TI 0-14844

CALCULATION OF DISTANCE FACTORS FOR 

POWER AND TEST REACTOR SITES 

Technical Information Document

By 

J. J. DiNunno 

F. D. Anderson

R. E. Baker 

R. L. Waterfield

March 23, 1962 

Division of Licensing and Regulation, AEC 

Washington, D. C.

2
J

I

LEGAL NOTICE 

This report was prepared as an account of Government sponsored work. Neither the United 

States. nor the Commission. nor any person acting on behalf of the Commission: 

A. Makes any warranty or representation, expressed or implied, with respect to the accu racy. completeness, or usefulness of the information contained in this report, or that the use of any Information, apparatus, method, or process disclosed In this report may not Infringe 

privately owned rights; or 

B. Assumes any liabilities with respect to the use of. or for damages resuting from the use of any information, apparatus, method, or process disclosed in this report. 

As used in the above, "person acting on behalf of the Commission" includes any em ployee or contractor of the Commission, or employee of such contractor, to the extent that 

such employee or contractor of the Commission, or employee of such contractor prepares, 

disseminates, or provides access to, any Information pursuant to his employment or contract 

with the Commission. or his employment with such contractor. 

This report has been reproduced directly from the best 

available copy. 

Printed in USA. Price $1.00. Available from the Office of 

Technical Services, Department of Commerce, Washington 

25, D. C.
I. PURPOSE 1 

II. INTRODUCTION 3 

III. BASIC CRITERIA 5 

IV. POSTULATION OF YAJOR RACTOR ACCIENT 8 

(V. ANALYTICAL MMHOD 13 

A. PAmdamental Assumptions 14 

B. Inhalation Doss Calculations 18 

C. 'External Gazmna Dose Calculations 25 

D. Results 28 

VI. CCOXARISOK OF ANALYTICAL FXTHOD TO EXISTING REACTOR SITES 35 

VII. APPENDIX 37 

A. Relationship of the Sutton Diffusion Parameter and the 37 

Generalized Gaussian Parameter 

B. Bibliography 38 

(C. List of Symbols and Definitions 39 

IREF.ENMCES 4

V
TiD-14844 

REACTOR TECHNOLOGY

CALCULATION OF DISTANCE FACTORS FOR POWER 

AND TEST REACTOR SITES* 

Technical Information Document 

By

J. 

F. 

R. 

R.

J. 

D. 

E. 

L.

DiNunno 

Anderson 

Baker 

Watdrfield

(

March 23, 1962

(

Division of Licensing and Regulation 

U. S. Atomic Energy Conmission

*Second printing--minor editorial changes made from the first printing.
I. PURPOSE 

It is the intent that this document to provide reference information and 

guidance on procedures and basic assumptions whereby certain factors pertinent 

to reactor siting as set forth in Title 10 Code of Federal Regulations Part 100 

(1) (10 CFR 100) can be used to calculate distance requirements for reactor sites 

which are generally consistent with current siting practices. 

For any proposed reactor: the performance experience accumulated elsewhere; 

the engineering safeguards; the inherent stability and safety features; and 

the quality of design, materials, construction, management and operation are 

all important factors that must be included in .the evaluation of the suit

ability of a site. 

For a particular site; size, topography, meteorology, hydrology, ease 

of warning and removing people in times of emergency, and thoroughness of 

plans and arrangements for minimizing injuries and interference with offsite 

activities, all enter an evaluation. 

Consideration of these as well as other aspects of hazards evaluation 

involves so many different situations and such complex technological problems 

that it would be quite impossible to anticipate and answer all questions that 

will arise. 

This technical document sets forth one method of computing distances and 

exposures, for one general class of reactors. In developing this example 

conservative assumptions have been intentionally selected. 

Designers of reactors are expected to examine all significant aspects of 

the hazards and safety problem they believe are appropriate to the particular 

1
situation with which they are dealing. In any case, the designer and/Qr , 

applicant bears the responsibility for justifying all the assumptions and 

methods of calculation used in a hazards evaluation. The fact that aspects 

of the problem are not considered in the example set forth here, does not in 

any way relieve the designer and/or applicant of the responsibility for 

carefully examining, in his particular case, every significant facet of the 

hazards and safety problem.

2
II. INTRODUCTION

An applicant for a license to construct a power or tent reactor is 

required by Atomic Energy Commission (AEC) regulations, Title 10 Code of 

Federal Regulations Part 50 (10 CFR Part 50), to submit in support of his 

application a hazards summary report that includes details pertinent to 

( the site proposed for the reactor. Approval or disapproval is given by 

the Commission after review and evaluation of the reactor design and the 

proposed location by the Division of Licensing and Regulation and the 

Advisory Committee on Reactor Safeguards (ACRS). Such review and evaluation 

includes an analysis of the consequences of potential accidents. 

The probability and consequences of major reactor accidents have been 

the subject of widespread interest and study since the earliest days of 

reactor development. To date, however, the technology has not progressed 

to the point where it is possible to assign quantitative numbers to all the 

( significant factors relative to safety or to predict with surety the probabil

ities of malfunctioning of engineering features of plant design under all 

operating conditions that might exist. There is rather general agreement, 

however, as expressed in the Brookhaven report, "Theoretical Possibilities 

and Consequences of Major Accidents in Large Nuclear Power Plants",(2) that 

the probability of a major accident in reactor plants constructed and operated 

in accordance with general practices now observed is exceedingly small. 

The following is quoted from the report: 

"As to the probabilities of major reactor accidents, 

some experts believe that numerical estimates of a quantity 

3

'i
so vague and uncertain as the likelihood of occurrence of 

major reactor accidents has no meaning. They decline to 

express their feeling about this probability in numbers. 

Others, though admitting similar uncertainty, nevertheless, 

ventured to express their opinions in numerical terms.... 

However, whether numerically expressed or not, there was 

no disagreement in the opinion that the probability of 

major reactor accidents is exceedingly low." 

This low probability of occurrence is due to both the inherently safe features 

of reactors and the safeguards that have been engineered into the plants as 

a part of deliberate and planned effort to insure safety. The question of 

suitability of a site for a reactor, however, requires consideration not 

only of the factors influencing the probability of occurrence of an accident, 

but also the risk in terms of possible exposure of people to the hazardous 

consequences of such an accident. Although the probability of a serious 

accident may be primarily a function of facility design and the risk in 

terms of exposure may be primarily a function of location, the two are not 

independent. Site c"hacteristics may dictate the inclusion of specific 

engineered safeguard features and a proposed facility design in turn may 

have marked influence on the acceptability of the site for location of the 

reactor. 

Values of radiation exposure dose that can be used as reference values 

in the evaluation of reactor sites have been set forth in 10 CFR 100. 

Considerations that led to the establishment of these reference values and 

the site criteria in which they are embodied are discussed in the sections 

that follow. In addition, a hypothetical case is analyzed to illustrate 

the calculation of distance factors as required by 10 CFR 100.

14
III. BASIC CRITERIA

The AEC has set forth in 10 CFR 100 a number of the factors con

sidered by the Commission in the evaluation of reactor sites and the 

general criteria used at this time as guides in approving or disapproving 

proposed sites. One of the factors identified is the following: 

"Population density and use characteristics of the mite environs, 

including, among other things, the exclusion area, low population 

zone, and population center distance." 

The guides (10 CFR 100.11) also set forth pertinent factors to be considered 

in estimating the exclusion area, low population zone and population center 

distance. 

