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HOME HELP O A K RIDGE N A T I O N A L LABORATORY operated by UNION CARBIDE CORPORATION f o r the

U.S. ATOMIC ENERGY COMMISSION ORNL- TM- 730

/sa

MSRE DESIGN A N D OPERATIONS REPORT PART Ill. NUCLEAR ANALYSIS

P. J. B, H.

N. Haubenreich R. Engel E. Prince C. Claiborne

NOTICE T h i s document contains information of o preliminary nature and was prepared primarily for internal use at the Oak Ridge National Laboratory. It i s subC;l; t o revision or correction and therefore does not represent a final report. Information i s not t o be abstracted, reprinted ar otherwise given public dissemination without the approval of the ORNL patent branch, Legal and Information Control Departmont.


7 LEGAL

T h i s report was prepored as an account of Government sponsored work.

Neither the United States,

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

A.

Makes any warranty

or

representation. expressed or implied, w i t h respect t o the accuracy,

completeness, or usefulness of the information contained i n t h i s report, or that the use of any information,

apparatus,

privotely o w m d rights;

6. Assumes

methad,

or process disclosed i n t h i s report may not infringe

or

any l i a b i l i t i e s w i t h respect t o

the

use of, or for damages resulting from the use of

any information, apparatus, method, w process disclosod in t h i s report.

As used i n the above, "person acting on behalf of the Commission" includes any employee or Commission, or employer of such contractor, to ths extent that such employee or contractor of the Commission, or employee of 5uch cantroctor prepares, disseminotes, or provides access to, any information pursuant t o h i s employment as contract w i t h the Commission,

cantractor of th.

or i

h i s o m p l o y m n t w i t h such contractor.


--

OFNL TM-730

Contract No. W-7405-eng-26

MSRE DESIGN AND OPERATIONS REPORT I

PfiRT 111. NUCLEAR ANALYSIS

'I

P. N. J. R. B. E. H. C.

Haubenreich Engel Prince Claiborne

DATE ISSUED

FEB - 3 1564 e

OAK RIDGE NATIONAL LABORATORY Oak Ridge, Tennessee operated by UNION CARBIDE CORPORATION f o r the U.S. ATOMIC ENERGY COMMISSION


I

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A

iii

C

PRE FACE

w

This r e p o r t i s one of a s e r i e s of r e p o r t s t h a t describe t h e design and operation of t h e Molten-Salt Reactor Experiment. All t h e r e p o r t s a r e l i s t e d below. The design and s a f e t y a n a l y s i s r e p o r t s (ORNL TM-728 and O m TM-732) should be issued by spring of 1964, and t h e others should be issued i n t h e summer of 1964.

O m TM-728

MSRE Design and Operations Report, P a r t I, Description of Reactor Design, by R. C. Robertson.

ORNL TM-729

MSRE Design and Operations Report, P a r t 11, Nuclear and Process I n s t m e n t a t i o n , by J. R. Tallackson.

ORNL TM-730*

MSRE Design and Operations Report, P a r t 111, Nuclear Analysis, by P. N. Haubenreich and J. R. Engel.

O m TM-731

MSRE Design and Operations Report, P a r t I V , Chemistry and Materials, by F. F. Blankenship and A. Taboada.

ORNL TM-732

MSRE Design and Operations Report, P a r t V, Safety Analy s i s Report, by S o E. Beall.

o m

MSRE Design and Operations Report, Part VI, Operating L i m i t s , by S. E. Beall.

TM-733

**

MSRF: Design and Operations Report, P a r t V I I , Fuel Hand l i n g and Processing Plant, by R. B. Lindauer.

**

MSRE Design and Operations Report, P a r t VIII, Operating Procedures, by R. H. Guymon.

**

MSRE Design and Operations Report, P a r t I X , Safety Procedures and Emergency Plans, by R. H. Guymon.

**

MSRE Design and Operations Report, P a r t X, Maintenance Equipment and Procedures, by E. C. Hise.

**

MSRE Design and Operations Report, P a r t X I , Test Program, by R. H. Guymon and P. N. Haubenreich.

**

MSRE Design and Operations Report, P a r t X I I , L i s t s : Drawings, Specifications, Line Schedules, Instrument Tabulations (Vols 1 and 2).

*Issued. *Qese r e p o r t s w i l l be t h e l a s t i n t h e s e r i e s t o be published; rep o r t numbers w i l l be given them a t t h a t time.

t


v CONTENTS

........................................................... .......................................................... 1. INTRODUCTION .................................................. 2. PRELIMINARY STUDIES OF CORE PARAMETERS ........................ 2.1 Introduction ............................................. 2.2 Effect of Core Size ...................................... 2.3 Effect of Volwne Fraction in One-Region Cores ............ 2.3.1 First Study ....................................... 2.3.2 Second Study ...................................... 2.4 Two- and Three-Region Cores .............................. 2.4.1 Channeled Graphite Cores .......................... 2.4.2 Cores with Moderator in Reflector and Island ...... 2.5 Cores Containing INOR-8Tubes ............................ 2.6 Conclusions .............................................. 3. CRITICALITY. FLUX DISTRIBUTIONS. AND FEACTrvTITY COEFFICIENTS .................................................. 3.1 Description of Core ...................................... 3.2 Calculational Model of Core .............................. 3.3 Fuel Properties .......................................... 3.4 Cross Sections and Effects of Inhomogeneity of Core ...... 3.4.1 Resonance Neutrons ................................ 3.4.2 Thermal Neutrons .................................. 3.5 Criticality Calculations ................................. 3.6 Flux and Fission Distributions ........................... 3.6.1 Spatial Distribution .............................. 3.6.2 Energy Distribution ............................... 3.7 Reactivity Effects of Nonuniform Temperature ............. 3.7.1 One-Region Model ..................................

