ATOMIC ENERGY W^Km L'ENERGIE ATOMIQUE OF PROGRAM … · AECL-7616 ATOMIC ENERGY W^Km L'ENERGIE ATOMIQUE OF CANADA LIMITED ^MtoJF DU CANADA LIMITEE PROGRAM FOR ANALYZING POWER BOOST

AECL-7616

ATOMIC ENERGY W^Km L'ENERGIE ATOMIQUEOF CANADA LIMITED ^ M t o J F DU CANADA LIMITEE

PROGRAM FOR ANALYZING POWER BOOST TESTS

Programme pour analyser les essaes d'augmentation de puissance

C. A. WILLS

Chalk River Nuclear Laboratoriss Labcratoires nucleaires de Chalk River

ChHk River, Ontario

March 1982 mars

ATOMIC ENERGY OF CANADA LIMITED


by

C. Anne Wills

Mathematics and Computation BranchChalk River Nuclear LaboratoriesChalk River, Ontario Canada KOJ 1J0

1982 March

AECL-7616

L'ENERGIE ATOMIQUE DU CANADA, LIMITEE

Programme pour analyser les essais d'augmentation de puissance

par

C. Anne Wills

Résumé

Toute augmentation rapide de la puissance d'un réacteur produit unedéfaillance dans le combustible. On a planifié et exécuté des expé-riences permettant d'étudier les conditions pouvant exister dans leréacteur NRU après une telle défaillance. A partir des concentrationsde certains isotopes relève' s â différents moments au cours d'uneexpérience et provenant, par exemple, du programme SARGS et de l'histo-rique de la puissance du réacteur, ce programme permet de calculer lestaux de libération, les coefficients de fuite et les dégagements frac-tionnels pour les isotopes. Ces valeurs peuvent être soit impriméessoit présentées sous forme de courbes. Des diagrammes de désinté-gration concernant quelques nombres de masse sont établis. Ecrit enFORTRAN, le programme est exécuté sur le système CDC 66OO-CYBER 170.

Département de mathématiques et de calculsLaboratoires nucléaires de Chalk RiverChalk River, Ontario, Canada KOJ 1J0

Mars 1982

AECL-7616

ATOMIC ENERGY OF CANADA LIMITED


by

C. Anne Wills

ABSTRACT

A rapid increase of power in a reactor produces a failurein the fuel. Experiments to study the conditions in theNRU reactor after such failures have been planned and carriedout. Given the concentrations of specified isotopes at anumber of times over the length of an experiment as produced,for example, from the program SARGS and the power history ofthe reactor, this program calculates the release rates, escaperate coefficients, and fractional releases for the isotopes.These values may be optionally printed and plotted. Decayschemes for a limited number of mass numbers are implemented.The program is written in FORTRAN and runs on the CDC 6600 -CYBER 170 system.

Mathematics and Computation BranchChalk River Nuclear LaboratoriesChalk River, Ontario Canada KOJ 1J0

1982 March

AECL-7616

TABLE OF CONTENTSPage

1. Introduction

Calculations2

2. Formulas and Calculations 2

2.1 Release Rate2.2 Escape Rate Coefficient and Fractional Release

3. Programming Notes '?

3.1 Input Data Files 1 2

3.2 Data Structures 1 3

3.3 Subroutine Descriptions ^

4. Running the Program 2 8

4.1 Card Image Input 2®4.2 Sample Deck 3 3

4.3 Output 3 3

5. References 40

LIST OF FIGURESPage

1. Hypothetical Decay Scheme 6

2. Power Boost Test program Logic 10

3. Records in Input File from SARGS 1 4

4. Data Array Structure 16

5. Information Table 18

6. Sample Decay Schemes 19

7. Subprogram Dependencies 21

8. Decay Schemes Implemented in the Program 23

9. Flowchart for POWCAL 2 5

10. Table Produced by BURFEL 3 0

11. Default Table of Constants 3 2

12. Sample Concentration Output 34

13. Sample Rêase Rate Output 35

14. SampJe Escape Rate Coefficient Output 36

15. Sample Fractional Release Output 37

16. Sample Plot of Concentration and Release Rate 38

17. Sample Plot of Escape Rate Coefficient and Fractional Release 3 9

PROGRAM FOR ANALYZING POWfK BOOST TESTS

by

C. Anne Wills

1. INTRODUCTION

This program has been written specifically fo; analyzing the resultsfrom the power boost tests in the U-2 loop of .he NRU reactor. Thefuel defect tests in the 0-2 loop are analyzed by the three programs X2FM,GRAAS, and SUMRT [7]. This program is a replacement for SUMRT and it isneeded for several reasons.

(a) The power boost tests are performed over a shorter period of timethan those that SUMRT was written to handle. The arrays in SUMRTare very large in order to process data covering several months andtwo temporary disk files are used for intermediate storage of theresults. A program which uses less core is thus more efficient.

(b) The power boost tests are designed specifically to look at short-lived isotopes. Also,since the tests run for only one or two days,the conditions in the loop can be held constant. The loop modelused is/ therefore, much simpler than the general one provided forin SUMRT.

(c) A modified version of the GRAAS program outlined in [7], calledSARGS, is used for the initial analysis of the data. In additionto the identification and area calculation of peaks in the spectra,SARGS also calculates concentrations for the small number of isotopesbeing analyzed. The output file from SARGS contains times and con-centrations and the calculation of concentration in SUMRT is notneeded.

(d) In addition to the SUMRT output of concentrations and releaserates, escape rate coefficients and fractional releases are alsocalculated and output. Additional routines are needed to providethese values.

(e) Where possible, the routines in the SUMRT library have been usedin this program. However, the output requirements for the powerboost tests are slightly different. The printed output has adifferent format so a replacement routine was necessary for this.Since the data covers a shorter period of timer the smoothedconcentration could usefully be added to the normal concentrationplots.

- 2 -

The following sections of this report give the theoretical develop-ment of the calculations implemented in the program, an overviewof the logic of the program, details of the data structures used, ashort description of each subroutine, a user's guide for running theprogram, and a sample run showing the format of the output.

2. FORMULAS AND CALCULATIONS

The power boost test program calculates:

(a) Release rate(b) Escape rate c.'efficient(c) Fractional release

Spectral data recorded over a period of time is input to the programSARGS. It calculates concentrations for various isotopes at the timeof each spectrum. From this information the power boost test programproduces release rates for each of the isotopes at the time of eachspectrum. The development of the equation used to calculate releaserates is given in Section 2.1.

From the release rate of an isotope and the quantity of that isotopepresent in the fuel, the escape rate coefficient and fractionalrelease can be calculated. This is done for each isotope at thetime of each spectrum. The equations used for calculating thesequantities are outlined in Section 2.2.

2.1 Release Rate

For any isotope where the losses due to the decay, deposition, neutroncapture, degassing, and purifier.tion are small during one recirculationtime and where a counting period is long compared to the recirculationtime, the loop may be approximated by a pot model. If C(t) is theconcentration in atoms/m3 and R(t) is the release rate in atoms/sat the defect at time t, then this model states

^ = R(t) - aVC(t) (1)

where V is the recirculating volume of the loop in kg/m and a representsthe losses in the loop in s""1. The measurements actually made in the loopare of the activity concentration N(t) in Bq/m3, which yields the concen-tration when divided by the natural decay constant of the isotope. Thismeasurement is not made at the source, but at a position quite close to itwith a transport time T. Normally, the transport time can be neglectedbut for short-lived isotopes it must be included.

- 3 -

From the measured activity concentration at time t+T, the activityconcentration and the concentration at defect at time t is known.

-ATN (t + T) = N (t) e

= Ac(t) e"XT

thereforeXT

C(t) = - N (t + T) (2)

Substituting (2) into (i) yields the release rate at the defect interms of the measured activity concentration

AT AT

v V ^ _ L T 1 = R(t) _ av

R(t) = j e^l-lf-Ct + T> + «N(t + T)j (3)

Converting from volume to mass, where M is the mass of therecirculating volume in the loop and p is the density of watergives

R ( t )

The losses in the loop are defined as

a = A + B + $ (5)

where A is due to natural decay; 6 is due to purification; and$ is due to neutron absorption.

The natural decay is defined by

A = y± (6)1/2

where t. ,„ is the half-life of the nuclide in seconds. The purificationis defined by

0 - TT (7)

- 4 -

where f is the purification flow rate in kg/s and M is the massof the recirculaîng volume in kg. If no losses occur due to purificationfor a particular isotope/ 8=0. The neutron absorption is defined by

V$ = _±£. a(j,(t) (8)

V

where

v is the volume of the test section of the loop (in m ),TS

V is the recirculating volume in the loop (in m ) .

