Radionuclide Pathways

4/22/2010
Introduction
Introduction

GeneralRadionuclides released into the environment by a facility, as well as the radiation emitted by that facilin a dose to the public.The NRC limits on the exposure to the public are fo10 CFR 20: § 20.1301 Dose limits for individual members of the p(a) Each licensee shall conduct operations so that—(1) The total effective dose equivalent to individual memthe public from the licensed operation does not exceed 0mSv) in a year, exclusive of the dose contributions from background radiation . . .
Introduction

GeneralMeasurements must be made “as appropriate” in tenvironment and effluents:§ 20.1302 Compliance with dose limits for individual of the public.(a) The licensee shall make or cause to be made, as apprsurveys of radiation levels in unrestricted and controlled radioactive materials in effluents released to unrestricted controlled areas to demonstrate compliance with the dosfor individual members of the public in § 20.1301.
Introduction

GeneralThere are different ways to show compliance. One determine the highest TEDE to a member of the pumeasurement or calculation: § 20.1302 Compliance with dose limits for individual of the public.(b) A licensee shall show compliance with the annual do20.1301 by—(1) Demonstrating by measurement or calculation that theffective dose equivalent to the individual likely to receihighest dose from the licensed operation does not exceed annual dose limit; or
Introduction

GeneralAnother method to show compliance is to compare concentrations in the effluent at the facility boundain Appendix B: (2) Demonstrating that—(i)The annual average concentrations of radioactive mareleased in gaseous and liquid effluents at the boundary unrestricted area do not exceed the values specified in tappendix B to part 20; and(ii) If an individual were continuously present in an unrarea, the dose from external sources would not exceed 0(0.02 mSv) in an hour and 0.05 rem (0.5 mSv) in a year
Introduction

General
Introduction

GeneralWhen demonstrating compliance by determining thlikely dose to an individual, one or both of the followbe done. Each has advantages and disadvantages

1. Collection and/or analysis of environmental m

the boundary of the unrestricted area and/or residence of the individual expected to receivhighest dose. (environmental monitoring/surv

2. Pathways analysis

(mathematical calculation)
Introduction

General1. Collection and/or Analysis of Environmental MeAdvantages:• If the radionuclides are at high enough levels to 

measured, a direct measurement eliminates the degree of uncertainty associated with a mathempathways analysis. 

In extreme cases, the radionuclide concentration 

exposed individual (s) might be measured direct131 in thyroid), or the dose might be estimated bchromosomal analysis.
Introduction

General1. Collection and/or Analysis of Environmental MeDisadvantages:• Radionuclide concentrations in the air, water, so

food samples might be too low to be measured. 

• The concentrations exhibit considerable variatio

one location to another. Even if the radioactive mcould be measured, an excessively large numbesamples might have to be collected to permit a reasonable estimate of the dose. 
Introduction

General2. Pathways AnalysisAdvantages:• A pathways analysis can predict concentrations 

environment that are below our ability to measucollected sample.

• The analysis can predict the concentration in a

not just a few locations.
Introduction

General2. Pathways AnalysisDisadvantages:• There can be substantial uncertainty associated 

mathematical analysis even when the source term known precisely:- There are uncertainties in how closely the math

equations reflect the actual radionuclide pathwa

- There are uncertainties in the input parameters 

equations.
Introduction

Purpose of the PresentationThe purpose of this presentation is to provide sominto how a pathways analysis might be performed. words, to show how mathematical models can be uestimate the concentration of radionuclides in the environment and thereby calculate the dose to the environment and thereby calculate the dose to the 

The methodology of Regulatory Guide 1.109 will bconsidered and some example calculations will be “by hand.”In the “real world”, these calculations would be percomputers.
Environmental Inventory
Environmental Inventory

GeneralThe environmental inventory is the total activity of radionuclide in the environment as a result of releaa facility (e.g., Bq of Cs-137).Although it doesn’t assist in estimating the dose to Although it doesn t assist in estimating the dose to 

public, the environmental inventory concept can prinsight into the levels of radionuclides in the enviro
Environmental Inventory

