57
NO-4 OECD THEORmCAL ANALYSIS OF BURN-UP EXPERIMENTS WITH THE HBWR SECOND FUEL CHARGE INSTITUTT FOR AlOMENERGI OECD HALDEN REACTOR PROJECT P.O. BOX 175 . HALDEN . NORWAY

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Page 1: OECD - inis.iaea.org

N O - 4

OECD

THEORmCAL ANALYSIS OF BURN-UP EXPERIMENTS W I T H THE HBWR SECOND FUEL CHARGE

INSTITUTT FOR AlOMENERGI

OECD HALDEN REACTOR PROJECT

P.O. BOX 175 . HALDEN . NORWAY

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THEORETICAL ANALYSIS OF BURN-UP EXPERIMENTS WITH THE HBWTR SECOND F U E L CHARGE

by

K. E k b e r g and S . E . Wennemo-Hanssen

F e b r u a r y , 1970

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CONTENTS

FOREWORD

1. INTRODUCTION AND SUMMARY

2. CORE CHARACTERISTICS

3 . GENERAL DESCRIPTION OF BURN-UP ANALYSIS

4 . ISOTOPIC COMPOSITION OF BURNED F U E L

4 . 1 Isotopic Var ia t ion of U-235 4 . 2 Iso topic Var ia t ion of P u - 2 3 9 , Pu -240 and P u -4 . 3 Di scuss ion

5. CRITICAL SIZE AND REACTIVITY COEFFICIENTS

5. i Analys i s of the F reBh F u e l Sys tem 5. 2 Analys i s of the Burned F u e l Sys t em

5 . 2 . 1 Water Level Reac t iv i ty Coefficients 5. 2. 2 C r i t i c a l Size 5 . 2 . 3 T e m p e r a t u r e Reac t iv i ty Coefficients

6. POWER REACTIVITY E F F E C T S

6. 1 Void Dis t r ibu t ion 6.2 F u e l T e m p e r a t u r e 6 .3 Lat t ice P a r a m e t e r s 6 .4 Reac t iv i ty Ca lcu la t ions 6 .5 Di scuss ion

6 . 5 , 1 P o w e r Dis t r ibu t ion 6 . 5 . 2 Con t ro l Rod Effects 6 . 5 . 3 F u e l T e m p e r a t u r e s

6 .6 Conclus ions

LIST OF R E F E R E N C E S

LIST OF TABLES

LIST OF FIGURES

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FOREWORL)

The present report is one in a series covering the experimental and operating experience with the Halden Boiling Water Reactor, KBWK, during the three year period 1967 to 1969.

The reactor was built in the years 1955 - 195b by the Norwegian Institutt for Atomenergi, and has since- 1958 been operated internationally as one of the joint undertakings of the OMCD European Nuclear Energy Agency, The operation has been sponsored through four succeeding international agreements of which the latest was acceded by Institutt for Atomenergi, Norway; The Danish Atomic Energy Commission; The Atomic Energy Commission of Finland; A West-German industrial ^roup "consisting of Siemens-MchueUcrtwcrko AG, Allgemeine Elektrieitiits-Gesellschaft (AEG)» and Nuklcar-Chemie und -Metaliurgio G.m.b.M. (NUKICM); Comitate Nazionalc per 1'Energia Nucleare, Italy; Reactor Centrum Nederland; Aktiebolngct Atomenergi, Sweden; The Government of .Switzerland; The United Kiu^.om Atomic Energy Authority; and the Japan Atomic Energy Research Institute. The Government of Ausirin and the Atotnic Energy Commission of the United States have participated as associated parties.

The research and development programme is centred around irradi­ation of a wide variety of power reactor fuel assemblies developed in the participating organizations, and on developing systems and methods for integrated direct digital control of the reactor and reactor plant. The fuel irradiation programme comprises: basic studies of interaction between fuel and cladding; operation with partly molter, facl; development of in-core instruments, e .g. for the determination of channel power, fission gas pressure and central oxide temperature and for burn-out detection. The computer control programme includes work on dynamic control applying modern contro'i. methods, power distribution evaluation and control, sequence control, plant monitoring and alarm analysis as well as operator - process communication.

The reactor is operated at power levels up to 25 WW and at 240 C,

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1. INTRODUCTION AND SUMMARY

A series of in-pile and out-of-pile experiments to determine burn-up characteristics was conducted in 1966 with the second fuel charge of the Halden Boiling Heavy Water Reactor (1). The experiments were performed in order to obtain results against which theoretical reactor physics models for heavy water lattices could be tested. The average burn-up for the fuel at the time of the experiments was 5430 MWd/tU.

In this report the results of the theoretical analysis related to the above experiments are presented. The comparison of calculated and measured data comprises the following i tems:

Isotopic composition o f the burned f ael. Critical size of the core an*1 reactivity coefficients at low power. Reactivity effects induced by power changes.

The experimental and theoretical results for the burned fuel are com* pared with the corresponding results for the unburned core. The theore­tical and experimental analyses of the fresh fuel core have been described in previous reports (?), (3). Some of the calculations made previously have been repeated, making use of more sophisticated methods presently available.

In the comparison of experimental and theoretical results less signi­ficance has been attached to th** '' - *ed core than to the fresh, because of the larger experimental errors tor the burned state. The inferior experi­mental accuracy was mainly caused by the strong background source of photo-neutrons in the burned core, which made it necessary to use more approximate methods.

Furthermore» the use of HBWR as a fuel testing facility has consti­tuted elements of uncertainty in the results of the burn-up analysis. The introduction of test assemblies during the irradiation period, usually with high enrichments, may have changed the spectral conditions for certain standard assemblies compared to the conditions in an environment of standard assemblies only. Because of the frequent change of the core loading, it has been considered too tedious to .account for the irradiation history of each assembly separately. The theoretical burn-up analysis

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has therefore been made as if the core al l the t ime consis ted of standard second charge fuel a s s e m b l i e s only.

A l s o , poss ible spectral effects of the control rods present in the reactor during the irradiation period have been neglected in the theoretical ana lys i s .

The resul ts of the theoretical analysis of the burned HBWR second fuel charge may be summarized as fo l lows:

The calculated isotopic composit ion of the burned fuel, both by the two group lattice parameter s c h e m e REBUS-2 (4) and the multigroup trans ­port theory code F L E F (5), i s characterized by an overest imation of the total production of plutonium isotopes . Regarding each isotope separate ly , REBUS-2 predicts well the contents of Pu-?.39 and P u - ? 4 1 , but overes t imates the content of Pu-240 , while FLEF calculates correct ly the content of Pu-240 and overes t imates the contents of Pu-239 and P u - ? 4 1 .

Using REBUS-2 and a two dimensional two group diffusion theory reactor code , one obtains a reactivity value of the burned reactor at low temperature and clean crit ical conditions which is low by about 2%. F o r • the corresponding unburned sys t em the underestimation is about 3 .5%.

The calculated temperature reactivity coefficients for the burned core are in very good agreement with the experimental results at 70 and 155 C. At 205 C the calculations sl ightly underestimate the absolute magni ­tude of the coefficient. For the fresh fuel the calculated temperature coef­f icients are in agreement with the measured values only at 60°C, while at higher temperatures there is a c lear tendency of calculating too large negative coeff ic ients . The results both from the theoretical and the exper i ­mental analysis c lear ly indicate that the temperature reactivity coefficients are l e s s negative for the burned than for the fresh fuel s y s t e m .

The decrease in reactivity caused by an increase in reactor power is g r o s s l y overest imated in the theoretical analys i s . The calculations show that the reactivity effect is more negative in the burned than in the fresh condition. Th« experiments do not give a c lear indication on this point, because of the strong interaction effects caused by the control rods which were present during the measurements on fresh fuel .

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2. CORE CHARACTERISTICS

The HBWR second charge fuel a s s e m b l i e s are of c lus ter type with 7 s tr ingers in a hexagonal pattern. The centre to centre distance between the s tr ingers is 7.3 c m . The s tr ingers contain s intered U O , pel lets enriched to about 1. 5% by weight in U-235 , and canned in Z i r c a l o y - 2 . Each stringer cons is ts of two segments separated by a spacer region of Z i r c a l o y - 2 . A pel let of natural UO-, is placed at each end of the enriched parts of the s e g m e n t s . The s tr inger a s sembly is surrounded by a shroud of Z i r c a l o y - 2 , which s e r v e s the purpose of defining the coolant flow. The des ign of the fuel part of the fuel a s sembly i s shown in Figure 1.

The fuel a s sembly charac tar i s t i c s , based on an analys is of a sample of 20 a s s e m b l i e s , are summarized below:

Radius of fuel pel lets 0. 6294 c "u Density of fuel pel lets (;>0oC) 10. S42 g / c m 3

Length of enriched sect ion per segment 30. 0 cm Length of natural sect ion per segment 3 . 2 cm Average enrichment (nat. parts inc l . ) i . 5 0 3 w / o U-235 Radial gap between fuel and cladding 0. 009 cm Outer radius of cladding 0. 7146 c m Thickness of cladding 0. 0762 c m Outer radius of shroud 3 .65 cm Thickness of shroud 0 .1075 c m

The fuel a s s e m b l i e s were arranged in an open hexagonal lattice with a lattice pitch of 13. 0 c m . The core loading during the experiments with the burned fuel consisted of 100 a s s e m b l i e s and is shown in Figure 2 . The fuel e lement positions 1-1 and 3-4 were empty and the posit ion 2-2 occupied by a "water chemistry sampling tube". The various typ'es cf experimental equipment pr- sent in non-fuel posit ions are described in (1).