2a is the cross section of the isotope (in m /n).

<f>(t) is the flux in the reactor core at time t (in n.m .s ).

Substituting equations(5), (6), (7) and (8) into equation (4), andreplacing p by 10~3 kg/m3, the density of the water in the loop, gives

B(t) = 103 J eX

Equation (9) is implemented in the program. The calculation of thereactor flux is discussed in Section 2.2.3.

2.2 Escape Rate Coefficient and Fractional Release

The escape rate coefficient is defined by [6]

K(t) = |}g- (10)

where R(t) is the release rate at time t in atoms/s and Q(t) is thequantity of the isotope in the fuel element in atoms at time t.The escape rate coefficient in the fuel element at time t, E(t), isthus in units of s~*. The fractional release is defined as

where A is the loss of the isotope due to radioactive decay as definedin (6), a is the cross section of the isotope, and $ , ,t) is the flux

elm

- 5 -

in the defective fuel element at time t. Equations (10) and (11)are easily calculated if Q(t) is known. The quantity of each isotopein the fuel element at any time can be calculated from the pow-rhistory of the reactor during the test.

2.2.1 Quantity of an Isotope in the Fuel Element

Consider first the simple case of an isotope with no precursorand no daughter. The isotope will be created within the fuelelement and will be removed from the system due to natural decay,neutron capture, and/or purification. The rate of change of thequantity of the isotope can be written as [3]

-XQ(t) - a$elm(t)Q(t) + YZf*(t) (12)

where

Q(t) is the number of atoms of the isotope present in the fuel elementat time t.

X is the radioactive decay constant of the isotope in s" as definedby (6) .

2a is the cross section of the isotope in m .

$ , (1;) is the flux in the fuel element at time t in neutrons/m .elm

Y is the direct fission yield of the isotope in atoms/fission.

E,<f>(t:) is the number of fissions per second in the fuel element at time t.

Given the number of atoms of the isotope present in the fuel elementat the time of the reactor start up, the above differential equationcan be solved for the quantity of the isotope present at any subsequenttime t.

The power boost program has been set up to calculate the quantity of anisotope which exists in a more complicated decay scheme. Any portionof the hypothetical decay schemes of 4 isotopes A, B, C, and D shownin Figure 1 can be solved.

- 6 -

< >

\ /ll-f)U-g)

Figure 1: Hypothetical Decay Scheme

A fraction of isotope A decays to isotope B, while the remainder decaysto isol'pe C. The value of f could be 1.0 which would mean that all ofisotope A decays to isotope B. Similarly a fraction of isotope B decaysto isotope C, while the remainder decays to isotope D. Each of the fourisotopes here may be created in the fuel element and/or through thedecay of the other isotopes. Each of the four isotopes may be removedfrom the system due to natural decay and/or neutron capture. The systemof four differential equations to be solved is

-XAA(t) - aA$elm(t)A(t) +YAIf*(t) (13)

H51i-± = _x B(t) - a * , (t)B(t) + y 2-0(t) + f X A(t) (14)dt B B elm B f A

-\,C(t) - oc»olm{t)C{t) + YcSf«(t) + (l-f)AAA(t) + gXBB(t)~ ^ - = -\,C(t) - oc»olm{t)C{t) + YcSf«(t) + (l-f)AAA(t) + gXB

- Velm(t)D(t) + Vf* ( t ) + ^ " ^ V ^ 5 + hAcC(t)

With suitable choices of f, g, h, y , y , and y equations (13), (14),(15), and (16) are solved in this program for all specified isotopes.The value E.<(> is related to the power in the reactor and is discussedin Section 2.2.2. The flux in the fuel element * eim(

t') c a n b e calculatedfrom the power history of the reactor and is discussed in Section 2.2.4.

- 7 -

2.2.2 Fuel Element Power

The power (in kW) of the reactor is known at various times during thetest. To get the total energy released by the reactor, these values ofpower must be multiplied by the factor 201/188 [ 1]. Using the conversionfactor

3.1 x 10 ° fissions = 1 watt second, or

X kW = 3.1 x 10 fissions/s

the values of power can be expressed in fissions/s.

The total reactor power and the power in an individual fuel element areassumed to vary together. The average power in the reactor, Pav,and inthe defective fuel element,P ,are also known. Thus, if P(t) isthe reactor power (in kW) at time t, then

^ =P(t) x|||x 3.1 x 1 0 1 3 x % ^ - (17)av

is the power in the fuel element at time t in fissions/s. The valueobtained from equation (17) is used in solving the differential equations(13) to (16) .

2.2.3 Reactor Flux

The reactor power and reactor flux are assumed to vary together. Theaverage reactor flux $ during the test is also known. If P(t) isagain the reactor power (in kw) at time t, then

a v$(t) = P(t) x ~ (18)

av

is the reactor flux at time t. If the average reactor power is inkw and the average reactor flux in neutrons/(m2•s), then $(t) will alsobe in neutrons/(m2•s). The value obtained from (18) is used in calculatingthe release rate [9].

- 8 -

2.2.4 Fv.el Element Flux

Definition of the symbols for flux to be used:

$ -average reactor fluxav 3

$> . -average defective fuel element fluxelmav

$(t) - reactor flux at time t

$ . (t) - defective fuel element flux at time telm

<j) - average relative reactor flux

<fs . - average relative fuel element fluxelroav

A plot of the relative flux is available for the duration of the testwhich also shows the contribution to the total flux of each fuel element.Assuming that the flux follows a cosine curve, the average relativeflux is:

(19)

The average relative flux for the defective fuel element can be approximatedfrom the plot. The reactor flux and flux in a particular fuel element areassumed to vary together. The flux in the defective fuel element at timet is:

® , *(t)t) _ elmav

av 7T J cos 6d8

elm $ (20)

Substituting (18) into (20) gives the element flux at time t in termsof the power at time t (which is known):

$. t3_. elmav

$ pav av

» P(t) (21)elmav p (21)

av

- 9 -

The average element flux is not known bv>t can be calculated from therelative flux values that are known:

$ 4> ,= _av elmav

elmav <t>

Substituting (22) and (19) into (21) gives the element flux at time tin terms of known quantities:

(t)av elmav

* i (t) * =elmv ' q> Pav av

IT - , P(t) ,_-..2 $av *elmav P ~ (23)

This value will be in the same units as $ (neutrons/(m .s)) and is usedin solving the differential equations (13; to (16).

3. PROGRAMMING NOTES

A flowchart showing the logic of the power boost test program is shownin Figure 2. The main program has a linear flow with one loop. Theuser's data cards are read first. Then the SARGS input file is read, andthe concentrations printed for each isotope at the time of each spectrum.The input file containing the reactor power history is read and thequantity of each isotope present in the fuel element at the time of eachspectrum is calculated and saved. The loop in the program is needed tocalculate for one isotope at a time: the release rate, escape ratecoefficient, and fractional release at the time of each spectrum. Then theplots of concentration, release rate, escape rate coefficient, andfractional release vs.time for the isotope are produced. Finally,when all isotopes have been looked at, the release rate, escape ratecoefficient, and fractional release for each isotope at the time of eachspectrum are printed.

The two input files necessary to run the program are discussed in Section3.1. The data structures used to store information in the program aredescribed in Section 3.2. A brief description of each subroutine appearsin Section 3.3.

- 10 -

READINRead user input data includinginformation about loopconditions and calculationoptions.

RDTAPERead input file from SARGS.

Print concentrationinformation.

Set up vector linkingisotopes in informationtable to isotopes in dataarrays.

POWCALFrom reactor power historycalculate reactor flux andquantity of each isotope infuel at time of eachspectrum.

$

Figure 2: Power Boost Test Program Logic

- 11 -

Yes

No

Print allrelease rates.

Plot concentration versustime for isotope.

Print all escaperate coefficients.

Calculate release rate forisotope and plot vs. time.

Print all frac-tional releases.

Calculate escape ratecoefficient for isotopeand plot vs. time.

Calculate fractional releasefor isotope and plot vs.time.

Figure 2: Power Boost Test Program Logic (continued)

- 12 -

3.1 Input Data Files

The SARGS program (maintained by the Reactor Control Branch) analyzesa number of spt»ctra each counted at different times. The output fromthis program is a table of concentrations and errors for selectedisotopes at the time of each spectrum. This information is read intothe power boost, test program from unit 9.

The power histcry of the reactor for the test is available from theprogram DATSUM (maintained by the Fuel Engineering Branch). Thisfile consists cf a list of times and the reactor power at each ofthese times. '. t is read into the power boast test program from unit 1.