GeneralThe environmental inventory is calculated as follow

A is the environmental inventory (e.g., Bq)Q is the release rate (e.g., Bq/s)λ is the decay constant of the radionuclide (e.g., 

t is the duration of the release (e.g., s)
Environmental Inventory

Example 1.A facility releases 0.01 GBq/day of I-131. Calculate the environmental inventory after 365 dacontinuous release.The decay constant for I-131 is:
Environmental Inventory

Example 1.The half life of I-131 is sufficiently short that the eq(maximum) activity has been achieved. Extending duration of the release beyond 365 days will not inthe environmental inventory.
Environmental Inventory

Example 2.A facility releases 0.01 GBq/day of Cs-137. Calculaenvironmental inventory after 365 days of continuorelease.The decay constant for Cs

-137 is:

The decay constant for Cs 137 is:
Environmental Inventory

Example 2.Even though they have the same release rates (GBduration of release, the Cs-137 environmental invemuch greater than that of I-131. Furthermore, the Cinventory continues to increase for approximately 1before reaching its maximum activity.
Conceptual Site Model
Conceptual Site Model

GeneralThe conceptual site model (CSM) is a “picture” of thProducing this picture involves identifying the:

• Source term

• Exposed population of concern

Exposed population of concern

• Exposure pathways

Whether or not it is considered part of the CSM, site

information will eventually be needed about wind dirwind speed, atmospheric stability, soil characteristicsurface and groundwater flow, etc.
Conceptual Site Model

GeneralThe conceptual site model can vary dramatically frotype of facility to another, e.g.: nuclear power pla

acceleratorlow level waste si

uranium recovery uranium recovery 

decommissioned 
Conceptual Site Model

Source Term – Nuclear Power PlantThe primary source terms are the release rates (e.gthe radionuclides in the gaseous and liquid effluentsThese release rates are usually known fairly accurabecause the effluents are monitored closelybecause the effluents are monitored closely.

The source term might include more than a dozen fiproducts and activation products.
Conceptual Site Model

Source Term – AcceleratorThe primary source term might be the release rate olived radionuclides (e.g., C-11, N-13, O-15) in the stgases. Another important source term might be neutron anAnother important source term might be neutron an

shine, i.e., exposure of the public to scattered neutrogamma rays from the facility.These release rates are usually known fairly accurato monitoring. 
Conceptual Site Model

Source Term – Low Level Waste SiteThe primary source term might be the total activities buried radionuclides. Since there are no stack or liquid effluent discharge monitor considerable uncertainty can exist regardinmonitor, considerable uncertainty can exist regardin

at which the material is released to the environmentRadionuclides get into the air via evaporation and suspension. The buried material can get into the grovia leaching.
Conceptual Site Model

Source Term – Uranium Recovery FacilityThe source term would typically be the activity of the processed each year. If there are mill tailings impouthe concentration in the impoundments would be neRadon releases are a major concern at both convenuranium mills and in-situ leach facilities. Surface runoff into offsite lakes or streams and the rairborne particulate uranium and is much more of aconventional mills than in-situ operationsContamination of groundwater is a concern at all urarecovery facilities.These releases can be difficult to quantify. 
Conceptual Site Model

Source Term – Decommissioned PropertyThe principal source term is usually the concentratioradionuclides in the surface soil.
Conceptual Site Model

Exposed Population of ConcernIn most cases, the population of concern is the maxexposed individual. This is usually the individual livinnearest downwind residence. In the case of decommproperty, it would likely be a residential farmer living contaminated landcontaminated land.

In other cases, the concern might be the dose to the downwind community.
Conceptual Site Model

Exposure Pathways - Nuclear Power PlantExposure pathways are often divided into those of t

• aquatic ecosystem• terrestrial ecosystem

The aquatic and terrestrial exposure pathways on thtwo slides are identified in Regulatory Guide 1.109.Other significant pathways identified at a facility muaccounted for in the dose calculations.
Conceptual Site Model

Exposure Pathways - Nuclear Power PlantImportant pathways for the aquatic ecosystem:

Potable Water: water 

 man

Aquatic Foods: water

 fish

 man

Aquatic Foods: water fish man

Shoreline Deposits: water 

 sediment 

 shore

Crops irrigated with contaminated water:

water 

 crops 

 man

soil
Conceptual Site Model

Exposure Pathways - Nuclear Power PlantImportant pathways for the terrestrial ecosystem:

