ORNL-TM-0730.txt

 

operated by
UNION CARBIDE CORPORATION
for the

U.S. ATOMIC ENERGY COMMISSION

 

OAK RIDGE NATIONAL LABORATORY

ORNL- TM- 730

MSRE DESIGN AND OPERATIONS REPORT

PART [1l. NUCLEAR ANALYSIS

. R. Engel
E. Prince

. C. Claiborne

+*

. N. Haubenreich

T o0

NOTICE

This document contains information of a preliminary nature and was prepared
primarily for internal use ot the Oak Ridge National Laboratory. It is subject
to revisien or correction and therefore does not represent a final report. The
information is not to be abstracted, reprinted or otherwise given public dis-
semination without the approval of the ORNL patent branch, Lagal ond Infor-
mation Control Department.

/o0

 
 

 

 

LEGAL NOTICE

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

ror the Commission, nor any person acting on behalf of the Commission:

A. Mckes any warranty or representotion, expressed or implied, with respect to the accuracy,
completeness, or usefulness of the information contained in this report, or that the use of
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B. Assumes any liabilities with respect to the use of, or for damages resulting from the use of
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As used in the above, ‘‘person acting on behalf of the Commission' includes any employee o

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or his employment with such controctor,

 

 

 

 

 

 
wi

ORNL TM-730

Contract No. W-7405-eng-26

MSRE DESIGN AND OPERATIONS REPORT

PART ITT. NUCLEAR ANALYSIS

P. N. Haubenreich
Je« R. Engel

B. E. Prince

H. C. Claiborne

DATE TISSUED

FEB -3 1364

 

OAK RIDGE NATTICNAL. LABORATORY
Ogk Ridge, Tennessee
operated by
UNION CARBIDE CORPORATION
for the
U.S. ATOMIC ENERGY COMMISSICN
™1
iii
PREFACE

This report is one of a series of reports that describe the design
and operation of the Molten-Salt Reactor Experiment. All the reports are
listed below. The design and safety analysis reports (ORNL TM-728 and
ORNL TM-732) should be issued by spring of 1964, and the others should
be issued in the summer of 1964.

ORNL TM~728 MSRE Design and Operations Report, Part I, Description
of Reactor Design, by R. C. Robertson.
ORNL TM-729 MSRE Design and Operations Report, Part II, Nuclear and

Process Instrumentation, by J. R. Tallackson.,

ORNL TM-730% MSRE Design and Operations Report, Part III, Nuclear
Analysis, by P. N. Haubenreich and J. R. Engel.

ORNL TM-731 MSRE Design and Operations Report, Part IV, Chemistry
and Materials, by F. ¥F. Blankenship and A. Taboada.

ORNL TM-732 MSRE Design and Operations Report, Part V, Safety Anal-
ysis Report, by S. E. Beall.

ORNL TM-733 MSRE Design and Operations Report, Part VI, Operating
Limits, by 5. E. Beall.

** MSRE Design and Operations Report, Part VII, Fuel Han-
dling and Processing Plant, by R. B. Lindauer.

** MSRE Design and Operations Report, Part VIII, Operating
Procedures, by R. H. Guymon,

*x MSRE Design and Operations Report, Part IX, Safety Pro-
cedures and Emergency Plans, by R. H. Guymon,

*K MSRE Design and Operations Report, Part X, Maintenance
Equipment and Procedures, by E. C. Hise.

*% MSRE Design and Operations Report, Part XI, Test Program,
by R. H. Guymon and P. N. Haubenreich.

*% MSKE Design and Operations Report, Part XII, lists:

Drawings, Specifications, Line Schedules, Instrument
Tabulations (Vols 1 and 2).

¥Tssued.,

*¥These reports will be the last in the series to be published; re-
port numbers will be given them at that time.
CONTENTS
Preface oo iiervenrenesrtnoasonees cestarannen Cesiersscessatsaavss e iii
Abstract cevvievenan cesesssacs teereens seesenesassertessataanssatas e 1
1. INTRODUCTION eeonvsvnnoncoss thesesanen cereaseesues coeeresuns ceas 3
2. PRELIMINARY STUDIES OF CORE PARAMETERS «vvevesns et e reeenenaen 4
2.l Introduction cesvesesesssessssrosssnssansesas corevevresn s . Y
2.2 Effect of Core Size cvvevrnens creerereseeses Cresrsanranens 4
2.3 Effect of Volume Fraction in One-Region COTe€S .veeevesssn . 5
2.3.1 First Study seeeeeses Cresersaasseans Chresiersaenaas 5
2.3.2 Second StUAY veeeserensscsvennnas Cereeace e 8
2.4 Two- and Three-Region COTeES .uiievssssssnnssos it cseneanns 9
2.4.1 Channeled Graphite COreés .uieecessserscssvesssenses 9
2.4.2 Cores with Moderator in Reflector and Island ...... 12
2.5 Cores Containing INOR-8 Tubes ...u... Ce it esaacaeenaaane 13
2.6 CONClLUSLIONS tevvesnerscassssscacnsssssnsssssosssnsansonsesse 13
3. CRITICALITY, FLUX DISTRIBUTIONS, AND REACTIVITY

COEFFICIENTS tvvvecovensasens ceeeseseanns PP 15
3.1 Descripbtion Of COre sieieeertesesesescsssessnnsssonsssassness 15
3.2 Calculational Model Of COTE tieensnscersssnssssssssssnssnns 15
3.3 Fuel Properties .veeeereccans . Cre e s et eseraesa et e 20
3.4 Cross Sections and Effects of InhomOgenelty of Core ...... 20
3.4.1 Resonance Neubtrons ..eeses. Cieecestartiassssnatesas 21
3.4.,2 Thermal Neublrons .iiveessssssssceasoas cheieeaneans . 22
3.5 Criticality Calculations ...... Creereaseareses cecesarresns 23
3.6 Flux and Fission Distribufions iveeiieriiecrssnsrsoccnssoccses 25
3.6.1 Spatial Distribution ...... testaean e e Ceessenssens 25
3.6.2 Energy Distribulion sieeveessecrsossescsarsssranannas 34
3.7 Reactivity Effects of Nonuniform Temperature ...cevececess 37
3.7.1 One-Region Model ..uiiicesecerseenescnossssssonononss 37
3.7.2 Multiregion Model ...ieeieietssssssassssseasasaonnans 41

3.8 Reactivity Effects of Changes in Densities of Fuel
Salt and Graphite sevsesesovasesnssasscsasassssasessssnns 48
3.9 Summary of Nuclear Characteristics tiveeieerecssocsasscsss 49
4, CONTROL ROD CALCULATTONS . iuivereeerononeosseearsassannsnonanas 53
4.1 Control Rod Geomelry viveeveeeeeceesssscannns Ceacerriseaans 53
4.2 Method of Calculation of Rod React1v1ty tesessaasannereann 53
4.2,1 Total Worth seeeeeieennsnons cereas cesesteanaas cenen 53
4.2.2 Differential Worth c.ievecececas Ceeseesesteanasreans 57
4.3 Results of Calculations ..veeesecss Ceesesreserecseeserean . 58
4.,3.1 Total Reactivity Worth ...... Cerersaas et ecretreens 58
4.3.2 Differential Worth ..ieeeeeeeeenenertocacesssscssncas 58
5. CORE TEMPERATURE |, ,.....cecveevnenens cereseeas ceesenereasans vos 60
5.1 Overall Temperature Distributions at Power .isieesceesoesns 60

5.1.1 Reactor RegioOns sieeeeses Cetetisessessaseateas teaas 60
10.

5‘2

5.3

vi

5.1.2 Fuel Temperatures .eeeeveess

5.1,3 Graphite Temperatures .......

Average Temperatures at Power .....
5.2.1 Bulk Average Temperatures
5.2.2 Nuclear Average Temperatures

*» ® 0

Power Coefficient of Reactivity ......

DELAYED NEUTRONS «veeesosnserocsscasnsns

6.1 Method of Calculation seeesecesssoses .

6.2 Data Used in Computaltion .eieerecreccnscnnes
6.2.1 Precursor Yields and Half-Lives .....
6.2.2 Neutron ERErgiesS teeeessscescosses
5423 AEE tiieersenrasesotscttirssanssesatorens
6.2.4 MSRE DImensions eeeseeecsccsssesssonsrsns

6.3 Results of Computation s.eeeerecsconesnsns

6.4 Nomenclature for Delayed Neutron Calculations

POISONING DUE TO XENON-135 ........ Ceceneanree

7.1 Distribution of Iodine and Xenon .eesceees

7.2

Sources of Todine and Xenon
Remova_. of Iodine and Xenon
Sources of Todine and Xenon
Removal of Todine and Xenon

~3 -2 -2 =1 ~1 2
H o
oyt W

in Fuel " & 0 8 »

from Fuel

in Graphite
from Graphite ..

Detailed Calculations eseeeeeeees
Approximate Analysis «.... .o

Reactivity Effects of Xenon-135 .......

POISONING DUE TO OTHER FISSION PRODUCTS

8.1 Samerium-14%9 and Other High-Cross-Section Poisons

8.2

EMPLOYMENT OF CONTROL RODS IN OPERATION +eveeenn.

Low~Cross-Section PoisONs veeesvses

General Considerations
Shim Requilrements
Shutdown Margins cieseceeveses

2 & % ¢ 8 & 4 4 8 880 0

* 9 % % 8 s &8 e & 8

4 ® 5 4 5 8 B 0 ® 0 &P YR DL

. 8 e 08

¢« & & 5" s

o 85 0o s & & 00

* 88

» &

Typical Sequence of Operations seeseeveerecrecccenocsnnes

NEUTRON SOURCES AND SUBCRITICAL OPERATION seeveecvsrococeces

10.1
10.2

10.3

Intreoduction
Internal Neutbtron SOUrCeS seseses s
10,2.1 Spontaneocus Fission .

® B & 0 0 9P BB B A S EE SN

"8 P B OB

® & & 8 0 & v 8 0

10.2.2 Neutrons from (¢,n) Reactions in the Fuel ......
10.2.3 Photoneutrons from the Fuel ceveeccessan

Provisions for External Neutron Source and Neutron

DeteCtOr'S veeeesncessssnsssnnsss
10.3.1 External SOUIrCE srseassoss

. &

10.3.2 Neutron Detectors ceeeesess

Neutron Flux in Subcritical Reactor ......

Requirements for Source .ieeeeven.s

" e 8 & 5 4 0

s % 8 0 8 00

® ¢ P e 0 s

® s & & S e

. & % & 0 ¥ @

* R P

61
64
69
69
70
71

74

74
75
75
75
75
76
"6
78

81

81
81
82
82
82
83
84
85

20

90
91

96

96
97
98
98

100

100
100
100
100
101

105
105
105
106
109
11.

12.

13.

vii

10.5.1 Reactor Safely iveeeveeeeerennns tressreena cesaen
10.5.2 Preliminary ExXperiments cvveeeeeseecsosscoonnnes
10.5.3 Routine Operation sesveeeseseecssscessssssaesons
10,6 Choice of EXternal SOUTCE tiveeereserorrosseasssserssns .
KINETICS OF NORMAL OPERATION cveevveescansss seeresasersar s
11,1 Very Low POWET .siveeserrosvrensasns tesarsenoaaaranas N
11.2 Self-Regulation at Higher POWeTr tivvivritoeneasnonesennss
11.2.1 Coupling of Fuel and Graphite Temperatures cevee
11.2.2 Transport Lags and Thermal Inertia .cviveveesces
11.2.3 Simulator Studies teveeeessens tecernecanas cieeas
11.3 Operation with Servo Control .eiereeseosees cesssasanesas
KINETICS TN ABNORMAL SITUATIONS — SAFETY CALCULATIONS civiven.
12.1 Introduction ssiiveveseesns escassestnes teterenscasans s
12.2 General Considerafions veeeeseeessssansenss crsesesseneas
12.3 TIncidents Leading to Reactivity Addition ..iveceveneenes
12.4 Methods Of ANalysSis seveesoesenreotoencacncnnns ¢reseesn
12.4,1 Reactivity-Pover Relatlons .................. oo
12.4.2 Power-Temperature Relations ...eiveceens csrsesnes
12.4.3 Temperature-Pressure Relations ....e.e. Cieeassas
12.4.4 Nomenclature for Kinetics Equations ..eeeeesees.
12.5 MSRE Characteristics Used in Kinetics Analysis .i.ceeees.
12.6 Preliminary STUAIES veuivrerenssecarostssasenssssoscencans
12.6.1 Early Analysis of React1v1ty Incidents «vieivesns
12.6.2 Comparison of MURGATROYD and ZORCH Results .....
12.7 Results of Reactivity Accident Analyses ci.eveeressanses
12.7.1 Uncontrolled Rod Withdrawal Accident .eveievevees
12.7.2 Cold-Slug Accldent cvieievenensersnsneesens coe
12.7.3 Filling Accident veereeerinnnennonnorsanns ceeees
12.7.4 Tuel Pump PoOWEr FAIlUIe vveveeveeressonacnnennsos
12.7.5 ConCluSIiOn teeeensesrseesetseassscascssnsacannes
BIOLOGICAL SHIELDING 4t eeeeeeeocesnsscssnsassssosssscnnnensas
13,1 General ..e.ieeeessorsrssssssssesssssessessssonssoscaneses
13,2 Overhead Biological Shielding .veeecevereen.. Cetiereaenn
13.2.1 Geometry ..... ceee s Ceseseercses et ettt aannnea
13.2.2 Bource Strengths svvveiiitreeeessennnens tesaesaa
13.2.3 Estimated Dose Rates .veeieerreocorensosncsonnense
13.3 ZLateral Biological Shielding .veeetvroescsseasscsscansnss
13.3.1 Basic Shield Arrangement ...ee.es e rs et aaaaases
13.3.2 South Electrical Service ROOM ¢ieseesess Cesaense
13.3.3 Cooclant Cell and Fan HOUSE +sevesecarons teresenes
13.3.4 Source Strengths teeieeiisseeasescscenssasennsssns
13.3.5 Calculation Methods s.viecvceceennns ceseerasanenn
13.4 Conditions After Reactor Shutdown ..eveeeceseoss Ceceran
1305 SUMMATY teiveescecststecetntsensssnsnnensscess ceraesaeans

13.6 DNomenclature for Biological Shielding Calculations .....

112

112
112
113
113
114
121
viii

MISCELLANEOUS teerevsvenerans theetsertesatareenne vresesresanns 179
14,1 Radiation Heating of Core Materials ..ecvvvnen. crscannn . 179
14,2 Graphite Shrinkage .eeeeveveceenees ettt seeesatetaneses 183
14.3 Entrained Gas in Circulating Fuel ..... veserecrnernnaees 184
14.3.1 Introduction ...... Ceteiesereranens Cirereesaaes . 184
14.3.2 Injection and Behavior Of G85 veeveceesnnss P <
14.,3.3 Effects on Reactivity ...ovvvvnn teasaeseresncana 185
14.4 Choice of Polson Material ....... cerreasans Cesebeveanss . 189
14.4.1 BOTOR cveseaans Ceeeretsessenaanans Crrereesnanns 189
14.4.2 Gadolinium .seeevees Cerri sttt et e et ennns Ceeereans 190
14.5 Criticality in Drain and Storage Tanks ceeeeeses. cevesss 191

REFERENCES ............. a " 8 @ " 0 S & 8 B 2 8 0 e e 4 5 8 & 8 8 PP G T e a e " 8 s v 0 196
MSRE DESIGN AND OPERATTIONS REPORT

 

PART III. NUCLEAR ANALYSIS

 

P. N. Haubenreich
J. R. Engel

B. E. Prince

H. C. Clailborne

ABSTRACT

Preliminary considerations of the effects of core size
and fuel-to-moderator ratio on critical mass and fuel concen-
tration led to the specification of a core about 4.5 £t in
diameter by 5.5 £t high for the MSRE. The average fuel frac-
tion was set at 0.225, as a compromlse between minimizing the
critical mass and minimizing the reactivity effects of fuel-
salt permeation of the bare graphite moderator.

The nuclear characteristics of the reactor were examined
for three combinations of fissile and fertile material (UF,
and ThF,) in a molten carrier salt composed of lithium, be-
ryllium, and zirconium fluorides. Fuel A contained Thly
(~1 mole %) and highly (~93%) enriched uranium (~0.3 mole %);
fuel B contained highly enriched uranium (~0.2 mole %) and no
fertile material; and fuel C contained uranium at 35% enrich-
ment (~0.8 mole %) and no thorium. The radial distribution of
the thermal neutron flux 1s strongly influenced by the presence
of three control-rod thimbles near the axis of the core, with
the result that the radial thermal flux maximum occurs about &
in. from the axis. The axial distribution is essentially sinus-
oidel. The magnitude of the thermal flux depends on the choice
of the fuel; the maximum varies from 5.6 X 1013 neutrons cm™?
sec™ for fuel B (at 10 Mw thermal) to 3.3 x 10*3 for fuels A
and C. Both the fuel and the moderator temperature coeffi-
cients of reactivity are substantially negative, leading to
prompt and delayed negative power coefficients. Reactivity
coefficients were also calculated for changes in uranium con-
centration, Xet3? concentration, and fuel-salt and graphite
densities.

Temperature distributions in the fuel and graphite in the
reactor were calculated for the design power level. With the
fuel inlet and outlet temperatures at 1175 and 1225°F, re-
spectively, the fuel and graphite reactivity-weighted average
temperatures are 1211 and 1255°F, respectively. Fuel permea-
tion of 2% of the graphite volume would increase the graphite
weighted average temperature by 7°F. The power coefficient
of reactivity with the reactor outlet temperature held con-
stant is —0.006 to —0.008% 8k/k per M.
Circulation of the fuel at 1200 gpm reduces the ef-
fective delayed neutron fraction from 0.0067 to 0.0036.

Xenon poisconing is strongly dependent on the major com-
peting mechanisms of stripping from the fuel in the pump
bowl and transfer into the bare graphite. The equilibrium
poisoning at 10 Mw is expected to be between —1.0 and —1.7%
8k/k.

The fuel contains an inherent neutron source of over
10° n/sec due to O,n reactions in the salt. This meets all
the safety requirements of a source, but an external source
willl be increase the flux for convenient monitoring of the
subcritical reactivity.

The total worth of the three control rods ranges from
5.6 to 7.69 Sk/k, depending on the fuel salt composition.
Shutdown margins at 1200°F are 3.5% 8k/k or more in all
cases. One rod will be used as a regulating rod to control
the flux level at low power and the core outlet temperature
at high power. In general, the reactor is self-regulating
with respect to changes in power demand because of the nega-
tive temperature coefficients of reactivity. However, the de-
gree of self regulation is poorer at lower powers because of
the low power density and high heat capacity of the system.
The control rods are used to improve the power regulation as
well as to compensate for reactivity transients due to xenon,
samarium, power coefficient, and short-term burnup.

Calculations were made for conceivable reactivity acci-
dents involving uncontrolled control-rod withdrawal, "cold
slugs,"” abnormal fuel additions, loss of graphite, abnormal
filling of the reactor, and primary flow stoppage. No in-
tolerable conditions are produced if the reactor safety system
(rod drop &t 150% of design power) functions for two of the
three control rods.

The bioclogical shield, with the possible addition of
stacked concrete blocks in some areas, reduces the calculated
radiation dose rates to permissible levels in all accessible
areas.
1. INTRODUCTION

The design of the MSRE and the plans for its operation require
information on critical fuel concentration, reactivity control, kinetics
of the chain reaction, nuclear heat sources, radiation sources and
levels, activation, and shielding. This part on Nuclear Analysis deals
with these topics. Its purpose is to describe fully the nuclear char-
acteristics of the final design of the MSRE and, to some extent, to show
the basis for choosing this design. Methods and data used in the calcu-
lations are described briefly. Detailed descriptions of the calculations
and the sources of the basic data can be found in reports which are

cited.
2. PRELIMINARY STUDIES OF CORE PARAMETERS

2.1 Introduction

The original concept of the MSRE core was a cylindrical vessel con-
taining 2 graphite moderator with small channels through which circulated
a molten-salt fuel. During the early stages of MSRE deslgn, the nuclear
effects of two importart core parameters were surveyed. These were the
overall dimensions of the core and the ratio of fuel to graphite in the
core. Most of the calculations were for one-regicn cores, but some cal-
culations were made for cores consisting of two or three concentric re-
gions of differing volume fractions. Critical concentration and inventory
of U??° and the important coefficients of reactivity were the bases for
comparison and for choice of the final design parameters.

Some calculations were made for an alternative core design in which
the fuel circulated through INOR-8 tubes in a graphite core. The nuclear
characteristics of the reactor were calculated for several combinations
of tube diameter and thicxness.

A11 of these computations were performed on the IBM 704, using GNU,
a multigroup, diffusion theory code.! Data from BNL-325 (ref 2) were
used in preparing 34-group cross sections for the computations.3 The
cross sections were averaged over & l/E spectrum within each group. Those
used for thorium and U?38 in the resonance energy ranges were appropriate
for infinite dilution in a moderator, and a temperature of 1200°F was
assumed in determining the cross sections for the thermsl and last epi-
thermal groups. In all of the calculations except some of those for
tubed cores, the core materials were assumed to be homogeneously mixed

within a region.

2.2 Effect of Core Size*

The effect of core size was explored for cores containing 8 vol %
fuel salt having the density and the nominal composition listed for
fuel I in Table 2.1. Atomic densities of the constituents other than
uranium were computed from this specificaticon, and the GNU code was
used to compute the critical concentration of uranium. A graphite density

of 1.90 g/cc was assumed.
Table 2.1. Nominal Fuel Compositions and Densities
Used in MSRE Survey Calculations

 

Fuel type I II 11T

Composition (mole %) LiF® 64 64 70
BeF, 31 31 23
ThF,, 4 0 1
Zr¥, 0 4 5
UF,° 1 1

Density (g/cc) 2.2 2.2 247

 

%0.003% 116, 99.997% Li”7.
93,56 U235, 6.5% U238,

Computations were made for cores 5.5 and 10 ft high and 3.5, 4.0,
4.5, and 5,0 £t in diameter. Figure 2.1 shows critical concentrations
of uranium obtained by these calculations. Also shown in Fig. 2.1 are

U235

values of critical mass. These are the masses of in a core of the

nominal dimensions. (A zero extrapolation distance was assumed.)

2.3 Effect of Volume Fraction in One-Region Cores

2.3.1 First Study”

The first survey of the effect of varying volume fraction in a one-
region core was for a core 4.5 £t in diameter and 5.5 £t high. Five
different fuel volume fractions, ranging from 0.08 to 0.16, were con-
sidered. The critical concentrations of uranium were computed, and these
were used with the fuel volume fraction and the nominal core dimensions

Ue33, U235 were also

to compute critical masses of Total inventories of
computed, assuming that an additional 46 ft3 of fuel is required outside
the core.

One set of calculations was made with fuel I of Table 2.1. In these
calculations the graphite density was assumed to be 1.90 g/cc. Results

are shown in Fig. 2.2 by the curves labeled "Composition A."
UNCLASSIFIED
ORNL— LR—DWG 50592A

 

 

 

 

 

 

 

 

 

 

 

 

 

 

=
= 3
16p]
W
<
=
1
<
O =
= > &
—_ Q
1 ©
© £
=
5
=
&
-
0 0
35 4.0 4.5 50

CORE DIAMETER (ft)

Fig. 2.1. Critical Concentration and Mass as a
Function of Core Size,

A similar set of calculations was made with fuel II of Table 2.1,
with the results shown in Fig. 2.2 by the curves labeled "Composition B."
Not all of the differences in the two sets of curves are attributable to
the substitution of zirconium for the thorium in the fuel salt, because
a different graphite density, 1.96 g/cc, was used in the calculations for

fuel IT, which would reduce critical concentrations for this case.
UNCLASSIFIED
ORNL—-LR-DWG 52050

 

 

 

 

 

 

80 160
®
INVENTORY, COMPOSITION A
—-_
70 ’///, 140
@
A /
/‘ 120

€0 .\ —
RN

I ™~

 

 

INVENTORY, COMPOSITION B

 

 

 

 

A
—_ —f—————— \
g A &
= =
o 40 80 —
M n
3 ' 3
D
® o
CRITICAL MASS,
COMPOSITION A
| |
30 | — 60

——————

20 ‘// ‘ 40
o/

 

CRITICAL MASS,
COMPOSITION B

——————
10 A 20

 

 

 

 

 

 

 

 

0.08 0.10 0.12 0.44 0.16
VOLUME FRACTION FUEL SALT

Fig. 2.2. Critical Mass and Total Inventory of
U%3° as Functions of Fuel Volume Fraction, Calculated
for Early Fuels.
2.3.2 Second Study5'6

After mechanical design and chemistry studies had led to firmer
velues for the core vessel dimensions and the fuel composition, another
study was made of the effect of fuel volume fraction, the results to be
used in specifying the fuel channel dimensions. Core dimensions were

27.7-in. radius and 63-in. height, with extrapolation distances of 1 in.

on the radius and 3.5 in. on each end added for the criticality calcula-

tions. Fuel III of Table 2.1 was used, and a graphite density of 1.90

g/cc was assumed. Fuel volume fractions from 0.08 to 0.28 were considered.
Calculated critical concentrations of uranium are shown in Fig. 2.3.

Also shown are inventories of U??°, based on a fuel volume of 38.4 £t2

UNCLASSIFIED
ORNL~ LR— DWG 57685

 

70 l

 

 

CIRCULATING SYSTEM INVENTORY (kg OF U239)

 

 

 

 

 

 

 

 

 

~ &
[ ] #

\0-_._'___.. (;é}
20 - —e—0.2
2
=
<
o
; -

10+ — e - — 0.1

0 0
O 5 10 15 20 25 20

FUEL SALT (vol %)

Fig. 2.3. Effect of Fuel Volume Fraction on Crit-
ical Concentration and Inventory.

v
external to the core. The GNU results were also used to compute the re-
activity changes resulting from fuel temperature changes and from the
permeation of 7% of the graphite volume by fuel salt.* Results are sum-
marized in Table 2.2.

2.4 Two- and Three-Region Cores’:®

2.4.1 Channeled Graphite Cores

One way of reducing the critical mass is to use a nonuniform dis-

tribution of fuel in the core, with the fuel more concentrated near the

 

*This fraction was at that time the estimated fraction of the
graphite volume accessible to kerosene.

Table 2.2. Effect of Fuel Volume Fraction on
Nuclear Characteristics of MSRE2

 

Fuel fraction (vol %) 12 14 16 20 24 28

Critical fuel conc. 0.296 0.273 0.257 0.238 0.233 0.236
(mole % U)

Critigal mass (kg of 11.0 11.8 12.7 14.8 17.4 20.5
U23 )

SystemP U?35 51.0 48.6 47 ol 47.1 48 .7 524
inventory {(kg)

Fuel temp. coeff. x 10° =3,93 —3.83 -3.70 =3.44 -=3.,16 —2.86
[(8k/k)/°F]

Permeation effectC 11.4 9.7 8.3 6ol b o 3.5
(% &k/k)

 

®Core dimensions: 27.7-in. radius, 63-in. height,

Nominal composition of fuel: LiF-BeF,-ZrF,-ThF,-UF,;, 70-23-5-1-1
mole %,

Temperature: 1200°F,

Fuel density: 2.47 g/cc,

Graphite density: 1.90 g/cc.

bCore plus 38.4 £t? of fuel.
“Permeation by fuel salt of 7% of graphite volume.
10

center. This could be done in the MSRE by designing the graphite pieces
to give a greater fuel volume fraction toward the center of the core. A
reduction in critical mass, if accompanied by an increase in the concen-
tration of U?2° in the fuel salt, does not necessarily imply a reduction
in fissile material inventory in the MSRE because most of the fuel is
external to the core.

In order to explore the effects of nonuniform fuel distribution in
the MSRE, a set of calculations was made in which the core was subdivided
into either two or three regions with different fuel volume fractions.
Fuel IIT of Table 2.1 and graphite having a density of 1.90 g/cc were
assumed. Overall dimensions of the core were taken to be 27.7-in. radius
and 63-in. height. Radial and axial extrapolation distances of 1 and 3.5
in. were added to these dimensions. The critical fuel concentration, the
core inventory (or critical mass), and the total inventory were computed.
Flux and power distributions were also obtained.

Three cases of two-region cores were considered. In each the core
consisted of two concentric cylindrical regions, with the inner con-
taining 24 vol % fuel and the outer, 18 vol % fuel. Results are sum-

marized in Table 2.3.

Table 2.3. Some Characteristics of Two-Region Reactors

 

critical fuel o itical Mass  System® Inventory

 

Volume Ratio®  C trati
ciume h&atlo ?Irlll(olig ?rf;aU;on (kg of U235) (kg of U235)
50/50 0.232 15.1 46,5
60/40 0.234 15.7 47 oo
70/30 0.236 16.3 48 o4

 

®Ratio of inner region (24 vol % fuel) to outer region (18 vol %
fuel).

bIncluding 38.4 £t external to the core.
11

In the three-region cases the core was divided into concentric
regions of equal volume. Thirteen cases were calculated, with the re-
sults shown in Table 2.4, Although the critical mass was markedly re-
duced in some cases, this was accompanied by a higher fuel concentration,
which raised the fissile material inventory external to the core. As a
result, in no case was the total inventory greatly reduced below the
minimum for one-region cores.

The heat generation per unit volume of fuel follows closely the
shape of the thermal neutron flux in all cases. Table 2.4 shows that
the ratio of radial peak to average thermal neutron flux was significantly
reduced in some cases. (For a uniform core the ratio is 2.32.) The ef-

fect on flux shape is illustrated for some of the cases in Fig. 2.4.

Table 2.4. Some Characteristics of Three-Region Reactors

 

 

Fuel Critical Fuel Critical Sy stem® Thermal Flux
Fraction® Concentration Mass Inventory Ratioc, Radial
(vol %) (mole % U) (kg of U?3°) (kg of U?3?) Peak/Av
25, 13, 7 0.243 11.3 4 a2 1.86
40, 13, 7 0.273 16.9 53.8 1.45
10, 13, 7 0.324 10.1 54,0 2.38
25, 20, 7 0.237 12.8 45.1. 2.03
25, 6, 7 0.257 10.1 44 9 1.69
25, 13, 10 0.243 12.0 4 8 1.89
25, 13, 4 0.243 10.5 43.3 1.84
40, 20, 7 0.272 18.8 55.6 1.48
10, 6, 7 0.361 8.6 57.5 2.18
25, 20, 10 0.237 13.5 45.7 2.06
25, 6, 4 0.258 9.3 b y2 1.66
40, 13, 10 0.273 17.8 54.8 1.45
10, 13, 4 0.325 9.1 53.0 2.35

 

a . . . .
In inner, middle, and outer concentric regions of equal volume.

bIncluding 38.4 ft° external to the core.
12

UNCLASSIFIED
ORNL—LR— DWG 55954A

 

2.5 T . -
|

 

 

|
‘\\\\Q UNIFORM

1.5 (0.25. 0.13, 0.07) P L _{0.40, 0.13,0.07) —
i

 

 

 

 

 

{0.40, 0.13, 0.07)

1.0 ! N \

(0.25,0.13, 0.07)

0.5 j UNIFORM ::\\

(0.10, 0.13, 0.07)
{ 1

 

 

 

 

 

(THERMAL FLUX)/{MEAN THERMAL FLUX)

 

 

 

 

 

 

 

o |
0 5 10 t5 20 25 30 35
SPACE POINT NUMBER

Fig. 2.4. Comparison of Thermal Flux Shapes in
Three-Region Reactors. Numbers in parentheses refer
to fuel volume fraction in inner, middle, and outer
region of reactor, respectively.

Table 2.5. Characteristics of Cores with Lumped Moderator

 

Critical Concentration Critical Mass

Moderator (mole % ) (kg of U235)

 

5-in. Reflector Thickness, No Island

Graphite 1.04 250
Be 0.72 175
BeO 0.76 186

10-in. Reflector Thickness, l-ft-dlam Island

Graphite 0.67 93
Be 0.25 34
BeO 0.28 39

 

2.4.2 Cores with Moderator in Reflector and Island®

 

Brief consideration was given to a core which was essentially one

large fuel channel, with the moderator confined to a surrounding region
i3

and a central island. Calculations for this type of core were made as
an adJjunct to those for the multiregion, channeled graphite cores, using
the same fuel and overall core dimensions. Three moderators were con-
sidered: graphite (p = 1.90 g/ce), beryllium (p = 1.84 g/cc), and be-
ryllium oxide (p = 2.90 g/cc). Typical results are given in Table 2.5.

