NUREG-1887

RASCAL 3.0.5: Description of

Models and Methods

U.S. Nuclear Regulatory Commission

Office of Nuclear Security and Incident Response

Washington, DC 20555-0001
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NUREG-1887

RASCAL 3.0.5: Description of

Models and Methods

Manuscript Completed: August 2007

Date Published: August 2007

Prepared by

S.A. McGuirea

J.V. Ramsdell, Jr.b

G.F. Atheyc

aoffice of Nuclear Security and Incident Response

U.S. Nuclear Regulatory Commission

Washington, DC 20555-0001

bPacific Northwest National Laboratory

P.O. Box 999

Richland, WA 99352

cAthey Consulting

P.O. Box 178

Charles Town WV 25414-0178

Prepared for

Office of Nuclear Security and Incident Response

U.S. Nuclear Regulatory Commission

Washington, DC 20555-0001

Abstract

The code currently used by NRC's emergency operations center for making dose projections for

atmospheric releases during radiological emergencies is RASCAL version 3.0.5 (Radiological

Assessment System for Consequence AnaLysis). This code was developed by NRC. The first version was

created about 20 years ago. Since then the code has been undergoing continual improvement to expand

its capabilities and to update the models used in its calculations. This report describes the models and

calculational methods used in RASCAL 3.0.5. This report updates and supercedes the information in

NUREG-1741, "RASCAL 3.0: Description of Models and Methods," 2001.

RASCAL 3.0.5 evaluates releases from: nuclear power plants, spent fuel storage pools and casks, fuel

cycle facilities, and radioactive material handling facilities.

While RASCAL 3.0.5 operates as a single piece of software, it is really a set of inter-linked modules each

with a different function. These are:

I. Source term: this module calculates a time-dependent source term, which for nuclear power

plants, is composed of about 50 radionuclides including parents and daughters. This module is

unique in the world for its ability to model a wide variety of accidents based on plant conditions

for many different facility types.

2. Meteorological data processor: this module inputs weather observations and forecasts along with

local topography to generate time-dependent wind fields that will transport the plume.

3. Atmospheric transport and diffusion: this module uses the wind fields with a two-dimensional

Gaussian puff model to transport the plume downwind and to calculate concentrations of each

radionuclide as a function of time and location.

4. Dose calculator: this module calculates various types of doses resulting from airborne releases

(TEDE, thyroid, acute, etc.) to individuals at each location from three dose pathways - inhalation,

cloudshine, and groundshine. It also calculates the longer-term intermediate phase doses from

deposited radionuclides. The calculations are completely consistent with the EPA protective

action guide manual and the methods adopted by the Federal Radiological Monitoring and

Assessment Center (FRMAC).

5. Display of results: this module allows the user to display a wide variety of calculated results as

either a picture of the plume footprint on a map background for each of the result types or as

numeric table.

6. Uranium hexafluoride module: for uranium hexafluoride releases, RASCAL contains a heavy gas

model to account for the exothermic reaction with air and gravitational slumping of the plume.

iii

Table of Contents

A b stract ... ... . ... .... ... ... . .... ... .... .... ...

L ist of F igures ..................................

L ist of T ables ...................................

Acknow ledgm ents ...............................

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix

ix

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x i

I Nuclear Power Plant Source Term Calculations ...........

1.1 Nuclear Power Plant Parameters ..................

1 1. 1 Core Inventories ...........................

1.1.2 Coolant Inventories ........................

1.1.3 Reactor Coolant System Water Mass ..........

.1 .4 Reactor Containment Volumes ...............

1. 1.5 Reactor Power Levels ......................

1.1.6 Fuel B urnup ..............................

1. 1.7 Number of Assemblies in the Core ............

1.1.8 Design Pressure ...........................

1.1.9 Design Leak Rate ..........................

1.2 Source Term Types ............................

1.2.1 Basic Method to Calculate Source Terms .......

1.2.2 Time Core Is Uncovered Source Term .........

1.2.3 Ultimate Core Damage State Source Term ......

1.2.4 Containment Radiation Monitor Source Term ...

1.2.5 Source Term Based on Coolant Sample ........

1.2.6 Source Term Based on Containment Air Sample .

1.2.7 Source Term Based on Effluent Release Rates or C

1.2.8 Monitored Release - M ixtures ................

1.3 Release Pathw ays .............................

1.4 Release Pathway Models and Reduction Mechanisms .

1.4.1 Containment Leakage in PWRs ...............

1.4.2 Containment Leakage in BWRs ...............

1.4.3 Containment Bypass .......................

1.4.4 Steam Generator Tube Ruptures in PWRs ......

1.5 Leakage Fractions .............................

1.5.1 Percent Volume per Time ...................

..............

..............

..............

..............

..............

...................

...................

...................

...................

...................

oncentrations .......

...................

...................

...................

...................

...................

...................

... . . 1-1

.... . 1-1

... . . 1-1

..... 1-3

..... 1-4

1-5 

1-5 

. -5 

1-6 

1-6 

1-6 

1-6 

1-6 

..... 1-7

.... 1-10

1-11

.... 1-18

1-19

1-19

.... 1-19 .... 1-22

.... 1-24

.... 1-25

.... 1-25

.... 1-26

.... 1-26

.... 1-28

... 1-28

... 1-29

1-29

... 1-30

... 1-30

... 1-31

.... 1-36

1.5.2 Leak Rate Based on Containment Pressure and Hole Size .

1.5.3 Coolant Flow Rate ................................

1.5.4 Direct Release to Atmosphere .......................

Decay Calculations in the Source Term ....................

Quality Assurance for the Source Term Calculations .........

R eferences .. ... .................................. ...

1.6

1.7

1.8

2 Spent Fuel Storage Source Term Calculations .......................................... 2-1

v
2.1 Basic Method to Calculate Spent Fuel Source Terms ................................ 2-1

2.2 Spent Fuel Radionuclide Inventories ............................................. 2-1

2.3 Fractions of Inventory Available for Release in Spent Fuel Accidents ................... 2-2

2.3.1 Spent Fuel Pool W ater Drained ............................................ 2-3

2.3.2 Fuel Dam aged Under W ater ............................................... 2-4

2.3.3 Release from a Dry Storage Cask ........................................... 2-4

2.4 Release Pathways and Reduction Factors ......................................... 2-4

2.5 Leakage F ractions ............................................................ 2-5

2.6 R eferences ................................................................. 2-5

3 Fuel Cycle and M aterials Source Term s .. ; ............................................ 3-1

3.1 Basic M ethod to Calculate the Source Term ....................................... 3-I

3.2 UF6 Releases from Cylinders ............. ......... ........................... 3-1

3.3 UF 6 Releases from Cascade Systems ............................................. 3-3

3.4 Fires Involving Uranium Oxide ................................................. 3-5

3.5 Explosions Involving Uranium O xide ............................................ 3-6

3.6 C riticality A ccidents .......................................................... 3-7

3.6.1 Prom pt Shine Dose Calculation ............................................ 3-10

3.7 Sources and M aterial in a Fire ................................................. 3-10

3.8 Isotopic Release Rates and Concentrations ....................................... 3-13

3.9 Computing Uranium Specific Activity from Enrichment ............................ 3-13

3.10 R eferences ............................................................... 3-13

4 Transport, Diffusion, and Dose Calculations ...................... 4-1

4.1 Theoretical Bases for Gaussian M odels ........................................... 4-1

4. 1.1 G aussian Puff M odel .................................................... 4-2

4.1.2 Straight-Line Gaussian Plume M odels ....................................... 4-3

4.1.3 Treatment of Calm W inds ................................................. 4-4

4.1.4 M odel Domains and G rids ................................................ 4-6

4.2 T ransport .................................................................. 4-6

4.2.1 Puff M odel Transport .................................................... 4-6

4.2.2 Plum e M odel Transport .................................................. 4-7

4.3 D ispersion Param eters ........................................................ 4-8

4.3.1 N orm al D ispersion ...................................................... 4-8

4.3.2 Low Wind Speed (Building Wake) Correction .............................. 4-9

4.3.3 Puff M odel D ispersion Parameters ......................................... 4-1I

4.3.4 Plume M odel Dispersion Parameters ....................................... 4-12

4.3.5 Calm Wind Dispersion Parameters for the Puff Model ......................... 4-12

4.3.6 Calm Wind Dispersion Parameters for the Plume Model ...................... 4-13

4.4 M ixing Layer T hickness ...................................................... 4-13

4.5 Stack Plum e R ise ........................................................... 4-13

4.5.1 F inal Plum e R ise ....................................................... 4-13

4.5.2 T ransition Plum e R ise ................................................... 4-16

4.5.3 Effective Release H eight ................................................ 4-17

4.5.4 Effective Release Height for Fires ......................................... 4-17

4 .6 D eposition ................................................................ 4-18

4.6.1 D ry D eposition ........................................................ 4-18

4.6.2 W et D eposition ........................................................ 4-19

vi
4.6.3 Total Surface Deposition ...............

4.7 Depletion Due to Deposition .................

4.8 Radiological Decay and Ingrowth .............

4.9 Dose Calculations ..........................

4.9.1 Inhalation Doses ......................

4.9.2 Groundshine Doses ....................

4.9.3 Cloudshine Doses .....................

4.9.4 Open- and Closed-Window Dose Rates ....

4.9.5 Total Effective Dose Equivalent ..........

4.9.6 Total Acute Bone Dose Equivalent .......

4.10 R eferences ..............................

5 UF6 Transport and Diffusion Model ................

5.1 UF6 Model Assumptions and Equations .........

5.2 Chemical/Thermodynamic Model .............

5.2.1 Compressibility Factor ..................

5.2.2 UF6 D ensity .........................

5.2.3 UF6 Vapor Pressure ...................

5.2.4 U F6 Enthalpy .........................

5.2.5 Uranium Enrichment ...................

5.2.6 HF-HO System ......................

5.2.7 HF Self Association ...................

5.2.8 Partial Vapor Pressures of HF ...........

5.2.9 Partial Vapor Pressure of H20 ...........

5.2. 10 Enthalpy of HF-H20 Vapor Mixtures .....

5.2.11 Enthalpy of HF-H20 Liquid Mixtures ....

5.2.12 UOF, Enthalpy ......................

5.2.13 Mixture Enthalpies and Plume Temperature

5.3 Dispersion and Deposition of HF and U0 2F 2 ......

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

.4-19

.4-20

.4-20

.4-20

.4-20

.4-21

4-21

4-27

4-28

.4-29

.4-29

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

.... 5-1

.... 5-1

.... 5-4

.... 5-4

.... 5-4

.... 5-5

.... 5-6

.... 5-7

.... 5-7

.... 5-7

.... 5-8

.... 5-8

.... 5-9

.... 5-9

.... 5-9

.... 5-9

... 5-11

5.4 C alculated R esult Types ................................................... ... 5-12

5.5 Comparison of RASCAL UJF6 Plume Model with Experimental Measurements and Results from

O ther M odels .............................................................. 5-14

5 .6 R eferences ................................................................ 5-15

6 M eteorological D ata Processor ...................................................... 6-1

6.1 Model Domain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 -1

6.2 M eteorological Stations ......................

6.3 M eteorological Data Input ...................

6.3.1 Surface W inds ........................

6.3.2 Atmospheric Stability Class .............

6.3.3 Precipitation Type ....................

6.3.4 M ixing Height ........................

6.3.5 Tem perature .........................

6.3.6 Pressure .............................

6.3.7 H um idity ............................

6.3.8 Temporal Interpolation of Input Values ....

6.4 Other Meteorological Parameters ..............

6.4.1 Monin-Obukhov Length ................

..................................

..................................

..................................

..................................

..................................

..................................

..................................

..................................

..................................

..................................

..................................

6-1

6-3

6-3

6-3

6-5

6-5

6-5

6-6

6-6

6-6

6-8

6-8

vii
6.4.2 W ind Speed vs. Height ................................................... 6-8

6.4.3 M ixing H eight .......................................................... 6-9

6.4.4 Dry Air and W ater Vapor Density ......................................... 6-12

6.4.5 Precipitation R ate ...................................................... 6-13

6.5 Calculating Spatially Varying Meteorological Conditions ........................... 6-14

6.5.1 W ind F ields ..................................................... ...... 6-14

6.5.2 Adjustment of W ind Fields for Topography ................................. 6-15

6.5.3 Stability and Precipitation ................................................ 6-15

6.5.4 M ixing H eight ......................................................... 6-16

6.6 Calculating Meteorological Conditions at the Source ............................... 6-16

6.7 R eferences ................................................................ 6-16

7 Interm ediate Phase Dose Calculations ................................................. 7-I

7.1 Interm ediate Phase D oses ...................................................... 7-1

7.1.1 G roundshine D oses ...................................................... 7-1

7.1.2 Inadvertent Ingestion Doses ............................................... 7-4

7.1.3 Inhalation D oses ......................................................... 7-4

7.1.4 Precalculated Intermediate Phase Dose Conversion Parameters ................... 7-6

7.1.5 Dose Conversion Parameter Calculations with Delayed Reentry .................. 7-6

7.2 D ecay and Ingrow th ......................................................... 7-7

7.3 Derived Response Levels (DRLs) .............................................. 7-11

7.3.1 Exposure Rate Derived Response Levels .................................... 7-1I

7.3.2 Marker Nuclide Derived Response Levels ................................... 7-12

7.4 R eferences ................................................................. 7-12

viii
List of Figures

1.1 PW R Containment M onitor Response ................................................ 1-13

1.2 BWR Mark I and IIDry Well Containment Monitor Response ........................... 1-14

1.3 BWR Mark I and II Wet Well Containment Monitor Response ........................... 1-15

1.4 BWR Mark III Dry Well Containment Monitor Response ..... ....................... 1-16

1.5 BWR Mark III Wet Well Containment Monitor Response ............................ 1-17

4.1 Ratios of predicted concentrations in wakes by a model without wake correction to observed

concentrations as a function of wind speed ........................................... 4-10

5.1 Comparison of UF6Plume model predictions of average uranium concentrations with measured

concentrations and predictions of other models ....................................... 5-14

List of Tables

1. Nuclear Power Plant Core Inventory During Operation for Low Enriched Uranium Fuel ....... 1-2

1.2 Radionuclide Concentrations in Reactor Coolant ....................................... 1-4

1.3 BWR Event Timings and Fraction of Core Activity Inventory Released ..................... 1-8

1 .4 PWR Event Timings and Fraction of Core Activity Inventory Released ..................... 1-9

1.5 Fraction of Total Noble Gas Activity for each Noble Gas Nuclide at Shutdown ............. 1-20

1.6 Fraction of Total Radioiodine Activity for each Radioiodine Nuclide at Shutdown ........... 1-20

1.7 PWR Release Pathways Available for Each Source Term Type .......................... 1-23

1.8 BWR Release Pathways Available for Each Source Term Type .......................... 1-23

1.9 Summary of Nuclear Power Plant Reduction Factor Multipliers .......................... 1-24

1. 10 Methods for Specifying Release Rate for each Release Pathway ........................ 1-28

1. 11 Short-lived Daughters Assumed to be in Equilibrium with the Parent Activity .............. 1-31

1.12 Spreadsheets Prepared for Quality Assurance Testing of the RASCAL 3.0.5 Time-dependent

S o urce T erm ... ... ... . ... . ........ ...... . .... .... .... .... . .. . ... .... ... . ... . .. 1-3 3

2.1 Fuel Release Fractions Used in Spent Fuel Accidents ................................... 2-2

3.1 U F6 C ylinder Inventories ......................................................... 3-2

3.2 Default Release Fractions and Rates Based on UF6 Form and Cylinder Damage Type ......... 3-2

3.3 UF 6 Release Fractions Based on Valve Location ....................................... 3-2

3.4 Pathways with/without UF6 Conversion Prior to Release to Atmosphere .................... 3-3

3.5 Paducah GDP Buildings and Default Inventory and Release Rates ......................... 3-4

3.6 Portsmouth GDP Buildings and Default Inventory and Release Rates ...................... 3-4

3.7 Fractions Available for Release and Inhalation Fractions Used in Uranium Oxide Fires ........ 3-6

3.8 Fractions Available for Release and Inhalation Fractions Used in Uranium Oxide Explosions ... 3-7

3.9 Fission Yields Used in Criticality Calculations ..................................... 3-8

3.10 Activity (Ci) Released in Criticality of 10"' Fissions ................................... 3-9

3.11 Fire Release Fractions by Compound Form ......................................... 3-11

3.12 Fire Release Fractions by Element ................................................ 3-12

3.13 Uranium Specific Activity for Different Enrichments ................................. 3-13

4.1 Constant Values for Calculation of Atmospheric Dispersion Parameters .................... 4-9

4.2 RASCAL 3.0.5 W ashout Coefficients .............................................. 4-19

6.1 Estimated Pasquill-Gifford Stability Class Based on NRC Delta TM Method ................ 6-4

6.2 Estimated Atmospheric Stability Class for Missing Stability Classes ....................... 6-4

ix
6.3 Limits of Atmospheric Stability Classes Based on Time of Day, Wind Speed, and Precipitation . 6-5

6.4 Precipitation Rates as a Function of Precipitation Climate Zone .......................... 6-14

7.1 Radionuclides with Implicit Daughters Assumed in Intermediate Phase Dose Calculations ...... 7-7

7.2 RASCAL Intermediate Phase Decay Chains .......................................... 7-9

x
Acknowledgments

The development of the RASCAL code would not have been possible without the dedicated work of

many talented individuals. Thomas McKenna, Joseph Guitter, and Len Soffer played an important role in

developing the models used in the early versions of RASCAL. Frank Congel, Joseph Holonich, Edward

Jordan, Melvyn Leach, Charles Miller, Aby Mohseni, Cheryl Trottier, Mike Weber, Richard Wessman,

Peter Wilson, and Roy Zimmerman all enthusiastically supported the project.

Andrea Sjoreen and Christian Fosmire contributed to the development of earlier versions of RASCAL.

A large number of people have contributed to the more recent development of RASCAL during its

transition from RASCAL 3.0 introduced in 2001 to RASCAL 3.0.5 introduced in December 2006. They

include: Bob Bores, Lou Brandon, Mark Cunningham, Paul Elkman, Michelle Hart, Rick Hasselberg,

Felicia Hinson, Tony Huffert, Cyndi Jones, Elaine Keegan, Steve Klementowicz, Terry Kraus, Steve

LaVie, Bob Meck, Jocelyn Mitchell, Carlos Navarro, Ron Nimitz, Nancy Osgood, John Parillo, Bill

Rhodes, Jason Schaperow, Art Shanks, Fritz Sturz, Randy Sullivan, Elizabeth Thompson, Charles

Tinkler, Bruce Watson, and Michael Williamson.

We would also like to thank the many RASCAL users and students who have taken RASCAL training for

the many helpful comments that they provided to us.

xi

1 Nuclear Power Plant Source Term Calculations

RASCAL 3.0.5 has a module called "Source Term to Dose" that first calculates a time-dependent "source

term," for the atmospheric release of radioactive materials. The source term is the rate at which

radioactive material is released from the facility into the atmosphere. The code next calculates the

atmospheric transport and dispersion and the deposition of the radioactive materials that were released.

Finally, the code calculates doses from the cloud shine, ground shine, and inhalation pathways as a

function of location.

This chapter describes how the "Source Term to Dose" module in RASCAL 3.0.5 calculates the timedependent source term for nuclear power plant accidents. The methods used in the RASCAL 3.0.5 source

term calculations for nuclear power plant accidents are based largely on the methods described in

NUREG-1228 (McKenna and Giitter 1988).

Before we describe the detailed methods that RASCAL 3.0.5 uses to calculate specific a source term

types, we first describe the nuclear power plant parameters that are used in the calculations.

1.1 Nuclear Power Plant Parameters

1.1.1 Core Inventories

For nuclear power plant source terms based on core damage, the radionuclide inventories assumed to be

in the reactor core are shown in Table 1.1.

The values in Table 1.1 are for low-enriched uranium fuel. The values were derived from Table 2.2 of

NUREG-1228 (MeKenna and Glitter 1988). The derivation was done by dividing the fission product

inventories in NUREG-1228 by 3 to convert from Ci/MWe to Ci/MWt, and then rounding to 2 significant

figures. The inventories of nuclides with a half-life of more than one year were scaled up from a bumup

of 18,000 to 30,000 MWD/MTU.

The inventories in NUREG-1228 were derived from the Reactor Safety Study, WASH-1400. Table VI

13-1 of WASH-1400 ranked the nuclides in the core by importance to early health effects. The nuclides

with greater importance for early health effects were included in the NUREG-1228 core inventory list. In

additional, NUREG-1228 added noble gases that had lesser importance for early health effects because

noble gases are the most likely group of fission products to be released to the environment by a nuclear

power plant accident. According to Figure 2-4 of NUREG-1228, the iodine and tellurium nuclides

contribute almost two-thirds of the bone marrow dose for a major nuclear power plant release. Krypton,

cesium, strontium and barium are the other major contributors.

1-1
Table 1.1 Nuclear Power Plant Core Inventory During Operation for Low Enriched Uranium

Fuel (30,000 MWD/MTU burnup)

Nuclide Core Inventory Ci/MWt Nuclide Core Inventory Ci/MWt

Ba-140 5.30e+04 Ru-103 3.70e+04

Ce-144 2.80e+04 Ru-106 1.33e+04

Cs- 134 4.17e+03 Sb-127 2.00e+03

Cs-136 1.00e+03 Sb-129 1.10e+04

Cs-137 2.67e+03 Sr-89 3.1Oe+04

1-131 2.80e+04 Sr-90 2.00e+03

1-132 4.00e+04 Sr-91 3.70e+04

1-133 5.70e+04 Te-129m 1.80e+03

1-134 6.30e+04 Te-131m 4.00e+03

1-135 5.00e+04 Te-132 4.00e+04

Kr-85 3.17e+02 Xe-131m 3.30e+02

Kr-85m 8.00e+03 Xe-133 5.70e+04

Kr-87 1.60e+04 Xe-133m 2.00e+03

Kr-88 2.30e+04 Xe-135 1.10e+04

La-140 5.30e+04 Xe-138 5.70e+04

Mo-99 5.30e+04 Y-91 4.00e+04

Np-239 5.50e+05

Reference: Derived from NUREG-1228, Table 2.2 (McKenna and Giitter 1988) which in turn derived

its table from WASH-1400

The inventories in Table 1.1 are based on a burnup of 30,000 MWD/MTU. RASCAL 3.0.5 adjusts the

inventory of radionuclides that have a half-life exceeding one year to account for burnup. The inventory

for the specified actual bumup, 'ICTUAL, is calculated only for nuclides with a half-life of more than one

year using the Equation 1.2 below. There is no burnup adjustment for nuclides with a half-life less than

one year.

B URNUPACTUAL

ACTUL = 130,000 X 30,000 MWD / MTU (1.1)

If the reactor is shut down prior to the start of the release, the radionuclide inventories are adjusted to

account for radiological decay and ingrowth. In addition, at the end of each time step, the activities of the

nuclides present are adjusted to account for radiological decay and ingrowth. The minimum activity of a

nuclide allowed in a source term time step is 101" Ci.

1-2
1.1.2 Coolant Inventories

RASCAL 3.0.5 uses coolant inventories for some accident types. The concentrations that RASCAL 3.0.5

uses for normal coolant are given in Table 1.2. Those normal coolant concentrations are taken from

ANSI/ANS 18.1-1999. During steady-state conditions, iodine and other fission products may escape from

fuel rods having clad defects and enter the reactor coolant system. Since the internal pressure in the fuel

rod is balanced with the coolant pressure outside the fuel rod during steady-state conditions, the rate of

escape is low. The fission products that do escape into the reactor coolant system are continually

removed by the reactor coolant system purification cleanup resulting in a low equilibrium concentration.

However, if a reactor transient causes the pressure of the reactor coolant system to decrease rapidly, the

escape rate from fuel rods can increase and cause a temporary increase, or "spike," in the coolant

concentrations. There is also a belief that coolant water can enter fuel rods through cladding defects. If

the reactor coolant system pressure suddenly decreases, this water could leach off iodine and cesium salts

deposited on the inner clad surfaces, increasing the iodine and cesium available for escape during the

transient.

RASCAL 3.0.5 can also calculate an inventory for "spiked" coolant. RASCAL 3.0.5 assumes that the

concentrations of halogens (iodine) and alkali metals (cesium) in the coolant increase by the spiking

factor. RASCAL 3.0.5 uses a default spiking factor of 100, but the user can enter a different value.

1-3
Table 1.2 Radionuclide Concentrations in Reactor Coolant

PWR coolant BWR coolant PWR coolant BWR coolant

Nuclide concentration concentration Nuclide concentration concentration

Ci/g Ci/g Ci/g CCiigdi/g

Ba-140 1.30e-08 4.00e-10 Mo-99 6.40e-09 2.00e-09

Ce-144 4.00e-09 3.00e-12 Np-239 2.20e-09 8.00e-09

Co-58 4.60e-09 1.00e-10 Ru-103 7.50e-09 2.00e-11

Co-60 5.30e-10 2.00e-10 Ru-106 9.00e-08 3.00e-12

Cs-134 3.70e-11 3.00e-11 Sr-89 1.40e-10 1.00e-10

Cs-136 8.70e-10 2.00e-11 Sr-90 1.20e-11 7.00e-12

Cs-137 5.30e-11 8.00e-11 Sr-91 9.60e-10 4.00e-09

H-3 1.00e-06 1.00e-08 Tc-99m 4.70e-09 2.00e-09

1-131 2.00e-09 2.20e-09 Te-129m 1.90e-10 4.00e-1 1

1-132 6.00e-08 2.20e-08 Te-131m 1.50e-09 1.00e-10

1-133 2.60e-08 1.50e-08 Te-132 1.70e-09 1.00e-11

1-134 1.00e-07 4.30e-08 Xe-131m 7.30e-07 0

1-135 5.50e-08 2.20e-08 Xe-133 2.90e-08 0

Kr-85 4.30e-07 0 Xe-133m 7.00e-08 0

Kr-85m 1.60e-07 0 Xe-135 6.70e-08 0

Kr-87 1.70e-08 0 Xe-138 6.10e-08 0

Kr-88 1.80e-08 0 Y-91 5.20e-12 4.00e-11

La-140 2.50e-08 4.00e-10

Mn-54 1.60e-09 3.50e-1 1

Reference: ANSI/ANS 18.1-1999.

1.1.3 Reactor Coolant System Water Mass

The mass of water in the reactor coolant system for each plant is stored in the RASCAL 3.0.5 facility

database. The values are in kilograms of water. The values are converted into gallons for display to the

user by the user interface.

The RCS coolant system water masses were estimated for each reactor. The document ANSI/ANS 18.1

Radioactive Source Term for Normal Operation of Light Water Reactors provided the following

information:

1-4
Reactor Mass of water in reactor vessel Source table

(BWR) or RCS (PWR)

BWR 1.7e5 kg 1

reference at 3,400 MWt

PWR - with u-tube SG 2.5e5 kg 2

reference at 3,400 MWt

PWR with once-thru SG 2.5e5 kg 3

reference at 3,400 MWt

For each reactor, the actual licensed power (MWt) was divided by the reference power (3,400 MWt),

then multiplied by the mass of the water (kg from above table) to estimate the coolant mass.

For example, Beaver Valley Unit I (a PWR) had a licensed power of 2,652 MWt. Thus:

(2652 / 3400) x 2.5e5 = 1.95e5 kg of water in the RCS

This method produces only the approximate mass. More accurate site-specific values could be obtained

from plant technical specifications, but the improved accuracy was not thought to be worth the effort.

1.1.4 Reactor Containment Volumes

The containment volumes in the RASCAL 3.0.5 database were taken from NUREG/CR-5640 (Lobner,

Donahoe, and Cavallin, 1990). For PWRs, the volumes are the total containment volumes. For BWRs,

the volumes are the drywell volumes. Units in the database are in cubic feet.

1.1.5 Reactor Power Levels

Reactor power levels are listed in the RASCAL 3.0.5 database in units of MWt. These represent the

maximum power at which the reactor is allowed to operate. This value is used as the default value for

average reactor power but may be changed by the user from the RASCAL 3.0.5 user interface. These

values were originally taken from the U.S. Nuclear Regulatory Commission Information Digest. They

have been updated for RASCAL 3.0.5 to be current with NRC approved power upgrades as of December

2006.

Website: www.nrc.gov/reactors/operating/licensini/power-uprates.html

1.1.6 Fuel Burnup

Two burnup numbers are contained in the RASCAL 3.0.5 database. The first is the average fuel bumup

(MWD/MTU) for each reactor. A value of 30,000 MWD/MTU is used in the database for all reactors.

This represents a core that is roughly two-thirds of the way to end of core life assuming typical current

fuel management practices. The value changes with time and with the mix of old and new fuel in the

core. The value should represent an average over the entire core. The user can change the value if more

information is available, but usually this will not significantly change the calculated projected doses.

This burnup number is used to adjust the available inventory of radionuclides with a half-life greater than

one year (see Section 1.1.1).

1-5
The second burnup number is the average bumup for spent fuel in storage. A value of 50,000

MWD/MTU is used in the database. Again, the user may change the value if a better number is available.

The spent fuel bumup is used to generate source terms for spent fuel accidents using the method in

Section 1.1.1.

1.1.7 Number of Assemblies in the Core

The RASCAL 3.0.5 database contains the number of fuel assemblies in each reactor core. The values are

taken from NUREG/CR-5640 (Lobner, Donahoe, and Cavallin, 1990). The numbers are used only with

spent fuel accident calculations when estimating the source term activity for a fuel assembly (see Chapter

2).

1.1.8 Design Pressure

A design pressure for each reactor containment is included in the RASCAL 3.0.5 database. The values

are in pounds per square inch. The design pressures are taken from NUREG/CR-5640 (Lobner, Donahoe,

and Cavallin, 1990). This value is not changeable by the user from the RASCAL 3.0.5 user interface. The

design pressure is not used in RASCAL 3.0.5 calculations, but the user can compare the actual

containment pressure with the design pressure to determine if the actual leak rate is likely to be near or

below the design leak rate.

1.1.9 Design Leak Rate

A design leak rate for each reactor containment is included in the RASCAL 3.0.5 database. The values

are in percent of containment volume per day at design pressure. The design leak rates are taken from

NUREG/CR-5640 (Lobner, Donahoe, and Cavallin, 1990). This value is not changeable by the user from

the RASCAL 3.0.5 user interface. The design leak rate is the default containment leak rate, but the

RASCAL 3.0.5 user can select any other leak rate more appropriate for a particular accident.

1.2 Source Term Types

1.2.1 Basic Method to Calculate Source Terms

A source term is defined as the activities of each radionuclide released to the environment as a function

of time. The basic method to calculate a source term is to divide the nuclear power plant into

compartments and then calculate the activities entering the compartment and the activities being removed

from the compartment during time steps of fairly short duration. The time steps generally have a 15-

minute duration.

As an example, consider a loss-of-coolant accident after reactor shutdown in which fuel is damaged and

radionuclides are released to the containment and then to the atmosphere. The first compartment is the

fuel. RASCAL 3.0.5 will first calculate the release from the fuel to the containment atmosphere. Since

the reactor is shutdown, no new fission products are being produced. The radionuclide inventory of the

fuel is being depleted during each time step by radiological decay and by release to the containment. In

addition, there will be ingrowth of some radionuclides in the fuel due to the radiological decay of their

parents.

1-6
The second compartment is the containment atmosphere. The activity entering the containment

atmosphere during a time step is the activity released from the fuel during that time step. Activity is

removed from containment atmosphere during the time step by radiological decay, removal processes

(for example, removal by containment sprays), and leakage to the environment.

Time steps may be of varying length. A source term time step starts whenever the user changes any of the

time-dependent data or every 15 minutes, whichever occurs first. Time steps may be no less than 1

minute and must be an integral number of minutes. Before passing the source term to the atmospheric

transport model, RASCAL 3.0.5 converts the source term time steps into 15-minute time steps that start

on the hour because the atmospheric transport models require that regularity.

The remainder of this chapter describes in detail how RASCAL 3.0.5 calculates the time-dependent

source term for various accident types.

1.2.2 Time Core Is Uncovered Source Term

Perhaps the most powerful and important source term type that RASCAL 3.0.5 calculates is based on the

time that the core is uncovered. Almost all of the radioactivity at a nuclear power plant is contained in

fuel rods. A large release is not possible unless many fuel rods are substantially damaged. The only way

this can reasonably occur is by loss of water from the primary coolant system so that the reactor core is

left uncovered by water. If a user estimates how long a reactor core will not be covered with water,

RASCAL 3.0.5 can estimate the amount of core damage that will occur and from that estimate the

activity of each fission product nuclide that will be released from the core.

When a RASCAL 3.0.5 user specifies how long the core is uncovered, RASCAL 3.0.5 will estimate how

much core damage will occur based on the damage timings in Tables 1.3 for BWRs and 1.4 for PWRs.

(Tables 1.3 and 1.4 are taken from Tables 3-12 and 3- 13 in NUREG-1465, Soffer et al. 1995.) For

example, if a BWR or PWR core is uncovered for 15 or 30 minutes, the estimated damage is 50% or

100% cladding failure, respectively. If a BWR core is uncovered for 1 hour, the estimated damage will be

100% cladding failure plus 33% core melt.