Preface Abstract

3.7.2 Multiregion Model

.................................

iii 1

3 4 4

4 5 5

8 9 9 12 13 13

15 15 15

20 20 21 22 23 25 25 34

37 37 41

3.8 Reactivity Effects of Changes in Densities of Fuel

......................................

Salt and Graphite 3.9 S m a r y of Nuclear Characteristics

W

b

....................... 4. CONTROL ROD CALCULATIONS ...................................... 4.1 Control Rod Geometry ..................................... 4.2 Method of Calculation of Rod Reactivity .................. 4.2.1 Total Worth ....................................... 4.2.2 Differential Worth ................................ 4.3 Results of Calculations .................................. 4.3.1 Total Reactivity Worth ............................ 4.3.2 Differential Worth ................................ 5 . CORE mMâ‚Ź'ERAm .............................................. 5.1 Overall Temperature Distributions at Power ............... 5.1.1 Reactor Regions ...................................

48 49 53 53 53 53 57

58 58 58

60 60 60


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vi

................................ ............................ ........................... ........................ .....................

5.1.2 Fuel Temperatures 5.1.3 Graphite Temperatures 5.2 Average Temperatures at Power 5.2.1 B u l k Average Temperatures 5.2.2 Nuclear Average Temperatures 5.3 Power Coefficient of Reactivity

......................... 6. TIELAYED NEUTRONS ............................................. 6.1 Method of Calculation ................................... 6.2 Data Used in Computation ................................ 6.2.1 Precursor Yields and Half-Lives .................. 6.2.2 Neutron Energies .................................

.............................................. .................................. 6.3 Results of Computation .................................. 6.4 Nomenclature for Delayed Neutron Calculations ........... 7. POISONING DUE TO XENON-135 ................................... 7.1 Distribution of Iodine and Xenon ........................ 7.1.1 Sources of Iodine and Xenon in Fuel .............. '7.1.2 Removal of I o d i n e and Xenon f r o m Fuel ............ 7.1.3 Sources of Iodine and Xenon in Graphite .......... 7.1.4 Removal of Iodine and Xenon from Graphite ........ 7.1.5 Detailed Calculations ............................ 7.1.6 Approximate Analysis ............................. 7.2 Reactivity Effects of Xenon-135 ......................... 8. POISONING DUE TO 0"ER FISSION PRODUCTS ...................... 8.1 Samarium-149 and Other High-Cross-Section Poisons ....... 6.2.3 Age

6.2.4 MSRE Dimensions

............................... 9. EMPLOYMENT OF COWROL RODS IN OPERATION ...................... 9.1 General Considerations .................................. 8.2 Low-Cross-Section Poisons

....................................... ........................................ .......................... 10. NEUTRON SOURCES AND SUBCRITICAL OPERATION .................... 10.1 Introduction ........................................... 10.2 Internal Neutron Sources ............................... 10.2.1 Spontaneous Fission ............................ 9.2 Shim Requirements 9.3 Shutdown Margins 9.4 Typical Sequence of Operations

...... ....................

n) Reactions in the Fuel 10.2.2 Neutrons from (a, 10.2.3 Photoneutrons from the Fuel 10.3 Provisions for External Neutron Source and Neutron Detectors 10.3.1 External Source 10.3.2 Neutron Detectors 10.4 Neutron Flux in Subcritical Reactor 10.5 Requirements for Source

............................................ ................................ .............................. .................... ................................

61 64 69 69 70 71

d

74 74 75 75 75 75 76 76

I

78

81 81 81 82

82 82 83 84 85 90 90 91

96 96

97 98 98 100 100 100 100 100 101

105 105 105 106 109

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b


vii W

................................. ........................ ............................... .............................. 11. KINETICS OF NORMAL OPERATION ................................. 11.1 V e r y Low Power ......................................... 11.2 Self-Regulation at Higher Power ........................ 11.2.1 Coupling of Fuel and Graphite Temperatures ..... 11.2.2 Transport Lags and Thermal Inertia ............. 11.2.3 Simulator Studies .............................. 11.3 Operation with Servo Control ........................... 12. KINETICS IPJ ABNORMAL SITUATIONS .SAFETY CALCUL?ITIONS ........ 12.1 Introduction ........................................... 12.2 General Considerations ................................. 12.3 Incidents Leading to Reactivity Addition ............... 12.4 Methods of Analysis .................................... 12.4.1 Reactivity-Power Relations ..................... 12.4.2 Power-Temperature Relations .................... 12.4.3 Temperature-Pressure Relations ................. 12.4.4 Nomenclature for Kinetics Equations ............ 12.5 MSRE Characteristics Used in Kinetics Analysis ......... 12.6 Preliminary Studies .................................... 10.5.1 10.5.2 10.5.3 10.6 Choice

12.6.1 12.6.2 12.7 Results 12.7.1 12.7.2 12.7.3 12.7.4 12.7.5

Reactor Safety Preliminary Experiments Routine Operation of External Source

......... ..... ................ ........... ............................. ............................... ........................ .....................................