2.5 Cores Containing INOE~8 Tubes

Nuclear characteristics were also computed for cores in which the
fuel was contained in tubes of INOR-8 passing through the core. The
preliminary calculations for this type of core treated the fuel, graphite,
and INOR-8 of the core as a homogeneous mixture. Results of these calcu-
lations were reported in MSRP progress reports.®»” In later calculations,
hitherto unreported, the GNU code was used to calculate flux distributions
and disadvantage factors in a typical cell of fuel, INOR-8, and graphite.
When the heterogeneity of the core was taken into account, calculated
critical concentrations were increased over those from the homogeneous
approximation. Results of the heterogeneous calculations are given in

Table 2.6.

2.6 Conclusions

At a very early stage of the design it was decided that the core
would be approximately 4.5 £t in diameter and 5.5 £t high after some
calculations showed that the critical mass was relatively insensitive
to core dimensions around this point (Fig. 2.1).

The volume fraction of fuel in the core was set at 0.225 after cal-
culations showed that a fraction of 0.24 gave the lowest critical concen-
tration of uranium and that the reactivity increase due to fuel perme~
ation of the graphite was much lower around this point than at lower
volume fractions. (Four half-channels O0.2- by l.2-in. in each 2- by
2-in. graphite block were chosen to give a fuel fraction of 0.24; round-
ing the corners of the channels reduced the fraction to 0.225.)

Only brief consideration was given to cores of two or three regions
with differing volume fractions, because calculations showed these had

little, if any, advantage over the uniform, one-region core.
Table 2.6. Some Characteristics of Cores with INOR-8 Tubes

 

Fuel fraction (vol %) 10 10 10 14 14 14 18 18 18

Tube thickness (mil) 40 60 80 40 60 80 40 60 80

Critical fuel conc. 0.74 0.96 1.22 0.64 0.86 1.12 0.62 0.86 1.15
(mole % U)

system U?3° inventory (kg) 128 165 210 118 158 206 122 169 226

Neutron Balance

Absorptions: INOR g.7 10.9 12,5 10.7  12.3  13.8 10.6  12.8  l4.1
graphite + salt 2.9 2.5 2.1 2.5 2.0 1.7 2.2 1.7 1.4
Ue3° 50 .4 50.9 51.3 50.9 51.5 52.2 51.5 52.3 53.3
y238 0.4 0.5 0.6 0.5 0.6 0.7 0.6 0.8 0.9
Th 3.0 2.7 2.5 4al 3.7 3.3 5.0 beals 4.0
Fast leakage 24,9 2445 24.1 24 o4 24,5 2440 25.1 2b o4 23.6
Slow leakage 9.7 8.0 6.9 6.9 5et 4.3 5.0 3.6 27

 

Note: Core radius, 27.7 in.; core height, 63 in.; fuel volume external to core, 40 ft2; nominal
fuel composition, LiF-BeFp-ZrF,-Tht,-UF,, 70-23-5-1-1 mole %; tube OD, 3 in.

T
15

3. CRITICALITY, FLUX DISTRIBUTIONS, AND REACTIVITY COEFFICIENTS

3.1 Description of Core

The final design of the core and reactor vessel is ghown in the cut-
away view in Fig. 3.1. Fuel salt, after entering through a flow distrib-
utor, passes down through an annular region between the INOR-8 vessel and
the INOR-8 core can to the lower head. The lower head contains anti-swirl
vanes which direct the flow inward and a moderator support grid, both of
INOR-8, The fuel flows from the lower head up through a iattice of hori-
zontal graphite sticks, through the channeled region of the core and into
the upper head. The channeled region of the core consists of 2-in.-square,
vertical graphite stringers, with half-channels machined in each face to
provide fuel passages. The regular pattern is broken near the axis of
the core, where three control rod thimbles and a graphite sample assembly
are located. TFigure 3.2 shows a typical fuel channel and the section

around the core axis.

3.2 Calculational Model of Core

Critical fuel concentrations, flux and power distributions, and re-
activity coefficilents were calculated for the reactor, taking into account
as much detaill as was practical, The actual core configuration was rep-
resented for the nuclear calculations by a two-dimensional, 20-region
model in r-z geometry (cylindrical with angular symmetry). This model is
shown in vertical section in Fig. 3.3, indicating the relative sizes and
positions of the regions within which the material composition was con-
sidered to be uniform. The region boundaries and the volume fractions of
fuel, graphite, and INOR-8 in each region are summarized in Table 3.1,
The boundaries of each of these 'macroscopic" regions were chosen to rep-
resent as closely as possible those gross geometrical and material prop-
erties which determine the neutron transport in the core. This choice
was made within the practical limitations on the number of dimensions and
mesh points in the numerical calculations.

Use of two-dimensional geometry resulted in a large saving in com-
puting time, and was considered an adequate representation for most pur-

poses. The major approximation involved wasg in the representation of the
UNCLASSIFIED
ORNL-LR-DWG 61097R

FLEXIBLE CONDUIT TO
CONTROL ROD DRIVES

  
 
  
 
 
  
  
 
   
 
 
 
  
  
 
   

SAMPLE ACCESS POR

COOLING AIR LINES

ACCESS PORT COOLING JACKETS

FUEL OUTLET

 

REACTOR ACCESS PORT

 

CONTROL ROD THIMBLES

CORE //f////

CENTERING GRID

 

FLOW DISTRIBUTOR

GRAPHITE-MODERATOR)
STRINGER \

 

 

FUELINLETJ/
REACTOR CORE CAN—

-
REACTOR VESSEL—T:

 

 

*’fiz;ERATOR

SUPPORT GRID

ANTI-SWIRL VANES
VESSEL DRAIN LINE

 

Fig. 3.1. Cutaway Drawing of MSRE Core and Core Vessel.
17

UNCLASSIFIED
REACTOR § ORNL-LR-DWG 60845A1

CONTROL ROD

\\-\-- GUIDE TUBE

31— GUIDE BAR

 

 

 

 

 

TYPICAL —
FUEL CHANNEL §§§§

- R -~ R - R - REACTOR ¢

~=— 2,00 *!

  

/)
' R 7N\
0.200-in. R~ g N~
0.400 1.~ R = REMOVABLE

STRINGER

4 GRAPHITE IRRADIATION ¢
SAMPLES ( 7/g-in.DIA) ~

|

2 in. TYPICAL

Y

Fig. 3.2. MSRE Control Rod Arrangement and Typi-
cal Fuel Channel.

small central region of the core which includes the three control rod
thimbles and the graphite specimens. The model contains the same amounts
of fuel, graphite, and INOR-8 as the actual core, but the arrangement is
necegsarily different. The INOR-8 is of the thimbles represented by a
C,e10~in, ~thick, 6.00-in.-0D annulus, which has a volume and an outside
surface area equal to those of the INOR-8 of the three thimbles. Just
inside the INOR-8§ annulus is a region containing low-density fuel, repre-
senting a mixture of the voids inside the thimbles and the extra fuel sur-
rounding the thimbles and the specimens, At the center of the core is a
cylinder of normal core composition (0,255 fuel, 0.775 graphite by volume).
Other assumptions made in the calculations are that the temperature
is uniform at 1200°F, that there is no permeation of the graphite by the
fuel, and that there are no fission product poisons in the core. The
graphite was assumed to be pure carbon, with a density of 1.86 g/cc. Re-
activity effects due to deviations from these assumptions were tested asg

perturbations, as described later in this chapter.
 

 

.18:

UNCLASSIFIED
ORNL~LR-DWG 73610R

 

 

-

 

 

 

i

 

 

 

 

 

 

 

o|2

 

 

 

 

C

 

 

Lel o b ol 1.1
02 46 8 10
' INCHES

- Fig. 3.3, Twenty-Region Core Model for Nuclear Calculations.

Table 3.1 for explanation of letters.

4)

W

See
Table 3.1.

Twenty-Region Model of MERE Core Used in Nuclear Calculations

(See Fig. 3.3 for graphical location of regions)

 

Radius (in.)

Height (in.)

Composition (vol %)

 

 

 

Region Region Represented

Inner Outer Bottom Top Fuel Graphite INOR-8

A 0 29.56 74,92 76 .04 0 0 100 Vessel top

B 29.00 29,56 -92.14 74,92 0 100 Vessel side

C 0 29.56 —10.26 -9.14 0 0 100 Vessel bottom

D 3.00 29.00 6747 74.92 100 0 0 Upper head

BE 3.00 28.00 66.22 67.47 93.7 3.5 2.8

F 28.00 29.00 0 67.47 100 0 0 Downcomer

G 3.00 28.00 65.53 66,22 4.6 5.4 0

H 3.00 27475 64459 65.53 63.3 36.5 0,2

I 27.75 28.00 0 65.53 0 0 100 Core can

J 3,00 27.75 5.50 64.59 22.5 77.5 0 Core

K 2,90 3.00 5.50 74.92 0 0 100 Simulated thimbles

L 0 1.94 2.00 64459 22.5 77.5 0 Central region

M 1.94 27,75 2.00 5.50 2245 77.5 0 Core

N 0 27.75 0 2.00 23.7 76.3 0 Horizontal stringers

0 0 22.00 —l.41 0 66.9 15.3 17.8

P 0 29.00 -9.14 -1.41 90,8 0 9.2 Bottom head

Q 0 1.94 66,22 74.92 100 0 0

R 0 1.94 65.53 66,22 g9.9 10.1 0

S 0 1.94 64.59 65.53 43.8 56,2 0

T 1.94 2.90 5.50 74,92 1008 0 0 Fuel and voids

 

aDensity, 0.46 X density of normal fuel.

61
20

3.3 Fuel Properties

The nuclear characteristics of the reactor were calculated for three
different fuel salts, deseribed in Table 3.2. (Uranium concentrations
are approximate, based on Initial estimates of concentrations required

for criticality. The exact critical concentrations are given in Sec 3.9.)

3.4 Cross Sections and Effects of Inhomogeneity of Core

The group cross sections to be used in diffusion calculations prop-
erly should take into account the effect of fuel composition and lumping
on the neutron energy spectra and spatial distributions in the fuel and

in the graphite.

Table 3.2, MSRE Fuel Salts for Which Detailed Nuclear
Calculations Were Made

 

Fuel Type A B C

 

Salt composition (mole %)

LiF> 70 66.8 65
BeFs 23,7 29 29,2
ZrF, 5 e 5
ThF, 1 0 0
UF,; (epprox) 0.3 0.2 0.8
Uranium composition (atom %)
U234 1 1 0.3
U23° 93 93 35
U236 1 1 0.3
U238 5 5 YA
Density at 1200°F (1b/ft3) 144.5 134.5 142.7

 

999,9926% 117, 0.0074% LiS.
21

3.4.1 Resonance Neutrons

Fuels A and C contain important amounts of strong resonance absorbers,
thorium in fuel A and U?2% in fuel C., The effective resonance integrals

for these materials depend on their concentration in the fuel and on the

effective surface-to-volume ratio of the fuel channels. Figure 3.4 1lius-
trates how the effective resonance integral Tfor U238 varies over the con-
centration range of interest for the MSRE., This curve was calculated by
Nordheim's numerical integration program for resonance integral computa-
tions.® In this calculation, the actual two-dimensional transverse sec-
tion of the MSRE lattice geometry (Fig. 3.2) was approximated by slab

geometry with a surface-to-volume ratio of salt equal to the effective

UNCLASSIFIED
ORNL DWG, 63-3147

260

240 B=

220

200

180

1?38 EFFECTIVE RESONANCE INTEGRAL (barns)

160

 

1ko
0 0.2 0.4 0.6 0.8 1.0

238

U™"F, CONCENTRATION (Mole %)

Fig. 3.4. Variation of U?2® Effective Resonance Integral with
U?38F, Concentration in MSRE Lattice.
22

ratio in the actual lattice. The effective ratio is affected by Dancoff
effects (shielding from neighboring channels), which reduces the effective
surface-to-volume ratio for resonance capture in the MSRE lattice by about
30%.9 These calculations of effective resonance integrals were used in
initial estimetes of the critical concentration of U??° in each fuel.

In preparation for the refined calculations of critical concentra-
tion, which were to be done by a 33-group diffusion method, a new set of
multigroup cross sections was prepared for the core with each of the three
fuel compositions. Group cross sections for the 32 fast groups were gen-
erated by use of the IBM 7090 program GAM-1,10 This program is based on
a consistent P-1 approximation to the Boltzmann equation for neutron slow-
ing-down, and averages the cross sections over an energy spectrum above
thermal which is appropriate for a single-region reactor with a macro-
scopically uniform composition. Corrections for the shielding effects
associated with the fuel channels are automatically included in the GAM-1
program. For the MSRE calculations, a set of cross sections was generated
for each fuel composition, assuming a one-region reactor with a lattice
like that in the main part of the actual core (22,5 vol % fuel, 77.5 vol %
graphite).

A minor complication in the GAM-1 calculation of MSRE cross sections
was that the available version of the GAM-1 cross-section library tape
did not include Lis, Li7, and Flg, which are important components of the
MSRE fuel. This was circumvented by simulating their effect on the neutron
spectrum by the inclusion of an amount of oxygen equivalent in slowiling-
down power (gzs) to the lithium and fluorine actually present. Fast group
cross sections for Li6, Li7, and F'? were compiled from basic cross-sec-

tion data, independently of the GAM-1 calculation.

3¢4.2 Thermal Neutrons

 

Average cross sections for the thermal group were calculated by use
of two thermalization programs for the IBM 7090. Reference calculations
for each fuel at 1200°F were made with THERMOS, which computes the thermal
spectrum in a one-dimensional lattice cell.l! The cell model used was
that of a cylindrical graphite stringer, surrounded by an annulus of salt.

For other calculations in which the effects of changes in temperature and
23

thermal cutoff energy were studied, a simpler and more rapid thermaliza-
tion program was employed, based on the Wilkins "heavy gas" space-inde-
prendent model.

Lumping reduces the thermal utilization in the MSRE lattice because
of the thermal flux depression in the fuel, but this effect is not large.
(For salt with the maximum uranium content of interest in the MSRE, 1 mole
% UF;, the flux depression in the fuel was about 3.5%.) Furthermore, the
normal temperature of 1200°F is above the temperature at which crystal
binding effects in graphite must be considered.l® TFor these reasons, it
was found that good agreement with the THERMOS model could be obtained
by combining the Wilkins thermal spectrum calculation with a one-group
P-3 calculation of the spatiasl disadvantage factor. These approximations
were used wherever possible in order to save computer time. For some of
the studies of the temperature coefficient of reactivity, however, it was
necessary to use the THERMOS program in order to vary the temperature of
the fuel channel independently of that of the graphite. These studies are
described more fully in Sec 3.7.

3.5 Criticality Calculations

Critical fuel concentrations were computed with MODRIC, a multigroup
diffusion program for the IBM 7090, MODRIC is a one-dimensional program
with provision for approximating the neutron leakage in the direction
transverse to that represented in the one-dimensional model. For the
calculation of critical concentration, the reactor was represented by a
cylinder with regions and materials corresponding to the midplane of the
model shown in Fig. 3.3, Axial leakage was taken into account by the in-

clusion of a specified axial buckling, based on earlier calculations of
the axial flux shape. In the computations for fuels A and B, the concen-

trations of all uranium isotopes were varied together in all regions to
find the critical concentration. For fuel C, the U?38 concentration was
held constant and those of the other uranium isotopes were varied. (Re-

sults are summarized in Table 3.5, Sec 3.9,)
24

In addition to the critical concentration, the MODRIC calculations
gave two-group constants for each region represented. These were to be
used in & two-group, two-dimensional calculation. It was therefore nec-
egssary to perform other MODRIC calculations to include regions missed by
the midplane radial calculations. For these calculations the reactor was
represented by a multilayer slab, with regions corresponding to an axial
traverse through the model of Fig. 3.3, and a radial buckling based on
the radial MODRIC calculations, ©Slabs corresponding to two different
traverses were calculated, one corresponding to the core centerline and
the other to a traverse just outside the rod thimbles. These axial cal-
culations, using the critical concentrations given by the radial calcula-
tions, gave values of keff between 1,004 and 1.021. This is considered
to be good agreement, in view of the fact that the axial calculations are
less accurate than the radial because the equivalent transverse buckling

is more subject to error in the axial calculations,.

The two-group constants obtained from MODRIC were used in calcula-
tion of the model of Fig. 3.3 by the two-group, two-dimensional program
EQUIPOISE-3.1% 19 These two-group calculations gave keff of 0.993, 0.997,
and 0,993 for fuels A, B, and C, respectively, further confirming the

critical concentrations found by the radial MODRIC criticality search.

In all of these calculations it was assumed that the core tempera-
ture was uniform at 1200°F, the control rods were withdrawn, and the core
contained no fission product polsons. The calculated critical concentra-
tions are therefore those which would be attained during the initial crit-
ical experiments with clean, noncirculating fuel and with all rods fully
withdrawn. During subsequent operations, the concentration must be higher
to compensate for all of the effects (poisons, rods, and the loss of de-
layed neutrons) which tend to decrease reactivity. The total of these
effects is expected to be about 4% dk/k. Table 3.5 (Sec 3.9) lists the

critical concentration for normal operation, which would include these

effects, The increases in the critical concentration from the clean crit-
ical experiment were computed from values of the concentration coefficient
of reactivity (3k/k)/(8C/C), produced by the MODRIC criticality searches.
25
3,6 TFMux and Fission Distributions

3.6.1 Spatial Distribution

Two-group fluxes and adjoint fluxes were produced by the EQUIPOISE-3
calculations. TFigures 3.5-3.8 show the axial and radial distributions
Tor fuels B and C. The fluxes for fuel A are within 2.,5% of those for
fuel C. The radial distributions are for an axial position that corre-
sponds to the maximum in the thermal flux, which is at a position very
close to the core midplane., The axial distributions are at a position
8.4 in. from the core centerline*; this radius corresponds to the maximum
value of the thermal flux.

The MODRIC calculations gave gpatial flux distributions for each of
33 energy groups. 1t was necessary to normalize the MODRIC fluxes to cor-
respond to the neutron production at 10 Mw, and the normalization factor
was obtained by comparing the MODRIC thermal fluxes with the 10-Mw values
computed by EQUIPOISE. (The shapes of the thermal fluxes were very sim-
ilar.) The high-energy MODRIC fluxes were then multiplied by the normal-
ization factor to obtain the predicted high-energy neutron fluxes in the
reactor., Figure 3.9 shows the radial distribution, near the core mid-
plane, of the neutron fluxes with energies greater than 0.18 Mev and with
energies greater than 1.05 Mev., Figure 3.10 shows the axial distribution
of the same energy groups 3 in. from the core centerline, which is about
the location of the rod thimbles and the test specimens. (The values
shown in Figs. 3.9 and 3.10 were computed for fuel C, but these wvery-high-
energy fluxes are not sensitive to the fuel composition.)

The spatial distributions of the fission density were obtalned from
the EQUIPOISE-3 calculations. Figures 3.11 and 3.12 show the axial and
radial distributions of the fission density in the fuel, for fuel C. The
same calculations also gave total fissions in each region., Table 3.3 sum-
marizes, for fuel C, the fraction of the total fissions which occur in

the major regions of the reactor.

 

*The datum plane for the axial distance is the bottom of the hori-
zontal graphite bars at the bottom of the core.
UNCLASSIFIED
ORNL DWG. 63.8148

. c

TS SUod

20

 

-~
s

80

70

30 40
AXIAL POSITION (in.)

20

10

-10

from Core

11.

8.4

Axial Distribution of Two-Group Fluxes

Fig. 3.5.
Center Line, Fuel B.
(x 1073) (x 10%9)

)

-1
sec

-2

FAST FILUX (neutrons cm

-10 0 10 20 30 Lo 50 60
AXTAL POSITION (in.)

Fig. 3.6. Axial Distribution of Two-Group Fluxes 8.4 in.
Center Line, Fuel C.

UNCLASSIFIED
ORNL DWG, 63-8149

z ppy
Slhean

 

70 80

from Core

L
28

1 UNCLASSIFIED
(x 10 3) ORNL DWG. 638150

 

******

    

1
)
5

sec”

-2

FLUX (neutrons cm

........

......

+++++

0 5 10 15 20 25 30
RADIUS (in.)

Fig. 3.7. Radial Distribution of Two-Group Fluxes Near Core Mid-
plane, Fuel B.
29

 

(x 1013) UNCLASSIFIED
ORNL DWG, 638151
16
14
12
~ T
r-;] 4]
o 10 @
@
@ o
o g
1 u
&
o w
o
g a
o 8 2
B g
3 a
O ~
.
5 &
E —
g © %
2
P &
L
2
0 SAEE Shethon :
0 5 10 15 20 25 30
RADIUS (in.)

Fig. 3.8. Radial Distribution of Two-Group Fluxes Near Core Mid-
plane, Fuel C.
30

(x 1013) UNCLASSIFIED
ORNL DWG. 63.8152

-2
sec

FLUX (neutrons cm

 

0 5 10 15 20 25 30
RADIUS (in.)
Fig. 3.9, High-Energy Neutron Fluxes: Radial Distribution Near
Core Midplane at 10 Mw.
sSec

FIUX (neutrons cm =

ol

-10 0

Fig, 3,10,

 

10

UNCLASSIFIED
ORNL. DWG, 63.8153

¢¢¢¢¢¢

20 30 ] 50 60 70

AXTAL POSITION (in.)

High-Energy Neutron Fluxes: Axial Distribution 3 in.

from Core Center Line at 10 Mw.

 

TE
UNCLASSIFIED
ORNL DWG. 63.8154

REIATIVE FISSION DENSITY,

 

0 5 10 15 20 25 30
RADIUS (in.)

Fig. 3.11. Radial Distribution of Fuel Fission Density Near Core
Midplane, Fuel C.
REIATIVE FISSION DENSITY

UNCLASSIFIED
ORNL DWG. 63-.8155

1.0

T
: ;
0.8 o

0.6

0.4

 

-10 0 10 20 30 4O 50 £0 70 8o
7, AXIAL POSITION (in.)}

Fig. 3.12. Axial Distribution of Fuel Fission Density 8.4 in. from
Core Center Line, Fuel C.

23
34

Table 3.3, Fission Distribution by Major Region
(See Fig. 3.3 for graphical location of regions)

 

Fraction of Total Fissions

 

Major Region Regions (4)
Downconmer T 2.9
Lower head o, P 2ot
Main core J, L, M, N, T 89.1
Upper head D, E, G, H, Q, R, S 5.6

 

3.6.2 Energy Distribution

 

The energy distribution of the neutron flux at a given location is
influenced by the nuclear properties of the materials in the general vi-
cinity of the point. As a result, the flux spectrum varies rather widely
with position and fuel composition. The MODRIC calculations produced av-
erage distributions of flux as a function of energy within each reactor
region as well as the detailed distributions as functions of position and
energy. Figure 3,13 shows the average fluxes, per unit lethargy, in the
largest core region (Region J of Fig. 3.3) for each of the 32 nonthermal
energy groups. The fluxes are normalized to unit thermal flux in each
case. The maximum lethargy of the thirty-second or last epithermal group
is 17, which corresponds to a neutron energy of 0.414 ev. This is also
the maximum energy (minimum lethargy) of neutrons in the thirty-third or
"thermal" group. The effect of the strong resonance absorbers, thorium
in fuel A and U%3® in fuel C, in reducing the flux in the region just
above the thermal cutoff is readily apparent.

The distribution of fissions as a function of the lethargy of the
neutrons causing fission is the product of the neutron flux and the fis-
sion cross section, Figure 3.14 shows the average fission density, per
unit lethargy, in the largest core region, normalized to one fission in
that region, as a function of neutron energy for fuel C. The resonances
in the fission cross section are reflected by the peaks at the higher

lethargies (lower energies). Integration of the plot in Fig. 3.14 to a
NEUTRON ENERGY (ev) UNCLASS!FIED
ORN{L. DWG., 63.81556

 

107 10° 10° 1% 103 10° 10 1
0.35%
0.30
0.25
o
O 0.20
=
2
1&
0.15
0.10
0.05
0
4 6 8 10 12 1k 16 18

LETHARGY, u

Fig. 3.13. Average Flux Spectra in Largest Core Region.

Ge
UNCLASSIFIED
ORNL DWG. 63.8157

NEUTRON ENERGY (ev)

1

10

LETHARGY, u
Density as a Function of Lethargy of Neutrons

ission

Fig. 3.14. F
Causing Fission, Fuel C.

106

 

w (e (W)= /1™ (0)73)

o
37

given lethargy gives the cumulative fraction of fissions caused by neu-
trons with less than the specified lethargy. Figure 3.15 illustrates the
result of this operation for fuel C in the largest core region. This
figure indicates that 17.7% of the fissions in this region are caused by
nonthermal neutrons, The average fraction for the entire reactor is 20.2%,
indicating that fast fissions account for a relatively larger fraction of
the total in other regions. This 1s particularly true in the upper and
lower heads, where the absence of graphite produces a much lower ratio of

thermal to fast flux than exists in the main portion of the core.

3.7 Reactivity Effects of Nonuniform Temperature

Changes in the temperature of the core materials influence the re-
activity through changes in the neutron leakage and absorption probabili-
ties. The reactivity change between two isothermal conditions can be ex-
pressed in terms of a single temperature coefficient of reactivity. When
the reactor operates at power, however, the core is not isothermal; in
fact, the overall shapes of the temperature distributions in the fuel and
in the graphite are quite dissimilar. For this reason, and also because
different thermal time constants are involved in fuel and graphite tem-
perature changes, separate consideration of the reactivity effects of
these changes 1s necessary. To delineate the factors governing the reac-
tivity-temperature relation, calculations were first performed using a
simplified model of the reactor, that of a single-region cylinder in which
composition and temperature were macroscopically uniform. These are dis-
cussed in Sec 3.7.1l. Analysis based on the multiregion model of Fig. 3.3

is considered in Sec 3.7.2.

3.7.1 One-Region Model

 

For this analysis, use was made of the GAM-1 program in order to
calculate macroscopic cross sections averaged over the energy spectrum
above thermal. Cross sections for the thermal group were averaged over
a Wilkins spectrum. The lower energy cutoff for the GAM-1 calculation
was equal to the upper cutoff for the Wilkins thermal spectrum. The two-

group parameters obtained in this way were then used to calculate the
38

UNCLASSIFIED
ENERGY OF NEUTRON CAUSING FISSION (ev) UNCLassIFIED
107 108 10° ot 103 10° 10 1
0.20

0.10

CUMULATIVE FRACTION OF FISSICNS

 

0 2 4 6 8 10 12 14 16 18
LETHARGY OF NEUTRON CAUSING FISSION

Fig. 3.15, Cumulative Fraction of Fissions Caused by High-Energy
Neutrons, Fuel C.
39

multiplication constant of the cylinder, based on the standard two-group
diffusion equations. In this calculation, the geometric buckling used
was that of a cylinder, 59 in, in diameter by 78 in. high. Three tem-
perature conditions were considered: (1) salt and graphite at 1200°F,
(2) salt at 1600°F, graphite at 1200°F, and (3) salt and graphite at
1600°F. The temperature coefficient of reactivity was obtained from the

approximate relation

1 3k x(2600) _ y(1200)

EST = (3.1)

 

200 k(lQOO)

Two special considerations are of importance in analysis of tThe MSRE
temperature coefficlent. The first is the position chosen for the thermal
energy cutoff, which 1s the approximalte energy above which thermal motion
of moderator atoms may be neglected. Since a cylindrical core of this
size has a large neutron leakage fraction, unless the cutoff energy is
chosen high enough the total effect of temperature on thermal neutron
leakage is underestimated. This effect is indicated in Fig. 3.16, curve
(a). Here the total temperature coefficient of reactivity (fuel + graph-
ite) of the core fueled with fuel C is plotted vs the upper energy cutoff
of the thermal group. The coefficient tends to become independent of the
cutoff energy for cutoffs in excess of about 1 ev.

The second consideration is the effect of the salt temperature on
the thermal spectrum. For this calculation, it was necessary to employ
the THERMOS program so that the temperatures of the salt channels and
graphite could be varied independently. The results of this analysis for
fuel C may be seen by comparing curves (b) and (c¢) in Fig. 3,16. Curve
(b) was calculated by neglecting the change in thermal spectrum with salt
temperature. This difference is a consequence of the fact that the light
elements in the salt, lithium, beryllium, and fluorine, contribute sub-
stantially to the total moderation in the MSRE core.

Similar calculations based on the one-region cylindrical model were
made for fuels A and B. The values of the reactivity coefficients for
all fuels obtained at the asymptotic cutoff energies are summarized in
Table 3.4. All calculations were based on the wvalues of volumetric ex-

pansion coefficients at 1200°F (see Table 3.4).
40

- UNCLASSIFIED
(x 10 5) ORNL DWG. 68159

TEMPERATURE COEFFICTENT OF REACTIVITY [(°F) ]

CUTOFF ENERGY (ev)

 

CURVES:

Included

(a) Total (Fuel + Graphite)

(b) Fuel; Thermal Spectrum
Assumed Independent of
Salt Temperature

(c¢) Fuel; Dependence of
Thermal Spectrum on
Salt Temperature

Fig. 3.16. Effect of Thermal Cutoff Energy on Temperature Coeffi-

cient of Reactivity, Fuel C.

Table 3.4. Temperature Coefficilents of Reactivity Obtained
from One-Region Model

(Calculations based on expansion coefficients, at 1200°F, of
1.18 X 1072 ¢/°F for salt and 1.0 X 1072 ¢/°F for graphite)

 

 

 

 

Fuel A Fuel B Fuel C
Temperature coefficient of
reactivity [(8k/k)/°F]
salt —3.03 X 1077 ~4,97 X 107  =3.28 x 1077
Graphite —3,36 X 1077 —=4.91 x 1072 -3,68 x 10°°
Total —6.39 X 107°  -9.88 x 1077  —6,96 x 1077

 
41

3.7.2 Multiregion Model

To study the effects of the macroscopic distribution of materials
composition and temperature on the reactivity-temperature relations, use
was made of first-order perturbation theory.16 For this purpose, it 1is
convenient to utilize the concept of a nuclear average temperature, This
quantity is defined as follows: At low power, reactor criticality is
assumed to be established at isothermal conditions in fuel and graphite.
Then, with the graphite temperature held constant, the fuel temperature
is varied according to a prescribed distribution, thus changing the re-
activity. The fuel nuclear average temperature, T;, is defined as the
equivalent uniform fuel temperature which gives the same reactivity change
as that of the actual temperature distribution. Similarly, the graphite
nueclear average temperature, Tg, is defined as the uniform graphite tem-
perature which gives the same reactivity change as the actual graphite
temperature profile, with the fuel temperature held constant.

The relations between the nuclear average temperature, T*, and the

temperature distributions, T(r,z), are of the form

 

* j;eactOr Tx(r,z) GX(T,Z)r dr dz
reactor Gx(r,z)r dr dz
where
* * % .

and ¢1, %5, ¢:, ¢: are the unperturbed values of the fast and slow fluxes
and the fast and slow adjoint fluxes, respectively., The coefficients Gij
are constant over each region of the unperturbed reactor in which the nu-
clear composition is uniform, but vary from region to region. These quan-
tities involwve the temperature derivatives of the macroscopic nuclear
constants; that is, in obtaining Eq. (3.3), the local change 3% in the
macroscopic cross sections was related to the local temperature change

OT through the approximation

8x(r,z) = g% I (r,z) . (3.4)
42

This approximation is adequate 1f the gpatial wvariation in temperature is
relatively smooth within a given region.

Temperature coefficients of reactivity which are consistent with the
definitions of the nuclear average temperatures were also obtained from
perturbation theory., The complete temperature-reactivity relation is ex-

pressed as

Bk ¥ ¥ * K
- = 0BT, + agSTg , (3.5)
where
* * *
3T = T — Tg (3.6)

*
and & 1is the appropriate temperature coefficient of reactivity. The
fuel and graphite reactivity coefficients are related to the weight func-
tions G(r,z) as follows:
¢ (r,z)r dr dz
. . ,
o = reactor x (3.7)

X
j;eactor F(r,z)r dr dz

where

* *
F(I’,Z) = V2f1¢1¢1 + V2f2¢2¢2 . (3.8)

The principal advantage ol expressing the reactivity change with tempera-
ture in the form of Egq. (3.5) is that the reactivity coefficients, a*,
and the weight functions G(r,z) depend only on the conditions in the un-
perturbed reactor. Use of this approximation thus simplifies the calcu-
lation of the reactivity effects of a large number of temperature distri-
butions.

Reactivity coefficients and temperature weight functions for the
fuel salt and graphite were evaluated for the 20-region model of the MSRE
core (Fig. 3.3), fueled with fuel C. The resulting weight functions are
shown in Figs., 3.17-3.20. These figures correspond to axial and radial
traverses of the core which intersect at the approximate position of max-
imum thermal flux. Corresponding weight functions for fuels A and B do
not differ qualitatively from these results. The discontinuities in the

welght functions occur as the effective concentrations of salt, graphite,
REIATIVE IMPORTANCE

1.0

Fig. 3.17.
as a Function of
Line,

UNCLASSIFIED
DWG. 63.8160

 

10 20 30 40 50 60 70 80

AXTAL POSITION (in.)