1-7
Table 1.3 BWR Event Timings and Fraction of Core Activity Inventory Released

BWR core inventory release fraction

Nuclide group Cladding failure Post-vessel melt-

(gap release Core melt phase through phase

phase) (in-vessel phase) (ex-vessel phase)

(0.5 hr duration) (1.5 hr duration) (3.0 hr duration)

Noble gases (Kr, Xe) 0.05 0.95 0

Halogens (I, Br) 0.05 0.25 0.30

Alkali metals (Cs, Rb) 0.05 0.20 0.35

Tellurium group (Te, Sb, Se) 0 0.05 0.25

Barium, strontium (Ba, Sr) 0 0.02 0.1

Noble metals (Ru, Rh, Pd, Mo, Tc, 0 0.0025 0.0025

Co)

Cerium group (Ce, Pu, Np) 0 0.0005 0.005

Lanthanides (La, Zr, Nd, Eu, Nb, Pm, 0 0.0002 0.005

Pr, Sm, Y, Cm, Am)

Reference: Table 3-12 from NUREG-1465 (Soffer et al. 1995)

The fractions shown in these tables are for the particular phase. They are not cumulative. Thus, the total

fraction of core inventory released in a vessel melt-through accident is the sum of the fractions for

cladding failure, core melt, and vessel melt-through.

The data in Tables 1.3 and 1.4 are the result of an expert elucidation process that considered a range of

severe accident sequences. These release fractions do not envelop all potential severe accident sequences,

nor do they represent any particular accident sequence. However, the timings in Tables 1.3 and 1.4 for

the start of each fuel damage state was based on the accident sequence that could lead to the earliest fuel

failures. The timings and release fractions in Tables 1.3 and 1.4 are essentially based on a large break

loss-of-coolant accident with the reactor at full power and without the operation of emergency core

cooling systems. This situation leads to very rapid uncovering of the core.

However, if there were a small break in the reactor coolant system or the emergency core cooling systems

initially operated successfully, the core will remain covered while the rate of decay heat production

decreases. At lower decay heat production rates, the duration of each release phase is likely to increase

and the release fractions during each release phase may well be overestimated by Tables 1.3 and 1.4.

However, RASCAL 3.0.5 does not adjust its releases to account for that situation. Users of the time-coreis-uncovered source term option should understand that RASCAL 3.0.5 is likely to overestimate the

speed and magnitude of the release and thus also overestimate the projected radiological doses. RASCAL

3.0.5 users should inform decisionmakers of that fact.

1-8
Table 1.4 PWR Event Timings and Fraction of Core Activity Inventory Released

PWR core inventory release fraction

Nuclide group Cladding failure Post-vessel melt-

(gap release Core melt phase through phase

phase) (in-vessel phase) (ex-vessel phase)

(0.5 hr duration) (1.3 hr duration) (2.0 hr duration)

Noble gases (Kr, Xe) 0.05 0.95 0

Halogens (I, Br) 0.05 0.35 0.25

Alkali metals (Cs, Rb) 0.05 0.25 0.35

Tellurium group (Te, Sb, Se) 0 0.05 0.25

Barium, strontium (Ba, Sr) 0 0.02 0.1

Noble metals (Ru, Rh, Pd, Mo, Tc, Co) 0 0.0025 0.0025

Cerium group (Ce, Pu, Np) 0 0.0005 0.005

Lanthanides (La, Zr, Nd, Eu, Nb, Pm, 0 0.0002 0.005

Pr, Sm, Y, Cm, Am) I

Reference: Table 3-13 from NUREG-1465 (Softer et al. 1995)

For PWRs, the time the core is uncovered should be the time that the coolant drops below the top of the

active fuel. At this level cladding failure will begin. The gap activity in each fuel rod is released suddenly

when the cladding fails at some location due to overpressure. The rods near the center of the core will

fail earliest with additional rods failing as the core continues to heat. This process takes about half an

hour.

For BWRs, the cladding damage does not start until the water uncovers about 1/3 of the way down the

fuel element. Prior to that time boiling water below will keep the fuel cool enough to prevent melting of

the cladding.

For calculations using the time core is uncovered source term type, RASCAL 3.0.5 will first calculate the

activity released from the fuel to either the containment atmosphere or to the coolant as appropriate for

the release pathway that the user has selected. The equation is

Ai(k) = I AFi(k) (1.2)

where

Ii = the core inventory of radionuclide i

AF1(k) = the available fraction of the inventory of radionuclide i available for release from the fuel

during time step k

To illustrate how AF.(k) is calculated, consider a PWR for the fourth 15-minute time step (45 minutes to

60 minutes), during which time we are entirely in the core melt phase. During the core melt phase, 95%

1-9
of the noble gases would be released over 1.3 hours according to Table 1.4.The available fraction for the

release of noble gas activity from the fuel to the containment, AFng(4), during that fourth 0.25 hour

duration time step would be:

0.95

AFg(4)z 0.25hr 1.3hr (1.3)

If the user enters a time at which the core is recovered with water, core damage is assumed to stop and

the release of material from the core stops at that time.

1.2.3 Ultimate Core Damage State Source Term

The user can specify the maximum damage that is expected to occur by selecting a core-damage state

directly. The state that is selected will establish the source term. The user can select: normal coolant

activity, spiked coolant activity, or I to 100% cladding failure.

The user also selects the time at which the maximum damage is expected to occur. For example, if the

user believes that a maximum damage of 10% cladding failure may occur, the user enters the time at

which he believes 10% of the cladding will have failed.

Normal Coolant

For normal coolant releases, RASCAL 3.0.5 uses the coolant concentrations from Table 1.2 decayed

from the time of shutdown to the time entered as the point of maximum damage.The reactor coolant

system inventory I, is the concentration of radionuclide i times the total coolant mass.The available

fraction for release is the mass of coolant escaping during the time step divided by the total coolant mass.

Spiked Coolant

Spiked coolant may be seen following reactor shutdown, startup, rapid power change, and reactor coolant

system depressurization. Rapid increases in the iodine and other fission-product concentrations in the

coolant'as high as 3 orders of magnitude may occur. The default spiking factor is 100, but the user can

select a spiking factor from 1 to 1000.

For spiked coolant releases, RASCAL 3.0.5 uses the coolant concentrations (Table 1.2). The

concentration of all halogens (iodine) and alkali metals (cesium) in the coolant are multiplied by the

spiking factor.

For both normal and spiked coolant releases, only the steam generator and containment bypass release

pathways is available. The user must specify the mass leak rate at which coolant escapes the reactor

coolant system. Generally, the leak rate can be assumed to be the same as the makeup flow needed to

maintain the water level.

Cladding Failure

For cladding failure, RASCAL 3.0.5 uses available fractions (AFs) determined from Tables 1.3 and 1.4.

Thus, for example, if the user entered 4% cladding failure for a BWR, the iodine release from the fuel

1-10
would be: core inventory of iodine x 0.04 (fraction of cladding that failed) x 0.05 (the halogen available

fraction for 100% cladding failure in Table 1.3).

In RASCAL 3.0.5, the user can no longer select core melt or vessel melt-through as he could in previous

versions of RASCAL. For accidents proceeding to core melt, the user interface screen tells the user to

use the "time core is uncovered" source term type. For accidents with core melt, the timing of the release

would not be at all realistic using the ultimate core damage state source term option. In addition, while

the user may have a relatively good idea of when core damage may begin, he may have less knowledge of

when the maximum damage will occur. For these reasons, it is required that for accidents that are

expected to proceed into core melt, the use of the "time core is uncovered" source term type should give

more realistic results.

1.2.4 Containment Radiation Monitor Source Term

RASCAL 3.0.5 can use containment radiation monitor readings to estimate source terms that occur

through the containment leakage release pathway. The user enters containment radiation monitor

readings and the times of the readings. The entry of multiple readings allows the modeling of core

damage that is progressing with time.

Figures 1.1 through 1.5 show the containment radiation monitor readings that can be expected due to

radionuclides in the containment atmosphere from coolant or core damage. The figures show the

calculated monitor readings at 1 hour and 24 hours after shutdown. These figures are taken from Figures

A.5 through A. 12 in RTM-96 (McKenna, et al. 1996). The bars in these figures represent the calculated

containment radiation monitor readings for I to 100% of the labeled core-damage state.

The data in these figures were calculated for a reactor power of 3000 MWt. RASCAL 3.0.5 scales the

monitor reading entered by the user to account for the difference in the 3000 MWt reactor power used to

produce the figure and the actual reactor power. This scaled monitor reading, R, is calculated by

3000 x MRR - (1.4)

Power

where

MR = the containment monitor reading entered,

Power = the reactor power, MWt.

To estimate a source term from the scaled monitor reading, RASCAL 3.0.5 first determines which figure

should be used based on the containment type and, for BWRs, the monitor location (dry well or wet

well). Next, RASCAL 3.0.5 determines if the data for containment "sprays on" or for "sprays off' should

be used.

RASCAL 3.0.5 then adjusts the data in the figure for the time between shutdown and the monitor

reading. If the hold-up time entered is less than 1 hour, the data for 1 hour is used without adjustment. If

the holdup time is greater than 24 hours, the data for 24 hours is used without adjustment. If the holdup

time is between 1 hour and 24 hours, RASCAL 3.0.5 does a linear interpolation to calculate a new I to

1-11
100% bar for actual holdup time (the time between the shutdown time and the time of the monitor

reading).

Figures 1.1 to 1.5 show the containment monitor readings for: (1) normal coolant, (2) spiked coolant, (3)

cladding failure, and (4) core melt. If a containment radiation monitor reading exceeds the value of 1%

core melt, RASCAL 3.0.5 assumes that core melt has begun and uses a core melt source term.

If the containment radiation monitor reading is less than the value for 1% core melt, the core damage

state is assumed to be cladding failure. The data in the figures for normal and spiked coolant are not used

in RASCAL 3.0.5.

Users of the containment radiation monitor source term type should be aware of certain limitations on the

calculated results:

° The figures represent typical reactor plants. Plant-specific conditions may make differences.

" The figures are appropriate for large-break loss of coolant accidents. If there is a small break the

containment activity may rise very slowly at first causing RASCAL 3.0.5 to underestimate the

amount of core damage that has occurred.

• Thermal stratification in the containment may effect the results. The containment atmosphere near

the containment radiation monitors may not be representative of the containment atmosphere as a

whole.

" The containment radiation monitor source term is a lagging indicator of core damage and cannot

predict core damage that will occur in the future. Thus, it will be much later in its estimates of

projected doses compared to the "time core is uncovered" source term.

1-12
Figure 1.1 PWR Containment Monitor Response

le+6 -

le+5 -

i -

-c

._m le+3 --

0.-

0 le+2

ck

0 Key to Spray Status an - Damage Amount

(• --- Sprays Sprays

fl ZOff On

0 le-I _ :"

_-- 0% 10o/

le-21% 1%

1 - H

ld

)%

1 e-3

1-13
Figure 1.2 BWR Mark I and II Dry Well Containment Monitor Response

1-14
Figure 1.3 BWR Mark I and H1 Wet Well Containment Monitor Response

1-15
Figure 1.4 BWR Mark III Dry Well Containment Monitor Response

1-16
Figure 1.5 BWR Mark III Wet Well Containment Monitor Response

1-17
When RASCAL 3.0.5 determines that the estimated core-damage state is cladding failure or core melt, it

then computes the fraction of either state that the reading represents. This percentage cannot be more

than 100%. The percentage, P, of the damage state selected is calculated by

R

P 10Ox RID ,- (1.5)

where

PID = the meter reading assumed for 1% of the core-damage state for a 3,000 MWt reactor.

The user should be very cautious in interpreting RASCAL 3.0.5 results based on containment radiation

monitor readings because the calculations are subject to large uncertainties. First, the model assumes that

the containment radiation monitor readings represent the full amount of damage that has occurred.

However, if the fission products are delayed in entering the containment, the containment monitor

readings may significantly lag behind the amount of damage that has occurred.

The model also assumes uniform mixing of fission products in the containment atmosphere. Inconsistent

readings may be caused by uneven mixing in containment such as if steam rises to the top of the dome or

if there is insufficient time for uniform mixing to occur. If uniform mixing has not yet occurred, the

monitor readings may significantly misrepresent the amount of damage that has occurred.

The model also assumes that an unshielded monitor sees a large fraction of the containment volume. If

that is not true, significant error could result. Because the mix is most likely different from that assumed

in the calibration of the monitor, the actual reading at the upper end of the scale could differ significantly

if a shielded detector is used for the higher radiation measurements.

1.2.5 Source Term Based on Coolant Sample

The measured concentrations of radionuclides in a nuclear power plant coolant sample can be used to

define the source term when the activity being released is activity that comes from the coolant. The user

must specify coolant radionuclide concentrations by nuclide.

The two release pathways that can release coolant are a steam generator tube rupture and a containment

bypass pathway. The user must specify the leak rate at which coolant escapes the reactor coolant system.

Generally, the leak rate can be assumed to be the same as the makeup flow needed to maintain the water

level.

RASCAL 3.0.5 calculates how much activity will be released with the escaping coolant during the first

15-minute time step. For the second time step, RASCAL 3.0.5 decreases the concentration of

radionuclides in the coolant to account for what has escaped. It is assumed that the makeup water being

added to the primary system is clean water. Radioactive decay and ingrowth are also being accounted for

to adjust the concentrations during each time step.

The reduction factors that are applied before the release to the environment are discussed later in this

chapter.

1-18
1.2.6 Source Term Based on Containment Air Sample

RASCAL 3.0.5 can use the concentration of radionuclides measured in a containment air sample to

define the activity released by a containment leakage pathway. (A containment air sample cannot be used

to define the activity released in the steam generator tube rupture or containment bypass pathways

because containment air does not exit by those pathways.)

The user enters the concentration (activity/unit volume) for each nuclide in the containment atmosphere.

Multiplying the radionuclide concentrations in the containment air (activity/unit volume) times the

volumetric release rate (volume/time) will equal the activity release rate (activity/time).

For PWRs, the volumes are the total containment volumes. For BWRs, the volumes are the drywell

volumes. Therefore, for BWRs, RASCAL 3.0.5 analyzes only containment air samples that are taken

from the drywell.

If the containment is under pressure, the density of the containment atmosphere will be greater than the

density of air at normal atmospheric pressure. RASCAL 3.0.5 does not correct for this difference. The

code assumes that the measurement data has been corrected for pressure. The code assumes that the data

are entered in terms of activity/unit volume at the containment pressure. If the sample results are reported

for the volume at atmospheric pressure, the user should increase the reported activity to account for the

higher atmospheric density in the containment before the sample results are entered into the code.

1.2.7 Source Term Based on Effluent Release Rates or Concentrations

RASCAL 3.0.5 can generate a source term based on effluent measurements. The user can enter the

effluent release rates (activity/unit time) by radionuclide. No radioactive decay is calculated prior to

release, but radioactive decay is calculated after release. The release is assumed to be direct to the

atmosphere so that reduction factors (e. g., filtering) cannot be applied.

Alternatively, the user can enter the effluent concentration (activity/unit volume) by radionuclide and the

flow rate (volume/unit time). The activity of each radionuclide released to the environment is computed

as the concentration times the volumetric release rate to the environment times the release duration. The

effluent concentrations may be decayed over a selected time period prior to the start of release to the

environment. Decay continues over the duration of the release.

Up to three sets of release rates or concentrations can be entered along with their start and end times.

1.2.8 Monitored Release - Mixtures

Nuclear power plants often report effluent mixtures of radionuclides by reporting the activities of each of

three components of the mixture: noble gases, iodides, and particulates.

In RASCAL 3.0.5, a monitored mixture release may start before or after reactor shutdown. The

measurement of the effluent release rate must occur during the release because if the release is not

occurring, there is nothing to measure. The default for the time of measurement is at the start of the

release because it is assumed to be likely that the plant operators will note the release rate as soon as it

starts.

1-19
Before shutdown, the noble gas and iodine radionuclides are assumed to be in radiological equilibrium

and present in the same proportion as in the core inventory shown in Table 1.1. The fraction of each

noble gas nuclide in the noble gas portion of the sample is shown in Table 1.5. Radiolodines are shown in

Table 1.6.

Table 1.5 Fraction of Total Noble Gas Activity for each Noble Gas Nuclide at Shutdown

(burnup = 18,000 MWD/MTU)

Noble Gas Core activity inventory Fraction of total

Nuclides before or at shutdown, noble gas activity

Ci/MWt

(from Table 1.1)

Kr-85 190 0.0018

Kr-85m 8,000 0.0458

Kr-87 16,000 0.0916

Kr-88 23,000 0.1317

Xe-131m 330 0.0019

Xe-1 33 57,000 0.3264

Xe-133m 2,000 0.0115

Xe-135 11,000 0.0630

Xe-138 57,000 0.3264

Table 1.6 Fraction of Total Radioiodine Activity for each Radioiodine Nuclide at Shutdown

(burnup = 18,000 MWD/MTU)

Iodine Core activity inventory Fraction of total

Nuclides before or at shutdown, radioiodine activity

Ci/MWt

(from Table 1.1)

1-131 28,000 0.1176

1-132 40,000 0.1681

1-133 57,000 0.2395

I-134 63,000 0.2647

1-135 50,000 0.2101

RASCAL 3.0.5 calculates the effluent rates for individual nuclides in a monitored mixture release using

the above tables in the following manner.

1-20
If a monitored mixture release ends before shutdown, the noble gas and radioiodine are assumed to

remain in the same proportions that they have in the core inventory. The activity effluent release rate for

each noble gas or iodine radionuclide A, is calculated by multiplying the total noble gas or iodine effluent

rate A by the fraction for radionuclide i in Table 1.5 or Table 1.6, as appropriate.

A = AFi (1.6)

where

Ai= the activity release rate of radionuclide i

A the total measured activity release rate of noble gases or radioiodines, as appropriate

F= the fraction of nuclide i in the mixture from Table 1.5 or 1.6, as appropriate

Particulates are more difficult to calculate because there are so many possible radionuclides that could be

released as particulates. We have taken the approach of assuming that the particulates are composed of

cesium iodide (50% Cs-137 + 50% 1-131). These radionuclides were selected because they are both

present in the core and coolant in relatively large amounts, they are both relatively volatile and readily

released from damaged fuel, and they are both biologically significant. This approach is likely to

overestimate the dose from particulates, but since releases should be filtered the particulate release rate

should be low and an overestimate of the dose from particulates should have little practical consequence.

No radiological decay correction is done for particulates.

Case 2: Release starts before reactor shutdown and ends after reactor shutdown. Measurement is

made before or at reactor shutdown.

If the sample measurement is made at or before reactor shutdown, each noble gas and iodine nuclide is

assumed to be present in the monitored sample in the fractions shown in Tables 1.5 and 1.6. Thus, the

release rate for each nuclide for any time step prior to shutdown is simply the effluent rate multiplied by

the appropriate fraction in Table 1.5 or 1.6 as shown in the equation above.

For a time step after shutdown, the activity effluent release rate is assumed to decrease due to

radiological decay. Thus, the effluent activity release rate does not remain constant, but instead decreases

with time. The activity effluent release rate at or before shutdown from the equation above is corrected

for radioactive decay factor as shown in the equation below. (The in-growth of daughters from the decay

of the noble gases is not included in the release because they would be filtered out before release.)

Ai(t) = Aoiexp[-Pu(t - to)] (1.7)

where

Af(t) = the decay-corrected activity release rate for nuclide i at time t

Aoi = the activity release rate of nuclide i at time of shutdown t,

Ai = the radiological decay constant of nuclide i

1-21
Case 3: Release starts before or after reactor shutdown and ends after reactor shutdown.

Measurement is made after reactor shutdown.

This calculation is done in three steps. First, the un-normalized fraction of each radionuclide in the

mixture sample Fi(t) must be determined for the sample time tI. This is done by applying a decay

correction to the fractions in Tables 1.5 and 1.6.

Fi(ts) = FPo exp[- A4(t, - to)] (1.8)

where

Fi(t) = the un-normalized decay-corrected fraction of activity for nuclide i at sample time t,

Foi = the fraction of the activity of nuclide i at time of shutdown time t, from Table 1.5 or 1.6

2I = the radiological decay constant of nuclide i

Next, the activity release rate of each radionuclide in the sample Af(t) is then calculated by normalizing

the fractions and multiplying by the effluent release rate for that radionuclide group.

Ai(t,) = A(ts)[Fi/ F,)] (1.9)

where

Aft) = the activity release rate of nuclide i at sample time t, (after shutdown)

A(t) the total noble gas or radioiodine activity release rate at the sampling time t,

EF', = the sum of the fractions of the activities for the radionuclide group at the sampling time

(to normalize the fractions for each nuclide)

The last step is to apply a correction for radiological decay. This is shown in the equation below

A,(t) = A,(ts) exp[- ,(t - t,)] (1.10)

where

Ai(t) = the decay-corrected activity effluent release rate for nuclide i at time t

A,(t) the activity effluent release rate of nuclide i at time of sample t,

2i = the radiological decay constant of nuclide i

Note that if the time t is earlier than the sample time t, the exponent in the equation will be positive and

the radiological decay correction will increase the activity effluent release rate to be greater than it was at

the sample time..

1.3 Release Pathways

After the RASCAL 3.0.5 user has selected a source term type and entered the needed data for that source

term type, he must select a release pathway to the environment. The release pathways that are available

for selection will depend on the reactor type (PWR or BWR) and the source term type that the user

selected.

1-22
For PWRs, there are four potential release pathways: containment leakage, containment bypass, steam

generator tube ruptures, and direct to atmosphere. The release pathways available for those source term

types are shown in Table 1.7.

For BWRs, there are also four potential release pathways: leakage from the drywell via the wet well,

leakage through the dry well wall, containment bypass, and direct to atmosphere. The release pathways

available for each source term type are shown in Table 1.8.

Table 1.7 PWR Release Pathways Available for Each Source Term Type

Release pathway

Source term type Containment Containment Steam Direct to

leakage bypass generator atmosphere

tube rupture

Time core is uncovered X X X

Ultimate core damage state - X x

with spiked coolant release

Ultimate core damage state - X X X

with cladding damage

Containment monitor readings and X

containment air sample

Coolant sample X X

Effluent releases (rates, X

concentrations, and mixtures)

Table 1.8 BWR Release Pathways Available for Each Source Term Type

Release pathway

Source term type Leakage from Leakage from Bypass Direct to

dry well the dry well containment atmosphere

through the through the

wet well dry well wall

Time core is uncovered X X X

Ultimate core damage state X X X

Containment monitor readings and X X

containment air sample

Coolant sample X

Effluent releases (rates, X

concentrations, and mixtures)

1-23
1.4 Release Pathway Models and Reduction Mechanisms

Each of the pathways listed in the previous section, except direct release to the atmosphere, will have its

own characteristic potential reduction mechanisms. The reduction factors that RASCAL 3.0.5 uses are

described below.

All the reduction factors are assumed to operate on all radionuclides except noble gases. None of the

reduction factors reduce the activity of the noble gas release to the environment. All nuclides subject to a

given reduction mechanism are assumed to have the same reduction factor. Radioiodines are treated the

same as all other non-noble gas nuclides. The reduction factor multipliers are listed in Table 1.9 and

described in detail in the sections below.

Table 1.9 Summary of Nuclear Power Plant Reduction Factor Multipliers

Reduction mechanism or cause Reduction Factor Multiplier

Containment sprays (reference: NUREG/CR-4722, Figure 5) First 0.25 h: exp(-12t)

After 0.25 h: exp(-0.2t)

Containment natural processes during hold-up (reference: First 1.75 h: exp(-1.2t)

NUREG-1 150, Appendix B) 1.75 to 2.25 h: exp(-0.64t)

After 2.25 h: exp(-0.15t)

PWR Ice condenser - no fans or recirculation 0.5

PWR Ice condenser - 1 h or more recirculation 0.25

BWR release pathway from drywell via wet well with sub- 0.01

cooled pool water

BWR release pathway from drywell via wet well with saturated 0.05

pool water

Plate out for containment bypass pathway 0.4

Steam generator tube rupture - partitioned (break underwater) Partitioning factor (steam

concentration as fraction of SG

water concentration)

0.02

Steam generator tube rupture - not partitioned (break above Partitioning factor (steam

water level) concentration as fraction of SG

water concentration)

0.5

Steam generator tube rupture - condenser off gas release 0.05

Steam generator tube rupture - safety relief valve release 1

Filters 0.01

Lower limit on reduction multiplier (except for filters) 0.001

Lower limit on reduction multiplier for containment sprays 0.03

(reference: NUREG/CR-4722, Figure 5)

Reference: NUREG-1228 except as noted for some specific table lines.

1-24
1.4.1 Containment Leakage in PWRs

While radionuclides are held up in the containment atmosphere, they are subject to removal from the

atmosphere by water sprays and by natural processes that cause deposition on containment surfaces. If

containment sprays are operating, they rapidly reduce the concentrations of all radionuclides except for

noble gases. If the sprays are not operating, the natural processes such as gravitational settling and plateout on containment surfaces by turbulent impaction gradually reduce airborne concentrations of

particulates and reactive gases.

The reduction factors RF for sprays and for natural processes during holdup without sprays are both

modeled as exponential functions of time t

RF = e-(1.11)

where

A = a reduction constant for sprays or natural processes.

Both sprays and natural processes have multiple values for ?. The removal rate is larger at early times

and slower at later times. Sprays and natural processes can remove particulates more readily initially and

then more slowly as the readily removable particles have already been removed.

Since the user can enter release and reduction data that changes with time, it is possible to turn the sprays

on and off several times. The initial spray, Xk, applies to (1) all the activity in containment the first time

the sprays are turned on, and (2) all the activity that enters the containment the first time that sprays are

active. If the sprays are turned off and then turned back on,. only the continuing kc is used. The initial k,

for holdup applies only if the sprays were never turned on. Otherwise the continuing kc is used.

RASCAL 3.0.5 nuclear power plant source term calculations include a maximum effectiveness for sprays

and a maximum effectiveness for all reduction, excluding filters. See Table 1.9. For each, the appropriate

reduction factor or product of reduction factors computed at each time step is compared to the maximum

and is not allowed to surpass it.

For PWRs with ice condenser containments, additional reductions can be taken due to interaction of the

containment air with the ice. If the fans are recirculating the containment air through the ice beds for at

least an hour, the activity entering the containment is reduced by using a reduction factor RF multiplier

of 0.25. If the fans are not operating the reduction factor RF. multiplier is 0.5.After the ice beds are

exhausted, the reduction factor RFi multiplier is 1.

1.4.2 Containment Leakage in BWRs

For BWRs, the model for reduction of radionuclides in the drywell air by sprays or natural processes is

the same as for PWRs as described above. However, an additional reduction mechanism can be applied if

the release from the dry well is through the wet well water.

If the release it through the wet well water and the water is sub-cooled (below the boiling point), an

additional reduction factor RFi multiplier of 0.01 is applied to all nuclides except noble gases. If the wet

well water is saturated (boiling), the reduction factor RFi multiplier is 0.05.

1-25
1.4.3 Containment Bypass

Containment bypass is a coolant release from the reactor coolant system to an auxiliary building or

directly to the environment without passing through the containment atmosphere. The containment

bypass release model and the reduction mechanisms are the same for PWRs and BWRs. Therefore, this

section applies equally to both.

The bypass model was substantially revised in RASCAL 3.0.5 compared to previous versions. In

previous models, activity escaping the fuel was transported immediately to the environment. Essentially,

the previous model did not model holdup. Thus, the release rate was unrealistically fast and much too

large for small leaks. The new RASCAL 3.0.5 model first distributes activity released from the fuel into

the coolant with uniform concentrations. The flow rate of coolant to the environment then determines

how quickly radionuclides escape to the environment.

For the bypass model, RASCAL 3.0.5 first calculates the initial concentration of each radionuclide in the

coolant. If the user selects the coolant source term type, the initial coolant concentration of each

radionuclide is entered directly. If the user selects the ultimate core damage state source term type, the

radionuclide activity by nuclide (calculated as described in Section 1.2.3) is assumed to enter the primary

coolant system. The initial concentration of each radionuclide is the activity entering the primary coolant

system divided by the total coolant volume. If the user selects the time core is uncovered source term

type, the initial coolant concentration is the activity released from the core during the first 15-minute time

step divided by the total coolant volume.

The coolant concentrations are then multiplied by a reduction factor for plateout. The plateout multiplier

for containment bypass is 0.4, which is taken from NUREG-1228. The plateout mechanism is plateout

within the reactor coolant system.

The user then enters the coolant escape rate in terms of volume per unit time. Generally, the user can

estimate the escape rate based on the make-up needed to maintain water levels. RASCAL 3.0.5 then

calculates the activity escaping the primary coolant system during the time step by multiplying the

radionuclide concentration in the coolant times the volume that escapes during the first time step.

For subsequent time steps, the concentration in the coolant is reduced to account for the activity that has

escaped from the primary system. If the time core is uncovered source term type is being used, new

activity enters the coolant system during each time step as described in Section 1.2.2. Thus, the coolant

concentrations are being augmented during each time step by new radioactive material entering the

coolant.

Radioactive decay and ingrowth are also calculated during each time step.

RASCAL 3.0.5 does not calculate any holdup or plateout in any secondary structure such as auxiliary

building. However, release to the environment can be reducedby filters, if applicable.

1.4.4 Steam Generator Tube Ruptures in PWRs

The steam generator tube rupture model in RASCAL 3.0.5 is substantially changed from the model used

in previous versions of RASCAL. In previous RASCAL versions, the steam generator partitioning factor

1-26
was treated as a removal factor. In the new RASCAL 3.0.5, the radionuclides that enter the steam

generator are truly partitioned. Therefore, there can be buildup of those radionuclides in the steam

generator. The result is that the new RASCAL model will predict larger releases if the release duration is

very long.

RASCAL 3.0.5 calculates the activity concentration in the primary coolant system the same way it

calculated the concentration for containment bypass described in Section 1.4.3 above. The activity

escaping the primary coolant system and entering the steam generator is also calculated by the same

method as for bypass accidents except that no reduction factor for plateout is used.

As with the bypass release path, the RASCAL 3.0.5 user specifies the flow rate from the primary coolant

system to the secondary system, which can perhaps be estimated from the makeup flow needed to

maintain the water level in the primary system. The default flow rate into the steam generator is 500

gallons/minute, which is considered equivalent to the rupture of one tube in one of the steam generators.

For U-tube steam generators, the RASCAL 3.0.5 user specifies whether the tube rupture is above or

below the water level in the steam generator. For once-through steam generators, the rupture is always

assumed to be above the water level.

If the break is below the water level, the activity entering the steam generator is assumed to be evenly

mixed in the steam generator water. The initial activity concentration (Ci/lb) in the steam generator is the

activity that entered the steam generator during the first time step divided by the weight of the steam

generator water. The default weight of water in a steam generator is 93,000 lbs, but the user can change

the value if better information is available.

The activity concentration for non-noble gases in the steam that exits the steam generator is assumed to

be the concentration in the steam generator water times a partition factor. If the rupture is below the

water level, the partition factor is 50. In other words, the concentration of a non-noble gas radionuclide in

the steam is assumed to be one-fiftieth (0.02) of the concentration in the steam generator water. If the

break is above the water level, the partition factor is 2. In other words, the concentration in the steam is

half the concentration in the water.

Note that partition factors are hold-up factors, not removal factors. The partition factors slow the release

of radionuclides from the steam generator, but do not prevent it. As long as the steam generator is not

isolated, the steam will continue to remove radionuclides from the steam generator water. The removal

rate for the steam is the concentration in the steam times the flow rate of steam. The default for the

steaming rate in a steam generator is 75,000 lbs/hr, but the user can change this value if better

information is available.

Each time step, RASCAL 3.0.5 recalculates the concentration of radionuclides in the steam generator

water by subtracting the activity removed in the steam during the previous time step and by adding any

new activity entering from the primary coolant system through the rupture.

There are two paths by which the radionuclides in the steam can escape to the environment. The first is

the safety relief valve and the other is the condenser off-gas exhaust (or steam-jet air ejector in some

plants).

1-27
RASCAL 3.0.5 assumes that there is no removal of radionuclides as the steam exits through the safety

release valve. If the exit is through the condenser off-gas exhaust, RASCAL 3.0.5 assumes that filters

remove 95% of the non-noble gas radionuclides (multiplies activity by 0.05).

1.5 Leakage Fractions

Four methods for specifying leakage fractions for release to the environment are available in RASCAL

3.0.5: (1) specifying the percent of activity present that is released per unit time, (2) specifying a

containment pressure and hole size, (3) specifying a coolant flow rate (volume or mass per unit time),

and (4) specifying a "direct" release, with all activity released during the selected release duration. The

methods for specifying release rates available for each release pathway are shown in Table 1.10.

Table 1.10 Methods for Specifying Release Rate for each Release Pathway

Release pathway Method for specifying release rate

Containment leakage % of containment volume per time or

Containment pressure and hole size

Containment bypass Coolant flow rate

Steam generator tube rupture Coolant flow rate

Monitored effluent releases Direct to atmosphere

1.5.1 Percent Volume per Time

This release rate method releases the activity in a fixed fraction of the containment or confinement

volume per unit time.

The leakage fraction LF is used to calculate the fraction of the radionuclide inventory in the containment

atmosphere that is released to the environment during each 15-minute time step. At each time step the

radionuclide inventory in the containment atmosphere is adjusted to account for radiological decay and

ingrowth, additions to the containment atmosphere radionuclide inventory if core damage is still

occurring, removal of radionuclides from the containment atmosphere by sprays or plate-out, and

removal from the containment atmosphere by release to the environment.