3.1.1 Input from SARKS

The file from -3ARGS contains information about the experiment and con-centrations of specified isotopes. The first record on the file containsa comment about the experiment and the names and energies of the isotopesfor which concentrations have been calculated. The record is read by:

READ(9) (ICOMS(I),1-1,6),DUM1,(ISOL(I),1-1,N),SUM2,(lENRG(I),1-1,N)

where ICOMS contains up to 48 characters identifying tha experiment,ISOL contains the names of the isotopes, and IENRG contains the integervalues of the energies, The variable N is the number of isotopes analyzedby SARGS and is input separately to the program (see Section 4).

The number of spectra NSPEC identified and analyzed by SARGS must beknown and is also input separately to the program. The next NSPEC recordson the SARGS input file each contain a tagword, date, and time correspondingto a particular spectrum. These records will be in ascending order by dateand time. Each record is read by the statementt

READ(9) ITAG,IYEAR,IMONTH,IDAY,IHOUR,IMIN,ISEC.

All of these values are integers.

Each of the next NSPEC records (from record #NSPEC+2 to record #2*NSPEC+1)contains the total counts and the concentrations of the Nisotopes in aparticular spectrum.

These records are in the same order as the first group of records con-taining the times. For example, the date for the first spectrum isstored in record #2 and the concentration information for that spectrumin record #NSPEC+2. Each record is read by the statementi

READ(9) TOTAL,(CONC(I),I-1,N)

'.f'nese are all real values and the concentrations are in MBq/ra .

- 13 -

The .last NSPEC records (from record #2*NSPEC+2 to record #3*NSPEC+1)contain values proportional to the errors in the concentrations of eachisotope in each spectrum. Again, these records are in the same orderas the first group of records, so the error information for the firstspectrum is stored in record #2*NSPEC+2. Each record is read by thestatement:

READ(9)DUMMY,(ERROR(I),I=1,N)

The errors are real values and are actually the relative error in thaarea of the peak in the spectrum that the concentration was calculatedfrom.

Figure 3 illustrates the structure of this file.

3.1.2 Reactor Power History

The reactor power history file contains the power of the reactor atvarious times during the test. Each record on the file can be read by:

READ(l,100) IDATE,SECOND,POWER,IFLAG100 FORMAT(A6,2,F6.0,F8.2,R2)

The date is in the form YYMMDD, where each of YY. MM, and DD representtwo integers. The value of SECOND is the number of seconds since mid-night on the given date. The reactor power is given in kilowatts. Thevariable IFLAG is not used. The file should cover the entire test.

3.2 Data Structures

Three major data structures are used throughout the power boost testprogram. Three srrays are used for storing the original data read fromSARGS and are overwritten with the values of release rate, escape ratecoefficient, and fractional release as the calculations progress. Theyare described in Section 3.2.1.

The information table contains constants and other pertinent values forall isotopes that might be needed by the power boost test program. Itis in alphabetical order by isotope name and is printed except for itslast column at the start of each run. It is discussed in Section 3.2.2.

The decay scheme table is used mainly for communication with thelibrary routine RKFINT which integrates the differential equations toget the quantities of each isotope present in the defective fuel element.It translates the decay schemes into the appropriate equations and arrayelements. It is described in Section 3.2.3.

- 14 -

Dates

Concentrations •

Errors

Titles

Spectrum 1

Spectrum 2

Spectrum NSPEC

Spectrum i

Spectrum 2

Spectrum NSPEC

Spectrum 1

Spectrum 2

Spectrum NSPEC

Figure 3: Records in Input File from SARGS

- 15 -

3.2.1 Data Arrays

The COMMON block DATA consists mainly of a large table with 200 rowsand 73 columns. This table has been further subdivided into 3 dataarrays with 24 columns each and one array with one column, each arrayhaving 200 rows. The array with one column is called DATE throughoutthe program and contains the Julian date for each spectrum analyzedby SARGS. The other 3 arrays are used for storing data at variousstages in the program. Values corresponding to the spectrum countedat time DATE(i) will be found in row i of the data arrays. The namesand energies of the isotopes in the order analyzed by SARGS are storedin arrays ISOL and IENRG of COMMON block PRINT. Values correspondingto isotope name ISOL(j) and energy IENRG(j) will be found in column jof the data arrays. Thus the power boost test program can analyzeup to 200 spectra and 24 isotopes. If more are to be analyzed, thearray bounds must be checked and increased. During a particularrun the data arrays may not be entirely filled. The variables NSPECand ISOTOP also in common block DATA contain the actual number ofspectra f.id isotopes, respectively, being analyzed. Figure- 4 illustratesthe dependence of these various arrays.

For convenience, call the data arrays ARRAY1, ARRAY2, and ARRAY3 in theorder they appear in COMMON block DATA. The contents of these threearrays will be described by referring to the flovr chart in Figure 2.After subroutine RDTAPE has been executed (S) ARRAY1 contains concen-trations and ARRAY2 contains the errors in the concentrations. Aftersubroutine POWCAL has been executed (B) ARRAY3 contains the quantitiesof each isotope in the defective fuel element. When the loop in theprogram has been completed © ARRAY1 contains release rates , ARRAY2 escaperate coefficients, and ARRAY3 fission releases.

3.2.2 Information Table '

This table is used throughout the program and contains constants forcertain isotopes. The table contains one row for each isotope andis ordered alphabetically on the isotope names. It may be changedby the user for a run but may contain a maximum of 30 entries unless thearray bounds are increased. The variable NUMTAB indicates the number ofisotopes stored in the table. The table is often referred to byassigning a vector with a unique name to each column.

The contents of each column are:

(a) Isotope name(b) Half-life or natural decay constant(c) Loss due to purification (a value other than 0.0 here means

that the isotope is affected by purification and the purificationloop was open during the entire test)

DATE(l)

DATE(2)

DATE(i)

DATE(NSPEC)

ISOL(l) j ISOL(2)

llENRG(l) |IENRG(2) [

ARRAY (1,1)

ARRAY (2,1)

ARRAY (i,l)

ARRAY(NSPEC1)

ARRAY (1,2)

ARRAY (2,2)

ARRAY (.1,2)

ARRAY(NSPEC.2)

\ ISOL(j)

|lENRG(j) \

ARRAY (l,,j)

ARRAY (2,..j")

ARRAY (i, j)

ARRAY(NSPEC. i)

* |lSOL(ISOTOPl|

IENRG(ISOToj)

ARRAY(1,ISOTOP)

,I5OTOP)

ARRAYCd'.ISOTQP)

ARRAY(NSPEC. ISOT(}P)

Figure 4 : Data Array Structure

- 17 -

(d) Cross section(e) Fission yield(f) Quantity of isotope in the fuel at reactor start up(g) Column number in data arrays where information for the isotope is stored

(A value of 0 means the isotope has no corresponding column in the dataarrays.)

This is illustrated in Figure 5. The array ISOL is used to access the dataarrays shown in Figure 4.

3.2.3 Decay Scheme Tables

The subroutine ESCAPE sets up a vector and two tables stored in COMMON blockTEMP which define the various decay schemes that are implemented in thepower boost test program. Each of th.se three structures has 24 columnscorresponding to the isotopes stored in the 24 columns of the data arrays.The contents of these arrays will be illustrated by using the decay schemefor mass number 131 (see Figure 8) and the isotope SSHIRJ. whose precursorsand daughters have been neglected. The rows of the information table forthe isotopes involved are shown in Figure 6 as are the other arrays to bediscussed below.

The array ITABLE contains the isotopes involved in each decay schemeimplemented. These isotopes are identified by their row numbers in theinformation table. Thus, the decay scheme for 8 5 mKr contains only itselfso it is represented by 2. This is stored in the column in ITABLEcorresponding to &5mKx. The decay scheme for mass number 131 is representedby 3,4,5,1. It is stored in the column of ITABLE corresponding to thefirst isotope of the decay scheme, when the isotopes are arranged in alphabet-ical order. In this cise it is stored in the column corresponding to -^ll.

The array N contains the number of isotopes in each decay scheme in ITABLE.Thus N(i) is the number of isotopes in the decay scheme stored in column iof ITABLE. Since no decay schemes appear in columns 2 and 4 of ITABLE,N(2) = N(4) = 0.