Submersion: air 

 man (noble gases only

Inhalation: air 

 man

External Gamma: air

 ground

 man

Food: air

 vegetables/produce

 

soil

air

 forage 

 milk

 man

soil

air

 forage 

 meat

 man

soil
Conceptual Site Model

Exposure Pathways - Nuclear Power Plant
Conceptual Site Model

Exposure Pathways - Nuclear Power PlantAt a nuclear power plant, one of the more important involves the deposition of radionuclides on pasture the consumption of milk.

air

 forage 

 milk

 man

soil

Since cows consume large areas of pasture grass (high levels of deposited radionuclides can be found I-131 is particularly important because it has a short and milk is one of the few foods consumed immediaproduction.
Mathematical Models of 

Environmental Trans

por
Mathematical Models of Environmental Tr

GeneralOnce the conceptual site model has been developenecessary to generate the mathematical equations 

• Describe the rate and direction of the radionuc

through the environment

• Calculate the concentration of the radionuclide

different components of the environment

• Estimate the dose to the public
Mathematical Models of Environmental Tr

GeneralThere are two approaches to the mathematical mod

Systems Analysis Approach

• Dynamic, calculates concentrations and exp

any specified timeany specified time. 

• Requires considerable amount of input data.• Too complicated for routine use.

Concentration Factor Approach

• Only calculates annual average concentratio

exposures.

• Limited input data required.• Simple, appropriate for routine use.
Mathematical Models of Environmental Tr

Systems Analysis Approach• The following slide shows an SA conceptual mod

compartmentalized terrestrial environment.

• The compartmental concentrations are symbolize

Greek letter 

P

• The transfer coefficients (

J) indicate the rate of m

of the radionuclides between compartments.

• The arrows indicate the direction of movement be

compartments. Note that arrows sometimes go in directions between two compartments.
Mathematical Models of Environmental Tr

SAMTE(I
Mathematical Models of Environmental Tr

Systems Analysis Approach• Differential equations showing the rate of change 

radionuclide concentrations in the various envirocompartments are set up and solved.

• As an example, we will set up the differential equ

compartment three (pasture grass):compartment three (pasture grass):

• The solution to this equation, which gives the 

concentration in pasture grass (

P

3) at a specified 

rather complicated.
Mathematical Models of Environmental Tr

Systems Analysis ApproachThe following figure illustrates the ability of the SA ato model the environment as a function of time. In th131, a short-lived nuclide, is modeled.
Mathematical Models of Environmental Tr

Concentration Factor Approach• The following slide shows a CF conceptual mode

compartmentalized aquatic environment.

• The compartmental concentrations are symbolize

letter X.

• The arrows indicate the direction of movement be

compartments. Note that arrows only go in one dAveraged over a year, the net movement of radiomaterial is in one direction only.

• The concentration factors (F) next to the arrows i

the ratio of the concentrations in the two compart
Mathematical Models of Environmental Tr

ConcentratFactor ModAquatic Ec(ICRP 29)
Mathematical Models of Environmental Tr

Concentration Factor ApproachThe general form of the equation that estimates the concentration in compartment y is:

C

x

C

y

F

C

y = C

x x F

Example: using the aquatic ecosystem model in the slide, the concentration in fish (X

2) is the concentrat

water(X1) multiplied by the bioaccumulation factor (F

X

2 = X

0 x F20
Mathematical Models of Environmental Tr

Concentration Factor ApproachGeneral form of the equation estimating the dose to 

D = C x U x DF

D is the annual dose (e.g., mSv)

C is the concentration in the product being cons

inhaled (e.g., Bq/kg)

U is the rate of consumption or inhalation (e.g., DF is the dose conversion factor (e.g., mSv/kg)
Mathematical Models of Environmental Tr

Calculating the Concentrations in Air and WaterThe starting point (first compartment) in the terrestrienvironment is the air.The first compartment in the aquatic environment is C l l ti th t ti i i d t b C

alculating the concen

trations in air an

d wa

ter 

base

discharge rate requires environmental transport equthat model the dilution of the effluent in the atmosphand/or surface water (e.g., river, lake).These can be complicated.
Mathematical Models of Environmental Tr