The composition of moderator and coolant during the various phases of the reactor's life t ime has been as fo l lows:

F r e s h fuel experiments 99 . 75 w / o D 2 0 , 0. 25 w / o H z O Irradiation period (average values) 99. 65 w / o D 2 C 0.35 w / o H 2 0 Burned fuel experiments 99 .62 w / o D 2 0 , 0. 38 w / o H 2 0

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5 - FIG. 1 J

HBWR SECOND CHARGE FUEL ASSEMBLV

| SS «hroud top extension

SS end grid

. . . . . . outside diam. ?. 3 cm Zlrcalloy .hroud ^ ^to.,* 0.1 cm

Zlrcalloy top extemian roda

SS apacer

*i_. i i« .<. i . iMi_. outaide diam. l . « c m Ziroalloy cladding w a l l thick,,.,, 0 .076 cm Natural UO ; pellet diam. 1. 259 cm

"1.5 wt % enriched UO, pellet diam. 1.259 cm denaity UO, « .54 i / c m ' at 20°C atomic .atft O/U 2.00 - 2.03

B _l Natural U 0 2 pellet

Zircalloy central spacer

c c thickness 0.05 cm SS .pacer w e l g b t 4 0 g

Zircalloy bottom extension rods total weight 1410.5 g

SS bottom grid

SS bottom piece

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CORE LOADING DURING MACROSCOPIC BURN-UP MEASUREMENTS

H B W R - U STANDARD ELEMENT WHICH HAS STAVED IN A FIXED CORE POSITION DURING CORE LIFE

HSWR-H STANDARD ELEMENT WHICH HAS CHANGED CORE POSITION DURING CORE LIFE

INSTRUMENTED FUEL ELEMENT WITH HBWR-n DESIGN

WATER CHEMISTRY PROGRAM PROSE

© CONTROL STATIONS

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3. GENERAL DESCRIPTION OF BURN-UP ANALYSIS

The axial distribution of burn-up for all 100 fuel assemblies used during the final experiments has been determined through gamma scanning and is given in (1). The normalisation of the gamma scanning profiles was made by determining die absolute burn-up of two of the assemblies by mass spectromctrlc analysis of the fission product molybdenum, using the iso-topic dilution technique.

During the burned fuel experiments the core had a burn-up dis tr i ­bution which was uniform in the sense that the seven annuli, in which the core is naturally divided, had approximately the same average burn-up.

.However, between the individual assemblies within one annulus the vari­ation was sometimes considerable. As only two-dimensional codes were available, this azimuthal variation could not be taken into account in the calculations.

In the chemical analysis for determining the absolute burn-up, the quantity primarily determined is the number of"fissions per initial metal atom" in the fuel. The conversion from this quantity to the burn-up in MVi /tU requires the use of the quantity "average energy release per fission". The burn-up data given in (l) are basad partly on the value 210 MeV/fission and partly on the value ?00 MeV/fission. In order to have consistency with the corresponding constants in the data libraries of the codes REIJUS-2 (4) and FLEF (5) which are used in the. theoretical burn-up analysis, .all the experimental burn-up values in (l) have been-recalculated using the value ''OS MeV/fission. This value of the constant takes into account that the energy release per fission is not the same for the various fissile isotopes. It was obtained for the IIB*VR-II fuel based oh calculations by FLEF , giving the total number of fissions occurring in the various fuel isotopes in the burn-up interval 0 - &000 MWd/tU..

In the theoretical burn-up analysis the core has.been divided axially in eight fuel regions of equal thickness and a spacer region. It has been assumed that each fuel region has homogeneous properties with respect to void, fuel temperature and specific power production, and that these proper­ties remain unchanged during the burn-up. The properties of the various regions are summarized in Table I.

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Table I

Characterist ics of the Axial Subregions Used in the Theoretical Burn-Up Analysis

Region Axial Region Extension

(cm) *>

Specific Power (w/g uo 2 )

Fuel T e m p e ­rature

(°C)

Coolant Void Fract ion

Burn-Up Reached (MWd/tU)

1 1 5 0 . 8 - 1 7 1 . 7 5 .8 350 0 .65 2870 ?. 1 3 0 . 1 - 1 5 0 . 8 8 . 5 . 400 0 .60 4170 3 109 .3 -130 .1 10.5 445 0 .55 5150 4 8 8 . 5 - 1 0 9 . 3 12 .6 495 0 .50 6240 5 6 2 . 4 - 33 .2 13 .9 535 0 .40 6830 6 4 1 . 6 - 62 .4 13.9 535 0 .30 6830 7 2 0 . a - 4 1 . 6 12 .6 495 0 .15 6240 S 0 - 2 0 . 8 10.5 445 0 .05 5150

From lower end of fuel.

The power of the reactor during the burn-up varied between 14 and 20 MW with a time average of about 16 MW. The speci f ic power production for each region given in Table I is based on the assumption that the axial power distribution on the average has been proportional to the axial burn-up distribution» determined through gamma scanning of the burned fuel a s s e m b l i e s .

The temperature of moderator and coolant was 210 C «*•. ^rrnal ope ­rational conditions of the reactor . Based on this value and a total average power level of 16 MW, the void fractions and i\ .»l temperatures given in Table I have been est imated, making use of the ^ -U. ulational resul ts given in (3) and (6) respect ive ly .

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4. ISOTOPIC COMPOSITION OF BURNED FUEL

The isotopic composition and che absolute burn-up of two irradiated fuel assemblies. No. 02-07? and No. Of-117, have been determined by chemical and mass spectrometries methods. The samples to be analysed were taken at several axial heights and both from the central stringer and the stringers in the outer ring. For assembly No. 02-117 samples from two outer stringers» diagonally oppositely to each other, were analysed. For assembly No. 02-072 samples were taken only from one of the outer s t r ingers . In Table II are given the results of the experimental determi­nation of burn-up along with axial positions and initial contents of U-235 for the various samples analysed.

The theoretical analysis of the' isotopic composition of the fuel as a function of burn-up has been made with the lattice burn-up codes FLEF (5) and REBUS-2 (4).

FLEF is a one-dimensional multigroup transport theory code. The space and energy dependence of the neutron flux is calculated in up to 58 energy groups and up to 20 space points. The integral transport equation is solved for the homogenized cluster with the number of energy groups condensed- to 25 or less . The burn-up part of the code is described in (7).

REBUS-2 is based on the Westcott formalism for calculation of spectnim weighted cross sections. The neutron temperatures in different regions of the lattice cell are calculated according to empirical formulae given by Sokolowski (8).

Based on the physical data given in Table I, FLEF and REBUS-2 have been used to calculate the isotopic composition of fuel as a function of burn-up for each of the eight axial subregions of the core. For the same burn-up. the calculated isotope concentrations were found to depend only weakly on- the axial position. Compared to the probable errors in the experimentally determined concentrations, the influence of the axial de­pendence is negligible.

Experimental and calculated concentrations of the isotopes U-235, Pu-239, Pu-240, and Pu-241 as a function of burn-up are presented in Figures 3 through 7. The calculated concentrations for each axial region

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Table II

Characterist ics of the Samples Used in the Isotopic Analysis of the Burned Fuel

Burn-up values from Table IV and VII in (1) are renormalized to 203 M e V / f i s s ion . F o r 02-072 each sample value is the average of 3 values from 3 radial positions in the rod.

Assembly No.

Axial . Position '

(cm)

Initial Enr . in U-235 ( w / o )

Burn -up (MWd/kgU; Assembly No.

Axial . Position '

(cm)

Initial Enr . in U-235 ( w / o ) Sample Average

Centre 3 . 3 3 1 02-117 157 1.476 Ring, left

Ring, right

Centre

3 .08 Fai led

5 .13

3 .11

02-117 129 1.476 Ring, left Ring, right

Centre

5.34 5 .60

6 .25 ] ]

5 .40

02-117 102 1.476 Ring, left Ring, right

C entre

7 .04 7 .12

7 .29 1 1

6 .95

02-117 68 1.490 Ring, left Ring, right

Centre

7.79 8 .08

7 .10 } 7.84

02-117 41 1.490 Ring, left Ring, right

C entre

7 .19 7 .72

1.68 } 7 .40

1.78 02-072 165 1.503 Ring, right 1 .80 j 02-072 128 1.503

Centre Ring, right

3 . 1 0 3 . 5 0

1 ;

3 .45

02-072 95" 1.503

!

Centre Ring, right

4 . 4 6 4 . 7 5 } 4 . 7 0

x) Relative to lower end of fuel. ,

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- 11 FIG. 3

ISOTOPIC COMPOSITION OF FUEL VERSUS BURNUP. CONCENTRATION OF ^ FOR SAMPLES HAVING VARIOUS INITIAL CONCENTRATIONS.

1.3

1.2

1.1

1.0

Initial cone: 1.503 w/o

1.2

3 1.1

1.0

0.9

0.8

0.9

0.8

Initial cone: 1.476 w/o

• Control otringor o Out»r otringor — Calculator FLEF

REBUS-2

Moaourtd

Initial cone: 1.490 w/o

ti

Control

Exp. orrori:* 0.01 in 2 3 5 U I i 5 Yi in burnup

Control

Control

4 5 6 BURNUP (MWd/kgU )

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ISOTOPIC COMPOSITION OF FUEL VERSUS BURNUP TOTAL CONCENTRATION OF PLUTONIUM ISOTOPES RELATIVE TO TOTAL C^NCEt/TriATION OF URANIUM ISOTOPES.