Specifically, 10 CFR 100 requires an applicant for a construction 

permit to determine the following:(1) 

"(1) An exclusion area of such size that an individual located 

( at any point on its boundary for two hours immediately 

following onset of the postulated fission product release 

would not receive a total radiation dose to the whole body 

in excess of 25 rem or a total radiation dose in excess 

of 300 rem to the thyroid from iodine exposure. 

(2) A low population zone of such size that an individual 

located at any point on its outer boundary who is exposed 

to the radioactive cloud resulting from the postulated 

fission product release (during the entire period of its 

passage' would not receive a total radiation dose to the

5
whole body in excess of 25 rem or a total radiation dose 

in excess of 300 rem to the thyroid from iodine exposure. 

(3) A population center distance of at least 1 1/3 times the distance 

from the reactor to the outer boundary of the low population zone. 

In applying this guide due consideration should be given to the 

population distribution within the population center. Where very 

large cities are involved, a greater distance may be necessary 

because of total integrated population dose considerations." 

In these criteria, two concepts are worthy of particular comment: 

Note 1: Exposure Limits 

The whole body dose of 25 rem referred to in the above excerpts from 

10 CFR 100 corresponds numerically to the once in a lifetime accidental or 

emergency dose for radiation workers, which, according to NCRP recommenda

tions(3), may be disregarded in the determination of their radiation exposure 

status. However, neither its use in the context of this regulation nor that 

of a correspondingly low internal organ dose (such as, for example, the 300 

rem to the thyroid might be considered in this application) is intended to 

imply that these numbers constitute acceptable emergency doses to the public 

under accident conditions. Rather, this 25 rem value and the 300 rem thyroid 

value have been set forth in these guides as reference values which can be 

used in the evaluation of reactor sites for reactors that reflect through 

their design, construction and operation an exceedingly low probability for 

a major accident, and through location and other safeguards against the 

hazardous consequences of an accident, should one occur, a low probability 

of public damage from such accidents. These exposure values cannot be 

considered as being independent from the likelihood of serious accidents 

nor from considerations of the total number of persons that might be exposed. 

They have been set forth as reasonable bases for reactor site evaluations 

in the context of considerations such as those indicated in Section V. of 

this document.

0

&
Note 2: Population Center Distance 

One basic objective of the criteria is to assure that the cumulative 

exposure dose to large numbers of people as a consequence of any nuclear 

accident should be low in comparison with what might be considered reasonable 

for total polulation dose. Further, since accidents of greater potential 

hazard than those comonly postulated as representing an upper limit are 

conceivable, although highly improbable, it was considered desirable to 

provide for protection against excessive exposure doses of people in large 

centers, where effective protective measures might not be feasible. Neither 

of these objectives were readily achievable by a single criterion. Hence, 

the population center distance was added as a site requirement when it was 

found for several projects evaluated that the specifications thereof would 

approximately fulfill the desired objectives and reflect a more accurate 

guide to current siting practices. In an effort to develop more specific 

guidance on the total man-dose concept, the Counission intends to give 

further study to the subject. Meanwhile, in recognition of the problem, 

the population center distance to very large cities may have to be greater 

than those suggested by these guides.

7
IV. POSTULATION OF A MAJOR REACTOR ACCIDENT 

In evaluating proposed reactor sites, the basic safety questions involve 

the possibility of accidents which might cause radioactivity release to areas 

beyond the site, the possible magnitudes of such releases and the consequences 

these might have. Practically, there are two difficult aspects to the estimation 

of potential accidents in a proposed reactor which affect the problem of site 

evaluation. 

1. The necessity for site appraisal arises early in the life 

of a project when many of the detailed features of design 

which might affect the accident potential of a reactor are 

not settled. 

2. The inherent difficulty of postulating an accident representing 

a reasonable upper limit of potential hazard. 

In practice, after systematic identification and evaluation of foresee

able types of accidents in a given facility, a nuclear accident is then 

postulated ihich vould result in a potential hazard that would not be exceeded 

by any other accident considered credible during the lifetime of the facility. 

Such an accident has come to be known as the "maximum credible accident". 

for pressurized and boiling water reactors, for example, the "maximum 

credible accident" has frequently been postulated as the complete loss of 

coolant upon complete rupture of a major pipe, with consequent expansion of 

the coolant as flashing steam, meltdown of the fuel and partial release of 

the fission product inventory to the atmosphere of the reactor building. 

There may be other combinations of events which could also release significant 

8
. amounts of fission products to the environment, but in every case, for the 

events described above to remain the maximum credible accident the probability 

of their occurrence should be exceedingly small, and their consequences 

should be less than those of the maximum credible accident. In the analysis 

of any particular site-reactor combination, a realistic appraisal of the 

consequences of all significant and credible fission release possibilities 

is usually made to provide an estimate in each case of what actually con

stitutes the "maximum credible" accident. This estimated or postulated 

accident can then be evaluated to determine whether or not the criteria set 

out in 10 CFR 100 are met. As a further important benefit, such systematic 

analyses of potential accidents often lead to discovery of ways in which 

safeguards against particular accidents can be provided. 

(Since a number of analyses have indicated that the pipe rupture-meltdown 

sequence in certain types of water cooled reactors would result in the re

lease of fission products not likely to be exceeded by any other "credible" 

accident, this accident was designated the "maximum credible accident" (MCA) 

for these reactors. The remainder of this discussion will refer chiefly to 

this type of reactor and this type of accident. Corresponding maximum 

credible accidents can by similar analyses be postulated for gas-cooled, 

liquid metal cooled, and other types of reactors. 

Power and test reactors presently being operated or constructed near 

inhabited areas, pursuant to licenses issued by the Conmission, are enclosed 

within external containment vessels of some type. This outer barrier to 

fission produ:t release to the atmosphere has within its enclosure all or 

a substantial part of the primary plant coolant piping systems representing 

an inner barrier. Cladding on the fuel provides an additional barrier that 

acts as a retaining "can" for the fissionable material and the fiscion products 

formed. Thus, gross release of fission products to the atmosphere would only 

occur after the breaching of the two inner barriers, the fuel cladding and 

the primary system, and then the external barrier, the containment building.

9
A gross release of fission products into the reactor building might be 

initiated by: (i) a nuclear power excursion which would cause pressures in 

the primary cooling system sufficient to rupture the coolant piping or some 

part of the system; or (2) a failure of the piping or other parts of the 

system due to some defect in the materials. In either case, loss of the 

coolant would set the stage for possible fuel meltdown from the heat of fission 

product decay. 

The rupture of the coolant system from high internal pressures due 

to uncontrolled internal heat generation would only occur after such failures 

as the following: 

1) reactivity control mechanisms fail to function; 

2) high-pressure relief systems fail to perform; 

3) pressures exceed rupture limits of the piping material. 

These prior failures need not occur for the case of a spontaneous pipe 

rupture. However, for such a case, the assumption of a complete shear of a 

pipe represents an extremely unlikely event. Nevertheless, assuming that 

such a break Dccurs and coolant is lost, fuel melting would require that: 

1) decay heat is sufficient to increase fuel element temperature 

to the melting point, and 

2) safeguard systems usually provided to flood or spray the core 

with water are either inoperative or insufficient to keep fuel 

elements from melting. 

From such considerations, and from detailed analysis of the inherent 

self-stabilizing characteristics and engineered "accident prevention" safe

guards, assurance is obtained that the likelihood of a major reactor accident 

is extremely small. Yet such a possibility for a serious accident cannot be 

conpletely discounted and the conse~uences, therefore, must be considered. 