Relative Nuclear Importance of Fuel Temperature Changes
Position on an Axis Located 8.4 in. from Core Center

£y
UNCLASSIFIED
ORNL DWG, 63-8161

 

RETATIVE IMPORTANCE

RADIUS

15
{(in.)

Fig. 3.18. Relative Nuclear Importance of Fuel Temperature Changes
as a PFunction of Radial Position in Plane of Maximum Thermal Flux.
RETATTVE IMPORTANCE

 

0.8E

0.4

 

UNC{ ASSIFIED
ORNL DWG. 63.8162

.....

~~~~~
............

 

-10 0 10 20 30 4o 50 60 70

AXTAL POSITION (in.)

Fig. 3.19. Relative Nuclear Importance of Graphite Temperature
Changes as a Function of Position on an Axis Located 8.4 in, from Core
Center Line.

QY
46

UNCLASSIFIED
ORNL DWG. 638163

RETATIVE IMPORTANCE

 

0 5 10 15 20 25 30

-

RADTIUS (din.)

Fig. 3.20. Relative Nuclear Importance of Graphite Temperature
Changes as a Function of Radial Position in Plane of Maximum Thermal
Flux.
477

and INOR-8 change from region to region. From the definition of these
functions, the point values reflect directly the reactivity effect of &
change in fuel or graphite temperature in a unit volume at that point.
This occurs through changes in the local unit reaction and leakage rates,
reflected in Gij of Eq. (3.3), and through variation in nuclear importance
with position, reflected in ¢;¢j'

Although the method presented above 1s an attempt to account approxi-
mately for macroscopic variations in reactor properties with position, it
should be noted the basic model is still highly idealized. The exact
nature of the discontinuities in the weight functions would undoubtedly

differ from those shown in Figs. 3,17-3.20, Since the reactivity change

is an integral effect, however, these local differences tend to be
"smeared out" in the quantities determining the operating characteristics.
Consider, for example, the large increase in the fuel temperature weight-
ing functions, corresponding to the region of salt plus void surrounding
the control rod thimbles. This reflects both the higher average U232
concentration and the lack of graphite to dilute the effect of a salt
temperature increment on the density of this region. Thus both the av-
erage reaction rate and the scattering probability for neutrons entering
this region are more sensitive to changes in the salt temperature. How-
ever, when integrated over the volume, this region contributes only about
5% to the total fuel temperature coefficient of reactivity.

The temperature coefficients of reactivity obtained from the multi-
region model were in reasonably good agreement with the coefficients
listed for fuel C in Table 3.4. The fuel coefficient was about 3% smaller
and the graphite coefficlent about 15% smaller than those of the homoge-
neous cylinder. The difference in coefficients for the graphite occurs
because the wvolume of the core actually occupied by the graphite is
slightly smaller than the effective "nuclear size" of the cylinder. How-
ever, the validity of the assumptions concerning the space dependence of
the thermal spectrum over the peripheral regions of the core is uncertain,
s0 the values given in Table 3.4 are recommended as design criteria until

further studies concerning these corrections can be made.
48

3.8 Reactivity Effects of Changes in Densities
of Fuel Salt and Graphite

Included in the category of reactivity effects of graphite and salt
density changes are those due to graphite shrinkage, fuel soakup, en-
trained gas, and uncertainties in measured values of the material densi-
ties at operating conditions. Density coefficients of reactivity were
calculated for the simplified, one-region-cylinder model of the core.

In these calculations, as in the similar analysis of the temperature re-
activity coefficients (Sec 3.7), lattice effects of heterogeneity were
considered. The density coefficients relate the fractional change in

multiplication constant to the fractional changes in densities;

ok BNS ?HS

The values of the coefficients, B, obtained for the three fuel salts
studied are included in Table 3.5. These results directly indicate the
reactivity effect of uncertainties in the measured values of the material
densities. 1In order to apply the resulis to calculate the effects of
graphite shrinkage and fuel soakup, some assumptions must be made con-
cerning the changes in the lattice geometry produced by these perturba-
tions. If shrinkage is uniform in the transverse direction across a
graphite stringer, and if the center of the stringer remains fixed during
contraction, the effect will be to open the gaps between stringers and
allow fuel salt to enter the gaps. The homogenized density of the graph-
ite remains constant; however, the effective salt density, NS, is in-
creased. If vy and vg are the volume fractions of salt and graphite in

the lattice, the fractional change in salt density is calculated as

dvV_ = —OV (3.10)
S g

and

v_ oV v
S.S-._-E8_E&_ L | (3.11)
vsvg v
49

where f; is the fractional decrease in graphite volume due to shrinkage.
From Eq. (3.9), the reactivity change is

ok v
+ = B, ;f f1 = 3.44 B_ f1 , (3.12)
in which the salt/graphite volume ratio, 0.225/0.775, has been inserted.
Use of the above,}elation in conjunction with the density coefficients
indicates that shrinkage of the graphite by 1% of its volume corresponds
to reactivity additions of about 0.65% &k/k in fuels A and C and 1.2%
8k/k in fuel B.

Fuel soakup reactivity additions may also be estimated from Eq.
(3.12). For this purpose the graphite shrinkage fraction fj; need only
be replaced by f2, the porous volume fraction of graphite which is filled
with fuel salt.

3.9 Summary of Nuclear Characteristics

The nuclear characteristics of the MSRE have been calculated for
three fuel mixtures, designated A, B, and C, which differ primarily in
content of fuel and/or fertile material, The distinguishing features of
the three fuels are as follows: fuel A contains uranium highly (~93%) en-
riched in U?3% and 1 mole % thorium; fuel B contains highly enriched ura-
nium but no fertile material; and fuel C contains about 0.8 mole % uranium
with the U2’ enrichment reduced and no thorium. The characteristics of
the reactor with each of the three fuels are summarized in Table 3.5. The
uranium concentrations and inventories are listed for the initial, clean,
noncirculating, critical condition and for the long-term operating con-
dition. The neutron fluxes are given for the operating uranium concen-
trations, and the reactivity parameters apply to the initial critical
concentration.

Detailed neutron balances were calculated by the computer programs
for each of the three fuels, The neutron balance for the reactor filled
with fuel C at the clean, critical concentration is summarized in Tables
3.6 and 3.7. Neutron absorptions and leakages associated with various
portions of the reactor vessel and its contents are listed in Table 3.6.
Table 3.7 gives a detailed breakdown of the neutron absorptions by ele-

ment in each region of the reactor.
50

 

 

Table 3.5. Nuclear Characteristics of MSRE with Various Fuels
Fuel A yel B Fuel C
Uranium concentration (mole %)
Clean, noncirculating
ge35 0,291 0.176 0.291
Total U 0,313 0.189 0.831
Operatinga
U?3 0.337 0.199 0. 346
Total U 0.362 0.214 0.890
Uranium inventory® (kg)
Initial criticality
U233 79 . 48 77
Total U 85 52 218
Operatinga
y=3 91 55 92
Total U 28 59 233
Thermal neutron fluxes® (neutrons
e~ sec”t)
Maxcimum 3.31 x 1013 5.56 x 1013 3.29 x 1013
Average in graphite-moderated 1.42 x 1013 2.43 % 1013 1,42 x 1013
regilons
Average in circulating fuel 3,98 x 1012 6.81 x 1012 3,98 x 10%?
Reactivity coefficientsd
Fuel temperature [(°F)~1] —3,03 X 1077 =4.97 x 1077  -3,28 x 10°7
Graphite temperature [(°F)~1] —=3,36 x 1077 —=4,91 x 107° —=3,68 x 10°%
Uranium concentration 0.2526 0,3028 0.1754¢
0.,2110%
Xel3% concentration in core —1.28 x 108 —2,04 x 108 —1.33 x 108
(atom/barn-cm)~1
Xel3? poison fraction 0,746 -0.691 —0.752
Fuel salt density 0.190 0.345 0.182
Graphite density Q.755 0.735 0.767
Prompt neutron lifetime (sec) 2.29 x 104 3.47 X 1074 2.40 x 104

 

a

b

At operating fuel concentration, 10 Mw,

d

At initial critical concentration.

Fuel loaded to compensate for 4% dk/k in poisons.
Based on 73.2 ft? of fuel salt at 1200°F.

Where units are shown, coefficients

for variable x are of the form (1/k)/(dk/dx); other coefficients are of the

form (x/k)/(dk/dx).

e . . . s oy
Based on uranium isotopic composition of clean critical reactor.

TBased on highly (~93%) enriched uranium,
51

Table 3.6, Neutron Balance for Fuel C, Clean, Critical

(per 10° neutrons produced)

 

 

 

 

 

 

 

 

Absorptions
Region
g2 33 ye38 Salt® Graphite INOR Total
Main coreP 45,459 7252 4364 795 1380 59,250
Upper head® 3,031 928 675 1 131 4y 766
Lower headd 1,337 449 294 0 1480 3,560
Downconmer 1,496 338 203 0 0 2,037
Core can O 0 O 0 3635 3,635
Reactor wvessel 0 0 0 0 3056 3,056
Total 51,323 8967 5536 796 9682 76,304
Leakage
curface

Fagt Slow Total

Top 1,991 10 2,001

Sides 19,619 1004 20,623

Bottom 1,068 4 1,072

Total 22,678 1018 23,696

 

aConstituents other than U235 and U238,
bRegions J, K, L, M, N, and T (Fig. 3.3).
®Regions D, E, G, H, Q, R, and S (Fig. 3.3).
d'Regng:i_cms 0 and P (Fig. 3.3).
Table 3.7. Detailed Distribution of Neutron Absorptions with Fuel C

 

Absorptions per 10° Neutrons Produced

 

 

 

Regiona
ge3s  y?38 R34 yR3é 146 1i’  Be zr  F{n,x) F(n,y) GCraphite INOR Total
A 0 0 0 0 0 0 0 0 0 0 324 324
B 0 0 0 0 0 0 0 2578 2,578
C 0 0 0 0 0 0 154 154
D 1,518 546 8 4 26 13 27 185 115 37 0 0 2,478
E 571 155 3 1 11 6 8 by 30 11 0 123 964
F 1,496 338 7 2 27 17 14 77 39 20 0 0 2,037
G 424 105 2 1 7 5 27 17 0 0 598
H 494 114 2 1 5 26 15 1 8 687
I 0 0 0 0 0 0 0 0 0 3635 3,635
J 42,837 6768 160 48 905 510 221 1247 517 480 762 0 54,456
K 0 0 0 0 0 0 0 0 0 0 0 1380 1,380
L 304 58 1 0 6 4 2 11 5 3 7 0 402
M 1,149 199 4 1 23 13 6 37 14 13 20 0 1,480
N 419 85 2 1 8 5 3 17 6 6 0 557
0 438 112 2 1 8 5 4 28 12 7 0 790 1,407
P 899 337 5 2 11 g 15 120 b 22 0 690 2,153
Q 19 7 0 0 0 0 2 1 0 0 0 30
R 3 0 0 0 0 0 0 0 5
S 2 0 0 0 0 0 0 0 0 0 0 3
T 750 142 3 1 15 9 5 29 13 9 0 0 976
Total 51,329 8967 199 63 1056 599 315 1850 828 621 796 %82 76,304

 

8 etters refer to designations in Table 3.1 and Fig. 3.3.

cs
53

4, CONTROL ROD CALCULATIONS
4.1 Control Rod Geometry

The MSRE control element consists basically of a hollow poison
cylinder, 1.08 in. OD X 0.12 in. thick. Figure 3.2 illustrates those
details of the configuration of the element which are important in de-
termining the reactivity worth of the rods. Three such elements are
used, located in a square array about the core center in the positions
shown in Fig. 3.2. The fourth position of the array is occupied by a

graphite sample assembly.

4.2 Method of Calculation of Rod Reactivity

4.2.1 Total Worth

Several practical simplifications and approximations were necessary
in order to estimate the reactivity worth of the control element described
above. These were made in accordance with the present "state of the art"
in control rod theory, reviewed in ref 17. ©Several of the computational
devices used in the present studies are discussed in this report. The
basic physical assumptions involved in the MSRE design calculations are
as follows:

a. The Gdp03-Als03 poison cylinders are assumed to be black to
thermal neutrons and transparent to neutrons above thermal energies
( 21 ev). The former assumption should be excellent, since the poison
material has an absorption-to-scattering ratio in excess of 10° in the
thermal energy range. The latter assumption is in error, since c¢dt?® and
Gd**7 resonances occur in the epithermal range, and thus have the effect
of producing a "gray region" in aebsorption at these energies. Because
these resonances are closely spaced and have large resonance scattering
components, it is difficult to obtain meaningful estimates of the reso-
nance self-shielding in the posion tube. Since the total epithermal
absorption is expected to be only a fraction of that in the thermal

region, this effect was neglected in the calculations.
54

b. Transmission of thermal neutrons through the INOR-8 thimbles
and across the gap between thimble and cylinder was calculated using
the P-1 approximation. The average absorption-to-scattering ratio for
thermal neutrons traversing the INOR-8 is about 0.1. This means that
diffusion theory should be adequate in calculating the thimble trans-
mission, relative to the other simplifications used in the rod worth
calculations. The basic mathematical relations involve the control ele-
ment blackness, B, which is the probability of capture for thermal neu-

trons incident on the outside surface of the thimble. This eXpression
+ .18
is

F(p,/L)
B=1- B-§TE§7ET— 5 (4.1)

where B is the probability that neutrons entering the gap from the
thimble miss the central poison cylinder, and pg and pg are the inner
and outer radii of the thimble. The function F(x) is defined in terms

of Bessel functions:

 

 

To(x) + a Ko(x) + 22 I1(x) — 2> a K (x)
Flx) = 2D 2D ;
Io(x) + a Ko(x) — jE-Il(X) tT-@a K (x)
~ Tale,/L) "-§%~-%4§—§- To(e, /L)
K1 (o, /L) +-§%—-%45—§— Ko (p /L) .

In the above formulas, D and L are the thermal diffusion coefficient and
diffusion length in the INOR-8. When the central poison tube 1s with-
drawn, B is equal to unity. With the rod in place, Newmach's approxi-
mation for B was used.l? This is based on the assumption that the
angular distribution of neutrons entering the gap is correctly given by

P-1 theory. For a black central cylinder, the resulting expression is

l—-1r + f(r
s =1 (4-2)
55

where

r = pI’Od/pg 2

af
R
}._l
|
K

f(r) =1 —-%— sin™ r -

Equations (4.1) and (4.2) were applied to the calculation of the
rod reactivity worth by the use of a linear extrapolation distance
boundary condition at the control element surface. The extrapolation
distance depends not only on the control element blackness, but also on

20

the relative size of the control region. The expression used was

o

= - 4
Mex = F/am = Mr 3BT g(DO/Atr) ’ (4.3)

where n is the outward normal to the control surface and Ktr is the
transport mean free path for thermal neutrons in the core. As indicated
in Eq. (4.3), the function g(y) depends only on the ratio of the control
radius to the transport mean free path; this function increases from zero
at y = 0 to 0.623 for large y. Reference 19, p 725, gives a plot of the
value of Aex/%tr vs y for black cylinders (B = 1). This was used to de-
termine g(y) for thermal neutrons incident on the MSRE element.

c. The remaining simplifications in the reactivity worth calcula-
tions deal with the geometry of the reactor core and control rcd con-
figuration. These calculations of Bk/k due to insertion of the central
poison cylinders were made using the EQUIPOISE-3 program. Use of this
numerical solution method, together with the practical restriction to
two-dimensional calculations, required that the reactor-rod configuration
be approximated in x-y geometry. The configuration used for a model is
shown in Fig. 4.1l. This figure represents a horizontal cross section of
the core. The basic model is that of a parallelepided with square base.
The control regions are represented by regions of square cross section,
with the perimeter of each square equal to the actual circumference of
the control thimble. Thus the total effective absorptions of the control
regions were equal in the model and the actual element. The overall

transverse dimension of the core was s0 chosen that the total geometric
1
2
4
6
8

10
12
14
16

20
22
24
26
28
30
32
34
36
38
40

42
43

 

56

UNCLASSIFIED
ORNL-DWG 63-7317
AX=MESH SIZE (cm)
' Ax= Ax=|Ax=
1.00 | 154 1 1.00
i
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 4243

Ax = AX =
1.44 5.03

AX =
1.44

Ax =
5.03

 

 

 

-

24.78 in.

n
M
5

Ll

-

n
~
5

L

ro
B
W
>

-

-l
o
-~
3

LEL

 

21.78 in.

S = SAMPLE HOLDER

Fig. 4.1L. Cross Sectional Model of MSRE Core Used in Equipoise
Calculations of Control Rod Worth.
57

buckling in the transverse (x—y) dimension was equal to0 the effective
radial buckling of the actual cylindrical. core. Axial leakage was ac-
counted for by insertion of an effective axial buckling. Because of the
limitation of the calculations to two dimensions, it was necessary to
assume that the layout shown in Fig. 4.1 extended completely through the
active length of the core. In actuality, the maximum penetration dis-
tance for the poison cylinders is slightly less than this length.

The model shown in Fig. 4.1 is based on practical limitations con-
cerning the total number of mesh points in the EQUIPOISE program. The
attempt was made ©o0 adjust the mesh size so that minimum error is oOb-
tained in the central region of the core where the control elements are
located. This is the region of maximum nuclear importance, and also
that of maximum spatial flux variation when the rods are inserted. Repre-
sentation of the reactor transverse boundary as a square is expected to
generate relatively little error in the calculations of the total rod
worth.

The effect of the graphite sample holder was neglected in these
preliminary calculations. Further studies are planned to examine this

effect, and also to improve on some of the above approximations.

4,2.2 Differential Worth

 

Determination of the worth of partially inserted rods is of impor-
tance in setting control rod speeds, in setting limiting rod positions,
and in predicting the required rod motion during stertup and normal op-
eration. In keeping with the practical restriction to two-dimensional
diffusion calculations, a preliminary estimate of the differential worth
was based on an r—z geometry model of the core. The three control ele-
ments were replaced by a single absorber shell, concéentric with the core
axis. The relative change in 8k/k was calculated as a function of the
venetration distance of the shell in the core. The radius and thickness
of the shell were determined by equating the effective surface-to-volume
ratio of the shell to that of the actual elements. The relative change
in 8k/k was then normalized to the total rod worth obtained from the cal-

culations described in Sec 4.2.1.
58

4.3 Results of Calculations

4.3.1 Total Reactivity Worth

 

The total control worth of all three rods inserted all the way
through the core, obtained from the calculations described in the pre-
vious section, i1s listed in Table 4.1. The worth of the individual rods
was also estimated for one of the fuel salts (fuel A), and the results
are included in Table 4.l. When converted to represent fractions of the
total worth of all three rods, these latter results should be nearly
equal for all three fuel salfs. Note that the rod worths are not addi-
tive, since there is appreciable "shadowing" between the rods. Also,
rods 1 and 3 are worth slightly more than rod 2, due to the relatively
greater influence of flux depression, caused by thimbles 1 and 3, on the

position of rod 2.

4.3.2 Differential Worth

 

Results of the r—z calculation for the partially inserted rod bank
are shown in Fig. 4.2. This 1s a plot of the fraction of the total axial
core height to which the rods are inserted. It is important to note that
these results apply to the three rods moving as a unit; effects of moving
a single rod with the others held fixed in some partially inserted posi-

tion are not treated in these calculations.

Table 4.1. Control Rod Worths in the MSRE

 

 

. . Worth
Fuel Rod Configuration (% Sk/k)

A 3 Rods in 5.6
Rod 1 in, rods 2 and 3 out 2ot

Rod 2 in, rods 1 and 3 out 243

Rods 1 and 3 in, rod 2 out bok

Rods 1 and 2 in, rod 3 out 4.1

B 3 Rods in 7.6
C 3 Rods in 5.7

 
FRACTION OF TOTAL WORTH

59

UNCLASSIFIED

ORNL-LR-DWG 57687A

 

 

 

 

 

 

 

 

 

 

 

 

 

1.0 —
0.8 f——t——
0.6 —
0.4 [——- - o
0.2 ——- -
0
0 0.2 0.4 0.6 0.8

Fig. 4.2.

FRACTION OF LENGTH INSERTED

BEffect of Partially Inserted Rods.

1.0
60

5. CORE TEMPERATURES

When the reactor is operated at power there is a wide range of
temperatures in the graphite and fuel in the core. The temperature dis-
tribution cannot be observed experimentally, but some information on the
distribution is necessary for the analysis of reactivity changes during
power operation. The method by which MSRE core temperatures were pre-
dicted is described in detail in ref 21. The calculational method com-
bines the flow distribution in a hydraulic model of the core with the
power—density distribution predicted for the nuclear model. The nu-
merical results presented here were computed with the power—density dis-
tribution appropriate for fuel C, but calculations for fuels A and B gave
practically the same results. (The numerical results in ref 17 were
computed for fuel B, with a slightly different model from that used in

the calculations whose results are reported here.)

5.1 Overall Temperature Distributions at Power

The temperature distribution in the MSRE core can be regarded as a
composite of the overall temperature distributions in the fuel and moder-
ator, upon which are superimposed local temperature variations within
individual fuel channels and moderator stringers. The overall tempera-
ture distritutions are determined by the gross distribution of the power
density and the fuel flow pattern. The local variations depend on the
fluid flow and heat transfer conditions associated with the individual
channels. Since the overall temperature distributions contribute most
to the temperature-induced reactivity effects, these are described in
detail. Details of local temperature variations are considered only
where such consideration is essential to evaluating the overall distri-

bution.

5.1.1 Reactor Regions

 

A significant fraction of the nuclear power produced in this re-
actor is generated in the fuel-containing regions of the reactor vessel

outside the fuel-graphite matrix which forms the main portion of the
61

core. These regions contribute to the total temperature rise of the
fuel as it passes through the reactor and must, therefore, be included
in the core temperature calculations. The 20-region model of the re-
actor (see Fig. 3.3 and Table 3.1) used for the nuclear calculations was
also used to evaluate the core temperatures. The regions designated J,
L, M, N, and T were combined to form the main portion of the core, and
the remaining fuel-bearing regions were treated separately.

Hydraulic studies on one-fifth-scale and full-scale models of the
reactor vessel showed that the vertical fuel velocity varies with radial
position in the main portion of the core. The velocity is nearly con-
stant over a large portion of the core, but higher velocities occur near
the axis and near the ocuter radius. To allow for this, three radial
regions were used in calculating the temperature distributions in the

main portion of the core.

5.1.2 Fuel Temperatures

 

Nearly all of the nuclear power is removed from the reactor vessel
by the circulating fuel stream, so that the fuel temperature rise and
flow rate define the operating power level of the reactor. The tempera-
ture calculations were based on a nominal power level of 10 Mw, with a
50°F temperature rise across the reactor and a fuel flow rate of 1200
gpm. The reactor inlet and outlet temperatures were set at 1175°F and
1225°F, respectively. These temperatures permit presentation of the
distributions in abolute terms, but the shape of the distributions is
unaffected by this choice.

Peripheral Regions. — Approximately 14% of the reactor power is

 

produced in or transferred to the fuel~bearing regions surrounding the
main portion of the core. Since the temperature rise of the fuel, as
it passes through any one of these regions, is small compared with the
rise in the main portion of the core, no attempt was made to evaluate,
exactly, the fuel temperature distributions in each peripheral region.
Instead, the mean temperature rise for each region was calculated from
the fraction of the total power produced in the region and the fraction

of the total flow rate through it. The inlet temperature for each region
62

was assumed constant at the mixed-mean outlet temperature of the pre-
ceding region. Fach peripheral region was assigned an approximate bulk
average temperature midway between the inlet and outlet temperatures.
Table 5.1 summarizes the flow rates, heat rates, and fuel temperatures
in the various reactor regions.

Main Portion of the Core. — The wide variations in fuel tempera-

 

ture, both radially and axially, in the main part of the core necessitate

a more detailed description of the temperature distribution.

Table 5.1. Flow Rates, Heat Rates, and Temperatures
in Reactor Regions®

 

 

Region Flow Heat RateP Temperagure RiseP Average ?emperaturec
(gom) (ko) (°F) (°F)
D 1142 355.3 1.9 1225.2
E 1142 115.8 Q.6 1224.0
F 1200 378.2 1.9 1176.0
G 1142 g2.7 0.4 1223.5
H 1142 95.7 0.5 1223.0
J 1142 g121.3 4247 d
L 17 59.3 20.9 d
M 1183 223.0 1.1 d
N 1200 84.1 0.4 d
0 1200 89.9 0.4 1178.4
P 1200 252.8 1.3 1177.6
Q 17 3.9 1.4 1201.0
R 17 0.7 0.2 1200.2
S 17 0.5 G.2 1200.0
T 41 136.9 20.0 d

 

aRegions not containing fluel are excluded.

bAt 10 Mw. Includes heat transferred to the fuel from adjoining
regions.
CWwith T, = 1175°F, T__. = 1225°F.
in ou

t
dActual temperature distribution calculated for this region. See
text.
63

The average temperature of the fuel in a channel at any axial posi-
tion is equal to the channel inlet temperature plus a rise proportional
to the sum of the heat generated in the fuel and that transferred to it
from the adjacent graphite as the fuel moves from the channel inlet to
the specified point. The heat produced in the fuel follows very closely
the radial and axial variation of the fission power density. Since the
heat production in the graphite is small, no great error is introduced
by assigning the same spatial distribution to this term. Then, if
axial heat transfer in the graphite is neglected, the net rate of heat
addition to the fuel has the shape of the fuel power density. The fuel
temperature rise is inversely proportional to the volumetric heat ca-

pacity and velocity. Thus

Tf(r,z) = Tf(z =0) + f(‘) w

Pf(r,z) dz (5.1)
where Qf is an equivalent specific power which includes the heat added

to the fuel from the graphite. The channel inlet temperature, Tf(z = 0),
is assumed constant for all channels, and its value is greater than the
reactor inlet temperature because of the peripheral regions through
which the fuel passes before it reaches the inlet to the main part of

the core. The volumetric heat capacity, (pcp)f, is assumed constant, and
only radial variations in the fuel velocity, u, are considered. It is
further assumed that the radial and axial variations in the power-density

distribution are separable:

P(r,z) = A(r) B(z) . (5.2)

Then

(Qf)m A(r) z
(pcp)f u(r) J; B(z) dz . (5.3)

Tf(r,z) = Tf(z = 0) +
If the sine approximation for the axial variation of the power density
(Fig. 3.10) is substituted for B(z), Eq. (5.3) becomes

(z =0) + Kifl‘%{cos o — cos [?e?jli'é’” (z +5.72)N> . (5.4)

Tf(r,z) = T,
64
In this expression, k is a collection of constants,

78.15 (Qf)m
J
T (pcp)f

 

(5.5)

K=

and

0 (0 + 5.72) . (5.6)

_ T
78.15
The limits within which Eq. (5.4) is applicable are the lower and

upper boundaries of the main part of the core, namely, 0 = z = 64.6 in.
It is clear from this that the shape of the axial temperature distribu-
tion in the fuel in any channel is proportional to that of the central
portion of the general curve [1 — cos B]. The axial distribution for the
hottest channel in the MSRE is shown in Fig. 5.1, where it is used to
provide a reference for the axial temperature distribution in the graphite.
The radial distribution of the fuel temperature near the core mid=-
plane is shown in Fig. 5.2 for the reference conditions at 10 Mw. This
distribution includes the effects of the distorted power-density distri-
bution (Fig. 3.11) and the radial variations in fuel velocity. At the
reference conditions the main core inlet temperature is 1179°F and the
mixed-mean temperature leaving that region is 1222°F. The additional
heat required to raise the reactor outlet temperature to 1225°F is
produced in the peripheral regions above the main part of the core. The
general shape of the radial temperature profile is the same at all axial

positions in the main portion of the core,

5.1.3 Graphite Temperature

Since &11 of the heat produced in the graphite must be transferred
to the circulating fuel for removal from the reactor, the steady-state
temperature of the graphite is higher than that of the fuel in the ad-
jacent channels. This temperature difference provides a convenient
means of evaluating the overall graphite temperature distribution; that
is, by adding the local graphite-fuel temperature differences to the

previously calculated fuel temperature distribution.
65

UNCLASSIFIED
ORNL DWG. 63.8164

1300

1280

1260

1240

1220

TEMPERATURE (°F)

1200

1180

 

1160
0 10 20 30 4o 50 0 70

AXTAL POSITION (in.)

Fig. 5.1. Axial Temperature Profiles in Hottest Channel and Adja-
cent Graphite Stringer.

Nearly all the graphite in the MSRE (98.7%) is contained in the
regions which are combined to form the main portion of the core. Since
the remainder would have only a small effect on the system character~
istics, the graphite temperature distrivbution was evaluated for the main
part of the core only.

Local Graphite-Fuel Temperature Differences. — In order to evaluate

 

the local graphite-fuel temperature differences, the core was considered
in terms of a number of unit cells, each containing fuel and graphite.

Axial heat transfer in the graphite was neglected and radially uniform
1280

1280

1270

1260

1250

1240

1230

TEMPERATURE (°F)

1220

1210

1200

1190

1180

Fig. 5.2.

 

66

UNCLASSIFIED
ORNL DWG. 63-8165

5 0 15 20 25 30
RADIUS (:n.)

Radial Temperature Profiles Near Core Midplane.
67

heat generation terms were assumed for the fuel and graphite in each
cell. In general, only the difference between the mean temperatures of
the graphite stringers and fuel channels was calculated as a function of
radial and axial position.

The difference between the mean graphite and fuel temperatures in a

unit cell can be broken down into three parts:

1. +the Poppendiek effect, which causes the fuel near the wall of a

channel to be hotter than the mean for the channel;

2. the temperature drop due to the contact resistance at the graphite-

fuel interface; and

3. the temperature drop in the graphite resulting from the internal

heat source.

When a fluid with an internal heat source flows through a channel,
the lower velocity of the flulid near the channel wall allows that part
of the fluid to reach a temperature above the average for the channel.
This effect 1s increased when heat is transferred into the fluid through
the channel walls, as is the case in the MSRE. Equations have been
developedzz’23 to evaluate the difference between the temperature of the
fluid at the wall and the average for the channel. These equations were
applied to the reactor, assuming laminar flow in all of the channels.
This tends to overestimate slightly the temperature rise in the few
channels where the flow may be turbulent.

No allowance was made for a temperature difference due to the con-
tact resistance at the graphite-fuel interface in these calculations. An
estimate of this resistance was made by assuming a l-mil gap, filled with
helium, between the graphite and fuel. This rather pessimistic assump-
tion led to a temperature difference which was very small compared with
the total.

The difference between the mean temperature of a graphite stringer
and the surface temperature was calculated for two simplified geometries:
a cylinder with a cross-sectional area equal to that of a stringer and a
slab with a half thickness equal to the normal distance from the center

of a stringer to the surface of a fuel channel. The value assigned to
68

the graphite was obtained by linear interpolations between these results
on the basis of surface-to-volume ratio.

The local graphite-fuel temperature difference was calculated as a
function of position in the core for three degrees of fuel soakup in the
graphite: 0, 0.5, and 2.0 vol % of the graphite. In each case, uniform
distribution of the fuel within the graphite was assumed. Table 5.2
gives the maximum difference between mean stringer and mean fuel channel
temperatures for the three conditions. The distribution of the fuel
soaked into the graphite has little effect on the total temperature dif-
ference. For 2 vol % permeation, concentration of the fuel near the

outer surface of the graphite increased the AT by 2°F.

Table 5.2. Maximum Values of Graphite-Fuel Temperature
Difference as a Function of Fuel Permeation

 

Fuel Permeation

 

 

(vol % of graphite) 0 0.5 2.0

Graphite-fuel temperature difference (°F)
Poppendiek effect in fuel 55.7 58.3 65 4
Graphite temperature drop 5.5 6.7 9.8
Total 6L.2 65.0 75.2

 

Overall Distribution. — Since the Poppendiek effect and the tempera-

 

ture drop through the graphite are both influenced by the heat generated
in the graphite, the spatial distribution of the graphite temperature is
affected by the graphite power-density distribution. The graphite power
density is treated in detail in Sec. 1l4.1, for fuel C with no fuel per-
meation of the graphite. The distribution shown in Figs. l4.1 and 14.2
was used to evaluate the graphite temperatures in Figs. 5.1 and 5.2.
Figure 5.1 shows the axial distribution of the mean temperature in a
graphite stringer adjacent to the hottest fuel channel. Because of the
continuously increasing fuel temperature, the axial maximum in the graph-

ite temperature occurs somewhat above the midplane of the core. The
69

overall radial distribution of the graphite temperature near the core

midplane is shown in Fig. 5.2.

5.2 Average Temperatures at Power

The concept of average temperatures has a number of useful applica-
tions in operating and in describing and analyzing the operation of a
reactor. The bulk average temperature, particularly of the fuel, is
essential for all material balance and inventory calculations. The nu-
clear average temperatures of the fuel and graphite, along with their
respective ftemperature coefficients of reactivity, provide a convenient
means of assessing the reactivity effects associated with temperature
changes. Both the bulk average and nuclear average temperatures can be
described in terms of the reactor inlet and outlet temperatures, but,
because of complexities in the reactor geometry and the temperature dis-