Early Analysis of Reactivity Incidents Comparison of MURGATROYD and ZORCH Results of Reactivity Accident Analyses Uncontrolled Rod Withdrawal Accident Cold-Slug Accident Filling Accident Fuel Pump Power Failure Conclusion

13. BIOLOGICAL SHIELDING

.........................................

................................................ .......................... ....................................... ............................... ........................... ........................... ....................... .................. ..................... ............................... ............................ ...................... ................................................

13.1 General 13.2 Overhead Biological Shielding 13.2.1 Geometry 13.2.2 Source Strengths 13.2.3 Estimated Dose Rates 13.3 Lateral Biological Shielding 13.3.1 Basic Shield Arrangement 13.3.2 South Electrical Service Room 13.3.3 Coolant Cell and Fan House 13.3.4 Source Strengths 13.3.5 Calculation Methods 13.4 Conditions After Reactor Shutdown 13.5 Summary 13.6 Nomenclature for Biological Shielding Calculations

Y

.....

109 110 110 111 112

112 112 113 113 114 121 122 122 122 124 127 127 128 131 133 135 136 136 136 137 137

142 145 151 154 157

157 157 157 161 164 168 169 169 171

174 175

177 177 178


viii

14.

15.

................................................ 1 4 . 1 Radiation Heating of Core Materials .................... 14.2 Graphite Shrinkage ..................................... 14.3 Entrained Gas i n C i r c u l a t i n g Fuel ...................... 1 4 . 3 . 1 I n t r o d u c t i o n ................................... 14.3.2 I n j e c t i o n and Behavior of Gas .................. 14.3.3 E f f e c t s on R e a c t i v i t y .......................... 14.4 Choice of Poison Material .............................. 14.4.1 Boron .......................................... 14.4.2 Gadolinium ..................................... 14.5 C r i t i c a l i t y in Drain and Storage Tanks ................. F33FERENCES ..................................................... MISCELLANEOUS

179 179

183 184 184 185

185 189 189 190 191 196


. 1

MSRE DESIGN AND OPERATIONS REPORT PART 111. iWCL;EAR ANALYSIS

P. N. Haubenreich J. R. Engel

B. E. Prince H. C. Claiborne ABSTRACT Preliminary considerations of the effects of core size and fuel-to-moderator ratio on critical mass and fuel concentration led to the specification of a core about 4.5 ft in diameter by 5.5 ft high for the MSRE. The average fuel fraction was set at 0.225, as a compromise between minimizing the critical mass and minimizing the reactivity effects of fuelsalt permeation of the bare graphite moderator. The nuclear characteristics of the reactor were examined for three combinations of fissile and fertile material (UF4 and ThF4) in a molten carrier salt composed of lithium, beryllium, and zirconium fluorides. Fuel A contained ThF4 (-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% enrichment (-0.8 mole %) and no thorium. The radial distribution of the thermal neutron flux is 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 8 in. from the axis. The axial distribution is essentially sinusoidal. The magnitude of the thermal flux depends on the choice neutrons cm-* of the fuel; the maximum varies from 5.6 x ''ees for fuel B (at 10 Mw thermal) to 3.3 x loL3 for fuels A and C. Both the fuel and the moderator temperature coefficients of reactivity are substantially negative, leading to prompt and delayed negative power coefficients. Reactivity coefficients were also calculated for changes in uranium concentration, Xe135 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, respectively, the fuel and graphite reactivity-weighted average temperatures are 1211 and 1255OF, respectively. Fuel permeation 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 constant is -0.006 to -0.008% 6k/k per Mw.