If a major release of fission products to the environment should occur, 

the potential exposure doses to persons off-site are extremely difficult to 

determine with exactness because of the complex and interwoven technical 

10
parameters involved. The amount of each kind of radioactive material present 

in a reactor system can be estimated fairly closely, as a function of the power 

level history, but the quantity of this material that would be released as 

a result of an accident is unpredictable. Quantities in the order of 10 per 

cent of the gross activity have been assumed in the past. Experimental data 

would indicate these values to be conservative for accidents of the type 

usually visualized. The exact release can vary so much with the reactor system 

and with the detailed nature of an accident that the degree of conservatism in 

the assumptions made in any given case, is not known. Further, there is a 

multiplicity of possible combinations of the physical and chemical form of 

the radioactive materials released into the containment vessel and of the 

ways that atmospheric conditions might cause these radioactive materials 

to be transported to regions beyond the site boundary. 

In accidents of the "maximum credible" type, it is usually assumed that 

the radioactive materials, along with erosion and corrosion products, would 

be dispersed in the coolant through melting or/rupture of fuel elements, 

and then find passage to the outer containment barrier through breaches in 

the coolant system. On breaching, the expansion to a larger volume and a 

lower pressure in the containment vessel would result in stes.,, in addition 

to the gaseous fission products, and production of vapors as well as liquid 

( and solid aerosols of a wide range of sizes. Some ejected materials may con

ceivably burn on contact with air, and thus increase the volatiles and 

fractions of fine particles. At the same time, a certain amount of the 

airborne fission products would be removed by such phenomena as adsorption, 

deposition, plate-out and steam condensation within the reactor building 

or containment structure. The removal process would be complicated by 

conversion of normally gaseous fission products into solids by decay, and 

condensation of volatiles. Removal by adsorption and settling processes 

would be affected by turbulence. Superimposed upon these factors is the 

radioactive decay resulting in reduction of source strength with time by

11

.
conversion to more stable isotopes. All of these factors make it difficult 

to determine with any exactness the radioactive content of the. air which 

might leak out of the containment vessel. 

The objective of estimating the radioactive inventory within the outer 

containment barrier is to attain a starting point for calculating the potential 

radiological hazard in the surrounding environs. For people in the proximity 

of the reactor building, the confined radioactive inventory represents a 

decaying source of direct gamma radiation which is attenuated by such factors 

as the structural shielding, distance, and shielding by the topography. For 

those at more distant points, the transport by air of the radioactive 

materials which might leak from the containment vessel is the major radio

logical consideration. For air transport, factors such as the physical 

nature of the material leaking from the containment vessel, release height, 

particle deposition with distance, wind direction, speed and variability, 

and air temperature gradients become important in determining the extent of 

these potential hazards. The meteorologicai factors will be a function of 

the region in which the reactor is located as well as the time of the day 

and season. Finally, when estimates have been made of the potential 

concentration of radioactivity likely to result at any distant point from 

the "maximum credible accident", there still remains a difficult problem 

of translating atmospheric concentrations into whole body or thyroid ex

posure doses to people at these points. For internal doses, the con

trolling ones, there are assumptions to be made about rates of breathing, 

percentage retention in the body, and cumulative doses to internal organs 

resulting from retained materials. As the last exercise, there is the 

problem of establishing some acceptable exposure dose criteria, within 

the context of this procedural operation, for a comparative measure of 

the -acceptability or unacceptability of the estimated exposures result

ing from the hypothetical accident. It is from a study of these complex 

interwoven technical parameters that the values for the exclusion area, 

low population zone and population center distance must be determined.

12
V. ANALYTICAL METHOD

In the procedural method described herein for calculating reactor distances 

for power and test reactors, the highly complex phenomena involving parameters 

which may vary over wide ranges of values have been made manageable by simplify

ing assumptions, specifying that certain secondary factors are to be ignored, 

( and fixing the values of certain key parameters. In utilizing this method, it 

is recognized that: 

1) there is a substantial degree of judgment involved in 

establishing the basic assumptions and assigning definitive 

values to variable parameters; 

2) the results obtained are approximations, sometimes relatively 

poor ones, to the result which would be obtained if the effects 

of the full play of all the variables and influencing factors 

could be recognized and fixed with certainty--an impossibility 

( in the present state of the art; 

3) the net effect of the assumptions and approximations is 

believed to give more conservative results (greater distances) 

than would be the case if more accurate calculations could be 

made. 

While this approach represents a considerable simplification in the 

handling of the many complex phenomena involved, it represents the same very 

conservative approach to site selection that has characterized such evalua

tions in the past.

13
A. Fundamental Assumptions 

The fundamental assumptions upon which the distances are calculated 

with estimates of the degree of conservatism represented in each case are 

as follows. 

1. Experts agree and experience to date, though limited, 

confirms that there is only an exceedingly small probability 

of a serious accident in reactors approved or likely to be 

approved for construction(2) The probability is still lower 

for an accident in which significant amounts of fission 

products are released into the confined primary coolant 

system and a great deal lower for accidents which would 

release significant quantities of radioactivity from the 

primary system into the reactor building. 

2. It is assumed that the reactor is a pressurized water type 

for which the maximum credible accident will release into 

the reactor building 100 percent of the noble gases, 50 

percent of the halogens and 1 percent of the solids in the 

fission product inventory. Such a release represents 

approximatel7 15 percent of the gross fission product 

activity.(11) 

3. Fifty percent of the iodines in the containment vessel is 

assumed to remain available for release to the atmosphere. 

The remaining fifty percent of the iodines is assumed to 

absorb onto internal surfaces of the reactor building or 

adhere to internal components. Rather than the assumed 

reduction factor of two, it is estimated that removal of 

airborne iodines by various physical phenomena such as 

adsorption, adherence and settling could give an effect of 

3-10 reduction in the final result. Credit has not been 

taken for the effects of washdoln or filtering from
protective safeguards such as cooling sprays and internal air 

recirculating systems. Washdown features and filtering networks 

could provide additional reduction factors of 10-1000. 

4. The release of available (airborne) radioactivity from the 

reactor building to the environment is assumed to occur at a 

constant leakage rate of 0.1 per cent per day. The leakage 

and pressure conditions are assumed to persist throughout the 

effective course of the accident, which for practical purposes, 

would be until the iodine activity becomes insignificant. The 

maximum pressure within the reactor building and the leakage 

rate would actually decrease with time as the steam condenses 

from contact with cooling surfaces. By assuming no change in 

leak rate as a function of pressure drop, it is estimated that 

the final off-site doses calculated may be too high by factors 

of 5-10. 

5. Atmospheric dispersion of material from the reactor building 

is assumed to occur according to the well-known relationship 

(4) developed by 0. G. Sutton involving meteorolojical factors 

of wind velocity, atmospheric stability, and diffusion para

meters. Application of this treatment to reactor hazards 

analysis was discussed in WASH-740, (2 and AECU-3066.(5) 

Recently a simplified method of dispersinn calculation has 

been proposed, by Pasquill( 6 ' and Meade,7)" which reflects ( recent dispersion field trails, as well as current dispersion 

theories. In the hypothetical situation examined here the latter 

metho,' gi'ves the same numerical results as the Sutton method for 

distances out to about seven miles. Beyoni this distance, the 

new methol predicts somewhat greater concentrations. 

6. The assumption is made that a shift in wind direction does not 

occur for the duration of the leakage of the fission products 

from the containment barrier. If leakage from the containment 

barrier is assumed to occur over a significant time period, (in 

the order of days) a reduction factor of 2-50 could result from

15

1 4
shifts in wind directions. iind meandering from any one center

line direction might also result in a reduction factor of approxi

mately 3. 

7. Atmospheric dispersion is assumed to occur under inversion type 

weather conditions. For weather conditions which exist for 75 

percent or so of the time at most sites, the atmospheric 

dispersion conditions could be more favorable, by factors of 

5.1Oo.(8) 

8. Cloud depletion as ground deposition (particulate fallout) is 

not assumed during cloud travel. Such deposition during cloud 

travel could reduce the low population zone distance by factors 

of 2-5. 