tributions, the numerical relations are not obvious.

5.2.1 Bulk Average Temperatures

Bulk average temperatures (f) were obtained by weighting the overall
tempersture distributions with the volume fraction of salt or graphite
and integrating over the volume of the reactor.

The fuel bulk average temperature was calculated for the fuel with-
in the reactor vessel shell. (The contents of the inlet flow distributor
and the outlet nozzle were not included.) A large fraction of the salt
in the vessel is in the peripheral regions, where detailed temperature
distributions were not calculated. In computing the average for the re-
actor, average temperatures shown in Table 5.1 were used for these re~
gions. The average temperature in the main part of the core was computed
by numerical integration of the calculated temperature distribution. At
the reference condition (1175°F inlet, 1225°F outlet), the fuel bulk
average temperature for all of the fuel in the reactor vessel was com-
puted to be 1199.5°F. Thus, assuming linear relationships, the fuel

bulk average temperature is given by

T, = Tin + O.49(Tout — Tin) . (5.7)
70

Only the graphite in the main portion of the core had to be included
in the calculation of the graphite bulk average temperature, since this
region contains 98.7% of all the graphite. For fuel C with no permeation,
the bulk average graphite temperature at the 10-Mw reference condition is
1229°F. This temperature increases with increasing permeation of the
graphite by fuel; earlier calculations of this effect showed a 4.4°F in-
crease in graphite bulk average temperature as the fuel permeation was

increased from O to 2%.

5.2.2 Nuclear Average Temperatures

 

The nuclear average temperatures (T*) of the fuel and graphite were
calculated in the same way as the bulk average temperatures, except that
the temperature distributions were weighted with their respective nuclear
importances as well as with the amounts of material. The temperature
weighting functions described in Sec. 3.7.2 include all of the nuclear
average weighting factors. These functions were applied to the fuel
temperature distribution and resulted in a fuel nuclear average tempera-
ture of 1211°F when the inlet temperature is 1175°F and the outlet is
1225°F, With the same inlet and outlet temperatures and no fuel per-
meation, the graphite nuclear average temperature was calculated to be
1255°F. (With 2% permeation the calculated graphite nuclear average
temperature would be higher by 7°F.)

The relations between inlet and outlet temperatures, nuclear average
temperatures, and power are all practically linear so that the following

approximations can be made:

out = iy + 50 P, (5.8)
* Tout * Tin
Tp=|—————|+L1P=T_, —1.4P, (5.9)
Tout i Tin
T; = |———— ] +55P=1T . +3.0P, (5.10)

where the temperatures are in °F and P is the power in Mw.
71
5.3 Power Coefficient of Reactivity

Whenever the reactor power i1s raised, temperatures of the fuel and
graphite throughout the core must diverge. As shown in the preceding
sections, the shape of the temperature distributions at power and the
relations between inlet, outlet, and average temperatures are inherent
characteristics of the system which are not subject to external control.
The relation of the temperature distribution at high power to the temper-
ature of the zero-power, isothermal reactor, on the other hand, can be
readily contreclled by the use of the control rods. When the reactivity
effect of the rod poisoning is changed, the entire temperature distribu-
tion 1is forced to shift up or down as required to produce an exactly
compensating reactivity effect.* Normally the rods are adjusted concur-
rently with a power change, to obtain a desired temperature behavior (to
hold the outlet temperature constant, for example). The ratio of the
change in rod peisoning effect, required to obtain the desired result, to
the power change is then called the power coefficient of reactivity.**

Because of the way in which the nuclear average temperature 1s de-
fined, the effect of fuel temperature changes on reactivity is proportional
to the change in the nuclear average temperature of the fuel. Reactivity
effects of graphite temperature changes are similarly described by the
change in graphite nuclear average temperature. The net effect on reac-

tivity of simultanecus changes in fuel and graphite temperature 1s

LK * *
= AT+ 0 AT (5.11)

where Q% and ag are the fuel and graphite temperature coefficients of

reactivity. The change in rod polsoning is equal in both sign and

magnitude to the reactivity effect of the temperature changes. (If the

 

*This statement and the discussion which follows refer to adjust-
ments in rod positions and temperatures which are made in times too
short for significant changes in other reactivity effects, such as xenon
poisoning.

**Note that the power coefficient does not have a single value, as
does a coefficient like the temperature coefficient, because its value
depends on the arbitrary prescription of temperature variation with
power.,
72

effect of the desired temperature change is to decrease the reactivity,
the rod poisoning must be decreased an equal amount to produce the tem-
perature change.) Thus Eq. (5.11) can be used to evaluate the power
coefficient of reactivity. When Egs. (5.9) and (5.10) for Tg and Tg are
substituted, Eq. (5.11) becomes either

AR
—— .(x—.a »
= (Qé + a%)amout + (3.0 : 1.4 f)AP (5.12)
or
T + T
Ak out in
= = —_ T OO e . .
= (o% + a%)a,( 5 ) + (5.5 - 1.1 f)AP (5.13)
If T, 18 held constant during power changes (i.e., if AT L 18 Zero),
the power ccoefficient is
Ak/k
= 3,008 — 1.4 ., .
—5 3.0 . 1.4 ap (5.14)

Similarly, if the mean of the inlet and outlet temperatures is to be held

constant,

Nk /k
—_ . a . e
A 5.5 ag + 1.1 - (5.15)

 

If there is no adjustment of reactivity by the control rods, the
temperatures must change with power level in such a way that Ak/k is
zero. (This mode of operation might be called "hands-off" operation,
because the rods are not moved.) The power coefficient of reactivity in
this case is by definition equal to zero. The change in temperatures

from the zero-power temperature, Tg, is found from

ékE = o ATY + cngT; =0, (5.16)
0L (T — Tg) = —G%(T;-— Ty) « (5.17)
73

In conjunction with (5.9) and (5.10), this leads to

 

o Yoty aé
r - -0 O, + aé P, (5.18)
T = Ty + ;i:iiff__ P (5.19)
g Q% + Q% ?
3.0 0 - 1.4«

o x
T " g

Note that the changes with power depend on the values of af and ag’ hence
on the type of fuel in the reactor.

Thus it has been shown that the power ccefficient of reactivity de-
pends on the type of fuel and also on the chosen mode of control. Table
5.3 lists power coefficients of reactivity for three fuels and three
modes of control. Also shown are temperatures which would be reached at

10 Mw if the zero-power temperature were 1200°F.

Table 5.3. Power Coefficients of Reactivity
and Temperatures at 10 Mw

 

 

 

Power Coefficient Temperaturesa
o
Mode of Control (% Bk/k) Mo ( F)
Fuel A Fuel B Fuel C T T, ™
out in f g
Constant Tout —0.006 -0.008 —0.006 1200 1150 118 1230

T o+ T,
COnstant——‘?flz—m —0.022 —-0.033 —0.024 1225 1175 1211 1255

"Hands-off"
Fuel A O 1191 1141 1177 1221
Fuel B 0 1192 1142 1178 1222
Fuel C Q 1191 1141 1177 1221

 

“System isothermal at 1200°F at zero power.
T4

©. DELAYED NEUTRONS

The kinetics of the fission chain reaction in the MSRE are influ-
enced by the transport of the delayed neutron precursors. An exact
mathematical description of the kinetics would necessarily include, in
the equation for the precursor concentrations, terms describing the
movement of the precursors through the core and the external loop. In
order to render the system of kinetics equations manageable, the trans-
port term was omitted from the equations used in MSRE analysis (see
Sec 12.4.1). Thus the equations which were used were of the same form
as those for a fixed-fuel reactor. Some allowance for the transport of
the delayed neutron precursors was made by substituting "effective"
values for delayed neutron yields in place of the actual yields. The
kinetics calculations used "effective" yields equal to the contributions
of the delayed neutron groups to the chain reaction under steady-state

conditions.
6.1 Method of Calculation

In the calculation of the effective contributions during steady
power coperation, nonleakage probabilities were used as the measure of
the relative importance of prompt and delayed neutrons. Spatial distri-
butions for the precursors during steady operation were calculated and
were used, together with the energy distribution, in computing nonleakage
probabilities.?%

The MSRE core was approximated by a cylinder with the flux (and
precursor production) vanishing at the surfaces. Flow was assumed to be
uniformly distributed. With these assumptions, the spatial distribution
of precursors of a particular group in the core was found to be of the

form

 

-A\t_z/H
+ [Sl sin %; - 52 cos-%?— + Sse ¢ ] Jo (?}gf) . (6.1)

(See Sec 6.4 for definition of symbols.)
75

For the purpose of computing nonleakage probabilities, the spatial

distribution of each group was approximated by a series:

 

v o jmr ’IITZ
s(r,z) = L Y Amdo <—R—> sin(é ) . (6.2)

m=1 n=1

The coefficients, Amn’ were evaluated from the analytical expression for
S(r,z). The nonleakage probability for a group of neutrons was then
computed by assigning a nonleakage probabllity to each term in the series

equal to
(6.3)

where

3N\ ' 2
2 [ B nr
BZ ( = ) +< H) . (6.4)
The energy distribution of each delayed neutron group was taken into

account by using an appropriate value for the age, 7, in the expression

for the nonleakage probability.

6.2 Data Used in Computation

6.2.1l Precursor Yields and Half-ILives

The data of Keepin, Wimett, and Zeigler for fission of U?3° by

thermal neutrons were used.?’ Values are given in Table 6.1.

6.2.2 Neutron Energies

Mean energies shown in Table 6.1 for the first five groups are
values recommended by Goldstein.?® A mean energy of 0.5 Mev was assumed

for the shortest-lived group, in the absence of experimental values.

6.2.3 Age

Prompt neutrons, with an initial mean energy of 2 Mev, have an age

to thermal energies in the MSRE core of 292 cm? (this value was computed
by a MODRIC multigroup diffusion calculation). The age of neutrons from
the different sources was assumed to be proportional to the lethargy;

that is,

log (E,/E.. )

= v T . (6.5)
i ~ log (Epr/Eth) pr

T

Computed values of T, are given in Table 6.1,

Table 6.1. Delayed Neutron Data

 

Group 1 2 3 4 5 6
Precursors half-life (sec) 55.7 22.7 6422 2.30 0.61 0.23
Fractional yield of 2.11 14.02 12.54 25.28 7 40 2.70

precursors, 1048,
(neutrons per
104 neutrons)
Neutron mean energy (Mev) 0.25 0.46 0.40 0.45 0.52 0.5

Neutron age in MSRE (ecm®) 256 266 264 266 269 268

 

6.2.4 MSRE Dimensions

 

The computation of B* for the nonleakage probabilities used R = 27.75
in. and H = 68.9 in. The volume of fuel within these boundaries is 25.0
ft2?. At a circulation rate of 1200 gpm, residence times are 9.37 sec in

the core and 16.45 sec in the external loop. A thermal neutron diffusion

length appropriate for a core with highly (~93%) enriched uranium and no

thorium was used (L? = 210 cm?®).

6.3 Results of Computation

The core residence time, in units of precursor half-lives, ranges
from 0.2 to 4l. Because of this, the shapes of the delayed neutron
sources in the core vary widely, as shown in Fig. 6.1, when the fuel is

circulating. (The source strength is normalized to a production rate of
77

UNCLASSIFIED
ORNL-LR-DWG 73620R

 

 

 

 

(x1079)
2.8 l
GROUP f'/z (sec)
{ 56
> 4 2 23
' 3 o.2
4 2.3
5 0.6
>0 o J 0.2

(SEE FIG 6.2 FOR GROUP
4 DISTRIBUTION)

 

1.6

.2 / / \
)
0.8 / S \
I .
. 1

O 0.2 0.4 0.6 0.8 {.0
RELATIVE HEIGHT

Fig. 6.1. Axial Distribution of Delayed Neutron Source Densities
in an MSRE Fuel Channel. Fuel circulating at 1200 gpm.

 

 

 

 

RELATIVE DELAYED NEUTRON SOURCE DENSITY (cm~—3)

 

N

 

 

 

 

 

 

 
78

1 neutron/sec in the reactor.) Figure 6.2 compares source distributions
for one group under circulating and static conditions. The reduction in
the number of neutrons emitted in the core is indicated by the difference
in areas under the curves. A greater probability of leakage under circu-
lating conditions is suggested by the shift in the distribution, which
reduces the average distance to the outside of the core.

Table 6.2 summarizes important calculated quantities for each group.
The total effective fraction of delayed neutrons is 0.00362 at a 1200-gpm
circulation rate and is 0.00666 in a static core. The total yield of

precursors is 0,00641.

Table 6.2. Delayed Neutrons in MSRE at Steady State

 

Group 1 2 3 4 5 6
Circulating:
0, 0.36 0.37 0.46 Q.71 0.96 0.99
P, /P 0.68 0.72 0.87 0,91  1.00  1.03
1’ pr
*
B:/Bs 0.25 0.27  0.40 0.e7  0.97  1.02
104B§ 0.52 3.73 4,99 16.98 7.18 2.77
Statics
P, /Ppy 1.06  1.04  1.04  1.04 1.03  1.03
1o4a§ 2.23  1l4.57 13.07 26.28 7 .66 2.80

 

6.4 Nomenclature for Delayed Neutron Calculations

Amn Coefficient in series representation of S
B? Geometric buckling

B Initial mean neutron energy

Eth Thermal neutron energy

H Height of core
79

UNCLASSIFIED
ORNL -LR-DWG 73621

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(x1079)

o 7 TN\

5 5 / \

> / \

% /STATIC \

S, / A

O / 7\

/ / \

S 3 / \

; / /lRCULATlNG \

o 2 / / \

< // \

R \

g // / \

5 \

o V \
O

O 0.2 0.4 0.6 0.8 1.0
RELATIVE HEIGHT

Fig. 6.2. Effect of Fuel Circulation on Axial Distribution of
Source Density of Group 4 Delayed Neutrons. TFuel circulating at 1200
gpm.
Jo

80

Bessel function of first kind

mth root of Jg(x) = O

Neutron diffusion length

Nonleakage probability

Radial distance from core axis

Qutside radius of core

Neutron source per unit volume of fuel
Residence time of fuel in core

Axial distance from bottom of core
Fractional yield of neutrons of group 1
Effective fraction of neutrons of group i
Fraction of group 1 emitted in core
Precursor decay constant

Neutron age
81

7. POISONING DUE TO XENON~135

Changes in the concentration of Xel3? in the core produce changes
in reactivity that are about as large as those from all other factors
combined.* In order to use the net reactivity behavior during power oOp-
eration to observe changes in such factors as burnup, fuel composition,
and graphite permeation, the xenon poisoning must be calculated quite ac-

curately from the power history.

7.1 Distribution of Iodine and Xenon

The first step in calculating the xenon poisoning is to calculate
the behavior and distribution of I'3% in all parts of the reactor. (This
information is, of course, necessary because most of the Xel?? is formed
by decay of I135,) From this one proceeds to calculate the concentration
of Xel?? in the fuel salt, in various parts of the graphite, and elsewhere
throughout the reactor.

A number of production and destruction mechanisms for both xenon and
iodine which involwve the chemical and physical behavior of the isotopes
can be postulated and described mathematically, at least in principle.
Some of these mechanisms can be eliminated immediately as insignificant,
while others can be shown to be highly significant., There remain, how-
ever, a number of mechanisms whose significance probably cannot be evalu-
ated until after the reacfior hag been operated and the operation carefully

analyzed.

7.1.1 Sources of Iodine and Xenon in Fuel

The only significant source of T135 in the circulating fuel is the
direct production from fission; the iodine precursors in this chain have
half-lives t00 short to have any significant effect.

The principal sources of Xel33 in the fuel are the decay of I'3? in
the fuel and direct production from fission., However, a third potential

source exists 1f iodine is trapped on metal surfaces in the primary loop,

 

*See list of reactivity shim requirements, Table 9.1.
82

and the xenon formed by the decay of this iodine does not immediately re-
turn to the circulating stream, In this case, the xenon must be treated
separately from that produced by decay of ilodine in the circulating stream,
because the delay in the return of the xenon to circulation changes the

destruction probabilities.

7.1.2 Removal of Iodine and Xenon from IFuel

The principal removal mechanism for iodine is radloactive decay.
However, consideration must also be given to the possibility of iodine
migration into the graphite and to metal surfaces, If these processes
occur, they will modify the overall xenon behavior. Volatilization or
stripping of iodine in the pump bowl and destruction by neutron capture
are both regarded as insignificant.

There are a number of competing mechanisms for the removal of Xenon
from the fuel., The most important of these are stripping in the pump
bowl and migration to the graphite. Of lesser importance, but still sig-
nificant, are decay of and neutron capture by xenon in the fuel itself.

Decay of xenon trapped on metal surfaces must also be considered.

7.1.3 Sources of Iodine and Xenon in Graphite

Unless permeation of the graphite by fuel occurs, the only source of
iodine in the graphite is migration from the fuel. If fuel permeation
does occur, the direct production of iodine in the graphite by fission
must be considered.

The major source of xenon in the graphite is migration from the
fuel., Other sources which may or may not be important are decay of iodine
in the graphite and direct production from the fission of fuel soaked into

the graphite.

7.1.4 Removal of Iodine and Xenon from Graphite

Because of the low neutron absorption cross section of 1135, the
only mechanism for its removal from the graphite is by radiocactive decay
to Xel3?, 1In the case of xenon, both decay and neutron capture are im-

portant.
83

In all cases where the transfer of an isotope from one medium to
another is involved, only the net transfer need be considered; therefore,
these can be regarded as one-way processes, with the direction of trans-

fer being indicated by the sign of the term.

7.1.5 Detailed Calculations

 

A get of simultaneous differential equations has been developed to
describe, in mathematical terms, all of the mechanisms discussed above,
These equationg also take into account radial and axial variations in the
fuel flow pattern throughout the core and within individual fuel channels,
as well as the owverall distribution of the neutron flux. The equations
can, theoretically at least, be programmed for solution by a large com-
puter to give detailed spatial distributions of iodine and xenon in the
core. An actual solution of the equations requires detalled information
about a number of the chemical and physical parameters of the system,
vhich is not currently available. However, some qualitative comments can
be made about the nature of the results that can be expected.

The digtribution of xenon in the fuel within the core will probably
be relatively uniform, because of the mixing in the external loop and the
fact that most of the xenon is produced from iodine that was formed in
earlier passes through the core. Some depletion may occur along the re-
gion near the centerline of the core, because of the higher neutron flux
and because the higher fuel turbulence facilitates transfer to the graph-
ite. However, the mixed-mean concentration at the core outlet must be
somewhat higher than at the inlet to allow for stripping in the pump bowl
and decay in the external loop.

The overall radial distribution of xenon in the graphite may exhibit
a minimum, due to burnout, at the radius corresponding to the maximum in
the thermal flux. This minimum is reinforced by the fact that the flux
maximum occurs in the low-velocity region of the core, where transfer
from the fuel is slowest. In the axial direction, the highest xenon con-
centrations will probably occur near the inlet to the core; the neutron
flux is low in this region, and turbulence near the entrance of the fuel
channels tends to promote transfer from the fuel. This distribution may,
however, be significantly affected by axial diffusion in the graphite

stringers.
84

7.1.6 Approximate Analysis

In order to provide a bagis for estimating the reactivity effect of
Xel35 in the reactor, an approximate analysis of the steady-state xenon
distribution was made.?’ For this approach, the scope of the problem was
reduced to include only the major behavior mechanisms. It was assumed
that all of the iodine remains with the fuel in which it is produced;
this completely eliminated iodine from the steady-state mathematical ex-
pressions. The core was divided into four radial regions on the basis
of fuel velocity, and an overall mass-transfer coefficient was calculated
for xenon transfer from fuel to graphite in each region. Axial varia-
tiong in xenon concentration in both fuel and graphite were neglected.
Average xenon burnup rates were calculated on the basis of the average
thermal neutron flux in the reactor. Fuel permeation of the graphite was
neglected.

Because of uncertainties in the physical parameters, the xenon be-
havior was calculated for relatively wide ranges of the following vari-
ables:

1. Stripping efficiency in the pump bowl. The ultimate poisoning
effect of the xenon is most sensitive to this quantity, which also has
the greatest degree of uncertainty associated with it. The entire range,
from O to 100% efficiency, was considered.

2. Fuel-to-graphite mass-transfer coefficient. This quantity can
be calculated with reasonable confidence but the xenon poisoning is rel-
atively sensitive to the results. Values differing by a factor of 2 from
the expected value were considered. '

3., Diffusion coefficient for xenon in graphite., The uncertainty
associated with this quantity is quite large but its effect on the poi-
soning, within the range of expected values, is small., Two values, dif-
fering by a factor of 100, were considered.

The xenon poisoning is determined primarily by tThe xenon which dif-
fuses into the graphite. Nearly all of the xenon that does not migrate
to the graphite is stripped out in the pump bowl, leaving only a small
fraction (<1% of the total) to be destroyed by neutron absorption or

radioactive decay in the fuel. The xenon migration to the graphite is
85

not significantly affected by the choice of fuel, because all three fuels
have similar physical properties. However, the choice of fuel has some
effect on the poisoning, because this determines the flux level in the
reactor at design power (see Table 3.5). This is illustrated by the fact
that 49% of the Xel2” that enters the graphite is destroyed by neutron
absorption at the flux level associlated with 10-Mw operation with fuels
A and C, whereas 62% is destroyed by this mechanism with fuel B.

Figure 7.1 illustrates the effect of stripping efficiency on the
fraction of Xel?? produced in the reactor which migrates to the graphite.
This figure also shows the effect of changing the diffusion coefficient,
D, in the graphite by a factor of 100. It is expected that the average
value of the graphite diffusion coefficient in the MSRE will be between
the values shown. Figure 7.2 shows the effects of increasing and de-
creasing the mass-transfer coefficient, K, by a factor of 2 from the ex-
pected value, Kg. The curves in Fig. 7.2 are based on the higher of the

two graphite diffusion coefficients,

7.2 Reactivity Effects of Xenon-135

Once the spatial distribution of xenon in circulation and that re-
tained on the graphite has been calculated, it is possible to relate theo-
retically the xenon reactivity effect to the poison distribution. This
relation is most conveniently expressed in terms of a reactivity coeffi-
cient and an importance-averaged xenon concentration.?® The method for
calculating these quantities is similar to that used in obtaining the re-
activity effect of temperature (Sec 3.7). In the case of xenon, however,
the weight function for the poison concentration is proportional to the

product ¢§¢2:

 

* a *
. j;raphite iy, 922 av, + Joars Tge02%2 avy :
Ny, = T % s 7.1)
reactor b202 AV

*
where Nke is the importance-averaged concentration per unit reactor vol-
ume , and N%e and Nie are the local concentrations, per unit volumes of

*
graphite and salt, respectively. The quantity NXe 1s also the uniform
86

UNCLASSIFIED
ORNL DWG. 63-8166

FRACTION OF Xe'l>” MIGRATING TO GRAPHITE (%)

 

0 20 40 &0 80 100
STRIPPING EFFICIENCY (%)

Fig. 7.1, Effect of Stripping Efficiency and Graphite Diffusion
Coefficient on Xenon-135 Migration to Graphite.
87

UNCLASSIFIED
ORNL DWG. 63-8167

100

80

70

Lo -

FRACTION OF Xe > MIGRATING TO GRAPHITE (%)

30

20

 

10
Q 20 ho 60 80 100

STRIPPING EFFICIENCY (%)

Fig. 7.2. Effect of Mass-Transfer Coefficient on Xencon-135 Migra-
tion to Graphite.
88

equilibrium concentration of xenon in the reactor, which produces the
same reactivity change as the actual distribution. In relating N;é to
the total reactivity change, it is convenient to define a third quantity,
the effective thermal poison fraction, P;e. This is the number of neu-
trons absorbed in xenon per neutron absorbed in U235, weighted with re-

spect 10 neutron importance :

 

*
P* “Xe j;eactor P2%2 AV N* (7.2)
Xe - | (Nps0256501 + Nasa3500s) av 2 '
resctor ‘25017 F1¥L 25 2%2
where
Nps5 = concentration of U235, per unit reactor volume,

a{fg = 7Je35 microscopic absorption cross section for fast (1) and
thermal (2) neutrons,

a.

Yo xenon thermal absorption cross section.

*
The relation between total xenon reactivity and PXe is given by28

- _ P, . (7.3)

* *
(8k) j;Eactor (N250%%0101 + Na505°0292) AV *
oK * _
Xe (VEpp 9101 + vEFp9105) AV Xe

j;eactor

Thus, if knowledge of the xenon distribution can be obtained from separate
experiments or calculations, the calculation of the total Xenon reactivity
involves three steps: (a) obtaining N;é from Eq. (7.1), (b) calculating
P;e from N;e by use of Eq. (7.2), and (c) calculating 8k/k from Eq. (7.3).
Alternatively, the above relations may be used in a reverse manner if
knowledge of the distribution is inferred from reactivity measurements

at power.

The numerical values of the xenon reactivity coefficients obtained
for the three fuels under consideration are given in Table 3.5. Both the
coefficients relating dk/k to the poison fraction and to the importance-
averaged xenon concentration are listed.

Xenon concentrations calculated by the approximate method described
in Sec 7.1.6 were used with the reactivity coefficients to obtain esti-
mates of the xenon poisoning in the MSRE., Since the simplified analysis

used only the average neutron flux, the calculated xenon concentrations
89

were space-independent and, therefore, independent of the importance-
weighting functions. (The weighted average of a constant function is the
same constant, regardless of the shape of the weighting function.) It
may be noted that peaking in the xenon distribution toward the center of
the core would make the importance-weighted average concentrations higher
than the calculated values, while peaking toward the outside of the core
would have the opposite effect.

Xenon reactivity effects were calculated for all three fuels; the
results are listed in Table 7.1. The expected values are based on a
graphite diffusion coefficient of 1.5 X 1077 ftz/hr and the calculated
mass-transfer coefficients. The minimum and maximum values were obtained
by applying the most favorable and unfavorable combinations of these two
variables, within the limits discussed in Sec 7.1.6., The reactivity ef-
fects for fuels A and C are the same because the average thermal fluxes
are the same and the reactivity coefficients do not differ within the
accuracy of these calculations. The higher reactivity effect with fuel B
is ©to be expected, because of the higher flux associated with this mix-
ture. Changes in pump bowl stripping efficiency would have the same rel-

ative effect on fuel B as is shown for fuels A and C.

Table 7.l. Reactivity Effects of Xel33

 

 

Fuel A or C Fuel B
Pump bowl stripping efficiency (%) 25 50 1.00 50
Reactivity effect (% 8k/k)
Expected -1.2 0,7 0.5 0.9
Minimum —1.0 0.5 0.3 0.5

Maximum —1.7 —1.2 ~0.9 -1.5

 
20
8. POISONING DUE TO OTHER FISSION PRODUCTS

Many fission products other than Xel?? contribute appreciably to the
neutron absorptions in the reactor after long operation at high power.
There are a few stable or long-lived fission products with high cross sec-
tions, the most important of which is amt4?, The poisoning effect of this
group of fission products saturates in a period of a few weeks or months,
but undergoes transients following power changes. In addition, there is
a slowly rising contribution to the poisoning from lower-cross-section

nuclides which continue to build up throughout power operation.

8.1 Samarium-149 and Other High-Cross-Section Poisons

Samarium-149 is the next most important fission product poison after
Xe135, having a yield of 00,0113 atom/fission and a cross section of about
40,000 barns. Unlike Xe*??, it is a stable nuclide, so that once the re-
actor has been operated at power, some St 42 poison will always be present.
The poison level changes, however, following power changes.

Samarium-149 is the end product of the decay chain

149
Nd149 _@__; Pm149 _5_3.L_1._'-h_.> om (stable) ,

For all practical purposes the effect of Ndl4° on the time behavior of
sm14? can be neglected., If it is further assumed that there is no direct
yield of Sml%%, and no burmup of Pml%%, the equations governing the Sm'4®

concentration are

These equations can be solved to obtain the poisoning, P, due to the Sl 42

in a thermal reactor:

V%en  MenTsm

Zp
2y Ty Iy

 

g
i
91

The reactivity effect of the Sml4° is simply related to P, in the case

of a thermal reactor, by

where f is the thermal utilization factor in the core.

Figures 8.1-8.3 show the type of behavior which can be expected of
the Sml%® effect in the MSRE, Figure 8.1 shows the transient following
a gtep increase to 10 Mw from a clean condition. The steady-state poison-
ing is independent of power level, but the rate of buildup is a function
of the power, in this situation. This curve was calculated using ¢ = 1 X
1013, O = % X 10%, y = 0,0113, and fXF/EU = 0.8. When the power is re-
duced the sml%® builds up, because the rate of production from ml4? ge-
cay 1ls temporarily higher than the burnup of Smt4?, Figure 8.2 shows the
reactivity transient due to S buildup after a reduction to zero power
from the steady state approached in Fig., 8.1. After the smt4? has built
up to steady state at zero power, a step increase back 1o 9 = 1 x 10%°3
results in the transient shown in Fig. 8.3.

In addition to the simple production of Smt4? through Pm14?, some
may be produced by successive neutron captures and beta decays in a chain
beginning with Pnl47, This source can become important after a long time
at a high flux,

Other high-cross-section poisons which are important are Sml’l, qdl??,
Gal37, Eul’%, and 0d1l3. The effect of these nuclides amounts to about
0.2 of that of the sm'*?, and saturates in roughly the same length of
time. Some of these fission products have relatively short-lived parents,

so that they undergo transients similar to sm'4? after changes in power,

8.2 Low-Cross-Section Poisons

The large majority of the fission products may be regarded as an ag-
gregate of stable, low-cross~section nuclides, The effective thermal
cross section and resonance integral of this aggregate depend in an in-
volved menner on the energy spectrum of the flux, the fuel nuclide, and
the amount of fuel burnup which has occurred.??: 30 At 1low fuel burnup,

in a thermal reactor fueled with U235, a good approximation 1s that each
UNCLASSIFIED
QORNL DWG. 63.8168

92

 

TIME {days )

t ¢ = 1 x 1013 After Startup with Clean

isoning a

am14? Po

Fig. 8.1.

Fuel.
dk/k (%)

1.02

1.00

0.96

0.9

0.92

0.9

_ Fig. 8.2,
at o = 1 x 1013,

UNCLASSIFIED
ORNL DWG, 63-8169

 

TIME {(days )

sml%® Poisoning at Zero Power After Reaching Steady State

€6
5k/x (%)

1L.00

0.98

0.9

0.94

0.90

UNCLASSIFIED
ORNL DWG. 638170

 

1 2 3 i 5 6 T 8
TIME (days }

Fig. 8.3. om'%Y Poisoning After Step to ¢ = 1 x 101? from Peak
Low-Power Poisoning.

76
-

95

fission produces one atom with a cross section of 43 barns and a reso-
nance integral of 172 barns.°t In a predominantly thermal reactor with
a thermal flux of 1 X 10%?, the poisoning effect of this group of fission
products increases initially at a rate of about 0.003% 8k/k per day.
96

9. EMPLOYMENT OF CONTROL RODS IN OPERATION

The control rods are used to make the reactor subcritical at times,
to regulate the nuclear power or fuel temperature, and to compensate for
the changes in reactivity which occur during a cycle of startup, power
operation, and shutdown. The manner in which the control rods are em-
ployed is dictated by their sensitivity and total worth, the reactivity
shim requirements, and certain criteria related to safe and efficient op-
eration. These factors and a normal program of rod positions during an

operating cycle are summarized briefly here.

9.1 General Considerations

The drive mechanisms for the three rods are identical, and each rod
has practically the same worth. Thus any one of the rods can be selected
to be part of the servo control system which controls the reactor fission
rate at power below 1 Mw or the core outlet temperature at higher powers.
The other two rods are moved under manual control to shim the reactivity
as required. The servo-controlled rod is called the regulating rod; the
other two, shim rods. All rods are automatically inserted or dropped
under certain conditions, so that all perform safety functions. (For a
description of control and safety systems see Part II. Nuclear and Process

Instrumentation. )

 

The criteria for the rod employment are as follows:

1. The reactivity is limited by fuel loading to the minimum required
for full-power operation. Thus, at full power, with maximum poison and
burnup, the rods are withdrawn to the limits of their operating ranges.

2. The maximum withdrawal of the shim rods ig set at 54 in. to avoid
waste motion at the beginning of a rod drop.

3. The normal operating range of the regulating rod is limited by
the reduced sensitivity at either end to between 15-in, and 45-in. with-
drawal. (In this range the rod changes reactivity at 0.002 to 0.04% 3k/k
per sec while being driven at 0.5 in./sec.)

4.  Rod movements are programmed to minimize error in calculated rod