Calculating the Concentrations in Air and WaterRegulatory Guide 1.111 Methods for Estimating AtmTransport and Dispersion of Gaseous Effluents in RReleases from Light-Water-Cooled Reactors and pracceptable means to estimate the concentrations in gaseous effluents.The equations in this Regulatory Guide are those of Gaussian plume model.The meteorological input parameters typically consi“real,” rather than worst case, meteorological data. 
Mathematical Models of Environmental Tr

Calculating the Concentrations in Air and WaterRegulatory Guide 1.113 Estimating Aquatic DispersEffluents from Accidental and Routine Reactor Relethe Purpose of Implementing Appendix I describes aacceptable method to estimate the radionuclide concentrations in water due to li

quid effluent release

An excellent discussion of these types of calculationincluding examples, is provided in Till and Grogan’s Radiological Risk Assessment and Environmental A(2008).
Mathematical Models of Environmental Tr

Computer Codes for Estimating the Dose to the The Environmental Protection Agency has developecomputer code called CAP88-PC which can be usedemonstrating compliance with 40 CFR 61 Subpart Clean Air Act standard (NESHAPS) that applies to Dfacilities emittin

g radionuclides to air. This code incog 

parts of NRC Reg Guide 1.109. A similar code, COMPLY, is used by NRC licensees DOE federal facilities to demonstrate compliance wiNESHAPS.
Mathematical Models of Environmental Tr

Computer Codes for Estimating the Dose to the The EPA’s PRESTO computer codes estimate dosepublic as a result of releases from the land disposal level radioactive waste. One example is PRESTO-Ewhich calculates the maximum annual whole body dcritical 

p

o

pulation 

grou

p

(CPG

). Others include PR

p p g p( ) EPA-POP, PRESTO-EPA-DEEP, PRESTO-EPA-BR

PATHRAE-EPA. The MILDOS-AREA computer code can be used to the radiation doses received by individuals and the population within an 80-km radius of an operating urecovery facility (uranium mill or in situ leach). 
Mathematical Models of Environmental Tr

Computer Codes for Estimating the Dose to the The primary computer code used to calculate the dopublic from decommissioned property is the RESRA(produced at Argonne National Laboratory and suppthe NRC). A similar but less complex code, DandD, also be used.
Regulatory Guide 1.109

Calculation of Annual Doses to Man 

Routine Releases of Reactor Effluen

the Purpose of Evaluating Complianc

10 CFR Part 50, Appendix I
Regulatory Guide 1.109

GeneralNRC Regulatory Guide 1.109 provides an acceptablfor calculating the annual doses to the public as a reroutine releases from a nuclear power plant. Once radioactive material is in the environment, the facility that released it is irrelevant. As such the equaRegulatory Guide 1.109 can be used to estimate the due to the releases from other types of facilities.
Regulatory Guide 1.109

Appendix AEstimating the annual dose due to four aquatic pathw

1. Potable Water2. Aquatic Foods 

3. Dose from Shoreline Deposits4. Dose from Foods Irrigated with Contaminat

- Vegetation (crops)- Milk- Meat
Regulatory Guide 1.109

Appendix BEstimating the following doses from noble gases disto the atmosphere:

1. Annual Gamma Air Dose from Noble Gas Relea

Free-Standing Stacks More than 80 Meters High

2. Annual Gamma Air Dose from All Other Noble G

Releases and Annual Beta Air Dose from All NoReleases

3. Annual Total Body and Skin Doses from Noble G

Effluents
Regulatory Guide 1.109

Appendix CEstimating the doses via additional pathways from raand other radionuclides discharged to the atmosphe

1. Annual external dose from Direct Exposure to A

Deposited on the Ground Plane. 