9. In calculating the airect gamma dose, credit is not taken for 

shielding by the containment structure and applicable reactor 

shielding or topography. In some cases it is recognized that 

such shielding could reduce the direct gamma dose by a factor 

of 2-1000. 

10. Decay of fission products is assumed while they are confined to 

the containment building but is not assumed during their transit 

to the receptor point. The decay enroute is not significant for 

the conditions of release considered here but would lower the 

calculated doses slightly if included. 

11. In determining the whole body direct gamma dose, only the 

external gamma dose due to the fission products contained in 

the reactor building was considered significant for the assumed 

conditions. The whole body direct gamma dose due to the cloud 

passage for the assunmed conditions would contribute only on the 

order of 1 to 10 percent of the total whole body direct gar..a 

dose at the exclusion and low po-ulation zone distances. (5) 

Thus, even if the postulated maxi=.= credible accident should occur, 

the resulting exposure doses would probably be many times lower than those

calculated by the indicated method.
Oh the other hand, there are potential, conceivable conditions which 

would result in larger fission product releases than those assumed to be 

released in the maximum credible accident, and the consequences could be 

more hazardous. Other potentially more hazardous factors than those 

represented by the example calculation include the following conditions. 

1. Total radioactivity release to the containment vessel could 

theoretically be up to six times as large as those assumed. 

Release of long-lived fission products to the containment 

vessel could theoretically be up to 99 times as large as 

that assumed. Such releases would increase doses to the lung, 

bone, and total body. 

(2. For some sites, the atmospheric diffusion conditions for a 

small proportion of time could be worse than those assumed in 

these calculations. Such diffusion conditions could result 

in an increase in the inhalation doses. 

3. If the external containment structure should be rendered 

completely ineffective at the outset of the accident, the 

consequences of the "maximum credible" accident would be 

increased many orders of magnitude. In such a case, the 

dose from the cloud and ground contamination could become 

( significant in determining the external dose. 

Although the analytical approach presented herein does not take into 

account the effects of the full play of all the variables and influencing 

factors, it is considered to be a reasonable procedure that results in 

distances roughly reflecting current siting practices for water-cooled 

reactors. The assumptions made can be used as a point of departure for 

consideration, of particular site requirements resulting from evaluation 

of the characteristics of a particular reactor, its purpose, and the 

proposed plan of operation. 

17
B. Inhalation Dose Calculations 

The potential doses to the critical organs as a consequence of inhala

tion of a portion of the passing cloud were determined in the manner indicuted 

below. For the specific conditions of this example, the thyroid dose is 

controlling and although the method is quite general, the results of the 

calculation are specific for the iodine release. If the type and conditions 

of release were different, the controlling dose could be that to the lung, 

bone, gut, or other critical organ. 

The amount of radioactive material inhaled by a person standing a 

distance, d (meters), downwind for timet(seconds), on the centerline 

of a cloud of radioactive material being continuously emitted from a ground 

level source is given by equation (1). 

Arm R VPo curies. . . . . . . . . . ) 

Trfl~ 

Where: 

Ar is the amount of radioactive material inhaled from the cloud, 

(curies),during exposure for t seconds. 

R is the breathing rate, (meter 3 .secondl). 

Q is the amount of radioactive material in the total cloud, per 

megawatt reactor power, as it passes the receiver point d aeters 

downwind, (curies.Mw'l),during the time interval •. 

P is the rated reactor power level, (Megawatts). o 

u is the average wind speed, (meters.second'l). 

y' , c are standard de'-iations of the cloud centerii-,e concentration~s 

in the vertical and horizontal directions, respectively.* 

r = "l C dln/2 o- = 1C dln/2 

Sz z 

C ,C are the virtual diffusion coefficients in the vertical and 

horizontal planes, respectively, (meters/). 

"See Appendix A for further discussion. 

18
n is the stability parameter, (dimensionless). 

d is the distance downwind, (meters). 

Equation (1) is the time integrated expression resulting from the 

0. G. Sutton model of atmospheric diffusion, neglecting depletion of the 

cloud either by radioactive decay or scavenging during transit, .multiplied by 

the breathing rate. 

Meteorological parameters were selected to be indicative of slow 

dispersion at a rate estimated to occur at a reasonable frequency. Such 

conditions could be expected to apply between 15 percent and 25 percent of 

the time in most areas of the United States. They would correspond closely 

to Pasquill's type F, stable dispersion regime, which has a frequency of 

occurrence (in England) in this range, according to Beattie. (9 

parameter values used were: 

Z - 1 meter.sec-1 

C = 0.40 meters n/2 

C = 0.07 meters n/2 z 

n = 0.5 

2d 2-] '11/2 = d"75 0..• 

y -- [1/2 C 2 d 2-n' l2; d 

2 75 

crz= [ 1/2 C. z2d 2-n ]112 = 0.07 d-. 

The "source term", Q.,in equation (1) will be dependent upon the amount of 

radioactive material which has accumulated in the reactor during operation. 

A simplified formula for the reactor inventory, t, for a specific isotope 

is given by equation (2). 

qt = po0 x 3.2 x 1016 x W (l-e"ArTO) 

3.7 x 1010 

qt z 0.865 x 106 Po L(l-e"XrTo) (curies) ........... ... (2) 

W here: 

t is the amount of isotope type i contained by the reactor 

at shutdown, (curies). 

P0 is the rated reactor power level, (Megawatts). 

19
9. S 

3.2 x 1016 is the number of finsions.second.-,megawatt'l" 

Tj is the fission yield, (atomsfisiOn'j ) 

r is the radiological decay constant for the isotope, equal to 

0.693 , (secondsl). 

T 

T is t~e radiological half-life for the isotope, (secondsl). 

r 

T is the time interval during which the reactor has operated, 

(seconds). 

3.7 x 1010 is the number of disintegrations-sec .'curie 

When the reactor has been operated for a time interval such that 

0T » T , the term a A1"T 0 becomes insignificant and the resulting formula for 

the "saturation" inventory,,%, is given by equation (3)

% = o.865 Io0 Po Lt (curies) ................... (3) 

Note that this is only true when To>>Tr, and therefore does not hold for very 

long-lived isotopes. The approximation is adequate for iodines but inadequate 

for Sr-90. Saturation values for the several iodine isotopes per Megawatt 

are given in Table I. 

Table I. Saturation Inventory of Iodine Isotopes 

)u) Yield (l1) ' [ 

Isotope (sec- 1 ) (W) (curies/Mw) 

131 9.96 x 10l-7 2.9 2.51 x 10 0 

132 8.26 7 10-5 4.4 3.81 x l0 

133 9.20 x 10-6 6.5 5.63 x 104 

134 2.20 x 10"4 7.6 6.58 x 104 

135 2.86 x lO-5 5.9 5.10 x 10 

The amount of a specific isotope,Q, * per Megawatt power, which is 

released from the reactor building to the atmosphere during the time interval, 

r, assuming constant leak rate and radioactive decay only until release, is 

given by equation (4). 

20

J
qr -- YpFb rn_°•~ 1dt (curies'Mw- 1) 

=r F F[ (cl~ 4 

IP J >+Xr 

Where:. P is unit reactor power (one megawatt). 

F 1is the fraction of the isotope released from the primary p 

containment system to the building. 

Fb is the fraction of the isotope which remains airborne and 

available to be released from the building to the atmosphere. 