worth due to interaction or shadowing effects.
97

5. While the core is being filled with fuel, the rods are withdrawn
so that the reactor, when full, will be suberitical by about 1.0% 8k/k.
This allows the source multiplication to be used to detect abnormalities,
and provides reserve poison which can be inserted in an emergency.

6. Before the circulating pump is started, the rods are inserted

far enough to prevent any cold slug from making the reactor critical.

9.2 ©Shim Requirements

The reactivity changes due to various causes during an operating
cycle depend, for the most part, on the type of fuel in the reactor. The
amounts of rod poison which must be withdrawn to compensate for various
effects are summarized in Table 9.1. Equilibrium samarium poisoning and
the slow growth of other fission products and corrosion products are com-
pensated by fuel additions rather than by rod withdrawal.

The largest single item in Table 9,1, the xenon poisoning, depends
on the flux, the stripper efficiency, the xenon diffusivity in the graph-
ite, and the fuel-graphite xenon transfer. The tabulated values of xenon
effect were calculated for a stripper efficiency of 50%, xenon diffusivity
in the graphite of 1.5 x 107° ftz/hr, and a mass transfer coefficlent of

0.08 ft/hr. There is considerable uncertainty in these factors, and the

Table 2.1. Rod Shim Requirements

 

Effect (% 8k/k)

 

 

Cause

Tuel A Fuel B Fuel C
Loss of delayed neutrons 0.3 0.3 0.3
Entrained gas 0.2 0.4 0.2
Power (0—10 Mw) 0.06 0.08 0.06
Xel3? (equilibrium at 10 Mw) 0.7 0.9 0.7
Samarium transient 0.1 0.1 0.1
Burnup (120 g of U?37) 0.03 0.07 0.03

 

e

Total 1.4 1.9 1.4

 

 
98

xenon effect could be as little as one-third or as much asg twice the

values tabulated.

9.3 Shutdown Margins

When the rods are withdrawn to the limits set by criteria 2 and 3,
the combined poison of the three rods is 0.5% 8k/k. The useful worth of
the rods, from full insertion to the upper end of thelr operating ranges,
is therefore less than the total worth (Table 4.1) by 0.5% 8k/k.

The minimum shutdown margin provided by the rods is the difference
between the useful worth of the rods and the shim requirements (Table
9.1)., (The shutdown margin will be greater than the minimum whenever any
of the effects in Table 9.1 are present.) Minimum shutdown margins for
fuels A, B, and C are 3.7, 5.2, and 3.8% ok/k, respectively. These mar-
gins are equivalent to reductions in critical temperatures of 580, 530,
and 550°F, respectively. If the 10-Mw equilibrium xenon poisoning were
twice the values shown in Table 9.1, the minimum shutdown margins would
correspond to critical temperature reductions of 470, 440, and 450°F, re-
spectively. Thus criterion 6 is easily satisfied by fully inserting the
rods before the pump is started.

9.4 Typical Sequence of Operations

At the beginning of an operating cycle, when the core is being filled
with fuel, the rods are positioned so that the reactor should be slightly
subecritical when full. The rod poisoning which 1s necessary at this time
depends on the total shim requirements and the current effects of samarium
and burnup. (Xenon and other factors causing reactivity loss during op-
eration will not normally be present during a fill.) Assuming that the
shim requirements are as shown in Table 9.1 and that the fuel has peak
samarium, no xenon, and no burnup during a fill, the rods would be posi-
tioned to poison 2.8, 3.3, or 2.8% dk/k with fuels A, B, and C, respec-
tively. This would leave 2.8, 4.3, or 2.9% dk/k in reserve, to be in-
serted if abnormal conditions should require a rod scram, If the shim
requirements are greater than shown in Table 9.1, the reserwve is accord-

ingly less. During the fill all three rods will be at equal withdrawal.
99

This is to provide the best protection if only two of the three rods drop
when called for.

Before the pump is started, all three rods are fully inserted to give
full protection against a cold slug making the reactor critical. {The
rod position indicators can also be calibrated at this time.)

After the pump is running, the shim rods are withdrawn to a prede-
termined point, and then the reactor is made critical by slowly withdraw-
ing the regulating rod. The amount of shim rod withdrawal is chosen to
make the critical regulating rod position well below the position of the
shim rods but within the range of adequate sensitivity. (The regulating
rod and shim rod tips are kept separated to reduce the nonlinearities in
worth which result from the regulating rod tip moving into and out of the
shadow of the shim rods.)

After the power is raised and more rod poison must be withdrawn, the
shim rods are withdrawn together, if they are not already fully withdrawn,
until they reach the maximum desirable withdrawal. The regulating rod is
then allowed to work its way up, under control of the servo system, to
shim for further reactivity changes.

Table 2.2 summarizes rod positions and poisoning during the typical

operating cycle with fuel C in the reactor.

Table 9.2. Rod Positions During Typical Operation, Fuel C

 

 

 

Rod Position Rod Poisoning
Condition (in. withdrawn) (% 3k/k)
Regulating  Shims  Regulating Shims  Total

Filling core (1% sub- 28.5 28.5 0.9 1.9 2.8
critical)

Starting fuel pump 0 0 1.9 3.8 5.7

Going critical, no Xe, 28.4 54 1.2 0.1 1.3
peak Sm, no burnup

At 10 Mw, no Xe, peak Sm, 29.4 54 1.1 0.1 1.2
no burnup

At 10 Mw, equilibrium Xe 39.3 54 0.6 0.1 0.7
and Sm, no burnup

At 10 Mw, equilibrium Xe 39.9 54 0.5 0.1 0.6

and Sm, 120 g of U233
burnup

 
100

10. NEUTRON SOURCES AND SUBCRITICAL OPERATION

10,1 Introduction

When the reactor is subcritical, the fission rate and the neutron
filux will depend on the neutron source due to various reactions and the
multiplication of these source neutrons by fissions in the core. The fuel
itself is an appreciable source of neutrons due to (a,n) reactions of
alpha particles from the uranium with the fluorine and beryllium of the
salt. There ig also a contribution from spontaneous fission. Thus the
core will always contain a source whenever the fuel is present. After
high-power operation the internal source will be much stronger, because
of photoneutrons produced by the fresh fission products. For the initial
startup, an external source can be used to increase the flux at the cham-

bers used to monitor the approaxh to criticality.

10.2 Internal Neutron Sources

10.2.1 Spontaneous Figsion

 

An absolutely reliable source of neutrons is the spontaneous fission
of the uranium in the fuel. Uranium-238 is the most active, in this re-
gard, of the uranium isotopes in the MSRE fuel. If fuel C, containing
0.8 mole % uranium of 35% enrichment, is used, the spontaneous fission
source will be about 10°/neutrons sec. If highly (~93%) enriched uranium
is used, the spontaneous fission source will be very small. Table 10.1
lists the specific emission rate of neutrons due to spontaneous fission

2  Also shown are the amounts of uranium in the core

of' each isotope.3
(clean, critical loading) end the resulting total spontaneous fission

neutron sources for the fuels whose compositions are given in Table 3.1.

10.2.2 Neutrons from (&,n) Reactions in the Fuel

Alpha particles from uranium decay interact with some of the constit-
uents of the fuel salt to produce a strong internal source of neutrons.--
All of the uranium isotopes are alpha-radicactive and any of the uranium
alphas can interact with the fluorine and the beryliium in the fuel salt

to produce neutrons. The more energetic of the alpha particles can also
101

Table 10,1. Neutron Source from Spontaneous Fissions in MSRE Core®

 

 

 

. o Fuel A fuel B Fuel C
Specific
Emission
Isotope Rate Mcb Source MCb source Mcb Source
[n/(kgesec)] (kg) (n/sec) (keg) (n/sec) (kg) (n/sec)
U234 6.1 0.3 2 0.2 1 0.2 1
yR35 0,51 27.0 14 16.5 8 26.4 13
236 5.1 0.3 2 0.2 1 0.2 1
U238 15,2 1.5 22 0.9 13 47,5 722

40 23 737

 

MEffective” core, containing 25 £t3 of fuel salt.

b . ‘3 .
Mass in core at clean, critical concentration.

produce neutrons by interaction with lithium, but the yield is negligible
in comparison with that from fluorine and beryllium, Table 10.2 summa-
rizes the specific yields and gives the neutron source in the core for
the clean, critical loading with different fuels. About 97% of the neu-
trons are caused by alpha particles from U22%, Thus the (®,n) source is

proportional to the amount of U234 present.

10.2.3 Photoneutrons from the Fuel

Gamma rays with photon energies above 1.67 Mev can interact with the
beryllium in the fuel salt to produce photoneutrons. This source is un-
important before operation, when only the uranium decay gammas are present,
but after operation at significant powers, the fission product decay gam-
mas produce a strong, long-lived neutron source.

Figures 10,1 and 10,2 show the rate of photoneutron production in
the MSRE core after operation at 10 Mw for periods of 1 day, 1 week, and
1 month., The source is proportional to the power, and the source after
periods of nonuniform power operation can be estimated by superposition

of sources produced by equivalent blocks of steady-~-power operation.
Table 10.2.

Neutron Sources from (O,n) Reactions in MSRE Core”

 

 

 

 

 

Fyy Alpha Fuel A Fuel B Fuel C

Tsotope (Mev) [27?2:§?i9?] Yield Source Yield Source Yield Source

& (n/10% @) (n/sec) (n/10% ) (n/sec) (n/10% a) (n/sec)
ye34 477 1.64 x 1031 7.0 3.3 X 10° 7.8 2.3 x 10° 7.6 2.8 x 10°
4ea72 0.64 x 1012 6.6 1.2 X 10° 7.3 0.8 x 10° 7.1 1.0 x 10°
U235 4,58 0.79 x 107 5.4 1.1 x 103 6.0 0.8 x 103 5.9 1.2 X 103
A 0.24 x 107 47 0.3 x 10° 5.3 0.2 x 103 5.2 0.3 x 103
lra 40 6.56 X 107 e 3 7.5 x 103 L8 5.2 x 103 7 8.1 x 10°
v 20 0.32 x 107 3.2 0.3 x 103 3.7 0.2 x 103 3.6 0.3 x 103
U236 e 50 1.72 x 10° 49 2.4 x 103 5.5 1.7 X 103 5,4 2.1 x 103
o de5 0.63 x 107 45 0.8 x 102 5.1 0.6 x 103 5.0 0.7 x 103
y238 4.19 0.95 x 108 3.1 4 3.6 3 3.5 1.6 X 102
4a15 0.28 x 108 2.9 1 344 1 3.3 0.4 % 102
4o X 10° 3.2 X 105 3.9 X 107

 

Bprrective” core, containing 25 £13 of fuel salt of clean, critical concentration.

<0t
103

UNCLASSIFIED
ORNL DWG. 63.8171

10

10

SOURCE STRENGIH (neutrons/sec)

 

L 8 12 16 20 phy 28

TIME AFTER SHUTDOWN (hr)

Fig. 10.1. Photoneutron Source in MSRE Core After Various Periods
at 10 Mw,
104

UNCLASS!FIED
9 ORNL DWG, 638172

SOURCE STRENGTH (neutrons/sec)

 

1 10 100
TIME AFTER SHUTDOWN (days)

Fig. 10.2. Photoneutron Scurce in MSRE Core After Various Periods
at 10 Mw.
105

The gamma-ray source used in the calculations is group IV of Blomeke
and. Todd,34 which includes all gamma rays above 1.70 Mev. The probability
of one of these gamma rays producing a photoneutron was approximated by
the ratio of the Beg(y,n) cross section to the total cross section for
gamma-ray interaction in a homogeneous mixture with the composition of
the core. A Be?(y,n) microscopic cross section of 0.5 mb was used, and
the total cross section was evaluated at 2 Mev. These assumptions lead

to a conservatively low estimate of neutron source strength.

10.3 Provisions for External Neutron Source and Neutron Detectors

10.3.1 External Source

 

For reasons which will be described later, it is desirable to supple-
ment the inherent, internal source with a removable, extraneous source.
Therefore, a thimble is provided inside the thermal shield on the opposite
side of the reactor from the nuclear instrument shaft. The thimble is a
1-1/2-in. sched 40 pipe of type 304 stainless steel, extending vertically
down to about 2 ft below the midplane of the core. It is mounted as close

as possible to the inner surface of the shield for maximum effectiveness.

10.3.2 Neutron Detectors

A nuclear instrument shaft is provided for all the permanently in-
stalled neutron detecting instruments. This is a water-filled 3-ft-diam
tube which slopes down to the inner surface of the thermal shield with
separate, inner tubes for the various chambers. The shaft contains ten
tubes, of which seven will be used for routine power operation (two wide-
range servo-operated fission chambers, two compensated ion chambers, and
three safety chambers). This leaves three tubes in which auxiliary or
special~purpose chambers could be installed. Any chamber in the instru-
ment shaft is in a sloping position, with the upper end farther from the
core (and hence, in a lower flux) than the lower end. As a result, a
long chamber in the instrument shaft is exposed to a lower average flux

than a shorter one,
106

Two vertical thimbles, similar to the source thimble but made of Z- -
in. sched 10 pipe, are installed in the thermal shield to accommodate tem-
porary neutron detectors. The two detector thimbles are located 120 and
150° from the source thimble, one on either side of the permanent nuclear
instrument shaft. The advantage of these vertical thimbles is that they
place the entire length of a chamber close to the inner surface of the

thermal shield, where it is exposed to a higher average neutron Ilux.

10.4 DNeutron Flux in Subcritical Reactor \

Changes in the reactivity of the subecritical reactor can be monitored
if the fissions caused by the source neutrons produce a measurable neutron
flux at the detectors mounted outside of the reactor vessel. The flux
at a chamber depends on the source — its strength, the energy of the neu-
trons, and, in the case of an extermal source, its location both with re-
spect to the core and with respect to the chamber. The flux also depends
on the amount of multiplication by fissions and the shape of the neutron
fux distribution in the core, which is determined by the location of the
source and the wvalue of k in the core.

The count rate produced by a given chamber depends on the chamber
sensitivity as well as on the neutron flux. Of interest in establishing
the neutron-source requirements are the sensitivities of the chambers
which will be used to observe the behavior of the reactor under subcrit-
ical conditions, The fission chambers, which will be used to monitor
routine approaches to critical (as well as power operation) are 6 in.
long and have a counting efficiency of 0.026 count per neutron/cmz. In
addition, BF3; chambers are available; they will be used during the initial
critical experiments (and possibly to monitor routine reactor fills).
These have a sensitive length of 26-1/4 in. and a counting efficiency of
14 counts per neutron/cm®.

The steady-state flux in the core and thermal shield with a source
in the thermal shield source tube was calculated?® Ffor two core condi-
tions: the first, with no fuel in the core; the second, with the core
filled with fuel salt containing 0,76 of the clean, critical uranium con-

centration. In the latter case keff was calculated to be 0,91. Contri- ~
107

butions from the internal neutron source were neglected. The calculated
ratios of thermal neutron fluxes at the chambers to the source strength
(n.eutrons/cm2 per source neutron) are given in Table 10.3. As a first

approximation, the ratios of flux or count rate to source strength at

keff above 0.9 can be assumed to change in proportion to the inverse of
(1-%k ff)
When the multiplication is high, that is, when (1 —k ) is quite

eff
small, most of the neutrons are produced by fissions in the core, with a

spatial source distribution close to the fission distribution in a crit-
ical reactor. The relation between the core power, or fission rate, in
the critical core and the flux in the thermal shield was calculated in

the course of the thermal shield design, using DSN, a multigroup, trans-
port-theory code. For the case of a thick, water-filled thermal shileld,
when the core power is 10 Mw, the predicted thermal neutron flux reaches

a peak, 1 in. inside the water, of 1.2 X 101? neutrons cm™? sec™t, The

ratio of peak flux to power is 1.2 X 10° neutrons cm™? sec™?t per watt,

or 1.5 X 10°% neutrons em™? sec™! per neutron/sec produced in the core.
It was estimated that a 6-in.-long chamber at maximum insertion in the

instrument shaft would be exposed to an average flux of roughly 1 X 1077

Table 10,3, Fluxes Produced at Neutron Chambers
by an External Source

 

Average Flux/Source Strength

 

 

Location ggzgzir {[H/(Cm .sec)]/(n/sec)}
(in.) No Fuel E_.o = 0.91
X 1076 X 1076
120° thimble Any 13 18
150° thimble Any . 9
Instrument shaft (~180°) 6 2

26 0.6 1.7

 
108

2 sec™! per neutron/sec produced. For a 26-in.-long chamber,

neutrons cm-
the corresponding value is about 3 X 1078, A chamber in one of the ver-
tical tubes Jjust inside the inner wall of the thermal shield would be ex-

posed to an average Tlux of about 3 X 1077 neutrons cm~? sec™1

per neu-
tron/sec produced in the core.

With both an external and an internal source present, the flux at a
particular location in the thermal shield can be roughly approximated by

an expression of the form

fexsex finsin
®=Db8, Tt T (10.1)

 

The quantities Sex and Sin are the strengths of the external and internal
sources, respectively. The factors fex and fin indicate the fraction of
neutrons, produced in the core Ifrom the corresponding source neutrons,
which reach the location in question. ©Since these factors depend on the

flux shape, the values vary somewhat with ke The factor b is propor-

tional to the fraction of the neutrons from ifie external source which
reach the thermal shleld without first entering the core, that is, by
scattering around the core. This factor 1s essentially independent of
keff'

The calculation of the flux distribution with an external source and
no fuel in the core indicated that fex is essentially zero for this con-
dition. Also, when there is no fuel in the reactor, Sin = 0. Thus, for

this condition Eq. (10.1) reduces to

¢ = bS . (10.2)
ex

This expression permits direct evaluation of b for wvarious locations from
the above calculation,

When the reactor is near critical, the variation in fex and fin with
k can be neglected to obtain approximate values for these quantities.
The value of fin for various locations was cobtained from the critical
flux distribution, and feX was Obtained from the distribution at keff =
0.91.

The values obtained for the factors at the various proposed neutron

chamber locations are listed in Table 10,4. These factors can be usged to
109

Table 10.4. Flux/Source Factors in MSRE

 

 

Location Cham}"?i n%fingth (CE_Z ) (fglzg ) (iflllg )
X 1076 x 1077 x 1077
120° thimble Any 13 5 3
150° thimble Any 4 5 3
Instrument shaft 6 2 4 1
26 0.6 1 0.3

 

estimate the flux at the chambers for different source conditions either
when the reactor is empty or when it is near critical (keff z 0.95).

10,5 Requirements for Source?3?

A neutron source must perform several functions in the operation of

a reactor, and each function places different requirements on the source.

10.5.1 Reactor Safety

The most important function of a neutron source in the reactor has
to do with reactor safety. If an adequate source is present, the statis-
tical fluctuations in the level of the fission chain reaction will be
negligibly small and the level will rise smoothly as the reactivity is
increased to make the reactor critical. Furthermore, when the reactor
becomes supercritical, the level will be high enough that temperature
feedback becomes effective, and safety actions can be taken before enough
excess reactivity can be added to cause a dangerous power excursion.

As shown in Secs 12,2 and 12.7, the strength of the inherent (o-n)
source is enough to satisfy the safety requirements for a source. This
is convenient because the (@-n) source will always be present whenever
there is any chance of criticality. This assurance of an adequate in-

ternal source eliminates the usual safety requirement that an extraneous
110

source bhe installed and its presence proved by significant count rates

on neutron chambers before a startup can begin.

10.5.2 Preliminary Experiments

 

An extraneous source and sensitive neutron chambers are useful in
the MSRE primarily because they comprise a means of monitoring the reac-
tivity while the reactor is subecritical, or of following the nuclear power
behavior at levels below the range of the ilonization chambers which pro-
vide Iinformation at high power.

For the initial critical experiment, it is desirable to have a sig-
nificant neutron count rate before any fuel is added to the reactor. This
guarantees that the condition of the reactor can be monitored at all times
during the experiment. Table 10,5 lists the external source strength re-
quired to produce a count rate of 2 counts/sec on the wvariousg chambers

with no fuel in the reactor.

10,5.3 Routine Operation

 

After the preliminary experiments, only the chambers in the nuclear
instrument shaft will be available to monitor the reactor flux.

The function of the neutron source in routine operation is to permit
monitoring the flux during reactor startups so that the operation is or-
derly. A normal startup of the MSRE involves two separate steps: (1)
filling the reactor with fuel salt and (2) withdrawing the control rods

Table 10.5. External Source Required for 2 Counts/sec
with No Fuel in Reactor

 

 

source
. Chamber Counting Efficiency
St th
Location Type {(counts/sec)/[n/(cm?esec)]} (n?i?%)
120° thimble BF5 14 1 x 104
150° thimble BF; 14 4 X 10%
Instrument shaft Fission 0.026 4 x 107

BF3 14 2 x 10°

 
111

to make the reactor critical. Although the first operation will normally
leave the reactor subcritical, it is desirable to monitor the flux during
this step to ensure that no abnormal conditions exist. This requires that
a significant count rate exist before the fill is started, and the source
requirements are the same as for the initial critical experiment. The
second phase of the startup involves changing the multiplication constant
from about 0.95 (the shutdown margin attainable with the control rods)

to 1,0, This operation should, if possible, be monitored by instruments
which are still useful after criticality is attained; in the MSRE, these
instruments are the servo-operated fission chambers. A source of 8 X 108
neutrons/sec is required to produce a count rate of 2 counts/sec on a

fully inserted fission chamber when k = 0,95,

10,6 Choice of Extermal Source

The source requirements of the MSRE can be met in a number of ways.
One of the most desirable sources from the standpoint of cost and ease
of handling is the Sb~Be type, and such a source that meets the calculated
requirements can be easily obtained. However, Sbl?4 nas only a 60-day
half-life, so the initial intensity of such a source must be substantially
greater if frequent replacement is to be avoided. The calculated require-
ments can also be met with a Pu-Be source. Such a source would be more
expensive, and there is a containment problem because of the plutonium
content. On the other hand, the long half-life of plutonium would elimi-
nate the problems associated with source decay.

Becauge the flux calculations are subject to substantial errors, the
final specification of the source will be based on measurements to be
made shortly after the reactor vessel containing the core graphite is in-
stalled inside the thermal shield. (The construction and startup schedule
is such that there is time for procurement of a source after these meas-

urements and before the source is needed for nuclear operation.)
112

11. KINETICS OF NORMAL OPERATION

Studies of the kinetic behavior of the reactor fall into two cate-
gories. One deals with the behavior in normal operation, when the re-
actor is subjected only to moderate changes in load demand and to small,
random disturbances or "noise.” The concern here is with stability —
absolute and relative. (Absolute stability means that a disturbance
does not lead to divergent oscillatlions; relative stability refeers to
the magnitude and number of oscillations which occur before a transient
dies out.) The other category of kinetics studies treats the response
of the system to large or rapid changes in reactivity such as might
occur in abnormal incidents. Studies of the first kind are covered in
this chapter. The next chapter deals with safety studies, or kinetics

under abnormal conditions.

11.1 Very Low Power

When the MSRE is operated at very low power, with the temperature
held constant by the external heaters, the fission chain reaction is
controlled by the control rods alone. The kinetic behavior of the fission
rate under this condition is determined by the prompt neutron lifetime
and the effective delayed neutron fractions and is not unusual in any
way. The neutron lifetime is between 2 and 4 X 104 sec, depending on
the fuel salt composition. (For comparison, the lifetime in mosit
water-moderated reactors is between 0.2 and 0.6 x 10™* sec, and large,
graphite-moderated reactors have lifetimes of about 10 X 10™4 sec. )
Although the effective delayed neutron fractions are considerably lower
than in a fixed-fuel reactor using U235, this presents no important

problem of control.

11.2 Self-Regulation at Higher Power

When the reactor power is high enough to have an appreciable effect
on fuel and graphite temperatures, the power becomes self-regulating.

That is, because of the negative temperature coefficients of reactivity,
113

the nuclear power tends to follow the heat extraction, or load, with-
out external control by the rods. The kinetic behavior under these
conditions is governed by the fuel and graphite temperature coefficients
of reactivity, power density, heat capacity, heat transfer coefficients,

and transport lags in the fuel and coolant circuits.

11.2.1 Coupling of Fuel and Graphite Temperatures

 

One characteristic of the MSRE which profoundly influences the
self-regulation is the rather loose coupling between the fuel and the
graphite temperatures. This 1s caused by a low ratio of heat transfer
to thermal inertia and a disproportion of heat generation between the
fuel and graphite.

Heat transfer between the graphite and fuel is about 0.020 Mw per
°F of temperature difference. The total heat capacity of the graphite
is 3.7 Mw-sec per °F of temperature change. The ratio of heat transfer
to graphite heat capacity is only about 0.005°F/sec per °F. This means
that with a temperature difference of 100°F between the fuel and the
graphite, the heat transferred is only enough to raise the graphlte tem-
perature at 0.5°F/sec.

The heat capacity of the fuel in the core is 1.7 Mw-sec/°F, less
than half that of the graphite. But 93% of the fission heat is generated
in the fuel; only 7% in the graphite. Thus, the core fuel temperature
tends to change much more rapidly than that of the graphite whenever
there is an imbalance between the heat generation and the heat removal
from the core. Such imbalances would occur, for example, in any power
excursion or undershoot, or whenever the fuel inlet temperature changes.

The difference in the time responses of the fuel and graphite tem-
peratures makes it necessary to treat them separately in any analysis of

the MSRE kinetics.

11.2.2 Transport Lags and Thermal Inertia

 

The kinetic behavior of the reactor is determined not only by the
core characteristics but also by the characteristics of the entire heat-
removal system, which includes the radiator, the coolant salt loop, the

fuel-coolant heat exchanger, and the fuel circulating loop.
114

The coolant loop contains 44 ft? of salt, with a total heat ca-
pacity of 2.9 Mw—sec/°F. At an 850-gpm circulation rate, the loop cir-
cuit time is 23 sec. There is 67 £t of fuel salt in circulation, having
a total heat capacity of 4.6 Mw-sec/°F. The fuel circulation rate is
1200 gpm, giving a circuit time of 25 sec. There is also additional
thermal inertia due to the metal of the piping and heat exchanger.

Because the circuit times are rather long and the heat capacities
are large compared with the normal operating power, the system response

to changes in heat removal at the radiator is rather slow.

11.2.3. Simulator Studies

 

The kinetics and stability of normal operation were studied by a
detailed simulation of the entire reactor system with an analog computer.
By this method it was feasible to include the many effects of fluid
mixing, loop transit times, heat capacities, heat transfer-4AT relations,
temperature coefficients of reactivity for the fuel and graphite, and
the reactivity-power relations.

Studies of operation at power without external contrcl of the re-
activity were carried cut with two different analog representations of
the reactor. In the first model, the core was represented as a single
major region comprised of two subregions of fuel and one subregion of
graphite., Figure 1l1l.1l is a schematic diagram which shows the treatment
of the thermal effects in the fuel and graphite in this model. In the
second model, the core was subdivided into nine major regions, as shown in
Fig. 11.2. Thermal effects were treated separately for each major region
by the same relations used for the single major region in the first model
of the core. The purpose of the subdivision of the core was to better
approximate some of the effects of spatial variation of the power gener-
ation, fuel and graphite temperatures, and the nuclear importance in the
actual core. Temperaturegs in each of the nine regions were weighted to ob-
tain the averages which determine the net effect on reactivity.

Figures 11.3 and 1l.4 show the response of the system with the nine-
region core model to changes in simulated power demand in the absence of

external control action. In both cases the demand was changed by changing
115

UNCLASSIFIED
ORNL—-DOWG 63-7318

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

GRAPHITE
-7
_\.._,-,-a—- FUEL-GRAPHITE
/4-’“;’/’ \ HEAT TRANSFER
— FUEL FUEL L =
(Tehin——_ Te/ - Tio | = (7T¢lour = 7f2
7r = Try
— 7
“— /

— !
T PERFECTLY MIXED SUBREGIONS

Fig. 11.1. Analog Model of Reactor-Core Region. Nuclear power is
produced in all three subregions.

UNCLASSIFIED
ORNL-DWG 63-7319

(7¢douT

¢ !

 

 

 

 

*—“

D
~

 

— -
——t—

 

 

 

 

 

 

 

 

 

 

 

 

| FLow
(7¢) 1N
Fig. 11.2. Schematic Breakdown of 9-Region Analog Model.
1240

1220

1200

1180

TEMPFRATURE (°F)

1160

1140

12

10

FILUX POWER (Mw)

Fig. 11.3,
Power Demand.

 

116

UNCLASSIFIED
ORNL DWG, 63-8228

200 400 00 800 1000

TIME (sec)

Response of 9~Region Model of MSRE to an Increase in
117

UNCLASSIFIED
ORNL DWG. 63-8173

1280

1240

TEMPERATURE (°F)

1200

1160

10

FLUX POWER (Mw)
O

 

0 100 200 300 400 500 600 700 800 900
TIME (sec)

Fig. 11.4. Response of 9-Region Model of MSRE to a Decrease in
Power Demand.
118

the simulated air flow through the radiator, the ultimate heat sink in
the reactor system. For the power increase in Fig. 11.3, the simulated
air flow was raised from 3% to 100% of the design value at O.5%/sec. As
shown, there was a moderate power overshoot and about 15 min was required
for the power and the fuel temperatures to approach steady-state values.
The response to & decrease in alr flow to 8% of the design value at 3%/sec
is shown in Fig. 1l.4. In this simulator test, the temperature of the
graphite in an important region of the core (region 3 in Fig. 11.2) was
recorded.

Besides showing the transient response of the reactor system, Fig.
11.4 illustrates the shift in steady-state temperatures at different
powers which results if there 1s no adjustment of the control rods. This
shift comes about because the heat generated in the graphlite must be
transferred to the fuel for removal from the core, causing the fuel and
graphite temperatures to diverge. Since the temperature coefficients of
reactivity of both the fuel and the graphite are negative, the tendency
of the graphite temperature to rise at higher powers forces the fuel tem~
perature to decrease to keep the net reactivity change zero.

Figures 11.5 and 11.6 show the response of the simulated nuclear
power in the one-regiorn core model to changes in power demand similar to
those used to produce Figs. 11.3 and 1ll.4. It may be noted that the
simulation involving the simpler core model shows a significantly greater
tendency toward sustained power oscillation at low powers. The reason for
the different results i1s not clear. The reactor system models differed in
several respects beside the core, and, because the calculations were done
at different stages of the reactor design, they used somewhat different
values for the current reactor design data.

Despite the differences in the simulator results, an important con-
clusion can be drawn from them. That is: although the negative tempera-
ture coefficients of reactivity make the reactor capable of stable self-
regulation, an external control system is desirable because the reactor
is loosely coupled and sluggish, particularly at low power. (Neither of
the models included compressibility effects due to entrained gas, but

inclusion of these effects would probably not change the conclusion. )
UNCLASSIFIED
ORNL DWG. 638174

 

 

 

10

FLUX POWER (Mw)

200 Loo 600 800 1000 1200 1400 1600

TIME (gec)

Pig. 11.5. Response of 1-Region Model of MSRE to an Increase in
Power Demand.

   

61T
UNCLASSIFIED
ORNL DWG. 638175

 

(#90) SEMO4 XNTd

1800

1600

1400

1200

1000

800

600

Loo

200

TIME (sec)

Response of 1-Region Model of MSRE to a Decrease in

Fig. 1l.6.

Power Demand.
121

11.3 Operation with Servo Control

In order to eliminate possible oscillations and to obtain the de-
sired steady-state temperature-power relations, a servo control system
was designed for use in operation at powers above 1 Mw. One control rod
is used as part of a servomechanism which regulates the nuclear power as
required to keep the fuel temperature at the reactor vessel outlet within
narrow limits. Simulator tests showed that the servo control system was
capable of holding the fuel outlet temperature practically constant during
load changes betwee 1 and 10 Mw in times of the order of 5 to 10 min with-
out significant overshoot of the nuclear power.

At powers below 1 Mw, the servo control is switched to control the
flux, or nuclear power, at a set point, and the temperature is controlled
by manual adjustment of the radiator heat removal. Adjustment of the ex-
ternal heaters may alsc be used at times.

The design and performance of the servo control system are described

in detail in Part II. Nuclear and Process Instrumentation.
122

12. KINETICS IN ABNORMAL SITUATIONS — SAFETY CALCULATIONS

12.1 Introduction

There are several concelvable incidents which could result in re-