* L &

Circulation of t h e f u e l a t 1200 gpm reduces t h e eff e c t i v e delayed neutron f r a c t i o n from 0.0067 t o 0.0036. Xenon poisoning i s strongly dependent on t h e major competing mechanisms of s t r i p F i n g from t h e f u e l i n t h e pump bowl and t r a n s f e r i n t o t h e bare graphite. The equilibrium poisoning a t 10 Mw i s expected t o be between -1.0 and -1.7% 6k/k. The f u e l contains an inherent neutron source of over lo5 n/sec due t o CXn, r e a c t i o n s i n t h e s a l t . This meets a l l t h e s a f e t y requirements of a source, but an e x t e r n a l source w i l l be increase t h e f l u x f o r convenient monitoring of t h e subcritical reactivity. The t o t a l worth of t h e t h r e e c o n t r o l rods ranges from 5.6 t o 7.6% 6k/k, depending on t h e f u e l s a l t composition, Shutdown margins a t 1200째F a r e 3.5% 6k/k o r more i n a l l cases. One rod w i l l be used as a r e g u l a t i n g rod t o c o n t r o l t h e f l u x l e v e l a t low power and t h e core o u t l e t temperature a t high power. I n general, t h e r e a c t o r i s s e l f - r e g u l a t i n g with respect t o changes i n power demand because of t h e negat i v e temperature c o e f f i c i e n t s of r e a c t i v i t y . However, t h e degree of s e l f r e g u l a t i o n i s poorer a t lower powers because of t h e l o w power density and high heat capacity of t h e system. The c o n t r o l rods a r e used t o inprove t h e power r e g u l a t i o n as well as t o compensate f o r r e a c t i v i t y t r a n s i e n t s due t o xenon, samarium, power c o e f f i c i e n t , and short-term burnup. Calculations were made f o r conceivable r e a c t i v i t y accidents involving uncontrolled control-rod withdrawal, "cold slugs, '' abnormal f u e l additions, l o s s of graphite, abnormal f i l l i n g of t h e r e a c t o r , and primary flow stoppage. No int o l e r a b l e conditions a r e produced i f t h e r e a c t o r s a f e t y system (rod drop a t 150% of design power) functions f o r two of t h e t h r e e c o n t r o l rods. The b i o l o g i c a l shield, with t h e possible a d d i t i o n of stacked concrete blocks i n some areas, reduces t h e c a l c u l a t e d r a d i a t i o n dose r a t e s t o permissible l e v e l s i n a l l accessible areas.

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#


. 3

1. INTRODUCTION The design of t h e E R E and t h e plans f o r i t s operation r e q u i r e information on c r i t i c a l f u e l concentration, r e a c t i v i t y c o n t r o l , k i n e t i c s of t h e chain reaction, nuclear heat sources, r a d i a t i o n sources and l e v e l s , a c t i v a t i o n , and s h i e l d i n g . w i t h these topics.

This p a r t on Nuclear Analysis deals

I t s purpose i s t o describe f u l l y t h e nuclear char-

a c t e r i s t i c s of t h e f i n a l design of t h e MSRF and, t o some extent, t o show .

*

t h e basis f o r choosing t h i s design.

l a t i o n s a r e described b r i e f l y .

Methods and data used i n the calcu-

Detailed d e s c r i p t i o n s of t h e c a l c u l a t i o n s

and t h e sources of t h e b a s i c data can be found i n r e p o r t s which a r e cited.


4

2.

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PRELIT4IFJARY STUDIES OF CORE P M T E R S

2.1

Introduction

The original concept of the MSRE core was a cylindrical vessel containing a graphite moderator with small channels through which circulated a molten-salt fuel.

During the early stages of MSRE design, the nuclear

effects of two importark 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-region cores, but some calculations were made for cores consisting of two or three concentric regions of differing volume fractions. Critical concentration and inventory of U235 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 INOFL-8 tubes in a graphite core. The nuclear characteristics of the reactor were calculated for several combinations

of tube diaqeter and thiclrness. U of these computations were performed on the IBM 704, using GNU,

a aultigroup, diffusion theory code.’

Data from BNL-325 (ref 2) were

used in preparing 34-group cross sections for the

computation^.^

The

cross sections were averaged over a 1/E spectrum within each group. Those used for thorium and U238 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 thermal and last epithermal groups.

In all of the calculations except some of those for

tubed cores, the core Taterials were assumed to be homogeneously mixed within a region.

2.2 Effect of Core Size4 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 specification, and the GNU code was used to compute the critical concentration of uranium. A graphite density of 1.90 g/cc was assumed.


5

f

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w

Table 2.1. Nominal Fuel Compositions and Densities Used in MSRE Survey Calculations

Fuel type Composition (mole %)

LiF" BeF2 ThF4

ZrF4 uF4b

Density (g/cc)

I

I1

I11

64 31

64 31

70

4 0 1

0

1

4

5

1

1

2.2

2.47

2.2

23

a

0.003% Li6, 99.997% Li7. b93.5% U235, 6.5% U 2 3 8 .

Computations were made for cores 5.5 and 10 ft high and 3.5, 4.0,

4.5, and 5.0 ft in diameter. Figure 2.1 shows critical concentrations of uranium obtained by these calculations. Also shown in Fig. 2.1 are values of critical mass. norr;inal dimensions. 2.3

These are the masses of U235 in a core of the

(A zero extrapolation distance was assumed.)

Effect of Volume Fraction in One-Region Cores

2.3.1 First Study4 The first survey of the effect of varying volume fraction in a oneregion core was for a core 4.5 ft in diameter and 5.5 ft high.

Five

different fuel volume fractions, ranging from 0.08 to 0.16, were considered.

The critical concentrations of uranium were computed, and these

were used with the fuel volume fraction and the nominal core dimensions to compute critical masses of U235. Total inventories of U235 were also 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. W

calculations the graphite density was assumed to be 1.90 g/cc. are shown in Fig. 2.2 by the curves labeled "Composition A."

J

In these Results


6

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UNCLASSIFIED ORNL- L R - DWG 5 0 5 9 2 A

50

3

10

_ I )

0

I

3.5

I

I

4.5 CORE DIAMETER ( f t ) 4.0

I I

5.0

Fig. 2.1. C r i t i c a l Concentration and Mass as a Function of Core Size.