Sis given by equation (2). 

is the rate of leakage from the reactor building to the 

atmosphere, (seconds"1 ). 

r is the radiological decay constant, (seconds-). 

Sis the time interval since the start of release during which 

exposure is assumed to take place, (seconds). 

Consideration is given to a reactor which has been operated for a 

sufficiently long time period that saturation values, q., for the iodine 

isotopes may be assumed in equation(4). Furthermore, because the radii 

for establishing the limit of the exclusion area and the low population 

zone are determined by the doses resulting from two hour and infinite 

( exposure, respectively, t may be assumed to be 7200 seconds and infinity. 

Two forms of the equation are therefore necessary for the evaluation. 

For exclusion distance: 

"F F +Xr_)720o 

For low population zone distance: 

x F b x[qs] X (curies.¶w,") ................ .(6) 

The model assumed in developing equation (4) is somewhat oversimplified 

because it assumes that the fission product is formed directly by fission

21
process rather than through decay. Actually, most of the iodine isotopes 

are formed from the decay of tellurium or, as is generally the case, from 

the decay of antimony and tellurium. The actual formation is of the type 

A-e.B-..C rather than formation of C directly. When the half lives of the 

precursors are short compared to that of the iodine considered, the effect 

of the precursors may be ignored and the model is adequate, but when the 

half life of one or more of the precursors is long compared to the iodine 

isotope considered, that half life will be the controlling factor in the 

decay chain after shutdown and the source determination must consider this 

factor. In the case of 1132, the complete decay chain and half lives 

involved are: 

Sb1 32 (l.9 minute)-.*Te 132 (77 hour)-. 1132(2.4 hour). 

If the reactor has been in operation sufficiently long to establish 

radiological equilibrium, the activity of the TeI• and the 1132 are equal. 

Since the activity of 1132 after reactor shutdown will be determined by. 

the decay rate of the Te 1 3 2 , equations(4%(% and(6)may be used to determine 

the 1132 source terms if the decay constant of the Te 1 3 2 is used in place 

of the decay constant of 1132I A more exact determination of the source 

term for 1131 would also consider that amount which would be produced 

from the Sbl 3 1 -*Te1 3 1 chain subsequent to shutdown. The amount is relatively 

insignificant and the calculation would needlessly complicate the example. 

Values for %for the exclusion and low population distance can be readily 

determined because values for all the factors have been given or calculated. 

Table II contains a listing for each of the iodine isotopes and the two time 

periods involved using the values: 

F = 0.5, p 

Fb a 0.5, 

-o0.1% day-". 

S0.001 day".0 

= 1.16 x 10-8 sec"1 . 

22
The breathing rate, R!,in equation (1) is also a variable. The "standard 

is considered to breathe 20 meters'.day'l; half during the active 

8 hours and the remaining half during his relatively inactive or resting 

Table II Amount of Iodine Released in Time 

Qr (curies.Nwr) 

Iodine V = 2 hours (Low population 

Isotope (Exclusion area) zone) 

131 5.20 x 10"1 7.20 x 10 1 

132* 5.95 x 10"I 4.42 x 101 

133 1.15 x 100 1.75 x 101 

134 6.80 x 10o" 8.70 x 10o1 

135 9.65 x 10l1 5.15 x 100 

( includes Te 1 3 2 contribution following shutdown for t= c. 

These values of Q will be used directly in evaluating 

equation (1). 

hours. Since concern for personnel in the exclusion zone is based on two 

hours of inhalation, consider the breathing rate to be characteristic of 

the active portion of the normal work day, 

R = 10 meters3/8 hours = 3.47 x lO74(m3.sec']). 

( For the low population zone, the average breathing rate is assumed, 

R = 20 meters 3/24 hra = 2.32 x lO'k(m3.secl). 

Since values have been given or calculated for all factors in equation 

(1), the amount inhaled A,, can be determined for various distances, d, down

wind. When the amount inhaled of a specific isotope is determined, the dose 

to the critical organ which will be delivered by this amount can be calculated. 

The dose rate, D', to the critical organ such as the thyroid at any time 

subsequent to the inhalation is given by equation (7). 

23
D' (rads.sec 1 ) = A (curies) x 3.7 x 101 0 (i.Lse-N'l.curio 1) 

x f x f(Mov.dis•

1 ) 1.6 x 106(erg.Mev)oiJet a 

* *(grams) 100 (ergs.gC' 1 .rad"1 ) 

5.92 x102 AT a~ . .2aL(rads"-ec'). . ... (7 

a 

Where.: 

Ar is given by equation (1). 

a is the fraction of the amount inhaled which is deposited in the 

critical organ. 

t is the effective energy absorbed by the critical organ per dis

integration, (New). 

Xez Xr +4b = 0.693, (e T 0 

Xb is the biological el'imination rate for the isotope, (sec1). 

T is the effective half life for the isotope in the body, (sec). 

a is the mass of the crAtical organ, (grams). 

And the dose to the critical organ, delivered in tise,T is given by equation (8). 

DT=i0 D' dt 

5.92 x 102 Ar fat I-e "e (radT) 

- o.6•3 T 

DT=~ D 102 A 1a f.•xlO ~ ZTLT-e T 0 F 0: _7 (rads) ........... (8) 

When the timeTS(over which the dose is determined) is such greater than 

0.693 T 

the effective half life of the isotopes, the quantity•e Te 0 becomes 

insignificant and the dose to the critical organ is given by equation (9). 

..= 8.54 x 102 ArfaI T e (rads) ................ .. (9) 

Using equation (9), R has been evaluated for the iodine isotopes and the 

values are presented in Table III. 

24

I
Table III Dose to Critical Organ Per Iodine Curie Inhaled 

Iodine 

Isotope Te (sec) DO/At(rads.curie 1 ) 

131 6.57 x 0 5 .4$ x 106 

132 8.39 x lo3 5.35 x 3 04 

133 7.52 x l04 4.o x l0 

134 3.11 x 103 2.5 x 104 

135 2.42 x l10 1.24 x lo5 

C. External Gamma Dose Calculations 

The external gamma radiation dose at the exclusion and low population zone 

distances due to fission products contained in the reactor building were deter

mined in the following manner. The source of radiation was considered to be 

( those fission products released from the primary system to the containment 

building--krypton, xenon, iodines, and a mixture of the remaining "solid" 

mixed fission products. 

From a point source of radiation-given off by a specific gamma emitting 

isotope, the dose rate at a distanced (meters)laway in air is given by 

equation (10). 

Dose rate, D'Crads.sec&1) F xP (Mw) x[2 a](curies.mi~l) 

x 3.7 x 10I0 (dis.sec'.curie"I) x EI(Maev.dis ") 

x 1.6 x lO16 (ergs.mev"1) x pa(meter'l) B e ud-eArt 

+ 1.293 x l03(grams.-eter•a ) x 102 (*rgs.gram,'-rad 1 ) 

x 4r1 2 (meter 2.) ....... .................. (1) 

In equation (10), the dose buildup factor, B, is expressed by equation 

(12) (l0a). 

B = 1 + ku d . . . . . . . . . . . . . . . . . (lOs) 

After combining terms, equation (10) can be expressed as -2- j d - A r t ( a s s c l " . ( i 

D' = 0.985 Sox rpx PoPa d + k-dte x 

DI a C -crt

25
Where: 

S is the initial gamma source strength for the specific isotope 

at shutdown, (Mev.Sec'l.Mw-1). 

F is the fraction of the isotope released to the reactor building. p 

P0 is the rated reactor power level, (Mw). 

Pa is the energy absorption coefficient, (meter 1 ). 

k is the linear absorption constant, (22-a). 

l-a 

pu is the linear absorption coefficient, (meter1). 

d is the distance to receptor, (meters). 