activity increases larger or faster than those encountered in normal
operation of the reactor. Iach of these incidents rmust be examined from
the standpoint of reactor safety, to determine whether there is a possi-
bility of damage to the reactor or hazard to personnel., Because the
concern is safety, a conservative approach must be used. If the analysis
of an incident indicates that the consequences may be intolerable, then
protection must be provided to guard against damage and ensure the safety
of reactor operation. (Control and safety systems are described in Part

II. iuclear and Process Instrumentation.)

 

12.2 General Considerations

The most likely form of damage from excessive reactivity additions
in the MSRE is breach of the control rod thimbles in the core by a com-
binetion of high fuel temperature and the high pressure produced in the
core by the rapid thermal expansion of the fuel.

The severity of the power, temperature, and pressure transients
associated with a given reactivity incident depends upon the amount of
excess reactlivity involved, the rate at which it can be added, the ini-
tial power level, the effectiveness of the inherent shutdown mechanisms,
ancd the efficacy of the reactor safety system. All of these factors de-
bend to some extent on the fuel composition, because this determines the
magnitude of the various reactivity coefficients and the control rod worth
(see Tables 3.5 and 4.1).

In general, equivalent physical situations lead to larger amounts
of reactivity and greater rates of addition with fuel B than with either
A or C. This is a consequence of the larger values of the reactivity
coefficients and control rod worth, the absence of the poisoning effect

of thorium or U?38) and the lower inventory of U??® in the core.
123

The power and temperature transients associated with a given re-
activity incident increase in severity as the initial power level is
reduced. The reason for this is that, when the reactor becomes critical
at very low power, the power must increase through several orders of
magnitude before the reactivity feedback from increasing system tempera-
tures becomes effective. Thus, even slow reactivity ramps can introduce
substantial excess reactivity if the reactor power is very low when
Kepr = 1

The power level in the MSRE when the reactor is just critical de-
pends on the strength of the neutron source, the shutdown margin prior
to the approach to criticality, and the rate at which reactivity is
added to make the reactor critical. The minimum neutron source strength
which must be considered is 4 x 10° neutrons/sec, which is the rate of
production in the core by (G-n) reactions in the fuel salt. Ordinarily
the effective source will be much stronger, because an external Sb-Be
source will normally be used to supply about 107 neutrons/sec to the
core and, after the reactor has operated at high power, fission product
gamma rays will generate up to 1010 photoneutrons/sec in the core. The
ratio of the nuclear power at criticality to the source strength varies
only #10% for reactivity addition rates between 0.05 and 0.1% 8k/k per
second and for the maximum shutdown margins attainable in the MSRE. For
these conditions, the power level at criticality is about 2 mw if only
the inherent (Q-n) source is present, and is proportionately higher with
stronger sources. The power level at criticality increases for lower
rates of reactivity addition.

The principal factor in the inherent shutdown mechanism for the MSRE
is the negative temperature coefficient of reactivity of the fuel salt.
Since most of the fission heat is produced directly in the fuel, there is
no delay between a power excursion and the action of this coefficient.
The graphite moderator also has a negative temperature coefficient of re-
activity; but this temperature rises slowly during a rapid power tran-
sient, because only a small fraction of the energy of fission is absorbed
in the graphite. As a result, the action of the graphite temperature
coefficient is delayed by the time required for heat transfer from the

fuel to the graphite. Since fuel B has the largest negative temperature
124

coefficient of reactivity, a given reactivity incident produces smaller
excursions with this fuel than with either of the other two.

The MSRE safety system causes the three control rods to drop by
gravity when the nuclear power reaches 15 Mw or when the reactor outlet
temperature reaches 1300°F. In the anslysis of reactivity incidents,
conservative values were assumed for delay time and rod acceleration,
namely, O.1 sec and 5 ft/sec2, respectively. It was also assumed that

one of the three rods failed to drop when called for.

12.2 Incidents Leading to Reactivity Addition
In the MSRE the conceivable incidents which could result in signifi-
cant additions of reactivity include the following:

. uncontrolled rod withdrawal,

cold-slug accident,

abnormal concentration of uranium during fuel additions,
displacement of graphite by fuel salt,

. premature criticality while the core is being filled,

oo o~ W

. fuel pump powér failure.

Estimates of the maximum addition rates and total reactivity as-
sociated with the first four incidents, together with the initial con-
ditions postulated, are summarized in Table 12.1. Brief descriptions of
these postulated incidents and the bases for the rates listed in Table
12.1 are as follows.

1. Simultaneocus, continuous withdrawal of all three rods is ini-
tiated, starting with the reactor critical at 1200°F and the rod tips
near the position of maximum differential worth. The rod withdrawal
speed is 0.5 in./sec and the maximum differential worth was obtained from
Fig. 4.2.

2. The cold-slug accident occurs when the mean temperature of the
core salt decreases rapidly because of the injection of fluid at ab-
normally low temperature. Such an accident would be created by starting
the fuel circulating pump at a time when fuel external to the core has
been cooled well below that in the core, if such a situation were pos-

sible. A detailed study was made for a case in which fuel at 900°F is
Table 12.1. Maximum Expected Reactivity Additions in Postulated Operating Incidents

 

Maximum Estimated
Incident Description Reactivity Rate

[ (% 8k/k)/sec]

Maximum Total
Reactivity

(%)

Initial Power
Level Assumed
in Accident

(w)

 

1 Uncontrolled withdrawal of 3 rods 0.10
2 Cold-slug accident® 0.16
3 Abnormal concentration of uranium 0.12
during fuel addition at pump
bowl
4 Graphite stringer breakage 0.02

l.5

C.37

0.22

0.002°
1000

0,01

.01

 

“Determined by maximum operating excess reactivity (~d%) .

bPower at keff = 1 for minimum neutron source.

©900°F fuel salt pumped. into core, which is initially critical at 1200°F.

Gt
126

pumped at 1200 gpm into the core, which is initially critical at a uni-
form temperature of 1200°F. The maximum reactivity addition rate in this
case depends on heat transfer between salt and graphite and transient nu-
clear heating before the core is filled. The product of the salt temper-
ature reactivity coefficient and the temperature decrease (300°F) divided
by the core fluid residence time gives the rough estimate of reactivity
addition rate listed in Table 12.1.

3. A maximum of 120 g of highly enriched uranium can be added as
frozen salt at the pump bowl. An upper limit on the transient caused by
a bateh going into circulation was found by assuming that the fresh salt
failed to mix gradually and passed through the core as a "front" of highly
concentrated uranium. The rate listed in Table 12.1 is the meximum rate
of addition, accounting for the change in nuclear importance as the con-
centrated salt moves upward through the channels. The total reactivity
added would increase to a maximum when the uranium is near the center of
the core, then decrease as the fuel exits.

4. Replacement of graphite by fuel produces a reactivity increase.
Breakage of a graphite stringer into two pieces while fuel is circulating
through the core could allow the upper section to float upward and fuel
salt to move into the space about the fracture, were it not for the re-
straining rods and wires through the lower and upper ends of the stringers.
An upper limit of the potential reactivity increase due to loss of graph-
ite was calculated by assuming that the entire central graphite stringer
was replaced by fuel salt. The total reactivity, listed in Table 12.1,
is small, compared with that in the other incidents, and requires a time
approximately equal to the core residence time for its addition.

Incidents 5 and 6 are not included in Table 1lZ2.1l, since the condi-
tions important to these incidents cammot be simply characterized by a
reactivity addition rate.

In brief, the filling accident is postulated to occur as follows:
When the reactor is shut down, the fuel salt is drained from the core.
During the subsequent startup, the fuel salt and graphite are preheated
and the control rods are positioned so that the reactor remains sub-

critical while filling. Criticality with the core only partially filled
127

could result, however, if the core or salt temperature were abnormally
low, the fuel salt were abnormally concentrated in uranium, or the con-
trol rods were fully withdrawn.

In the case of the fuel pump power failure, there is an increase in
reactivity because delayed neutron precursors are no longer swept out of
the core when the pump stops. More important, from the standpoint of
rising temperatures, is the sudden decrease in heat removal from the
core,

From the reactivity additions listed in Table 12.1, it 1s apparent
that of the four incidents listed, the rod withdrawal and the cold-slug
accident are potentially the most serious. The analysis of these inci-
dents and of the filling accident and the pump stoppage are described in

the sections which follow.

12.4 Methods of Analysis

The general method used to estimate the consequences of the various
incidents was numerical integration, by means of a digital computer, of
the differential equations describing the nuclear, thermal, and pressure
behavior of the reactor. In the development of the methods of analysis,
realistic rather than pessimistic approximations were made wherever pos-
sible. The conservatism necessary in an appraisal of safety was then
introduced by the choice of the initial conditions for the postulated
incidents.

The mathematical procedures developed for the analysis of the MSRE
kinetics are described in this section. Symbols used in this description

are defined in Sec 12.4.4.

12.4.1 Reactivity-Power Relations

 

The time dependence of the nuclear power was described by the well-

known relation

N
P+ _fl AT (12.1)
i=1

_k(1-8)-1

P Z
128

Six groups of neutrons were included in the summation. The effec-
tive number of precursors (actually, the latent power agsociated with
their decay was represented by the equation for fixed-fuel or noncircu-

lating reactors:

 

r, = - NI (12.2)
An allowance was made for the effects of circulation on the contribution
of delayed neutrons by using reduced values of Bi (see Chap. 6).

The effective multiplication constant, k, was represented by the
sum of several terms:

k=1 4k - (TF-T0) ~ ocg(Tg ~ Tgo) . (12.3)

Here kex is the reactivity added by all means other than changes in the
fuel and graphite temperatures. Temperature effects are represented by
the last two terms in (12.3): Q%(T? — T?O) is the reactivity effect of
changes in fuel temperature, which responds rapidly to power changes,
and Qé(Tg ~— Tgo) is the effect of the graphite temperature, which responds
more slowly.

The equations gilven above are intrinsically space-independent ap-
proximations in which the response of the reactor is characterized by
the time behavior of the total power, a single temperature for the fuel
and another for the graphite, and the two parameters G% and aé. In order
to complete the mathematical description of the reactor kinetics, the fuel
and graphite temperature distributions must be reduced to a single charac-
teristic temperature for each, which are related to the heat generation
rate, P. The relations must necessarily involve heat removal from the
core, heat capacities of the fuel and the graphite, and heat transfer

between fuel and graphite.

12.4.2 Power-Temperature Relations

 

Two different models were used to approximate the exact thermal

relations in the core.
ot

129

The first power-temperature model assumed that the effective average
temperature in the core was simply a weighted average of the inlet and

outlet fuel temperatures:

*

T, = OT o + (1 - Q)Tfi . (12.4)
It was also assumed that the nuclear average temperatures for the fuel
and graphite were identical with the bulk average temperatures, which
are governed by

8,Tp = 1-9y)P- WCP(TfO - Tfi) + h(Tg — T

£ (12.5)

o)

Séfig = yP — h(fig-m'fif) . (12.6)

These approximations were combined with the neutron kinetics equations
in an IBM 7090 program called MURGATROYD.>®

In the second model, an approximate calculation was made of the time
dependence of the spatial temperature distributions of the fuel and graph-
ite. These temperature distributions were then weighted with respect to
nuclear importance in order to obtailn single nuclear average temperatures
for the fuel and graphite. The average temperatures then determined the
reactivity feedback. In calculating the temperature profiles, the shape
of the core power distribution was assumed to be time-independent; how-
ever, the magnitude of the total power varied in accordance with Eq.
(12.1).

The temperature distributions as a function of time were calculated
by replacing the macroscopic heat balance Egs. (12.5) and (12.6) by

"local" heat balances on salt and graphite in the individual channels:

 

 

 

 

 

an an . 0 h(Tg-— Tf)
US TSt 5. T T eoc. (12.7)
Pr-ep Py
oT & h{(T —~ T
g___ g _ ( g f) (12.8)
ot o C a p C ’

g g g8 ¢
130

T = T(r,z,t), ¢ = o(r,z,t) .

Note that the fluid temperature equation is now a partial differential
equation, because of the presence of the transport term u(BTf/Bz). The

shape of the axial power distribution was assumed to be sinuscidal:

 

L - F P(t .
®f(r,z,t) = ( 7)Vf(r) (t) 3-81n-%?-, (12.9)
@g(r,z,t) =.Z_Eifgrfflgil€§.sin.%§-. (12.10)
g

With the above approximations, it was possible to reauce the procedure

of solving (12.7) and (12.8) to numerical integrations over only the time
variable. The temperature at any point along the channel depends on the
temperature distribution along the channel at the time the fuel enters
the channel and the subsequent power-time history. The power-time re-
lation was again obtained by integrating Eqs. (12.1) and (12.2). How-
ever, the temperature feedback terms are now based on nuclear average
temperatures, in which the fuel and graphite temperature profiles at
time t are weighted with respect to nuclear importance [see Eq. (3.2) for
the general definition of the nuclear average temperature]. Using the
sinusoidal approximation for the axial variation of the importance func-

tion and I(r) to represent the radial variation of the importance:

R H
— ine L2
. J; J; [Tj(r,z,t) Tfi] I(r) sin T odr dz
Tj(t) - Tgy = , (12.11)
R H
jfl jfi 1(r) sin? 22 r dr dz
/0 Y0 H

 

Jg=1T, 8 .

With the further assumption that heat conduction effects are small com-
pared with the heat generation terms, the radial dependence of the tem-
perature rise is proportional to the radial power density, so that (12.11)

may be further simplified:
131

 

 

H
_ ip2 22
. . J; [Tj(z,t) Tfi] sin® — dz
Tj(t) - Tpy = Fp 7 , (12.12)
Jfl sin2¥55 dz
0 H
J=1%, g,
where
R
J; F(r) I(r) r ar
F; = . (12.13)

R
J; I(r) r ar

The procedure for solution of the kinetics equations thus consists of
calculating the temperature profiles from Egs. (12.7) and (12.8), the
nuclear average temperature from Eq. (12.12), and the power-time behavior
from Egs. (12.1), (12.2), and (12.3). An IBM 7090 program, ZORCH, was
designed to obtain the solution of this set of equations by numerical

approximation methods .37

12.4.3 Temperature-Pressure Relations

During any excursion in the fuel temperature, the pressure in the
core will rise and fall as the fuel expands and contracts. These changes
result from the inertial effect of acceleration of the fuel salt in the
reactor outlet pipe leading to the pump bowl, changes in friction losses
in the pipe, and the compression of the gas space in the pump bowl. If
the fluid is assumed to be incompressible, so that there is no effect of
pressure on reactivity, the hydrodynamics equations can be solved in-
dependently of the power-temperature equations. A simplified model of
the primary salt system, similar to that utilized by Kasten and others
for kinetics studies relating to the Homogeneous Reactor Test,38 was
used for approximate calculations of the pressure rise. It is assumed
that the fluid density can be adequately approximated by a linear de-

pendence on the temperature:
132

o(T.) = ¢° +§§— (T, — T2) , (12.14)
T

where Tf is the bulk average temperature of the salt in the reactor core.
The other basic relations required for calculation of the pressure rise
are the force balance on the fluid in the outlet pipe and the equation of

continuity for the core salt:

M - - - 2
Toe, U = A(pc P, fUu<) , (12.15)
. A
p=—-V—pO(U—UO) . (12.16)
f

The compression of the gas in the pump bowl is assumed to be adiabatic:

vE = pO (vt 12.17
Py Vp = Pplp) ( )
The resulting equation for the pressure rise is36

p_ - p0 = C1l% + Coy + Ca¥ (1 + Caf)] (12.18)

In this expression x and y are the dimensionless power and the dimension-

less fluid temperature, defined as
x = P/F° , (12.19)

8p(Tp = Tp )

= =S5 .

and the constants are defined as

Ve 1 9p M(1 — )PP
ClL=—"" <5 o=, (12.21)
A p° OT, ld4g AS,
. (nA) 144g A
= — 0w .
Cz Py VoM ’ (12.22)
133

l44gCA
Cy = 2Ug-——35——-, (12.23)
V(1 - 7)F 3p

 

2AU°%8 0" 5T
f

The first term on the right hand side of {12.18) arises from acceleration
of fluid in the outlet pipe, the second results from the compression of
the pump bowl gas, and the last represents the pressure drop due to
friction loss in the pipe. This equation is the basic approximation for
the transient core pressure rise utilized in the kinetics programs ZORCH

and MURGATROYD.

12.4.4 Nomenclature for Kinetics Eguations

A Cross-sectional area of outlet pipe

ap Cross-sectional area of fuel channel

ag Cross-sectional area of graphite stringer
Ci Constant defined by Eq. 12.21

Co Constant defined by Eq. 12.22

Ca Constant defined by Eq. 12.23

Cy Constant defined by Eq. 12.24

£ Friction loss in outlet pipe

F Radial distribution of power density

F; Importance-weighted average of F

g, Dimensional constant,(ft*lbmass)/(secz-lbfgrce)
H Height of core

h Heat transfer factor, graphite to fuel

I Radial distribution of nuclear importance
k Multiplication factor

kex Reactivity added by external means

£ Neutron lifetime

M Mass of fuel in outlet pipe to pump

N Number of delayed neutron groups

n Ratio of gpecific heats
134

Power

Pressure in core

b kg W
0

g

Pressure in pump howl

Hd

Radius of core

Radial distance from core center line
Total heat capacity of fuel in core
Total heat capacity of graphite

Local temperature of fuel

H &Jd m n H
H R M

Local temperature of graphite

H

Nuclear average temperature of fuel

3

Nuclear average temperature of graphite

H ] ok Hhk 07

H

Bulk average temperature of fuel

H|

Bulk average temperature of graphite

o

Fuel inlet temperature

H
[

Fuel outlet temperature

H
o

Time
Velocity of fuel in a channel
Velocity of fuel in outlet pipe

< O £ o H o3

Hy

Volume of fuel in core

<3

Volume of graphite in core

o

Volume of gas in pump

&S

Heat capacity of fuel flow

3

Normalized power
Normalized fuel temperature

Axial distance from bottom of core

Q N <9 N

H

Fuel temperature coefficient of reactivity
Graphite temperature coefficient of reactivity
Fraction of neutrons in delayed group i

Total fraction of delayed neutrons

Fraction of heat produced in graphite

Latent power associated with delay group i

.

Temperature weighting factor

Decegy constant for group 1

T Y O MR T o Q
e e R

Density

©
Q

Volumetric heat capacity

¢ Power density

Superscript O refers to initial conditions
135

12.5 MSRE Characteristics Used in Kinetics Analysis

Table 12.2 summarizes the properties of the MSRE which affect the

kinetics and gives the values which were used in the last analysis.

Table 12.2. MSRE Characteristics Affecting Kinetic Behavior

 

Fuel Salt

 

A

B C

 

Prompt neutron lifetime (sec) 2.29 x 10~%

Temperature coefficients of
reactivity [(8k/k)/°F]

Fuel —3.03 x 10™°

Graphite —3.36 X 1077
Fuel density (1b/ft3) 144
Delayed neutron fraction

Static

Circulating

Residence times (sec)
Core
External to core

Fraction of heat generation
In fuel
In graphite

Core heat capacity [(Mw-sec)/°F]
Fuel
Graphite

Graphite-to-fuel heat transfer
(Mw/°F)

Core fuel volume (ft3)

Fuel volumetric expansion co-
efficient (°F 1)

Length of line to pump bowl (ft)
Cross sectional area of line (ft?)
Friction loss in line [psi/(ft/sec)?]
Pumb bowl initial pressure (psig)
Volume of gas in pump bowl (ft3)

Ratio of specific heats of helium
(c_/c_)
v

3.47 X 10-4 2.40 x 10°%

97 x 107° 3,28 x 10°°
91 X 10°° —3.68 x 10™?

134 143

o
—4’l

0.006e7
0.0036

9.37
16.45

0.933
0.067

1.74
3.67

0,020

25.0
1.18 x 1074

16.0
0.139
0.020
5
2.5
1.67

 
136

1l2.6 Preliminary Studies

12.6.1 Early Analysis of Reactivity Incidents>®

 

An early study was made in which each of the accidents described in
Sec 12.3 was analyzed, using the space~independent kinetics program
MURGATROYD to calculate power, temperature, and pressure excursions.
Some calculations of the response of the reactor to arbitrary step and
ramp additions of reactivity were also made, in order to better define
the limits which would lead to internal damage to the core. The nuclear
characteristics used in this study were similar to those listed in Table

12.2 for fuel A.

The results of the preliminary study indicated that none of the
accidents analyzed could lead to catastrophic failure of the reactor.
The extreme cases of cold-slug accidents, filling accidents, and uncon-
trolled rod withdrawal led to predicted core temperatures high enough to
threaten internal damage. Because each of these accidents could happen
only by compound fallure of protective devices, and because 1in each case
there existed means of corrective action independent of the primary pro-
tection, damage was considered to be very unlikely in the cases considered.

The calculated response to arbitrary step and ramp additions of re-
activity indicated that damaging pressures could occur only if the addi-
tion were the equivalent of a step of about 1% 5k/k or greater, well

beyond the severity of foreseeable accldents.

12.6.2 Comparison of MURGATROYD and ZORCH Results

 

After the digital program ZORCH became available, some kinetics
calculations were made to compare the excursions predicted by this method
with those computed with MURGATROYD. As expected, differences were found
in the calculated power, temperature, and pressure excursions obtained
from the two kinetics programs. The differences arise because the ap-
proximations used in MURGATROYD for the nuclear average temperature and
the rate of heat removal from the reactor are poor during a rapid power
transient, whereas these quantities are treated much more realistically

in ZORCH.
137

An example of the differences in MURGATROYD and ZORCH results is
illustrated in Fig. 12.1, where the power and-temperature transients
following a prompt-critical step in reactivity are compared. Because
ZORCH computes a spatial temperature distribution and gives the greatest
welght to the most rapidly rising temperatures, its nuclear average tem-
rerature rises more rapidly than the fuel bulk average temperature or the
temperature computed by MURCATROYD. The power excursion is therefore
cut off at a lower peak than that calculated by MURGATROYD. The inte-
grated power is also less in the ZORCH results, causing a smaller rise
in the mixed-mean temperature of the fuel leaving the core (TO in Fig.
12.1). The highest temperature in Fig. 12.1, (To)max’ is the temperature
Predicted by ZORCH for the outlet of the hottest fuel channel. This fuel
would mix in the upper head of the reactor vessel with cooler fuel from

other channels before reaching the ocutlet pipe.

12.7 Results of Reactivity Accident Analyses

The results of the most recent analyses of the important reactivity

accidents are described in this section.

12.7.1 Uncontrolled Rod Withdrawal Accident

This accident is most severe when criticality is achieved with all
three control rods moving in unison at the position of maximum differen-
tial worth. Since this condition is within the range of combinations of
shutdown margin and rod worth for all three fuels, it was used as a basis
for analyzing this accident. The maximum rates of reactivity addition by
control-rod withdrawal are 0,08, 0,10, and 0.08% 8k/k per second when the
system contains fuels A, B, and C, respectively. The initial transients
agssociated with these ramps were calculated for_fuels B and C starting
with the reactor Jjust critical at 0.002 w and 1200°F. (The transients
for fuel A would be practically the same as for fuel C.)

The first 15 sec of the transients in some of the variables are
shown in Figs. 12.2 and 1l2.3 for fuels B afid C respectively. The curves

illustrate the behavior of the power, the fuel and graphite nuclear aver-

¥

age temperatures, Tf

and Tg, the temperature of the fuel leaving the
138

UNCLASSIFIED
ORNL DWG. 63-8229

1600

1500

1400

TEMPERATURE (°F)

1300

1200

120

100

POWER (Mw)

40

 

0 1 2 3 4 5 6 T 8 9 10
TIME (sec)

Fig. 12.1. Power and Temperature Transients Following a Prompt
Critical Step in Reactivity; Fuel A; Comparison of ZORCH and MURGATROYD

Kinetics Models.
139

UNCLASSIFIED
ORNL DWG. 63.8176

TEMPERATURE (°F)

POWER (Mw)

 

c 2 L & 8 10 12 14 16
TIME (sec)

Fig. 12.2. Power and Temperature Transients Produced by Uncon-
trollied Rod Withdrawal, Fuel B.
140

UNCLASSIFLED
ORNL DWG, 63.8177

1300

1800

1700

1600

1500

1400

TEMPERATURE (°F)

1300

500

Loo

300

200

POWER (Mw)

100

 

0 2 Y 6 8 10 12 14 16

TIME (sec)

Fig. 12.3, DPower and Temperature Transients Produced by Uncon-
trolled Rod Withdrawal, Fuel C.
141

hottest channel, (To)max’ and the highest fuel temperature in the core,

(Tf)max'

Although the rate of reactivity addition was lower for fuel C than
for fuel B, the excursions were more severe for fuel C because of the
smaller fuel temperature coefficient of reactivity and the shorter prompt
neutron lifetime associated with this mixture. The power excursion oc-
curred somewhat later with fuel C because of the greater time required
to reach prompt criticality at the lower ramp rate.

During steady operation the maximum fuel temperature occurs at the
outlet of the hottest channel. However, during severe power excursions
which are short compared with the time of transit of fuel through the
core, the maximum fuel temperature at a given time may be at a lower
elevation in the hottest channel, where the power density is relatively
higher. This is illustrated by the difference between the maximum fuel
temperature and the temperature at the outlet of the hottest channel
during and immediately after the initial power excursion. These two
temperatures then converged as the fuel was swept from the region of
maximum power density toward the core outlet, while the power was rela-
tively steady. The rise in the mixed-mean temperature of the fuel
leaving the core is about half of that shown for the hottest fuel channel.

The transient calculations were stopped before fihe fuel that was af-
fected by the initial power excursion had traversed the external loop and
returned to the core. The trends shown in Figs. 12.2 and 12.3 would con-
tinue until the core inlet temperature began to rise, about 16 sec after
the initial excursion in the outlet temperature. At that time, the power
and the outlet temperatures would begin to decrease; the nuclear average
temperatures would continue to rise as long as rod withdrawal were con-
tinued. However, the rise in graphite temperature resulting from heat
transfer from the fuel would reduce the rate of rise of the fuel nuclear
average temperature.

It is clear from Figs. 12.2 and 12.3 that intolerably high fuel tem-
peratures would be reached in this accident if complete withdrawal of the
control rods were possible. ©Since the reactor safety system provides for
dropping the control rods on high power, the accident involving fuel C

was also examined in the light of this action. It was assumed that only
142

two rods dropped (0.1l sec after the flux reached 15 Mw, with an acceler-
ation of 5 ft/secz), while the third continued to withdraw. The initial
transients for this case are shown in Fig. 12.4. The flat portion in the
maximum fuel temperature reflects the time required for the fuel that was
heated by the initial excursion to pass out of the core. Dropping two
control rods in this accident reduced the temperature excursions to in-
significant proportions from the standpoint of reactor safety. Since

the reactor cannot be made critical by withdrawing only one control rod,
failure of the rod-drop mechanism on one rod does not impair the safety

of the system.

The core pressure transients were small in all of the rod withdrawal
accidents. With no corrective action, the pressure increases were 18 and
21 psi for the cases involving fuels B and C, respectively. Simulation
of the control-rod drop limited the pressure excursion with fuel C to

8 psi.

12.7.2 Cold-Slug Accident

 

The kinetic behavior was calculated for a postulated incident in
which one core-volume of fuel at 900°F suddenly entered the core, which
was initially critical at 1200°F and 1 kw. The resulting power-tempera-
ture transients are summarized in Fig. 12.5, as calculated for fuel salt
B. The maximum values reached for power and temperature were higher for
this case than for salt C. The maximum pressure achieved was about © psi
with either salt.

The temperature plots given in Fig. 12.5 exhibit the following
features: There was an initial 300°F drop in the reactor inlet temper-
ature, which remained at 900°F until the core was filled with the cooler
fluid. As the volume of the core occupied by the cold slug became larger,
the fuel nuclear average temperature decreased slowly, adding reactivity.
When the reactivity approached prompt critical, the reactor period became
small and substantial nuclear heating occurred. This caused the fuel nu-
clear average temperature to rise sharply and limit the power excursion.
The additional heat generation was reflected as a rise in the channel

outlet temperature. At the time the leading edge of the cold slug reached
143

UNCLASSIFIED
ORNL DWG. 63.8178

TEMPERATURE (°F)

POWER (Mw)

 

6 8 10 12 1k 16

TIME (sec)

Fig. 12.4. Effect of Dropping Two Control Rods at 15 Mw During
Uncontrolled Rod Withdrawal, Fuel C.
144

UNCLASSIFIED
ORNL DWG. 638179

1600

1400

400

300

200

POWER (Mw)

100

 

5.0 10.0 15.0 20.0 25.0

TIME (sec)

Fig. 12.5. Power and Temperature Transients Following a 900°F
Cold Slug Accident; Fuel Salt B; No Corrective Action.
145

the top of the core, there was a sharp drop in the channel outlet temper-
ature. Simultaneously, the reactor inlet salt temperature returned to
1200°F as the available amount of cold fluid was exhausted. The channel
outlet passed through a maximum upon arrival of the fluid heated at the
center of the core by the initial power transient, then decreased until
finally the rise in salt inlet temperature was again reflected {(about 9.4
sec later) as a rise in the channel outlet temperature.

It is apparent that the excursions in temperature and pressure re-
sulting from the nuclear incident are less important than the rapid rates
of change of temperature calculated for the incident. The latter could
result in large transient stresses in the inlet and outlet piping and in

the fuel pump.

12.7.3 Filling Accident

Conditions Teading to Filling Accident. — Normal procedure for start-
up of the MSRE requires that the reactor and fuel be heated by electric

 

heaters to near the operating temperature before the fuel is transferred

from the drain tank to the core. The control rods normally are partially
inserted during a fill, so that the reactor is suberitical at normal tem-
perature with the core full of fuel. Criticality is attained by further

rod withdrawal after the fuel and coolant loops have been filled and cir-
culation has been started.

Criticality could be reached prematurely during a startup while the
core is being filled if: (a) the control rods were withdrawn from the
positions they normally occupy during filling; (b) the core temperature
were abnormally low; or (¢) the fuel were abnormally concentrated in ura-
nium. Interlocks and procedures are designed to prevent such an accident.
If, despite the precautions, the reactor were to become critical under
such conditions, there would be a power excursion, the size of which would
depend on the source power and the rate of reactivity addition. The core
temperature would rise rapidly during the initial power excursion; then,
1f fuel additiofi were continued, it would rise in pace with the increase
in critical temperature. The consequences of a number of filling acci-
dents were analyzed, and the principal results are summarized in this

section. Detailed description of these studies is contained in ref 40.
146

Reactivity Addition., — The amount of reactivity available in a fill-

 

ing accident depends on the conditions causing the accident and the char-
acteristics of the fuel salt. In the case of filling the reactor with
the control rods fully withdrawn, the excess reactivity is limited to the
smount in the normal fuel loading. Only about 3% dk/k will be required
for normal operation (see Table 9.1), and the uranium concentration in
the fuel will be restricted by administrative control to provide no more
than required. Filling at the normal rate with all rods fully withdrawn
results in a reactivity ramp of 0.01% 8k/k per second when k = 1. The
power excursion assoclated with this ramp is well within the range of
control of the rod safety system. Full insertion of any two of the three

control rods is adequate for shutdown of the full core.

In filling the fuel at an abnormally low temperature, excess reac-