Consider the case in which the release rate is specified to be 100%, which corresponds to total

containment failure. This rate is equal to 25% per 15-minute time step. During the first time step 25% of

the activity in the containment will be released. For the second time step, the activity remaining in the

containment will be reduced by subtracting the activity that escaped during the first time step. Then any

applicable reduction factors such as removal by containment sprays or plateout will be calculated. Then

the 25% leak will be applied to the remaining activity in the containment. Because only 25% of the

material in the containment can be removed each time step, there will still be some activity remaining in

the containment after an hour even at a leak rate of 1 00%/hr.

1-28
1.5.2 Leak Rate Based on Containment Pressure and Hole Size

RASCAL 3.0.5 can calculate the leak rate through a hole in the containment if the hole size and

containment pressure are known. RASCAL 3.0.5 uses Equation 6-39 from Blevins 1984 for

incompressible flow through a thin square-edged orifice. The hole is assumed to be the orifice. The mass

flow rate out of containment, MFR(k) during time step k, is

MFR(k) = C (--4-),]2,o (PR (k) - P2) g (1.12)

where

C = 0.63, an experimentally measured discharge coefficient that rarely varies outside the

range of 0.59 < C < 0.65 and is dimensionless,

D = hole diameter in inches,

p = density of containment atmosphere in pounds per cubic inch,

P,(k)= pressure in containment during time step k in pounds per square inch,

P2 = atmospheric pressure in pounds per square inch,

g = acceleration of gravity in inches per second per second to convert between pounds and

a mass unit.

The leakage fraction from containment to the atmosphere during step k, LF(k), is

LF(k) = MFR(k) t (1.13)

pVc

where

t = duration of time step k in seconds

V, = the containment volume.

If the containment pressure is less than atmospheric pressure, the leak rate is zero. The code does not

compute the change in containment pressure, but the user can enter changing containment pressures as

the assessment proceeds.

1.5.3 Coolant Flow Rate

Containment bypass accidents are accidents in which coolant is released without going through the

containment. When the coolant escapes, it is no longer pressurized. At atmospheric pressure, the coolant

will flash into steam, and the radionuclides in the coolant will become airborne. The coolant mass flow

rate times the radionuclide concentration will give the radionuclide release rate. Alternatively, the

coolant mass flow rate divided by the total coolant volume will give the leakage fraction for the

radionuclides in the coolant.

Normally, it will not be possible to measure the coolant mass flow rate directly. However, the makeup

flow needed to maintain pressure or water levels in the reactor coolant system can usually be readily

determined. This makeup flow can be used as an estimate of the mass flow rate for escaping coolant.

1-29
For steam generator tube rupture accidents the makeup flow rate can be used as an estimate of the

coolant mass flow rate from the reactor coolant system to the steam generator. The steaming mass flow

rate in the steam generator is then a measure of the rate at which water is being removed from the steam

generator. The radionuclide concentration in the steam will be the concentration in the steam generator

water times the appropriate partitioning factor. The concentration in the steam times the steaming mass

flow rate equals the escape rate from the steam generator.

1.5.4 Direct Release to Atmosphere

The direct release to atmosphere pathway is used with the three monitored effluent release source term

types: (1) activity release rate by nuclide, (2) activity release concentration by nuclide and flow rate, and

(3) monitored mixtures release rate. These releases are assumed to be measured after any removal or

reduction processes have acted and represent the actual release rate to the atmosphere. Therefore, no

reduction mechanisms can be applied to the releases.

The user sets a start and a stop time for the release. If the source term type is activity release rate by

nuclide or activity release concentration by nuclide and flow rate, the activity release rate and the

composition of the effluent are assumed to be constant over the interval. If the monitored mixture source

term type is selected, the release rate and composition of the effluent changes with time to account for

radiological decay. This was described in Section 1.2.8.

1.6 Decay Calculations in the Source Term

Many of the source term calculations in RASCAL 3.0.5 require the calculation of radiological decay.

Because the Source Term to Dose model requires that decay calculations be performed at least every 15

min, it was determined that a significant amount of calculation time could be saved by precalculating

decay over that period for all of the radionuclides in RASCAL. Since the source term calculations may

also require decay over longer or shorter periods, decay was also pre-computed for 1 and 5 minutes, 1

hour, and 1, 14, and 182 days. One implication of this is that decay cannot be calculated for less than 1

minute.

The decay data used in RASCAL 3.0.5 is the decay data used in creating the dose factors in Federal

Guidance Report No. 12 (USEPA 1993). The decay data file used by source term calculations was

created by running a program called Chain (Eckerman et.al 2006), that was originally written by K. F.

Eckerman to read the decay data used in creating the dose factors in Federal Guidance Report No. 12 and

to solve the Bateman equations.

The source term model computes decay incrementally, starting with the longest time period for which

decay data have been precalculated and stored. For each time period, the activity of the parent and its

daughter products are summed. The process is repeated until the correct decay time is reached. For

example, assuming that 72 minute of decay are required, the subroutines find the required nuclide decay

data using a binary search and then sum it for 1 hour, then for 5 minutes twice, then for 1 minute twice.

The Source Term to Dose user interface code extracts the required 5-minute and 15-minute decay data

for the radionuclides in the source term and passes them to the transport and diffusion models for the

calculation of decay during atmospheric transport.

1-30
The activities of the short-lived daughters are initially set equal to their parents times the branching ratio,

if applicable. These are listed in Table 1.11.

Table 1.11 Short-lived Daughters Assumed to be in Equilibrium with the Parent Activity

Parent (branching ratio) Daughter

44Ti 44Sc

68Ge 'Ga

88Kr 88

Rb

"Mo (0.876) 99mTC

1

0Ru 1

06Rh

109

Cd lOsmAg

113

Sn 113min

126

Sn 126mSb 12 6

Sb

1297'e (0.65) 129

Te

135l (0.154) 1

3

SmXe

1

37

Cs (0.947) 1

37

m Ba

144Ce 144Pr

1.7 Quality Assurance for the Source Term Calculations

In order to demonstrate that the source term calculations were being done correctly, RASCAL 3.0.5 time

dependent source terms were compared with spreadsheet calculations. RASCAL 3.0.5 generates and

displays source terms by nuclide for 15-minute time steps. A set of spreadsheets was prepared to

duplicate the calculations in RASCAL 3.0.5.

A spreadsheet was developed for each source term type. The equations programmed in the spreadsheets

were done to represent the methods and models described in this report. As such, the spreadsheets

represented our understanding of how the calculations should be correctly done. On the spreadsheets,

various combinations of release pathways, reduction mechanisms, and other operating conditions were

programmed.

Several nuclides were then used for each case. A noble gas was used because no reduction mechanism

should operate on noble gases. Also, in each case, a non-noble gas was used to test the reduction

mechanisms.

These spreadsheet results were compared to the RASCAL 3.0.5 time dependent source term results for

the selected nuclides for at least 10 time steps. If the results were in agreement, I was concluded that the

calculations were being done in the same way. This was taken as demonstrating that the RASCAL 3.0.5

calculations were correct because the likelihood of both being programmed incorrectly in the same way

was considered extremely unlikely.

1-31
Table 1.12 lists the spreadsheets that were prepared, the source term conditions that were used, the

release pathways and reduction mechanisms that were applied.

1-32
Table 1.12 Spreadsheets Prepared for Quality Assurance Testing of the RASCAL 3.0.5 Time-dependent Source Term

Source term type Source term conditions Release pathway Release pathway conditions Nuclides

tested

Time core is uncovered Uncovered 2.5 hours Containment leakage Leak rate = 1%/h 1-131

Sprays on and off

Uncovered 2.5 hours Steam generator tube rupture Through steam jet air ejector 1-131

Leak rate = 1 gal/min

Partitioned

Uncovered 2.5 hours Containment bypass Leak rate = 1 gal/min 1-131

No filters

Ultimate core damage 50% cladding failure Containment leakage Leak rate = 1%/h 1-131, 1-133, (core damage) Sprays on and off Kr-88

75% cladding failure Containment leakage Leak rate = 10%/h 1-131, 1-133,

Sprays on and off Kr-88

50% cladding failure Steam generator tube rupture Through steam jet air ejector 1-131, 1-133,

Leak rate = 100 gal/min Kr-88

Partitioned

75% cladding failure Steam generator tube rupture Through safety valve 1-131, 1-133,

Leak rate = 250 gal/min Kr-88

Not partitioned

50% cladding failure Containment bypass Leak rate = 100 gal/min 1-131, 1-133,

No filters Kr-88

90% cladding failure Containment bypass Leak rate = 250 gal/min 1-131, 1-133,

Filtered Kr-88

Ultimate core damage

(coolant release)

Increased fuel pin leakage

Spiking factor = 100

Steam generator tube rupture Through steam jet air ejector

Leak rate = 1000 gal/min

Partitioned

1-131, 1-133,

Kr-88, Sr-90

1-33
Source term type

I

Source term conditions

Increased fuel pin leakage

Spiking factor = 50

Release pathway Release pathway conditions Nuclides

tested

Steam generator tube rupture Through safety valve

Leak rate = 200 gal/min

Not partitioned

1-131, 1-133,

Kr-88, Sr-90

Increased fuel pin leakage Containment bypass Leak rate = 100 gal/min 1-131,1-133,

Spiking factor = 100 Filtered Kr-88, Sr-90

Increased fuel pin leakage Containment bypass Leak rate = 300 gal/min 1-131, 1-133,

Spiking factor = 50 No filters Kr-88, Sr-90

Coolant sample 1-131 - 500 pCi/g Steam generator tube rupture Through steam jet air ejector 1-131, 1-133, 1-133 - 200 pCi/g Leak rate = 1000 gal/min Kr-88, Sr-90

Kr-88 - 1000 pCi/g Partitioned

Sr-90 - 600 pCi/g

1-131 - 500 pCi/g Steam generator tube rupture Through safety valve 1-131, 1-133,

1-133 - 200 pCi/g Leak rate = 500 gal/min Kr-88, Sr-90

Kr-88 - 1000 pCi/g Not partitioned

Sr-90 - 600 pCi/g

1-131 - 300 pCi/g Containment bypass Leak rate = 1000 gal/min 1-131, 1-133,

1-133 - 150 pCi/g No filters Kr-88, Sr-90

Kr-88 - 650 pCi/g

Sr-90 - 500 pCi/g

1-131 - 150 pCi/g Containment bypass Leak rate = 400 gal/min 1-131, 1-133,

1-133 - 300 pCi/g Filtered Kr-88, Sr-90

Kr-88 - 450 pCi/g

Sr-90 - 600 pCi/g

Containment air sample 1-131 -45 Ci/m 3 Containment leakage Leak rate = pressure of 45 lb/in2 with 2 in 1-131,1-133,

1-133 -40 Ci/m 3 diameter hole Kr-88, Sr-90

Kr-88 - 30 Ci/m 3

Sr-90 - 35 Ci/m 3

1-34
Source term type Source term conditions Release pathway Release pathway conditions Nuclides

tested

1-131 - 300 Ci/mr Containment leakage Leak rate = Total failure (100%/h) 1-131, 1-133,

1-133 -400 Ci/mr3 

Kr-88, Sr-90 Kr-88 - 500 Ci/m 3

Sr-90 - 600 Ci/m 3

Monitored mixtures NG - 2000 Ci/s Direct 2.5 hour release duration All noble

1- 4 Ci/s gases and

Part - 2 Ci/s iodine from

Not shutdown core inventory

+ Cs-137

NG - 2000 Ci/s Direct 2.5 hour release duration All noble

1- 4 Ci/s gases and

Part - 2 Ci/s iodine from

Meas 15 min before core inventory shutdown + Cs-137

1-35
1.8 References

American National Standard Institute (ANSI/ANS). 1999. Radioactive Source Term for Normal

Operation ofLight Water Reactors. ANSI/ANS-18.1-1999, American Nuclear Society, La Grange Park,

Illinois.

Blevins, Robert D. 1984. Applied Fluid Dynamics Handbook. Krieger Publishing Company, Malabar,

FL, 1984.

Eckerman, K.F., et al. 2006. User's Guide to the DCAL System. ORNL/TM-2001/190. Oak Ridge

National Laboratory, Oak Ridge, Tennessee.

Lobner, P., C. Donahoe, and C. Cavallin. 1990. Overview and Comparison of U.S. Commercial Nuclear

Power Plants. NUREG/CR-5640, SIC-89/1541, U.S. Nuclear Regulatory Commission.

McKenna, T. J., and J. Giitter. 1988. Source Term Estimation During Incident Response to Severe

Nuclear Power Plant Accidents. NUREG-1228, U.S. Nuclear Regulatory Commission.

McKenna, T. J., et al. 1996. Response Technical Manual: RTM-96. Vol. 1, Rev. 4, NUREG/BR0150, U.S. Nuclear Regulatory Commission.

Sjoreen A. L., T. J. McKenna, and J. Julius. 1987. Source Term Estimation Using MENU-TACT.

NUREG/CR-4722, U.S. Nuclear Regulatory Commission.

Soffer, L., et al. 1995. Accident Source Terms for Light- Water Nuclear Power Plants, Final Report.

NUREG-1465, U.S. Nuclear Regulatory Commission.

U. S. Environmental Protection Agency (EPA). 1993. "External Exposure to Radionuclide in Air Water,

and Soil." Federal Guidance Report No. 12, EPA-402-R-93-081, U.S. Environmental Protection

Agency.

U.S. Nuclear Regulatory Commission (NRC). 1975. Reactor Safety Study: An Assessment ofAccident

Risks in U.S. Commercial Nuclear Power Plants, NUREG-75/014 (WASH-1400). U.S. Nuclear

Regulatory Commission.

U.S. Nuclear Regulatory Commission (NRC). 1990. Severe Accident Risks: An Assessment for Five US.

Nuclear Power Plants. NUREG-1 150. U.S. Nuclear Regulatory Commission.

1-36
2 Spent Fuel Storage Source Term Calculations

RASCAL 3.0.5 can calculate source terms for three types of spent fuel storage accidents: (1) releases

from spent fuel stored in a pool when the water drains from the pool causing the fuel to become

uncovered, overheating the fuel, and causing cladding damage, (2) releases from spent fuel stored in a

pool when the fuel is damaged while it is under water, and (3) releases from spent fuel in a dry storage

cask when an accident causes both damage to the cladding of the fuel and loss of the integrity of the cask.

2.1 Basic Method to Calculate Spent Fuel Source Terms

The method to calculate source terms for spent fuel accidents is similar to the method for the nuclear

power plant accident source terms, but it is simpler. The method is simpler because the model assumes

that the entire release from the spent fuel is released instantly. This approach does not account for the

time that it takes for radionuclides to escape from the damaged spent fuel, but the amount escaping is

correct even though the timing is not realistic.

To perform the calculation, RASCAL 3.0.5 first calculates the activity of each radionuclide i that is

present in the spent fuel (the "inventory I,"). Second, it calculates the fraction of the inventory of each

radionuclide i that is available for release from the spent fuel for the accident being evaluated, the

available fraction AF,. Third, the product of those two terms is multiplied by a reduction factor RFi (for

example, for reduction by filters). Reduction factors can include several factors working simultaneously.

Last, RASCAL 3.0.5 calculates the source term by radionuclide Si(k) released to the atmosphere during

time step k by multiplying by the leakage fraction LF(k) for time step k. These calculations are described

by the equation:

Si(k) = L x AFi x RFi x LF(k) (2.1)

where

S.(k) = activity of radionuclide i released to the environment during time step k,

I, = inventory of radionuclide i

AFJ = fraction for radionuclide i available for release

RF. = reduction factor for radionuclide i

LF(k) = leakage fraction to the environment during time step k.

2.2 Spent Fuel Radionuclide Inventories

To calculate the inventory of each radionuclide in the spent fuel at the time of the accident I,, RASCAL

3.0.5 starts with the inventories per MWt in Table 1.1, "Nuclear Power Plant Inventory During Operation

for Low Enriched Uranium Fuel (30,000 MWD/MTU)." The core inventory is calculated by multiplying

by the reactor power. The default reactor power is 100% of the rated power but can be changed by the

user if appropriate.

The inventories of radionuclides with a half-life of longer than one year from Table 1.1 are then adjusted

for bumup using Equation 1.2. The default bumup for spent fuel is 50,000 MWD/MTU, but the user can

adjust this value if desired.

2-1
RASCAL 3.0.5 then calculates the radionuclide inventories in a single fuel assembly by dividing the

bumup corrected core inventory by the number of assemblies in the core (from the reactor database).

These are the inventories present in a fuel assembly at the time of reactor shutdown. If the spent fuel

involved in the accident is specified in terms of "batches," the batch inventories are calculated by

dividing the core inventories by 3. (A batch is assumed to be one-third of a core.)

The inventories at the time of the accident are then calculated by correcting for radiological decay and

ingrowth since their last irradiation.

For spent fuel assemblies damaged underwater or stored in dry casks, the user defines how long ago the

fuel was removed from the reactor. A radiological decay correction using that duration is applied to all

the damaged fuel. Decay and ingrowth are calculated using the methods described in Section 1.7.

A different scheme is used with the pool drained scenario. The user defines fuel amounts as either

assemblies or batches in 3 age classes: less than 1 year, I to 2 years, and longer than 2 years. All fuel in

each age category is decayed for a set time. For fuel that has been out of the reactor for 0 to 1 year, the

decay time is set to one week. This simple approximation can greatly overestimate the size of the release

if the fuel has been in storage much longer than one week. For fuel that has been in storage for 1 to 2

years, the decay time is set equal to 1 year. For fuel that has been out of the reactor for more than 2 years,

the decay time is set equal to 2 years.

2.3 Fractions of Inventory Available for Release in Spent Fuel Accidents

The fractions of the radionuclide inventories that are available for release during an accident AF. are

shown in Table 2. 1.

Table 2.1 Fuel Release Fractions Used in Spent Fuel Accidents

Release fraction by release type

Nuclide group Cold gap Hot gap Cladding

fire

Noble gases (Xe, Kr) 0.4 0.4 1

Halogens (I, Br) 3x10-3 3x10-2 0.7

Alkali metals (Cs, Rb) 3x103 3x102 0.3

Tellurium group (Te, Sb, Se) 1x104 1x10"3 6x10-3

Barium, strontium (Ba, Sr) 6x10-7 6x106 6 x10"4

Noble metals (Ru, Rh, Pd, Mo, Tc, Co) 6x10-7 6x10-6 6x10-6

Cerium group (Ce, Pu, Np) and Lanthan ides 6x 10-7 6x 10-6 2x 10-6

(La, Zr, Nd, Eu, Nb, Pm, Pr, Sm, Y, Cm, Am)

Source: Table 3.2 in NUREG/CR-6451 (Travis, Davis, Grove, and Azarm 1997) rounded to I significant figure. The

cladding fire release fractions are the geometric mean of the high and low fractions.

2-2
2.3.1 Spent Fuel Pool Water Drained

Spent fuel in a spent fuel pool must remain covered with water to remove decay heat or else the fuel will

heat up and the fuel cladding may be damaged. If the cladding is damaged, radioactive materials may be

released from the fuel. The model in RASCAL 3.0.5 for estimating the release of radioactive materials

from damaged spent fuel is based on information in NUJREG/CR-6451 (Travis, Davis, Grove and Azarm

1997).

The RASCAL 3.0.5 model assumes that cladding damage will not occur until the cladding temperature

exceeds 1,200 OF. If this temperature is not reached, there will be no release. When fuel recently put into

storage is uncovered but the pool is not totally drained, the model assumes that the spent fuel must be

uncovered for more than 2 hours in order for the fuel to reach 1,200 OF. Therefore, no release will occur

if the fuel is uncovered for less than 2 hours.

The assumption of no cladding damage in less than two hours is based on the heat-up rate of 30-day-old

fuel. Because it does not give credit for heatremoval by steam cooling, this assumption is usually

conservative.

If the spent fuel has been out of the reactor long enough, the fuel may never reach 1,200 °F, the

temperature for cladding damage. The RASCAL 3.0.5 model assumes that the temperature of the fuel

will not become high enough to cause cladding damage if PWR fuel that has been out of the reactor for

more than 1 year or if BWR fuel that has been out of the reactor for more than 0.5 year. This is based on

the observation that one-year-old fuel PWR required 10 hours or more to reach 1,200 OF. With steam

cooling this PWR fuel is not expected to reach this temperature.

In summary, there will be no release under the following conditions:

The pool is not totally drained so that steam cooling can occur and

- the spent fuel is uncovered for less than 2 hours

- or -

- the spent fuel has been in storage for longer than 1 year for PWR fuel or 0.5 year for BWR fuel.

The pool is totally drained but for less than 2 hours and

- the spent fuel has been in storage for longer than 1 year for PWR fuel or 0.5 year for BWR fuel.

A release is expected if the above conditions are not met. The available fractions (AF.) will normally be

those for a hot gap release using the release fractions in Table 2.1. However, under certain circumstances,

the temperature of the fuel can rise so high that a cladding fire will result. In those circumstances, the

available fractions will be those in Table 2.1 for a cladding fire.

The cladding fire release fractions are used under the following conditions:

The pool is totally drained for at least 2 hours during which no steam cooling occurs and the

pool contains BWR fuel or high density racked PWR fuel less than 1 year in storage.

2-3
For PWR fuel, the user enters the number of fuel batches or assemblies that are one, two, and three years

old. For BWR fuel, the user enters the number of fuel batches or assemblies that are 180 days and two

years old. (No other fuel ages are allowed.) If the reactor is a PWR, the user enters whether the density of

the fuel pool racking is high or low. The user enters: the length of time the fuel is uncovered, if and when

the fuel was recovered, and if and when the pool was drained. When the fuel is uncovered, there is no

fission product reduction due to scrubbing in the pool.

RASCAL determines which fuel release fractions to use based on conditions in the pool, the fuel racking,

and the fuel age. If the pool is never totally drained, only fuel that has been in storage for one year or less

is considered to be damaged and the release fractions used are those for a hot-gap release. In a PWR with

high-density pool racking or in a BWR, if the pool is totally drained for at least 2 hours all fuel is

damaged and the release fractions used are for a fire release. In a PWR with low-density pool racking if

the pool is totally drained for at least 2 hours a fire release occurs in all fuel that has been in storage for

one year or less. Fuel that has been stored for more than one year is involved in a fire release only if there

is at least one batch of fuel that has been in storage for one year or less. If all fuel is older than one year,

then hot-gap release fractions are used for all the fuel.

2.3.2 Fuel Damaged Under Water

Fuel that is mechanically damaged under water is assumed to remain cold but experiences cladding

failure. The available fractions AFi are the cold gap release fractions in Table 2.1. All damaged fuel is

assumed to have been stored for the same length of time.

2.3.3 Release from a Dry Storage Cask

A release from a dry storage cask accident may be assumed to occur in two situations: (1) an accident

causes damage to the cladding of the fuel stored in the cask and also causes the integrity of the fuel cask

to be lost, or (2) cooling is lost for more than 24 hours resulting in fuel heat up and cladding failure with

subsequent loss of cask integrity.

For either accident type, the user defines the number of fuel assemblies involved in the accident by either

selecting the type of fuel cask or by directly entering the number of assemblies. If the user specifies the

cask type, the calculations can only be done for a single cask. The major fuel damage option allows the

user to specify what percentage of the stored fuel has sustained the damage.

For the first accident type, mechanical damage to cladding and the cask, the assemblies would be

damaged without heating. Therefore, the available fractions AF. will be the cold gap release fractions in

Table 2.1. For an accident with loss of cooling for more than 24 hours, cladding failure is assumed to

occur because the temperature rise causes melting of the cladding. For this case, the hot gap release

fractions in Table 2.1 are used for the AFi.

No release is assumed to occur if cooling is lost for less than 24 hours or the cask is engulfed in a fire

because the casks are designed to maintain their integrity in those situations.

2.4 Release Pathways and Reduction Factors

For all spent fuel accidents, the RASCAL 3.0.5 user specifies the times for the start and the end of the

release.

2-4
For spent fuel pool accidents, the release from the spent fuel is assumed to be into a building. If the

release pathway to the environment passes through filters, a reduction factor of 0.01 is applied to all

radionuclides except noble gases.

For spent fuel damaged underwater in a spent fuel pool, a reduction factor of 0.01 is applied to all

radionuclides except noble gases to account for scrubbing by the water in the pool. This factor is in

additional to reduction by building filters.

For dry cask storage accidents, there are no reduction mechanisms to reduce the amount of activity

released.

2.5 Leakage Fractions

For all spent fuel accidents, the user specifies the leak rate to the environment in terms of %/hour with a

maximum rate of 100%/hour. For fuel casks stored outdoors, the user would normally select 100%/hour

to indicate a very fast transfer rate to the environment.

2.6 References

Travis, R. J., R. E. Davis, E. J. Grove, and M. A. Azarm. 1997. A Safety and Regulatory Assessment of

Generic BWR and PWR Permanently Shutdown Nuclear Power Plants. NUREG/CR-6451, BNLNUREG-52498, U.S. Nuclear Regulatory Commission.

2-5

3 Fuel Cycle and Materials Source Terms

The source term calculations in RASCAL estimate the amount of radioactive (or hazardous) material

released based on a wide variety of potential radiological accident scenarios. The source term

calculations performed that pertain to fuel-cycle facility and materials accidents can be generally

categorized as (1) fuel-cycle facility/UF6 accidents, (2) uranium fires and explosions, (3) criticality

accidents, and (4) isotopic releases (e.g., transportation, materials).

3.1 Basic Method to Calculate the Source Term

RASCAL 3.0.5 calculates source terms by time steps. For each time step, RASCAL 3.0.5 first calculates

the activity that is present (the "inventory T"). Second, RASCAL 3.0.5 calculates the fraction of the

inventory that is released from the reactor fuel FRF. Third, the product of those two terms is multiplied

by a reduction factor RF (for example, for reduction by filters or containment sprays). Reduction factors

can include several factors working simultaneously. Last, RASCAL 3.0.5 calculates the source term S

released to the atmosphere .by multiplying by the leakage fraction LF. These calculations are described by

the equation:

Si(k) = L(k) x AFi(k) x RF(k) x LF(k) , (3.1)

where

S,(k) = activity of radionuclide i released to the environment during time step k,

I,(k) = inventory of radionuclide i at time step k,

AF,(k) = available fraction for release for radionuclide i during time step k,

RFi(k) = reduction factor for radionuclide i during time step k,

LF(k) = leakage fraction to the environment during time step k.

The time steps may be of varying length. A source term time step starts whenever the user changes any of

the time-dependent data or every 15 minutes, whichever is less. Time steps may be no less than 1 minute

and must be an integral number of minutes. Before passing the source term to the atmospheric transport

model, RASCAL 3.0.5 converts the source term time steps into 15-minute time steps that start on the

hour because the atmospheric transport model requires that regularity.

3.2 UF6 Releases from Cylinders

Starting Inventory

The inventory (I) of UF6 available for release from cylinders can be described by the user in two ways:

1. The user specifies the number and types of cylinders releasing their contents. Table 3.1 lists the

cylinder types available and the mass of UF6 each contains. Each cylinder is assumed to be filled to

its capacity. The total starting inventory is the sum of the number of each type of cylinder times the

amount of UF 6 in that type of cylinder.

2. The user specifies a total mass of UF6 in cylinders that can be released.

3-1
Table 3.1 UF6 Cylinder Inveni

Cylinder type Available inventory of UF6 (kg)

2.5 ton (30A, 30B) 2,277

10 ton (48A, 48X) 9,539

14 ton (48Y, 48G, 48F, 48H) 12,338

Release fractions and release rates

The user next selects the form of the UF6 (liquid, solid, or solid in a fire) and the type of cylinder damage

leading to the release (rupture or valve/pigtail failure). Specifying these serves only to set the default

release fractions and release rates shown in Table 3.2.

ladle 3.2 Delault Release iFractions and Rates Bsased on UF6 iorm and Cylinder Damage Ty]

Cylinder rupture Valve or pigtail failure

Form of UF6 Release fraction Release rate (kg/s) Release fraction Release rate (kg/s)

Liquid 0.65 32 see table 3.3 4

Solid 1.0 0 1.0 0

Solid in fire 1.0 8 1.0 1

)e

,3otirce: R I IVl S•upplemlenLS for r'adclUaf andi rortSMOUtnI Gaseous D/iffusion rianlSl I YY /.

There is one special case where the UF6 is liquid and the release is caused by a valve or pigtail failure. In

this case, the valve location is used to set the maximum release fraction. The relationship between valve

position and release fraction is shown in Table 3.3. (All cylinders are assumed to have the same

maximum release fraction and release rate.)

Table 3.3 IF. Release Fractions Based on Valve Location

Maximum

Valve position release fraction

360 0 - top 0.3870

270' - side 0.5528

1800 - bottom 0.9222

Source: The release fractions were computed using data taken from Table 22 of Williams (1995, NURE(G/CR-4360).

The mass of UF6 available for release is the starting inventory (I) times the available fraction (AF).

3-2
Release pathways

RASCAL 3.0.5 has three possible release pathways for UF6 cylinder releases: direct to the atmosphere,

through a building, or through filters. For some pathways, it is assumed that the UJF 6 will be fully

converted to HF and U0 2F 2 before entering the atmosphere. Table 3.4 lists the situations where the UF 6

is converted before release.

Table 3.4 Pathways with/without UF6 Conversion Prior to Release to Atmosphere

Pathway No conversion of Complete

UF, conversion to HF

& UO2F2

Direct

- liquid X

- solid X

- solid in a fire X

Through building X

Through filters X

UF6 is converted as I kg of UF6 = 0.88 kg UO2 F2 + 0.23 kg HF. To determine the uranium activity from

the uranium mass and enrichment, RASCAL converts the mass of UF 6 to activity using the enrichment

level and the specific activity. This conversion described in Section 3.9.

The direct to atmosphere pathway assumes that all material released from the cylinder(s) enters the

atmosphere without being acted upon by any reduction mechanisms. The leak rate to the atmosphere is

the leak rate from the cylinder(s). The UF6 available for release is divided by the release rate to determine

how many time steps are required for the release to complete. The UF 6 is released at a constant rate until

exhausted.

Releases through a building or filters both allow the user to specify a release fraction for the HF and the

U0 2F2 , a building air exchange rate (changes per hour), and a start and end time for the release. This

release fraction is different from that described earlier. These numbers represent a reduction due to the

building or filters; the previous was a reduction by the cylinder.

No radiological decay is computed in UF6 accident scenarios.

3.3 U F6 Releases from Cascade Systems

The UF6 cascade release accident type is available only for the Portsmouth and Paducah gaseous

diffusion plants. In addition, the cascade release source term option is available only for certain buildings

of those facilities. Tables 3.5 and 3.6 list the building names and information about the default

inventories and release rates.

3-3
Table 3.5 Paducah GDP Buildings and Default Inventory and Release Rates

Building name Cells per unit Number of units Avg cell inventory Release rate

(Ibs) (Ibs/sec)

C-331 10 4 4,400 130

C-333 10 6 9,500 130

C-335 10 4 4,600 130

C-337 10 6 8,400 130

C-310 10 1 150 130

Source: RTM Supplement for Paducah Gaseous Diffusion Plant, 1997.

Table 3.6 Portsmouth GDP Buildings and Default Inventory and Release Rates

Building name Cells per unit Number of units Avg cell inventory Release rate

(Ibs) (Ibs/sec)

X-326 20 2.5 1,000 130

X-330 10 11 5,000 130

X-333 10 8 5,000 130

Source: RTM Supplement for Portsmouth Gaseous Diffusion Plant, 1997.

Starting inventory

This starting UF6 inventory (I) may be entered: (1) directly as a total mass of UF 6 available for release or,

(2) as the mass of UF6 per cell and the number of units or cells in the cascade that are involved in the

release. When the number of cells is entered, the amount of material available is the product of the

number of cells times their inventory. When the number of units is entered, the amount of material is the

cell inventory time the cells per unit times the number of units.

This starting inventory (I) is multiplied by the user entered fraction available for release from the cascade

to the building. This value has a default of 1.0 and represents material removed by the structure due to

natural processes. The user also enters the rate at which the material escapes from the cascade into the

building. Each building has a default release rate that can be changed by the user.

Release pathway

The release pathway is based on two building configurations: summer and winter.

In the summer configuration, it is assumed the building is sufficiently open to the atmosphere (hot inside

with all doors and windows open) that released UF6 has essentially an unobstructed path to the outside.

This UJF 6 is released to the atmosphere at the defined cascade release rate. There is no application of

fractions available for release or start and end of release. Also, there is no conversion before release to

HF and U0 2F2.

In the winter configuration, the UF6 enters the building at the defined release rate and is converted as:

3-4
1 kg of UF6 = 0.88 kg U0 2F2 + 0.23 kg HF.

To determine the uranium activity from the uranium mass and enrichment, RASCAL converts the mass

of UF 6 to activity using the enrichment level and the specific activity. This conversion described in

Section 3.9.

Releases through a building or filters both allow the user to specify a release fraction for the HF and the

U0 2F2, a building air exchange rate (changes per hour), and a start and end time for the release. This

release fraction is different from that described earlier. These numbers represent a reduction due to the

building or filters; the previous was a reduction by the cylinder.

No radiological decay is computed in UF 6 accident scenarios.