2. Annual Dose from Inhalation of Radionuclides 3. Concentrations of Airborne Radionuclides in Fo

- Forage, Produce and Leafy Vegetab- Milk - Meat 

4. Annual Dose from Atmospherically Released 

Radionuclides in Foods 
Regulatory Guide 1.109

Generalized EquationThe annual dose calculations in Regulatory Guide 1performed via equations that take following generaliz

Raipj = Cip x Uap x Daipj

R is the annual dose equivalent (e.g., mrem/yC is the concentration (e.g., pCi/liter)U is the usage factor (e.g., liters/year ingestedD is the dose factor (e.g., mrem/pCi ingested)

Subscripts: i radionuclide for which the calculation is pe

p pathway for which the calculation is performj organ for which the calculation is performea age group for which the calculation is perfo

(0-1, 1-11, 11-17, 17+)
Regulatory Guide 1.109

Conservatism in CalculationsTo demonstrate compliance with the regulations, the from submersion and inhalation might be calculated location with the highest ground-level concentrations Similarly, the external exposures due to contaminatiodeposited on the ground might be calculated for the where the highest ground level deposition is assumeoccur. The same location might be chosen to estimadoses due to the ingestion of food.
Regulatory Guide 1.109

Conservatism in CalculationsThe total dose to a tissue is the sum of the doses to tissue from all the pathways (e.g., inhalation, externaexposure, milk, etc.). For a given pathway, a dose could be calculated for the fo r age gro ps and the highest of these co ld bthe fo

u

r age gro

ups and the highest of these co

uld b

the summation. For example, the reported thyroid dobe that for the baby's thyroid from drinking milk, plus to the child's thyroid due to inhalation, plus the dose adult's thyroid from ingesting contaminated food.

A less conservative approach is to calculate the dose pathway to a maximally exposed “real” person (e.g., at the nearest residence within 5 miles). 
Regulatory Guide 1.109

Computer Codes to Perform Reg Guide 1.109 Ca• Some NRC power plant licensees use in-house s

spreadsheets. 

• Some use commercially available software (e.g., 

RETDAS from Vertech Software). 

• Some use a combination of three NRC codes:

LADTAP II - dose assessments for liquid effl

pathways

GASPAR II - dose assessments for gaseous e

pathways.

XOQDOQ - atmospheric dispersion and depo

calculations.
Regulatory Guide 1.109

Computer Codes to Perform Reg Guide 1.109 CaThe NRC staff use the code NRCDOSE to confirm thlicensee's calculations. NRCDOSE incorporates the three codes LADTAP II, II, and XOQDOQ. The earlier version of the code, Poperated as a spreadsheet
Regulatory Guide 1.109

Dose Factor IssuesThe dose factors for the various organs calculate thto 50 years after the ingestion/inhalation, i.e., a CDRegulatory Guide 1.109 does not use tissue weightior calculate an effective dose equivalent. The total of Reg Guide 1 109 is the total energy deposited in of Reg Guide

1.109 is the total energy deposited in 

divided by the body mass. When a radionuclide is uniformly distributed in the bRegulatory Guide 1.109 total body dose factors appeffective dose equivalent factors in Federal Guidanc11. Otherwise, their dose factors can be quite diffeMost codes (e.g., GASPAR, LADTAP) do not use thfactors in Regulatory Guide 1.109. 
Example Calculations fo

Regulatory Guide 1 109 Regulatory Guide

1.109
Example Calculations for Regulatory Guid

IntroductionWe will perform example dose calculations for membpublic exposed to releases from a hypothetical nucleplant. The methodology is that of Regulatory Guide 1The pathways, radionuclide, organ, and age group fo

e perform the e ample calc lations are

w

e perform the

e

xample calc

ulations are:

Pathways (p): each of the four aquatic pathwa

described in Appendix A.

Radionuclide (i): I-131 (

8 = 0.0036 hr-1

)

Organ (j): thyroidAge Group (a): adult, 17+ years
Example Calculations for Regulatory Guid

Basic Site Specific DataDischarge rate (Q): 4 Ci of I-131/year in liquid effluenVolumetric flow rate of liquid effluents (F): 2000 ft

3/s
Example Calculations for Regulatory Guid

1. Potable Water PathwayCalculation of the dose to an adult’s thyroid due to dwater contaminated with I-131. The I-131 was relealiquid effluents into a body of water (e.g., river) from drinking water was obtained.