*tO '

3.0+

2.54

2.0

1.5

«5 1.0

s R ~ 0.54

Exp. error* : * 2 V. in Pu/O t 5 */• In burnup

Central

• Centra, stringer 0 Outer stringer Measured

— Calculated FLEF — Calculated REBUS-2

6 BURNUP t MWd/kg U)

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FIG. 5

ISOTOPIC COMPOSITION OF FUEL VERSUS BURNUR CONCENTRATION OF 2 3 9 P U .

Exp. errors : * 0.005 In 2 3 B P u ] i 5 */• in burnup

Out»r

C»ntrg|

« C*ntral stringer") o Outer stringer J

Measured

Calculated FLEF Calculated REBUS-2

-—* 4 5 6 BURNUP I MWd/kgUI

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- u I FIG.6 |

ISOTOPIC COMPOSITION OF FUEL VERSUS BURNUP. CONCENTRATION OF 2 4 0 P u .

.07

i .06' 3 a. o

.05'

.04

.03-•

.02'

Central stringer " Outer stringer

- Calculated FLEF

- Calculated REBUS-2

Measured

Exp. errors : i 0.0015 in Z 4 0 P u J / s 5 7. in burnup

i 5 6 BURNUP (MWd/kg U }

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FIG. 7

ISOTOPIC COMPOSITION OF FUEL VERSUS BURNUP. CONCENTRATION OF 2 4 1 P u .

1 i / Outer /

.014 \ / / Central \ / /

.012 • Central stringer') V / / o Outer stringer ) Measured / / '/"

Calculated FLEF / / / .010 Calculated REBUS-2 / / / *

.008 Exp.errors : t O.OOOSin M , P u I / / / t 5 V. in burnup / / /

.006 ///

.004

.002

/ / / • •

1 i • i i 1 i 1—*•

BURNUP (MWd / kg U)

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is taken at a burn- p value equal to the measured burn-up of the sample taken from that region.

In REBUS-2 it is only possible to have one fuel zone in the unit ce l l , and one can therefore not calculate the variation in isotopic c o m ­position between the central stringer and the s tr ingers in the outer ring. When the REBUS-2 results are to be compared with the results of exper i ­ments and FLEF calculations, the latter may be represented through the values for the outer ring, which in practice are very c lose to the average values for the ce l l .

With reference to the experimental points plotted in Figures 3 through 7 one should note that the experimental burn-up values are different for the central and the peripheral rod at the s a m e axial posit ion. To facil itate a comparison with the calculated va lues , the experimental paints for both types of rods have been plotted at burn-up values equal to the assembly average values for that axial position ( last column, of Table II).

For one of the as sembl ie s analysed, No. 02-117, the initial enrich­ment in U-235 was significantly lower than the average enrichment for the whole charge. The str ingers in the upper and the lower bundle of this assembly had enrichments of 1.476 w / o and 1.490 w / o , respect ive ly , while the average value for the charge i s 1.503 w / o . The proper initial enrichment for each sample was taken into account in the calculation of isotopic composi t ions . It was found that the variations in initial content only influenced the concentration of U-235 during burn-up and not the build­up of the Pu i sotopes .

In the following sect ions the comparison of experimental ly and theo­ret ical ly determined isotopic compositions of the burned fuel wil l be d i s ­cussed in some more detail .

4 .1 Isotopic Variation of U-235

The depletion of the isotopic concentration of U-235 as a function of burn-up is shown in Figure 3 . The measured and calculated concentrations are seen to agree wel l for the samples taken from as sembly No. 02-072 . F o r assembly No . 02-117 the calculated concentrations are higher than those determined experimentally.

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In the actual burn-up Interval by far the largest part of the fissionB take place in U-235 (about 80?i in the interval 0 - 7500 MWd/tU). The depletion of this isotope therefore wi l l be c lose ly related to the total burn-up of the fuel . Accordingly» the discrepancy between the measured and the calculated concentration of U-235 for as sembly 02-117 must be due to e i ther that

the experimental determination of burn-up has given too high values ', or that

the initial concentration has been assumed too low in the calculat ions .

In the way the theoretical analysis has been made, making use of experimental ly determined burn-up va lues , it iB therefore not possible to draw any conclusions about the ability of the codes to predict the depletion of U-235 as a function of burn-up.

The difference in concentration of U-235 between the central stringer and the s tr ingers in the outer ring as calculated by F L E F , is seen to be in sat isfactory agreement with the experimental r e su l t s .

4 . 2 Isotopic Variation of P u - 2 3 9 , Pu-240 and Pu-241

The measured and calculated total concentrations of Pu isotopes as a function of burn-up are shown in Figure 4 . It i s seen that both FLEF and REBUS-2 overest imate the total Pu production. The differences between FLEF and REBUS-2 are in general smal l , although REBUS-2 is in slightly better agreement with the experimental values at high burn-up. The diffe­rence in Pu content between the central s tr inger and the outer ring i s seen in average to be underestimated by F L E F .

The variation with burn-up of the concentration of the separate i sotopes , P u - 2 3 9 , Pu-240 and P u - 2 4 1 , are shown in Figures 5, 6, and 7 respect ive ly . The comparison of the measured and the calculated data may be summarized as fo l lows:

A s s e m b l y N o . 02-117 was analysed at Kjel ler , Norway, while N o . 02-072 was analysed at Studsvik, Sweden.

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- The concentration of Pu-239 is well predicted by REBUS-2, but, at high burn-up, overestimated by FLEF.

The concentration of Pu-240 is slightly overestimated by FLEF and strongly overestimated by REBUS-Zr

The ct. aeration of Pu-241 is calculated with satisfactory accuracy by REBUS-2, while FLEF clearly gives too high values.

The difference between the central stringer and the 3tringers in the outer ring is generally underestimated by FLEF.

4. 3 Discussion

The theoretical schemes for calculation of the isotopic composition as a function of burn-up are discontinuous in the respect that the neutron spectrum is assumed constant within certain intervals and is updated at the beginnings of the intervals only. The burn-up step length in the FLEF calculations, in practice limited by computing costs, was chosen to 500 MWd/tU, but with spectrum updating each second step only. A close analysis of the calculated isotopic variation with burn-up revealed that for one of the isotopes, Pu-241, the build-up rate was discontinuous. It was found that the increase in the concentration of this isotope was systematic­ally higher for the steps with unchanged spectrum than fox* the steps with updated spectrum. The integrated effect at a burn-up of 5500 MWd/tU amounted to approximately Z%, meaning that the calculated concentration of Pu- : 41 is overestimated by this quantity due to updating the spectrum each 1000 MWd/tU instead of each 500 MWd/tU. It must be assumed that a decrease in step length below 500 MWd/tU will produce a still further decrease in the calculated concentration and thus reduce the discrepancy between FLEF and experiments for this isotope.

For the other fuel isotopes the influence of the burn-up step length in the FLEF calculations was found to be negligible.

In the REBUS-2 calculations the step length is fixed by the programme, and it is not possible to carry through a similar investigation as was made for FLEF. The spectrum is"updated at steps of 100 MWd/tU at low burn-up values, with the step length gradually increasing to 800 MWd/tU at the

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highest burn-up values. In average the step lengtli is much smaller than for the r LEF calculations, and it is probable that the consequences of the discontinuous variation of the spectrum are negligible.

The disagreements found when comparing calculated and measured concentrations of U-225, indicate that the experimental determination of burn-up may have given systematically too high values-. If the burn-up values of the analysed samples are adjusted to give agreement between calculated and measured content of U-235, the apparent theoretical over-estimation of the production o£ Pu isotopes will be considerably reduced.

The systematic variation in the burn-up of the samples taken from diagonally opposite stringers in the assembly No. QZ -072 (see Table II), leads to the conclusion that the assembly must have been placed in a flux gradient during the irradiation. The variations are too large to be explained by normal macroscopic effects and must have been caused by either control rods or teat fuel assemblies of high enrichment. The presence of a flux gradient will not necessarily in itself influence the comparison of measured and calculated average isotope concentrations for the assembly, since the comparison is'made at the experimentally determined burn-up values. However, the gradient may have influenced the variation in i3otepic com­position between the central stringer and the outer s tr ingers. Expecially

•for the assembly No. 0?- 117» where only one of the outer stringers was analysed, the measured radial variation may not be representative.

The control.rods or the test fuel assemblies responsible for the observed flux gradient, also may have caused a hardening of the neutron spectrum. A calculation made by REBUS-2, in which the thermal neutron temperature of the cell was increased by 5 C and the epithermal index by 10%, gave the result that the total concentration <rf Pu isotopes, at a burn-up of 6400 MWd/tU, was increased by about 1 % only. It is accordingly concluded that the isotopic composition is rather insensitive to variation, in the spectral characteristics, although it is true that an assumption of a harder spectrum in the calculations will increase the Pu production and emphasize the overestimation already existing.

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5. CRITICAL SIZE AND REACTIVITY COEFFICIENTS

5. 1 Analysis of the Fresh Fuel System

The results of the experimental and the theoretical determination of critical size and reactivity coefficients for the unburned second charge at zero power conditions are reported in (?). The theoretical analysis was based on the lattice parameter code BURNUP-5 (9) and a one dimensional diffusion code (10). The corresponding analysis of the burned reactor, to be presented in section 5.2 in this report, is made with more up to date methods, i . e . the lattice code REBUS-2 (4) for determination of two group lattice parameters and the two dimensional diffusion code EQUIPOISE (11) for macroscopic calculations. In the discussion of the calculated results for the burned reactor, the corresponding results for the fresh reactor will have to play an important role. The theoretical analysis of the fresh system lias therefore heen repeated in this work using the same calcu­lational scheme as for the burned fuel analysis.