3.4 Fires Involving Uranium Oxide

Uranium oxide fires may occur in several different types of facilities. In the milling of uranium ore, a fire

can occur in a drum of milled ore or during the process of extracting solvent. After the ore is milled, the

production of reactor fuel begins with creating a powder from the U0 2. Both wet and dry processes are

used to produce this powder. Uranium-oxide-contaminated waste can be stored in several forms, and any

of these can be involved in a fire.

Inventory and fractions available for release

The user first selects one of five locations for the fire and specifies additional conditions. This defines

the default fraction available for release (AIFs) and inhalation fractions (IFs).The AFs and IFs are

considered to be conservative. The IF is the fraction of the material released that is expected to be

inhaled. The material is defined as all vapors and any particulate material that has a diameter of< 10 gim.

(Note that the IFs are not used in the source term calculation. They are used in the calculation of

inhalation dose to reduce the amount of material inhaled.) The default values for the AFs and IFs are

shown in Table 3.7 (DOE 1994).

3-5
Table 3.7 Fractions Available for Release and Inhalation Fractions Used in Uranium Oxide

Fires

Location of fire Condition AF IF

Production process Dry process 1 x 10-3 1

Wet process 3x1O.5 1

H EPA filter At high temperature 1 x104 1

Failure 1 1

Incinerator exhaust 4x 101 1

Waste fire Solid packaged in drums 5x10-4 1

Solid loosely packed 5x10.2 1

Combustible liquid 3x10.2 1

Non-combustible liquid 2x10.3 1

Uranium mill Drum in a fire 1 X10-3 1

Solvent extraction 3x10-2 1

Source. DOE 1994.

Next, the user specifies the mass of the U0 2 material at risk and specifies a uranium enrichment level.

RASCAL calculates the uranium mass by first multiplying the mass of UO2 by 0.88 (ratio of atomic

weights U and U0 2). Then, the uranium mass is converted to activity based on enrichment as described in

Section 3.9. The source term available for release is the product of this activity times the fraction

available for release.

Release pathway

Releases outside the building have no further reductions. The release rate to the atmosphere is constant at

a rate set by dividing the available activity for release (Ci) by the release duration specified.

Releases inside the building are similar but reduce the available activity to release before calculating a

release rate to the atmosphere. The inventory is multiplied by a reduction factor or 0.5 for unfiltered

releases and multiplied by 0.01 if filtered.

3.5 Explosions Involving Uranium Oxide

Uranium oxide explosions are characterized as (1) those caused by the detonation of high explosives in

contact with the material, (2) those caused by a fire (deflagration), and (3) those caused by a sudden

pressure change in the material container (venting). The U0 2 in the explosion may be in liquid, solid, or

powder form, or it simply may be surface contamination.

3-6
Table 3.8 Fractions Available for Release and Inhalation Fractions Used in Uranium

Oxide Explosions

Explosion characteristics Material form of the

uranium oxide

Fraction

available

for release

Inhalation

fraction

Detonation Liquid 1 1

Solid 1 2x101

Powder 1 2x10"1

Surface contamination 1 x10-3 1

Deflagration Liquid 1 x106 1

Solid 0 0

Powder 5x 10-3 3x101

Surface contamination 1 x10 3 1

Venting Liquid 2x10-3 1

Solid 0 0

Powder Ix101 7x101

Surface contamination 1 X 10-3 1

Source: DOE 1994.

Next, the user specifies the mass of the U0 2 material at risk and specifies a uranium enrichment level.

RASCAL calculates the uranium mass by first multiplying the mass of UO2 by 0.88 (ratio of atomic

weights U and U0 2). Then the uranium mass is converted to activity based on enrichment as described in

Section 3.9. The source term available for release is the product of this activity times the release fraction.

Release path way

Releases outside the building have no further reductions. The release rate to the atmosphere is constant at

a rate set by dividing the available activity for release (Ci) by the release duration specified.

Releases inside the building are similar but reduce the available activity to release before calculating a

release rate to the atmosphere. The activity is multiplied by 0.5 for unfiltered releases and multiplied by

0.01 if filtered.

3.6 Criticality Accidents

A criticality accident results from the uncontrolled release of energy from an assemblage of fissile

material. In RASCAL 3.0.5, a criticality accident may be modeled using the physical system scenarios in

NUREG/CR-64 10 (SAIC 1998) or using criticality data entered directly by the user.

3-7
The physical systems modeled are listed in Table 3.9 along with the assumed number of fissions in the

first burst and the total yield. The user selects whether to model a single or multiple bursts. The bursts are

assumed to come at 10 minutes intervals and continue for eight hours (total of 48 bursts).

Table 3.9 Fission Yields Used in Criticality Calculations

System modeled in the scenario Initial burst yield Total yield

(fissions) (fissions)

Solution <100 gal 1 x1017 3x101

Solution >100 gal IxIO18 3x1019

Liquid/powder 3x 102o 3x1020

Liquid/metal pieces 3x 1018 lx 1019

Solid uranium 3x1019 3x1019

Solid plutonium 1 x1018 1x10'8

Large storage arrays below prompt None 1x10 19

critical

Large storage arrays above 3x10 22 3x10 22

prompt critical

Source: SAIC 1998.

When using the physical systems, the number of fissions in a burst (FB) for all except the first burst is

FB - (3.2) (48-1l)

where

FT = the total yield (fissions) of the criticality (column 3 in Table 2.1),

F, = the yield (fissions) of the initial burst (column 2 in Table 2.1).

When defined by the user, the following parameters must be set:

number of fissions (F,) in the first burst,

number of fissions (FB) in the subsequent bursts,

burst interval in minutes, and

duration of the criticality.

This user defined method assumes that a multi-burst event will end after 48 bursts, irrespective of the

burst interval.

For both methods of defining the fission yield of the criticality, the user defines fractions available for

release. The available fractions are defined for noble gases, iodines, and other nuclides which have

default values of 1.0, 0.25, and 0.0005 respectively.

3-8
The user also defines shielding thicknesses for steel, concrete, and water. Those thicknesses are used to

calculate the reduction in the neutron and gamma prompt shine dose due to shielding.

The assumed amounts of each radionuclide released per 10"9 fissions are listed in Table 2.1 (SAIC 1998).

These values are based on ORIGEN calculations (ORNL 1989).

To calculate the source term, RASCAL first determines the initial activity of each radionuclide present as

the product of the yield of the initial burst (FI) (in 10'9 fissions) and the activity per 10i" fissions listed in

Table 3.10. For each following time step, RASCAL: (1) determines if the criticality is still occurring and

if enough time has passed for one or more subsequent bursts to have occurred, and if so, adds the

appropriate activity as the product of the yield from these burst (FB) and the activity per 1019 fissions, (2)

reduces the amount of activity for the amount released, and (3) applies the release fractions and

radiological decay to the result. A criticality will end when either the total number of allowed bursts have

been accounted for or when the "end of criticality" time entered by the user has been reached. If the user

selects a release duration that is not long enough to include all 48 bursts, the total activity released will

be less than the amount listed in Table 3.10.

Table 3.10 Activity (Ci) Released in Criticality of 10"9 Fissions

Radionuclide Activity (Ci) Radionuclide Activity (Ci)

Kr-83m 1.5E2 1-131 7.3E0

Kr-85m 8.9E1 1-132 1.0E3

Kr-85 1.3E-5 1-133 1.7E2

Kr-87 1.1E3 1-134 4.2E3

Kr-88 6.6E2 1-135 5.0E2

Kr-89 4.6E4 Sr-91 3.2E2

Xe-133m 1.9E-2 Sr-92 1.2E3

Xe-133 2.7E-3 Ru-106 2.OE-2

Xe-135m 3.3E2 Cs-137 1.OE-2

Xe-135 5.2E0 Ba-139 2.4E3

Xe-137 2.4E4 Ba-140 1.1E1

Xe-138 1.0E4 Ce-143 1.0E2

Source: SAIC 1998.

Release pathway

The criticality is assumed to take place inside a building. A leak rate to the atmosphere from this building

is selected from the following four choices:

100% /h (represents ordinary building ventilation)

50%/h

10%/h

4% /h (equivalent to 100% per day)

3-9
This release rate method releases a fixed fraction of the material per unit time. After the criticality stops,

the release rate to the environment decreases exponentially.

The user defines a start and end of the release to the atmosphere. This describes when the radionuclide

material generated by the criticality enters the environment.

The user may define reduction factors for noble gases, iodines, and other radionuclides. These are

multiplied times the appropriate nuclide activities to reduce the release.

3.6.1 Prompt Shine Dose Calculation

For criticality accidents, the criticality-shine dose is computed with the source term. The shielding

thicknesses entered by the user are used only in this calculation. The dose in rem, Dcrt, at 10 ft is

computed as (Hopper and Broadhead 1998)

Dcrit = Dgamna + Dneutron (3.3)

Dgamnla = Ix 10-'x FT x e (0.386 x S + 0.147 x C + 0.092 x W) (3.4)

D,,etron = 1 x 10- 14 x FT x e (0.256 x S + 0.240 x C + 0.277 x W) (3.5)

where

FT = the total number of fissions,

S = the thickness of steel shielding in inches,

W= the thickness of water shielding in inches,

C = the thickness of concrete shielding in inches.

Doses, D, at other distances are computed using the inverse square law as:

lo0ft 2

D(x) ) x D(lOft) (3.6)

where

x = distance in feet

3.7 Sources and Material in a Fire

In a fire release, the user enters the amount of each radionuclide present. No release occurs when the fire

is not burning and no other types of reduction are allowed. A fire may start and stop burning only once.

The default values for these fire reduction factors are from NUREG/BR-0 150 (McKenna et al. 1996).

The user can select fire release fractions by element, by the form of the compound, or by entering them

directly. The default fire release fractions used are shown in Tables 3.11 and 3.12. Note that the total

3-10
amount of activity released also depends on the release duration entered in the isotopic release pathway

form. For example, if the release duration is shorter than the duration of the fire, the amount of activity

released is reduced.

Table 3.11 Fire Release Fractions by Compound Form

Form of compound Release fraction

Noble gas 1.0

Very mobile form 1.0

Volatile or combustible compound 0.5

Carbon 0.01

Semi-volatile compound 0.01

Non-volatile compound 0.001

Uranium and Plutonium metal 0.001

Non-volatile in a flammable liquid 0.005

Non-volatile in a non-flammable liquid 0.001

Non-volatile solid 0.0001

Source: Table F-2, McKenna et al. 1996.

If the compound form is not known, the user enters the fire release fractions in Table 2. 1.

The fire release fraction is the fraction of the isotope released when the material is involved in a fire; it equals the total

activity released (Ci) divided by the activity involved in fire (C0).

3-11
Table 3.12 Fire Release Fractions by Element"

Release Release Release Release

Elementb fractionc Element fraction Element fraction Element fraction

H (gas) 0.5 Se 0.01 I 0.5 W 0.01

C 0.01 Kr 1.0 Xe 1.0 Ir 0.001

Na 0.01 Rb 0.01 Cs 0.01 Au 0.01

P 0.5 Sr 0.01 Ba 0.01 Hg 0.01

S 0.5 Y 0.01 La 0.01 TI 0.01

Cl 0.5 Zr 0.01 Ce 0.01 Pb 0.01

K 0.01 Nb 0.01 Pr 0.01 Bi 0.01

Ca 0.01 Mo 0.01 Pm 0.01 Po 0.01

Sc 0.01 Tc 0.01 Sm 0.01 Ra 0.001

Ti 0.01 Ru 0.1 Eu 0.01 Ac 0.001

V 0.01 Rh 0.01 Gd 0.01 Th 0.001

Cr 0.01 Ag 0.01 Tb 0.01 Pa 0.001

Mn 0.01 Cd 0.01 Ho 0.01 U 0.001

Fe 0.01 In 0.01 Tm 0.01 Np 0.001

Co 0.001 Sn 0.01 Yb 0.01 Pu 0.001

Zn 0.01 Sb 0.01 Hf 0.01 Am 0.001

Ge 0.01 Te 0.01 Ta 0.001

a Table F-3 from McKenna et al. 1996. The release fraction for ruthenium was changed from the value of

0.01 in NUREG- 1140 to a value of 0.1. NUREG- 1140 assumed that ruthenium was nonvolatile (McGuire

1988). However, research in NUREG/CR-6218 (Power, Kmetyk, and Schmidt 1994) indicates (in Table 5)

that at high temperatures ruthenium starts to become volatile. The ruthenium release fraction of 0.1 is less

than the value of 0.5 used in NUREG- 1140 for compounds because ruthenium is less volatile than other

volatile compounds, becoming highly volatile only at temperatures not normally reached in building fires.

The carbon release fraction is appropriate for carbon compounds other than CO,. Those compounds deliver

most of the dose. The dose conversion factors used for carbon are for those carbon compounds.

b If the specific physical form of the nuclide is known, Table 2.1 may be used.

c The fire release fraction is the fraction of the isotope released when the material is involved in a fire, and

equals the total activity released (Ci), users should divide by the activity involved in fire (Ci).

Fire release fractions are element specific. The fire reduction factors are shown in Tables 3.1 land 3.12

and are from NUREG- 1140 (McGuire 1988).

3-12
For all types of isotopic releases, if the user selects release units in mass, rather than activity, the source

term is converted to curies using the specific activity of each radionuclide. The user may specify the

enrichment level for enriched uranium. The enrichment level for natural uranium is assumed to be 0.7%

(McKenna, et al. 1996, Table E-5). Specific activity is computed as described in Section 3.9. For natural

and enriched uranium, radiological decay and dose are calculated assuming the properties of U238 and

U"', respectively. U2 34 is used rather than U.3. because U234 has a specific activity about 3 orders of

magnitude higher than that of U23

".

3.8 Isotopic Release Rates and Concentrations

These two source term types are discussed fully in Chapter 1. They are available for all the event types of

RASCAL 3.0.5 except spent fuel.

3.9 Computing Uranium Specific Activity from Enrichment

The specific activity of uranium is calculated using the user entered value for the enrichment. A cubic

spline is generated using the data points given in Table 3.13. This spline is then evaluated for the given

enrichment to provide the specific activity.

Table 3.13 Uranium Specific Activity for Different Enrichments

Enrichment Specific activity

(% 235U by weight) (pCi/g)

0.0 (depleted) 0.4

4.0 2.4

93.0 110.0

Source: Table E-5, NUREG/BR-0 105, McKenna, 1996

3.10 References

Hopper, C. M., and B. L. Broadhead. 1998. An Updated Nuclear Criticality Slide Rule. Vol.2,

NUREG/CR-6504, ORNL/TM-13322/Vol.2, U.S. Nuclear Regulatory Commission.

McGuire, S. A. 1988. A Regulatory Analysis on Emergency Preparedness for Fuel Cycle and Other

Radioactive Material Licensees (Final Report). NUREG-1 140, U.S. Nuclear Regulatory Commission.

McKenna, T. J. and J. Glitter. 1988. Source Term Estimation During Incident Response to Severe

Nuclear Power Plant Accidents, NUREG-1228, U.S. Nuclear Regulatory Commission.

McKenna, T. et al. 1996. Response Technical Manual: RTM-96. Vol. 1, Rev. 4, NUREG/BR-0 150,

U.S. Nuclear Regulatory Commission.

3-13
Oak Ridge National Laboratory (ORNL). 1989. ORIGEN2 Isotope Generation and Depletion Code,

CCC-371. Oak Ridge National Laboratory, Oak Ridge, Tenn.

Powers, D. A., L. N. Kmetyk, and R. C. Schmidt. 1994. A Review of the Technical Issue ofAir

Ingression During Severe Reactor Accidents. NUREG/CR-6218, SAND-94-073 1, U.S. Nuclear

Regulatory Commission.

Science Applications International Corp. (SAIC). 1998. Nuclear Fuel Cycle Facility Accident Analysis

Handbook. NURIEG/CR-6410, Science Applications International Corp., Reston, VA.

U. S. Department of Energy (DOE). 1994. Airborne Release Fractions/Rates and Respirable Fractions

for Non-Reactor Nuclear Facilities: DOE Handbook. Vol. 1, DOE-HDBK-3010094, U.S. Department of

Energy.

U. S. Nuclear Regulatory Commission (NRC). 1997. RTM-96 Supplement for the Paducah Gaseous

Diffiusion Plant, prepared by Pacific Northwest National Laboratory.

U. S. Nuclear Regulatory Commission (NRC). 1997. RTM-96 Supplement for the Portsmouth Gaseous

Diffusion Plant, prepared by Pacific Northwest National Laboratory.

Williams, W. R., 1995. Calculational Methods for Analysis of Postulated UF6 Releases, Vol. 1,

NUREG/CR-4360, U.S. Nuclear Regulatory Commission.

3-14
4 Transport, Diffusion, and Dose Calculations

RASCAL 3.0.5 uses Gaussian models to describe the atmospheric dispersion of radioactive and chemical

effluents from nuclear facilities. These models have frequently been used in licensing and emergency

response calculations made by the NRC staff, [e.g., PAVAN (Bander 1982), XOQDOQ (Sagendorf, Goll,

and Sandusky 1982), MESORAD (Scherpelz et al.1986; Ramsdell et al. 1988], because they quickly

provide reasonable estimates of atmospheric concentrations, deposition, and doses given relatively

limited information on topography and meteorology.

A straight-line Gaussian plume model is used near the release point where travel times are short and

plume depletion associated with dry deposition is small. A Lagrangian-trajectory Gaussian puff model is

used at longer distances where temporal or spatial variations in meteorological conditions and depletion

of the plume due to dry deposition may be significant.

This chapter begins with a short theoretical derivation of Gaussian plume and puff models, and then

describes the implementation of those models. The chapter concludes with a description of the dose

calculations in the models.

4.1 Theoretical Bases for Gaussian Models

The derivation of the Gaussian models used to describe atmospheric dispersion is discussed in many

texts. Various texts including Slade (1968), Csanady (1973), Randerson (1984), and Seinfeld (1986)

provide the bases for the following discussion. They may be consulted where additional detail is desired.

Atmospheric dispersion is governed, in part, by a differential equation called the diffusion equation. With

a set of assumptions that can reasonably be applied to atmospheric processes, the diffusion equation has a

specific, closed-form algebraic solution that is Gaussian. In one dimension, the solution is

X(x)/Q - (21U2 ,exp - -( x-x0 21 (4.1

where

x(x) = concentration at a distance x from the center of the concentration distribution, x,

Q = amount of material released,

a= dispersion parameter.

Atmospheric dispersion parameters are functions of either distance from the release point or time since

release. They may also be functions of atmospheric stability and surface roughness. Numerous

atmospheric dispersion experiments have been conducted to evaluate dispersion parameters and to

develop methods to predict dispersion-parameter values from readily available data. A number of these

experiments are described by Draxler (1984).

4-1
4.1.1 Gaussian Puff Model

Using the principle of superposition, the one-dimensional solution of the diffusion equation can be

expanded to three dimensions to get the basic Gaussian puff model. In a Cartesian coordinate system

with x and y axes in a horizontal plane and z in the vertical, the normalized concentration in the vicinity

of the puff is

X(x, y, z) ! Q = (9)3/ 2a c-r aejexp exp [ . (4.2)

This equation, when combined with a transport mechanism to move the center of the puff (xo, y,, z,,), is a

simplified version of the puff model in RASCAL 3.0.5. The dispersion parameters are shown as

functions of direction from the puff center. However, in most implementations of the puff model, the puff

is assumed to be symmetrical in the x and y directions. Hence, x and y may be replaced by the horizontal

distance r from the center of the puff.

The form of Eq. (4.2) shown is appropriate if the height of the center of the puff is such that vertical

dispersion proceeds unimpeded either by the ground or by an elevated layer of the atmosphere.

Unimpeded vertical dispersion is generally not the case. Typically, the earth's surface and the top of the

atmospheric mixing layer are assumed to be reflective surfaces. When these assumptions are made, the

vertical exponential term

is replaced by a sum of exponential terms that account for reflection. This sum is

jexp[I (2nHh z + exp[ HI(

where

H = height of the top of the mixing layer, and

h = release height.

In practice, only a small number of terms need be considered. In RASCAL 3.0.5, as in MESORAD

(Scherpelz et al. 1986; Ramsdell, et al. 1988), the summation is carried out from n = -2 to 2. This term

can be simplified if one or more of H, h, or z equals zero. For example, if H is large compared to cz and z

is zero, the summation may be replaced by

2exp [2 czh)]

4-2
At long down-wind distances where the vertical dispersion parameter is the same magnitude as the

mixing layer thickness, the puff model can be further simplified by assuming that material is uniformly

distributed in the vertical. With this last assumption, the puff model becomes

1 [FIIr_•121

,z(r)/Q - 2,Hexp 2 - , (4.3)

where

H = mixing layer thickness.

RASCAL 3.0.5 switches to the uniformly mixed model when u, > 1.05H.

4.1.2 Straight-Line Gaussian Plume Models

Puff models represent plumes as a series of puffs. Concentrations at a point in the plume are calculated

by adding the concentrations at the point associated with all puffs in the vicinity of the point. In effect,

the puff models perform a numerical time integration of concentration as puffs pass by the point. Near a

release point, the meteorological conditions may be assumed to be constant as the puff moves from the

source to the receptor. If the wind speed is assumed to be much greater than zero and the point for which

the concentration is to be calculated is sufficiently far down wind that the change in dispersion

parameters with distance as puffs pass the point can be neglected, then the puff model can be integrated

analytically to give a plume model.

Assuming that the x-axis is aligned with the mean transport direction and that the mean wind speed is u,

then the average concentration during plume passage is given by

Q'FyF. p (x-ut 2]

2"(x,yz)= 3xp - -p Idt (4.4) (2) a.(x)ay(x)az(x) 2 o/x) ]

where

X = average concentration,

Q' = release rate,

F,, F, = lateral and vertical exponential terms, shown above,

x.= downwind distance at which X, a,, ay and a, are evaluated,

u = wind speed,

t = time.

On integration, the plume model becomes

(x, y, z)/Q': F, , (4.5) 2mnu ao, -.

which is a simplified version of the straight-line Gaussian model used in RASCAL 3.0.5.

The straight-line Gaussian plume model for ground-level releases is frequently given as

4-3
1IQ,= expi- 2 (4.6)

where F, in Eq. (4.5) is the exponential term in Eq. (4.6).

When the release and the receptor are at ground level and H is large, the sum of exponential terms that

comprise F,.has a value of 2. Hence, the constant 2 in Eq. (4.5) does not appear in Eq. (4.6).

Another assumption that deserves comment is that the meteorological conditions are assumed to be

horizontally homogeneous and stationary. This means that the wind direction and speed responsible for

transporting the plume from the release point to the receptorand the turbulence responsible for diffusion

are assumed not to change with location throughout the model domain. It also means that the.

meteorological conditions do not change as a function of time during the release and time required for

transport. Together, these assumptions constrain the usefulness of the straight-line plume model to

estimating concentrations and doses at receptors near the release point for short-duration releases; at

longer distances another model is required.

4.1.3 Treatment of Calm Winds

The straight-line Gaussian plume model in Eq. (4.5) tends to overestimate concentrations and doses

during low-wind speed conditions and becomes undefined for calm wind conditions because wind speed

is in the denominator. This behavior results because the derivation of the straight-line Gaussian plume

model assumes that the wind speed is significantly greater than zero, thus eliminating a portion of the

solution of the dispersion equation that deals with low-wind speed diffusion.

To compensate for the missing part of the solution, many straight-line models assume a wind speed of 0.5

to I m/s when calm winds are encountered. However, this assumption does not address the other aspect

of calm winds - the lack of a well-defined wind direction. No entirely satisfactory wind direction

assumption exists for calm winds for a straight-line model.

The Gaussian puff model behaves well in calm winds if the dispersion parameters are a function of time

instead of travel distance. In models where the dispersion parameters are calculated as the function of

travel distance, dispersion ceases during calm winds, and the material distribution remains unchanged as

long as the wind is calm. In either case, deposition, depletion, exposures, and doses are calculated just as

they are during windy conditions.

RASCAL 3.0.5 generally uses dispersion parameters that are a function of distance, but shifts to

dispersion parameters that are a function of time when the wind speed falls below 0.5 m/s (1 mph).

The puff model does not have numerical problems with a calm wind. When a puff encounters a zero wind

speed, the puff remains stationary. As a result, there is no need to change to a special model when the

wind speed is low or zero. However, the puff model does change the method used to calculate dispersion

parameters when the wind speed is below 0.5 m/s. The calculation of dispersion parameters during low

wind speeds is discussed in Section 4.3.2.

4-4
In the plume model, when the wind speed falls below 0.5 m/s (1 mph), RASCAL 3.0.5 switches from the

standard Gaussian plume model previously described to a plume model derived by Frenkiel (1953). In

this model, described by Csanady (1973) and Kao (1984), the dispersion parameters of ac, ao, u are

assumed to be functions of along wind, cross wind, and vertical turbulence levels of ao, u, a,, and travel

time (e.g., a.=rt). With this assumption,

a,,______ + Ux YU U2"X2 ~ Ux\1 (4.7) X1Q'= ,,3/.2 ,-exp/--Tef- I,' ,X

(27r) j ' Yko-,,, r- [rr 2 a,, rfj 

where

a,,, a,,, and u., = along wind, cross wind, and vertical turbulence measures, respectively (m/s)

r = a pseudo-diagonal distance from a point directly above the release point to the intake.

The definition of r is

2= X 2 y ++ ,- (4.8)

where

x = the downwind distance,

y = the cross wind distance from the plume center line,

z = the vertical distance from the plume center line.

For positions under the center line of a plume, y = 0.0 and z = h+Alh where h is the release height and Ah

is the plume rise, if any. Thus,

r2 = x2 + (h + Ah) 2 (4.9)

Equation (4.7) is well behaved in low-wind speed conditions and gives finite X/Q values for calm wind

(mean wind velocity = 0) as long as a, and a, are nonzero. For calm winds (wind speeds < 0.5 m/s), Eq.

(4.7) has a simple form that is similar to the standard Gaussian puff model. It is

0r

X/Q = 3 2 2 Q (2 T) 32orý a. r2 (4.10)

The crosswind position y is assumed to be zero, and the resulting X/Q' is a function only of x and z. The

X/Q' calculated at each distance is applied in all directions.

4-5
4.1.4 Model Domains and Grids

The plume model and the puff model use different model domains. The plume model domain consists of

a polar grid with receptor nodes on circles at 10' intervals at eight radial distances that may be adjusted

to suit the problem at hand. The puff model domain consists of a square Cartesian grid with receptor

nodes uniformly spaced throughout the domain. The polar grid has a higher node density near the release

point than the Cartesian grid, and conversely, the Cartesian grid has a higher node density in the far field

than the polar grid.

The sizes of the model domains are linked. If the 10-mile Cartesian grid is selected, the polar grid will

have a default maximum radius of 2 miles. Similarly, the 25- and 50-mile Cartesian grids have

corresponding default polar grids of 5 and 10 miles, respectively. The default radial distances for the

polar grids should be satisfactory for most applications. However, the RASCAL 3.0.5 user can change

the radii values if other calculational distances are more appropriate.

In general, the receptor nodes for the two grids do not coincide. This fact leads to computational

differences in the doses reported in the maximum value tables in the model output for the two models for

wind directions other than north, east, south, or west. The doses reported for the close-in plume model

are for the plume centerline at each distance. The doses reported for puff model are the highest doses

calculated at nodes at about the nominal distance -- for example, 5 miles. The node with the highest dose

may or may not be on plume centerline, and may be nearer to or farther from the release point than the

nominal distance. When a direct comparison of doses calculated by the two models is desired, the wind

direction for the period of calculations should be north, east, south, or west. For these wind directions,

both the plume model and the puff model calculate plume centerline concentrations and doses.

4.2 Transport

Atmospheric transport refers to the movement of material with the wind from the source to downwind

receptors. The following two sections describe the treatment of atmospheric transport in RASCAL 3.0.5.

4.2.1 Puff Model Transport

Unlike the plume model, the puff model explicitly accounts for transit time in all calculations because the

model tracks the movement of individual puffs and calculates concentrations and doses based on puff

positions. As a result, dose rates calculated by the puff model may be used to estimate the time of arrival

of a plume and may be compared with dose rates measured in the field. Decay and ingrowth of

radionuclides and depletion of the puffs as a result of wet and dry deposition are calculated at 5-minute

intervals.

The puff model differs significantly from the plume model in that neither the wind data nor the wind

fields are modified to force the centers of puffs to pass directly over the receptor nodes. As a result, when

the wind direction is constant, the puff model may not calculate centerline concentrations and doses.

However, as time goes by and atmospheric conditions (wind direction, wind speed, stability, mixing layer

thickness, and precipitation) change, the puff model will give more realistic concentration and dose

patterns than the plume model. In addition, the puff model will give more realistic concentration and dose

patterns than the plume model when topography modifies the winds because the wind fields used by the

4-6
puff model may be modified to account for topography. The wind data used by the plume model are not

modified to account for topography.

The movement of puffs is controlled by the wind at the center of the puff as it moves through the model

domain. The spatial variation of winds is represented in the plume model by two-dimensional fields of

vectors that give the direction and speed of puff movement. These fields are prepared by the

meteorological model discussed in Section 6 and are updated at 15-minute intervals based on the

available wind data.

Calculation of puff movement is a six-step process. In sequence, the steps are

I. Make an initial estimate of the direction and speed of the puff movement given the current puff

position and height above ground using bilinear interpolation (Press, et al. 1986) of the vectors at the

nearest nodes of the field;

2. Make an initial estimate of the puff position at the end of the period using the initial estimates of

direction and speed;

3. Make a second estimate of the direction and speed of puff movement using the estimated puff

position at the end of the period;

4. Make a second estimate of the puff position at the end of the period using the estimate of direction

and speed from step 3;

5. Average the.end points calculated in steps 2 and 4;

6. Calculate the final estimate of direction and speed of puff movement using the puff's initial position

and the average end point calculated in step 5.

The actual puff movement for the period may take place in one or several steps. The step size is adjusted

to ensure adequate accuracy in the integration of concentrations that takes place at receptors. Errors in

the integration should be less than 5% at typical wind speeds. Larger errors may occur near the release

point in high wind speed conditions,, because the minimum step size is 30 seconds. These larger errors

should not be a problem because plume model output should be used for receptors near the release point.

The vector fields prepared by the meteorological program are for a height of 10 meters aboveground.

These vectors are used for puffs that represent ground-level releases. If the actual release height is greater

than 12 meters, a wind-speed profile is used to adjust the transport speed from 10 meters to the puff

transport height. The profile used to adjust the wind speed considers both surface friction and

atmospheric stability (see Panofsky and Dutton 1984, Sections 6.4-6.6).

4.2.2 Plume Model Transport

The RASCAL 3.0.5 plume model is a straight-line Gaussian model. As this name implies, the model

assumes straight-line transport based on the wind direction at the time and place of release. The plume

model rounds the wind direction to the closest 100 as it calculates the transport direction to ensure that

the axis of the plume passes directly over receptors.

4-7
As is common in straight-line Gaussian models, transit time is not considered in determining when

material arrives at receptors; material arrives at receptors at the time of release. As a result, dose rates

calculated by the RASCAL 3.0.5 plume model cannot be used to estimate the time of arrival of a plume

at a receptor and are not likely to correspond with dose rates measured in the field.

Transit time, calculated using the wind speed at the release height, is used to calculate the decay of

radionuclides between the source and the receptors. It is also used to calculate depletion of material in

the plume due to dry and wet deposition. Decay calculations are performed at 5-minute intervals;

depletion is calculated for the full transit time.

4.3 Dispersion Parameters

In RASCAL 3.0.5, the horizontal dispersion parameters (ay and cr) are calculated using empirical curves

derived from the results of a large number of dispersion experiments conducted in the 1950s and 1960s.

The experiments, which were conducted over relatively flat terrain, typically involved tracer releases

ranging from about 10 minutes to 1 hour in duration with ground-level concentration measurements at

distances ranging from 100 meters to several kilometers. Only a few direct measurements of vertical

dispersion parameters ((Y) were made. Consequently, vertical dispersion parameters were estimated with

dispersion models using measured values of the horizontal dispersion parameter and measured

concentrations. Dispersion parameters have been summarized in many forms. Perhaps the best known

summary is the set of dispersion parameter curves called the Pasquill-Gifford curves (Gifford 1976).

4.3.1 Normal Dispersion

Regulatory guidance published by the NRC includes graphic depiction of these curves, and numerical

approximations to the curves are included in many computer codes used by the NRC. In RASCAL 3.0.5,

dispersion parameters are estimated using the same basic algorithms that were used in earlier RASCAL

versions (Athey et al. 1993) and are used in other NRC codes including PAVAN (Bander, 1982) and

XOQDOQ (Sagendorf, et al., 1982). These parameterizations have generally been attributed to Eimutis

and Konicek (1972). However, the ay parameterization is properly attributed to Tadmor and Gur (1969),

and the az parameterization is properly attributed to Martin and Tikvart (1968).

The basic dispersion parameter relationships used in the NRC codes are

= -- a .YX0.9031

and

O0, = az(x)• xb; ) + c'(x) (4.12)

where

x = distance from the release point (in meters),

a,. is a function of stability class, and

a., b:, and cz are empirical values that are functions of stability class and distance.

4-8
Table 4.1 gives values for ay a~, b2, and cz. Note that 0.903 1, ay, az,, bz and c, are empirical values

evaluated by fitting curves. Of these constants, 0.903 1 and b, are dimensionless, c, has dimensions of

meters, and a., and a, have dimensions of m 0 ~ 1 and m(1 , , respectively.