A similar s e t of c a l c u l a t i o n s w a s made with f u e l I1 of Table 2.1,

with t h e r e s u l t s shown i n Fig. 2.2 by t h e curves l a b e l e d "Composition B." Not a l l of t h e d i f f e r e n c e s i n t h e two sets of curves a r e a t t r i b u t a b l e t o t h e s u b s t i t u t i o n of zirconium f o r t h e thorium i n t h e f u e l s a l t , because

a d i f f e r e n t graphite density, 1.96 g/cc, w a s used i n t h e c a l c u l a t i o n s f o r f u e l 11, which would reduce c r i t i c a l concentrations f o r t h i s case.


7 UNCLASSIFIED ORNL-LR- DWG 52050

80

160

I

I

INVENTORY, COMPOSITION

A

70

140

60

120

50

100

-

-

0, 1

0, Y

-

Y

v)

I+)

40

80

tn

N

m

3

N

3

30

60

,/’ 20

40

/ I

CRITICAL MASS, COMPOSITION B

.

10

0

20

L

I 0

0.08

0.10 0.12 0.14 VOLUME FRACTION F U E L SALT

Fig. 2.2.

0.16

C r i t i c a l Mass and Total Inventory of

U235 as Functions of Fuel Volume Fraction, Calculated f o r Early Fuels.


c

8 2.3.2

t

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Second Stud? * After mechanical design and chemistry studies had led to firmer

values 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 calculations. Fuel I11 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 U235, based on a fuel volume of 38.4 ft3

UNCLASSIFIED ORNL- LR- DWG 57685

70

60 I

Lo

Po

N

3

&

50

0

1

2.

4: \i

[L

40 2 W

>

z

--

t

’

+

0.4

I W

&

0.3

30

2.

I

cn

â‚Ź9

13

W -

z

0.2 5z

l-

a

20

0

E

a

0

LL 3

10

~

-t

0.1

*-+-

0

0

0

5

IO

15

FUEL SALT

20

25

30

(VOI7 0 )

Fig. 2.3. Effect of Fuel Volume Fraction on Critical Concentration and Inventory.


9 external to the core.

The GTNU 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 2.4.1

*

Two- and Three-Region Cores'

9

Channeled GraDhite 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 I

1

*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 MSREa Fuel fraction (vol %) Critical fuel conc. (mole U)

4

12

14

0.296

0.273

16

20

24

28

0.257

0.238

0.233

0.236

11.0

11.8

12.7

14.8

17.4

20.5

51.0

48.6

47.4

47.1

48.7

52.4

Fuel temp. coeff. x lo5 -3.93 [ (Gk/k)/'F]

-3.83

-3.70

-3.44

-3.16

-2.86

32.4

9.7

8.3

6.1

4.6

3.5

Critical mass (kg of $35)

. t

'

systemb

u235

inventory (kg)

Permeation effect' (46 W k )

a Core dimensions: 27.7-in. radius, 63-in. height, Nominal composition of fuel: L ~ F - B ~ F ~ - Z ~ F ~ - T ~ F 70-23-5-1-1 ~-UFL+, mole

k,

Temperature: 1200째F, Fuel density: 2.47 g/cc, Graphite density: 1.90 g/cc.

bCore plus 38.4 ft3 of fuel. C W

Permeation by fuel salt of 7% of graphite volume.


?

10

center.

This could be done i n t h e MSRE by designing t h e g r a p h i t e pieces

t o give a g r e a t e r f u e l volume f r a c t i o n toward t h e c e n t e r of t h e core.

4

A

reduction i n c r i t i c a l mass, i f accompanied by an increase i n t h e concent r a t i o n of U235 i n t h e f h e l s a l t , does not n e c e s s a r i l y imply a reduction i n f i s s i l e m a t e r i a l inventory i n t h e MSRE because most of t h e f u e l i s e x t e r n a l t o t h e core. I n order t o explore t h e e f f e c t s of nonuniform f u e l d i s t r i b u t i o n i n t h e MSRE, a s e t of c a l c u l a t i o n s was made i n which t h e core w a s subdivided i n t o e i t h e r two o r t h r e e regions with d i f f e r e n t f u e l volume f r a c t i o n s . Fuel I11 of Table 2 . 1 and graphite having a density of 1.90 g/cc were assumed.

Overall dimensions of t h e core were taken t o be 27.7-in.

and 63-in. height.

radius

Radial and a x i a l e x t r a p o l a t i o n distances of 1 and 3.5

i n . were added t o t h e s e dimensions.

The c r i t i c a l f u e l concentration, t h e

core inventory ( o r c r i t i c a l mass), and t h e t o t a l inventory were computed.

Flux and power d i s t r i b u t i o n s were a l s o obtained. Three cases of two-region cores were considered.

I n each t h e core

c o n s i s t e d of two concentric c y l i n d r i c a l regions, w i t h t h e i n n e r cont a i n i n g 24 vol $' f u e l and t h e outer, 18 v o l

%

fuel.

Results a r e sum-

marized i n Table 2.3.