The results irotn the repeated calculations along with the original experimental and calculated results are presented in Table III. It is seen that both calculational schemes give too low values for k ,, for the critical reactor. The degree of underestimation increases with increasing tempe­rature, meaning that the theory predicts too large negative temperature reactivity effects. This caiculational characteristic also appears through the comparison of calculated am' measured temperature reactivity coef­ficients .

In principle the REBUS-2/EQUIPOISE calculational scheme is an obvious improvement to BURNUP-5/L,INDE. The latter scheme, however, in practice is seen to predict criticality and temperature coefficients in better agreement with experiments. The main reason for this anom-'Uy is to be found in the differences in the thermal spectrum, i . e . the calculation of neutron temperature. In the BURNUP-5 calculations the neutron tempe­rature was assumed constant throughout the cell and equal to the physical temperature of the 3ystem. Compared to REBUS-2, which makes use of empirical formulae based on spectrum measurements (8), BUR.NUF-5 strongly underestimates the neutron temperatures, and thereby relatively

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- 2 1 -

o v e r e s t i m a t e s the r eac t iv i ty of the c e l l . T h e dif ference be tween the ne. i t ron t e m p e r a t u r e a s ca l cu la t ed in RE BUS-Z and the phys ica l t e m p e r a ­tu r e was found to i n c r e a s e with t e m p e r a t u r e . However , the e r r o r in the p red ic t ion of k » i n c r e a s e s by the s a m e amoun t for the two codes in going from low to high t e m p e r a t u r e . •

T a b l e III

M e a s u r e d and Calcu la ted Cr l t i c a l i t y and React iv i ty Coefficients for the C r i t i c a l R e a c t o r with F r e s h F u e l

Temp e r a t u r e (°C) 53. a 161.3 2 74. S

E x p e r i m e n t 1.000 1.000 1.000 k off HE BUS - ? /EOU [POISE 0.967 0.961 0.91' H

BU UNU V -•.-/' .IN DE 0. W 0. 9 >9 ' 0 . 9 - 5

' ( S p / a T ) c r E x p e r i m e n t - 4 7 t 4 - 6 6 ± 6 - 9 1 i 3

(pcm/°C) R E B U S - ' / E Q U I P O I S E BURNUP-5 /LINDE

- 4 4 . 8 - 4 7 . 5

- 8 ? . ? - 7 7 . 5

- 101 .0 - 9 7 . 5

( a P / o H ) c r E x p e r i m e n t 565 t 30 42 p, t 30 340 t 30 REBUS-7/EOUIPOSJ: 592 469 ' 347 DURNUP-5 /LINDE 540

• 440 330

Exponent ia l e x p e r i m e n t s a t low t e m p e r a t u r e were car r ied , out with the f r e sh second c h a r g e fuel and a r e r e p o r t e d in (12). Using the m a t e r i a l buckling d e t e r m i n e d in these e x p e r i m e n t s , REBUS-2 gives an effective mul t ip l i ca t ion fac tor of 0. 988, A s l ight ex t rapo la t ion in Table III gives a k „ = 0 .969 a t 20°C f rom REBUS-2/EQUIPOJSE ca l cu la t ions . Accord ing ly , it can be concluded that the s t rong reac t iv i ty u n d e r e s t i m a t e in the c a l c u ­la t ions is a r e s u l t of an u n d e r e s t i m a t e of the r eac t iv i ty of the c o r e i tself a s well a s of the ef fec t iveness of the r e f l e c t o r s .

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D. Z Analys is of the Burned JTuel Sys tem

The ca lcula t ions of c r i t i c a l s ize and r eac t iv i ty coefficients for the burned r e a c t o r at z e r o power condit ions have been made with the R E B U S - 2 / EOi;fPOISE s c h e m e . KEBUS-2 was f i r s t run for each of the eight ax ia l subreg ions of the c o r e , de sc r ibed in Table I , to d e t e r m i n e the isotopic c o m ­posit ion of the fuel a s a function of b u r n - u p . The tempera tu- r td and the d i s t r ibu t ions of power and coolant void in each reg ion were a s s u m e d to r e m a i n constant dur ing the burn-u.^ p r o c e s s . The r e su l t i ng isotopic c o m ­posi t ions for each reg ion , at the b u r n - u p va lues d e t e r m i n e d expe r imen ta l l y , were used as input to fur ther REBUS-2 ca lcu la t ions at z e r o power con­d i t ions , to d e t e r m i n e lat t ice p a r a m e t e r s a s functions of t e m p e r a t u r e .

The infinite mul t ip l ica t ion factor is chosen to r e p r e s e n t the la t t i ce p a r a m e t e r s obtained, and is p r e sen t ed as a function of t e m p e r a t u r e in Table IV. The ca lcula t ions a t z e r o power w e r e not made for t h o s e ' r e g i o n s lying above the c r i t i c a l wa t e r levels m e a s u r e d at the va r ious t e m p e r a t u r e s . In o r d e r to save c o m p u t e r t i m e , i t was a s s u m e d that the four lower reg ions of the c o r e , in the de t e rmina t ion of r eac t iv i ty coeff ic ients , joulcl be r e ­placed by one region having the a v e r a g e p r o p e r t i e s . Th is s e e m e d to be a safe assumpt ion from physical c o n s i d e r a t i o n s . On the o the r hand, the absolute level of reac t iv i ty is affected by this condensa t ion , a s is de sc r ibed in 5 . 2 . 7 .

The m a c r o s c o p i c ca lcula t ions were m a d e by the two g roup , two d imens iona l code EQUIPOISE. The g e o m e t r y used in the ca lcu la t ions is shown in F i g u r e t>. The re f lec tor reg ions contain U ? 0 and va r ious con­s t ruc t iona l m a t e r i a l s . Two group homogenized diffusion coefficients and m a c r o s c o p i c c r o s s sec t ions for these reg ions have been ca lcula ted as a function of t e m p e r a t u r e "based on the fo rmulae given in (13). The fo rmulae take into account both flux d e p r e s s i o n and r e s o n a n c e abso rp t ion in the con­s t ruc t iona l m a t e r i a l s .

The height of the u p p e r m o s t c o r e region has been i n c r e a s e d at the top by an amount equal to the ex t rapola t ion d i s t ance for t h e r m a l neu t rons ( i . e . the t h e r m a l diffusion coefficient for the region t i m e s a fac tor 2. 13).

Actual ly , the fuel continues a l s o above the ex t rapo la ted height of the c o r e . It will the re fore ex i s t a c e r t a i n probabi l i ty that a neutron, leaking

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23 [FIG. 8

SIMPLIFIED VERTICAL CROSS SECTION OF THE REACTOR USED IN THE THEORETICAL ANALYSIS OF THE BURNED FUEL SYSTEM AT ZERO POWER CONDITIONS.

84.8 S0.2

Variable

^ '

"I

1 CORE REGION 2

RADIAL REFLECTOR

! CORE REGION 3

RADIAL REFLECTOR

1 CORE REGION ^

RADIAL REFLECTOR

1 SPACER REGION

RADIAL REFLECTOR

j CORE REGION 5

RADIAL REFLECTOR 1 CORE REGION 6 RADIAL REFLECTOR

| CORE REGION 7

RADIAL REFLECTOR

J CORE REGION 8

RADIAL REFLECTOR

I BOTTOM REFLECTOR Zr

RADIAL REFLECTOR

1 BOTTOM REFLECTOR SI

RADIAL REFLECTOR

| BOTTOM REFLECTOR S2

RADIAL REFLECTOR

All dbtanets in cm.

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-24-

out of the c o r e at the top, shal l cause a f i s s ion , and that f i ss ion neu t rons shal l en te r the c o r e aga in . The neglect ion of the fuel region above the wa te r level thus .vill lead to au u n d e r e s t i m a t e of the r e a c t i v i t y . Based on calcula t ions made for the NORA r e a c t o r at Kje l le r (14), th is effect for the HBVVR will be l e s s than 100 p e m , and t he r e fo re m a y be neg lec ted .

Table IV

Calcula ted Infinite Mult ipl icat ion F a c t o r s for the Burned F u e l a t Z e r o P o w e r Condit ions as a Func t ion o£ T e m p e r a t u r e

Axu; Region N o .

B u r n - u p

(MWd/tU) 65 75

T e m p e r a t

150

u r e ( C)

lbO 2 00 210

1 2870 1.3491 1.3470 ? 4170 1.3246 1.3232 1.3168 1.3150 3 5150 1.3091 1.3081 1.3000 1.2988 1.2 934 1.2919 4 6240 1.2 793 1.2784 1.2718 1.2708 1.2666 1.2653 5 6830 1.2616 1.250? 6 6830 1.3609 1.2501 7 6?40 1.2794 1.2675 tj 5150 1.3086 1.2931 5-8 6260 1.2793 1.2784 1.2720 1.2710 1.2668 1.2654

F r e s h fuel 0 1.4493 1.4477 1.432S

1 1.4305 1.4203 1.4176

5 . 2 . 1 Water Level Reac t iv i ty Coefficients

The water level r eac t iv i ty coefficient has been ca lcu la ted a t t e m p e r a t u r e s and wa te r l eve l s in c o r r e s p o n d a n c e with the e x p e r i m e n t s . The coefficients have been obtained as the change in r eac t iv i ty of the system due to a change in the height of the top c o r e reg ion by 1 c m . B e c a u s e of the axial va r i a t ion of the b u r n - u p , a s t r a i g h t f o r w a r d p r o c e d u r e l ike this has to be applied with some c a r e . It was found sufficiently a c c u r a t e in the p r e s e n t s i tua t ion , because the c r i t i c a l wa t e r leve ls in a l l t h r e e c a s e s con­s i d e r e d happened to b e c lose to the middle of s o m e axia l subreg ion for which

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-25-

the a v e r a g e p r o p e r t i e s had been ca l cu l a t ed . T h e o r e t i c a l l y and e x p e r i ­menta l ly d e t e r m i n e d w a t e r level coeff icients a r e given in Table V.