The array AMOUNT contains information about branching in the decay schemes.The decay schemes may have up to 4 isotopes but only the first 2 maydecay into an isomeric and normal state. The 2 rows of AMOUNT correspondto these first 2 isotopes. If one or both of the first 2 isotopes in thedecay scheme does not decay into an isomeric state, the correspondingelement of AMOUNT is 0. Thus the first element of the column of AMOUNTcorresponding to SSmRj- ancj the second element of the column of AMOUNTcorresponding to " l j a r e Q_ J£ o n e Qf ^he first two isotopes in the decayscheme does decay to an isomeric state, the amount which decays to thatisomeric state is stored in the appropriate element of AMOUNT. Since13*Sb decays to n isomeric state, the first element of the column of AMOUNTcorresponding tr I3*i is 0.0044.

3.3 Subroutine Descriptions

A short description of the function of each .subroutine appears below. Themost complicated subroutine POWCAL is described in more detail than theothers.

Figure 5: Information Table

- 19 -

NAME

1-131

Kr-85m

Sb-131

Te-131m

Te-131

ALPHA BETA SIGMA YFRAC

.0291

.013

.026

.0044

.026

STQUAN ICOL

3

1

0

2

4

Information Table

ISOL

ITABLE

AMOUNT

DataArray

Kr-e5m Te-131m

1

t2

1-131

0

Te-131

4 0

3451

f l i t0 .0044

0 -

J

1

Figure 6: Sample Decay Schemes

- 20 -

Figure 7 shows the dependence of the subroutines on one another.A number of these routines are from AELIB and are described in f2].They are HEDERIV (1-12-10), LOCINT (2-3-01), POLFIT (1-11-00), PLOTM(2-1-00), RKFINT (1-17-00), and XPI (1-1-00). Two of the routines(MDFI and MDSTI) are from IMSL and are described in [5]. The routinesDATIME and JDTC are described in [4]. Finally, subroutines ARSORT,DATRAN, DISCON, FIT, HALFTF., PLTARR, SMDERV, and TIMDIS are from thelibrary for the SUMRT program. Descriptions of these routines will befound in the documentation for SUMRT.

3.3.1 EQNS

This subroutine defines the system of differential equations to besolved to find the quantities of specified isotopes in the fuel element.These are equations (13) to (16) defined in Section 2.2.1. The inputconsists of the variable ICOL, indicating the columns of ITABLE andAMOUNT which define the decay scheim_ (see Section 3.2.3), and thevariable N, indicating the number of isotopes involved in the decay schemeand thus the number of differential equations to use. The values in theappropriate column of ITABLE give the row numbers of the N isotopes intho information table.

The various values of X and a needed for equations (13) to (16) canbe picked out of the appropriate rows of the information table. Thevalues of f, g, and h will be 1.0 unless an isotope is decaying toan isomeric state. In that case it will be the ratio of tie appropriatevalue in AMOUNT (the first element for f and the second for g) to thefission yield of the precursor. For mass number 131 (see Figures 6and 8) this will be:

g = 1.0

h = 1.0

The fission yields must be calculated carefully. If an isotope has noprecursor and is not an isomer then y is the value of fission yield inthe appropriate row in the information table. For Sb, y = 0.026 (seeFigures 6 and 8).

If the element has a precursor,'is not an isomer, and there has been nointervening isomeric state it is: the second isotope in the decay scheme,the third isotope in the decay scheme and element 1 of AMOUNT is nonzero,or the fourth isotope and element 2 of AMOUNT is nonzero. Then y is thefission yield of the isotope minus the fission yield of its precursor(one back in the column of ITABLE). For I, y = 0.0291 - 0.026 = 0.0031.

1 1LOCINT PAGES

PBOOST

PLTARR

1 1DAT1ME JDTC

1 TPOWCAL

PLOTM

I 1

ESCAPE RDPOWR RKFINT

HOTAPE

1Jimr

READIN

1

XPI EQMS

1 1 1

ARSORT OATRRN

1

JDTC

HALFTB LOCT.JT

RELEAS

1 1

DATrKE JDTC PIJOTM SHDEBV

1 1DISCON HDSTI

1POLFIT

POLFIT TIKD1S FIT

HDEBIV POLFIT 1

Figure 7: Subprogram Dependencies

If there has been an intervening isomeric state the isotope is the thirdor fourth in the decay scheme and the first or second element, respectively/of AMOUNT is nonzero. Then Y is the fission yield of the isotopeminus the fission yield of the isotope before the isomeric state (two backin the column of ITABLE). For 131Te, y = 0.026 - 0.026 = 0.

If the isotope is an isomer, it is either the second or third one in thedecay scheme and the first or second element, respectively, in thecolumn of AMOUNT is nonzero. Then y is the fission yield of the isotopeminus the value in the appropriate element of AMOUNT. Thus for 131mrpe,Y = .0044 - .0044 = 0.

The subroutine evaluates the system of differential equations for agiven time T which is the number of seconds since the reactor start up.The array TIME contains two times so that TIME(l) < T < TIME(2). Thearrays POWER and FLUX contain the power in the fuel element (in fissions/s)and the fuel element flux (in neutrons/(m2•s), respectively, at each of thetimes in TIME. The power and flux in the fuel element at time T arecalculated by linear interpolation to give I tf> (t) (17) and $ e l m (t) (23),respectively.

3.3.2 ESCAPE

This subroutine defines the decay schemes which will be used in theprogram to calculate the quantity of each isotope present in the fuelelement. This is done by setting up the decay scheme table as definedin Section 3.2.3. Decay schemes are defined for the mass numbersindicated in Figure 8. Isotopes with mass numbers other than thesehave a short half-life compared to the number of counting periods of theexperiment and so have been neglected.

3.3.3 PAGES

This subroutine prints a data array. It is given the address of thefirst element of the array, the number of rows (spectra), and thenumber of columns (isotopes). The array is printed on pages containingup to 34 rows and 7 columns. If more than 7 isotopes have beenanalyzed, pages with the first 34 rows are printed until all columnsof the array are output before continuing on to the next 34 rows of the array.The title of the experiment and an appropriate title for the array areprinted at the top of each page. The name of each isotope and itsenergy as provided by SARGS are printed at the top of each column. Thetagword, time, and total count rate of each spectrum (input from SARGS)are printed at the start of each row. See Figure 12 for a sample page ofoutput from this routine.

- 23 -

MASSNUMBER131 .026 131ck .0044 131m .0044 131 .026 131

.0216 X .0031'

132 .0433 132 .0433 132T

133 .065 133m .065 133T .00191 133m .00191 133133 .00191 133mv .00191

' N^ .06499 S.0019

135 .069 134 .069 134 .078 134p. Te fe I Cs

.009'

135 .0617 135 .018 135m .018 135

.0437 ><TO23

137 .06 137 .06 137• Xe b Cs

.002'

138 .059 138,, .059 138» Xe te Cs

.008'

Figure 8: Decay Schemes Implemented in the Program

- 24 -

3.3.4 POWCAL

This subroutine calculates the quantity of each isotope in the data arraysthat is present in the fuel element at the time of each spectrum. A flow-chart is given in Figure 9.

Two things must be done before the calculations can proceed. Firstthe subroutine ESCAPE is called to define the decay schemes to be used.Next the initial conditions are defined at time T = 0. The fuel elementpower and flu? are 0 at this time. The quantity of each isotope presentat T = 0 is given in column 6 of the information table.

The quantity of each isotope present in the fuel element at the time ofeach spectrum would normally be calculated by integrating the differentialequations (13) to (16), saving the results at the specified times.However, it is not this simple because the values of Z ij)(t) and $(t) areonly known at the times when the reactor power is known. The algorithmgoes as follows:

(a) Read the next time and power from the reactor power history file.

(b) Calculate the fuel element power and flux at this time from thereactor power (see Sections 2.2.2 and 2.2.4).

(c) Use the AELIB routine RKFINT to integrate each of the decay schemesup to either the time at which the reactor power is known or thetime a spectrum was taken, whichever is earlier.

,'i If the integration was to the time of known reactor power, thenthat time and the values of fuel element power, fuel element flux,and quantity of each isotope in the fuel element then become theinitial conditions for the next integration. Go back to Step (a).

(e) If the integration was to the time of a spectrum, save thequantities of the appropriate isotopes in a row of the data array.Calculate the reactor flux at this time (see Section 2.2.3).Calculate the fuel element power and flux, and this time, and usethese values as initial conditions for the next integration. Goto Step (c) .

(f) When the integrations have been done up to the time of the lastspec trurn, return.

3.3.5 RDPOWR

This subroutine reads a record containing a time and a value of power fromthe power history file defined in Section 3.1.2. The time is converted toJulian time [4 3. If the time is after STOP (the user specified time ofthe stL'-.t of the test) the power and time are returned to the calling routine.If the time is prior to STUP the record is rejected and the power historyfile is read until a time after STUP is encountered. The variable IERR isset to 0 to indicate that an acceptable value has been returned.