tivity is added by means of the negative temperature coefficient of the
fuel. TFor fuel B (the mixture with the largest negative temperature co-
efficient of reactivity), cooling the salt to the liquidus temperature
(840°F) provides 1.9% excess reactivity. The reactivity addition rate
at k = 1 is 0,006%/sec. The shutdown margin provided by the control rods
is 5.2%,

In the case of filling of the reactor core with fuel abnormally con-
centrated in uranium, the mechanism assumed to cause the incident is that
of selective freezing of fuel in the drain tank., The crystallization
paths of all three salt mixtures under consideration are such that large
quantities of salt can be solidified, under equilibrium conditions,* be-
fore uranium (or thorium) appears in the solid phase. Selective freezing,
therefore, provides one means by which the uranium concentration can be
increased while the salt is in the drain tank., Since the reactor vessel
is the first major component of the fuel loop that fills on salt addi-
tions, approximately 40% of the salt mixture can be frozen in the drain
tank before it becomes impossible to completely fill the core.

The changes in liquid composition as selective freezing proceeds de-
pend on the initisl composition and the conditions of freezing. TFigure

12,6 shows the atomic concentrations in the remaining melt for fuel A as

 

*Very slow cooling.
147

UNCLASSIFIED
ORNL DWG. 63.8180

0.7

 

0. 0.05
0.4 0.0k
=
& 5
g %
0.3
g 0.03 i
= g
0. 0.02
0. 0.01
: : ‘ s o
0 0.1 0.2 0.3 0.k 0.5

WEIGHT FRACTION OF SALT FROZEN

Fig. 12.6. Ligquid Composition Resulting from Selective Freezing
of Fuel Salt A in Drain Tank.

a function of the fraction of salt frozen. The curves are based on the
assumption that only the equilibrium primary solid phase, €6LiF+BeF;+ZrF,,
appears.

The effect on premature criticality was evaluated for each of the
three salts with 39%, by weight, frozen in the drain tank as 6LiFeBeF-
7ZrF,.* Under these conditions the full reactor at 1200°F had about 4%
excess reactivity for fuels A and C and 15% for fuel B. Fuels A and C

 

*The composition of the solid phase has little effect on the nuclear
calculations as long as it does not include fissile or fertile material.
148

contain significant amounts of thorium and U238, respectively, which re-
main in the melt with the U?33 during selective freezing. The poisoning
effect of these species greatly reduces the severity of the filling ac-
cident when they are present. The excess reactivities in this accident,
with so much selective freezing, exceed the shutdown margin of the con-
trol rods. Thus it is necessary to stop the filling process to prevent

a second reactivity excursion after the rods have been dropped. The ac-
cident involving fuel B is the most severe; the reactivity addition rate
for this case is 0.025% ®k/k per second at k = 1, compared with 0.01%/sec
for fuels A and C.

Corrective Actions. — Control rod drop and stoppage of fuel addition

 

are considered as means for limiting the power excursion and stopping the
addition of reactivity. In the first case, dropping the rods on high
flux signal (15 Mw power) was found to be more than adequate for any fill-
ing accident in which the available excess reactivity does not exceed the
shutdown margin of the rods. For the more severe accidents, it is nec-
essary to supplement the rod drop by stopping the fill to prevent further
reactivity addition. '

Filling the reactor is accomplished by admitting helium, at 40 psig
supply pressure, to a drain tank and foreing the liquid fuel up through
the drain line into the primary system, Figure 12.7 is a simplified flow-
sheet of the reactor fill, drain, and vent systems showing only those
features which pertain directly to the filling accident. All valwves are
shown in the normal positions for filling the reactor from fuel drain
tank No. 1. Three independent actions are available to stop the addition

of fuel to the primary loop:

1. Opening HCV-544 equalizes the loop and drain tank pressure.

2, Opening HCV-573 relieves the pressure in the drain tank by venting
gas through the auxiliary charcoal bed to the stack.

3. Closing HCV-572 stops the addition of helium to the drain tank.

During a filling accident all three actions would be attempted simulta-
neously to ensure stopping the fill. The first two actions, in addition
to stopping the fill, allow the fuel in the primary loop to run back to
the drain tank. Stopping the gas addition only stops the fill, but the

salt flow does not stop instantaneously.
149

UNCLASSIFIED
ORNL-DWG 63-7320

[ ]
FP PCV-522

FHX
HOV-V
5§¥A D “r

 

UL

K] TO FILTER,

FAN, AND STACK
FFT
REACTOR FO-2 AUXILIARY
CHARCOAL
FFT BED

€D

00

1<
>

 

Fv_ FFT FD'ECJ Y )
FD-2 ga&\{ HCV-573
>
1><] 7~ 50-psig

DISK
FO-2

FFT
FD-1

 

 

40-psig
HELIUM
SUPPLY

Fig. 12.7. System Used in Filling Fuel Loop.

During filling, the flowing fuel in the drain line experiences a
small pressure drop. In addition, the gas displaced from the primary loop
must flow out to the stack through equipment which imposes some pressure
drop. Consequently, the pressure in the drain tank at any point in the
filling operation is greater than that required to maintain the liquid-
level difference under static conditions. As a result, when gas addition
is stopped, the fuel level in the primary loop coasts up until the dynamic
head losses have been replaced by an increase in the static head differ-
ence between loop and drain tank. If this coast-up occurs during a fill-
ing accident, the additional excess reactivity associated with the higher

level must be compensated for by the system.
150

Temperature Coefficient of Reactivity. — The temperature coefficient

 

of reactivity of the fuel in the partially filled core differs substan-
tially from that in the full system. In the full system, the thermal ex-
pansion of the salt expels fuel from the core. The effective size of the
core, however, remains essentially constant. Thermal neutron leakage also
increases, and both of these factors tend to reduce reactivity. In the
partially full core, fuel expansion increases the effective height of the
core. This tends to offset the decrease in reactivity due to increased
radial neutron leakage. The effective temperature coefficient of reac-
tivity of fuel B with the core 60% full is approximately —0.4 X 1072
(°F)™1, compared with —5.0 x 1077 (°F)~1l for the full core. The tempera-
ture coefficient of the graphite is not significantly affected by the
fuel level.

Maximum Filling Accident. - Only the most severe of the postulated

filling accidents was analyzed in detail. It was assumed that the uranium

 

in fuel B was concentrated to 1.6 times the normal value by selective
freezing of 39% of the salt in the drain tank. Several other abnormal
situations were postulated during the course of the accident, as follows:

1. The helium supply pressure was assumed to be 50 psig, the limit
imposed by the rupture disk in the supply system, rather than the normal
40 psig. This pressure gave a fill rate of 0.5 £t2/min when criticality
was achieved and produced a level coast-up of 0.2 ft after gas addition
was stopped.

2. It was assumed that only two of the three control rods dropped
on demand during the initial power excursion.

3. It was assumed that two of the three actions available for stop-
ping the fill failed to function. Only the least effective action, stop-
ping the gas addition, was used in the analysis. This allowed the fuel
level to coast up and make the reactor critical after the two control
rods had been dropped to check the initial power excursion.

The power and temperature transients associated with the accident
described abowve were calculated with the aid of both digital and analog
computers., ©Since the useful range of an analog computer is only about
two decades for any variable, the initial part of the power transient was
calculated with the digital kinetics program MURGATROYD, The digital
151

calculation was stopped at 10 kw when the power began to affect system
temperatures, and the digital results were used as input to start the
analog calculation. Since it was clear that the reactor would go critical
again after the control rods had been dropped, the analog simulation in-
cluded the compensating effects of the fuel and graphite temperature co-
efficients of reactivity. Because of the small fuel coefficient, it was
necessary to use a highly detailed model to represent heat transfer from
the fuel to the graphite during the transient.

The results of the maximum fill accident simulation are shown graph-
ically in Figs. 12.8 and 12.9. Figure 12.8 shows the externally imposed
reactivity transient exclusive of temperature compensation effects. The
essential features are the initial, almost-linear rise which produced the
first power excursion as fuel flowed into the core, the sharp decrease
as the rods were dropped, and the final slow rise as the fuel coasted up
to ite equilibrium level., TFigure 12.9 shows the power transient and some
pertinent temperatures. The fuel and graphite nuclear average tempera-
tures are the quantities which ultimately compensated for the excess re-
activity introduced by the fuel coast-up. The maximum fuel temperature
refers to the temperature at the center of the hottest portion of the
hottest fuel channel. The initial power excursion reached 24 Mw before
being checked by the dropping control rods, which were tripped at 15 Mw,
This excursion is not particularly important, because it did not result
in much of a fuel temperature rise. After the initial excursion, the
power dropped to about 10 kw and some of the heat that had been produced
in the fuel was transferred to the graphite., The resultant increase in
the graphite nuclear average temperature helped to limit the severity of
the second power excursion., Reactivity was added slowly enough by the
fuel coast-up that the rising graphite temperature was able to limit the
second power excursion to only 2.5 Mw. The maximum temperature attained,

1354°F, can be tolerated for long times.

12.7.4 Fuel Pump Power Failure

The consequences of Interruption of fuel circulation while the re-

actor is at high power were determined by analog computer simulation of
NET REACTIVITY (%)

1.0

0.%

-1.0

 

152

UNCLASSIFIED
ORNL DWG, 63.8181

 

=0 100 150 200 C 2% 300 350

Net Reactivity Addition During Maximum Filling Accident.
153

UNCLASSIFIED
ORNL DWG. 63.8182

1360

1320

1280 =

1240 +F

TEMPERATURE (°F)

1200 =

POWER (Mw )

 

0 oy 100 150 200 250 300 390

TIME (sec)

Fig. 12.9. Powver and Temperature Transients Following Maximum
Filling Accident.
154

the nuclear, heat transfer, and thermal convection equations for the sys-
tem. Failure of the fuel pump power supply, with subsequent coast-down
of the flow, was simulabted by causing the circulation rate to decrease
exponentially with a 2-sec time constant until it reached the thermal
circulation rate determined by the temperature rise across the core. As
the fuel circulation rate decreased, the effective delayed neutron frac-
tion was increased by 0,003 and the heat transfer coefficient in the heat
exchanger was reduced.

Figure 12.10 shows the results of a simulated fuel pump failure at
10 Mw, with no corrective action. The gain in delayed neutrons caused
the initial rise in the power. The decrease in heat removal from the
core, coupled with the high production, caused the core outlet tempera-
ture to rise. As the fuel flow and the heat transfer in the heat ex-
changer fell, the continued heat extraction at the radiator caused the
coolant salt temperature to decrease and reach the freezing point in less
than 2 min, (The behavior in simulator tests at lower power was similar,
but the coolant temperature remained above the freezing point if the ini-
tial power was less than 7 Mw.)

Practical measures can be taken to prevent freezing of the coolant
salt or overheating of the core in the event of fuel pump failure. These
consist of closing the radiator doors and inserting the control rods,
Figure 12.11 shows simulator results for a case in which these actions
were taken rather slowly, yet proved effective. One second after the

pump power was cut, a negative reactivity ramp of —0.075% 8k/k per second

was initiated, simulating insertion of the control rods at normal driven
speed, Beginning 3 sec after the pump power failure, the simulated heat
removal from the radiator tubes was reduced to zero over a period of about
30 sec.

12.7.5 Conclusion

The results of the analyses described here form part of the basis
for a comprehensive analysis of the safety of the reactor system. The
credibility and the importance of each accident are evaluated and dis-
cusged in the Safety Analysis Report.

 
155

UNCLASSIFIED

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ORNL-LR-DWG 67578
f T f
1 t
|
1400 T ""’i _/ - -‘---'-—-—.__\
‘ CORE OUTLET
‘ //
————__| CORE FUEL MEAN
1300 /‘// ’”>\\ |
A e
SV T GRAPHITE MEAN
. 1200 _ — e — — e
o
= e ——— INLE l .
" ~—|__CORE INLET }
:) .-._-—- !
—
§ 1100 '
w Ty I t ]
a RADIATOR INLET
w |
— \\ !
1000 . 7
i \_____
\\
\ \
\ \
900 ——— o
SALT LEAVING RADIATOR =]
— —
-..g-:
800
12 1
/-
10 \\
\\QSWER
— 8
=
=
N
& 6 \
= \
O
a 4 k\
0
0 20 40 60 80 100 120
TIME (sec)

Fig. 12.10,

Power and Temperature Transients Following Fuel Pump
Power Failure at High Power; No Corrective Action.
156

UNCLASSIFIED
ORNL-LR-DWG 67579

1300
CORE QUTLET

GRAPHITE MEAN

 

w
°
° 1200 E FUEL MEA
w
5 CORE INLET
—
<
o
w
& 1oo
= RADIATOR INLET
—
RADIATOR OUTLET
1000 DIATO -
FISSION POWER
3
=
a
L
=
O
c.

 

0 20 40 60 80 100 120
TIME (sec)

Fig. 12.11. Power and Temperature Transients Following Fuel Pump
Power Failure at High Power; Radiator Doors Closed and Control Rods
Driven in After Failure.
157

13. BIOLOGICAL SHIELDING

13.1 General

The basis for the design of all biological shielding is the recom-
mended maximum permissible exposure to radiation of 100 mrem/week, or 2.5
mrem/hr based on a 40-hr work week. The criterion for the MSRE biological
shield design is that the dose rate will not exceed 2.5 mrem/hr during
normal operation at any point on the shield exterior that is located in
an unlimited access area. This criterion inherently includes allowance
for significant underestimation of the hot-spot dose, with the general
area still below 2.5 mrem/hr.

As in most reactor designs (and particularly in the case of the MSRE,
since it has to fit within an existing reactor contaimment cell and build-
ing) nuclear, mechanical, and structural requirements, ag well as eco-
nomics, preclude the design of permanently installed shielding that re-
sults in a dose rate that is less than the permissible rate at all points.
Consequently, the final shield design allows for addition of shielding as

needed to reduce the radiation level at localized hot spots.

13.2 Overhead Biological Shielding

The calculations which are described in this section on the biolog-
ical shielding over the reactor cell were carried out at an early stage
of the design.4l The source strengths which were used, and which are re-
ported in this section, differ somewhat from those obtained from the
latest nuclear calculation (see Sec 13.3.4 for later results). The dif-
ferences would make no significant change in the prescribed shielding.

In this section, the calculations sometime refer to ordinary concrete,
which was initially considered for use. The final shield design is com-
posed of barytes concrete, ordinary concrete, and steel which is equiva-

lent to about 9 ft of ordinary concrete and about 7 £t for neutrons.

13.2.1 Geometry

The basic shield construction is shown in Fig. 13.1., Two separate

layers of concrete blocks are used; the majority of the lower blocks are
158

UNCLASSIFIED
ORNL—DWG 63-7321

-+—— BILOG NORTH

 

- Y -in. MAX. BLOCK SPACING

1 AT e . N TR BN |5
3ft 6in.)|| : . : UPPER SHIELD BLOCKS e

. - - o f] a

T . - ) s e s g e o
L e o . - - . - « e -

 

 

 

 

 

 

 

 

 

 

+
<t

\ ‘.‘n

 

 

 

'p:.‘._- . : L . Coe . "' : :_-.P- o '. ‘:

t;!2m~ ' é"*lRONENSERTS T oo

3ftein |t T L f "
T " LOWER SHIELD BLOCKS

e e ~f=Y-in. MAX. Co

Coigeelleridl st Tl - SPACING e T e %

 

o
\T\\ L

 

 

 

 

 

SUPPORT )
10ft Oin. SHOULDER

CELL
y WALL

131t 4in.

 

 

ORI NN

e

16 in.

|

-
727

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

/ REACTOR
/ VESSEL

\THERMAL SHIELD

SECTION A-A

T R BT, e P

 

 

 

ANy

    
 

 

 

16in.
3ft Oin.
Yo-in. MAX. GAP

SHIELD SUPPORT BEAM
{CONCRETE~FILLED T-BEAM)

Fig. 13.1. Elevation View of Basic Overhead Shield.
159

23-1/2 in. wide and 3-1/2 £t thick, and are barytes concrete. These
blocks do not extend completely across the cell but are intersected by

two shield support beams, shown in Figs. 13,1 and 13.2, which run at right
angles to the lower shield blocks. The top shield blocks are ordinary
concrete, 23-1/2 in. wide and 3-1/2 ft thick, and extend completely across
the cell. A thermal shield that is 16 in. thick and composed of about

half water and half steel surrounds the reactor except for a 2-ft-diam

UNCLASSIFIED
ORNL—DWG 63-7322

. i, .
(D REACTOR VESSEL, SHOWING MAXIMUM AND gft 3in, 2ft 67 in.

MINIMUM SOURCE FACES. 13in.

2ft tin.

@ PUMP BOWL

(® HEAT EXCHANGER ACTIVE
LENGTH CENTER

@ PUMP DISCHARGE LINE

-— — INDICATES CENTER OF SPACING | /
BETWEEN LOWER SHIELD /////
/

—=! 24in.

N
i

L0
| \ |
TZAeZ XA N o,

!
|
i

t
|
[

BEAMS

—— INDICATES CENTER OF
SPACING BETWEEN
UPPER SHIELD BEAMS

 

  
  
 
 

SHIELD SUPPORT
BEAMS

 

 

 

 

 

 

 

 

A

S

|
|
|
Vi
74t fin. \
|
\ !
_‘ig}{iy/_

Y

N
12 ft Oin.R—/

 

 

 

 

 

 

 

 

 

 

 

|
o
|
!

v
2

o

 

 

 

 

 

 

 

 

— 5 ft Sin.
PIPING SCHEMATIC

 

 

fe— 6 ft Sin, ——=

Fig. 13.2. Plan View of Basic Overhead Shield.
160

opening at the top. Obviously the maximum dose rate will exist over this
opening, in an area limited by the thermal shield.
The dose rates that will exist on top of the shield are due to two
conditions:
1., a general radiation level with the full thickness of the shield ef-
fective,

2. local peaks in the radiation level due to imperfections in the shield.

The general radiation levels above the shield have been based on the
relations given below for a constant-source-strength discsk source and for

cylindrical and truncated right-circular cone constant-volume sources 142

disk source,

S
¢ = Blut) —§- [B1(pnt) — E{(ut sec 0)] ; (13.1)
cylindrical source,
s RS |
¢ = B(p.t) m [F(Ql, p.t) + F(Qz, fJ.'t)] 3 (13.2)

truncated right-circular cone source,

S Es(ut sec 9)

¢ = Blut) Z}-r;- Ep(ut) ~ 7 | °

(13.3)

(See Sec 13,6 for definition of symbols.)

Ordinary concrete dose buildup factors and standard attenuation co-
efficients were used for the gamma rays. The buildup factors may be used
as indicated (constant for a particular case), since the s0lid angle in-
volved 1s small.

Neutron attenuation was estimated using neutron removal cross sec-
tions with a buildup factor of unity.

Neutron and gamma sources are given in Sec 13.2.2 dealing with source
strengths,

Estimates for the local peak dose rates that will occur above gaps
between adjacent shield beams were determined using the methods given

above for the solid shield with the appropriate effective source geometry.
161

The effective source geometry for a crack is illustrated in Fig.
13.3. For a given crack width, w, and a given distance, a, between the
dose point and the source, a fraction of the source has direct line of
sight to the dose point. This effective source is only attenuated by the
partial thickness of the shield, t. In these estimates buildup of scat-
tered photons has not been included, though the scattered photons make an
appreciable contribution.

Figure 13.2 shows the location of the primary reactor system with

respect to the spacings and locations of the shield blocks,

13.2.2 Source Strengths

The sources of radiation considered were fission product decay gam-
mas, N16 decay gammas, prompt fission gammas, thermal neutron capture
ganmas, and fast neutrons. [The F12(n,y)F?? reaction produces a 1.8-Mev
photon, but its contribution to the dose rate through the top shield is
negligible. ]

UNCLASSIFIED
ORNL—-DWG ©3-7323

7T 7 i
? }éégij;/ii;—/\“wHMIC// 3.5
NOMINAL P Y
SHIELD SN et
T}HCKNESS \§§§;;:\ §§E§;~E§gEgD i
R \\\\\\\\ t o

2

’ \/‘74“’(35)

,/ /—:_/4 TOTAL SOURCE

FACE
EFFECflVE SOURCE FACE

 

 

 

 

 

Fig. 13.3. Geometry for Determining an Effective Gap Source.
162

Fission Product Decay Gammas., — Goldstein“?® has reported the gammas
from the fission products to have an exponential energy spectrum and a
total energy decay rate of 5.5 Mev/fission at saturation. It was assumed
that this spectrum and decay rate was constant through the primary system.
Table 13.1 gives the fission product source strengths for a 10-Mw powexr

level snd a 62-ft2 total fuel volume.

Nitrogen-16 Decay Gamma Activity. — The reaction F19(n,)N28 (7.36-
sec half-life) is a high-energy reaction with an appreciable cross section
above 3 Mev, going to a maximum of ~310 mb at ~5.8 Mev, 4%

The N'® production rate was determined by numerically integrating the
neutron flux and reaction cross section over the energy range 3 to 10 Mev.
Fast neutron fluxes over this energy range were obtained from multigroup

reactor calculations.45

The activity in the primary system was based on Egq, (13.4), given
below, using a constant production rate in each region of the reactor

vessel.

Table 13.1. Saturated Fission Product Gamma-Ray Spectrum
(10 Mw, 62 ft° fuel)

 

 

Energy Range Average Energy Energy Emission Rate
(Mev) (Mev/photon) [Mev/(sececc)]
x 100
O0—1 0.41 31.5
1--2 1.41 36.1
3—4 341 9.66
) deg 41 416
5_5-4 501 0088

 

Total 103

 
163

The saturated activity at the reactor wvessel exit is

-A\t -\t

e e Yip(1l-e

AN = Pa(l - e s

~A\T -\t -\t -At
+ Pc(l —e 9Ye Y4 Pu(l - e u)} + {1 - e t} . (13.4)

The N*© production and decay rates are given in Table 13.2.

Neutron lLeakage and Gamma Flux Core Sources. — The fast neutron leak-

 

age and gamma flux from the top of the core were obtained from two-group,
two-dimensional reactor calculations.*? The neutron leakage rates at 10
Mw are 1.36 X 102 rfast neutrons/(sec-cm?) and 4.9 x 1010 thermal neu-
trons/(sececm?); the gamma fluxes are listed in Table 13.3. These leakage
rates and fluxes are at the surface of the reactor and should be repre-
sentative of a cosine, or Fermi, source. It was assumed that they had a
cosine distribution; therefore they were increased by factors of 4 and 2,

respectively, and treated as an isotropic source , 8

Table 13.2. N1® Saturated Activity

 

 

Region Production Rate Average Decay Rate®
[atoms/(secscc)] [Mev/ (sececc)]
Reactor outlet piping 0 2.7 % 1010
Pump (bypass flow) 0 1.25 x 1015P
Piping 0 2,42 X 1010
Heat exchanger 0 2.20 x 1010
Piping 0 1.97 x 101°
Reactor inlet 0 1.82 x 101°
Annulus | 0.176 x 1010 1.67 x 101°
Lower header 0.176 x 1010 1.52 x 1010
Core 1.10 x 101° 2.43 x 1019
Upper header 0.176 % 1010 3.0 x 1010

 

%6.13-Mev y in 75.9% of decays and 7.10-Mev y in 6.1% of decays,

PUnits of Mev/sec, assuming all N*% in the bypass flow decays in
the pump bowl,
164

Table 13.3. Gamma Fluxes from Top of Reactor Vessel,
at 10 Mw Reactor Power

 

Gamma, Flux

Energy (Mev) [Mev/(sececm?)]

 

x 1012

5 2.50
4.28
3.63
1.85
1.08
0.80
10 1.14

Qg o NV H OO

 

Iron and Concrete Capture Gammas. — The energy spectrum of the cap-

 

ture gammas was obtained from the data of Troubetzkoy and Goldstein., %7
In both the reactor thermal shield and the biological shield, the capture
gamma source was assumed to be a plane isotropic disk source located two

fast neutron relaxation lengths from the inside of the shield.,%®

13.,2.3 Estimated Dose Rates

 

Tables 13.4—13.6 show the relative contributions of the individual
sources as a function of the shield thickness and spacing between the
blocks, These values have hbeen compiled in Table 13,7 for a maximum block
spacing (1/2 in,).

The results have been presented only as a function of ordinary con-
crete, assuming that for gamma attenuation the barytes concrete may be
accounted for by a ratio of the densities. The attenuation of neutrons
is essentlally identical in either barytes or ordinary concrete, as shown
by the data of Blizard,4® Hence, for the neutron dose rate results, a
given thickness of barytes concrete will have the same effect as the iden-

tical thickness of ordinary concrete.
165

Table 13.4. Gamma Dose Rates Above the Primary System Components
for a Solid Shield, at 10 Mw Reactor Power

(A1l values given as tissue dose rates, mrem/hr)

 

Thickness of Ordinary Concrete, ft

 

 

 

 

 

 

 

 

 

 

Component
7 8 9
Pump bowl®
Fission products 9.5 (5.3) 1.2 (C.68) 0.16 (0.09)
N1€ bypass flow 8.0 (8.0) 1.5 (1.5) 0,28 (0.28)
N6 primary flow 6.3 (0) 1.2 (0) 0.22 (0)
Total 24 (13) 3.9 (2.2) 0.66 (0.37)
Heat exchanger
Fisgsion products 7.6 0.98 0.13
w6 10 1.9 0.35
Total 18 2.9 0.48
Pipingb
3.2 0.52 0.09
B 4.0 0.64 0.11
C 2.0 0.32 0.05
D 1.0 0.17 0.03
B 2.7 0. 44 0.07

 

®Values in parenthesis represent a possible lower limit.

bLoca‘bions shown in Fig. 13.2. Dose rates are for N1© activity and
Tission products.

Table 13.4 gives the gamma dose rates above the primary system com-
ponents vs the shield thickness for a solid shield, at a 10-Mw reactor
power level. Two values are given for the pump bowl, these represent es-
timates of an upper and lower limit, depending on how effective the pump
motor and the internal pump shield are in reducing the dose.

The incremental dose above a given source due to adjacent sources

has not been determined. Since the total dose rate will be less than the
166

Table 13.5. Dose Rates Above the Reactor Vessel
for a Solid Shield, at 10 Mw Reactor Power

(A11 values given as tissue dose rates, mrem/hr)

 

Thickness of Ordinary Concrete, ft

 

 

Source
7 8 9
Gamma rays
Core 136 28 6.2
Nt6 15 2.8 0.51
Iron capture 86 17 3ot
Concrete capture 19 1.0
Neutrons from core 1.8 0.10 0.005

 

sum of the individual dose rates, an upper limit for the combination may
be found by adding the dose rates directly above each of the sources; for
example, the total dose rate above the heat exchanger, including piping
lengths B and C, will be less than 0.64 mr/hr for 9 ft of concrete (0.64 =
0.48 + 0.11 + 0.,05).

The dose rates directly above the reactor vs feed of ordinary con-
crete are given in Table 13.5, for a solid shield and a 10-Mw power level.
The total dose rate is subdivided into the neutron and gamma contribu-
tions, as the shield is equivalent to ~9 ft of ordinary concrete for the
gammas and ~7 £t for the neutrons.

The effect of spacing between the upper shield blocks is shown in
Table 13.6 as a function of the nominal shield thickness and the face area
of the source covered by the gap, wL. These estimates are essentially
minimum values that may be expected above the gaps. Two factors that will
make the actual gamma dose rate higher are:

1. Scattered radiation; since buildup and sources from scattering were
not included in the estimate.

2. The uncollided radiation that is partially attenuated by the upper
shield blocks; that is, photons traveling at an angle from the shield
normal slightly greater than the included angle used to determine the
effective source.
167

Table 13.6. Effect of Spacing Between Upper Shield Blocks
on Dose Rates, at 10 Mw Reactor Power

(A11 values given as tissue dose rates)

 

Thickness of Ordinary
Concrete, It

 

 

source
7 8 9
Reactor gamma rays
[D/wL, mr/{hr.in.?)]
Core 69 12 2.2
N6 activity 7.8 1.3 0.21
Fe capture 2.0 1.7 0.29
Concrete capture 240
Reactor neutrons 273 11 0.42
[D/wL, mrem/(hrein.?)]
Pump bowl gamma rays
[D/wL, mr/(hr+in.?)]
Fission products 13 1.3 0.14
16 activity 10 1.7 0.27
Heat exchanger gamma rays
[D/W: IIlI‘/ (hrein, )]
Fission products 78 8.1 0.89
N16 activity 46 7.7 1.2
Pump discharge line®™ 680

[D/w?, mr/(hrein.?)]

 

gDue to coincidence of upper shield block spacing and lower shield
block and shield support beam spacing, shown in Fig. 13.2.
168

Table 13.7. Summary of Dose Rates Above Overhead Shield,™
at 10 Mw Reactor Power

 

Peaking at Cracks

 

 

source Solid Shield
Minimum Probable

Reactor

Gammas 14 80 160

Neutrons 1.8 4600 6000
Pump bowl gammas 0,88 10 20
Heat exchanger gammas 0.65 1.5 3
Pump discharge piping gammas 0,15 170b 340b

 

%3.5 ft of barytes concrete and 3.5 £t of ordinary concrete.

bDu.e to coincidence of gap between upper shield blocks with the gap
between the lower shield blocks and shield support beam.

The second factor given will also tend to make the actual fast neu-
tron dose rate higher.

The results given in Tables 13.4~13.6 have been interpolated and com-
piled in Table 13.7 to show the expected dose rate estimates abowve the
present reactor shield. Effective source face areas were based on l/2—in.
gap spacings and source lengths, L, shown in Fig. 13.2. For the reasouns
discussed, neutron and garma peak dose rates were arbitrarily increased
by factors of 1.3 and 2.0, respectively, to give the "probable" values
listed.

13.3 Lateral Biological Shielding

The biological shielding around the sides of the reactor and reactor
cell is composed of steel, water, magnetite sand, ordinary concrete, and
barytes concrete. The detailed arrangement of this shielding and the ad-
ditional shielding requirements due to the induced activity in the coolant

salt are discussed in the following sections.
169

13.3.1 Basic Shield Arrangement

Figure 13.4 shows the layout of the reactor cell, shielding, and ad-
Jjacent areas in plan view. Mogt of the cell walls and shielding were
buillt before the MSRE program, for an earlier reactor installation.

The thermal shield immediately surrounding the reactor vessel was
installed specifically for the MSRE. It consists of a steel tank, 16 in.
thick on the sides, filled with steel shot and water. The water is cir-
culated to remove the heat generated in the shield.

The major part of the lateral shield i1s an ~3=-ft-thick annulus formed
by two concentric cylindrical steel tanks (inner tank, 2 in. thick; outer
tank, 5/8 in. thick) enclosing the reactor cell. The hollow annular space
(33 in.) is filled with a compacted magnetite sand—water mixture with a
bulk density of at least 210 1b/ft3. Except in two large areas where
certain shield penetrations are located, the annulus is in turn surrounded
by a monolithic concrete wall with a minimum thickness of 21 in. The two
areas that lack the concrete portion of the shield are the south elec-
trical service area and the coolant cell. The south electrical service
area adjoins the north side of the reactor cell just below the transmittexr
room shown in Fig. 13.4. The coolant cell is southwest of the reactor
cell and is connected by a passageway along the shield wall and by a 7-
by 11-ft air duct to the blower house, or fan room, where the main cooling
fans are located. The fan room walls on thé west side and parts of the

north and south sides are louvered to admit air.

13.3.2 South Electrical Service Room

Because of the gap in the concrete wall around the reactor cell, the
dose rate in the south electrical service room will be too high for access
during high-power operation. The room will therefore be sealed to prevent
entry except when the reactor is shut down. The room itself is enclosed
in 2 ft of concrete (except for the narrow passageway leading around the
reactor cell to the northwest corner of the coolant cell). This should
be adequate to reduce the dose rate to less than 2.5 mrem/hr in the north
electrical service room and in the transmitter room located above. There
exists a possibility, however, that some minor hot spots may occur in the

north electrical service room along the 2-ft wall separating it from the
UNCLASSIFIED
ORNL DWG. €3-4347

   
 
  
  
  

    
 
 
 
 

PUMP

! SYSTE

|

    

 

FUEL
OFFICE LUBE OIl

  
  
  
 

   
 
 

 

BATTERY
ROOM

 

CHEMICAL
LABORATORY

COOLANT PUMP
UBE OIL 'SYSTEM

MAINTENANCE
SHOP

  
  
 
 
  
 
 
       

 

 

  

 

   
      

   
  

  
 
 

  
 
  
 

   
 

  
  
 

   
  

   
   
  
 
 

  
   
  

  

   
  

    
    

TO FILTERS
AND STACK
CELL VENTILATION
T AND BLOCK
VALVE
C SPECIAL
|| TRANS ROOM® EQuIP ROOM
EQ S$STORAGE I ;3%’ TO VAPOR
MAINTENANCE T oeRLL COND SYSTEM
PRATICE CELL Orann i HEAT ACTOR COOLANT FUMP
CELL EXCHANGER
B FUEL COCLANT SaLT
R A
1QUID WASTE CONTAMINATION!] |PROCESSING DRAIN TANK
CELL CELL ELL
REGULATOR
CELL
A

 

FUEL SALT FUEL SALT
ADDITI STORAGE
STATION TANK

  

 
 

      

FLUSH TANK
FUEL DRAIN
TANK NG 2

 

DIATOR

   
  

FUEL DRAIN T BLOWERS

TANK NO. t

 
 

THERMAL
SHIELD

  

REACTOR
CELL
ANNULUS

 
  

BLOWER

"ELEC. SERVICE AREA BELOW HOUSE

    

RADIATOR
BLOWERS

 
   
 

Fig. 13.4. Plan View of MSRE.

OLT
171

south electrical service room, due to the various penetrations in the an-
nular shield. The dose would depend on the material in the penetrations

and whether the penetrations could "see"

a strong source. These possible
hot spots would have only nuisance value and can be eliminated by local-
ized stacking of concrete blocks on either side of the wall separating
the two electrical service rooms. The 4-in.-diam holes that penetrate
the wall separating the two electrical service areas will obviously re-
quire plugs.

The 2-ft-thick floor of the transmitter room located directly over
the south electrical service room has a number of penetrations that will
require special attention in the way of additional shielding. These in-
clude several 4-in.-diam holes, an 8- by 30-in. opening which is traversed
by two electrical conduits, and the ventilating duct located on the south

wall of the transmitter room.

13.,3.3 Coolant Cell and Fan House

 

On the face of the annular shield where it is exposed to the coolant
cell, there are two segmental indentations in the vicinity of the coclant
line penetrations. These indentations are about 14 ft long and 4 ft high,
with a maximum depth of nearly 9 in. On the inner side of the indenta-
tions the steel tank thickness was increased from 2 in. to 4 in., but this
only partially compensates for the removal of the sand-water mixture where
the indentation is deepest.

Because of the gap in the concrete wall and the reduced thickness
of the annular shield, the dose rate in the coolant cell due to radiation
from the reactor cell alone would be much too high for personnel access
during power operation. Radiation in the coolant cell from this source
can be reduced by additional stacked block shielding against the reactor