Tabic V

M e a s u r e d and Calcula ted Water Level Reac t iv i ty Coeff icients for the Burned F u e l Sys t em (at H . )

T e m p .

(°C)

Water Level

(cm) -

5 p/5 H ( p e m / c m ) T e m p .

(°C)

Water Level

(cm) - M e a s u r e d Ca lcu la ted

. 65

150

300

153

174

193

77 i 9

94 t 11

-11 0 i 12

179 '

141

126

} Re la t ive to the Bot tom P l a t e

While the ca lcu la ted and the m e a s u r e d coeff icients for the f r e sh fuel s y s t e m , given in Table III, w e r e in reasonab ly good a g r e e m e n t , this is not the case for the burned s y s t e m .

G e n e r a l l y Bp/dH is known to d e c r e a s e s t rong ly a s the he ight of the c o r e i n c r e a s e s . In the one -g roup model it v a r i e s as l /H . The m e a s u r e d values in Tabic V, however , show a tendency in the opposi te d i r ec t i on . In d i s cus s ing th i s tendency one m u s t be a w a r e of the fact that the m e a s u r e ­m e n t s w e r e c a r r i e d out a t wa t e r l eve l s a t which the fuel b u r n - u p profi le was d e c r e a s i n g with i n c r e a s i n g he igh t . In p r inc ip le one sha l l t he r e fo r e expect l e s s reduc t ion in the w a t e r level coefficient with i n c r e a s i n g height c o m p a r e d to a f r e s h or a un i fo rmly burned c o r e . However , i t s e e m s v e r y unl ikely that this effect sha l l be s t rong enough to explain the e x p e r i m e n t a l r e s u l t s obta ined .

The m a i n r e a s o n for the l a r g e d i s c r e p a n c i e s between the m e a s u r e d and the ca lcu la ted va lues for the bu rned fuel is t h e r e f o r e m o s t probably to be found in the e x p e r i m e n t a l technique u s e d . The m e a s u r e m e n t s w e r e made by m e a n s of a r eac t iv i ty m e t e r , and It i s s ta ted in the d i s c u s s i o n of

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-26-

the results in (l) , that there is doubt about the applicability of such a technique in a burned D-O moderator! reactor because of the high back­ground source of photoneutrons. *

b.?.. ? Critical Size

To obtain a proper comparison between experimentally and theoretic­ally determined critical water levels, corrections have to be made for experimental equipment, control rod guide stays and three fuel element positions that were empty during the experiments.

The various types of experimental equipment present during the measurements are described in (l) . From a neutron physics point of view they can be considered as stainless steel tubes. The control rod guide stays are stainless steel tubes of diameter 3 mm and thickness 1. 5 mm. The reactivity value of the experimental equipment and the guide stays has been calculated by the computer code HE TAL which can be de­scribed as a simplified two dimensional version of the three dimensional heterogeneous diffusion code HETERO (15). The same code was also used for estimating the reactivity effect of three empty fuel element positions. The corrections obtained are listed in Table VI.

Table VI

Reactivity Corrections Related to the Burned Fuel System Criticality Analysis

Temperature

<°C)

Reactivity Effect (pem) Temperature

<°C) Control Rod Guide Stays

Experimental Equipment

Three Empty Fuel Positions

Condensation of Lower Core Half

65

i sa

200

- 1400

- 1400

- 1400

- 1000

- 1000

- 1000

- 675

- 600

- 555

(290)

337

(367)

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-27-

In Table VI is also given a correction for the reactivity error arising from condensing the four lower core regions into one at 1S0°C. The calculations at 65 and ?00 C were carried out both with and without such condensation. The correction at 150°C was obtained through a linear interpolation between the values lor the lower and the higher temperature.

The height of the top core region in the calculations is determined by the critical water level measured at the various temperatures. In practice this leads to top regions that are smaller than the regions assumed in the lattice parameter calculations. Because of the decreasing burn-up profile in the upper half of the core, the burn-up for the top region in each case therefore is underestimated in the calculations. An approximate investigation showed that the resulting overestimation of the reactivity of the system was not more than 50 pem in any of the cases, and corrections were found unnecessary.

The calculated effective multiplication factor for different tempera­tures for the critical burned fuel system is given in Table VII, the various reactivity corrections listed in Table VI being included. The er rors in the k ,, values account for an experimental uncertainty in the determination of the absolute burn-up of - 5%, They were obtained through calculations on a system having the same burn-up profile but an average burn-up 5% higher than the nominal value.

Table VII

Calculated k ,, for Different Temperatures for the Burned Critical System

Temperature

(°C)

Measured . Crit . Water Level *'

(cm) eli

65 153.3 t 1.0 0.981 i 0.007

150 173. 5 ± 1.0 0.981 t 0.006

200 192.7 ± 1 . 0 0.983 i 0.005

Relative to bottom plate

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JFI6.9 \

MEASURED AND CALCULATED CRITICAL WATER LEVELS FOR THE FRESH AND THE BURNED FUEL SYSTEM.

I A 200

Calculated burned fuel

E )80

hi > Hi

m | 160 •

< o

Measured burned fuel

a. o

U0

120

Calculated fresh fuel

100 SO 100 150 200

TEMPERATURE !°CJ 250

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29-

Thé reactivity equivalence of the uncertainty in the measured critical water level is approximately - 150 pcm, and comes in addition to the uncertainty due to the determination of burn-up.

A plot of calculated and measured critical water levels as a function of temperature for the burned fuel system is presented in Figure 9. For comparison, the corresponding values for the fresh system are also shown.

It is seen that the calculations underestimate the reactivity of the burned system. Taking into account that the reactivity of the fresh system at low temperature was underestimated by more than 3%, it may appear as if the decrease in reactivity due to burn-up is predicted too small.

However, the results for the fresh and the burned core are not imme­diately compatible, because of the large difference in the geometrical buck­ling of the two systems. It was concluded in Section 5.1 that the treatment of the reflectors in the calculations on the fresh system led to a reactivity underestimate. The importance of the reflectors will be reduced with increasing height of the system. Consequently, the underestimation of the effectiveness of the reflectors will be less important for the burned core than for the fresh, leading to a higher k f f in the former case.

It is documented in Table VI that the calculated reactivity for the burned reactor increases where the lower half of the core is treated as one instead of four regions with respect to burn-up. It is reasonable to assume that even the division of each half of the core in four regions gives an overestimate of the reactivity and accordingly contributes to the diffe­rence between the k ,* calculated for the burned and the fresh fuel system.

The calculated k , f for the burned reactor is seen to be fairly constant as a function of temperature. This indicates that the temperature reactivity effects are predicted with good accuracy.

5.2.3 Temperature Reactivity Coefficients

Theoretical temperature reactivity coefficients have been obtained at 70, 155 and ?.05°C by calculating the reactivity effects of temperature changes of 10°C. The results are given in Table VHI, along with the corresponding experimental values.

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Table VIII

Measured and Calculated Temperature Reactivity Coefficients for the Burned Fuel System

Tempera­ture <°C)

Mc.-surt-d Calculated Tempera­ture <°C) a P /aT

(pcm/°C) 3H /br lciR7°c)

a P / 3 T (wm/°C)

d : i c r / d T (cm/°C)

70

155

205

- 1 5 - + 4

- n i l

- 57 i 14

0.20 - 0.05

0 . 3 ' - 0.06

0.52 - 0. 10

- 5 5.8

- 46. 0

- 58.3

0. 189

0.326

0.462 1

In obtaining the experimental temperature coefficients use was made of the measured water level coefficients given in Table V. It was stated in Section 5,2.1 that there is doubt about the applicability of. the technique used in determining these values. The most reliable quantity in the experimental analysis of temperature effects is therefore the measured changes in critical water level per unit change in temperature, SU /h T. It is assumed that the most meaningful comparison between theoretical and experimental results is obtained using this quantity. Theoretical values for SH / o T have been obtained by dividing the calculated temperature coefficient by the calculated water level coefficient.

It is seen that the measured and the calculated values of dH / 3 T are in very good agreement at 70 and 155°C. At 205°C the calculated value would be somewhat too low, if one accepts the value of dH /&T = 0. 60 cm/ C given in (1). However, if the curve of H . versus tempera­ture is plotted, using the experimental results in (1), one finds that the upper part of the curve can equally well be drawn with a slightly different curvature, giving a value of 5H / d T at 205°C of 0.52 cm/°C. This value is in considerably better agreement with the theoretical value.

In Figure 10 the temperature coefficients for the fresh and the burned reactor have been compared. The experimental values for the burned system have been obtained making use of the calculated water level coef­ficients instead of the measured. The uncertainty in the calculated water

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- 31

FIS. JO

MEASURED AND CALCULATED REACTIVITY TEMPERATURE COEFFICIENTS FOR THE FRESH AND THE BURNEu FUEL SYSTEM.