- 2 5 -

ESCAPE

Define the decay schemes

Set initial conditions atreactor start upt=0, power=0, flux = 0

TIME (!)=<">

o- RDPOWR

Get next value of reactorpower at time DATPCW

Calculate at DATPOW- # seconds since reactor

start up- element power- element flux

TOUT=DATPOW-STUP

Figure 9: Flowchart for POWCAL

- 26-

For each isotope integratifrom TIME(l) to TOUT tofind quantity of eachisotope in fuel at TOOT.

Next integration to startfrom DATPOW; therefore,TIME(l) = TOUT saveelement power and elementflux at time DATPOW.

Yes

Calculate reactor flux attime DATE(i) and save.

Next integration to startfrom DATE(i); therefore,TIME(l) = TOUT calcu-late and save elementpower and element flux attime DATE(i).

Save quantity of each iso-tope in data array at timeDATE(i).

. .. _ 9: Flowchart I *t v FOfcCAL (continued)

NUMBER?ntity calculat

for allctr

Return

- 27 -

If a value of power is requested from RDPOWR and EOF is found, thereare not enough values on the power history file. A message is printedand the error flag IERR set to 1. This will cause immediate terminationof the calculations. The power history file should be extended toinclude the entire test.

3.3.6 RDTAPE

This subroutine reads the file from SARGS which has been discussed inSection 3.1.1. The number of spectra and the number of isotopes pro-cessed by SARGS are required as input to this routine. The time ofeach spectrum is saved in two formats. In Julian time [4] array DATEis appropriate for use in the calculations, and in display code arrayIDATE (YYYY-MM-DD and HH:MM:SS) is appropriate for output. Theconcentrations are saved as they are read in and the errors are trans-formed into errors in the actual concentration values and saved.

3.3.7 READIN

This subroutine reads the card image input containing the user'sinformation for the run. The method of input and values of variablesexpected are described in Section 4.

The dates read in are translated to Julian time [4] using DATRAN fromthe SUMRT subroutine library. The information table, augmented byany changes made for the run, is sorted into alphabetical order byisotope name and printed. The half-lives are translated intonatural decay constants by (6) and HALFTR from the SUMRT subroutinelibrary. All constants to be used in the calculations areprinted. The plot and print flags are translated from integer tological values. The number of spectra and isotopes to be expectedfrom the GRAAS program are checked. If they exceed the array boundsdefined in the program an error message is printed and the number ofspectra set to 0 so that processing will terminate.

3.3.8 RELEAS

This subroutine implements the calculation of the release rates asdescribed in Section 2.1. It is called once for each isotope. Firstall 0 values in the array of concentrations are removed. Next SMDERVis called from the SUMRT subroutine library to find the smoothedconcentrations and their derivatives. The release rate (9) is calculatedfrom these values at the time of each spectrum. Finally, the smoothedconcentration is plotted as a continuous line on the already existingconcentration plot.

- 28 -

4 . K'Ji'NING THE PROGRAM

In this section the information to be provided by the user is discussed,a sample deck given, and samples of the output provided.

4.1 Card Image Input

Input is prepared via card images for each run of the power bocF.ttest program. It provides values for constants describing conditionsin the reactor during the test, a description of the output file producedby SARGS, and user requests for the amount and format of the output. Aminimum of two and a maximum of six card images are required.

The first card contains up to three dates, relevant for the run. The firstdate and time is that of the start of the test. At this time it isassumed that the reactor power and flux are 0. This is also the timeat which the initial quantity of each isotope is known (column 6 in theInformation Table). The next two dates are the minimum and maximumtimes for the x-axis of the plots.

The format of the card is

"YY/MM/DD","HH:MM:SS","YY/MM/DD","HH:MM:SS","YY/MM/DD","HH:MM:SS"

where the commas may be replaced by any number of spaces.

If the results from the entire test are to be plotted, the minimum andmaximum plotting dates may both be omitted. In this case, a slashafter the first time signifies that they are missing.

"YY/MM/DD","HH:MM:SS"/

The second card is input data for a NAMELIST group. (See FORTRANExtended Version 4 Reference Manual, Revision E, pages 5-13 to 5-19 ,for more information,) The variables initialized in this way aradescribed below.

TMASS The mass (in kg) of the recirculating volume in the loop.

VOLRAT The ratio of the volume of the test section of the loopto the volume of the recirculating water in the loop.

TRTIME The transport time (in s) around the loop from the defectto the spectrometer.

AVPOWR The average power (in kw) in the reactor during the test.This is available from a table produced by the program BURFEL(Fuel Engineering Branch) ( ® in Figure 10).

- 29 -

ELMPOW The average power (in kW) of the defective element during thetest. This is available from a table produced by the programBURFEL ( @ in Figure 10).

AVFLUX The average flux (in n/(m2-s)) in the reactor during the test.This is available from a table produced by the program BURFEL( © in Figure 10).

RLFLUX The relative flux of the defective element.

ISOTOP The number of isotopes for which SARGS has output information.Must be < 24.

NSPEC The number of spectra for which concentrations have been outputby SARGS. Must be £ 200.

IFLAG The number of remaining cards to be read. These cards containchanges and additions for the information table. If thisvariable does not appear, there are no remaining cards to beread.

PLTFLG A flag indicating which plots are to be produced for eachisotope. The value consists of up to four concatenatedintegers with the following meanings:

1 - produce plots of concentration vs. time2 - produce plots of release rate vs. time3 - produce plots of escape rate coefficient vs. time4 - produce plots of fractional release vs. time

If this variable is not present/ no plots will be produced.

EXNO The number of millimetres/day to be used .in the time axis ofplots.

PRTFLG A flag indicating which values are to be printed for eachisotope. The value consists of up to four concatenatedintegers with the following meanings:

1 - produce listings of concentration2 - produce listings of release rate3 - produce listings of escape rate coefficient

4 - produce listings of fractional release

If this variable is not present, no listings will appear.

The format of the card used to input the NAMELIST information is:

$VARSIN variable=value, variable=value, ...$

13 H)t-i H-O iQ

a cn ita M

DO

K>MOVOCD-JOM/UkUl[OM-

H H H O O O O O O O O O MwHotoooia>ui*WioH5d

<>

CH

OH3 »

HQ>OhjcaMH

CDO•o

UIUIO i»WH u MJN MMMk O U MOO OlIOMIOtOtOtOtOtOIOIOMtOte -4«O -JUIM < BtOODAh H*Jfe JfO(AfUN}(«H4'tOtA)4i4}IOWlA)00 ^3^Jfe Hl/IOt 9

CO

U H H U1UM » U H U feMM IOMMWlOfe MOD* H-Jfc -JtOUWK>WUN>bJWtOWW09 O—I* HUlOt

O1U O-4 tOUl to to to to -J - Sfci

• • • MM1OM HUI WU1 t-'t-'t-'t-'i-'i-'t-'l-'t-^-'l-l-'itt - ' ~

0> to OI * 'ooui wio tofe uiuusiuiininuunuiuiuHnot oow M-J O

0000 to^l UU1 i-'t-'t-'t-'t-'l-'t-'t-'t-'t-'t-'t-'W tOUI *»0D f _

wem ^ oofft tom ^v^vowtotf totototototoyiM H uu i t o ^ cncnmuiuimuimuiuiLnLnan o o mooN | U few UUI tONIKlKlWKltOrOKJMWfOOJ OIN) feU RJSiO

§ °a a .

NilO UIO U>W t^^fefefefefefefefefeiUfeU N>tO M VlT'MlOM vJUl HOI SiOOUI-JOOUlOBODUlOIODUtOno OtOS tOUl

^^)^^^ ^ ^ J i ^^^^ ^ ^ JflD^ * l0v ^ ^ J J ^ ^ J Ji ^ " r* ^^ OOL^ C J 1)'• OH

IOOI (OiU lOOt OtOOOODMOODtOOODtOÎ O-J MO1 r > >tou too Hfe piuui * jfyrjfc j^fTîf^îr^î ' ^^ jf*^ o^? n~™

MI-" u to mw tn*>4**t*»jfcfe«»4fciiMe>«»iikw wio ton . . .