Table 2.3.

Some C h a r a c t e r i s t i c s of Two-Region Reactors

Volume Ratio"

C r i t i c a l Fuel Concentration (mole % U )

Critical

50150

0.232

15.1

46.5

60140

0.234

15.7

47.4

70130

0.236

16.3

48.4

Mass

(kg of U235)

Systemb Inventory (kg of U235)

?Ratio of i n n e r region (24 v o l $I f u e l ) t o o u t e r region (18 v o l $I fuel). bIncluding 38.4 f t 3 e x t e r n a l t o t h e core.

Y


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

(For a uniform core the ratio is 2.32.) The effect on flux shape is illustrated for some of the cases in Fig. 2.4.

reduced in some cases.

Table 2.4.

Fuel Fraction"

Critical Fuel Concentration (mole % U)

Critical Mass (kg of U 2 3 5 )

Systemb Inventory (kg of U 2 3 5 )

25, 13, 7

0.243

11.3

44.2

1.86

40, 1 3 , '7

0.2'73

16.9

53.8

1.45

10, 1 3 , '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

1 2 .o

44.8

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

44.2

1.66

40, 1 3 , 10

0.273

17.8

54.8

1.45

10, 1 3 , 4

0.325

9.1

53 .O

2.35

%I

!

Some Characteristics of Three-Region Reactors Thermal Flux Ratio, Radial Peak/Av

aIn inner, middle, and outer concentric regions of equal volume. v

bIncluding 38.4 ft3 external to the core.


12 V UNCLASSIFIED OWG 559548 ORNL-LR-

2.5

X

3 LL

2.0

J

a

z

W

I

t-

1.5

2

a W

5 \

5

t.0

A LL _I

a

z

t

w 0.5 I

c,

5

0

IO

15

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.

TaSle 2.5.

Moderator

Characteristics of Cores with Lumped Moderator C r i t i c a l Concentration (mole 3 U)

C r i t i c a l Mass (kg

of

u235)

5-in. Reflector Thickness, No Island Graphite

1.04

250

Be

0.72

175

Be0

0.76

186

10-in. Reflector Thickness, 1-ft-dim I s l a n d

2.4.2

Graphite

0.67

93

Be

0.25

34

Be0

0.28

39

Cores with Moderator in Reflector and Island6 Brief consideration was given to a core which was essentially one

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


and a central island.

Calculations for this type of core were made as

an adjunct to those for the multiregion, channeled graphite cores, using the same fuel and overall core dimensions. Three moderators were considered:

graphite (p

=

1.90 g/cc), 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 INOR-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. lations were reported in MSRP progress reports. 6~

Results of these calcuIn later calculations,

hitherto unreported, the GNIJ 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 w o u l d be approximately 4.5 ft in diameter and 5.5 ft 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 calculations showed that a fraction of 0.24 gave the lowest critical concentration of uranium and that the reactivity increase due to fuel permeation of the graphite was much lower around this point than at lower volume fractions.

(Four half-channels 0.2- by 1.2-in. in each 2- by

2-in. graphite block were chosen to give a fuel fraction of 0.24; rounding the corners of the channels reduced the fraction to 0.225.) Only brief consideration was given to cores of two or three regions v ?

with differing volume fractions, because calculations showed these had little, if any, advantage over the uniform, one-region core.


Table 2.6. Fuel fraction

(vol '$)

Tube thickness Critical fuel (mole 46U)

(mil)

INOR-

Tubes

10

10

14

14

14

18

18

18

40

60

80

40

60

80

40

60

80

128

(kg)

of Cores with

10

0.74

cont.

System U235 inventory

Some Characteristics

0.96 165

1.22 210

0.64 118

0.86 158

1.12 206

0.62 122

0.86 169

1.15 226

Neutron Balance 8.7

10.9

12.5

10.7

12.3

13.8

10.6

12.8

14.1

2.9

2.5

2.1

2.5

2.0

1.7

2.2

1.7

1.4

u235

50.4

50.9

51.3

50.9

51.5

52.2

51.5

52.3

53.3

u238

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

4.1

3.7

3.3

5.0

4.4

4.0

Fast leakage

24.9

24.5

24.1

24.4

24.5

24.0

25.1

24.4

23.6

Slow leakage

9.7

8.0

6.9

6.9

5.4

4.3

5.0

3.6

2.7

Note : Core radius, 27.7 in.; core height, 63 in.; fuel volume external to core, 70-23-5-l-lmole '$; tube OD, 3 in. composition, LiF-BeF2-ZrF4-ThF4-UF4,

40 ft3;

Absorptions:

INOR graphite

fuel

+ salt

.,.

,

nominal

r


15 v

3.

CRITICALIW, FZUX DISTRIEKJTIONS, AND mACTIVITY COEFFICIENTS 3.1

Description of Core

The f i n a l design of t h e core and r e a c t o r v e s s e l i s shown i n t h e c u t away view i n Fig. 3.1.

Fuel s a l t , a f t e r e n t e r i n g through a flow d i s t r i b -

u t o r , passes down through an annular region between t h e INOR-8 v e s s e l and t h e INOR-8 core can t o t h e lower head.