-100

j»-80

E it

<? < * •

-SO'

o MEASURED FRESH FUEL

D MEASURED BURNED FUEL

Cnlc.lrt«h lutl

-to

vCtttc. bufntd tun

-20

50 too 150 200 TEMPERATURE I °C )

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levcl coefficients has been set to 10%, which was the maximum deviation between calculated and measured bp/bl-l values for the unburned system.

The temperature coefficients are seen to be less negative for the burned than for the fresh system. The reduction in absolute value is less by the experiments than by the calculations. The calculations are in better agreement with the experiments for the burned than for the fresh core.

The tendency of REBUS-2 to calculate too negative temperature reactivity effects for fresh fuel is a known feature of this code (16), which has been confirmed through analysis of a large number of UO.,/0-,0 lattices.

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. 3 3 .

6. POWER REACTIVITY EFFECTS

Calculations of reactivity effects due to formation of coolant void and r i se in fuel temperature following an increase in reactor power, have been carried out both for the fresh and burned fuel system. The calcu­lations were made for total reactor powers of 6 and 12 MW and with the moderator temperature of 190 C and subcooling power of 0. 6 MW in corre­spondence with experimental conditions.

The calculational scheme can be divided into the following steps:

1. Calculation of void distributions. ?., Calculation of fuel temperatures. 3. Calculation of lattice parameters for the voided core. 4. Macroscopic calculations.

For the calculations under the points 3 and 4 the core was divided into eight subregions, four axially and two radially» each region having averaged properties with respect to void, fuel temperature and burn-up. The averaging was done by simple volnme weighting. The complete macroscopic geometry is shown in Figure 11.

6. 1 Void Distribution

The axial distribution of void in the coolant channel of a fuel assembly has been calculated as a function of total assembly power. The calculations were made by a computer programme similar to the VOIFLO programme (17), which takes into account void also in the subcooled regions of the channel.

In addition to the hydraulic characteristics of the channel the calcu­lated void distributions depend also on the axial power shape. The axial power shape, however, to some extent is determined by the void distr i­bution itself. In principle, to obtain a proper void distribution, one has to carry out an iterative procedure which shall continue until a void dis tr i ­bution is established which, when applied in a macroscopic calculation, results in a power distribution which is similar to the one assumed in the void calculation.

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- 34 -FI0.11

MACROSCOPIC GEOMETRY USED IN THE CALCULATIONS OF POWER REACTIVITY EFFECTS.

TOP REFLECTOR

RADIAL REFLECTOR

CORE REG. 1.1

CORE REG. 1.2

RADIAL REFLECTOR

CORE REG. 2,1

CORE REG. 2,2

RADIAL REFLECTOR

SPACER REGION

RADIAL REFLECTOR CORE

REG. 3,1 CORE

REG, 3,2

RADIAL REFLECTOR

CORE REG. *,1

CORE REG. .4,2

RADIAL REFLECTOR

BOTTOM REFLECTOR Zr

RADIAL REFLECTOR

BOTTOM REFLECTOR S1

RADIAL REFLECTOR

BOTTOM REFLECTOR S2

RADIAL REFLECTOR

61. S 23.3 50.2

All diltane»! in cni

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Such a procedure, however, is very time consuming. Taking into account that the reactivity effect due to a change in the power shape probably is small, a simplified scheme was used. In this scheme two sets of void distributions, based on two different power distributions, were calculated. First ly, it was assumed that the power and the void distr i­bution were unrelated, i . e . the power distribution was taken equal to the distribution valid at zero power conditions. This distribution was calculated for the burned fuel system by EQUIPOISE. Secondly, the power distribution was assumed proportional to the burn-up profile, as determined through the gamma-scanning of the burned fuel assemblies.

The results of the void calculations are given in Figure 12. The calculations were made for a moderator temperature of 190 C and a sub-cooled power of 6 kW per assembly, in accordance with the experimental conditions. It is seen that the calculated void distributions to some extent depend on the power distribution assumed. The maximum of the burn-up profile is shifted downwards in the core relative to the power distribution calculated at zero power conditions, and is seen to result in higher void fractions in the lower part of the channels. In the upper part the calcu­lated void fractions are about the same for the two distributions.

The implications of the coupling between power and void distributions are discussed further in Section 6. 5, 1.

6.2 Fuel Temperature

The fuel temperatures have been determined based on the calcu-lational results by Kjærheim and Rolstad (6), which give the temperature as a function of the linear heat load. The calculations were made for fuel rods similar to the HBWR second charge type, and take into account the influence of the gap between fuel and canning. Volume weighting has been used to find average values for each region.

Average values lor the linear heat load of the various core regions described in Figure 11 have been calculated corresponding to total reactor powers of 6 and 12 MW. Power f orm factors for the regions were deter­mined based on a radial power distribution as calculated by EQUIPOISE at

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CALCULATED AXIAL DISTRIBUTION OF COOLANT VOID FOR VARIOUS CHANNEL POWERS: SUBCOOLED POWER: 6kW. MODERATOR TEMPERATURE•• 190°C.

Power dlstr. assumed prop, to : Burnup profil*

— — Rower distr. at zero power

>**

0.2

60 BO 100 120 HO 160 AXIAL POSITION RELATIVE TO BOTTOM OF FUEL (cm)

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z e r o power conditions, a i d axial distributions porportional to the burn-up profile and the power distribution at z e r o power conditions respect ive ly .

The resulting fuel temperatures are given in Table IX.

Table IX

Calculated Average Fuel Temperatures in °C for the Various Core Regions at 190 C Coolant and Moderator Temperature

Reactor Power

Axial Region

No.

Axial Power Distribution Assumed: Reactor Power

Axial Region

No. Burn-up Profile "Zero Power"

Reactor Power

Axial Region

No.

R 1

adial Regie 2

in No . 1 2

1 254 23? 266 241

6 MW 2 3

296 316

260 275

313 310

272 270

4 296 260 274 246

1 318 276 343 292

12 MW 2 3

403 444

332 360

437 433

354 351

4 403 332 358 302

The calculations of fuel temperatures in (6) were based on the assumption of fresh fuel. The effect of burn-up was a l so investigated experimental ly in (6), with the result that the rod centre temperature seemed to increase with increasing burn-up. At a burn-up of 4900 MWd/tU the centre temperature had increased by about 40 C at an average l inear heat load corresponding to a reactor power of 12 MW. Certain reservat ions are made, however, in (6), and the poss ibi l i ty is admitted that the apparent increase may be caused by changes in the thermocouple charac ter i s t i c s .

Further , it is a complicated matter to take a centre temperature increase into consideration. F o r evaluating a rod average temperature, the radial temperature distribution must be known. Since the burn-up is not radially uniform, the teriiperature distribution will be different for the

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.38.

fresh and the burned state. It is therefore very difficult to find the relation between centre temperature and average temperature, and the values previously calculated have not been corrected.

6.3 Lattice Parameters

Two group lattice parameters for the eight core regions described in Figure 1 1 have been calculated by REBUS-2, using the void fractions and fuel temperatures'determined in the two previous sections, and the isotopic composition of the burned fuel determined through the REBUS-2 calculations in Section r>. ?. The void Tractions were estimated from the curves in Figure I?, with assembly power determined from the radial power distribution calculated at zero power conditions.

The lattice parameter calculations for the burned fuel system were carried out with axial power distribution both as proportional to the burn-up profile and as given by the calculated power distribution at zero power conditions. For the fresh fuel system only one set of lattice pari.meters, relating to the zero power uistribution was calculated.

6.4 Reactivity Calculations

The reactivity calculations, based on the macroscopic geometry shown in Figure 11, were made with EQUIPOISE. Two group constants for the various core regions were taken from the REBUS-2 calculations in the previous section and for the reflector regions by making use of the formulae in (13).

For the top reflector region straight above the core, it has been assumed that the void fractions inside the channels are the same as at. the top of fuel, and further that most of the steam leaves the fuel channels through the holes in the shrouds above the water surface level, thus causing little void in the reflector volume outside the shroud i . These assumptions are rather arbitral? as there is very little experimental information available regarding this pro­blem, and are quite different from those made in (3) where a quite high top reflector void content was assumed, of the order 25 - 30% at 12 MW, The effect of the void on the reflector constants was taken approximately into account by assuming that the void was homogeneously distributed throughout the volume of the top reflector.

The results of the reactivity calculations are given in Table X along with the corresponding experimental results for the fresh and the burned I

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fuel systems taken from (3) and (1). The power reactivity change in the calculations have been defined as

keff ( P ° w e r ' _ kcf£ { i e T O power) " ~ k -•£ (power) • k ,, (aero power)

In Table X are also given calculated values for the reactivity change for the fresh core extracted from (3).

Table X

Measured and Calculated Power Reactivity Changes (pcm)

Reactor Power (MW)

Fresh Fuel Burned Fuel Reactor Power (MW) Muasured Calc. 0 Calc.

in (3) Measured Calc. U 21 Calc. " '

6

12

-1060± 100

-17O0i?0O

- 869

-1300

- 999

-1819

- 600 i SD

-1100 ± 150

-".', -1026

-1645

Void and fuel temperature calculations based on axial power distributions proportional to:

' power distribution at aero power conditions

' burn-up profile, •

6. 5 Discussion

It is seen from the results in Table X that the calculations predict too large negative power reactivities for the burned fuel system and too small for the fresh system. Furthermore, while the experimental results give a reduction in the absolute magnitude of the reactivity effect as a result of burn-up, the calculations give the opposite tendency. In the following various effects will be discussed, which may have contributed to the dis­crepancies between the theoretical and the experimental results .

