of the export file. First, there is an 

option to strip * characters from the radionuclide names. This is useful when the export file is to 

be used with other software (e.g., National Atmospheric Release Advisory Center) that does not 

indicate that implicit daughters are built-in with the asterisk. Second, there is an option to use 

the RASCAL 4.2 format. This will not include all the release information but is retained for 

backward compatibility. This last option applies to the CSV format only.

There is also an option to filter the list of nuclides in the source term to be included in the export 

file. The default is to include all the radionuclides in the release to the atmosphere. However, 

this can be a list of 70 plus radionuclides and may be problematic when imported by other 

codes. The export process can be configured to export only a select set of radionuclides that 

are important to dose. Section 6 provides a detailed discussion of the RASCAL 4.3 importance 

calculation. The user may specify the filter to export only a certain top number of radionuclides 

that contribute to dose or to export all the nuclide needed to get a percentage of the dose.

Note: The Filter by Importance to Dose option should not be used if the exported source term 

file is to be imported into RASCAL 4.3. The import function in RASCAL 4.3 is not able to add 

any missing daughters. However, filtered files will import properly into RASCAL 4.3.1.

8.4 RASCAL 4.3 Source Term Merge/Export Tool

The Source Term Merge/Export tool adds an external capability to the RASCAL 4.3 STDose 

model. It provides two basic capabilities. First, it can export the atmospheric source term from 

a saved STDose case in either the CSV or XML format. Second, it can merge atmospheric 

source terms from multiple STDose model runs into a single new source term that can then be 

exported.

8.4.1 Load Cases

The merge/export tool works with completed and saved STDose case files. The saved cases to 

be exported or merged must include the calculated results. Cases saved before doing the dose 

calculations do not contain the source term information and cannot be used.

The load operation extracts the atmospheric source term component from the case file. If a 

single case is loaded it can only be exported. If multiple cases are loaded then they must be 

merged before exporting.
8-7

8.4.2 Merge

Before the merge begins, the user needs to review these parameters and select which values to 

use. There is no requirement that the source terms to be merged be from the same release 

point. No checking is done on the loaded cases to enforce a location match.

As such, the release height and latitude/longitude cannot be merged. The RASCAL user must 

select from one of the values used in the loaded cases. For example, only a single release 

height is allowed. If the RASCAL cases used differing release heights, the user must choose 

the height to be used in the merged file from one of the heights in the cases to be merged. The 

case title, analyst name, and site name can be edited as needed. The case descriptions for the 

cases to be merged are concatenated and presented in an editable form. The use may modify 

this text to adequately describe the merged source terms.

The time steps of the merge file begin with the earliest time found in the loaded cases. If the 

time steps of the other cases do not align exactly on the 15-minute steps, the activity is divided 

up between time steps as needed. There can be time gaps between the individual case source 

terms where no activity is released. The merge tool will build in the needed time steps with zero 

activity. The combined source terms cannot exceed 7 days in total duration.

8.4.3 Export

The export function in the Merge/Export tool operates the same and has the same options as 

the export in the STDose mode (Section 8.3).

8.4.4 Multi-Unit

The merging of atmospheric source terms provides a means to calculate doses for releases 

from multiple units on a single nuclear power plant site. This technique assumes that the 

releases occur at the same location. In reality, the individual release points may be separated 

by as much as several hundred feet. This separation may cause the results near the release 

points to be in error, but it should not have a significant effect on the results calculated for offsite 

locations.

The general procedure to be followed is to run RASCAL 4.3 for each release individually and 

save the cases as usual. When all individual cases have been run, use the Source Term 

Merge/Export tool to create and export a combined source term file. Then re-run RASCAL 4.3 

and import the merged combined source term file to calculate doses of the combined source 

term.

9-1

9.0 REFERENCES

[1] NUREG-1940, “RASCAL 4: Description of Models and Methods,” U.S. Nuclear 

Regulatory Commission, Washington, DC, December 2012.

[2] NUREG-1465, “Accident Source Terms for Light-Water Nuclear Power Plants,” U.S. 

Nuclear Regulatory Commission, Washington, DC, February 1995.

[3] NUREG-1935, Part 1, “State-of-the-Art Reactor Consequence Analyses (SOARCA) 

Report,” U.S. Nuclear Regulatory Commission, Washington, DC, November 2012.

[4] NUREG-1935, Part 2, “State-of-the-Art Reactor Consequence Analyses (SOARCA)

Report,” U.S. Nuclear Regulatory Commission, Washington, DC, November 2012.

[5] NUREG/CR-7110, Volume 1, Revision 1, “State-of-the-Art Reactor Consequence 

Analysis Project Volume 1: Peach Bottom Integrated Analysis,” U.S. Nuclear Regulatory 

Commission, Washington, DC, May 2013.

[6] NUREG/CR-7110, Volume 2, Revision 1, “State-of-the-Art Reactor Consequence 

Analysis Project Volume 2: Surry Bottom Integrated Analysis,” U.S. Nuclear Regulatory 

Commission, Washington, DC, August 2013.

[7] NUREG-1228, “Source Term Estimation During Incident Response to Severe Nuclear 

Power Plant Accidents,” U.S. Nuclear Regulatory Commission, Washington, DC, 

October 1988.

[8] NUREG/CR-3727, “Fission Product Removal in Engineered Safety Feature (ESF)

Systems,” U.S. Nuclear Regulatory Commission, Washington, DC, April 1984 (available 

in Agencywide Documents Access and Management System (ADAMS) under Accession 

No. 8405220035).