General Equation: Raipj = Cip

Uap

Daip

Uap = usage factor or intake rate of potable water = 

(see Table E-4 on page 39)

Daipj = ingestion dose factor = 1.95 x 10-3 mrem/pCi

(see Table E-11 on page 57)
Example Calculations for Regulatory Guid

1. Potable Water PathwayThe equation to calculate the concentration (C) in thwater can be derived from the following equation: 

Equat

Dividing both sides of the equation by U and D and dthe summation symbol (the latter is not necessary sivalues are specified for a, i, j and p) gives the followequation for the concentration. 
Example Calculations for Regulatory Guid

1. Potable Water Pathway

Symbol Meaning Value 

1100 converts (Ci/y) (ft

3/s) to pCi/l 1100

Q release rate of nuclide in the liquid effluents 4 Ci/y Q release rate of nuclide in the liquid effluents

4 Ci/y 

M

mixing ratio (the reciprocal of the dilution factor) - the average concentration in the drinking water divided by the average concentration in the liquid effluents - must be measure or calculated

10-3 

F volumetric discharge rate of the liquid effluent 2000 ft

3/s 

8 radionuclide decay constant 0.0036 hr-1 

t average transit time - from the time of discharge to the time of consumption 24 hrs 
Example Calculations for Regulatory Guid

1. Potable Water PathwayThe concentration of I-131 in the drinking water is:And, the annual dose to the adult thyroid is:

Raipj = Cip

Uap

Daipj

= 2.02 x 10-3 pCi/l x 370 l/y x 1.95 x 10-3 

= 1.46 x 10-3 mrem/year
Example Calculations for Regulatory Guid

2. Aquatic Foods (fish) PathwayCalculating the dose to an adult’s thyroid from inges

General Equation: Raipj = Cip

Uap

Daipj

U

a

p = usage factor or intake rate of potable water = 

(see Table E-4 on page 39)

Daipj = ingestion dose factor = 1.95 x 10-3 mrem/pCi

(see Table E-11 on page 57)
Example Calculations for Regulatory Guid

2. Aquatic Foods (fish) PathwayThe equation to calculate the concentration (C) in fisderived from the following equation: 

Equa

Dividing both sides of the equation by U and D and dthe summation symbol (the latter is not necessary sivalues are specified for a, i, j and p) gives the followequation for the concentration. 
Example Calculations for Regulatory Guid

2. Aquatic Foods (fish) Pathway

Symbol Meaning Value 

bioaccumulation factor - the ratio of the concentration in the aquatic food to the 

B concentration in water - the value of 15 l/kg 

indicates that there are 15 pCi of I-131 / kg of fish for every pCi/l in water.

15 l/kg 

t average transit time - from the time of discharge to the time of consumption 240 hrs 
Example Calculations for Regulatory Guid

2. Aquatic Foods (fish) PathwayThe concentration of I-131 in the fish is:And, the annual dose to the adult thyroid is:

Raipj = Cip

Uap

Daipj

= 1.39 x 10-3 pCi/l x 6.9 kg/y x 1.95 x 10-

= 1.87 x 10-4 mrem/year
Example Calculations for Regulatory Guid

3. Shoreline Deposits PathwayCalculation of the external dose to an adult’s thyroid contaminated shoreline deposits. 

General Equation: Raipj = Sip

Uap

Daipj

Uap = exposure time for shoreline activity = 8.3 hr/y

(see Table E-4 on page 39)

Daipj = external dose factor = 2.80 x 10-9 mrem/h per 

(see Table E-6 on page 41)
Example Calculations for Regulatory Guid

3. Shoreline Deposits PathwayEquation A-5 (p.14) calculates the radionuclide conc(S) in shoreline deposits:Symbol Meaning Value 

T radiological half life (days) 8.02 d 

C radionuclide concentration in water adjacent to sediment 2.02 x 10-3 pCi/l 

W shore width factor 0.2 

t

The length of time the sediment is exposed to the contaminated water - set at 15 years, the midpoint of facility operating life 

1.31 x 10

5 hrs 
Example Calculations for Regulatory Guid

3. Shoreline Deposits PathwayThe radionuclide concentration (S) in shoreline depoCalculation of the external dose to an adult’s thyroid contaminated shoreline deposits: 

Raipj = S U D

= 0.324 pCi/m

2 x 8.3 h/y x 2.80 x 10-9 mrem/h per p

= 7.53 x 10-9 mrem/y
Example Calculations for Regulatory Guid

4. Food Crop PathwayCalculation of the dose due to ingesting food crops iwith contaminated water.

General Equation: Raipj = Cip

Uap

Dai

Uap = usage factor or intake rate of food crops = 19

(see Table E-4 on page 39)