6, 5, 1 Power Distribution

A summary of the axial power distributions obtained from the macro­scopic calculations made under various conditions, is given in Table XI.

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It was found sufficient to represent the various distributions through the fraction of the total power liberated in each half of the c o r e .

Table XI

Calculated Axial Power Distributions

Fuel Condition Total Power (MW)

Power Distribution Assumed in Void Calculation

Resulting Fract ion of Power in Lower Half of Core

F r e s h Burned Burned Burned Burned Burned F r e s h F r e s h

1

0 0 6 6

12 12

6

1 2

Burned .zero power Burn-up profile ' Burned ,zero power Burn-up profile ' Burned, z e r o power Burned, aero power

0.541 0 .506 0 .525 0. 5?3 0.531 0 .529 0 .557 0 .559

1

A fraction 0. 57 in the lower half of the core .

It can be concluded from the results in Table XI that the distribution of the power between the upper and the lower half of the core is determined by the following c ircumstances :

Different thickness of bottom and top ref lector. Distribution of void. Distribution of burn-up.

The larger thickness of the bottom reflector compared to the top reflector i s seen to cause that 5 4 . 1 % of the total power for the fresh fuel sys tem at z e r o power conditions is produced in the lower half of the core . F o r the burned fuel sys tem the corresponding power production in the lower half is 50.6% only, meaning that the distribution of burn-up tends to shift the power profile upwards, because the upper half of the core i s l e s s burned than the lower .

Furthermore , it is seen that the power profile i s shifted downwards with increasing power of the reactor , i . e . as a result of the formation of

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vo id . F o r the burned fuel s y s t e m ne i the r of the two power d i s t r ibu t ions ini t ia l ly a s s u m e d in the ca lcu la t ion of void, is s een to be in a g r e e m e n t with the d i s t r ibu t ion obtained through the final m a c r o s c o p i c ca lcu la t ion . On the o ther hand, the two dif ferent ini t ial pofiles lead to final prof i les tha t a r e v e r y c lose to each o t h e r . It can be concluded that c o r r e c t l y p r e ­dicted d i s t r i bu t ions should have a s sumed that 52,4 and 53 .0% of the power product ion at 6 and 12 WW, r e s p e c t i v e l y , t akes place in the lower pa r t of the c o r e . It is s een that the c o r r e c t p rof i les a r e s i tuated s o m e w h e r e be tween the two ini t ia l profi les," howeve r , c l o s e r to the " z e r o power" than to the " b u r n - u p " prof i le .

F o r the unburned fuel s y s t e m m a c r o s c o p i c ca lcu la t ions only, with void f rac t ions obtained a s s u m i n g the burned fuel power d i s t r ibu t ion at z e r o power cond i t ions , w e r e c a r r i e d through. While the ini t ia l a s sumpt ion was that 50 .6% of the power should be produced in the lower half of the c o r e , the m a c r o s c o p i c ca lcu la t ions gave the va lues 55 ,7 and 55 .9% at 6 and 1? MW, r e s p e c t i v e l y . In fact , an ini t ial power profi le p ropor t iona l to the b u r n - u p p ro f i l e , with a f rac t ion 0. 57 in the lower half, would have been a v e r y good e s t i m a t e .

It is v e r y difficult to e s t i m a t e the unce r t a in ty in t roduced in power d i s t r ibu t ion and r eac t i v i t y by the a s s u m p t i o n s r ega rd ing the void d i s t r i ­bution in the top r e f l e c t o r . This m a y well be a ma jo r sou rce of e r r o r in the power void c a l c u l a t i o n s .

F r o m Table X i t is s een that the difference in power r eac t i v i t i e s be tween us ing the b u r n - u p profi le o r the burned fuel z e r o power p r o f i l e , is about 60 p c m . Knowing that the c o r r e c t profi le in the burned fuel c a l ­cu la t ions l i e s s o m e w h e r e in be tween the two appl ied , i t can be concluded tha t the m e a n values of the two s e t s of ca lcu la t iona l r e s u l t s a r e to be p r e ­f e r r e d in the c o m p a r i s o n with e x p e r i m e n t a l r e s u l t s .

F o r the f r e sh fuel s y s t e m , as the b u r n - u p profi le is a s a t i s f ac to ry approx ima t ion to the power d i s t r i bu t i on , the ca lcula ted reac t iv i ty values p r e f e r ab ly sha l l be about 60 pem m o r e negat ive than denoted .

A l so the r ad i a l power d i s t r ibu t ion in the r e a c t o r was found to be somewhat influenced through the produc t ion of void . The f rac t ion of the tota l power p roduced in the c e n t r a l region of the two r a d i a l reg ions was

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reduced from 60.5% at zero power to 59.3% at 12 MW, However, because the average void fraction of the core is independent of the radial power distribution, such a small change in the power distribution may safely be neglected in the, calculation of power reactivities,

6. 5. 2 Control Rod Effects

The measurements of power reactivity effects for the burned core were carried out with a system practically free from control rods. The fresh fuel system, however, had a large excess of reactivity, which had to be shimmed off through insertion of control rods. The neglection of the control rods in the calculations on the fresh fuel system may be the reason why tiie differences between experimental and calculated power reactivities are of opposite trends for the burned and the fresh fuel system. In the following the effect of the control rods therefore will be discussed in some detail.

An analysis of the various effects contributing to the power reactivity has revealed that the largest negative contribution comes from the increase of the diffusion coefficients of the core as a consequence oi the formation of void. If control rods are present in the reactor, an increase of the neutron diffusion length will not only increase the probability that neutrons shall leak out of the core, but also that they shall be absorbed in a control rod. Consequently, the control rods will be more efficient, i . e . take up a larger amount of reactivity, in a voided than in an unvoided reactor. In a reactor with control rods the observed reactivity decrease with increasing power, therefore also will be an effect of increased reactivity worth of the control rods.

The experimental results, as given in Table X, show the tendency that the power reactivity decreases in absolute magnitude as a result of burn-up. However, if it is assumed that the control rods present during the experiments at zero burn-up are responsible for a certain amount of the power reactivity measured, the difference in power reactivity between the unburned and the burned system may be an effect of withdrawal of control rods rather than an effect of burn-up itself.

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Ouring the fresh fuel measurements six control rods were inserted, of which two only partly. With the reactor physics codes presently avail­able at the Halden Project, it is not possible to represent this control rod configuration satisfactorily and at the same time take properly into account effects of void on the diffusion of neutrons. However, an approximative calculation has been carried out for a single control rod in the centre of the core, using the EQUIPOISE. The control rod was treated explicitly by applying the logarithmic-derivative black boundary condition at the surface of the rod. The results of the calculations are given in Table XII.

Table XII

Cal:ulated Power Reactivity for the Fresh Fuel System with One Control Rod in Centre of Core

Power (MW)

Clean Condition

eff (pcm) One Central Control Rod

*eff (pcm)

1.1668

1.1494

0 -1300

1.1203

1.1033

0 -1370

It is seen that the decrease in reactivity due to a power increase from zero to 1? MW is 70 pcm larger when the control rod is present. One cannot make quantitative corrections of the theoretical power reacti­vities on the basis of the calculation above because of its very approximate nature. However, the very important conclusion may be drawn that the calculation has verified that the presence cf control rods during the experi­ments with the fresh fuel system has contributed considerably to the power reactivity measured.

An equally significant proof of the control rod effect has been obtained experimentally. The measurement of power reactivities was made with the use of a calibrated control rod (3). During the calibration of this rod it was observed that the reactivity taken up by the rod was larger at high power than at low. The relative increase in *od worth upon an increase in power from 1 to 9 MW was found to be about 7%. According to REBUS-2/ EQUIPOISE calculations the amount of reactivity to be controlled in the

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f resh fuel sys t em at 6 2vJV.r is 13 .4%. If the change in rod ef fec t iveness is a s s u m e d l inea r within the power r a n g e , it can be concluded f rom the above expe r imen ta l r e su l t that the cont ro l rods take up about 590 pem m o r e reac t iv i ty a t 6 MW than at low power condi t ions . Subt rac t ing this contr ibut ion from the total power reac t iv i ty of - 1060 pem m e a s u r e d at 6 MW only - 470 pem r e m a i n s to account for the void and fuel t e m p e r a t u r e con t r ibu t ions . This is l e ss than the power r eac t iv i ty m e a s u r e d for the burned fuel s y s t e m at o MW , which was - b00 p e m .

Quanti ta t ively one should not p lace too much confidence in the r e s u l t above, because the m e a s u r e d change in cont ro l rod worth with i n c r e a s i n g power may well be encumbered with cons ide rab l e s y s t e m a t i c a l e r r o r s . Also , due to in terac t ion effects between the va r ious r o d s , the reac t iv i ty change m e a s u r e d for one pa r t i cu l a r rod, may not be r e p r e s e n t a t i v e for the ave rage change for each rod in the group of r o d s .

6 . 5 . 3 F u e l T e m p e r a t u r e s

The influence of poss ib le s y s t e m a t i c a l e r r o r s in es t imat ing , fuel • t e m p e r a t u r e s has been invest igated by ca lcu la t ing the fuel t e m p e r a t u r e r eac t iv i ty coefficient. The ave rage value of this coefficient in the t e m p e ­r a t u r e in te rva l from 190 C to 4b0 C was found to be - t . 6 p e m / C .