.". . . M . . . . . . . . . . . . . . . . . £ *UOt (Ofe W O riOtUI^JOAfeODOtfeOtOtJhOttO COMU* t WU1 O W tn~l-JW~JtOH»4tOU1vitOUIO COO

M

o clOtO WtO UICJ Cd^b^î^^b^^^fefefeU (OtO H *tit*

f i 0 * r K 3w in i ""w in"w w i* ' in in" r1? r°r HSG

VOH -4U1 MOI MODln«JODUIC90DmOIQDUlO>IO OnOO VOUItotn - - - -

MtOM WtO UIW Hite£»«»i|kifeJfci£»»ifrife*kW WIO t-'t-' H HC^ L v ^^V^^J J^^^^^ O ^ ^ ^^-jOP^^^^11 Op v \ ^"J^11^^^^"i 1 * I t^ T'^Kfif O D ^ J C3 *S^^S^ ^ • • • • • OHHtou <eo H * . gooM~ioo*.*.oj*.too»*.too >JH oo H4MM WtO UIW 0UkJkJ»*»i»*.*.<»Jk*»toOJ WtO MM

^ j ^ ^ ^ Pfcji w 0^C3 4 S ^ ^?*i)^^^ t^^ OP ^ i ^ ^ ^ ^ f^Ô^ ^^St 00 f*^ 00 r*0^ i ^ ^^ ^ ^ * 0^ S5 J * ^^ J 9 r^ J Cr ^ ^ J r ^ ^ G^ Q0 C^ ^ ^ ^ J SCf

COM M M 09tO OlODODOlODWOlOOOaOIOBOaUl tOtO WO 1}f

. . • • • • . . • . R H

H^00 ^J^J ^3^3 ^?^J \Q ft ft* Jt ftH** ^^ * ^^J 0^^^ 00^J CQ

tot-1 U>K) uiu> rffcOioirffccnLnrfhCr.ji^cntnu» w t o H'H' H 5j

lOOt 0010 OO O t0t-Jl-'l0|-'>-J\0>->>-'V0HJ}-4-J CJW1 «0» O !• • • • • • • • • • OE0*oyi enm o^t/i tnfovc{j)j '"*Jiji4ôcnô**>« coo w9o M ?*f-'H utto tnui ui(ji(jiui(jiuiuicnLn(/i(/iuiu> W M NJW t4

Wlh-» *h<TV -J00 HWCUH*U>tA>WUJUat-lOJU>00 0n*>4 ^ 0 0 O ?5UJJfc Oil-1 OU1 OHWOOWOOKOOHA IOVO **U1 3 \( J I Q OJVO *tf*O ffÔ^-Jff'h^^yfy^WOiJtl 'TO^P VO9^ ^ ^ Sd X

10•initfc

- OE -

- 31 -

The first nine characters on the card must be " $VARSIN ". Eachvariable listed above then appears (Lu any order) and is assigned avalue. A comma and any number of spaces separate the variables.The list ends with the character "$". If the statement will not fiton the 80 columns of a card, it may be continued on one or more cardsprovided each card except the last ends with a comma and all cards havea blank in column 1. Sample cards might look like:

$VARSIN TMASS=417., TRTIME=9, AVPOWR=2832., ELMPOW=29.39, AVFLUX=2.443E18,IS0T0P=17, NSPEC=128, PLTFLG=1234, EXNO150.0, PRTFLG=1234$

Note that since the variable IFLAG has not been given a value, thereare no remaining cards to read in.

A table of constants used by the program is shown in Figure 11. Itconsists of a list of isotopes with the half-life, factor for loss dueto purification, cross section, fission yield, and quantity presentin the fuel at the start up of the reactor of each. The half-life is given inseconds (S), minutes (M), hours (H), days (D), or years (Y). The factorBETA is given in s •. The cross section is in m2. The fractionalfission yield in atoms/fission and the quantity at the time ofreactor start up in atoms.

To add an isotope to the table, a card must be provided giving therequired information,in order. For example,

" Te-134", "M42.0", 0.0, 0.0, 0.690, 0.0

134would add the line for Te to the table if it was not already there.Note that the isotope name starts with a blank and that both the isotopename and its half-life must be enclosed in quotation marks. Also, thenumber in the half-life must contain a decimal. If two energies of anisotope have been processed by SARGS, the line for the isotope must beentered twice in the table. In the column headed "ISOTOPE" one line wouldcontain the isotope name (e.g. KR-B5M). and another the added line with theisotope name followed by an asterisk (e.g. KR-85M*).

To change a line in the table, the name of the isotope and the newvalues to be inserted are given as above with -1.0 in the place of anyvalue that is not to be changed. Thus, to give 137Cs a starting quantityof 1.2 x 1017 atoms, the card should read:

"CS-137",-1.0, -1.0, -1.0, -1.0, 1.2E17.

The table as it is used in each run is printed out and it should bechecked to ensure that any required changes have been made correctly.

- 32 -

TABLE OP CONSTANTS USED IN THIS RUNISOTOPE

CS-134

CS-137

CS-138

1-131

1-132

1-133

1-134

1-135

KR-85M

KR-87

KR-88

KR-89

KR-90

SB-131

TE-131M

TE-131

TE-132

TE-133

TE-134

XE-133M

XE-133

XE-135M

XE-135

XE-137

XE-138

XE-139

HALF LIFE

Y2.1

¥30.0

M32.2

D8.06

H2.3

H20.8

M53.0

H6.7

H4.48

M78.0

H2.8

M3.2

S32.0

H23.0

D1.2

M25.0

H78.0

M12.5

M42.0

D2.26

D5.29

M15.6

H9.1

M4.2

M14.5

S41.0

isle*,0.

0.

0.

. 840E-04

.840E-04

.840E-04

.840E-04

.840E-04

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

(1I8»0.

0.

0.

0.

0.

0.

0.

0.

c.0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

.290E-21

.290E-21

0.

0.

0.

FISSIONYIELD

.0780

.0620

.0670

.0291

.0433

.0669

.0780

.0617

.0130

.0250

.0360

.0459

.0560

.0260

.0044

.0260

.0433

.0650

.0690

.0019

.0669

.0180

.0640

.0600

.0590

.0540

(AT"<0.

0,

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0,

Note that the last column of the InformationTable as it is shown in Figure 5 is not printedby the program.

Figure 11Default Table of Constants

- 33 -

4.2 Sample Deck

Jobname,Bnnn-id,T50,1030.ATTACH(LGO,SOURCEPOWBOOST,ID=WILLS,CY=1)ATTACH(TAPE1,reactorpowerhi story,ID =aa)ATTACH(TAPE9,SARGSinput,ID=bb)ATTACH(SUMRTLIBRARY,ID=WILLS)LIBRARY(SUMRTLI)LGO.7/8/9"79/07/12" "12:00:00"/$VARSIN ELMPOW=29.39, EXNO=450.0, PLTFLG=1234, ISOTOP=17, NSPEC=128,AVFLUX=2.443E18, TMASS=417.0, TRTIME=9.0, AVPOWR=1832.0, PRTFLG=1234,RLFLUX=0.4256, VOLRAT=0.038$6/7/8/9

The binary version of the power boost program is attached as file LGO.The file attached as TAPE1 is the reactor power history file. The fileattached as TAPE9 is the SARGS input file. This run prints and plotsthe concentrations, release rates, escape rate coefficients andfractional releases.

4.3 Output

Sample output from the deck in Section 4.2 is shown on the followingpages. Figure 12 is a sample page of printed concentrations. Figure 13is a sample page of printed release rates. Figure 14 is a sample pageof printed escape rate coefficients. Figure 15 is a sample page ofprinted fractional releases. The times printed on these tables are theend of the period for which the spectrum was counted. Figure 16 is asample of plots of concentration and release rate for an isotope.Figure 17 shows plots of escape rate coefficient and fractional releasefor an isotope.

POWER BOOST TEST U2D-458

SUMMARY OF ISOTOPIC CONCENTRATIONSIN MEGA-BEQUERELS / M ** 3

TAGWORD

12

3

4

5

6

7

8

9

10

11

12

13

1415

16

17

18

19

20

21

22

23

24

2526

2728

29

30

31

32

33

34

DATE

1979-10-10

1979-10-10

1979-10-10

1979-10-10

1979-10-10

1979-10-10

1979-10-10

1979-10-10

1979-10-10

1979-10-10

1979-10-10

1979-10-11

1979-10-11

1979-10-11

1979-10-11

1979-10-11

1979-10-11

1979-10-11

1979-10-11

1979-10-11

1979-10-11

1979-10-11

1979-10-11

1979-10-11

1979-10-11

1979-10-11

1979-10-11

1979-10-11

1979-10-11

1979-10-11

1979-10-11

1979-10-11

1979-10-11

1979-10-11

TIME

11:13:08

11:48:39

12:24:13

12:52:30

14:20:04

15:45:58

17:11:53

18:37:49

20:03:49

21:29:52

22:55.-57

0:22:01

1:48:04

3:14:06

4:40:09

6:06:12

7:32:14

8:58:16

9:39:18

9:57:21

10:15:25

10:40:54

10:58:53

11:16:55

11:31:45

11:50:10

11:59:52

12:02:27

12:04:49

12:07:25

12:10:16

12:13:21

12:16:31

12:19:51

TOTALRATE

4828.