Daipj = ingestion dose factor = 1.95 x 10-3 mrem/pCi

(see Table E-11 on page 57)
Example Calculations for Regulatory Guid

4. Food Crop PathwayRadionuclide concentration in irrigated crops (Equat

( )f (

)

Deposition rate 

di

) o

f irrigation water 

(Equation 

A-9

)

di = Ciw I

Ciw, the concentration in the irrigation water (site-spe

set at the same concentration as in potable water.I, the irrigation rate (site-specific), is set at 0.1 l/m

2/h

di = 2.02 x 10-3 pCi/l x 0.1 l/m

2/hr = 2.02 x 10-4 
Example Calculations for Regulatory Guid

4. Food Crop Pathway

Symbol Meaning Value 

r The fraction of the deposited activity that is retained on the vegetation 1.0 

λEi

The effective removal rate constant from the vegetation.λEi = 

λi +

λw (see p. 4) where 

λw is the removal rate 

constant due to weathering. The latter is set at 0.0021 h-1

(Table E-15, p. 69), hence

λEi

= 0.0036

+ 0.0021

0.0057 h-1 

(Table

E 15, p. 69), hence

λEi 0.0036 0.0021

te The time crops are exposed during the growing season 1440 h 

Yv The agricultural productivity or yield (wet weight) 2.0 kg/m2 

fI The fraction of the year that crops are irrigated 1.0 

Biv Concentration (bioaccumulation) factor from soil in 

pCi/kg wet weight in crops per pCi/kg in dry soil

0.02 

tb Time the soil is exposed to contaminated water - set at 

15 years, the midpoint of the facility operating life

1.31 x 105 h 

P Surface density of dry soil 240 kg/m2 

th Holdup time between harvest and consumption of food 336 h 
Example Calculations for Regulatory Guid

4. Food Crop PathwayRadionuclide concentration in irrigated crops (Equat
Example Calculations for Regulatory Guid

4. Food Crop PathwayThe annual dose to the thyroid of an adult due to the of vegetation is calculated using the generalized equ

R = C x U x D

3 C/ /

3 

= 5.28 x 10-3

p

Ci/kg x 190 kg

/y x 1.95 x 10-3 m

= 1.96 x 10-3 mrem/y= 1.96 x 10-5 mSv/y
Example Calculations for Regulatory Guid

5. Milk PathwayCalculation of the dose due to drinking milk from anidrank contaminated water and grazed on pasture irrcontaminated water.

General Equation: Raipj = Cip

U

a

p

Daip

pj

p

p

Uap = usage factor or intake rate of milk = 110 l/yr

(see Table E-4 on page 39)

Daipj = ingestion dose factor = 1.95 x 10-3 mrem/pCi

(see Table E-11 on page 57)
Example Calculations for Regulatory Guid

5. Milk PathwayEquation A-11 (p. 16) calculates the concentration (C

milk:

CiA = FiA (CiF

Q

F + CiAw

Qaw

)

The equation calculating CiF, the concentration in the 

feed, can be derived from Equation 

A-13. It is essen

same as Equation A-8 used to calculate the concentvegetation but some input parameters will differ (e.g
Example Calculations for Regulatory Guid

5. Milk Pathway

Symbol Meaning Value 

FiA Stable element transfer coefficient - ratio of radionuclide concentration in milk to daily intake rate 0.06 d 

Q

F Consumption rate of contaminated forage/feed by animal 50 kg/d 

CiAw Concentration in animal's drinking water 2.02 x 10-3 pCi/l 

p

QAw Animal's consumption rate of contaminated water 60 l/d 

di Deposition rate from irrigated water 2.02 x 10-4 pCi/m

2/h

r The fraction of the activity deposited on the vegetation that is retained on the vegetation 1.0 

λEi

The effective removal rate constant from the vegetation.λEi = 

λi +

λw (see p. 4) where 

λw is the removal rate 

constant due to weathering . The latter is set at 0.0021 h1 (Table E-15, p. 69), hence 