It was ment ioned in Sect ion t . ? that t h e r e was some indicat ion that the fuel t e m p e r a t u r e i n c r e a s e s with i n c r e a s i n g b u r n - u p . Assuming that the m e a s u r e d i n c r e a s e of 40 C in c e n t r e rod t e m p e r a t u r e for the burned fuel a l so is the change in the ave rage rod t e m p e r a t u r e s , use of the above t e m p e r a t u r e coefficien indica tes that the ca lcu la ted power r e a c t i v i t i e s for the burned s y s t e m may be about 60 pem too l i t t le nega t ive .

6. 6 Conclus ions

It has been es tab l i shed both through e x p e r i m e n t s and ca l cu l a t i ons , that the reac t iv i ty taken up oy a control r o d , due to the fo rma t ion of void, i n c r e a s e s with i nc reas ing power of the r e a c t o r . While the e x p e r i m e n t s on the f r e sh fuel s y s t e m had to mclude a cons ide rab l e amount of cont ro l led r e a c t i v i t y , the e x p e r i m e n t s on the burned s y s t e m w e r e c a r r i e d through wita a c o r e p rac t i ca l ly f ree f rom con t ro l r o d s . It can be s ta ted with a r a t h e r high d e g r e e of confidence, tha t the l a r g e reduc t ion in absolu te

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magnitude of the measured power reactivities for the burned core relative to the fresh core is partly or entirely caused by the different amounts of control rods present in the two cases.

The theoretical analysis, not taking into account the effect of control rods, gives *e result that the power reactivity slightly increases in absolute magnitude as å consequence of burn-up. Because of the large uncertainties concerned with the control rod effect, it is impossible to have this tendency confirmed (or the opposite) through comparison with the experimental results.

Taking into account that a considerable amount of the power reactivity measured at zero burn-up is due to the presence of control rods, it must

• be concluded that the calculations predict too large negative power reacti­vities both for the fresh and the burned fuel system. Fjor the burned system the overestimation amounts to 65% at 6 MW and 46% at 12 MW,

The inability of the theory to predict power-reactivities correctly may be due to inadequacies in the

calculation of void fractions and fuel temperatures calculation of lattice parameters for the voided system macroscopic representation.

The accuracy in the prediction of void fractions is difficult to esti­mate. The computer programme used for this calculation has been tested against experiments and found fairly reliable what concerns the void fraction at the exit of the cooling channels. It is seen from Figure 12, however, that the exit void fraction is only weakly influenced by the power distribution and the void fraction in the lower.parts of the channels. It is therefore quite possible that the programme for instance calculates too large void fractions in average for the core.

The increase in fuel temperatures is responsible for a minor part only ( <20%) of the total power reactivities calculated. It is accordingly little probable that errors in the estimation of fuel temperatures have caused e r rors in the calculated power reactivities that contribute signi­ficantly to the discrepancy between the experimental and theoretical data.

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The lattice parameter code REBUS-2 has been systematically tested against a large number of void reactivity experiments (16). For fuel assemblies similar to the HBWR second charge, there was found a distinct tendency of the code to calculate too negative reactivity effects due to coolant void. It can therefore be concluded that at least some of the discrepancy between calculated and measured power reactivities is due to systematic e ••*•'* ̂ r s in the calculation of lattice parameters as a function of void.

The macroscopic representation of the core through regions having average properties may have contributed to the calculational e r ro r . The main reason for this is that the void is not distributed linearly neither in the radial nor in the axial direction, nor is the reactivity effect of void a linear function of the void itself. Furthermore, the neglection of the fact that the burn-up of the fuel assemblies varies strongly, leading to random variations in the channel powers, may have fortified the consequences of the simplified macroscopic treatment.

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LIST OF REFERENCES

B. Blomsnes. B. Danielsson, V. Gustavssoti, E. Johansson, R.W. Keaten, T.H. Korpås, J .E . Lunde, H. Smidt Olsen, P . Svensson, J.K. Trengereid: Burn-Up Experiments with the HBWR Second Fuel Charge, HPR-86 (1968).

J . E . Lunde and O. Øye: Temperature Reactivity Effects in the HBWR Second Fuel Charge, HPR-38 (1964).

F .W.A. Habermann/K. Jahren, J . E . Ijunde, A. Rumpold and O. Øye: Coolant Void Reactivity Effects in the Second Charge of HBWR. Part III: Integral Experiments. HPR-41 (1964).

P . E . AhlstrSm and B. Eriksson, RFR-542, RFR-550, RFR-560 andER-13/67, Internal Reports, AB Atomenergi, Stockholm, Sweden (1966-67).

A. Jons son and Å. Ahlin, RFR-699, Internal Report, AB Atomenergi, Stockholm, Sweden (1 968).

G. Kjærheim and E. Rolstad: In-Pile Determination of UO» Thermal Conductivity, Density Effects and Gap Conductance, HPR-80 (1967).

A. Rumpold: The Burn-Up Routine in the Transport Code FLEF, HPR-84 (1967),

E. Sokolowski, TPM-FFR-77 and TPM-FFR-80, Internal Reports, AB Atomenergi, Studsvik, Sweden (1967).

P . E . AhlstrSm: Calculations of Lattice Parameters as a Function of the Irradiation. Presented at the EAS Symposium on "Measure­ments and Calculations of the Influence of Burnup on Reactivity" at Risjt, Denmark (September 1961).

S. Linde: The Multigroup Diffusion Equation, 1 Space Dimension, AE-35, AB Atomenergi, Stockholm, Sweden (1960).

M. L. Tobias and T .B . Fowler: EQUIPOISE - An IBM-704 Code for the Solution of Two-Group, Two-Dimensional, Neutron Diffusion Equations in Cylindrical Geometry, ORNL-2967, Oak Ridge National Laboratory, Oak Ridge, Tennessee (I960).

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12. H. Smidt Olsen: Reactivity Tests and Exponential Experiments with HBWR Second Charge Fuel Elements, HPR-34 (1964).

13. J . Davidson, R. Solheim and V. Tosi: Criticality Experiments with 24, 36 and 100.Elements of the Second Fuel Charge of HBWR, HPJR-48 (1964).

14. J. Nitteberg, Personal Communication (1965),

15. '.. Jonsson and G. Naslund, RFN-266/RFR-603, Internal Report, AB Atomenergi, Stockholm, Sweden (1967).

16. P . E . Ahlstrdm, RFR-697, Internal Report, AB Atomenergi, Stockholm, Sweden (1968).

17. K.O. Solberg, P . Bakstad and J . Rasmussen: VOIFLO I - A Steady State FORTRAN Code for the Hydraulics of a Boiling Loop, KR-B5, Institutt for Atomenergi, Kjeller, Norway (1964).

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LIST OF TABLES

Page:

Table I Character is t ics of the Axial Subregions Used in the Theoret ical Burn-Up Analys is 8

Table II Character is t ics of the Samples Used in the Isotopic Analysis of the Burned Fuel 10

Table III Measured and Calculated Crit ical ity and Reactivity Coefficients for the Crit ical Reactor with F r e s h Fue l 21

Table IV Calculated Infinite Multiplication Fac tors for the Burned Fuel at Zero Power Conditions as a Function of Temperature 24

Table V Measured and Calculated Water Level Reactivity Coefficients for the Burned Fuel System (at H ..) 25

' v cr i t ' Table VI Reactivity Correct ions Related to the Burned Fuel

System Crit ical ity Analysis 26

Table VII Calculated k „ for Different Temperatures for the Burned Crit ical System 27

Table VIII Measured and Calculated Temperature Reactivity Coefficients for the Burned Fue l System 30

Table IX Calculated Average Fuel Temperatures in C for the Various Core Regions at 190°C Coolant and Moderator Temperature 37

Table X Measured and Calculated Power Reactivity Changes 39

Table XI Calculated Axial Power Distributions 40

Table XII Calculated Power Reactivity for the F r e s h Fue l Sys tem with One Control Rod in Centre of Core 43

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LIST OF FIGURES

P a g e :

F igure 1 HBWR Second Charge Fue l Assembly 5

F igu re 2 Core Loading during Macroscopic Burn-Up Measurements 6

F igure 3 Isotopic Composition of Fue l verBus Burn-Up. Concentration of U-235 for Samples having Various Initial Concentrat ions 11

F i g u r e 4 Isotopic Composit ion of F u e l v e r s u s Burn-Up . Total Concentration of Plutonium iBOtopes Relative to Total Concentration of Uranium Isotopes 12

F igure 5 Isotopic Composition of Fue l ve r sus Burn-Up . Concentration of Pu-239 13

F igure 6 Isotopic Composition of Fue l ve r sus Burn-Up. Concentration of Pu-240 14

F igure 7 Isotopic Composition of F u e l ve r sus Burn-Up. Concentration of Pu-241 15

F igure 8 Simplified Vert ical C r o s s Section of the Reactor Used in the Theore t ica l Analysis of the Burned Fuel System at Ze ro Power Conditions 23

F igure 9 Measured and Calculated Cr i t i ca l Water Levels for the F r e s h and the Burned Fue l System 28

F igure 10 Measured and Calculated Reactivity Tempera tu re Coefficients for the F r e s h and the Burned Fuel System 31

F igure 11 Macroscopic Geometry Used in the Calculations of Power Reactivity Effects 34

F igure 12 Calculated Axial Distribution of Coolant Void for Various Channel Powers . Subcooled Power: 6 kW. Moderator Temperature: 190°C 36