Table 4.1. Constant Values for Calculation of Atmospheric Dispersion Parameters

Stability Class

Distance Range (in) A B C D E F G

ay all x 0.3658 0.2751I 0.2089 0.147 1 0.1046 0.0722 0.0481

a, x<loom 0.192 0.156 0.116 0.079 0.063 0.053 0.032

100 m < X< 1000 M 0.00066 0.0382 10.113 0.222 0.211 0.086 0.052

1000 m <x 0.00024 0.055 0.113 1.26 6.73 18.05 10.83

b,, x < 100 mn 0.936 0.922 0.905 0.881 0.871 0.8 14 0.814

100 m < X< 000M 1.941 1.149 10.911 0.725 0.678 0.74 0.74

1000 M< X 2.094 1.098 0.911 0.516 0.305 0.18 0.18

CZ x < 100 m 0.0 0.0 0.0 0.0 0.0 0.0 0.0

00 m <X <1000m 9.27 3.3 0.0 -1.7 -1.3 -0.35 -0.21

1000 M< X -9.6 2.0 0.0 -13.0 -34.0 -48.6 -29.2

4.3.2 Low Wind Speed (Building Wake) Correction

Atmospheric dispersion experiments did not stop after development of the PasquilIlI-Gifford curves.

However, the emphasis of the experiments did shift. For example, there have been experiments that

examined dispersion in the vicinity of buildings and other experiments that examined dispersion under

low wind-speed conditions. Ramsdell (1990) describes corrections to the basic dispersion parameter

relationships in Eq. (4.11) and (4.13) that improve the dispersion parameter estimates in the vicinity of

building wakes.

More recent analysis of dispersion and turbulence data (Ramsdell and Fosmire 1998) suggests that the

apparent enhanced dispersion noted in the vicinity of buildings at low wind speeds in wake dispersion

experiments is caused by underestimation of dispersion by the basic dispersion algorithms rather than by

increased turbulence in the vicinity of buildings.

This point is illustrated in Figure 4.1 which shows the ratios of normalized concentrations (X/Q)

predicted in building wakes to observed concentration normalized to actual release rate as a function of

wind speed. If the errors in the predicted values were associated with the wake, they should increase with

wind speed. The fact that the errors are greatest at very low speeds and decrease with increasing wind

4-9
speed indicates that the problem is underestimation of dispersion in low wind speeds. The original

conclusion that the enhanced dispersion was due to building wakes appears to be incorrect.

A m

i F- +t jr)

A A

0

0

(I,

-0

0

0~

1E+04

1E+03

1E+02

1E+01

1 E+00

1E-01

. . . . .

.. .. . . . . . . .

A

A

a

A

AC

A

-A

A

A: --f

i ..... A • - A

ýA

I .A A

4A

... . .. .: ... .. ... .; .... .: :. ::. . F . : .:.:.. 

• i .. ... . .. .: . .. . . .

. . , . . . . . . . . .. . . . . .. . . . . . . . . . . . . . . . . . • . .

.i ...i ...... ..• .... .:: ........... .! . .

[ :: -

A:A

A:

A .i A.. .. . .•. . . . 5 . .: 2 ! ! ! :

.!• :..!..::. A .. A : ... .: k {:

! A .. . .. . .... ... . ... .! . . . . : .. . . .. . .

!• -i ... " A• ! ...

•I •A: .::. ..

. . A .. ... .: . . !..

7 AA

-- - - - -- - - -

A -&A

A

0 2 4 6 8 10 12

Wind Speed (m/s)

Figure 4.1 Ratios of predicted concentrations in wakes by a model without wake correction to

observed concentrations as a function of wind speed.

To account for the underestimation of dispersion at low wind speeds, enhanced dispersion parameters

were developed. The enhanced dispersion parameters, E, and E, are defined as

I(U2 + A C21/

=(C-2 + A U-2)/2

(4.13)

(4.14)

4-10
and where the enhancement terms, Aoy2 and Ac1

2, have the form

A o 2(t) = A( 1 - (1 + t/T)exp( - t/T). (4.15)

where

t= transport time (distance divided by the wind speed in the plume model and time since release

in the puff model),

A,= 0.5T 2 (T is the horizontal time scale for wake turbulence),

A = 0.5T2/(2+z/L),

T= B "

2

/u*,

B = projected building area,

u*= scaling wind speed (friction velocity) calculated from the wind speed, stability, and surface

roughness using the wind profile relationships discussed in Section 6.4.2,

z = release height (all releases are assumed to be 2! 10 m), and

L = Monin-Obukov length which is a function of stability. Evaluation of L is described in

Section 6.4.1

Near the release point, the enhancement terms are primarily functions of wind speed and distance, they

are weakly dependent on stability, and they are independent of building dimensions. The enhancement

terms increase with increasing distance from the release point until they reach an asymptotic limit that is

a function of the building area. The terms are large for low wind speeds and decrease as the wind speed

increases. They are negligible for wind speeds above about 4 m/s.

This behavior is supported by a more recent analysis of dispersion and turbulence data (Ramsdell and

Fosmire 1998). The results of that analysis also suggests that the enhanced dispersion noted in the

vicinity of buildings at low wind speeds in wake dispersion experiments may be as much an artifact

caused by underestimation of dispersion by the basic dispersion algorithms (Eqs. 4. 11 and 4.12) as it is

due to increased turbulence in the vicinity of buildings. Consequently, use of the building wake

correction option is recommended for all releases other than isolated stacks.

4.3.3 Puff Model Dispersion Parameters

In the puff model, the wind direction, wind speed, and stability are permitted to change as a function of

time and position. As a result, puffs may follow curved trajectories and even return to the release point,

and stability may change along the puff's trajectory. If dispersion parameters were calculated directly, as

in the plume model, there could be discontinuities in the dispersion parameters and possible reduction in

plume dimensions with increasing time. Neither is consistent with the known characteristics of

atmospheric dispersion. Consequently, dispersion parameters for the puff model can not be directly

calculated from Eqs. (4.11) through (4.15) as is done in the plume model.

In the puff model, dispersion parameters are calculated in a four step process as the puffs move through

the model domain:

I ) Calculate virtual distances from the puff center to the release point based on the current puff

dimensions and the meteorological conditions at the position of the puff. The virtual distances are

imaginary distance which, if used in Eq. (4.11) (xvy) and Eq. (4.12) (x,,) with the meteorological

conditions at the puff position, would give the current dispersion parameters;

4-11
2) Add the distance to be moved during the next time step to the virtual distances;

3) Calculate the new dispersion parameters using the sums calculated in step 2; and

4) Add the enhancement term, if appropriate.

Separate virtual distances are required for the horizontal and vertical dispersion parameters because the

dispersion parameters increase at different rates. The equations for the virtual distances are

x/ -- (4.16)

and

x,= [ ])J. " (4.17)

These equations are just Eqs. (4.11) and (4.12) solved for x rather than U.

4.3.4 Plume Model Dispersion Parameters

The computational algorithms used in the plume model calculate dispersion parameters directly from

Eqs. (4.11) through (4.15) as the parameters are needed. Equations (4.11) and (4.12) are used for plumes

released from isolated stacks and for other releases if the building wake correction is not selected. If the

building wake options is selected, all five equations are used.

4.3.5 Calm Wind Dispersion Parameters for the Puff Model

The dispersion parameters used during windy conditions increase as the distance traveled increases.

During calm or near calm conditions, the distance traveled stops increasing, or increases very slowly. In

reality, atmospheric dispersion does not stop when the wind is calm.

The RASCAL 3.0.5 puff model switches from distance-based dispersion parameters to time- based

parameters during low wind speed (below 0.5 m/s ) conditions to account for continued dispersion. The

horizontal dispersion parameter is calculated for each time step is calculated as the parameter for the

previous step plus an increment that is only a function of the time step. It is

700

o-.(t+At)= .(t)+ 3600At (4.18)

where

u, = dispersion parameters (m) and,

At = time step (s).

4-12
Clearly then, the 700/3600 (-0.2) is the horizontal rate of growth of the plume (m/s). The horizontal rate

of growth of the plume is independent of stability at low wind speeds, just as the exponent of x in Eq.

4.12 is independent of stability.

The growth of the vertical dispersion parameter should be, and is, a function of stability even in low wind

speed conditions. Vertical dispersion parameters during low wind speed conditions are calculated by first

estimating a fictitious puff movement, Ax, from

Ax = O.4At (4.19)

This fictitious distance is then used, along with the current parameter value, in calculating the dispersion

parameter for the next step from Eqs 4.12 and 4.17.

4.3.6 Calm Wind Dispersion Parameters for the Plume Model

Unlike the Gaussian puff model in RASCAL 3.0.5, the straight-line Gaussian plume model does not do

well in low wind speeds, and becomes undefined if the wind speed becomes zero. Consequently,

RASCAL 3.0.5 changes models when the wind speed falls below 0.5 m/s. The low wind speed model is

given in Eq. 4.10. That model requires estimates of horizontal and vertical turbulence velocities (m/s)

rather than normal dispersion parameters (m). For the wind speeds of interest, the plume model uses

default turbulence velocities au = cv = a,, = 0.13 m/s, which are reasonable values for a wind speed less

than I m/s.

4.4 Mixing Layer Thickness

The mixing layer thickness is included in all dispersion calculations. The thickness is passed to the

atmospheric dispersion programs in the meteorological data files that are created by the meteorological

data processing program. The meteorological data processing program has three options for determining

the mixing layer thickness for each station. The thickness may be estimated from meteorological data and

surface roughness; it may be estimated from climatological data; or it may be entered directly. See

Section 6.4.3 for details related to estimation of mixing layer thickness.

4.5 Stack Plume Rise

RASCAL 3.0.5 estimates both transition and final plume rise for stacks using Briggs' equations (1969,

1975, and 1984). The transition rise equations are used near the stack until the plume rise exceeds the

final plume rise. In general, the numerical constants in the equations are dimensional, and the appropriate

metric (SI) units should be assumed.

4.5.1 Final Plume Rise

Plume rise is caused by vertical momentum of the exhaust gases in a stack and buoyancy due to

differences in density between the exhaust gases and the atmosphere. Equations for final plume rise for

both momentum- and buoyancy-dominated plumes are included in the models. In general, one factor or

the other will dominate. For a given set of stack and atmospheric conditions, the temperature difference

between the stack effluent and the atmosphere determines which factor is dominant. The initial step in

4-13
the plume-rise calculation is to determine the critical temperature difference given the stack effluent and

atmospheric conditions. If the difference in temperature is less than the critical temperature, plume rise is

calculated using momentum-rise equations; otherwise, it is calculated using buoyancy-rise equations.

Plume rise is corrected for stack downwash, when the stack exit velocity is less than five times the wind

speed.

4.5.1.1 Unstable and Neutral Atmospheric Conditions

In unstable and neutral atmospheric conditions, plume rise is dominated by momentum if the atmospheric

temperature is greater than the effluent. When plume rise is dominated by momentum, the plume rise is

estimated using Petersen and Lavdas' Eq. A-9 (1986)

Ah = 6r.•wpu(h.Y- (4.20)

where

Ahr = final plume rise estimate (m),

r• = stack radius (m),

wp= effluent initial vertical velocity (m/s),

u(hj = stack height wind speed (m/s).

If the ambient air temperature is less than the effluent temperature, a critical temperature is calculated

from either Petersen and Lavdas' Eq. A-3

At, = 0.0187wp 3T -/ 3 (4.21)

or Petersen and Lavdas' Eq. A-4

At, = 0.00456 7, , (4.22)

where

At, = critical temperature difference (K) and

TP = effluent temperature (K).

The choice between Eq. (4.21) and (4.22) is based on the value of a buoyancy-flux parameter, Fb. The

buoyancy-flux parameter is defined by Petersen and Lavdas' Eq. A-2 as

F, = g - 7.)IT, wIr,2 , (4.23)

where

g = gravitational acceleration (9.8 mis 2), and

4-14
T, = air temperature ('K).

If F, is less than 55, the critical temperature is given by Eq. (4.21), otherwise it is given by Eq. (4.22.

Equation (4.20) is used as long as the temperature difference, Tp - T,,, is less than At,.

When the temperature difference is greater than Ato, the plume rise is calculated using either Petersen and

Lavdas' Eq. A-7

A hf = 21.42 F, 14 u(hrY- (4.24)

or Petersen and Lavdas' Eq. A-8

Ahf = 38.71IF 06u(h. )- , (4.25)

again depending on the value Fb- Equation (4.24) is used when Fb is less than 55, otherwise Eq. (4.25) is

used.

4.5.1.2 Stable Atmospheric Conditions

As in unstable and neutral conditions, plume rise is dominated by momentum if the atmospheric

temperature exceeds the effluent temperature. If the effluent temperature is greater than the ambient

temperature, a Atc is calculated to differentiate between momentum- and buoyancy- dominated plumes.

The At, given by Petersen and Lavdas' Eq. A-I 1 is

At, = 0.0196w TS12, (4.26)

where

S = stability parameter associated with the frequency of vertical oscillation of air parcels in a stable

atmosphere.

The square root of S is known as the Brunt-VdiisdlNi frequency discussed in texts on the atmospheric

boundary layer, e.g., Panofsky and Dutton (1984) or Stull (1988). It is defined by

S =gTj' , (4.27)

where

ao/az = potential temperature lapse rate shown in Petersen and Lavdas' Eq. A-10.

Following Petersen and Lavdas, potential temperature lapse rates of 0.02°K/m and 0.035 °K/m are

assumed for Pasquill-Gifford stability classes E and F, respectively. A lapse rate of 0.05°K/m is

assumed for G stability class following Ramsdell, Simonen, and Burk (1994).

4-15
In stable conditions when the temperature difference is less than At,, plume rise is momentum dominated

and a plume rise estimate is made using Eq. (4.20). The plume rise also estimated using Petersen and

Lavdas' Eq. A-16 is

1.5 FoW, Ta-]l• (4.28) Ahs -S _u(h ffj

where

F,, = stack flow (m 3

/s).

The two plume rise estimates are compared, and the smaller value is selected.

When plume rise is determined to be buoyancy dominated in stable conditions, the stack-height wind

speed is compared with a critical wind speed to determine whether conditions are calm or windy. The

critical wind speed, uc, is calculated using Petersen and Lavdas' Eq. A-15

it = 0.2746F,," 4SI/8 (4.29)

If the wind speed is less than the critical speed, the plume rise calculated using Petersen and Lavdas' Eq.

A-14 is

Ahif 4.0Fo1/4s- 3

/

8

. (4.30)

Otherwise, the rise calculated using Petersen and Lavdas' Eq. A-I 3 is

¢ F, ,,

Ah = 2.6( " (4.31)

4.5.2 Transition Plume Rise

Near the stack, the plume gradually increases in height until the final plume rise is reached. RASCAL

3.0.5 calculates the plume rise in this transition area using two relationships presented by Briggs (1984).

For plumes without a significant buoyant flux, the transition rise is calculated by

r 1/3

Ah :~h[h, 3Fmx (4.32)

where

x = downwind distance, and

f8,, = 0.4 + 1.2/r•.

4-16
If buoyancy is determined to important based on the temperature difference using the tests described

..above, the transition rise is calculated by

I .• " 1/3

3 F,,x 3FX

Ah, = {[ [ h)]2 + [2,,u(h ) } (4.33)

where

flb has a value of 0.6.

4.5.3 Effective Release Height

If the isolated stack option is selected in RASCAL 3.0.5, the plume height is an effective release height.

The effective release height has three components: stack height, plume rise, and stack down wash. It is

calculated as

he = h, + Ah+ Ahd (4.34)

where

h, = stack height,

Ah = smaller of the transitional and final plume rise, and

Ahd = stack down wash.

The stack height is entered by the user, and the calculation of plume rise is previously described. Stack

down wash occurs when the stack exit velocity is less than or approximately the same magnitude as the

stack-height wind speed. It is an aerodynamic effect that reduces the stack height by up to three stack

diameters. Down wash is calculated in Petersen and Lavdas' Eq. A-I as

Ahd = 4rL u(hp) 1.5] (4.35)

when the ratio between the exit velocity and stack-height wind speed is less than 1.5. Otherwise, the

down wash is set to 0.0.

If the isolated stack .option is not selected, the release is treated as if it occurs from the surface of the

building. A default release height of 10 meters is assumed unless another, greater release height is

entered.

4.5.4 Effective Release Height for Fires

.If radioactive material becomes involved in a fire, it may be reasonable to consider the release as if it

were from an elevated source. In that case, the isolated stack option should be selected and an effective

release height should be entered in the form.

4-17
The primary cue for estimating the effective release height is smoke associated with the fire. If the smoke

is rising near vertically (low wind speeds), the height of the smoke plume where it levels off may be used

as the release height. If the smoke plume is more nearly horizontal (windy conditions), then it may be

appropriate to model the release in two parts, one with an estimated release height near ground level

(perhaps 10 meters) and the other with an estimated release height near the center of the plume where it

levels off.

If the release is modeled in parts, the consequences of the release must be estimated by combining the

consequences from the parts as in a weighted average. Unless there is evidence to the support other

weights, equal weight should be assigned to each part.

4.6 Deposition

RASCAL 3.0.5 calculates deposition for iodine and particles using the dry and wet deposition models

used in MESORAD (Scherpelz, et al. 1986; Ramsdell, et al. 1988) and earlier versions of RASCAL. The

activity deposited each time step is the product of the total deposition rate and the time-step duration. At

any time, the surface contamination (activity/M2) is the sum of the activity deposited in the current time

step plus previously deposited activity corrected for decay.

4.6.1 Dry Deposition

The dry deposition rate is given by

COd = Vadd , (4.36)

where

co = deposition rate in (activity/m )/s and

vdd = dry deposition velocity.

RASCAL 3.0.5 assumes a dry velocity of 0.003 m/s (0.3 cm/s). This deposition velocity was used

because data summarized by Sehmel (1984) indicate that it is a reasonable value for iodine assuming that

about one-third of the iodine in the atmosphere is associated with particles, another one-third is in the

from of reactive gases (e.g., 12 or HI) and the remaining one-third is in the form of non-reactive gases

(e.g., CH 3I). A deposition velocity of 0.003 m/s is slightly high for I fim particles. Noble gases (e.g., Kr

and Xe) do not deposit.

The assumption that about one-third of the iodine in the atmosphere is associated with particles, another

one-third is in the from of reactive gases (e.g., 12 or HI) and the remaining one-third is in the form of non

reactive gases (e.g., CH 3I) applies only to iodine that has escaped from the containment. The assumption

is not appropriate inside the containment. Within the containment most iodine would be in a particulate

form. However, the particulates are preferentially removed within the containment. Therefore, the iodine

that escapes to the atmosphere is likely to have much higher proportions of reactive and non-reactive

gases. In addition, iodine changes form readily in the atmosphere.

4-18
4.6.2 Wet Deposition

RASCAL 3.0.5 calculates wet deposition of particles and gases using a washout model with washout

coefficients that are only a function of precipitation type and a qualitative measure of intensity. In the

washout model, the wet deposition rate is

-X~dz A,= 

0

(4.37)

where

kP = washout coefficient that is a function of precipitation type.

The washout coefficients used in RASCAL 3.0.5 are listed in Table 4.2. These coefficients are based on

analyses of experimental data by Engelmann (1968). Hanna, et al. (1982) and Slinn (1984) point out that

the washout model is appropriate strictly for monodisperse aerosols and highly reactive gases only.

Table 4.2. RASCAL 3.0.5 Washout Coefficients

Precipitation Type Washout

Coefficient (h-')

light rain 0.79

moderate rain 2.2

heavy rain 4.0

light snow 0.36

moderate snow 1.2

heavy snow 2.3

Source: Engelmann (1968)

4.6.3 Total Surface Deposition

The total deposition rate at any point is the sum of the dry and wet deposition rates at that point. In the

plume model, the total deposition rate is a function of position only because the concentration in the

plume is a function of position. In the puff model, the total deposition rate is a function of position

because the concentration varies in space and meteorological conditions may vary in space. In both

models, the total deposition rate is a function of time because both the concentration and precipitation

may change with time.

RASCAL 3.0.5 calculates and stores deposition by radionuclide for all radionuclides except noble gases.

Noble gases are assumed not to deposit. However, RASCAL 3.0.5 does calculate the surface

contamination from Xe isotopes that result from decay of iodine, assuming that the Xe is trapped within

the remaining iodine. The Xe isotopes are not included in ground shine dose calculations. The Cs

4-19
daughters of Xe are included in the groundshine dose calculations. In general, the contribution of these

daughters to the total dose is small.

4.7 Depletion Due to Deposition

Both atmospheric models in RASCAL 3.0.5 calculate depletion caused by wet deposition. Only the puff

model accounts for depletion from dry deposition. The plume model does not account for depletion from

dry deposition because the calculation is relatively time consuming and dry deposition generally does not

result in significant depletion of the plume near the source.

In the puff model, the activity in the puffs (Q) is updated every 5 min. The activity removed from each

puff is determined by integrating the total deposition rate under the puff in space and time. In the plume

model, the fraction of activity remaining in the plume at each distance during periods of precipitation is

estimated assuming an exponential decrease in activity with travel time, i.e., Q'(x) = Q'oexp(-3⁄4x/u).

4.8 Radiological Decay and Ingrowth

The atmospheric dispersion and transport models in RASCAL 3.0.5 calculate radiological decay and

ingrowth at 5-minute intervals for both airborne and deposited radionuclides. The decay schemes include

as many as four progeny and account for branched decay chains. The 5-minute decay and ingrowth

calculations continue to the end of the calculation period specified by the user.

The 5-minute intervals for decay and ingrowth provides reasonably smooth changes in activity for longlived radionuclides, for example, radionuclides with half-lives of 30 minutes or longer. However, for

short-lived radionuclides, such as rubidium-88 (t,,2 = 17.8 min) or, barium-137m (ti12 = 2.5 min), there is a

significant decrease in activity present each decay interval. For example, barium-137m activity decreases

by about a factor of four every 5 minutes. If short-lived isotopes provide a significant contribution to

doses, the step changes in activity may be very evident in the doses and dose rates. Should this artifact of

the calculational procedure be observed, the doses and dose rates calculated just after decay calculations

are most nearly correct, and doses and dose rates calculated just prior to decay calculations are over

estimates.

RASCAL 3.0.5 groundshine dose calculations extend until 96 hours have elapsed from the beginning of

the model run specified by the user. Decay and ingrowth calculations during this extended period are

made at I-hour intervals.

4.9 Dose Calculations

RASCAL 3.0.5 calculated doses from inhalation, from groundshine, and from cloudshine.

4.9.1 Inhalation Doses

Committed effective dose equivalents (CEDE) and organ committed dose equivalents (CDE) are

calculated for 15-minute periods. These dose equivalents are the sums over all radionuclides of products

4-20
of the exposure to the radionuclide during the 15-minute period, a radionuclide and organ specific dose

factor, and the breathing rate. The general expression for the dose equivalents is

D15 = vDF JZf(t)dtI , (4.38) h 0

where

D,5 = effective or organ committed dose equivalent due to inhalation during a 15-minute period,

v, = breathing rate,

DF, = committed or organ specific dose factor for radionuclide n,

X,, = radionuclide n concentration,

t = time.

Inhalation dose factors used in RASCAL 3.0.5 are from Federal Guidance Report No. 11 (Eckerman,

Wolbarst, and Richardson 1988). RASCAL 3.0.5 uses a breathing rate of 3.33x10 4 m3

/s (20 I/min).

At the end of each 15-minute period, the committed dose equivalents at each receptor node are written to

* puff and plume model output files. They are then set to zero prior to beginning model calculations for the

next 15-minute period.

4.9.2 Groundshine Doses

The puff and plume models calculate groundshine dose equivalents as the sum over all radionuclides of

product of the surface contamination by the radionuclide and a radionuclide-specific dose factor. The

general expression for the groundshine dose equivalent is

where

D. DF o. t)dt (4.39)

D,, = dose equivalent from groundshine during the period,

DFn = radionuclide n specific ground-shine dose factor,

o,, = radionuclide n surface concentration, and

t = time.

The integration in Eq. (4.39) is from t to t+15 minutes. These integration times are used because the

surface concentration at any time is cumulative from the beginning of the event and is not set to zero at the

beginning of the period. After the surface is contaminated, groundshine doses can be incurred, even if

airborne material is not present.

4.9.3 Cloudshine Doses

RASCAL calculates cloudshine doses using four models. The models include a semi-infinite cloud model

and a finite-puff model originally developed for MESORAD (Scherpelz, et al. 1986). The first of these

models assumes that activity is uniformly distributed through a large volume, and the second assumes that

activity is concentrated in a finite number of points distributed through a volume to represent the actual

4-21
activity distribution. The use of the semi-infinite cloud model is usually inappropriate in the immediate

vicinity of the release point, and application of the MESORAD finite-plume model to cloudshine dose

estimates near the release point did not prove satisfactory. Consequently, two additional cloudshine dose

model have been developed and are used in RASCAL 3.0.5.

The new cloudshine models are based on line sources and plane sources and are analogous to the pointsource model. These models are used, along with the point-source model, until plumes and puffs grow to

sufficient size that the assumptions associated with the semi-infinite cloud model are met. The finiteplume, cloudshine models in RASCAL 3.0.5 make use of precalculated dose rate vs distance curves.

These curves are provided in the radionuclide database for each radionuclide for a I Ci (0.01 Sv) point

source, and a I Ci/m (0.01 Sv/m) infinite-line source. The remainder of this section describes the

cloudshine models.

4.9.3.1 Puff Model Cloudshine Dose Calculations

There are three stages in the cloudshine dose calculations. Near the source where puff dimensions are

small compared to the mean path length of photons, RASCAL uses a point-kernel dose model. When the

puff radius becomes sufficient (oy=4 00 m), cloud-shine dose rates beneath the centerline of the plume are

calculated using an infinite-slab model. The dose rate at ground level is calculated assuming that the

activity in the plume is equally divided among ten horizontal slabs with slab heights determined by the

release height and vertical dispersion coefficients. The change in dose rate with distance from slabs is due

only to buildup and absorption of photons; the change in dose rate across the plume is proportional to the

crosswind variation of activity concentration in the slab. This model will be discussed further. Finally,

when the vertical dimensions of the plume become sufficient (a,=400 m), cloudshine is calculated using a

semi-infinite cloud model.

The initial versions of RASCAL used the MESORAD finite-puff, cloudshine model (Scherpelz et al.

1986, Ramsdell et al. 1988). This model first calculates composite characteristics (photon energies,

photons per disintegration, etc.) of the gamma radiation from the radionuclide mix in a puff. Next, the

model calculates the dose rate vs distance from a point source having the composite characteristics using

Up (p) 2.13x 10 6 1,[f, B,(JP)e-,o"P ETW] (4.40)

4 4 np ( 2 

where

Dp '(p) = dose rate in (rem/h)/Ci,

p = distance from point source,

fy = fraction of disintegrations producing ys of energy, E,,

By(u.,p) = buildup factor for air,

/Iay = linear attenuation factor for air,

EY= gamma energy,

T= mass energy absorption coefficient for tissue (n,1pt,),

WY= ratio of whole body dose to surface dose.

The constant 2.13 x 106 is a collection of unit conversion constants to give dose rate in (rem/h)/Ci. The

components of the constant are described following Eq. 19 in Scherpelz, et al. (1986).

4-22
The model then calculates the dose rate at ground level as a function of horizontal distance from the

ground-level position of center of the puff. This calculation involves summation over volume elements

distributed throughout the puff.

D'(r)= D' p(PO )MAij (4.41)

I j k

where

D '(r) = dose rate at r,

r = distance from the receptor to the projection of the puff center on the ground,

i,j,k = indices associated with the volume elements,

D ',(Puk) = dose rate at distance p from a point source in volume element ijk,

Piqk = distance from the center of the volume element ijk to the receptor,

Mil = fraction of the total puff activity in volume element ijk.

For purposes of the cloudshine calculation, puffs were assumed to be circular cylinders with three layers.

The volume elements were defined in 3, 5, or 8 annular rings with either 6 or 16 sectors. The fraction of

activity in volume elements varied by annulus and level. Finally, the dose at a receptor for a period is

accumulated by summing the product of dose rates and the time step for all puffs for all time steps in the

period.

In RASCAL 3.0.5, this process has been modified by eliminating the calculation of composite

characteristics from the gamma energies. In its place, the puff model calculates the dose rate vs distance

from a point source that has all of the activity in the puff. Thus, Eq. (4.40) is replaced by

N O'p(p) E Q D'P,,(,p) (4.42)

n=l

where

N = number of radionuclides,

Qn = activity of radionuclide n in the puff,

Dp(p) = dose rate at distance p from a I -Ci point source of radionuclide n.

The overall puff geometry remains the same in the puff model as it was in earlier versions of RASCAL.

However, the internal geometry has changed. The puff is divided into ten layers with each layer

containing one-tenth of the activity. The number of annular rings has been fixed at six, with each ring

containing one-sixth of the puff activity, and the number of sectors has been fixed at 12. With these

changes, the number of volume elements has been increased, and the fraction of activity in each volume

element becomes 1/720 of the total activity. In the puff model, Eq. (4.41) becomes

D'(r) = I Z E D'p(Pk ) (4.43) 720 b s k

As before, symmetry is used to reduce the computational load.

4-23
When the horizontal dispersion parameter reaches 400 m, the puff radius is large enough that the

horizontal variations in the cloud-shine dose rate are directly proportional to the horizontal variation in

concentration in the puff. At this point, MESORAD changed to a semi-infinite cloud model, and previous

versions of RASCAL changed to calculating dose rates beneath the center of the puff using the finite-puff

model and dose rates elsewhere using the horizontal variation in concentration. The puff model changes

from the point-source based cloud-shine model used in earlier versions of RASCAL to a new plane-source

based model. The plane-source model assumes that the puff is a vertical cylinder as is assumed in the

point-source model. However, rather than assuming that activity is distributed among volume elements,

the activity is assumed to be concentrated on ten horizontal slabs (planes).

To calculate the activity in each slab, the concentration at the center of the puff (y--O) is first integrated

vertically from the bottom of the puff to the top. This is similar to the integration done in calculating the

depletion from wet deposition

f Qn O, e2dZ Q . 4.44)

=Z), .I 312,2 exp I exp[-O, ]dz=_Q exp - J( _.(2,T) -" 2~7" /a'fo; l { Oly]

where

(2), = vertically integrated concentration of radionuclide n at the center of the puff.

This concentration is then divided by the number of slabs (ten) to get the concentration in each slab.

Within the cylinder, the vertical position of the slabs is determined by the effective release height, the

mixing-layer thickness, and the vertical-dispersion coefficient. When a Gaussian distribution is partitioned

so the area under the curve is divided into ten equal parts and the center of mass of each part is

determined, these centers of mass fall at ±0.127a, ±0.385a, ±0.674;, +1.037a, and ±1.645a. Using this as

a basis, the slab heights are initially estimated as h_+0.127_, h_+0.385oF, he_+0.6740z, he±1.037a, and

h_+1.645G2 . The initial heights may lie below ground level or above the top of the mixing-layer. Any

heights that fall outside these bounds are adjusted to account for reflection by the boundaries. Signs of.

heights that are negative are changed to positive, and heights (hp) that are above the mixing layer are

replaced by 2H-hP.

The dose rate at ground level from a slab is calculated as

)=W _'r 2ýD,r _kAý 2e(445

D'2,(r,z). - exp - 04 o-. (I+ k ) - z) , (4.45)

where

z z height of the slab above the receptor, which is assumed to be at I m (m),

DFP, = dose factor radionuclide n for an infinite plane [(rem/s)/(Ci/m 2)1,

= total gamma ray absorption coefficient for air (m-'),

k = ratio of energy in scattered photons to absorbed energy.

4-24
The infinite plane dose factor is approximated by

DF, = DF i/241.2 (4.46)

where

DFic. = semi-infinite cloud-dose factor [(rem/s)/(Ci/m 3)] and

241.2 = constant with units of meters evaluated by comparing dose rates calculated by Eq. (4.45) with

semi-infinite cloud-dose rates in plumes for which the semi-infinite cloud model is appropriate.

Semi-infinite dose factors contained in Federal Guidance Report No. 12 (Eckerman and Ryman 1993) are

used to estimate the infinite-plane dose factors. These calculations were carried out for 30 radionuclides

that are typically released in reactor accidents involving fuel damage. The standard deviation of the

estimates of the constant value was 0.04.

In Eq. (4.45), the term (l+kpz) represents the buildup factor due to scattered photons, and exp(-ptz)

represents the absorption of energy by the air. These terms are discussed by Healy and Baker (1968) and

Healy (1984). In RASCAL 3.0.5, u and k are assumed to be constants with values appropriate for -0.7

MeV photons (,u=0.0 I, k= 1.4) based on Figure 16.4 of Healy (1984).

Ultimately, the dose rate at a receptor is

D'(r)- 2=af exp - 0.5 Z (I+ kz,) exp( uz) (4.47)

where the summation is over all slabs.

When the vertical extent of the puff is sufficient for the semi-infinite cloud model to be appropriate (oY

> 400 m, or a uniformly mixed plume with a vertical depth >600 m), the cloudshine dose rate is calculated

using the semi-infinite cloud model

D'(r)= [2(r)/Q]I Q, DF.ic (4.48)

n

where

[z(r)/Q] is calculated using Eq. (4.2) or a variation thereof, as appropriate.