λEi = 0.0036 + 0.0021 

0.0057 h-1 
Example Calculations for Regulatory Guid

5. Milk Pathway

Symbol Meaning Value 

te The time crops are exposed during the growing season 1440 h 

Yv The agricultural productivity or yield (wet weight) 0.7 kg/m2 

fI The fraction of the year that crops are irrigated 1.0 

Biv Concentration (bioaccumulation) factor from soil in pCi/k

g wet weight in 

c

rops per pCi/k

g in 

d

ry soil 0.02 

pC / g we we g c ops pe pC / g d y so

tb Time the soil is exposed to contaminated water - set at 15 years, the midpoint of the facility operating life 1.31 x 105 h 

P Surface density of dry soil 240 kg/m2 

th Holdup time between harvest and consumption of food/forage/feed 0 for pasture grass (2160 h for stored feed) 
Example Calculations for Regulatory Guid

5. Milk PathwayThe I-131 concentration in the forage is:

C = F (C

Q + C

Q

)

CiA 

=

FiA (CiF

Q

F

+

CiAw

Qaw

)
Example Calculations for Regulatory Guid

5. Milk PathwayThe I-131 concentration in milk is:

CiA = FiA (CiF

Q

F + CiAw

Qaw

)

= 0.06 (5.05 x 10-2 x 50 + 2.02 x 10-3 x 60

= 0.159 pCi/l
Example Calculations for Regulatory Guid

5. Milk PathwayThe annual dose to the thyroid of an adult due to the of milk is calculated using the generalized equation:

R = C x U x D

C/ /

3 / C

= 0.159 p

Ci/l x 110 l

/y x 1.95 x 10-3 mrem

/

p

Ci

= 3.41 x 10-2 mrem/y

= 3.41 x 10-4 mSv/y
Example Calculations for Regulatory Guid

6. Meat PathwayCalculation of the dose due to ingesting meat from athat drank contaminated water and grazed on pasturwith contaminated water.

General Equation: Raipj = Cip

U

a

p

Daip

pj

p

p

Uap = usage factor or intake rate of meat = 95 kg/y

(see Table E-4 on page 39)

Daipj = ingestion dose factor = 1.95 x 10-3 mrem/pCi

(see Table E-11 on page 57)
Example Calculations for Regulatory Guid

6. Meat PathwayThe only difference between the following equation tthe I-131 concentration in meat and that used to calcconcentration in milk is that the transfer coefficient, F

meat. According to Table E-1 (p. 37), an acceptable this transfer factor is 2.9 x 10-3 pCi/kg (per pCi inges

)

cattle per day . 

CiA = FiA (CiF

Q

F + CiAw

Qaw

)

= 0.0029 (5.05 x 10-2 x 50 + 2.02 x 10-3 x = 7.67 x 10-3 pCi/kg

In this example we assume that the parameters used 

dairy cattle also apply to the cattle from which meat 
Example Calculations for Regulatory Guid

6. Meat PathwayThe annual dose to the thyroid of an adult due to the of milk is calculated using the generalized equation:

R = C x U x D

3 C/ /

3 

= 7.67 x 10-3

p

Ci/kg x 95 kg

/y x 1.95 x 10-3 

= 3.41 x 10-3 mrem/y= 1.42 x 10-5 mSv/y
Example Calculations for Regulatory Guid

7. Total Dose from All Aquatic Pathways

Potable water 1.46 x 10-3 mrem/y

Aquatic Food (fish) 1.87 x 10-4 mrem/yShoreline Deposits 7.53 x 10-9 mrem/yVegetation (food crops) 1.96 x 10-3 mrem/yMilk 3.41 x 10-2 mrem/y

3

/

Meat 1.42 x 10- mrem

/

y

Total 3.91 x 10-2 mrem/
Selected References
Selected References

NCRP Report 76. Radiological Assessment: PredictiTransport, Bioaccumulation and Uptake by Man of Radioisotopes Released to the Environment. 1984.NRC. Regulatory Guide 1.109. Calculation of AnnuaMan from Routine Releases of Reactor Effluents for Purpose of Evaluating Compliance with 10 CFR ParAppendix I. 1977.NUREG-3332. Radiological Assessment: A Textbook Environmental Dose Analysis. Till. 1983.Till and Grogan. Radiological Risk Assessment and Environmental Analysis. Oxford University Press. 20