The lower head contains a n t i - s w i r l

vanes which d i r e c t t h e flow inward and a moderator support g r i d , both of INOR-8.

The f i e 1 flows from t h e lower head up through a l a t t i c e of h o r i -

z o n t a l g r a p h i t e s t i c k s , through t h e channeled region of t h e core and i n t o t h e upper head.

The channeled region of t h e core c o n s i s t s of 2-in.-square,

v e r t i c a l g r a p h i t e s t r i n g e r s , with half-channels machined i n each face t o provide f i e 1 passages.

The r e g u l a r p a t t e r n i s broken near t h e a x i s of

t h e core, where t h r e e c o n t r o l rod thimbles and a g r a p h i t e sample assembly are l o c a t e d .

Figure 3.2 shows a t y p i c a l f i e 1 channel and t h e s e c t i o n

around t h e core a x i s . 3.2

Calculational Model of Core

C r i t i c a l f i e 1 concentrations, flux and power d i s t r i b u t i o n s , and r e a c t i v i t y c o e f f i c i e n t s w e r e c a l c u l a t e d f o r t h e r e a c t o r , t a k i n g i n t o account a s much d e t a i l a s was p r a c t i c a l .

The a c t u a l core configuration was rep-

resented f o r t h e nuclear c a l c u l a t i o n s by a two-dimensional, 20-region model i n r - z geometry ( c y l i n d r i c a l with angular symmetry).

This model i s

shown i n v e r t i c a l s e c t i o n i n Fig. 3.3, i n d i c a t i n g t h e r e l a t i v e s i z e s and

?

p o s i t i o n s of t h e regions w i t h i n which t h e m a t e r i a l composition was cons i d e r e d t o be uniform.

The region boundaries and t h e volume f r a c t i o n s of

f u e l , g r a p h i t e , and INOR-8 i n each region a r e summarized i n Table 3.1. The boundaries of each of t h e s e "macroscopic" regions were chosen t o repr e s e n t as c l o s e l y a s p o s s i b l e those gross geometrical and m a t e r i a l prope r t i e s which determine t h e neutron t r a n s p o r t i n t h e core.

This choice

w a s made w i t h i n t h e p r a c t i c a l l i m i t a t i o n s on t h e number of dimensions and mesh p o i n t s i n t h e numerical c a l c u l a t i o n s .

Use of two-dimensional geometry r e s u l t e d i n a l a r g e saving i n computing t i m e , and w a s considered an adequate r e p r e s e n t a t i o n f o r most purposes.

The major approximation involved was i n t h e r e p r e s e n t a t i o n of t h e


16

UNCLASSIFIED ORNL-LR-DWG 6 1 0 9 7 R

FLEXIBLE CONDUIT TO CONTROL ROD D R I V E S S A M P L E ACCESS POR COOLING AIR L I N E S

ACCESS P O R T COOLING JAC K E T S

FUEL OUTLET

REACTOR ACCESS P O R T

CONTROL ROD T H I M B

FLOW D I S T R I B U T O R

GRAPHITE-

FUEL INLET REACTOR CORE C A REACTOR V E S S E L

A N T I -S W I R L VAN E S VESSEL DRAIN L I N E

Fig. 3.1.

PPORT GRID

Cutaway Drawing of E R E Core and Core Vessel.


17 UNCLASSIFIED ORNL-LR-DWG 60845Af

REACTOR

TYPICAL FUEL CHANNE57

7

i

5

/’

0

9

N

t

L ,/’

0.200-in. R’

0.400 in.-

4 GRAPH11-E IRRADIATION , SAMPLES ( 7/8-in. DlA ) ”

F i g . 3.2. M S E Control Rod Arrangement and Typic a l Fuel Channel.

sniall c e n t r a l region of t h e core which includes the t h r e e control rod thimbles and t h e graphite specimens.

The model contains t h e same amounts

of f’uel, graphite, and INOR-8 a s the a c t u a l core, but t h e arrangement i s necessarily different. 0.10-in.-thick,

The INOR-8 i s of t h e thimbles represented by a

6.00-in.-OD

annulus, w h i c h has a volume an& an outside

surface area equal t o those of t h e INOR-8 of the t h r e e thimbles. t

Just

i n s i d e t h e INOR-8 annulus i s a region containing low-density f’uel, representing a mixture of the voids i n s i d e t h e thimbles and the e x t r a f u e l surrounding the thimbles and t h e specimens.

A t the center of the core i s a

cylinder of normal core cornposition (0.255 f’uel, 0.775 graphite by volume). Other assumptions made i n t h e c a l c u l a t i o n s a r e t h a t t h e temperature i s uniform a t 1200°F, t h a t t h e r e i s no permeation of t h e graphite by t h e

f u e l , and t h a t t h e r e a r e no f i s s i o n product poisons i n the core.

The

graphite was assumed t o be pure carbon, with a density of 1.86 g/cc.

Re-

a c t i v i t y e f f e c t s due t o deviations from these assumptions were t e s t e d a s W

perturbations, a s described l a t e r i n t h i s chapter.