Ar is the radiological decay constant, (sec-). 

t is the time after shutdown, (sec). 

C is a constant defined by the equation. 

The termSo0 3combines three terms in equation (11): 

S 3x 3. x 010 x E (Mev.sec 1 . Mw-). 

Where: 

[i] is the saturation inventory, (curies.Mwl). 

p1 

El is the total gamma energX per disintegration, (Mev.disl). 

3.7 x 10 is the number of disintegrations.sec'l.curie-1. 

Table IV contains values of So, , S R, Tr us, ?a' k, and Eavg for the isotopes, 

the "solid" mixed fission products and the gross fission products assumed to 

be released to the reactor building. The values of a, Ua' and k are energy 

dependent. Hence, "average" energies, EavI were selected after reviewing 

the weighted spectrum for each isotope and mixtures.ll) The term SR is the 

product of S and F for the assumed release conditions. 0 p 

Integrating the direct gamma dose rate, Dl over a specific exposure time 

yields the direct gamma dose. 

Do =rDr dt(rads) 

0 dt 

D, - ZI-e J(rads) .............. .. (12) ^r

26
AaE AO Da Table IV. External Gnmma I Data

Gamma Source 

I. Iodine 

131 

132 

133 

134 

135 

Total Iodine 

II. Xenon 

1318 

133. 

133 

1350 

135 

Total Xenon 

III. Krypton 

83. 

850 

87 

88 

Total Krypton

(-11) "Average" 

Half Life Energy 

T E(Mev)

8.05 days 

2.4 hrs. 

20.8 hre. 

52.5 mine. 

6.68 hre 

12.0 days 

2.-3 days 

5.27 days 

15.6 mins. 

9.13 hrs. 

114 mina. 

4.36 hrs. 

78 mins. 

2.77 hre.

IV. Mixed Fission Products * 

"OSolids" (Varied)

0.4 0.8 

0.55 

1.3 

1.5 

o.163 

0.233 

0.O81 

0.520 

0.250 

0.02 

0.20 

2.00 

2.00

0.7

Initial(11) 

Source Strength 

So(Mev/sec-Mw)

3.63x1015 • 14 

2.82x10,• 

1.15X1015 

3.10xlO 

15 

1.5021012 

1.16x1013 

1.67210 14 

2.94x1014 

4.65x10"4 

9.70110J' 

6.35x102 

8.65xlO0 

4.8 4xI0 1 

2.44xI015 

3.0221010 

3.72x,016

Release Released 

Fraction Source Strength 

F SR (Yev/sec-Mw)

0.5 

0.5 

0.5 

0.5 

0.5 

0.5 

1.0 

1.0 

1.0 

1.0 

1.0 

1.0

1.0 1.0 

1.0 

1.0 

1.0

0.01

V. Gross Fission 

Products 

Total of 

l,II,IlI,lV

l.81x 11 4 

1.41x1015 

0.5710 15 

1.455x015 

5.1661ol 

1.50X1012 

1.1621013 14 

1.6711014 

2. 94xl014 

4.65x10• 

9.4ox 1 

8.65xlO 

4 .84xlOi 

2.441015 

3.0221015 

3.7241014 

9.4910o15

Linear(13) 

Absorption 

Coefficient 

p Crater-1)

1.23Xo21 

1.08X10•2 

7.2oo03 

6.7x10" 

2.2x,. 02 

1. ixi0:2 1.5x102,

Linear•(13) kiergyC(') 

Absorption Absorption, 

Constant Coefficient 

k Na(meter- )

2.22 

1.45 

1.85 

1.10 

1.02 

4.0 

3.2 

7.0 

1.9 

3.0

(dose considered 

1-610o-z 325 

5.8x2o03 0.9 

5.8x1073 0.9

1•OxlO"2 1.6

3.87103 

3.91xO0' 

3.4xlOo3 

3.3x10 3 

3. 3210w 

3.6xO0-3 

2.7x2.0-3 

3.9xlO'3 3. 6x,63

negligible) 3 

3.OxlO

3.8x•o;

""Solid" Fission Products have an effective half-life of 2.72 

hours during the first 2 hours of decay after long-time operation 

and have an effctive decay rate which follows t"UO21 after the 

first 2 hours.

o m
Considering the exclusion distance, the expose time is 2 hours and equation" 

(12) becomes: 

D [11.700) (rads). . . ... .() 

and for the low population zone, the exposure time is 30 days, which in 

several half-lives for the isotopes of the noble gases and iodine. Equation 

(13) for these isotopes, may be written as: 

In the case of the "solid" mixed fission products the dose for the first 

two hours was considered to be decaying exponentially with a half-life of 

2.72 hours (Ar = 7.05 x l1"- sec"1 ) and subsequently as t-0"21 based on 

interpretations of data from Blomeke and Todd.(ll) 

For the first two hours, the dose wasm 

D C r (-e areds .. . (15)... 

Ar 

and for the 30 days, the dose ans: 

D, " 1[,I'•l] + C 'Artl t2 t'O'21 dt 

-Ir-'7 .At"[Z0.7 t" 071 ra4 .. .. .. (6 

and since t2>> V'lt equation (26) can be written: 

Dy z C [I-e Ar"1l+ C -Irl C 0 - 9 (rad.). . . . . 9(17) Xr 0.79 

The total direct gamma dose is the sun of the doses from each of the source 

terms as determined by equations (13) and (15) for the exclusion area and 

equations (14) and (17) for the low population zone. 

D. Results 

-The results of the calculations performed for the inhalation (iodine) 

dose and the external gamma dose for the exclusion area (t= 2 hours) and 

the low population zone (MOeO and 30 days, respectively) are presented in 

28

I.J
(sanoq '--I GnTPVU UOTGn1[OX2

asoa 

C.PT:Icsc 0 T OTx6zec -ODC909 OT"al ju!ýOj T T sýonpo4j 

UOIGST'I 

PGOvOTOU 'A

OTXCSOIV -T 

c--; T-O'XZC 00-vuel i6OIXOTOZ

5-PM"6 C-014Z*6 -E-OEx5o*Y I O'EXTZOT 9_PM*9 41_olxo*5 Z.PIXZ5*Z E-OTX55-L

Z-OTXTL*t T-OTX0*Z OOTXC*l 

Z-OTXRY'T E-OM'Z OOTXZ5'C 

Z Z-OTXZ*C T- 0-,X*/*5 

,-oO= OT r-OIX960 OMYOZ 

(uoppqTX4uO5 *TqTBTTBa;-)