cell wall, but there remains the gamma radiation from the circulating
coolant salt, which becomes activated in passing through the fuel-coolant
heat exchanger. Access to the coolant cell during operation is therefore
prohibited.

Because of the very large duct comnecting the coolant cell and the
fan house, high radiation levels in the coolant cell lead to undesirably

high dose rates in the fan house. A close estimate of the dose rates at
172

various points in the fan house cannot be made, because of the complicated
geometry of sources and shielding. Using simplified line-of-sight methods
of calculation, and assuming no additional shielding, the dose rate at

the south louwvered wall in the vicinity of No. 2 fan was estimated to be
140 mrem/hr. Contributions from various sources to this dose rate are
itemized in Table 13.8.

The dose rate from the most important single source, the thermal
shield, could be reduced by the addition of dissolved boron in the thermal
shield water (10 g/liter would reduce the dose rate from 71 mr/hr to about
15 mr/hr, see Fig. 13.5), but the radiation from the other sources in the
reactor cell would still be too high. Therefore, additional shielding
will be added between the reactor cell and coolant cell to reduce the dose
rate from all sources in the reactor cell to a negligible level, thus ob-
viating the use of boron in the thermal shield water. A wall of stacked
barytes concrete blocks with a minimum thickness of 16 in. will be used
for this purpose.

With the additional shielding around the reactor cell, the dose rate
in the fan house is controlled by the gamma activity of the circulating
coolant salt. The highest dose rate from this source will be in the vi-
cinity of No. 4 fan., It is estimated that the dose rate here would be
16 mr/hr from the radiator and 11 mr/hr from the coolant pump and piping.
Most of the latter contribution will be eliminated by concrete blocks

stacked in the area between the radiator housing and the reactor shield.

Table 13.8, Dose Rates Near No, 2 Fan During 10-Mw Operation
(No additional shielding)

 

 

Source Dose (mrem/hr)
Core neutrons 4
Core gammas 15
Circulating fuel gammas 35
Thermal shield capture gammag 71

Radiator and coolant piping gammas 15

 
173

Nothing can be done to reduce the dose rate in the fan house from the ra-
diator without interfering with the air flow. However, there is normally
no need for access to this area during power operation, so the fan house
will be made a controlled-access area.

After the addition of the stacked block shielding described above,
it is estimated that the dose rate along the west louvered wall will prob-
ably not exceed 2.5 mrem/hr and will exceed this value somewhat along the
south louvered wall. If the dose outside the wall proves excessive, an
existing concrete block wall located a few feet outside the louvered wall

on the south side will be extended around the fan house asgs far as needed.

UNCLASSIFIED
ORNL DWG, 63-8183
100 -

 

10

DOSE (mr/hr)

1.0

0 20 Lo 60 80 100
BORON CONCENTRATION (g/liter)

Fig. 13.5. Biological Dose from Thermal Shield Capture Gammas as
a Function of Boron Concentration. Dose at louvered wall near No. 2 fan.
174

Adjoining the fan house on the north is a ramp leading down into the
coolant cell. The large cell exhaust penetration in the annular shield
is in line with this sloping passage. Although a 9-in. steel shadow
shield is provided in front of the exhaust line, the radiation leaking
from the reactor cell at this point will be unusually high. In addition,
radiation will scatter into this area from the passageway leading from
the south electrical service room. A stacked block wall, at least 1 ft
thick, with a labyrinth passage, will be provided at the base of the ramp

t0o reduce the dose rate outside to the tolerance level,

13.3.4 Source Strengths

The source strengths of the fuel salt activities and capture gammas
from the thermal shield were different from those used in the top shield
calculations, This reflects changes due to more recent calculations and
a need for more sophisticated calculations for the capture gammas because
of the more critical nature of the shielding in the fan house area.

Nitrogen-16 and Fluorine-20 Activity in Fuel Salt. — The source

strengths of the N6 and F?0 activities are summarized in Table 13.9,

Table 13.9. N6 and F?°0 Activities™ in the Fuel Salt
for 10-Mw Operation

 

Activity [dis/(sececm?)]

 

 

N16 FQO
Reactor outlet 4e62 X 10° 4ed8 X 107
Pump bowl inlet 4.18 x 10° 4e20 X 10°
Inlet to reactor downcomer 2.67 x 10° 3,13 X 10°
Average activity in circulating fuel 3.56 X 10° 3,73 x 10°
Average activity in external loop 3.56 X 10° 3,77 x 10°
Average activity in reactor vessel 3,56 x 107 3.72 x 10°
Total production rate (atoms/sec) 6.78 x 1017 7.12 X 1012

 

fCaleulated using latest neutron balances from MODRIC and EQUIPOISE
calculations for fuel B (see Chap. 3).
175

Capture Gammas in Thermal Shield. — The thermal flux distribution

 

used in calculating the capture gamma source strength in the thermal
shield is shown in Fig. 13.6. Thesge values were calculated with the re-

actor code DTK, a one-dimensional Sn transport calculation,

Induced Activity in Coolant Salt. — Practically all of the activation

 

of the coolant salt will occur in the heat exchanger, where it is exposed
to neutrons resulting from decay of the delayed neutron precursors in the

fuel salt and a small amount of fissioning.

For F2° gna N6 during steady-state operation, the saturated specific
activity, or source strength, of the circulating coolant at any time, €,

after leaving the heat exchanger tubes is

_ ATy
1= }e-m, (13.5)

S =
v P [l 8-7\le+sz

where p is the production rate per unit volume of coolant in the heat ex-
changer tubes, T, is the residence time in the heat exchanger tubes, and
Tz dis the residence time of the circulating stream outside of the heat
exchanger tubes. The saturated specific activity was calculated*® to be
7.25 x 10% and 2,55 x 10% dis/(em3+sec) for N1 and Fe0 respectively.

13.3.5 Calculation Methods

 

The core gammas and core N1©

activity were treated as uniform cylin-
drical sources and Eq. (13.2) was used for the dose rate calculation. It
wag possible to reduce all coolant salt dose rate calculations to simple
point and line sources. The capture gammas from the thermal shield may
be represented by a truncated right-circular cone source [Eq. (13.3)], but
because of the distance to the louvered wall, point source approximations
were used. The thermal shield was divided into 11 concentric cylinders,
and. each half of a cylindrical annulus was considered a disk with a radius
of 5 ft. DBecause of the distance involwved, each disk could then be
closely approximated by a point source based on the flux at the midplane
of the disk. The total dose rate is the sum of the contributions from

each energy group and each disk.
)

-1

THERMAL NEUTRON FLUX (neutrons cm—g sec

lOlO

Fig. 13.6.

 

176

  

i6 24 32
DISTANCE INTO THERMAL SHIEID (cm)

Thermal Flux in Thermal Shield

UNCLASSIFIED
ORNL DWG. 63-.8184

 

Lo

¢of MSRE.
177

13.4 Conditions After Reactor Shutdown

A1l areas external to the reactor cell will be accessible on an un-
limited basis minutes after reactor shutdown except under one condition.
When the coolant salt lines are drained, two 4-in,-diam holeg are left in
the shield. One of these coolant pipes {(1ine 200) "looks" directly at
the pump bowl; depending on the degree of drainage of the fuel salt, the
dose rate in the vicinity of this line can be several rem/hr. The other

1

coolant pipe (line 201) does not "see" any large source but will leak a

few mrem/hr of scattered radiation. There is no practical way of provid-
ing permanent shielding for the drained condition., Temporary shadow
shielding will be used for any maintenance work in the wvicinity of these

lines,

13.5 Summary

The solid portion of the overhead shield is sufficient to limit the
dose rate to less than 2.5 mrem/hr except directly over the reactor core,
where the dose rate was estimated to be 16 mrem/hr. Large dose rates up
to 7 rem/hr could exist over some points where the 1/2-in. gaps overlap.
However, it is planned to insert polyethylene and steel strips in the gaps
existing in the critical areas and finally to stack concrete blocks as
needed over any remaining hot spots.

The lateral shield with the additional 16-in. barytes block to be
installed and further field addition of concrete blocks where needed
should bhe adequate. If the dose rate at the louvered walls does exceed
2.5 mrem/hr, an existing concrete block wall located a few feet outside
the south louvered wall can be extended quickly and easily as far around

as needed.,
178

13,6 Nomenclature for Biological Shielding Calculations

&

Blut)
D

Eq{ut), E2(ut)

F(el: U—t), F(QZ) Ut)

e F > N

Subscripts:

S o m o= O P

Distance from source to dose point
Buildup factor
Dose rate

Attenuation functions, tabulated in
TID-700442

Attenuation functions, tabulated in
TID-700442

Source length

Concentration per unit volume
Production rate per unit volume
Radius of disk or cylindrical source

Source strength, number per unit time
per unit area, or unit volume

Regidence time

Regidence time

Time and thickness

Gap width

Self absorption distance
Decay constant
Attenuation coefficilent

Particle flux

Annmulus

Core

Lower header
source

Total

Upper header
179

14. MISCELLANEQOUS

1l4.1 Radiation Heating of Core Materials

Heat produced in the graphite by absorption of beta and gamma ra-
diation and the elastic scattering of fast neutrons amounts to about 7%
of the total heat produced in the reactor. This heating of the graphite
affects the overall kinetic behavior of the reactor through its effect
on graphite temperature response. Heat produced in the INOR parts of
the reactor, on the other hand, is a small fraction of the total and has
little effect on overall behavior. It is important, however, from the
standpoint of local temperatures.

The spatial distribution of the graphite heating was computed, with
the results shown in Figs. 14.1 and 14.2. In these computations the
main part of the core was treated as a homogeneous mixture, with gamma
energy being absorbed at the point of origin. (This is a reasonable
approximation for the MSRE, because the core is large and the channels
are small in relation to the mean free path of gamma rays.) Capture
gammas from the INOR control rod thimbles and core support grid were
treated separately, because the sources were quite concentrated.

Gamma-ray heating of INOR at a number of points on and inside the
reactor vessel was computed with digital computer codes NIGHTMARE*? and
20GH?C (a two-dimensional version of NIGHTMARE). These computations ob-
tained the gamma flux at one specified point by summing the contributions
of gammas originating in all parts of the reactor, using appropriate
attenuation and buildup factors. A multiregion model of the reactor
similar to that described in Sec 3.2 was used in these computations.
Values of gamma sources per fission and per capture were taken from ref
49. The source of fission product decay gammas was assumed to follow
the same spatial distribution as the fissions. Results of these calcu-
lations are given in Table 14.1.

A summary of the nuclear energy sources and the places where the
energy appears as heat is given in Table 14.2. The total energy which
heats the fuel as it passes through the reactor vessel is 196.7 Mev per

fission.
180

UNCLASSIFIED
DRNL DWG, 63-8185

HEATING (w/cc)

 

0 L 8 12 16 20 2l 28
RADIUS (in.)

Fig. 14.1. Heating in Graphite: Radial Distribution near Midplane
at 10 Mw.
181

UNCLASSIFIED
ORNL DWG. 63-8186

 

0.7
0.6
0.5
0.4

o

L

=

2

H

% 0.3
0.2
0.1

0 10 20 30 Lo 50 60 70

A¥IAL POSITIOK (in.)

Fig. 14.2. Heating in Graphite: Axial Distribution 8.4 in. from
Core Center Line at 10 Mw.
182

Table 14.1. Gamma Heating of INOR in MSRE, Operating at 10 Mw

 

Heat Source Calculation

 

 

Location (w/em?) Method Reference
Rod thimble, midplane 2.5 NIGHTMARE 7
Core can, midplane 0.2 NIGHTMARE “
Vessel, midplane 0.2 NIGHTMARE &
Upper grid 2.2 NIGHTMARE 4
Lower grid 1.8 NIGHTMARE 4
Upper head at fuel outlet 0.1 2DGH 50

 

Table 14.2. Energy Sources and Deposition in MSRE

 

Energy (Mev/fission)

 

 

 

 

Absorbed
source
Emitted Fuel Cell
. . Graphite and
Main Perlpheral External shield
Core Regions
Fission fragments 168 149.5 18.5 0 0 0
Fast neutrons 4.8 0.8 0.1 C 3.5 0.4
Prompt fission 72 1.9 0.7 C 445 0.1
gammas
Fission product 5.5 0.7 2.2 0.7 1.6 0.3
decay gammas
Fission product 8.0 2.7 3.0 1.3 1.0 0
decay betas
Capture gammas 6.2 1.2 242 0 2.6 0.2
Neutrinos 11 0 0 0 0 0

 

 

 

210.7 156.8 2647 2.0 13.2 1.0

 
183

14.2 Graphite Shrinkage

At the temperature of the MSRE core, fast-neutron irradiation causes
graphite to shrink. Shrinkage is proportional to the total exposure and
is greater in the direction of extrusion than in the direction normal toO
the axis of extrusion. Thus shrinkage will be nonuniform, leading to
changes in the core dimensions and the distribution of fuel and graphite
within the core. These changes produce slow changes in reactivity.

Available information on the behavior of MSRE graphite under nuclear
irradiation did not permit a detailed analysis, but some of the reactivity
effects were estimated, using preliminary information. The coefficient
for shrinkage parallel to the axis of extrusion (axial shrinkage) for a
grade of graphite similar to that to be used in the MSRE is about 2.06 X
10—2% per nvt for neutrons with energies greater than 0.1 Mev. The co-
efficient for EGCR graphite in the seme temperature range, between 5 and
8 x 10?1 nvt of neutrons with energies greater than 0.18 Mev, is about
1.8 x 10™2% per nvt. Also, for EGCR graphite the coefficient for shrink-
age normal to the extrusion axis (transverse shrinkage) is about half
that for axial shrinkage. On this basis the coefficients used in the
analysis described below were 2.06 X 1024 and 1.0 X 102%* per nvt (E >
0.18 Mev) for axial and transverse shrinkage, respectively. The neutron
flux distributions for energies greater than 0.18 Mev calculated for
fuel C were used (see Figs. 3.9 and 3.10). All of the reactivity effects
were based on one full-power year of reactor operation.

Since the MSRE graphite stringers are mounted vertically, axial
shrinkage causes, first of all, a shortening of the moderated portion of
the core. The amount of shrinkage in individual stringers depends on the
radial distribution of the fast flux, so that the top of the graphite
structure will gradually take on a dished appearance. The maxinum axial
shrinkage was estimated to be about 0.1l4 in./yr. Even if the entire
moderator structure were shortened by this amount, the effect on reac-
tivity would not be detectable. In addition to shortening the stringers,
axial shrinkage increases the effective graphite density in the main
portion of the core. The total axial shrinkage is equivalent to a uni-

form density increase of 0.11% per year. This corresponds to a reactivity
184

increase of 0.08% Ak/k per year. The nonuniformity of the density change
might increase the reactivity effect by as much as a factor of 2, but the
resultant effect would still be negligible.

A third effect of axial contraction is bowing of the stringers,
caused by the radial gradient in the neutron flux. This mechanism leads
to an increase in the fuel volume fraction in the main portion of the
core and has the same effect as increasing the fuel density. The maximum
bowing has been estimated at 0.1 in./yr.51 If it is assumed that the
bowing causes a uniform radial expansion of the graphite assembly, this
rate represents an equivalent increase in the fuel density of 3.2%/yr.
The associated reactivity effect is 0.6% Ak/k per year. Since both ends
of the graphite stringers are constrained from radial motion, uniform
expansion of the assembly will not occur. Instead, the stringers which
have the greatest tendency to bow will be partly restrained, while others,
in regions where the radial flux gradient is smaller, will be bulged out-
ward at the middle. The net result will be a much smaller fractional in-
crease in fuel volume than would be predicted for a completely uncon-
strained assembly.

Shrinkage of the graphite transverse to the direction of extrusion
adds to the effect produced by bowing. However, this effect 1s much
smaller because of the smaller shrinkage coefficient. The calculated re-

activity effect was 0.04% Ak/k per full-power year of operation.

14.3 Entrained Gas in Circulating Fuel

14.3.1 Introduction

The nuclear characteristics of the reactor are affected by the
presence of entrained helium bubbles, which circulate with the fuel
through the core. This gas, introduced through the action of the fuel
spray ring in the fuel circulating pump, reduces the effective density
of the fuel and makes the fuel-gas mixture compressible. The most im-
portant consequence is that there is a pressure feedback on reactivity,
which is positive for rapid changes in pressure and temperature and

negative for slow changes.
185

14.3.2 Injection and Behavior of Gas

 

A small fraction of the fuel pump discharge stream (50 gpm out of
1250 gpm) is diverted into a spray ring in the gas space in the pump
bowl. The purpose of the spray, or stripper, is to provide contact so
that Xe'?’ in the salt can escape into the gas space, which is continu-
ously purged. Salt Jetting from holes in the spray ring impinges on the
surface of the liquid pool in the pump bowl with sufficient velocity to
carry under considerable quantities of gas, and some of the submerged
bubbles are swefit through the ports at the pump suction into the main
circulating stream of fuel. A steady state is reached when the helium
concentration in the circulating stream has increased to the point where
loss of helium through the stripper flow equals the rate of injection.

At steady state the volume fraction of gas in the circulating stream
varies around the loop with the inverse of the local pressure, which
changes with elevation, velocity, and head losses. Pump loop tests
showed a volume fraction of 1.7 to 2.0% gas at the pump suction, which
is normally at 21 psia in the reactor. In the core, where the pressure
ranges from 39.4 psia at the lower ends of the fuel channels to 33.5 psia
at the upper ends, the equivalent volume fraction of gas is about 1.2%.
Yor rapid changes in core or loop pressure, the mass ratio of gas to
liquid remains practically constant and the volume fraction of gas in the
core decreases with increasing pressure. For very slow increases in 1loop
pressure the volume of gas in the core increases, because the ratio of
absolute presgures between the core and pump suction is reduced. (The
steady-state volume fraction at the pump suction is presumably independent

of pressure.)

14.3,3 Effects on Reactivity

 

The presence of the gas in the core has two effects on reactivity.
First, by making the fuel compressible, the gas introduces a pressure
coefficient of fuel density or reactivity. Secondly, the presence of the
gas modifies the fuel temperature coefficient of reactivity, because the
density of the salt-gas mixture changes with temperature at a different

rate from the density of the salt alone.
186
A detailed description of the reactivity effects of entrained gas
involves the following quantities:

f Volume fraction of gas in fuel stream at pump suction

Absolute pressure in the core

Pg Absolute pressure at the pump suction
T Temperature of the fuel in the core
g Volume fraction of gas in fuel in core
Py Density of liquid salt containing no gas
Pe Density of the fuel salt—gas mixture
1 9%
— ='5;T§f_ Temperature coefficient of salt density
pg Ok . .
B = 85;_ Fuel density coefficient of reactivity
—y Contribution to fuel temperature coefficient of re-

activity due to changes in neutron energies and
microscopic cross sections

The core pressure is related to the reactivity through the mean fuel

density in the core:

1 ok 1 Bpf

E5§=B¥ S - (14.1)

The fuel temperature affects the reactivity through the fuel density and
also through its effect on thermal neutron energy and microscopic cross

sections:

1 dk 1 Bpf
EB—T-=B'5;5T—7. (14.2)

The mean density of the fuel is given by

pp = (L= 08)o, . (14.3)

(The gas adds practically nothing to the fuel density.)
If there is no gas in the core, 6 = 0, P = Pys and the effect of

pressure on density is negligible. With no gas in the fuel,
e

187

d
5%—= -0 - 7 .

= |-

Rapid Changes. — During rapid changes in pressure and temperature,
the mass ratio of gas to liquid remains practically constant. (The change
in the amount of dissolved helium is negligible compared with the amount

in the gas phase.) In this case Pe is approximated by

[1 - (T ~ Tp)]

Pe = By 7 G5 T

pflo

 

, (14.4)

where the subscript O refers to initial conditions. If Eg. (14.4) is
used to obtain the partial derivatives of Ps required in (14.1) and (14.2),

these eqguations become

8[1 — (T — To)]

 

 

1 ok _
ES (1 - 90> T, T } (14.5)
[l—@(T“To)+ T E‘*fi—a P
and
(-2 a)
190k _ —op - TPt o)P —~ (14.6)
k of 1 - T — Tg) <1 - 90> To 27 '
l—Q',(T'—To)-F ——e—o'-— —T—P—O
At the initial point, when P = Pg and T = Ty,
1 ok POy
=5 Z-E%— (14.7)
and
1 ok 1
_kfi—w+7+<fl—a> 6o0B . (14.8)

These equations show that for rapid changes there is a positive pressure
coefficient of reactivity and that the magnitude of the negative tempera-
ture coefficient of reactivity is increased because the gas expands more
than the liquid (1/Ty is greater than Q).

Slow Changes. — During gradual changes in fuel loop temperatures and

pressure, f will probably remain equal to the volume fraction in the pump
188

bowl just outside the ports, which should be constant. The core mean pres-

sure is 15.6 psi higher than the pump suction pressure; therefore

0 =f 2 = f(P‘_PU'_@) , (14.9)
op = (1 -+ 5 %). (14.10)

If the partial derivatives of Pp required in Egs. (14.1) and (14.2) are
obtained from Eq. (14.10), Egs. (14.1) and (14.2) become

 

 

 

1 ok -
e . _Sf‘ = (14.11)
P +( 7 >15.6
and
Sk '
%fi =—ag -7y . (14.12)

Thus for slow changes, there is a negative pressure coefficient of reac-
tivity and the temperature coefficient is the same as if there were no
entrained gas.

Magnitude. — The magnitudes of pressure and temperature coefficients
of reactivity with entrained gas in the core are listed in Table 14.3 for
three different fuel salts, at the conditions listed at the bottom of the
table.

Importance. — During normal operation, the presence of entrained gas
introduces additional reactivity “noise" because its compressibility con-
verts fluctuations in core outlet pressure drop to reactivity perturba-
tions. In power excursions, the gas enhances the negative temperature
coefficient of reactivity. At the same time it superimposes a pressure
coefficient which makes a positive contribution to reactivity during at
least part of the power excursion. (See Sec 12.4.3 for discussion of
pressure behavior during power excursions.) In any credible power excur-
sion, the pressure rise, in psi, is numerically much smaller than the fuel
temperature rise, in °F, and the net reactivity feedback from pressure and

temperature is negative.
189

 

 

Table 14.3. Reactivity Coefficients with Entrained Gas in Core®
Fuel A Fuel B Fuel C
Fuel density coefficient of 0.1290 0.345 0.182
reactivity, B
ol (°F)™] —2.24 x 10™° —4,07 x 10™° —=2,15 x 1077
y[(°F)™*] —0.79 x 10~ —0.90 x 10~% —1.13 x 107
Fuel temperature coefficient
of reactivity [(°F)™]
No gas or slow changes —3.03 x 107" —4.97 x 10™° =3.,28 x 10~°
with gas
Rapid changes with gas  —3.14 x 1077 —5.17 x 107> =3.39 x 1077
Pressure coefficient of
reactivity (psi~t)
Slow changes with gas -3.8 x 107° 7.0 x 107 =3.7 x 10~
Rapid changes with gas +6.3 X 10™° +11.4 x 107  +6.0 x 10~

 

aEvaluated at T
e = 00012, and. X = lo

M

14.4 Choice of Poison Material

=136.5 psia (pump bowl pressure 5 psig),

There is avalilable a wide variely of materials that have been used

as neutron absorbers in reactor control rods.

The choice of poison ma-

terial for a given reactor application must be based primarily on the

overall sultability of the poison, considering the physical and chemical,

as well as the nuclear, environment.

If several acceptable materials

exist, the choice between them may be made on the basis of cost and ease

of procurement of the required form.

14.4,1 Boron

The first poison material considered for use in the MSRE was boron

because of its low cost, ready availability, and high neutron-capture

cross section in both the thermal and epithermsal energy ranges.
190

The shape of the poison elements was established by the mechanical
design of the rod assemblies, which required short, hollow cylinders of
poison. Pure boron carbide (B,C) was tentatively selected as the poison
material, to ensure long rod life. This material could easily be fabri-
cated in the desired shape and also have the stability against thermal
decompesition required for use at reactor temperatures. However, B,C is
highly abrasive and oxidizes in air at high temperature. These proper-
ties made it necessary to consider complete canning of the poison elements.

Essentially all of the poisoning by B,C is due to neutron absorptions
in B0, where the predominant reaction is B®(n,x)Li?. The alpha particle
ends as a helium atom, so that each neutron absorption results in the re-
placement of a single atom by two of approximately the same size. This
effect alone would lead to significant damage, due to volume increase in
the poison elements after long exposure. Howefer, the difficulty i1s com-
pounded, particularly in the case of canned elements, by the fact that
one of the nuclear reaction products is a gas. Only a fraction of the
helium produced escapes from the poison elements, but this fraction in-
creases with increasing neutron exposure. In addition, the amount escap-
ing cannoct be predicted reliably. Therefore, to be conservative, all cal-
culations of gas pressure buildup were based on the assumption that all of
the gas escapes. Calculations of the helium production rate in the MSRE
control rods indicated that the rod life would be severely limited by the
pressure buildup in completely sealed poison capsules. Since it appeared
infeasible to vent the capsules because of the oxidation problem, the use

of B,C was abandoned in favor of a more radiation-stable material.

14.4.2 Gadolinium

The poison material finally selected for use in the MSRE was gadolin-
ium, fabricated in ceramic cylinders containing 70 wt % Gdp03 and 30 wt %
A1,05. This material has satisfactory nuclear properties and was selected
over other, equally suitable materials on the basis of its moderate cost,
ready avallability, and the fact that it could be used without additional
development.

Natural gadolinium has two isotopes (155 and 157) with extremely

large thermal neutron-capture cross sections; the average 2200 m/sec
191

cross section for natural gadolinium is 46,600 barns. However, the neu-
tron~capture products of both isotopes are stable gadolinium isotopes
with very low cross sections, so that the neutron-capture efficiency is
very low, about 0.3 neutrons per atom of natural gadolinium. Gadolinium
also has a relatively low capture cross section for resonance-energy neu-
trons (about one-fourth that of boron). Thus, for rods which are "black"
to thermal neutrons, a boron~containing rod will control somewhat more
reactivity than one containing gadolinium.

Because of the large cross section, only a small amount of gadolin-
ium is required for "blackness" to thermal neutrons. However, this same
property results in very rapid burnout of a rod that is initially just
barely "black." Therefore, such a rod must have built into it sufficient
gadolinium to ensure that it remains "black" throughout its required life-
time. The low neutron-capture efficiency requires relatively large amounts
of gadolinium for this purpose.

The individual ceramic poison capsules on the MSRE control rods are
0.84 in. ID by 1.08 in. OD by 1.315 in. long. The elements contain about
sixty times the concentration of gadolinium required for “blackness" to
1200°F thermal neutrons. This is sufficient to maintain "blackness" in
those portions that are continuously exposed to the neutron flux for the
equivalent of about 50,000 full-power hours.

Since the end products of neutron absorption in gadolinium are other
isotopes of the same element, there is essentially no volume change associ-
ated with its exposure to neutron bombardment. As a result this material
may be expected to have reasocnable resistance to radiation damage; at least
the problem of gas production associated with the irradiation of boron is
avoided. Structural strength of the poison is of secondary importance,
because the elements are completely canned. However, completely leak-proof
canning is less important with Gd;0s; than with B,C, because of the greater

chemical stability of the former.

14.5 Criticality in Drain and Storage Tanks

Molten fuel salt with the uranium concentration required for criti-
cality in the core is not critical in the drain tanks or the storage tank,

This is s0 because there 1s much less moderator in the tanks than in the
192

core and the tanks are of smaller diameter than the core, and these ef-

fects outweigh the increased fuel volume fraction in the tanks.

Normally, when fuel salt is stored in either the drain tanks or the
storage tank, it is kept in the molten state. However, under some condi-
tions it may be desirable to allow the salt to solidify in a tank and
coocl to ambient temperature. Simply cooling the salt causes the reac-
tivity to increase because of the increased density and cross sections.
In addition, if the salt is cooled extremely slowly, it is possible for a
nonuniform composition to develop, with the uranium tending to be more
concentrated in the remaining melt as the slow freezing progresses. It
is conceivable that slow freezing could begin at the outside surfaces,
leading to a condition in which the uranium is all concentrated in a cen-
tral region surrounded by a neutron-reflecting layer of barren salt. Some
additional neutron reflection would occur if the cell containing the tank
were flooded with water. (The effectiveness of the water reflector is
limited by the furnace structure which surrounds each of the tanks.) Under

such abnormal conditions, criticality in the tanks is not impossible.

In order to outline the limiting conditions for criticality in the
tanks, some calculations were made with the multigroup neutron diffusion
program MODRIC. Effective multiplication constants were calculated for
fuels B and C in the drain and storage tanks, at 20°C, for various degrees
for uranium segregation.’? A major uncertainty in these calculations was
the density of the salt. In the absence of experimental information, a
conservative approximation was made by computing the density of the un-
segregated salt from the x-ray densities of the components. (The actual
density should be lower because the salt will not be a perfect crystal,
and cracks and voids will probably develop as the frozen salt cools.)
Calculations were made in both cylindrical and spherical geometry for the
case of uniform concentration, with the size of the sphere chosen to give
the same multiplication as in a cylinder having the actual dimensions of
the tanks. Calculations were made in spherical geometry with the uranium
concentrated by factors of 2, 4, and 10. In these cases, the uranium and

a stoichiometric amount of fluorine were assumed to be uniformly dispersed
193

in a sphere surrounded by a layer of uranium-free salt. The concentra-
tions of the other components were assumed to be uniform in both the fueled
and unfueled portions.

The results of the calculations are shown graphically for the storage
tank and a fuel drain tank in Figs. 14.3 and l4.4, respectively. If all
other conditions are equal, the reactivity is higher in the storage tank
than in a drain tank, because of the INOR coolant thimbles in the latter.
In the reflected cases, a practically infinite (50 em) Ho0 reflector was
assumed., This gives an overestimate of keff’ since the effective reflec-
tor thickness must be less because of the furnace. The amount of over-
estimation is not great, however, as shown by the comparison of the curves
for fuel B in the storage tank, bare and reflected. In one calculation
the salt density was assumed to be 95% of the upper limit used in the
other calculations. This was for the case of fuel B, concentrated by a
factor of 10 in the reflected storage tank, and gave a keff of 1.003, com-
pared with 1.024 for the higher density. Similar reductions might be ex~-

pected for the other cases,
194

UNCLASSIFIED
ORNL DWG. 63-8187

FUEL C,
REFLECTED

FUEL B,
REFLECTED

FUEL B,

1‘:ef':f‘

 

1 2 L 6 8 10
URANTUM CONCENTRATION FACTOR

Fig. 14.3. Effect of Uranium Segregation on Criticality in Fuel
Storage Tank at 20°C.
195

UNCLASSIFIED
ORNL DWG, 638188

1.
FUEL C,
REFLECTED
1.
1.00 FUEL B,
REFLECTED
0.96
G4
H
Q
L
0.92
0.88
0.84
0.80
0.76

 

0 1 2 k 6 8 10
URANTUM CONCENTRATION FACTCR

Fig. l4.4. BEffect of Uranium Segregation on Criticality in Fuel
Drain Tank at 20°C.
196 i

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-

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197

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!
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47, B, Troubetzkoy and H. Goldstein, "Gamma Rays from Thermal Neu-
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48. P, N, Haubenreich and B. E. Prince, Oak Ridge National Labora-
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9. M. L. Tobias, D. R. Vondy, and Marjorie P. Lietzke, "Nightmare —
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50, Oak Ridge National Laboratory, "MSRP Semiann. Progr. Rept. Feb.
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51. 8. E. Moore, Oak Ridge National Laboratory, personal communica-
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14.
15.
16.
17.
18.
19.
20.
21.
22
23.
24 .
25.
26.
27.
28
29.
30.
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33.
34.
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49,
50.
51.
52.
53.

94-95,
%.

97.

o8.

99.
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199

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