The semi-infinite dose factors from Federal Guidance Report No. 12 (Eckerman and Ryman 1993) are

used in this calculation.

4-25
4.9.3.2 Plume Model Cloudshine Dose Calculations

In the plume model, near the source, the plume is divided into a large number of equal-strength line

sources spaced to properly represent the distribution of activity in the plume. The dose rates from these

line sources are used to calculate the ground-level dose rate as a function of horizontal distance from the

plume axis. This relationship is then used to calculate dose rates and 15-minute doses at receptor

locations. When the width of the plume is sufficient (ay = 400 m), the plume model switches from the

line-source model to an infinite-slab model. Finally, when the vertical dimensions of the plume are

sufficient to make the semi-infinite cloud model appropriate (aY = 400 meters or a uniformly mixed plume

with a thickness of 600 meters), the plume model switches to a semi-infinite cloud model.

Dose rates from line sources are calculated using

N

D',(6)= Q'I.D'n(p) , (4.49)

n=[

where

D '(p) = dose rate (rem/s) at a distance p from an infinite line source of Q ' (Ci/m),

Q I = line-source strength (Ci/m), Q ",= Q ' /u where Q ' is in Ci/s,

D n(p) = line-source dose rate factor [(rem/s)/(Ci/m)] for radionuclide n.

Equation (4.49) is analogous to Eq. (4.42) with changes in the definitions of source term and dose factors.

The line-source dose rates are combined to get the plume dose rate by summing over all line sources, just

as the point-source dose rates were combined to get a puff dose rate. The number of line sources used is

determined by the horizontal dispersion parameter, oy. If a5y > 200 m, 100 lines (1Oxl0) are used to

describe the concentration distribution in the plume. Otherwise, the concentration distribution is described

by 36 lines (6x6). In either case, the lines are spaced horizontally and vertically such that each line

represents the same fraction of the total activity in the plume. The plume dose rate is given by

D'(y) - D D(YI , (4.50)

where

D '(y) = plume dose rate,

y = distance from the ground-level projection of the center of the plume,

CR = finite line correction factor,

N, = number of line sources (36 or 100),

i,j = line source indices,

D',(yj) = infinite line, line-source dose rate.

A finite-line source correction factor is included in Eq. (4.50) to account for the fact that the plume does

not extend upwind of the release point. A correction factor could be calculated by numerical integration of

4-26
a rather complex equation. However, an approximate correction factor of adequate accuracy for

emergency response dose calculations can be estimated using

C, = 0.5 1+ j) , (4.51) [(R' + h,)

where

x = downwind distance (m) to a point beneath the plume centerline at the intersection of the plume

centerline and a perpendicular line passing through the receptor,

R = distance (m) from the release point to the receptor,

he = effective release height.

In the case of a ground-level release and a receptor on the plume centerline, the correction factor will be

one. However, generally the correction factor is less than one. For a 0.7 MeV photon, the correction factor

given by Eq. (4.51) corresponds to a receptor at a position approximately 100 m off of the plume

centerline. Doses will be slightly over estimated for receptors that are closer than 100 m and slightly under

estimated for receptors that are farther than 100 m from the centerline.

When the horizontal dispersion parameter exceeds 400 m, the plume model shifts from a line-source

based, finite-plume model to an infinite-plane model. The infinite-plane model is similar to the model

used by in the puff model. The differences between the two models are associated with the calculation of

concentrations, not with the cloudshine calculation. Thus, Eq. (4.47) for the plume model becomes

et[- 0r) r (I + kuz,)exp( - ) (4.52)

Finally, when the vertical extent of the plume is sufficient (a, = 400 m, or a uniformly mixed plume with a

600 m vertical extent), the plume model shifts to a semi-infinite plume, cloudshine model. Equation (4.48)

for the plume model becomes

O'(r) = [,Z(r)/O']E Q',,DF.icn (4.53)

X(r)/Q 'is calculated using Eq. (4.5) or a variation thereof, as appropriate.

4.9.4 Open- and Closed-Window Dose Rates

The open- and closed-window dose rates, which are reported in mrad/h, are intended for use in

comparisons with field radiation measurements. The open-window dose rate has four components. These

components are gamma and beta radiation from airborne activity and gamma and beta radiation from

surface contamination. The closed-window dose rates have only the gamma radiation components.

Beta dose rates are calculated using the semi-infinite cloud model with appropriate dose factors. Similarly,

the gamma and beta groundshine dose rates are calculated using the models used to calculate external

4-27
doses to the body, with dose factors for air in place of dose factors for tissue. Dose factors used in these

calculations were extracted from the original data used in producing Federal Guidance Report No. 12 by

its authors, and are included in the RASCAL 3.0.5 radionuclide database.

The gamma dose rates for airborne activity in finite plumes are calculated using the same algorithms used

in the puff model and the plume model for finite-plume, cloudshine doses with adjustment for the

difference in energy absorption coefficients of tissue and air. The adjustment is made to the dose rates for

each isotope by multiplying the dose rate for tissue by the ratio of the semi-infinite cloud dose factor for

air and the semi-infinite cloud dose factor for tissue. Thus, the gamma dose rate for an isotope is

DF ... i,

O D DFSici (4.54)

where D 'is the cloudshine dose rate calculated for tissue. Semi-infinite cloud-dose factors for.tissue from

Federal Guidance Report No. 12 (Eckerman and Ryman 1993) are used in this calculation along with

semi-infinite cloud-dose factors for air calculated by A. L. Sjoreen using the methods listed in (Scherpelz

1986). The semi-infinite dose factors for air are included in the RASCAL 3.0.5 radionuclide database.

The open- and closed-window dose rates are larger than the sum of the cloudshine and groundshine doses

because the dose factors for air are larger than those for tissue. Typically, the cloudshine gamma dose rate

for air is about a factor 1.4 larger than the dose rate for tissue, and the groundshine gamma dose rate for

air is about a factor 1.3 larger than the dose rate for tissue. These ratios may be significantly larger greater

than 2) if radionuclides with low energy gamma emissions (<0. I MeV) contribute significantly to the dose

rates.

4.9.5 Total Effective Dose Equivalent

The early phase (plume phase) total effective dose equivalent (TEDE) that RASCAL 3.0.5 calculates is

the sum of the external gamma dose (cloudshine) from the plume, the committed effective dose equivalent

(CEDE), and the external dose over a four-day period from radionuclides deposited on the ground (4-day

groundshine dose). This TEDE is calculated assuming that no protective actions such as evacuation or

sheltering are taken. Thus, the calculations assume that people are outdoors during plume passage and will

remain outdoors exposed to ground shine from deposited radionuclides for four days after the

radionuclides have been deposited.

Thus, the early phase TEDE that RASCAL 3.0.5 calculates is larger than the TEDE that would be

expected for people who took protective actions or who continued their normal activities (spending much

time indoors).

The reason that RASCAL 3.0.5 calculates dose assuming that no actions to reduce dose are taken is to

determine if doses without any protective actions would exceed the EPA protective action guides. The

need for protective actions is based on the TEDE that would be received if no protective actions of any

type were taken, even actions such as simply spending some time indoors.

The RASCAL 3.0.5 dose estimates should not be used as an estimate of the TEDE that would be received

by people who did not intentionally take protective actions because even performing normal everyday

activities will reduce doses to below those estimated by RASCAL 3.0.5.

4-28
RASCAL 3.0.5 can provide a more realistic estimate of the doses that people would actually receive, but

that requires some effort. To account for evacuation, the end of calculation time can be set to the time at

which people evacuate. The TEDE then is the sum of the inhalation dose, cloudshine dose, and period

ground shine dose. If sheltering prior to evacuation is to be taken into account, each dose component must

be reduced by an appropriate reduction factor for sheltering before the three dose components are

summed.

4.9.6 Total Acute Bone Dose Equivalent

Total acute bone dose equivalent is another multiple pathway dose calculated in RASCAL 3.0.5. The total

acute bone dose equivalent is the sum of the cloudshine dose, the ground shine dose, and a 4-day

inhalation dose to bone red marrow.

4.10 References

Athey, G. F., et al. 1993. RASCAL Version 2.0 User's Guide. Vol. I., Rev. I., NUREG/CR-5247, U.S.

Nuclear Regulatory Commission. Washington, D.C.

Bander, T.J. 1982. PA VAN: An Atmospheric Dispersion Program for Evaluating Design Basis

Accidental Releases for Radioactive Materials from Nuclear Power Stations. NUREG/CR-2858, U.S.

Nuclear Regulatory Commission. Washington, D.C.

Briggs, G. A. 1969. Plume Rise, TID-25075, U.S. Atomic Energy Commission. Washington, D.C.

Briggs, G. A. 1975. "Plume Rise Predictions," Lectures on Air Pollution and Environmental Impact

Analyses. American Meteorological Society, Boston, Mass.

Briggs, G. A. 1984. "Plume Rise and Buoyancy Effects." Atmospheric Science and Power Production.

Ed. D. Randerson, DOE/TIC-27601, U. S. Department of Energy.

Csanady, G. T. 1973. Turbulent Diffusion in the Environment. D. Reidel, Boston, Mass.

Draxler, R. R. 1984. "Diffusion and Transport Experiments." Atmospheric Science and Power

Production. Ed. D. Randerson, DOE/TIC-27601, U. S. Department of Energy. Washington, D.C.

Eckerman, K. F., A. B. Wolbarst, and A. B. C. Richardson. 1988. Federal Guidance Report No. 11.

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

Inhalation, Submersion, and Ingestion. U. S. Environmental Protection Agency. Washington, D.C.

Eckerman, K. F., and J. C. Ryman. 1993. Federal Guidance Report No. 12. External Exposure to

Radionuclides in Air, Water, and Soil. U. S. Environmental Protection Agency. Washington, D.C.

Eimutis, E. C., and M. G. Konicek. 1972. "Derivations of Continuous Functions for the Lateral and

Vertical Atmospheric Dispersion Coefficients." Atmospheric Environment, 6:859-63.

Englemann, R. J. 1968. "Calculation of Precipitation Scavenging." Meteorology and Atomic Energy

1968. Ed. D. Slade, TID-24190, U.S. Atomic Energy Agency.

4-29
Frenkiel, F. N. 1953. "Turbulent Diffusion: Mean Concentration in a Flow Field of Homogeneous

Turbulence." Advances in Applied Mechanics, 3:61-107.

Gifford, F. A. 1976. "Turbulent Diffusion-Typing Schemes: A Review." Nuclear Safety, 17 No. 1: 68-86.

Hanna, S. R., G. A. Briggs, and R. P. Hosker. 1982. Handbook on Atmospheric Diffusion. DOE/TICI1 223, U.S. Department of Energy. Washington, D.C.

Healy, J. W., and R. E. Baker. 1968. "Radioactive Cloud-Dose Calculations." Meteorology and Atomic

Energy 1968. Ed. D. Slade, TID-24190, U.S. Atomic Energy Agency. Washington, D.C.

Healy, J. W. 1984. "Radioactive Cloud-Dose Calculations." Atmospheric Science and Power Production.

Ed. D. Randerson, DOE/TIC-27601, U. S. Department of Energy. Washington, D.C.

Kao, S. K. 1984. "Theories of Atmospheric Transport and Diffusion." Atmospheric Science and Power

Production. Ed. D. Randerson, DOE/TIC-27601, U.S. Department of Energy.

Martin, D. 0., and J. A. Tikvart. 1968. "A General Atmospheric Diffusion Model for Estimating the

Effects on Air Quality of One or More Source." 61S" Annual Meeting of the Air Pollution Control

Association for NAPCA, St. Paul, Minnesota.

Panofsky, H. A., and J. A. Dutton. 1984. Atmospheric Turbulence. J. Wiley & Sons, New York.

Petersen, W. B., and L. G. Lavdas. 1986. INPUFF 2.0 - A Multiple Source Gaussian Puff Dispersion

Algorithm User's Guide. EPA/600/8-86/024, Atmospheric Sciences Research Laboratory, U.S.

Environmental Protection Agency, Research Triangle Park, N.C.

Press, W. H., et al. 1986. Numerical Recipes: the Art of Scientific Computing. Cambridge University

Press, Cambridge, United Kingdom.

Ramsdell, Jr., J. V., et al. 1988. The MESORAD Dose Assessment Model, Volume 2: Computer Code.

Vol. 2., NUREG/CR-4000, U.S. Nuclear Regulatory Commission. Washington, D.C.

Ramsdell, Jr., J. V. 1990. "Diffusion in Building Wakes for Ground-Level Releases." Atmospheric

Environment, 24B:377-88.

Ramsdell, Jr, J. V., C. A. Simonen, and K. W. Burk. 1994. Regional Atmospheric Transport Code for

Hanford Emission Tracking (RATCHET). PNWD-2224 HEDR, Battelle, Pacific Northwest Laboratories,

Richland, Wash.

Ramsdell, Jr., J. V., and C. J. Fosmire. 1998. "Estimating Concentrations in Plumes Released in the

Vicinity of Buildings: Model Development." Atmospheric Environment, 32:1663-17.

Randerson, D. 1984. Atmospheric Science and Power Production. DOE/TIC-2760 1, U. S. Department of

Energy.

4-30
Sagendorf, J. F., J. T. Goll, and W. F. Sandusky. 1982. XOQDOQ: Computer Program for the

Meteorological Evaluation of Routine Effluent Releases at Nuclear Power Stations. NUREG/CR-4380,

U.S. Nuclear Regulatory Commission. Washington, D.C.

Scherpelz, R. I., et al. 1986. The Mesorad Dose Assessment Model. Vol. 1., NUREG/CR-4000, U.S.

Nuclear Regulatory Commission. Washington, D.C.

Sehmel, G. A. 1984. "Deposition and Resuspension." Atmospheric Science and Power Production. Ed. D.

Randerson, DOE/TIC-27601, U. S. Department of Energy. Washington, D.C.

Seinfeld, J. H. 1986. Atmospheric Chemistry and Physics of Air Pollution. John Wiley & Sons, New

York.

Slade, D. H. 1968. Meteorology and Atomic Energy 1968. TID-24190, U.S. Atomic Energy Agency.

Washington, D.C.

Slinn, W. G. N. 1984. "Precipitation Scavenging." Atmospheric Science and Power Production. Ed. D.

Randerson, DOE/TIC-27601, U. S. Department of Energy. Washington, D.C.

Stull, R. B. 1988. An Introduction to Boundary Layer Meteorology. Kluwer Academic Publishers,

Dordrecht, Netherlands.

Tadmor, J., and Y. Gur. 1969. "Analytical Expressions for Vertical and Lateral Dispersion Coefficients in

Atmospheric Diffusion." Atmospheric Environment, 3:688-98.

4-31

5 UF6 Transport and Diffusion Model

RASCAL 3.0.5 contains a special version of the plume model (see Chapter 4) modified to treat releases of

UF6 . The modifications include the introduction of a dense gas model to treat the gravitationally driven

spread of UF6 releases, a chemical/thermodynamic model to treat the reaction of UF6 with water (both

liquid and vapor) in the atmosphere, and a plume rise model to treat the vertical displacement of

HF/U02 F2 plumes when their densities become less than the density of air.

The dense gas and chemical/thermodynamic models are implemented in two control volumes, one for UF6

and a second for HF and U0 2F2. "Control volumes" as used in thermodynamics, are volumes in which

mass, energy, moisture, etc. are evaluated taking into account the quantities moving into and out of the

volume. The control volumes move downwind at the speed of the wind 1 meter above ground level. The

size of the control volumes are initially defined by the release rates of UF 6, HF, and UOF 2. As the control

UF6 + 2H 20--> U02F2 + 4HF + heat (5.1)

volumes move downwind, the volume of UF 6 is deformed by gravitational settling, and air and water

vapor are mixed into the UF6 volume. The chemical reaction is assumed to occur instantaneously as the

mixing takes place. The result of the reaction is a decrease of mass and volume of the control volume

containing UF 6 and increase in the mass and volume in the HF/UOEF, control volume. The temperatures of

these two control volumes are assumed to be identical and are determined from the initial temperature of

the released material, the air temperature, and the heat reaction of UF6 and water.

The output of the dense gas and chemical/thermodynamic model calculations is used as input to

atmospheric dispersion and deposition calculations. This input is a function of the distance from the

release point to the point at which all the UF6 has been converted to HF and UO2F2. After the UF6 is gone,

the HF and U0 2F2 source terms continue to decrease with distance to account for deposition as described

in Chapter 4.

5.1 UF6 Model Assumptions and Equations

The following assumptions were made in the development of the UF6 model.

1. The UF6 plume is released at or near ground level. (Elevated releases are not modeled.)

2. An initial UF6 control volume is defined by the UF6 release rate and density.

3. The initial cross section of the UF6 control volume is square with.

Q'UF6

UF6 - Q ,1 (5.2)

PUF6U

where

5-1
AuF6 = cross-sectional area (m2),

Q UF6 = UF6 release rate (g/s),

PUF6 = UF6 density (g/m 3),

u = wind speed at 1 m (m/s),

If the release includes HF and U0 2F2 in addition to UF6,. the area of the initial control volume is given

by V" + + v+'i.

ACV F6 (5.3)

U

where

V "F6 = the release rate of UF 6 (m3/s)

V HF = the release rate of HF (m3/s)

Vir = the volume flow of air that would be needed to generate the HF flow from a reaction of

the air with UF 6 (m3/s)

u = wind speed at 1 m. (m/s).

4. There is no diffusion of the UF 6 plume.

5. Deformation of the UF6 control volume is determined by gravitational slumping of the UF6.

6. The rate of change of the UF6 control volume width is given by

dwtF 6 k g HUF6 J (5.4)

where

WUF6 = UF6 control volume width (in),

t = time (s),

k = a slumping constant (dimensionless),

g = gravitational constant (m/s 2),

Pair = density of air (g/m 3),

HUF6 = thickness of the control volume (in).

7. The slumping constant has a theoretical value of 1.4 (2 /2) (Eidsvik 1980) but may be given a lower

value to account for surface resistance or to tune the model. A value of 1.3 is used as default in the

current version of the UF6 model in RASCAL.

8. Air is entrained into the UF6 control volume only through the top. Entrainment through the sides is

negligible because after only a few seconds the area of the top of the volume is much larger than the

area of the sides.

9. The rate of entrainment of air into the UF 6 is given by

5-2
dVair air = (5.5) UeWuF6U' I

where

Vair = air entrainment rate (m3/s),

ue = an entrainment velocity (m/s).

10. The entrainment velocity ue is given by

U (UF6 P.iru (5.6)

where u. is a scaling velocity (m/s) associated with atmospheric turbulence.

11. The water available for reaction with UJF 6 is determined by a combination of the water vapor in the

entrained air and precipitation entering the UF6 control volume.

12. The water available for reaction is given by

MH20 = Jon20vVair + PrWUF6UAtPH201 (5.7)

where

At = the duration of the time step (s)

mH20 = the rate at which water becomes available for reaction (g/s),

PH2ov = density of water vapor in the ambient air (g/m3),

p, = precipitation rate (m/s),

P1o201= density of liquid water (g/m3).

13. The reaction between UJF 6 and water is assumed to occur at the top of the UF6 control volume. The

volume of UF 6 involved in the reaction is subtracted from the UF6 control volume, and the masses of

air, HF, and U0 2F2 are added to the HFIUO2F, control volume. The volume of the HF/U0 2F 2 control

volume is increased by the volumes of the air and HF. The U0 2F2 formed in the UF6/H20 reaction is

present as small particles that are assumed to have negligible volume. The temperatures and volumes

of the control volumes are adjusted to conserve enthalpy in a constant pressure reaction.

14. Potential heat exchange with the ground and possible reaction of UF6 with water on the ground

surface are assumed to be negligible.

15. The ground is assumed to be a sink for UF6 that may be deposited on the ground. Any UF6 condensing

in the UF6 control volume is assumed to deposit on the ground. In addition, 25% of the UO2F, formed

in the UF6/H20 reaction is assumed to deposit at the time of the reaction, unless the UF 6 is released in

a fire. Wet deposition of UF 6 is not modeled because all water entering the UF 6 control volume is

assumed to react with UF6 to produce HF and UOF 2.

5-3
5.2 Chemical/Thermodynamic Model

The chemical/thermodynamic model in the UF 6 plume model is based on the description contained in

NUREG/CR-4360, Calculational Methods for Analysis of Postulated UF6 Releases (Williams 1985). The

initial release to the atmosphere may be UF6 or a mixture of UF6, HF, and U0 2 F2 . However, the

chemical/thermodynamic model is invoked only when the release includes UF 6. A release of HF and

U0 2F 2 is treated as a release of passive contaminants.

Air, water vapor, and HF are assumed to be ideal gases. A compressibility factor is used to account for the

deviation of UF6 behavior from that of an ideal gas. Although UF6 cannot exist as a liquid at atmospheric

pressures, equations for the density, vapor pressure, and enthalpy of liquid UF6 are included in the UF6

plume model because they were included in the computer code published by Williams (1985).

5.2.1 Compressibility Factor

Dewitt (1960) cites work by D. W. Magnuson in presenting the following relationship for a UF6

compressibility factor

Z= ( 3 ) (5.8)

where

Z = the compressibility factor, (dimensionless)

Tr= the temperature (°R),

P the pressure (psia)

4.892 = a constant with the dimensions (°R3

/psia)

5.2.2 UF6 Density

PUF6, = 330.0 - 0.180 352) (5.9)

The density of UF 6 is given by the following relationships. The relationships for the UF6 liquid and vapor

are based on the work of Dewitt (1960), and the relationship for the density of UF6 solid was derived by

Williams (1985) based on data presented by Dewitt.

The density of solid UF6 is given by

where

PUF6s = the density of the solid UF6 (lbm/ft3

),

T= the temperature (0F),

MW= the molecular weight of UF6.

5-4
The density of liquid UF6 is given by

PUF6, = (250.6- 0.1241Tf + 2.620x 10-4T2) MW- ) (5.10)

where

PUF61 = the density of the liquid UF6 (lbm/ft3),

Tf= the temperature (OF),

MW= the molecular weight of UF6.

The density of UF6 vapor is given by

MW. P. Z

Pir6v- R.T, ' (5.11)

where

R = universal gas constant, 10.73 (psia -ft3)/(lb-mol OR).

5.2.3 UF6 Vapor Pressure

The following relationships, based on the work of Dewitt (1960), describe the vapor pressure of UF6. The

constants in the relationships assume English units for pressure, temperature, and volume.

From 32'F to the triple point of 147.3 'F, the vapor pressure of UF6 in the solid phase is

P uF6 = e xp 10.44 + 9.642 x 10-3 I• - ( 3 +9 -i .1 , (5.12)

LFs= (Tl>+ 298.1)](.2

where

PuF6, = vapor pressure (psia) , and

Tf = temperature (°F).

From the triple point (147.3 °F) to 240 'F, the vapor pressure is given by

PUF6vI= exp 12.16- 4+ 136 (5.13)

, fo 2367.5)

And, from 276'F to the critical temperature (446 0

F) the vapor pressure is given by

5-5
F6.976x 103'1

U :6vh exp 13.76- (T, + 511.9) (5.14)

Between 240'F and 276 °F, the vapor pressure is estimated by a weighted average of Puf 6vl and Puffvh

-240.0)1 6 (5.15)

U~F6v = UF6v1(276.0 - +U6v/z 36.0 (.5

5.2.4 U F6 Enthalpy

Williams (1985) provides the following equations for the enthalpy of UF 6 using 25'C (77 'F) as a base.

The equations are to a large extent based on data of Dewitt (1960).

For solid UF 6, the enthalpy is given by

H = 50.446- 5.70531x 10- 2T + 1.27509 x 10- 4T 2 - 9645.63T- 1 (5.16) UF6s r r r

where HUF6, is the enthalpy (Btu/lbm).

For liquid UF6, the enthalpy is given by

HUF6I = 30.6133 + 5.10057 x 102 + 5.13165x 10x5T2

-6.139.34T-' +0.18268 J (5.17)

where

HLF61 = the enthalpy,

P = the atmospheric pressure (psia),

PO= the vapor pressure over liquid UF6 (psia),

P, = the density of the liquid (Ibm/ft3).

The last term in this relationship is a correction for supersaturated liquids, assuming an incompressible

fluid.

Finally, the enthalpy for UF 6 vapor is given by

5-6
HUF6, = 43.2614 + 9.21307 x 10-2 + 6.26265×10 6 T

2 + 2951.710-1

+ 3.0939 x 1 -3T(ZIP , - Z047 ,) (5.18)

where

ZPT = the compressibility factor at pressure P and temperature T.

The last term in this relationship is a compressibility correction. This term is small in the atmosphere

because atmospheric pressure is always near 14.7 psia.

5.2.5 Uranium Enrichment

William's (1985) model includes correction terms for the molecular weight to account for enrichment.

The correction terms are retained in the UF6 plume model. The molecular weight of enriched uranium is

input to the model along with the release rates. RASCAL 3.0.5 corrects for molecular weight, but, the

correction has only a ver small effect.

5.2.6 HF-H 20 System

William's (1985) model treats HF and H2 0 as a system for computation of vapor pressures and enthalpy

assuming that the HF and H20 are vapors in equilibrium with a condensed phase. It is unlikely that a

condensed phase will occur in the atmosphere because of the exothermic nature of the UF6/H20 reaction.

However, the equations for the condensed phase are included in the UF 6 plume model for completeness.

HF vapor in the atmosphere is assumed to exist as a set of polymers linked by hydrogen bonding. The

effects of this self association are included in the HF vapor pressure and enthalpy calculations.

5.2.7 HF Self Association

Williams (1985), Beckerdrite, Powell, and Adams (1983) report that the self association of HF is

reasonably modeled by assuming equilibrium among an HF monomer (HF),, an HF trimer (HF)3, and an

HF hexamer (HF)6. The partial pressure of HF is given by

pHF=p +KP3 +KP(519

(HF)1 " (HF) 6 (HF)1 ,(5.19)

where the second and third terms on the right are the partial pressures of the polymers and K3 and K 6 are

equilibrium coefficients. The equilibrium coefficients have been determined experimentally by Strohmeier

and Briegleb (Beckerdrite, Powell, and Adams 1983). Using these data, Williams (1985) derived the

K3 = exp(2.3884.0Tr-' - 51.2393) (5.20)

following relationships to estimate the coefficients

5-7
and

K6 = exp(40319.6T-7 - 87.7927) (5.21)

With self association, the effective molecular weight for HF for vapor-phase densities and mole fractions

is greater than the molecular weight of the HF monomer. It is

[ PF MW + K3 P3 MW + K 6 MWHttF)]

HF HQ (HF)1 (HF) (HF) MWHF=P.

3 6(HF) (5.22)

PHF

5.2.8 Partial Vapor Pressures of HF

If a condensed phase exists in the I-IF-H 20 system, the vapor pressure of HF is calculated using

relationships of the form

PHF = exp(AT7-' + B) , (5.23)

where

A and B = the model parameters that are a function of the weight fraction of HF in the condensed

phase.

Williams (1985) gives estimates of the coefficient values based on a figure supplied by Allied Chemical

(Brian C. Rogers). The differences between partial vapor pressures estimated using the model and the

figure, range from about I % for weight fractions near 1.0 to a maximum of 5% at weight fractions below

0.5. If a condensed phase does not exist, the partial vapor pressure of HF is calculated using an iterative

procedure along with estimation of the effective molecular weight.

5.2.9 Partial Vapor Pressure of H20

Until all the UF 6 has reacted with water, all water entering the plume will be used by the UF6/H 20 reaction

to form HF and U0 2 F2. Under these conditions, the H2 0 partial vapor pressure in the HF-H20 system will

be zero. Following conversion of all of the UF6, an initial estimate is made of the H20 partial vapor

pressure from the mass of water in the plume using the ideal gas law. The phase composition of the HFH20 system is determined by comparing the sum of the HF partial pressure and the initial estimate of the

H20 partial pressure with the total pressure of HF and H2 0 for an azeotropic mixture. If the sum is less

than the total pressure for the azeotropic mixture, there is no condensation phase and the initial HO

partial pressure estimate is used. If condensation occurs, an iterative procedure is used to determine the

partial pressure of HO. The procedure is described in detail by Williams (1985).

5-8
5.2.10 Enthalpy of HF-H 20 Vapor Mixtures

The enthalpy of HF-H20 vapor mixtures is given by

H HFH2Ov=- 1051.0+0.472T - 376.0+0.136T + 790.642W HF)+ 667.358W WHFv ,(5.24)

436. (HF)3 (HF)6

1 (.4

where

W(HF)3 and W1 HF)6 = the weight fractions of the HF polymers with respect to total I-fF,

WHF, = the weight fraction of I-IF in the HF-H20 vapor.

The heat of association for (HF) 3 is -790.642 Btu/Ibbm of (HF) 3 formed, and the heat of association of

(HF) 6 is -667.358 Btu/lbm of (HF)6 formed.

HFH201 = 4A + + cF w+, , (5.25)

5.2.11 Enthalpy of HF-H20 Liquid Mixtures

The enthalpy of a liquid HF-HO mixture is given by a relationship of the form

where the coefficients A,, Bi, and Ci are functions of the weight fraction WHFI of HF in the HF-H20 liquid

mixture. Williams (1985) provides correlations for estimating the coefficients that are based on an

enthalpy-concentration diagram provided by Brian C. Rogers at Allied Chemical.

5.2.12 UO2F2 Enthalpy

UO2F2 is formed as a product of the UF6-H 20 reaction. It is a solid with a heat capacity of 0.0821 Btu/(Ibm

'F). The enthalpy at any temperature, relative to a reference temperature is

HU02F2 0.0821(Tf - Trefj (5.26)

where

Tr = UO2F2 temperature, and

Tree = reference temperature (both in 'F or *R).

The reference temperature is 77°F in the UF 6 plume model.

5.2.13 Mixture Enthalpies and Plume Temperature

Mixing and reactions in the UF6 plume model are assumed to take place under constant pressure. The

following reference conditions are assumed for enthalpy calculations: a pressure of 1013.25 mb (I

5-9
atmosphere, 760 mm Hg, or 14.696 psia), a temperature of 25°C (77°F); a vapor state for UF6, H20, and

air; monomeric vapor for HF; and solid for UO 2F,. I

The enthalpy of the plume is calculated for the control volume as the control volume moves downwind.

The control volume initially consilts of the volume of the UJF 6 plus the volume of the entrained air and

water vapor and has an enthalpy equal to the sum of enthalpies of the UF6, air, and H2O. With the UF6-

HO reaction, the enthalpy of the control volume increases because of the heat release and changes in the

masses of the plume constituents.

The UF6-H2 0 reaction is limited by one constituent or the other. If the available water is the limiting

factor, the heat of reaction is calculated as

where

Hrxn = 25.199 x 103 MH2 0 (5.27) MWH520

Hr,,, z- heat of reaction (Btu),

mH2o = mass of water available for the reaction (Ibm),

MW,.,o = molecular weight of water (Ibm/Ibm-mole).

Otherwise, the heat of reaction limited by the available UF6 is calculated as

Hrx,, = 50.398 103 m' . (5.28) MW,

where

m,, = mass of UF6 available for the reaction (ibm),

MW, = molecular weight of UF6 (Ibm/Ibm-mole).

Note that the constants in Equations 27 and 27 have units of Btu/(lbm-mole).

With completion of the UF 6-H20 reaction, the enthalpy of the plume in the control volume is

Hplu,,me = AHair + AHH2 0 v + AHUF6 +AH HFH2o + AHu0 2 F2 + Hr.n (5.29)

The change in enthalpy of air is

air = 0.24037mar(T7r - 77.0) (5.30)

and, the change in enthalpy associated with entrained water is

AHH20 = (0.99783m H20 ,e + 0.472m H2ove)(Tir - 77.0) (5.31)

5-10
where

"'H 20, = mass of liquid water entrained, and

f,2oH,,, = mass of water vapor entrained.

Finally, an iterative procedure is used to arrive at a plume temperature that gives the same mixture

enthalpy. During this procedure, the phase composition of the HIF-H 20 mixture and UF6 are adjusted as

the temperature changes. The convergence criterion for plume temperature is 0.1 'C. This precision is

more than adequate because the plume temperature is used only in plume-rise calculations.

5.3 Dispersion and Deposition of HF and U0 2F2

The UF6 model works in two stages. In the first stage, the model calculates the spread of UF6 , the

conversion of UF6 to HF and U0 2F2, and the plume rise of the HF and U0 2F2. The products of this stage

are UJF 6, HF, and UO2F2 source terms and the plume rise of HF and UO2 F2, all as a function of distance

from the release point. In the second stage, a straight-line Gaussian model (based on the model described

in Chapter 4) is used to calculate airborne concentrations and deposition of HF and U0 2F2 at receptors on

a polar grid. The distance-dependent source terms calculated in the first stage are used as long as UF 6 is

present. After the UF6 is gone, the HF and UOzF2 source terms are depleted to account for deposition.

The UF6 chemical and thermodynamics models are run in the first stage while the control volume moves

downwind in small time steps. The maximum time step is 15 seconds. If, with the I-meter wind, the UF6

control volume would reach the first arc of receptors in less than 75 seconds, the time step is reduced so

that the control volume reaches the first arc at the end of fifthtime step. As the control volume moves

downwind, plume rise is calculated using the stable plume equations discussed in Section 4.5.2. In

addition, transition plume rise is calculated using

Ah, 1.6F1 3x 213 u-1 (5.32)

where

Ah, = transition rise (m) (Briggs 1984),

Fb = buoyancy flux (m 4

/s 3),

x = downwind distance, and

u = 10-m wind speed (m/s).