[9] NUREG/BR-0150, Volume 1, Revision 4, “Response Technical Manual (RTM)-96,” 

U.S. Nuclear Regulatory Commission, Washington, DC, March 1996.

[10] SECY-13-0112, “Consequence Study of a Beyond-Design-Basis Earthquake Affecting 

the Spent Fuel Pool for a U.S. Mark 1 Boiling-Water Reactor,” U.S. Nuclear Regulatory 

Commission, Washington, DC. October 9, 2013.

[11] U.S. Environmental Protection Agency (EPA), “PAG Manual Protective Action Guides 

And Planning Guidance For Radiological Incidents,” Draft for Interim Use and Public 

Comment, Washington, DC, March 2013.

[12] U.S. Food and Drug Administration, “Guidance Potassium Iodide as a Thyroid 

Blocking Agent in Radiation Emergencies; Availability” Federal Register, Vol. 66, 

December 11, 2001, p. 64046 (66 FR 64046).

[13] U.S. Food and Drug Administration, Revision 1, “Guidance for Industry – KI in 

Radiation Emergencies – Questions and Answers,” Rockville, MD, December 2002.
9-2

[14] EPA 402-R-99-001, “Cancer Risk Coefficients for Environmental Exposure to 

Radionuclides,” Federal Guidance Report No. 13, U.S. Environmental Protection 

Agency, Washington, DC, September 1999.

[15] 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, U.S. Environmental Protection Agency, Washington, DC. September 

1988.

[16] DCPAK3.02, “Dose and Risk Coefficient File Package for FGR 13,” FGR13PAK, Oak 

Ridge National Laboratory, Oak Ridge, TN. 2011.

[17] U.S. National Weather Service, “National Digital Forecast Database (NDFD),”

http://www.nws.noaa.gov/ndfd, Silver Spring, MD. November 2013.

[18] U.S. Geological Survey, “Global Digital Elevation Model (GTOPO30),” EROS Data 

Center Distributed Active Archive Center (EDC DAAC),

https://lta.cr.usgs.gov/GTOPO30, Sioux Falls, SD, 1996.

[19] Raytheon ITSS and U.S. Geological Survey, “Completion of the 1990's National Land 

Cover Data Set for the Conterminous United States,” Photogrammetric Engineering and 

Remote Sensing, Vol. 67, p. 650-662, Sioux Falls, SD, 2001.

[20] EPA-454/B-08-001, “AERSURFACE User’s Guide,” U.S. Environmental Protection 

Agency, Washington, DC, January 16, 2013.

[21] NUREG/CR-6703, “Environmental Effects of Extending Fuel Burnup Above 60 

GWd/MTU,” U.S. Nuclear Regulatory Commission, Washington, DC, January 2001.

[22] NUREG-1793, Supplement 2, “Final Safety Evaluation Report Related to Certification of 

the AP1000 Standard Plant Design,” U.S. Nuclear Regulatory Commission, Washington, 

DC, September 2011.

[23] 26A6642AH, Revision 9, “ESBWR Design Control Document,” GE-Hitachi Nuclear 

Energy Americas LLC, Wilmington, NC, December 2010 (available in ADAMS under 

Accession No. ML103440215).

[24] UAP-HF-13212, Revision 4, “Submittal of US-APWR Design Control Document 

Revision 4 in Support of Mitsubishi Heavy Industries, Ltd.'s Application for Design 

Certification of the US-APWR Standard Plant Design, Arlington, VA, September 10, 

2013 (available in ADAMS under Accession No. ML13262A304).

[25] AREVA NP Inc., Letter from Sandra M. Sloan Director of Regulatory Affairs, AREVA NP 

Inc. to Document Control Desk NRC, NRC:11:085 ‘Submittal of Revision 3 of the U.S. 

EPR Final Safety Analysis Report for Design Certification,’ Lynchburg, VA, August 10, 

2011 (available in ADAMS under Accession No. ML11230A572).
9-3

[26] 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.

[27] 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.

[28] ANSI/ANS-18.1-1999, “Radioactive Source Term for Normal Operation of Light Water 

Reactors,” American Nuclear Society, La Grange Park, IL, September 21, 1999.

[29] 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, 

DC, September 1993.

A-1

APPENDIX A NUREG-1940 ERRATA INFORMATION

The following appendix contains the errata information for NUREG-1940. The revised 

information is denoted in red (bold).

Section 4.5.2.2 Gases (page 4-20):

When the temperature falls below about -3oC, the physical characteristics of snow change. As a 

result, there is a significant decrease in the wet deposition velocity of gases. RASCAL 4 does 

not calculate scavenging of gases by snow when the temperature is less than -3oC (i.e., the wet 

deposition velocity is set to zero).

Section 6.4.3 Mixing Height, Equation (6-7) (page 6-11):

The exponential interpolation of the mixing height is:

HH(tt) = aa ∙ ee �− 24�, (6-7)

where

H(t) = mixing height (m) at time t

a = Hmorn /exp(-b)

bi = 24 ln(Haft/Hmorn) / (24 - tsunset)

Hmorn = morning mixing height (m)

Haft = afternoon mixing height (m)

tsunset = time of sunset (h)

Appendix A, Table A-4 RASCAL 4 Radionuclide Decay Chains (Page A-14):





NUREG

-1940

Supplement 1

RASCAL 4.3: Description of Models and Methods