4828.

4821.

6289.

1682.

1013.

1013.

1022.

1047.

1052.

1052.

1053.

1053.

1053.

1054.

1054.

1055.

1053.

2441.

3058.

3103.

2900.

2883.

2995.

3076.

3561.

6279.

10383.

14744.

19961.

25404.

29720.

31908.

34743.

XE-135250 KEV

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

503.

692.

709.

565.

515.

485.

463.

481.

1006.

2273.

3654.

5172.

6854.

8210.

9274.

10605.

KR-8SM151 KEV

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

108.

84.

116.

91.

86.

56.

58.

61.

615.

2177.

4017.

5612.

7831.

9458.

5927.

7277.

KR-882392 KEV

0.

0.

0.

0.

0.

0.

0.0.

0.

0.

0.

0.

0.

22.

0.

0.0.0.

0.

277.

0.

0.

0.

0.0.

425.

0.

2883.

8533.

10108.

16750.

21598.

29003.

30938.

KR-87403 KEV

0.

0.

0.

0.

0.

0.0.

0.

0.

0.

0.

0.

0.

0.

0.

0.0.0.

162.

307.

184.

155.

181,

266.

252.

254.

1581.

5234.

9016.

13091.

16747.

17968.

21290.

21470.

XE-138258 KEV

0.

0.

0.

0.

0.

0,

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

1026.

1373.

1527.

1204.

1177.

1294.

1391.

1647.

7269.

20650.

33731.

47878.

61240.

68574.

71388.

76435.

XE-135H527 KE*'

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

145.

197.

163.

196.

179.

152.

108.

184.

955.

3424.

5180.

7132.

9077.

9984.

10739.

12345.

KR-89586 KEV

0.

li.

0.

0.

0.

0.

0.

0.

0.

0.

0.r .

0 .

0.

0.

<:

0.

°- I0. **

360. '

0.

0.

0.

535.

0.

0.

2721.

6960.

10858.

16331.

16234.

1376T.

137'C .

114 7'!.

Figure 12

Sample Concentration Output

POWER BOOST TEST U2D-4S8

TAGWORD

1

2

3

4

5

6

7

8

D

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

DATE

1979-10-10

1979-10-10

1979-10-10

1979-10-10

1979-10-10

1979-10-10

1979-10-10

1979-10-10

1979-10-10

1979-10-10

1979-10-10

1979-10-11

1979-10-11

1979-10-11

1979-10-11

1979-10-li

1979-10-11

1979-10-11

1979-10-11

1979-10-11

1979-10-11

1979-10-11

1979-10-11

1979-10-11

1979-10-11

1979-10-11

1979-10-11

1979-10-11

1979-10-11

1979-10-11

1979-10-11

1979-10-11

1979-10-11

1979-10-11

TIME

11:13:08

11:48:39

12:24:13

12:52:30

14:20:04

15:45:58

17:11:53

18:37:49

20:03:49

21:29:52

22:55:57

0:2? 01

1:48:04

3:14:06

4:40:09

6.-06:12

7:32:14

8:58:16

9:39:18

9:57:21

10:15:25

10:40:54

10:58:53

11:16:55

11:31:45

11:50:10

11:59:52

12:02:27

12:04:49

12:07:25

12:10:16

12:13:21

12:16:31

12:19:51

TOTALRATE

4828.

4828.

4821.

6289.

1682.

1013.

1013.

1022.

1047.

1052.

1052.

1053.

1053.

1053.

1054.

1054.

1055.

1053.

2441.

3058.

3103.

2900.

2883.

2995.

3076.

3S61.

5279.

10383.

14744.

19961.

25404.

29720.

31908.

34743.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.0.

0.

0.

0.

0.

0.

0.

4.

1.

1.

-1.

-1.

-6.

3,

2,

1.

1

1

11

1

7

1

XE-135250 KEV

14415E+09

86341E+09

91792E+08

.08830E+09

.19622E+09

.24021E+08

.76530E+08

.43161E+09

.48280E+11

.80930E+11

.96901E+11

.98918E+11

.82305E+11

.41990E+11

.61653E+10

.38186E+11

SUMMARY OF ISOTOPIC RELEAfIN ATOMS / SECOND

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0,

0,

0,

1

5

-1

-7-8

-6

-2

5

9

1

1

1

1

8

6

6

KR-85H151 KEV

.54081E+08

.70453E+07

•55412E+07

.36210E+07

.15940E+07

.06572E+07

.07873E+07

.83417E+07

.05060E+10

.09585E+11

.18493E+11

.18770E+11

.07559E+11

.17682E+10

.60042E+10

.69751E+10

KR-882392 KEV

0.

0.

0.

0.

0.

0,

0.

0.

0.

0.

0.

0.

0.

8.

0.

0.

0.

0.

0.

1.

0.

0.

0.

0.

0,

2,

0

1.

1

1

1

1

1

1

04478E+07

.99557E+08

.32880E+08

.38248E+11

.73813E+11

.95330E+11

.97571E+11

.74595E+11

.46675E+11

.33924E+11

;E

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0,

0.

1,

7.

6

7

91

1

2

7

7

7

7

7

2

4

6

RATES

KR-87403 KEV

.02140E+08

.95478E+07

.79658E+07

.46702E+07

.86405E+07

.41164E+08

.91568E+08

.75492E+08

.04105E+10

.20118E+10

.34789E+10

.50906E+10

.68572E+ia

.02861E+09

.26742E+10

.16962E+10

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0,

0.

6

6

5

5

4

5

6

9

5

5

6

6

3

44

4

XE-138258 KEV

.55480E+08

.50661E+08

.95537E+08

.04398E+08

•81322E+08

.34579E+08

.61869E+08

.57882E+08

.fl486E+10

.59693E+10

.13019E+10

.71603E+10

.97017E+10

.33126E+10

.55581E+10

.60578E+10

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0,

0,

0

0,

9

9

8

6

6

5

6

8

1

1

9

8

7

8

9

1

XE-135M527 KEV

.15156E+07

.13109E+07

.39982E+07

.92792E+07

.12764E+07

.96952E+07

.60622E+07

.83801E+07

.16334E+10

.01637E+10

.07591E+09

.22824E+09

.79791E+09

.02478E+09

.12581E+09

.13740E+10

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0,

0,

0

-1.

0

0

0

6

0

0

1

1

9

8

6

5

4

4

KR-89586 KEV

.87979E+07

.67809E+08

.03844E+09

.06073E+09

.41816E+09

.48118E+09

.88619E+09

.15486E+09

.13560E+09

.77546E+09

1

1

Figure 13

Sample Release Rate Output

POWEK BOOST TEi'! ;>-'D-'lS3

SUMMARY OF ISOTOFIC ESCAPE RATE COEFFICIENTSIN SECONDS * 1

TAGWORD12

3

4

5

6

7

8

9

101112

131415

1617

IB

19

2021

22

23

24

25

26

27

28

29

30

31

32

33

34

DATE

1979-10-10

1979-10-10

1979-10-10

1979-10-10

1979-10-10

1979-10-10

1979-10-10

1979-10-10

1979-10-10

1979-10-10

1979-10-10

1979-10-11

1979-10-11

1979-10-11

1979-10-11

1979-10-11

1979-10-11

1979-10-11

1979-10-11

1979-10-11

1979-10-11

1979-10-11

1979-10-11

1979-10-11

1979-10-11

1979-10-11

1979-10-11

1979-10-11

1979-10-11

1979-10-11

1979-10-11

1979-10-11

1979-10-11

1979-10-11

TIME

11:13:08

11:48:39

12:24:13

12:52:30

14:20:04

15:45:58

17:11:53

18:37:49

20:03:49

21:29:52

22:55:57

0:22:01

1:48:04

3:14:06

4:40:09

6:06;12

7:32:14

8:58:16

9:39:18

9:57:21

10:15:25

10:40:54

10:58:53

11:16:55

11:31:45

11:50:10

11:59:52

12:02:27

12:04:49

12:07:25

12:10:16

12:13:21

12:16:31

12:19:51

TOTALRATE

4828.

4828.

4821.

6289.

1682.

1013.

1013.

1022.

1047.

1052.

1052.

1053.

1053.