The smaller of the transition and final rise is selected as the plume rise.

Dispersion of the HF and UO2F, plumes is calculated using the dispersion parameters that are used in the

main RASCAL 3.0.5 plume model. As long as unreacted UF6 is present, the HF and UOF 2 plumes are

assumed to be uniformly mixed in the vertical because the plumes are being fed by the UF 6 - H20 reaction.

Normalized HF and U0 2F2 concentrations in this range are given by

5-11
Q=())12U exp (5.33)

where

o-Uy+•- +y= 211/2 (5.34)

and

H- Ah, + 3o. (5.35)

In these last two Equations, oa. and a, are the horizontal and vertical dispersion parameters for a point

source plume (see Section 4.3), and WuF6 is the width of the UF6 control volume.

After all UF6 is converted to HF and UO2F2, their normalized concentrations are given by

1 [1 y

X/ Q' exp _ - F(x) (5.36)

where WUF6 is a constant equal to its value just before the last UF6 is converted to HF and UO2 F, and

o'[ + (5.37)

As with wL,F6, H is a constant equal to its value just before the last UF6 is converted to HF and UOF-,.

Finally, F(x) is the vertical distribution function described in Section 4. 1. I. The receptor height, z, is

assumed to be 1 meter.

5.4 Calculated Result Types

The RASCAL 3.0.5 UF6 plume model Calculates the following result types as a function of distance.

* Airborne uranium exposure (g-s/m3)

The airborne uranium exposure includes total exposure to uranium It includes contributions from both

UF6 and UOF,. For this calculation only, UF 6 is assumed to be a trace gas, not a dense gas.

5-12
0 Inhaled uranium (mg)

Inhaled uranium is calculated from the total exposure using a breathing rate passed from the user

interface. The default breathing rate is 3.33 X10 4 m3

/s.

Committed effective dose equivalent from inhaled uranium (rem)

The committed effective dose equivalent (CEDE) from uranium is calculated from the inhaled

uranium, the specific activity of the uranium, and the inhalation dose factors from Federal Guidance

Report No* I I (Eckerman et al. 1988). In addition, all dose calculations have been eliminated except

for the calculation of the inhalation CEDE for uranium. This CEDE can be considered equivalent to

the TEDE since cloudshine and groundshine doses are negligible. The UF 6 plume model does not

calculate cloudshine or groundshine doses because they are negligible.

" Deposited uranium (g/m2 )

Deposited uranium includes uranium in any UF6 that condenses before reacting with atmospheric

water and uranium in UO 2F, that deposits from U0 2F2 plume. UF6 vapor does not deposit, and there is

no enhanced deposition of UO2F2 following its formation.

" Average HF concentration in the lung (ppm by volume)

The HF concentration calculated by UF 6 plume model is the HF concentration in the lungs. The

concentration in the lungs includes inhaled HF plus HF formed as a result of the reaction of inhaled

UF6 with water in the lungs. If no UF6 is inhaled, the HF concentration in the lung is the same as the

concentration in the atmosphere.

" 1-h equivalent HF concentration in the lung (ppm by volume)

The I -h equivalent HF concentration in the lung is an effective concentration calculated for shortduration releases for comparison with toxicity limits. It is calculated as

Clhe '- C(t) (5.38) 3-600)

where

Ch, = lh equivalent concentration (ppm),

C(t) = average concentration for duration t (ppm),

t = duration of the exposure to concentration C(t) (s).

HF deposition (g/m').

HF deposition is calculated from the atmospheric HF exposure using a 0.003 m/s deposition velocity.

5-13
5.5 Comparison of RASCAL UF6 Plume Model with Experimental Measurements

and Results from Other Models

The transport and dispersion portions of the UF6 plume model have been evaluated for small UF 6 releases

by comparison with measurements from three French experiments and comparison with two other UF6

10000-

co

E

E

0

0

J.n1000-

100-

10-

1

1 10 100 1000

Obs. Concentration (mg/mA3)

models. Figure 5.1 shows the comparisons. The experiments, data, other models are described in

NUREG/CR-6481 (Nair et al. 1997). The figure compares average uranium concentrations predicted by

the RASCAL 3.0.5 UF 6 plume model and the other models with average concentrations measured between

10 and 500 meters from the release point. In general, RASCAL 3.0.5 UF6 plume model tends to overpredict the uranium concentrations by less than a factor of 2. The other models tend to over predict by

larger factors.

Figure 5.1 Comparison of UF6Plume model predictions of average uranium concentrations with

measured concentrations and predictions of other models.

5-14
5.6 References

Beckerdrite, J. M., D. R. Powell, and E. T. Adams. 1983. "Self-Association of Gases, 2: The Association

of Hydrogen Fluoride." J. Chem. Eng. Data, 28:287-93.

Briggs, G.A. 1984. "Plume Rise and Buoyancy Effects." Atmospheric Science and Power Production.

Ed. D. Randerson, DOE/TIC-27601, U. S. Department of Energy.

Dewitt, R. 1960. Uranium Hexafluoride: A Survey of the Physico-Chemical Properties. GAT-280,

Goodyear Atomic Corporation, Portsmouth, Ohio.

Eidsvik, K.J. 1980. "A Model for Heavy Gas Dispersion in the Atmosphere." Atmos. Environ.14:769-

777.

Nair, S.K., D.B. Chambers, S.H. Park, ZR. Radonjic, P.T. Coutts, C.J. Lewis, J.S. Hammond, and F. 0.

Hoffman. 1997. Review of Models Used for Determining Consequences of UF6 Release - Model

Evaluation Report. NUREG/CR-6481 Vol, U. S. Nuclear Regulatory Commission

Williams, W. R. 1985. Calculational Methods for Analysis of Postulated UF6 Releases. 2 Vols.,

NUREG/CR-4360, U. S. Nuclear Regulatory Commission.

5-15

6 Meteorological Data Processor

The meteorological data processor is the part of RASCAL 3.0.5 that allows the user to enter

meteorological data and prepares the data for use by the atmospheric transport and diffusion models.

Meteorological data for the site (release point) and as many as 35 additional meteorological stations may

be entered. All data must be entered manually at the present time. A future version of the meteorological

data processor may include options for importing meteorological data files.

The following sections describe the technical aspects of the meteorological data requirements and the

meteorological data processing.

6.1 ModeiDomain

Model domain refers to the area covered by the dose calculations in the source term to dose model. The

model domain for the puff model is square. The release point is at the center of the square. The user can

select a square that is 20, 50, or 100 miles (32, 80, and 160 km) on a side. The meteorological data

processor creates a meteorological file for the selected domain for use by the puff model. This file

describes the spatial and temporal variation of meteorological conditions at nodes on a Cartesian grid.

The meteorological data processor also creates a smaller file of meteorological data for the release point

for use by plume model and the UF6 plume model. This file describes the temporal variation of

meteorological conditions at the center of the polar grid used by these straight-line models.

Meteorological data must be entered for at least one location, generally the release site. If data are not

available for the release site, they may be entered for another location. However, the release location must

still be selected as if it had meteorological data because the location of the release site is used to fix the

position of the grid.

6.2 Meteorological Stations

Locations for which meteorological data are entered are called meteorological stations. Meteorological

stations may be within or near the model domain. Spatial fields of winds, stability, etc., are produced from

the station meteorological data. Section 6.3 discusses the meteorological data input.

Information on each station must be available before a station's meteorological data can be used in

generating the meteorological fields needed by the puff model. Files containing the required information

for each operating nuclear power plant, large fuel cycle facilities, and several major radioactive materials

facilities are included with RASCAL 3.0.5. Each file contains the information for the location of the site

and for some selected meteorological observation stations near the site.

Since the file for a specific site does all meteorological stations near the site and since the information for

meteorological stations can become outdated, the meteorological data processor provides the means to add

meteorological stations to the file or update information in the file.

6-1
The following information is needed for each meteorological station:

" A station identification. The station identification can be any 10 letter character; the release site ID is

appropriate for the first station in the station list; FAA or ICAO location indicators are appropriate for

national weather service or other stations that have them. A longer station name may be included for

each station for better identification.

* The latitude (positive north of the equator and negative south of the equator) and longitude (positive

east of the prime meridian and negative west of the prime meridian) of the station in decimal degrees.

* The elevation of the station in meters above mean sea level.

* The surface roughness for the station (in). Meteorological texts such as Panofsky and Dutton (1984)

and Stull (1988) provide guidance on estimating surface roughness. If no other information is

available, a default surface roughness of 0.2 m may be used.

* The height at which the wind measurements are made (in). The instrument height should be height

above ground level.

The meteorological data processor uses the station position to place station data at the proper location in

the modeling domain; station elevations are used in the potential flow model that adjusts wind fields for

topographic effects (Section 6.5.1), and the surface roughness and height of wind measurement are used in

calculating wind speed variation with height (Section 6.4.2).

The first station in the station file is the release point (the site). The latitude and longitude of the first

station will define the coordinates of the center of the model domain grid. Distances from the center of the

grid to the other stations are calculated using

Xrs =rA Ars COSts (6.1)

and

Yrs = reA Ors (6.2)

where

xrs = distance of the station east (+) or west (-) of the source (center of the grid) (km),

Yrs = distance of the station north (+) or south (-) of the source (center of the grid) (km),

re = radius of the earth (= 6370 km),

(p, = latitude of the center of the grid (release point),

Airs = longitude difference between the station and the source (center of the grid) (radians),

Apq, = latitude difference between the station and the source (center of the grid) (radians).

6-2
6.3 Meteorological Data Input

Station meteorological data are entered for specific dates and times. The data may be actual observations

(measurements) or they may be taken from meteorological forecasts. If available, the following data

should be entered for each station used:

* whether the data is an observation or a forecast

* the time of the data; (the program will round the time to the nearest quarter-hour. For example, an

entry of 12:07 would be changed to 12:00. Similarly, an entry of 14:22 would be changed to 14:30)

* surface-level wind speed

* surface-level wind direction

* estimated atmospheric stability

• precipitation type

* estimated mixing height (optional).

If the plume rise option is used the ambient air temperature should also be entered.

If the calculation is for a UF6 release, the following data should also be entered for the release point

(center of the grid):

* ambient air temperature

* pressure

* humidity measurement (dew point temperature, relatively humidity, or wet bulb temperature).

The air temperature is used in plume rise calculations in all three of the transport and diffusion models.

The air temperature, pressure, and humidity are used in the thermodynamic calculations in the UF6 plume

model. Pressure and humidity are used only by the UF 6 plume model.

The following sections describe the meteorological variables in more detail.

6.3.1 Surface Winds

The surface winds are made up of the wind direction (the direction from which the wind is blowing) and

the wind speed. Wind directions must be entered in degrees from 0' to 3600. Wind speed can be entered

in units of m/s, mph, or knots and can range from 0 to 30 m/s (or equivalent in other units).

6.3.2 Atmospheric Stability Class

Atmospheric stability may be entered either as a stability class (A - extremely unstable through G -

extremely stable) based on the general classification scheme discussed by Pasquill (1961), Gifford

(1961), and Turner (1964) or as temperature variation with height (dT/dz). If dT/dz is entered, it will be

converted to a stability class using the conversion table shown in Table 6.1 (NRC, 1972).

6-3
Table 6.1 Estimated Pasquill-Gifford Stability Class Based on NRC Delta TM Method

Stability dT/dz dT/dz

Class (°C/100 m) (-F/IO0 ft).

A <-1.9 <-1

B <-1.7 <-0.9

C <-1.5 <-0.8

D <-0.5 <-0..3

E < 1.5 < 0.8

F <4 <2.2

G -4 Ž2.2

Reference: NRC, 1972

If the user does not enter a stability class, Table 6.2 is used to estimate the stability class from wind speed,

precipitation type, and the time of day. Factors discussed by Turner (1964) were used in selecting the

stability classes for the table. Daytime is defined as one hour after sunrise to one hour before sunset.

Nighttime is defined as one hour before sunset to one hour after sunrise. The user may alternatively select

"persistence" to determine stability class. If persistence is selected, the stability entered for the earlier time

will be used.

Table 6.2 Estimated Atmospheric Stability Class for Missing Stability Classes

No or Light Moderate or Heavy

Wind Speed (mis) Precipitation Precipitation

Daytime

6.0 C C

> 6.0 D D

Nighttime

3.0 F E

3.1-5.0 E E

> 5.0 D D

The meteorological data processor will also compare the entered stability class with ranges of stability

classes that would be expected given the time of day and meteorological conditions and replace values

that are out of the expected range with more likely values. Table 6.3 is used to determine the reasonable

range of stability classes given the time of day, wind speed, and precipitation type. These ranges are based

on factors discussed by Turner (1964). If a meteorological station stability class falls within the reasonable

range, the stability class is not modified. But if the stability class falls outside the range, the stability class

is changed to the closest stability class within the range. The user has the option of turning this option off

if desired.

6-4
Table 6.3 Limits of Atmospheric Stability Classes Based on Time of Day, Wind Speed, and

Precipitation

No or Light Moderate or Heavy

Wind Speed (mis) Precipitation Precipitation

Daytime

•3.0 A-E C-E

3.1-5.0 B-D C-D

>5.0 C-D C-D

Nighttime

•3.0 C-G C-E

3.1 -5.0 D-F D-E

5.1-6.0 D-E D-E

>6.0 D D

6.3.3 Precipitation Type

Wet deposition in the plume model, puff model, and UF6 plume model and the reaction between UF6 and

water in the UF6 plume model are affected by precipitation. Information on precipitation may be entered

for each station during meteorological data entry by selecting one of seven precipitation types, or

unknown, if appropriate. Precipitation types are: none; light, moderate, and heavy rain; and light,

moderate, and heavy snow. Rain includes drizzle, freezing rain, and freezing drizzle. Snow includes snow

grains, snow pellets, ice pellets, ice crystals, and hail. The meteorological data processor estimates

precipitation rates from these precipitation types (see Section 6.4.6).

6.3.4 Mixing Height

The plume and puff models use the mixing height to limit vertical dispersion. Mixing heights may be

entered with the other meteorological data for a station. However, this information is generally not

available. Consequently, unless the option of entering mixing-height data is specifically selected, the

meteorological data processor will estimate mixing heights from wind speed and stability. There is also an

option of using climatological mixing-height estimates in place of measured or calculated values.

6.3.5 Temperature

The ambient air temperature should be entered for the release point. If the meteorological data are to be

used for consequence analysis for a ground-level release not involving UF 6, the temperature may be

omitted without affecting doses.

6-5
6.3.6 Pressure

The station atmospheric pressure (not sea-level pressure at the station) is needed for thermodynamic

calculations in the UF6 plume model. However, the calculations are not particularly sensitive to the

pressure as long as the pressure is within a few percent of the actual value. The meteorological data

processor includes default pressures for fuel-cycle facilities that should be adequate for most purposes

because atmospheric pressures rarely vary by more than ±5%. The program will convert pressures entered

in other units to millibars.

6.3.7 Humidity

Information on humidity is needed for chemical reaction and thermodynamic calculations in the UF 6

plume model. Humidity information may be entered for the release point as dew point temperature,

relative humidity, or wet bulb temperature. The meteorological data processor includes default humidity

information based on climatological data for fuel-cycle facilities. However, actual data should be entered

whenever possible because the calculations are very sensitive to humidity, and humidities have a wide

range of variation in the atmosphere.

6.3.8 Temporal Interpolation of Input Values

The atmospheric models in RASCAL 3.0.5 expect meteorological data on the 15-minute time interval

typically used to record meteorological data at U.S. nuclear power plants. Data from other meteorological

stations are not likely to be available on that interval. Consequently, the meteorological data processor

will estimate missing 15-minute data for each station by linear interpolation between observed values. For

example, if 10:00 and 11:00 observations are entered for a station, the program will estimate values for

10:15, 10:30, and 10:45. The program will not interpolate between observed and forecast values, or

between two forecast values.

The interpolation procedures are as follows:

Winds

" If the winds for both the earlier and later observation are valid, the winds are interpolated as follows:

1) The wind speed and direction are converted to U (east-west) and V (north-south) components.

2) The U and V component are linearly interpolated (i.e., U(t) = (UI - UX){(t-te)/(tjte)} + Ue where U1,

Ue, t

1, te are the U component and time of the later and earlier observations, respectively).

3) The U and V components are converted back to speed and direction.

" If the wind (either speed or direction) is missing for the later observation but not for the earlier

observation, the winds are set to. the wind of the earlier for times within 12 hours of the earlier

observation, otherwise they are assumed to be missing.

* If the wind is missing for the earlier observation, the winds at all times between the two observations

are also assumed to be missing.

6-6
Atmospheric Stability

" If both observations have valid atmospheric stabilities, the atmospheric stability is estimated using

linear interpolation between the two observations. If the atmospheric stability is given by a PasquillGifford stability class (1-7), then the interpolation is rounded to the nearest integer.

" If the atmospheric stability for the later observation is missing but not for the earlier observation, then

the atmospheric stabilities are set to the value of the earlier observation as long as the elapsed time

from the earlier observation is less than 12 hours. After 12 hours, the stabilities are set to missing.

* If the atmospheric stability for the earlier observation is missing, the atmospheric stabilities at all

times between the two observations are assumed to be missing.

Precipitation Type

If both observations have valid precipitation types, then the precipitation type for the earlier

observation is used when the time is less than or equal to halfway between the two observations. If

the time is greater than half way between the two observations, the precipitation type of the later

observation is used.

If the precipitation type for the later observation is missing but not for the earlier observation, then

precipitation types are set to the precipitation type of the earlier observation as long as the elapsed

time from the earlier observation is less than 12 hours. After 12 hours, the precipitation types are set

to missing.

* If the precipitation type for the earlier observation is missing, the precipitation type for all times

between the two observations will be set to missing.

Mixing Height

* Unless the mixing height is being entered directly (not calculated from the meteorological data or

from climatology), the method of estimating mixing heights being used for the earlier observation will

continue to be used.

* If the mixing heights are being entered directly, the technique used to interpolate stability is used to

estimate the missing mixing heights (see previous statement).

Temperature, Pressure, and Moisture

• The same technique previously explained is used to estimate missing stabilities is used for

temperature, pressure, and humidity.

" If data are missing between observed and forecast values, persistence will be used to estimate missing

values for all times up to the time of the forecast.

6-7
* For each station, data for all times before the first date and time with an entered value are assumed to

be missing. Likewise, data for all dates and times past the entered value are assumed to be missing.

6.4 Other Meteorological Parameters

Meteorological data entered for a station are used to evaluate additional parameters. The following

subsections describe these additional parameters.

6.4.1 Monin-Obukhov Length

The Monin-Obukhov length (L) is a scaling length for vertical motions in atmospheric boundary layer

studies that is used as a measure of atmospheric stability. It is used in wind profile, turbulence, and

mixing-layer depth calculations. Golder (1972) provides a graphical means for converting from PasquillGifford stability classes to Monin-Obukhov lengths using the surface roughness length (Section 6.4.2).

The meteorological data processor uses a procedure that was developed by Ramsdell, Simonen, and Burk

(1994) based on Golder's work to convert stability classes to Monin-Obukhov lengths.

6.4.2 Wind Speed vs. Height

The RASCAL 3.0.5 atmospheric dispersion models use winds that are representative of 10 meters above

ground level for ground-level release calculations and winds representative of the release height for

elevated release calculations. Wind measurements are not always made at these heights. Therefore, the

meteorological data processor adjusts wind speeds for the difference between the measurement height and

the height required for model calculations. A diabatic wind-profile model, which accounts for the effects

of surface roughness and atmospheric stability on variation of wind speed with height, is used for this

adjustment. No attempt is made to model the variation of wind direction with height.

The diabatic profile model is derived from atmospheric boundary layer similarity theory proposed by

Monin and Obukhov (1954). The basic hypothesis of similarity theory is that a number of parameters in

the atmospheric layer near the ground, including wind profiles, should be universal functions of the

friction velocity, a length scale, and the height above the ground. The length scale is referred to as the

Monin-Obukhov length and the ratio zIL is related to atmospheric stability.

The diabatic wind profile is

u(z) = k In( - , (6.3)

where

u(z) = wind speed at height z (m/s),

u. = friction velocity (boundary-layer scaling velocity) (m/s),

k =von Karman constant (=0.4),

zo = surface roughness length (m),

yi(z/L) = stability correction factor,

L = Monin-Obukhov length (m).

6-8
The surface roughness length is associated with small-scale topographic features. It arises as a constant of

integration in the derivation of the wind profile equations and is used in several boundary-layer

relationships. Texts on atmospheric diffusion, air pollution and boundary-layer meteorology (Panofsky

and Dutton 1984, Stull 1988) contain tables that give approximate relationships between surface

roughness and land use, vegetation type, and topographic roughness.

The term Vf(z/L) accounts for the effects of stability on the wind profile. In stable atmospheric conditions,

V1(z/L) has the form -az/L where cc has a value of 5. In neutral conditions V'(z/L) is equal to zero, and the

diabatic profile simplifies to a logarithmic profile.

In unstable air, W(z/L) is more complicated. According to Panofsky and Dutton (1984), the most common

form of V'(z/L) for unstable conditions, based on the work of Businger et al. (Paulson 1970) is

y( Ln = In( [( ] [ 2x)] 2 - 2tan-'(x) + (6.4)

where

x = (1-16z/L)" 4.

Equation (6.4) is used to estimate the friction velocity (u.) from the wind speed, surface roughness, and

Monin-Obukhov length. In unstable and neutral conditions, the use of Eq. (6.4) is limited to the lowest

100 meters of the atmosphere. In stable conditions, the upper limit for application of Eq. (6.4) is the

smaller of 100 meters or three times the Monin-Obukhov length.

6.4.3 Mixing Height

Heating of the surface and surface friction combine to generate turbulence that mixes material released at

or near ground level through a layer that varies in thickness from a few meters to a few kilometers. This

layer is referred to as the mixing layer. The atmospheric models in RASCAL 3.0.5 use the mixing height

(also referred to as the mixing-layer depth and mixing-layer thickness) to limit vertical diffusion.

The meteorological data processor has three methods for obtaining estimates of the mixing height at

meteorological stations. The mixing height may be entered directly, or it may be estimated by the program

from either current meteorological data or climatological information. Of the latter two options, estimation

of mixing height from current meteorological data is preferable to estimating the mixing height from

climatological data, if sufficient data are available.

The meteorological data processor uses algorithms developed by Ramsdell, Simonen, and Burk (1994 ) for

estimating mixing height from current meteorological data. The algorithms are based relationships derived

by Zilitinkevich (1972) for stable and neutral conditions.

For stable atmospheric conditions, the relationship is

H = k( . (6.5)

6-9
where

H = mixing height (m),

k =von Karman constant (0.4),

u. = friction velocity (m/s),

L = Monin-Obukhov length (in),

f= Coriolis parameter (1/s).

A 50-meter mixing height is used if the mixing height calculated by Equation 6.5 is less than 50 meters.

Similarly, if the calculated mixing height is greater than 2,000 meters, the mixing height is set to 2,000

meters.

For neutral and unstable conditions, the mixing height is calculated by

H= f , (6.6)

where

/? is a constant set to 0.2.

If the mixing height calculated by Equation 6.6 is less than 250 meters, the mixing height is set to 250

meters, and if the calculated mixing height is greater than 2,000 meters, the mixing height is set to 2,000

meters.

The mixing-layer thickness may also be estimated from climatological data. When this option is selected,

the mixing-layer thickness is estimated from typical morning and afternoon thicknesses for each month

using the method used in the Environmental Protection Agency's meteorological preprocessor code,

PCRAMMET (EPA 1999). The monthly morning and afternoon mixing-layer thicknesses were calculated

from daily data obtained from the Environmental Protection Agency's Support Center for Regulatory Air

Models (www.epa.gov/scramOOI/). The following rules are used in estimating mixing-layer thicknesses

from the monthly values.

* From midnight to sunrise - use the morning mixing height.

* From sunrise to 1400 - linearly interpolate between morning and afternoon mixing heights.

* From 1400 to sunset - use the afternoon mixing height.

* From sunset to midnight - use exponential interpolation between the afternoon and morning mixing

heights. For the last day of the month, use the morning of the next month.

The exponential interpolation of the mixing height is given by

H bt

6-10
where

H(t) = mixing height at time t (in),

a = Hmorn/exp(-b),

b = 24 In(H H,,fl)Hj(24- ts.... ),

Hýa, = morning mixing height (in),

Haf = afternoon mixing height (in),

tSunset = time of sunset (h).

The following equations (Stull 1988) are used in calculating sunset and sunrise times

sin v = sin 0sin S, - cos cos S, cos(T0) , (6.8)

where

v = local elevation of the sun,

ýp = latitude of the station,

6, = solar declination angle (angle of the sun above the equator),

T, = local time.

The solar declination angle is calculated using

0= .Cos 24 . -d~) (6.9) d,9

where

(pr = latitude of the tropic of Cancer (23.450),

d = Julian calendar day of the year,

d, = Julian calendar day of the summer solstice (173),

dy= average number of days per year (365.25).

The local time is defined as

( 7r t uic (6.10

To= 12 (6.10)

where

tu,,= time at the prime meridian,

2e = longitude (in radians) of the station.

Sunrise and sunset are calculated by setting the solar elevation angle to -0.8330 (the sun appears to rise

and set when it is 0.833 0 below the horizon) and solving for To using Eq. (6.10). Sunset is 24 h - To. The

equations for sunrise and sunset do not take into account the ellipticity of the earth's orbit, but it is

accurate to about ± 16 minutes.

6-11
6.4.4 Dry Air and Water Vapor Density

The UF 6 plume model requires estimates of the air density and water content of the atmosphere. These

two variables are estimated from the air temperature, station pressure, and humidity for the release

location. (The release location is assumed to be at the location of the first meteorological station. The

method used to calculate the dry air density and water-vapor density depends upon the variables used for

humidity and whether the temperature, pressure, and moisture variables exist.

The water vapor density is given by

e

pRT, (6.11)

where

p, = water vapor density (kg/m 3

),

e = vapor pressure (Pa),

R, = gas constant = 461.5 J/kg 'K,

T= temperature (°K),

and the dry air density can be estimated by

(p-e) (6.12)

Pd- RT

where

Pd = dry air density (kg/m3

),

p = total station pressure (Pa),

R = gas constant for dry air = 287.0 J/kg 'K.

The method used to calculate the vapor pressure e depends upon the moisture variable. If the moisture

variable is the dew point and precipitation is not occurring, then the vapor pressure is given by

e=e (), (6.13)

where

eS(Td) [mb] is the saturation vapor pressure at temperature Td (0 C).

According to Rogers and Yau (1989), the saturation vapor pressure is given by

e, (T) = e6.112 5 (T=6.l~eP(1.67 exp(17.67T T-24.) .(1) (6.14)

6-12
If the moisture is defined by the relative humidity and precipitation is not occurring, then the vapor

pressure is given by

RJIe (T)

e = , (6.15)

100

where

RH = relative humidity (percent),

e/(T) = Eq. (6.14).

If the moisture is given by the wet bulb temperature and precipitation is not occurring, then the vapor

pressure is given by

e= e,(T)-- [.- 00oo4(T- - Tw)] (6.16)

where

T,, is the wet bulb temperature [°C].

If precipitation is occurring, the air is assumed to be 95% saturated, so the vapor pressure is given by

e =: 0.95e, (T) ,(6.17)

where

e,(T) is given by Eq. (6.14).

During precipitation, Eq. (6.17) is usedregardless of the moisture variable.

If the temperature, pressure, or moisture variable is missing, the climatological values are used for the dry

air and water vapor density. If precipitation is occurring, the two densities will be based on Eqs. (6.12),

(6.14), and (6.17) with the temperature obtained from the climate file. If the climatological values are

missing, then the dry air density is assumed to be 1.2 kg/m3, and the water vapor density is assumed to be

zero.

6.4.5 Precipitation Rate

The RASCAL 3.0.5 atmospheric codes use precipitation rate to calculate the wet deposition rate for UJF 6

releases. When the precipitation type for a station is other than none or unknown, the meteorological data

processor estimates a precipitation rate (mm/h) for the station using the precipitation type and a

6-13
precipitation rate zone. Each site in the RASCAL database is assigned to one of three precipitation rate

zones. The precipitation zones, originally defined in Ramsdell, Simonen, and Burk (1994) are based on

annual precipitation. Zone 1 is for areas where the annual precipitation is less than 10 inches, zone 2 is for

areas where the annual precipitation is between 10 and 20 inches, and zone 3 is for areas where the annual

precipitation exceeds 20 inches. Most existing reactor sites are assigned to precipitation rate zone 3. Some

sites in the drier regions of the United States are assigned to zone 1. Precipitation rate zone assignments

are made in the climatology database and can be modified as appropirate.

The precipitation rates assigned by the meteorological data processor are listed in Table 6.4. These rates,

based on data collected in the Pacific northwest, should be conservative for most nuclear facilities in the

United States.

Table 6.4 Precipitation Rates as a Function of Precipitation Climate Zone

Precipitation Precipitation Rate (mm/h)

Type

Zone 1 Zone 2 Zone 3

Light rain 0.4 0.6 0.7

Medium rain 3.8 3.8 3.8

Heavy rain 3.8 3.8 8.5

Light snow 0.3 0.3 0.7

Medium snow 1.7 1.7 3.8

Heavy rain 1.7 1.7 3.8

6.5 Calculating Spatially Varying Meteorological Conditions

The puff model takes into account both spatial and temporal variations in the atmospheric conditions. The

meteorological data processor provides the gridded fields of the atmospheric stability class, the inverse

Monin-Obukhov length, the east-west (U) and north-south (V) components of the wind, the mixing height,

and the precipitation type and precipitation rate for each of the three puff model domains. The following

subsections describe the preparation of the fields from the station data.

6.5.1 Wind Fields

The puff model uses wind fields to calculate movement of puffs. These are fields of U (east-west) and V

(north-south) components of the wind vector. The wind fields are created from station wind data using a

I/r2 interpolation scheme, where r is the distance from the grid point to the station. This interpolation

scheme, which was used in earlier NRC codes such as MESOI (Ramsdell, Athey, and Glantz 1983) and

MESORAD (Scherpelz, et al. 1986; Ramsdell et al. 1988), is common in spatial interpolation of the wind

fields (Hanna, Briggs, and Hosker 1982).

6-14
6.5.2 Adjustment of Wind Fields for Topography

If the meteorological stations reporting data are well placed with respect to major topographic features,

the wind fields developed by interpolation will give reasonable puff trajectories. However, with one

meteorological station or a small number of stations, the wind fields may not properly reflect the effects of

topography. The meteorological data processor includes an option to use a simple one-layer model to

adjust wind fields for topography. Wind field adjustments are greatest for stable atmospheric conditions

(E, F, and G stability classes) and least for neutral conditions (stability class D). Wind fields are not

adjusted in unstable atmospheric conditions (stability classes A, B, and C). For this purpose only,

atmospheric stability at the release point (center of the model domain) is assumed to apply to the entire

domain.

The wind-field model in RASCAL 3.0.5 is a two-dimensional adaption of the wind fitting program

described by Ross et al. (1988) that is used in the NUATMOS and MATTHEW codes. In the RASCAL

3.0.5 implementation, wind fields created by interpolation are used as the starting point in the adjustment

process. The thickness of the mixing layer is calculated for each node in the model domain by computing

the difference between the top of the boundary layer and the terrain elevation. For those nodes where the

terrain rises above the top of the boundary layer, the program assumes that the boundary-layer thickness is

0.01 meter and sets the wind to zero. This technique is simple to implement and has proven effective at

generating flows that avoid obstacles such as mountain ridges.

The initial wind field is then adjusted using methods of variational calculus to produce a non-divergent

wind field in the boundary layer, subject to the constraint of minimum difference between the initial wind

field and the adjusted wind field. The procedure for adjusting the wind field involves solving Poisson's

equation. The code uses a nine-point Laplacian operator and a simultaneous relaxation technique to obtain

the solution.

The model has been tested and shows that the winds produced by the model flow around obstacles that are

well resolved by the grid. Obstacles having width of three grid points or greater are considered well

resolved. Smaller obstacles may or may not be resolved, depending on their shape and orientation relative

to the grid. For example, a ridge one grid point wide is well resolved if it runs in the x or y direction, but if

that same ridge is at 450 to the grid, it is not resolved.

The adjusted wind field is most accurate near stations and along trajectories that pass near stations. Wind

fields are less accurate elsewhere. Thus, it is desirable to have wind data near the release point and, if

possible, at downwind locations.

Topographic data are included in RASCAL 3.0.5 for all sites in the database. Sites not included in the

RASCAL database and the generic site do not have topographic data files. Therefore, the option of

modifying wind fields for topographic effects is not available for these sites.

6.5.3 Stability and Precipitation

The stability class and precipitation fields (precipitation type and precipitation rate) are based on data for

the closest meteorological station. Fields created in this manner include stability class, inverse MoninObukhov length, precipitation type, and precipitation rate. This procedure avoids averaging that would

minimize the effects of extreme stability or instability. It also provides maximum detail in treating isolated

precipitation events.

6-15
6.5.4 Mixing Height

Estimates of station mixing height are not considered particularly reliable. Therefore, the spatial variation

of the mixing height is modeled using two steps. The initial step is to create a mixing height field using

the mixing height for the closest station for each point in the field. If there is only one station the process

is terminated after this step. The second step is taken when there are two or more stations. In this step, the

mixing height at each point in the field is replaced by an average of the initial mixing height and the

mixing heights at 24 surrounding points. This second step smooths the mixing height field.