g-bTxqY*z 

c-oTx9ZOZ 

iE-YITI*T 

c-OTX96*T 

e-OTXZ5'T 

41-OTX5 5 * T 

4,-OTX50*T 

II-OTXSO*T 

5-OTX51-6 

w 0001

4,-oTxY6o8 

41-OTX5k*L 

ý-OMT s T

C-OTX21*T T-OTXCO"Z TOTx5C*L 

41-OTXC * L OTX*I*T OTXL*6 

5ý,OTxws T- OTM9*41 

ý890-C C- :5,Z T-OTX650T -OTX I OTII OTXT*9 Z

-OTXOT 0 T Z- OTXLZ-Z U61x%--E 

41-0 , c _OTXW'7[ OTX60*T

41-O'EXC6*T Z-OTXZROZ ooTx9z*z 

+1 OTX90 *E Z-OTXZO * Z 00TX-EVT 

6-OTx5zO9 C-OTXZ9*41 OIX5501 

-OTXES-T C-OTXCLOZ T CLeq 9 T-OTX 

C)-OTNO.c 41-OT)qk*5 Z-OTX99*C - AT=T 0 C - DIM9109

NOPTIOSU 

ajonpoij 

UOISSIa -AI 

UO'r4CUJ)l IV401 

as 

LR 

Mýq 

MC13 

uojd&X 9111 

UOUOX rPýOj 

5CT 

M5CT

CCT 

mCCT 

mICT 

UOUGX oil 

QUTPOI TVIOI 

M 

4ICT 

UT 

zCT 

TET 

OUTPOT *I 

GOMWS UUMD

.m 

cu

,V-O-EXU* 

1;0=: ZT 

OTx6**/ L'---

Z-OTXL9*1 

C- OTY-5L*k OIX59*c 

4C/--OTX5 Z * 6 

C- OTXTOOC 

v OTX6'7*T

ootxYO'6 

Ornng"i 

OOTXT9*T 

OOTXZ96T 

OOrA99*Z 

T-OTXC*5

Z-OTXLIIOL 

Z- OTXtT 0 41 

C-PIXV961 

C- oTx6C*,r 

C-O-CxgL'9 

Z-OTX90 Z 

R-0-09

OOTXT5-C 

OTX04/0 L 

T-OTXZOOT 

T

'OTXgZ:L 

T- z T-07pcý)Z 

OOTXZL'*T 

M-O-OT

ZOTXZ.T 

I OTX041 0 T 

OOTXZO*Z 

T 0" Ilz 

OoTx569,5 

T OTXY*L 

U1 OOT Z 00-OT U 0-09 V-0-OT

to OE = 2) GUOZ uoT,4vcnaod Ful

IXX/BPIB.Z) asoa WW6 4,09JTa

9-4-Ene voa wmmD foule-pa ,A aTqv.,
Table VI,- Inhalation Dose Results

Inaaion IodneDse rads/A2

Inhalation Source 

Icdine 

131 

132 

133 

134 

135 

0 Total Iodine

Exclu~sion Radius (T =- 2 hours)

6.02x1Q'~1 

3.36xl0o 

3.611101l 

l.33X1IO 

9: 4X107 

-101-

1 -1 

1.94110. 

1. 06X10... 

1. 16x10.3 

4 281102 

3 3.X0721 

_1 3.55X10

104M 

6. o2x1o0A 

3 36x10,' 

4.x1 

1. O10ao

1 _94x0 

1.08110ý] 

4 .28x10 6

. 3 .01X105 

3. 55X10O

Low Population Zone ( c

102M 

5.6110 1 

1.2411011 

3.661101 

3 .35xi10 

6.121102

103M :1O~ 

3.18xl0O 1.24x10:, 

1. 18x10 3 66x10 

I.C7xlO-- 3.35X10 " 

1.96W al 6.12x10-1

Values Assumed for Results: 

F b=a0.5 

F = 0.5 

; , 1 meter-sec 

C y 0.4+0 meters n? 

Cz z 0.07 meters D/Z 

n a 0.5 

X, 0.1 percent.duyiy

105m 

-2 

1.79xl104 

3 98Xl0.. 

3.66X104 

1. 07x1 

1.9(=1072
Tables V and VI. Based 

for reactors of various 

Table VII.

upon these results, initial estimates of distances 

power levels have been develo,.ed and are listed in

Table VII. Calculated Radii for Water Cooled Reactors

of Various Power Levels 

Exclusion Low popula

area tion zone 

distance distance 

(miles) (miles) 

0.88 13.3 

0.77 11.5 

0.67 10.3 

0.63 9.4 

0.58 8.6 

0.53 8.2 

0.48 7.2 

0.43 6.5 

0.37 5.4 

0.31 4.5 

0.29 3.4 

0.25 2.2 

0.21 1.4 

0.13 0.5

The estimated radii for power reactors are graphically represented 

in Figures 1 and 2. For the exclusion distance, doses from both direct 

gamma radiation from the reactor building and from iodine in the cloud 

escaping from the reactor building were calculated, and the distance 

established on the basis of the effect requiring the greater isolation. 

Figure 1 shows the thyroid and whole body doses for various power leveli. 

Under the conditions assumed, the doses resulting from the inhalation 

of the -isotopes of iodine are controlling for the low population zone 

distance and population center distance. However, it is possible that 

such may not always be the case and this should be checked for each case 

under consideration. The low population zone distance results from 

31

Population 

center 

distance 

(miles) 

17.7 

15.3 

13.7 

12.5 

11.5 

10.9 

9.6 

8.7 

7.2 

6.0 

4.5 

2.9 

1.9 

0-7

Power 

Level 

(Mw ) 

1500 

1200 

1000 

900 

goo 

800 

700 

600 

5CO 

400 

300 

200 

100 

50 

10
MILES 

0.25 0.50 0.75 

-l4 1! 

// 

- /~/

/ 0 

/ TOTAL THYROID DOSE FOR 

oIOS 

,// 

/ ~DIRECT GAMMA DOSE FORt / 2 HOURS EQUALS 25 RADS. 

II 

40 I10 

0 200 400 600 800 1000 1200 1400 

RADIUS (METERS) 

Figure 1. Exclusion Radius Determination.

32
MILES 

1.0 2.5 40.0

403 l0e 

RADIUS (METERS)

Figure 2. Population Radius Determination.

33

0.25

40s

404

(

l4o 

40'

40 L.. 

lol0
integrating the effects of iodine 131 through 135. The population center 

distance equals the low population zone distance increased by a factor

of one-third. Figure 2 shows the relationship between the inhalation and 

direct dose for various power levels.

34
, . . , 

VI. COMPARISON OF ANALYTICAL METHOD TO EXISTING REACTOR SITES 

As an indication of how the use of the above analytical method 

results in distances reflecting current siting practices, the method was 

Table VIII. Calculated Distances for Selected heactors

Power 

/ tor Level 

_tLt) 

Dresden 630 

Con. Ed. 585 

Yankee 485 

*PRDC 300

PWR 

Consumers 

*Hallam 

Pathfinder

270 

240 

240 

203

PG&E 202 

*Phila.Elec. 115

NASA 

River 

VBWR 

*Piqua

60 

60 

58 

50 

48

Exclusion Area 

Calculated Actual 

Distance A•istance 

tmiles) tmiles)

0.50 

0.48 

0.42 

0.31 

0.31 

0.30 

0.30 

0.29 

0.29 

0.26 

0.22 

0.22 

0.22 

0.21 

0.21

0.50 

0.30 

0.50 

0.75 

0.40 

0.50 

0.25 

0.50 

0.25 

0.57 

0.50 

0.50 

0.23 

0.40 

0.14

Low Population Area Population Center Distance 

Calculated Calculated Actual 

Distance Distance Distance 

(miles) tmiles) kmiles) 

7.4 9.9 14.0 

7.0 9.4 17.0 

6.3 8.4 21.0 

4.5 6.1 7.5

4.1 

3.9 

3.9 

3.4 

3.4 

2.4 

1.6 

1.6 

1.5 

1.4 

1.4

5.6 

5.2 

5.2 

4.6 

4.6 

3.2 

2.1 

2.1 

2.0 

1.9 

1.8

7.5 

135.0 

17.0 

3.5 

3.0 

21.0 

3.0 

25.0 

20.0 

15.0 

27.0

*NOTE: These reactors are not water moderated and are included in the table 

for illustrative purposes only. The distances for all reactors were 

based on the same assumption with respect to fission product release 

from the fuel and containment vessel and the subsequent dispersal 

events. There car. be considerable differences between reactor types 

in the events that could result in a major accident and the releases 

that might be experienced. This must be examined on an individual 

basis for each reactor and the distances determined accordingly.