1053.

1054.

1054.

1055.

1053.

2441.

3058.

3103.

2900.

2883.

2995.

3076.

3561.

6279.

10383.

14744.

19961.

25404.

29720.

31908.

34743.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0,

0.

0,

0,

0

1

4

4-2

-2

-1

9

7

5

7

8

9

9

747

XE-135250 KEV

.06720E-08

.75726E-09

.84829E-10

.72365E-09

.99105E-09

.56345E-09

.43534E-10

.60465E-09

.92628E-07

.68014E-07

.80197E-07

.36427E-07

.00456E-07

.32O38E-O7

.06813E-07

.59163E-07

IN SECONDS «* -1

KR-85M]

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0,0.

0.

0.

0.

1.

5.-1.

-6.-7.

-5.-1.

5.

7.

9.

1.

9.

8.

6.5.

5.

LSI KEV

46561E-10

40693E-11

46855E-11

92673E-11

64946E-11

66317E-11

93429E-11

25600E-11

84027E-08

38542E-08

00408E-07

94626E-08

89353E-08

67009E-D8

.31096E-Q8

.31375E-08

I -882392 KE '

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.0.

0.4.0.

0.

0.

0.

0.

1.

0.

0.0.

0.

0.

1.

0.6.

7,

8.8

7.

6

5

46962E-11

02157E-10

.13446E-10

.27152E-08

.76932E-08

.59052E-08

.53952E-08

.40944E-08

.1U41E-08

.47684E-08

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.0.

0.0,

0.

0

0

0

1

1

1

11

22

3

9

9

8

8

824

6

KR-87403 KEV

.59802E-1O

.24650E-10

.06744E-10

.17496E-10

.55044E-10

.21201E-10

.99434E-10

.94069E-10

.08025E-OB

.02755E-08

.97699E-08

.92259E-O8

.87155E-08

.27278E-09

.64377E-08

.52245E-08

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0,0.

0

2

22

11

12

2

91

1

1

66

66

XE-138258 KEV

.35423E-09

.34283E-09

.15271E-09

.82293E-09

.72251E-09

.89225E-09

.32958E-09

.42201E-09

.74684E-08

.Q2832E-07

.07455E-07

.12394E-07

.36475E-08

.67653E-08

.78731E-08

.66141E-08

0.

a.0.

0,

0.

0.

0.

0.

0.

0.

0.

0.

0.

0,

0,

0.

0

0

1

1

1

1

1

1

1

2

3

2

2

222

2

' 3

XE-135M327 KEV

.95369E-09

.93251E-09

.76331E-09

.44175E-09

.27330E-09

.23731E-09

.36432E-09

.16929E-09

-29574E-07

.95574E-07

.69258E-07

.48296E-07

.37981E-07

.46382E-07

.80613E-07

.48763E-07

Q.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0,0.

0,

0

0

-3

0

0

0

1

0

0

8

8

7

6

5

3

2

3

KR-89586 KEV

.95005E-10

.36497E-08

.54034E-09

.40169E-09

.24459E-08

.36149E-08

.08367E-08

.76600E-08

.99966E-08

.45188E-08

1

ON

1

Figure 14

Samule Escape Rate Coefficient Outnut

POWER BOOST TEST O2D-458

SOMARY OF ISOTOPIC FRACTIONAL RELEASES

5o§D1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

3?

34

DATS

1979-10-10

1979-10-10

1979-10-10

1979-10-10

1979-10-10

1979-10-10

1979-10-10

1979-10-10

1979-10-10

1979-10-10

1979-10-10

1979-10-11

1979-10-11

1979-10-11

1979-10-11

1979-10-11

1979-10-11

1979-10-11

1979-10-11

1979-10-11

1979-10-11

1979-10-11

1979-10-11

1979-10-11

1979-10-11

1979-10-11

1979-10-11

1979-10-11

1979-10-11

1979-10-11

1979-10-11

1979-10-11

1979-10-11

1979-10-11

TIME

11:13:08

11:48:39

12:24:13

12:52:30

14:20:04

15:45:58

17:11:53

18:37:49

20:03:49

21:29:52

22:55:57

0:22:01

1:48:04

3:14:06

4:40:09

6:06:12

7:32:14

8:58:16

9:39:18

9:57:21

10:15:25

10:40:M

10:58:53

11:16:55

11:31:45

11:50:10

11:59:52

12:02:27

12:04:49

12:07:25

12:10:16

12:13:21

12:16:31

12:19:51

4828.

4828.

4821.

6289.

1682.

1013.

1013.

1022.

1047.

1052.

1052.

1053.

1053.

1053.

1054 „

1054.

1055.

1053.

2441'.

3058.

3103.

2900.

2883.

2995.

3076.

3561.

6279.

10333.

14744.

19961.

25404.

29720.

31908.

34743.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

5.04387E-04

2.24841B-04

2.29143B-05

-1.28727E-04

-1.41365B-04

-7.38927E-05

4.45940E-05

3.59416B-04

2.80092B-02

3.62984B-02

4.16005E-02

4.42581B-02

4.25580E-02

3.459S1E-02

1.92271E-02

3.58801B-02

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

c.3.41016B-06

1.25807K-06

-3.41700E-07

-1.61170B-06

-1.779863-06

-1.31769B-06

-4.50066E-07

1.22295E-06

1.82426E-03

2.18378B-03

2.33627E-03

2.31427E-03

2.06933E-03

J..55198E-03

1.23574E-03

1.23639E-03

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

6.49988B-07

0.

0.

0.

0.

a.1.48561E-06

0.

0.

0.

0.

0.

1.64977B-06

0.

9.12027E-04

1.129G4E-03

1.24926E-03

1.24185E-03

1.07751E-03

8.88744E-04

7.96462E-04

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.0.

0.

0.

1.0789SE-06

8.41614B-07

7.20716E-07

7.93312B-07

1.04683E-06

1.49351E-06

2.02172E-06

2.66068E-06

6.13081E-04

6.0952417-04

6.06109E-04

6.02437E-04

5.98990E-04

1.53454E-05

3.13539E-04

4.40384E-04

XB-138258 KEV

0.

0.

0.

0.

U.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

2.95490E-06

2.94059E-06

2.70197E-06

2.28804E-06

2.16I99E-06

2.37504E-06

2.92396E-06

3.03398E-06

1.22337E-04

1.29069E-O4

1.34871E-04

1.41071E-04

7.98868E-05

8.38001E-Q5

8.51905E-05

8.36104E-05

XE-135M527 KEV

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

2.63819E-06

2.60959E-06

2.38111E-06

1.94689E-06

1.71941E-06

1.67082E-06

1.84232E-06

2.92933E-06

4.45044E-04

3.99132E-04

3.63597E-04

3.35290E-04

3.21361E-04

3.32705E-04

3.78930E-04

4.70956B-04

KR-89586 KEV

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

I).

-1.09416E-07

0.

0.

0.

3.78093E-06

0.

0.

2.36565E-06

2.32725E-06

2.00673E-05

1.76212E-05

1.40816E-05

1.04317E-05

8.30897E-06

9.56.61E-06

-4

I

Figure 15

Sample Fractional Release Output

- 38 -

POHER BOOST TEST U20-458 1-134 884 KEY

Figure 16

Sample Plot of Concentration and Release Rate

- 39 -

POWER BOOST TEST U2D-4SB 1-134 884 KEV

Figure 17

Sample Plot of Escape Rate Coefficient and Fractional Release

- 40 -

5. REFERENCES

[1] Christie, J., Private communication. Fuel Engineering Branch, CRNL.

[2] Evans, L.E.: AELIB User's Manual, atomic Energy of Canada Limited,Report AECL-6076, Revision C.

[3] Glasstone, S.: Principles of Nuclear Reactor Engineering,Van Nostrand, New York, 1955.

[4] Heal, K.G.: FORTRAN Subprograms to Utilize Julian Time for SequentialChronological Data Handling, Atomic Energy of Canada Limited, unpub-lished report CRNL-917, 1973 January.

[5] IMSL Library Reference Manual, Edition 7, Volume 2.

[6] Lipsett, J.J. and Macdonald, R.D.: "Another View of Fission Gas fromDefected CANDU Fuel Elements", paper presented at the IAEA Specialists'Meeting on the Behaviour of Defected Zirconium Alloy Clad Ceramic Fuelin Water Cooled Reactors, Chalk River, Ontario, 1979 September 17-21.

[71 Tseng, CM..- Data-Processing System for Analysis of Fuel-DefectExperiments, Atomic Energy of Canada Limited, unpublished reportCRNL-1459, 1976 February.

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