6.6 Calculating Meteorological Conditions at the Source

All of the RASCAL 3.0.5 atmospheric dispersion models require information about the wind speed, wind

direction, atmospheric stability, precipitation type, precipitation rate, mixing-layer depth, and temperature

at the source. If these meteorological data are available for the release point, which is considered to be at

the source, then those data are used. If no data are available for the release point, the wind speed, wind

direction, atmospheric stability, current weather, precipitation rate, and mixing-layer depth will be

estimated from the spatial meteorological data field. For the temperature, a default climatological value

will be used if it exists. The default climatological temperature varies by month and is obtained from the

climate file. If the climate file does not exists for the site, the temperature will be flagged as a missing

value.

6.7 References

Gifford, F. A. 1961. "Use of Routine Meteorological Observations for Estimating Atmospheric

Dispersion." Nuclear Safety, 2(4):47-51.

Golder, D. 1972. "Relations Among Stability Parameters in the Surface Layer." Boundary-Layer

Meteorology, 3(1):47-58, 1972.

Hanna, S. R., G. A. Briggs, and R. P. Hosker. 1982. Handbook on Atmospheric Diffusion. DOE/TIC11223, U.S. Department of Energy.

Monin, A. S., and A. M. Obukhov. 1954. "Basic Laws of Turbulent Mixing in the Ground Layer of the

Atmosphere." Trans. Geophys. Inst. Akad. Nauk, USSR, 151:163-87.

Panofsky, H. A., and J. A. Dutton. 1984. Atmospheric Turbulence. J. Wiley & Sons, New York.

Pasquill, F. 1961. "The Estimation of the Dispersion of Windborne Material." The Meteorological

Magazine, 90:33-49.

Paulson, C. A. 1970. "The Mathematical Representation of Wind Speed and Temperature Profiles in the

Unstable Atmospheric Surface Layer." J. of Applied Meteorology, 9:1884-89.

6-16
Ramsdell, Jr., J. V., G. F. Athey, and C. S. Glantz. 1983. MESOI Version 2.0: An Interactive Mesoscale

Lagrangian Puff Dispersion Model With Deposition and Decay. NUREG/CR-3344, U.S. Nuclear

Regulatory Commission.

Ramsdell, Jr., J. V., et al. 1988. The MESORAD Dose Assessment Model, Volume 2: Computer Code.

Vol. 2., NUREG/CR-4000, U.S. Nuclear Regulatory Commission.

Ramsdell, Jr., J. V., C. A. Simonen, and K. W. Burk. 1994. Regional Atmospheric Transport Code for

Hanford Emission Tracking (RATCHET). PNWD-2224 HEDR, Battelle, Pacific Northwest Laboratories,

Richland, Wash.

Rogers, R. R., and M. K. Yau. 1989. A Short Course in Cloud Physics. Pergamon Press, New York.

Ross, D. G. 1988. "Diagnostic Wind Field Modeling for Complex Terrain: Model Development and

Testing." J. of Applied Meteorology, 27:785-96.

Scherpelz, R. I., et al. 1986. The MESORAD Dose Assessment Model. Vol. 1., NUREG/CR-4000, U.S.

Nuclear Regulatory Commission.

Snedecor, G. W., and W. G. Cochran. 1980. Statistical Methods. 7th Edition, Iowa State University

Press, Ames, Iowa.

Stull, R. B. 1988. An Introduction to Boundary Layer Meteorology. Kluwer Academic Publishers,

Dordrecht, Netherlands.

Turner, D. B. 1964. "A Diffusion Model for an Urban Area." J. of Applied Meteorology, 3(l):83-91.

U.S. Environmental Protection Agency (EPA), 1995. PCRAMMET User's Guide, Office of Air Quality

Planning and Standards, Emissions, Monitoring, and Analysis Division, Research Triangle Park, N.C.

U.S. Environmental Protection Agency (EPA). 1999. PCRAMMET User's Guide. EPA-454/B-96-001

(Revised June 1999), Research Triangle Park, N.C.

U.S. Nuclear Regulator Commission (NRC). 1972. "Onsite Meteorological Programs." Regulatory Guide

1.23.

Zilitinkevich, S. S. 1972. "On the Determination of the Height of the Ekman Boundary Layer."

Boundary-Layer Meteorology, 3(2): 141-5.

6-17

7 Intermediate Phase Dose Calculations

This chapter describes the intermediate phase dose calculations in RASCAL 3.0.5. The intermediate phase

of a radiological emergency begins after the release has terminated. Dose calculations for the intermediate

phase are done to determine if the concentrations of radionuclides on the ground are likely to cause doses

to residents that would be in excess of the intermediate phase protective action guides established by the

U. S. Environmental Protection Agency (EPA 1992). Those protective action guides are 2 rem for the first

year, 0.5 rem for the second year, and 5 rem for the entire 50 years following the event.

In the Field Measurements to Dose module of RASCAL 3.0.5, the user enters the ground concentrations

of deposited radionuclides at a location. Then, RASCAL 3.0.5 calculates the intermediate phase doses for

the first year, the second year, and the cumulative dose over 50 years. The doses can be calculated with or

without a delay in reentry into the contaminated area. The reentry delay can be any number of days

between 0 to 730 days (2 years).

In addition, RASCAL 3.0.5 calculates "derived response levels" or "DRLs." A derived response level is a

measurable quantity that indicates that the deposited activity could result in an intermediate phase dose

equal to one of the intermediate phase protective action guides. One type of DRL is the closed window

(gamma) dose rate in mR/hour equal to the first, second, or 50 year intermediate phase PAG. The other

DRL is the ground concentration of a marker radionuclide equivalent to a PAG.

The DRLs are calculated for reentry delay times ranging from 0 days to 100 days. When significant

quantities of short-lived radionuclides are present, the DRLs will be different depending on how long after

the release the measurement is made. In addition, the assumed reentry delay will change the DRLs.

7.1 Intermediate Phase Doses

The intermediate phase doses calculated by RASCAL are the sums of three components: external dose

from groundshine, internal dose from the inhalation of resuspended particles, and internal dose from the

inadvertent ingestion of surface contamination.

Inadvertent ingestion is not included as a pathway in the EPA Protective Action Guide manual nor in the

assessments done by the Federal Radiological Monitoring and Assessment Center (FRMAC). Therefore,

the default intake for inadvertent ingestion in RASCAL is zero. However, the RASCAL user can include

inadvertent ingestion by selecting an intake larger than zero.

7.1.1 Groundshine Doses

RASCAL calculates groundshine doses Dgs(T) from the surface concentration for occupancy time intervals

T. The calculation is

Dg, (7) = GRF x[Cg, x g(=)] (7.1)

7-1
where

Dg/(T) = groundshine dose (rem) for occupancy time interval T,

GRF = ground roughness factor with a default value of 0.82 (dimensionless),

Cgi = initial (t = 0) ground surface concentration (Ci/m2) of radionuclide i,

DCPgsi(T) = intermediate phase groundshine dose conversion parameter [rem/(Ci/m 2)] for

radionuclide i and occupancy time interval T.

The occupancy time intervals T over which groundshine dose Dg,(T) is calculated correspond to the time

intervals for the intermediate phase in the EPA Protective Action Guide manual, specifically, for the case

of no reentry delay: zero to one year, one year to two years, and zero to 50 years. If the RASCAL user

specifies a reentry delay, the occupancy time interval then starts at the specified time of reentry.

In previous versions of RASCAL, the ground roughness factor GRF was 0.7. However, more recent

measurements (Anspaugh et al. 2002), based in large part on Chernobyl data, suggest that 0.82 is a more

realistic value. FRMAC has also recently adopted a GRF of 0.82.

The intermediate phase groundshine dose conversion parameters DCPgSi(T) are calculated as:

N

n=O

where

Eegn(T) = effective time of exposure to the parent nuclide (n = 0) or daughter (n 2! 1) for occupancy

time interval T accounting for decay, ingrowth, and weathering [s]

EDCý = effective dose rate coefficient for exposure to contaminated ground surface based on Table

111.3 of FGR 12 [Rem / (Ci s M2)]

The summation from n = 0 to n = N is over the parent and all daughters.

The effective dose rate coefficient for exposure to contaminated ground surface EDCn is equal to the

effective dose rate coefficient in Federal Guidance Report (FGR) No. 12 (Eckerman and Ryman 1993)

except when a nuclide has a short-lived daughter. For about 40 radionuclides with short-lived daughters,

the parent-daughter combination is treated as a single nuclide with the parent's half-life. The effective

dose rate coefficients EDC, assigned to the combination of the parent and implicit daughter is the sum of

the parent's effective dose rate coefficient from FGR 12 plus the daughter's effective dose rate coefficient

(corrected for branching ratio). The treatment of these combinations of parent plus implicit daughter is

discussed in more detail in Section 7.2.

The intermediate phase effective exposure duration Eegn(T) is for a specific exposure interval T and

accounts for the radiological decay of the parent radionuclide and the ingrowth and decay of daughter

radionuclides on the ground during the interval. It also accounts for weathering during the exposure

interval.

7-2
The groundshine effective exposure duration Eegn(T) for each radionuclide n is

Eeg,(T) = Ao-' JoA(t)W,(t)dt (7.3)

where

Ao = initial activity of the parent (Ci)

An(t) = activity of the radionuclide n (Ci)

W,(t) = groundshine weathering function (dimensionless)

The activity of the parent radionuclide as a function of time is given by the usual exponential relationship

A(t) = Ao exp(- b) (7.4)

where

Ao = initial activity, and

, = decay constant (s').

Activities for daughters are given by the Bateman equations (Benedict et al. 1987) modified to be

appropriate for activity rather than atoms (Strenge 1997) and to include branching fractions. These

equations are described in Section 7.2.

The groundshine weathering function W,(t) (Anspaugh et al. 2002), based in large part on Chernobyl data,

is a sum of two exponential terms

WsV(t)= Cle-a + C2e-Pt (7.5)

where

t = the time after deposition in days.

The first term describes the weathering during the first few years after deposition and the second term

describes long term weathering. The values of C, and C2 are 0.4 and 0.6, respectively, and the values of a

andf are 1.26x 10- d', and 3.8x 10-5 d', respectively. FRMAC has also recently adopted this weathering

function.

When Equations (7.4) and (7.5) are substituted into Equation (7.3), the resulting integral can be solved in

closed form. Equation (7.3) can also be integrated for daughters. These solutions, which are not shown

here, are used in intermediate phase groundshine dose calculations.

7-3
7.1.2 Inadvertent Ingestion Doses

Calculation of inadvertent ingestion doses is similar to the calculation of groundshine doses. It is as

follows

Ding(T) = ING x [Cgi x DCPing(T)] (7.6)

where

Dig(T) = inadvertent ingestion dose (rem) for occupancy time interval T,

ING = inadvertent ingestion rate (m2

/day),

Cgi = ground surface concentration (Ci/m2 ) of radionuclide i

DCPingi(T) = intermediate phase inadvertent ingestion dose conversion

parameter [rem /(Ci day`)]

The intermediate phase inadvertent ingestion dose conversion parameter DCPingi(T) is calculated

essentially the same as for groundshine in Equation 7.2.

N

DCPi,,gi (T) = [Eeingn (T) x EDCn] (7.7)

n=O.

The effective dose rate coefficients EDC, for inadvertent ingestion are based on Table 2.2 of Federal

Guidance Report No. 11 (Eckerman et a] 1988), and may include implicit daughters as was discussed in

Section 7.1.1 for groundshine doses.

The effective exposure duration Ee ingn(T) includes decay, ingrowth and weathering in the same manner as

described for groundshine above. The inadvertent ingestion weathering function used in RASCAL is the

same as that used for groundshine. The same weathering factor is used because no data could be found for

weathering applied to the inadvertent ingestion pathway. This approach is probably conservative because

removable radioactive materials on the most commonly touched surfaces are likely to be depleted quickly.

For reasonable inadvertent ingestion rates ING (zero to 10- m2/d), intermediate phase inadvertent

ingestion doses are generally small compared to groundshine doses.

7.1.3 Inhalation Doses

Intermediate phase inhalation doses are generally smaller than either intermediate phase groundshine

doses or inadvertent ingestion doses. The doses are calculated assuming that activity on the ground is

resuspended and then inhaled. The calculation is

D4Mlh(T= V0 x R,, [CX x DCP~lL hi M (7.8)

i=1I

where

Dilh(T) = inhalation dose (rem) for occupancy time interval T,

7-4
Vb = breathing rate (m3/s),

R= initial resuspension factor (rn')

Cgj= ground surface concentration (Ci/m2) of radionuclide i

DCPin hA(T) = inhalation intermediate phase dose conversion parameter [rem-s/Ci].

The default breathing rate Vb is 2.67x 10.4 m3/s, which represents a long term breathing rate that includes

both waking and sleeping breathing rates.

The inhalation intermediate phase dose conversion parameter DCFihi(T) includes decay and ingrowth and

the time-dependent (Weathering) portion of the resuspension function.

For inhalation, the intermediate phase dose conversion parameters include decay, ingrowth, and

resuspension. These dose conversion parameters are calculated as

where

N

DCPfhi (T) = -[Eea.(T) x ECF] (7.9)

n=O

DCPifh,(T) = intermediate phase dose conversion parameter for the parent radionuclide

Eean(T) = effective exposure duration to airborne activity of the parent nuclide (n = 0) or daughters

(nŽ 1) during T accounting for decay, ingrowth, and resuspension

ECF. = effective dose factor based on Table 2.1 in FGR 11 including implicit daughters as previously

described.

The summation is over the parent and all daughters.

The effective exposure duration to airborne activity, Eea/(T) for each radionuclide (parent and daughters)

is

Eean(T) = A,, IoA (t)R,(t)dt (7.10)

where

A/(t) = activity of the radionuclide

R,(t) = time-dependent resuspension factor

RASCAL implements the resuspension factor model in NCRP Report No. 129 (NCRP 1999). For the first

day, the initial resuspension factor is constant with a default value of 106 m'. Beyond 1,000 days, the

resuspension factor is also constant with a value of 10' m'. For days I through 1,000, the resuspension

factor R,(t) is modeled as

7-5
R, (t) = Ro / t (7.11)

where

R,, =initial resuspension factor with a default value of I 06/m

t = time in days

When expressions for the activity and the resuspension factor are substituted into Equation 7.11, the

effective exposure cannot be calculated by closed form integration. In RASCAL, the effective exposure

duration for intermediate phase inhalation doses is estimated using numerical integration.

7.1.4 Precalculated Intermediate Phase Dose Conversion Parameters

The RASCAL database contains precalculated dose conversion parameters for groundshine, inadvertent

ingestion, and inhalation for the first 30 days, the first year, the second year, and 50 years for 219

radionuclides. The precalculated dose conversion parameters reduce computing time and facilitate

comparison with hand calculations.

7.1.5 Dose Conversion Parameter Calculations with Delayed Reentry

Dose conversion parameters for delayed reentry are calculated as the difference between the factor

without delayed reentry and the factor for the delay period. For example, the first year dose conversion

parameter for a 30-day delay in reentry is calculated as

DCP(30d to ly) = DCP(O to ly) - DCP(O to 30d) (7.12)

where

DCP(30 d to I y) = dose conversion parameter over the interval from 30 days to 1 year

DCP(O to 1 y) = dose conversion parameter for the first year

DCP(O to 30 d) = dose conversion parameter for the first 30 days

Intermediate phase dose conversion parameters for the first year D(O to I y), the second year D(J to 2 y),

and 50 years D(O to 50 y) have been precalculated. Intermediate phase dose conversion parameters for the

delay period are calculated as needed, after the delay period is defined.

7-6
7.2 Decay and Ingrowth

In its calculation of intermediate phase doses, RASCAL accounts for decay and ingrowth using simplified

decay chains. In these chains, short-lived daughters are treated implicitly assuming that they are in

equilibrium with long-lived parents. Table 7.1 lists the decay chains that involve implicit daughters along

with the implicit daughter and their branching fraction. Effective dose rate coefficients for the implicit

daughters are added to the effective dose rate coefficient for the parent after accounting for branching

fractions.

Table 7.1 Radionuclides with Implicit Daughters Assumed in Intermediate Phase Dose

Calculations.

Parent Implicit Daughters (Branching Parent Implicit Daughters (Branching

Fractions) Fractions)

Zn-69m

Ge-68

Br-83

Sr-91

Zn-69 (0.9997)

Ga-68 (1.0)

Kr-83m (1.0)

Y-91m (0.578)

1

1

Zr-93 Nb-93m (1.0)

Zr-97 Nb-97m (0.947), Nb-97 (0.053)

Mo-99 Tc-99m (0.876)

Ru-103 Rh-103m (0.99974)

Ru-106 Rh-106 (1.0)

Pd-103 Rh-103m (0.99974)

%g-110m Ag-110 (0.0133)

Cd-115 In-115m (1.0)

In-114m In-114 (0.957)

Sn-113 In-113m (1.0)

Sn-126 Sb-126m (1.0)

Fe-129m Te-129 (0.65)

Te-131m Te-131 (0.222)

Te-132 1-132 (1.0)

Fe-133m Te-133 (0.13)

Te-134 1-134 (1.0)

1-135 Xe-135m (0.154)

Cs-137 Ba-137m (0.947)

Ce-144 Pr-144m (0.0178), Pr-144 (1.0)

Pb-211 Bi-211 (1.0), Po-211 (0.0027),

TI-207 (0.9973)

Pb-212 Bi-212 (1.0), Po-212 (0.6407),

TI-208 (0.3593)

Bi-212 Po-212 (0.6407), TI-208 (0.3593)

Rn-220 Po-216 (1.0)

Rn-222 Po-218 (1.0), Pb-214 (1.0), Bi-214 (1.0),

Po-214 (0.9998)

Ra-223 Rn-219 (1.0), Po-215 (1.0), Pb-211 (1.0),

Bi-211 (1.0), Po-211 (0.0028),

TI-207 (0.9972)

Ra-224 Rn-220 (1.0), Po-216 (1.0)

Ra-226 Rn-222 (1.0)

Ra-228 Ac-228 (1.0)

Ac-225 Fr-221 (1.0), At-217 (1.0), Bi-213 (1.0),

Po-213(0.9784), TI-209 (0.0216),

Pb-209 (1.0)

Ac-227 Fr-223 (0.0138)

Th-234 Pa-234m (0.998), Pa-234 (0.002)

U-240 Np-240m (1.0)

,m-242m Am-242 (0.9952), Np-238 (0.0048)

Am-243 Np-239 (1.0)

Cm-247 Pu-243 (1.0)

Es-254 Bk-250 (1.0)

/

7-7
RASCAL also truncates decay chains for deposited radionuclides in intermediate phase dose calculations

according to the following rules. Daughters that are noble gases are truncated from the chain because it is

assumed that the noble gas will become airborne and be carried away. The exception is when the noble

gas is short-lived so that it is included implicitly with the parent nuclide. For example, Xe-135m (half-life

of 15 minutes) is included implicitly with its parent 1-135, but the chain is truncated at that point because

the next nuclide in the chain, Xe-135, is a noble gas with a relatively long half-life ( 9 hours).

Decay chains are also usually truncated at the first very long-lived daughter in the chain (long relative to

the 50-year intermediate phase period) because it is assumed that the ingrowth of the daughter will not

cause sufficient concentrations of the daughter to contribute significantly to dose relative to the parent.

The exception is that Np-239 decay does include Pu-239 as a member of the chain because of the potential

dose importance of decay. Most of the simplification in the RASCAL decay chains occurs for high atomic

number parents (Rn and higher).

Table 7.2 lists the decay chains involving more than one explicit radionuclide. Radionuclides having

implicit daughters are shown in bold. All other radionuclides are assumed to decay to a stable isotope.

With these simplifications, no intermediate phase decay chain includes more than two generations of

explicit daughters. With branching, those two generations of daughters include up to three explicit

daughters in a few cases.

7-8
Table 7.2 RASCAL Intermediate Phase Decay Chains

Zn-69m1 -> stable

Ge-68 -> stable

Br-83 -> stable

Rb-89 -> Sr-89 -> stable

Sr-90 -> Y-90 -> stable

Sr-91 -> Y-91 -> stable

Y-91m -> Y-91 -> stable

Y-93 -> Zr-93 -> stable

Zr-93 -> stable

Zr-95-> Nb-95m -> Nb-95 -> stable

Zr-97-> stable

Nb-95m -> Nb-95 -> stable

Nb-97m -> Nb-97 -> stable

Mo-93 -> Nb-93m -> stable

Mo-99 -> Tc-99 -> stable

Tc-99m -> Tc-99 -> stable

Ru-103 -> stable

Ru-105 -> Rh-105 -> stable

Ru-106 -> stable

Pd-103 -> stable

Ag-110m -> stable

Cd-115 -> stable

In-114m -> stable

Sn-113 -> stable

Sn-121m -> Sn-121 -> stable

Sn-125 -> Sb-125 -> Te-125m -> stable

Sn-126-> stable

Sb-125 -> Te-125m -> stable

Sb-126m -> Sb-1 26-> stable

Sb-127 -> Te-127m -> Te-127 -> stable

Te-127m -> Te-127 -> stable

Te-129m -> 1-129 -> stable

Te-129 -> 1-129 -> stable

Te-131 m -> 1-131 -> stable

Te-131 -> 1-131 -> stable

Te-132 -> stable

Te-133m -> 1-133 -> stable

Te-133 -> 1-133 -> stable

Te-134 -> stable

1-135 -> stable

Cs-134m -> Cs-134 -> stable

Cs-137 -> stable

Ba-140-> La-140-> stable

Ba-141 -> La-141 -> Ce-141 -> stable

Ba-142-> La-142-> stable

La-141 -> Ce-141 -> stable

Ce-143 -> Pr-143 -> stable

Ce-144-> stable

Nd-147-> Pm-147 -> stable

Pm-148m -> Pm-148 -> stable

Pm-151 -> Sm-1 51 -> stable

W-187 -> Re-1 87-> stable

Pb-210 -> Bi-210 -> Po-210-> stable

Pb-211 -> stable

Pb-212 -> stable

Bi-210-> Po-210-> stable

Bi-212-> stable

Rn-220-> stable

Rn-222-> stable

Ra-223-> stable

Ra-224 -> Pb-212 -> stable

Ra-225-> Ac-225 -> stable

Ra-226-> stable

Ra-228 -> Th-228 -> Ra-224 -> stable

Ac-225-> stable

Ac-227 -> Th-227 -> Ra-223 -> stable

Th-227 -> Ra-223 -> stable

Th-228 -> Ra-224 -> Pb-212 -> stable

Th-229-> stable

Th-230 -> Ra-226 -> stable

Th-231 -> Pa-231-> stable

Th-232 -> Ra-228 -> Th-228 -> stable

Th-234-> U-234 -> stable

Pa-233-> U-233 -> Th-229 -> stable

U-232 -> Th-228 -> Ra-224 -> stable

U-233 -> Th-229 -> stable

U-234 -> Th-230 -> stable

U-235 -> Pa-231 -> stable

U-237 -> Np-237 -> Pa-233 -> stable

U-238 -> Th-234 -> U-234 -> stable

U-240 -> stable

Np-237 -> Pa-233 -> U-233 -> stable

Np-239 -> Pu-239 -> stable

Pu-237 -> Np-237 -> stable

Pu-238-> U-234 -> stable

Pu-241 -> Am-241-> stable

Pu-244 -> Pu-240 -> stable

Am-242m -> Cm-242 -> Pu-238-> stable (0.823)2

.-> Pu-242 -> stable (0.172)2

Am-242 -> Cm-242 -> Pu-238 -> stable

Am-243 -> Pu-239 -> stable

Cm-242 -> Pu-238 -> stable

Cm-243 -> Am-243 -> stable (0.0024)2

-> Pu-239 -> stable (0.9976)2

Cm-244 -> Pu-240 -> stable

Cm-245 -> Pu-241 -> Am-241 -> stable

Cm-247 -> Am-243 -> Pu-239 -> stable

Es-254 -> Cf-250 -> Cm-246 -> stable

' Bold indicates implicit daughters included as shown

in Table 7.1. 2 Branching fraction

7-9
The following equations describe the activity of the parent and explicit daughters as a function of time.

Given the measured activity of a radionuclide at time zero, the activities of the radionuclide and daughters,

if any, following the measurement are given by the Bateman Equations (e.g., Benedict et al. 1987),

modified to give activities (disintegrations/time) rather than number of atoms (Strenge 1997). The

Bateman Equation for the parent radionuclide is

AP(t) = Ap(O)e-A'l (7.13)

where

AP(t) = activity of the parent at time t following the measurement,

Ap(O) = measured activity, and

Ap = decay constant of the parent.

The activity of first-generation explicit daughter radionuclides, assuming none of the daughter is present

initially, is

Ad,(,) = AP(0) 2 --Ad (eA - e-Ad'I) (7.14)

where

AdN(t) = activity of the first-generation daughter at time t,

fd= fraction of disintegrations of the parent that yield the daughter

2dl = decay constant for the daughter.

This relationship applies to each first-generation daughter of the parent.

Although there may be more than one second-generation daughter for a parent radionuclide, RASCAL

assumes simplified decay chains that include, at most, a single second-generation daughter. The activity of

second-generation daughter radionuclides, assuming none of the preceding first generation daughter and

none second-generation daughter are present initially, is

Ad 2 (t) = Ap(O)x fd, Adlf,2 

2 d2 x

e-Ap e- Ad, e--Ad2 ) (7.15)

where

Ad2(t) = activity of the second-generation daughter at time t following the measurement,

7-10
fd2 = fraction of first-generation daughter disintegrations that yield the second generation daughter,

and

2 d2 = decay constant for the second-generation daughter.

In the above equations, the time-dependent activities of the parent and daughters are functions of the

initial (measured) activity of the parent.

7.3 Derived Response Levels (DRLs)

A derived response level is a measurable quantity that indicates that the deposited activity could result in

an intermediate phase dose equal to one of the intermediate phase protective action guides. One type of

DRL is the closed window (gamma) dose rate in mR/hour equal to the first, second, or 50 year

intermediate phase PAG. The other DRL is the ground concentration of a marker radionuclide equivalent

to a PAG.

RASCAL computes two sets of DRLs - one set for use with measured exposure rates (meter readings), and

the other for use with measurement of the surface contamination of a marker radionuclide. In either case,

the DRLs are based on an assumed mixture of radionuclides on the surface. In RASCAL, DRLs are

computed for first year, second year, and 50 years for a range of times from 0 to 100 days since the initial

measurement.

7.3.1 Exposure Rate Derived Response Levels

The exposure rate derived response level (DRL) is the exposure rate that will occur when the ground

concentration present will cause a dose to an inhabitant that is equal to the intermediate phase protective

action guide. Thus, an exposure rate measurement survey instrument can be used to identify areas where

doses might exceed the intermediate phase protective action guides.

Exposure rate DRLs are calculated using equations developed from methods described in the FRMAC

Manual (SNL 2003). However, the RASCAL DRLs include an inadvertent ingestion component that is not

included in the FRMAC computational method. The basic equation used in RASCAL for exposure rate

DRLs is

1.429 x (C x GRFox ECFoj x 3600.)

DRLexp =PAGx n (7.16)

(f iý fx DCP~) + (uING x DC~i~gi) + (R,, x Vb x DCJpflhi]

where

DRLe,p = derived response level for exposure. (mR/hr)

PAG = EPA protective action guide. (mrem)

1.429 = conversion factor from mrem to mR from EPA 1992, page 7-11

7-11
ECFegi = exposure rate dose coefficient for contaminated soil from Table 111.3 of FGR No. 12

(Eckerman and Ryman 1993)

3600 s/hr converts the exposure rate to an hourly rate.

The occupancy time interval for the intermediate phase dose conversion parameters are usually for the

occupancy time intervals established for the EPA protective action guides for the intermediate phase.

7.3.2 Marker Nuclide Derived Response Levels

In some instances it may be difficult to use the exposure rate DRIL to identify areas where doses might

exceed the protective action guides. Examples are when the exposure rate is near background levels or

when there are no gamma-emitting radionuclides in the mix. In those instances, it may be easier to

measure the surface concentration of a particular marker radionuclide rather than the exposure rate.

The marker nuclide DRL is the concentration of that nuclide expected to cause doses to inhabitants equal

to the protective action guides. Following the method in the FRMAC Manual (SNL 2003), RASCAL

calculates marker DRLs as follows

DRLiark = PAG x Cgk

SCýj [(GRF x DCP ~+ (ING x DCFPng) + (R,,, x VX x (7.17),

where

Cgk ý ground concentration of the marker radionuclide (mCi/rn2 )

As with the exposure rate DRLs, the RASCAL calculation includes an optional inadvertent ingestion

component not included in the FRMAC DRL calculation.

7.4 References

Anspaugh, L. R., S. L. Simon, K. I. Gordeev, I. A. Likhtarev, R. M. Maxwell, and S. M. Shinkarev. 2002.

"Movement of Radionuclides in Terrestrial Ecosystems by Physical Processes. Health Physics 82(5):669-

679.

Benedict, M., T. H. Pigford, and H. W. Levi. 1987. Nuclear Chemical Engineering, 2 nd Ed. McGrawHill, New York.

Eckerman, K.F., A. B. Wobarst, and A.C. B.Richardson. 1988. Limiting Values of Radionuclide Intake

and Air Concentration and Dose Conversion Factors for Inhalation, Submersion, and Ingestion. Federal

Guidance Report No. 11. EPA-520/11-88-020, U.S. Environmental Protection Agency.

Eckerman, K. F. and J. C. Ryman. 1993. External Exposure to Radionuclides in Air Water, and Soil.

Federal Guidance Report No. 12. EPA-402-R-93-081, U.S. Environmental Protection Agency.

7-12
National Council on Radiation Protection and Measurements (NCRP). 1999. Recommnended Screening

Limits for Contaminated Surface Soil and Review of Factors Relevant to Site-Specific Studies. NRCP

Report No. 129. National Council on Radiation Protection and Measurements, Bethesda, Maryland.

Sandia National Laboratories (SNL). 2003. FRMAC Assessment Manual, Volume 1 Methods.

SAND2003-107P, Sandia National Laboratories, Albuquerque, New Mexico.

Strenge, D. L. 1997. "A General Algorithm for Radioactive Decay With Branching and Loss from a

Medium," Health Physics 73:953-957.

U.S. Environmental Protection Agency. 1992. Manual of Protective Action Guides and Protective

Actions for Nuclear Incidents. EPA 400-R-92-001.

7-13

NRC FORM 335 U.S. NUCLEAR REGULATORY COMMISSION 1. REPORT NUMBER

(9-2004) (Assigned by NRC, Add Vol., Supp., Rev.,

NRCMD 3.7 and Addendum Numbers, if any.)

BIBLIOGRAPHIC DATA SHEET

(See instructions on the reverse) NUREG-1887

2. TITLE AND SUBTITLE 3. DATE REPORT PUBLISHED

RASCAL 3.0.5: Description of Models and Methods MONTH YEAR

August 2007

4, FIN OR GRANT NUMBER

Ri110

5. AUTHOR(S) 6. TYPE OF REPORT

Stephen A. McGuire

James Van Ramsdell, Pacific Northwest Laboratories Final technical report

George F. Athey, Athey Consulting 7. PERIOD COVERED (Inclusive Dates)

NA

8. PERFORMING ORGANIZATION - NAME AND ADDRESS (It NRC. provide Division. Office or Region, U.S. Nuclear Regulatory Commission, and mailing address. if contractor,

provide name and mailing address.)

Divsion of Preparedness and Response

Office of Nuclear Security and Incident Response

U. S. Nuclear Regulatory Commission

Washington, DC 20555

9. SPONSORING ORGANIZATION - NAME AND ADDRESS (If NRC, type 'Same as above", if contractor, provide NRC Division. Office or Region, U.S. Nuclear Regulatory Commission.

and mailing address.)

same as above

10. SUPPLEMENTARY NOTES

Supercedes NUREG-1741.

11. ABSTRACT (200 words or less)

The code currently used by NRC's emergency operations center for making dose projections for radiological emergencies is

RASCAL version 3.0.5 (Radiological Assessment System for Consequence AnaLysis). This code was developed by NRC. The

first version was created about 20 years ago. Since then the code has been undergoing continual improvement to expand its

capabilities and to update the models used in its calculations. This report describes the models and calculational methods

used in RASCAL 3.0.5. This report updates and supercedes the information in NUREG-1741, "RASCAL 3.0: Description of

Models and Methods," 2001.

RASCAL 3.0.5 evaluates releases from: nuclear power plants, spent fuel storage pools and casks, fuel cycle facilities, and

radioactive material handling facilities.

12. KEY WORDS/DESCRIPTORS (List words or phrases that will assist researchers in locating the report.) 13. AVAILABILITY STATEMENT

RASCAL, emergency response, dose assessment, dose projections, plume modeling unlimited 14. SECURITY CLASSIFICATION

(This Page)

unclassified

(This Report)

unclassified

15. NUMBER OF PAGES

16. PRICE

NRC FORM 335 (9-2004) PRINTED ON RECYCLED PAPER
Federal Recycling Program

UNITED STATES

NUCLEAR REGULATORY COMMISSION

WASHINGTON, DC 20555-0001

OFFICIAL BUSINESS