35
applied to a number of reactor projects that have been proposed o# are 

currently authorized for construction. These results are given in 

Table VIII.

36
VII. APPENDIX 

A. RelationshiD of the Sutton Diffusion Parameter and the Generalized 

Gaussian Parameter 

The traditional form of the 0. G. Sutton atmospheric diffusion 

equation describing the centerline concentration downwind of a 

continuous point source is generally written: 

v-I

Q1. Z C 

Sy Cd 2 -n 

This equation was based on an extension of diffusion theory, an 

assumed homogeneous isotropic source, and an assumed three dimen

sional Gaussian distribution model. 

When the receptor and cloud centerline are coincident with 

the ground level, the concentration is assumed to be doubled as 

a consequence of "ground reflection".: 

X =- 2 

Q1 r :• Cy C d2

-n 

The diffusion coefficients, Cy and CO are mathematical 

quantities which represent the diffusion capability of the atmos

phere. However, Sutton and others found it necessary to determine 

values of Cy and C. indirectly from data obtained through experi

mental field measurement. By expressing the diffusion coefficients 

in terms of standard deviations of the Gaussian distribution model 

which is assumed to describe the spacial relationship of cloud 

37
concentration, the resulting equation may be written in the more 

useful form: 

S= 1 

Where: 

0- and a are the standard deviations of the cloud 

concentration in the vertical and horizontal direc

tions, respectively. 

The factor of two which was introduced for "ground reflection* has been 

included in this equation. The equation in this form, with the Gaussian 

parameters, permit direct interpretation of expdrimental data obtained 

from field measurements. 

The relationship between the generalized diffusion parameters (14) 

and the more familiar Sutton parameters (4) are expressed ass 

Cr = -n/2 

y= 1 C y dl 

Orz 0 &, d1-/ 

In the generalized form, the parameters a' and 06 are functions of dis

tance and can be approximated directly from anemoneter records if 

appropriate averaging techniques are supplied 

B. Bibliozraphr 

The following reference documents contain information pertaining to 

data obtained from various reactor projects and from associated 

analytical programs. The following list constitutes a brief summary 

of the information available on certain factors pertinent to reactor 

siting. 

1. McCullough, C. R., Safety Aspects of Nuclear Reactors, D. Van Nostrand 

Comparn, Inc., Princeton, New Jersey, 1957. 

2. Rockwell3, T., "Reactor Shielding Desin Manual", TID-7004, Yarch 1956. 

38
3 .ldtchie, R. H., "Dosimetry Aspects of Nuclear Accidents", Nuclear 

"Safety, 2(1) pp 71-75, September 1960. 

4. Culver, H. N., "4aximum Credible Accident Exposures at Reactor Site 

Boundaries", Nuclear Safety, 2(1) pp 83-96, September 1960. 

5. Proeress in Nuclear Safety - Series 4, "Technology, K.ngineering and 

Safety", Hurst, R., Lyon, R. N., and Nicholls, C. M. - Editors, 

Pergamon Press, New York, New York, 1960. 

6. Britten, R. 0., "Reactor Containment", ANL-5948, May 1959. 

C. List of Symbols and Definitions 

Symbol Rerresents Dimensions 

At Amount of radioactive material inhaled by curies 

an individual during a specific time 

period. 

( B Build up factor. 

C Cz Meteorological virtual diffusion metersn/2 coefficients in the vertical and 

horizontal planes, respectively. 

d Distance from the source of radiation or meters 

release point. 

D Dose rate delivered by an exposure to rads'sec-" 

radiation. 

DT, Dew Dose delivered during time interval IT" or rads 

infinite time. 

D1 Dose delivered by direct exposure to gamma rads 

radiation. 

E Effective energy absorbed by the critical Mev.dis"I 

organ per disintegration. 

Eavg Average energy assumed for selecting Mev'dia-I 

values ofu . 

El Total gamma energy emitted per disintegration. Mev.dis"1 

fa Fraction of inhaled material which is 

subsequently deposited in the critical 

organ. 

rb Fraction of material released to the 

reactor building and available to be 

released to the atmosphere. 

F Fraction of inventory released from the 

P primary system to the reactor building.

39
List of Symbols and Definitions (Cont'd.) . -

Dimensions

k 

a 

n 

P 

Po 

q3 

qt 

R 

Sot S

r 

t, T 

T 

0 

y5, b' e' r 

lft2 

CrC 

zP

Linear absorption constant, s ). 

Mass of the critical organ. 

Meteorological stability partamter. 

Rated reactor power level. 

Unit reactor power (1 megawatt). 

Saturated reactor inventory for a 

specific isotope. 

Reactor inventory for a specific 

isotope after a finite operating 

time. 

Amount of a specific isotope released 

to the atmosphere during a finite time 

interval per megawatt reactor power. 

Breathing rate. 

Source terms at shutdown - sotal and 

released to reactor building. 

Time variables. 

Reactor operating time. 

Biological, effective, and radiological 

half-lives. 

Average wind speed. 

Exposure time intervals. 

Standard deviations *F Cloud concentration. 

Fission yield. 

Biological, effective, and radiological 

elimination and decay constants. 

leak rate from the containments shell 

(reactor building) 

Linear and energy absorption coefficients

40

i

grams 

curieW 

curies 

curies'*w"1 

meterse*.se-1 

VAv. sec-l. •M-1 

seconds 

seconds 

seconds 

meters" sec 1 

seconds 

nuclei fission-I 

second"l 

second

meter"I
]REFERENCES 

1. "Reactor Site Criteria", Title 10, Code of Federal Regulations, 

Part 100 (10 CFR 100), February 11, 1961. 

2. "Theoretical Possibilities and Consequences of Major Accidents in 

Large Nuclear Power Plants, " WASH-740, March 1957. 

3. "Permissible Dose From External Sources of Ionizing Radiation", NBS 

Handbook No. 59, w/addendum of April 1958, September 24, 1954. 

4. Sutton, 0. G., "A Theory of Eddy Diffusion in the Atmosphere", 

Proceedings of the Royal Society (London), 135A:143, 1932. 

5. "Meteorology and Atomic EnerM0", AECU-3066, July 1955. 

6. Gifford, F. A. Jr., "Use of Routine Meteorological Observations for 

Estimating Atmospheric Dispersion", Nuclear Safety, 2(4) pp 47-51, 

June 1961. 

7. Meade, P. J., "Meteorological Aspects of the Safety and Location of 

Reactor Plants", World Meteorological Organization, Technical Note 

No. 33, pp 13-22, 1960. 

8. Hosler, C. R., "Low-Level Inversion Frequency in the Contiguous 

United States", Monthly 6eather Review, 89 pp 319-339, September 1961. 

9. Beattie, J. R., "An Assessment of Environmental Hazards from Fission 

N Product Releases", AHSB(S)R9, May 1961. 

3.0. "Report of ICRP Committee II on Permissible Dose for Internal Radiation 

(1959)", Health Physics (Journal), Volume 3, June 1960. 

11. Blomeke, J. 0. and Todd, M. F., "Uranium-235 Fission Product Production 

as a Function of Thermal Neutron Flux, Irradiation Time, and Decay Time", 

O14L-2127, Part 1, Volume 1 and 2, November 1958. 

12. Goldstein, H., The Attentuation of Gamma Rays and Neutrons in Reactor 

Shields, May 1957. 

13. The Reactor Handbook, AECD-3645, Volume 1, "Physics", February 1955. 

14. Gifford, F. A. Jr., "Atmospheric Dispersion Calculations Using the 

Generalized Gaussian Plume Model", Nuclear Safety, 2(2) pp 56-59, 

December 1960.