18 UNCLASSIFIED ORNL-LR-DWG 73610R

D

RS'

-K -T

J

1-

-F -0

\

I

M N 0

P

u

0 2 4 6 8 i O INCHES

Fig. 3.3.

Twenty-Region Core Model for Nuclear Calculations. See

Table 3.1 for explanation of letters.


Table 3.1.

Twenty-Region Model of MSIiE Core Used i n Nuclear Calculations (See Fig. 3.3 for g r a p h i c a l l o c a t i o n of r e g i o n s )

Radius ( i n . )

Composition (vol $)

Height ( i n . )

Region

Region Represented Inner

Outer

Bottom

Top

Fuel

Graphite

INOR-8

A

0

23.56

74.92

76.04

0

0

100

Vessel t o p

B

29.00

29.56

-9.14

74.92

0

0

100

Vessel s i d e

-9.14

0

0

100

Ve s s e l bottom

100

0

0

C

0

29.56

D

3.00

29.00

E

3.00

28.00

F

28.00

29.00

G

3.00

28.00

65.53

66.22

H

3.00

27.75

64.59

I

27.75

28.00

J

3.00

K

-10.26

67.47 66.22

74.92 67.47

93.7

Upper head

3.5

2.8

0

0

94.6

5.4

0

65.53

63.3

36.5

0

65.53

0

0

100

Core can

27.75

5.50

64.59

22.5

77.5

Core

2.90

3.00

5.50

74.92

0

0

L

0

1.94

2.00

64.59

22.5

77.5

M

1.94

27.75

2.00

5.50

22.5

77.5

0 100 0 0

N

0

27.75

0

2.00

23.7

76.3

0

0

0

29.00

-1.41

0

66.9

15.3

17.8

P

0

29.00

-9.14

-1.41

90.8

0

9.2

Q

0

1.94

66.22

74.92

0

0

R

0

1.94

65.53

66.22

89.9

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

0

0

0

67.47

?Density, 0.45 X d e n s i t y of normal fuel.

100

100

100"

Downcomer

0.2

Simulated thimbles Central region Core Hori zont a 1 s t r i n g e r s Bottom he ad

Fuel and voids


20

3.3

Fuel P r o p e r t i e s

J

The nuclear c h a r a c t e r i s t i c s of the r e a c t o r were c a l c u l a t e d f o r t h r e e d i f f e r e n t f i e 1 salts, described i n Table 3.2.

(Uranium concentrations

are approximate, based on i n i t i a l e s t i m a t e s of concentrations required

for criticality.

3.4

The exact c r i t i c a l concentrations a r e given i n See 3.9.)

Cross Sections and E f f e c t s of Inhomogeneity of Core

The group c r o s s s e c t i o n s t o be used i n d i f f u s i o n c a l c u l a t i o n s prope r l y should take i n t o account t h e e f f e c t of f u e l composition and lumping on the neutron energy s p e c t r a and s p a t i a l d i s t r i b u t i o n s i n t h e f u e l and i n the graphite.

Table 3.2.

MSRE Fuel S a l t s f o r Which Detailed Nuclear Calculations Were Made

A

B

C

LiFa

70

66.8

65

BF2 ZrF4

23.7'

29

29.2

ThF4

Fael Type S a l t composition (mole $ )

1

4 0

0

0.3

0.2

0.8

u234

1

1

0.3

u235

93

93

u236

1

1

0.3

~ 2 3 8

5

5

64.4

144.. 5

134.5

~4

5 (approx)

5

Uranium composition (atom $ )

Density a t 1200째F ( l b / f t 3 )

a99.9926% L i 7 , 0.0074$ L i 6 .

35

142.7'

V


21 L

Resonance Neutrons

3.4.1

Fuels A and C contain important amounts of strong resonance absorbers, thorium i n f i e 1 A and U238 i n f i e 1 C.

The e f f e c t i v e resonance i n t e g r a l s

f o r these materials depend on t h e i r concentration i n t h e f u e l and on t h e e f f e c t i v e surface-to-volume r a t i o of t h e fuel channels.

Figure 3.4 i l l u s -

t r a t e s how the e f f e c t i v e resonance i n t e g r a l f o r U238 v a r i e s over t h e conc e n t r a t i o n range of i n t e r e s t for t h e MSRT3.

This curve w a s c a l c u l a t e d by

Nordheim's numerical i n t e g r a t i o n program f o r resonance i n t e g r a l computations.

I n t h i s c a l c u l a t i o n , t h e a c t u a l two-dimensional transverse sec-

t i o n of t h e MSRE l a t t i c e geometry (Fig. 3.2) w a s approximated by s l a b geometry with a surface-to-volume r a t i o of s a l t equal t o the e f f e c t i v e

UNCLASSIFIED ORNL DWG. 63-8147

0

0.4

0.2

U23817k

W

0.6

0.8

1.o

CONCENTRATION (Mole $)

Fig. 3 . 4 . Variation of U238 E f f e c t i v e Resonance I n t e g r a l with U238F4 Concentration i n MSRE L a t t i c e .


r a t i o i n the a c t u a l l a t t i c e .

The e f f e c t i v e r a t i o i s a f f e c t e d by Dancoff J

e f f e c t s (shielding from neighboring channels), which reduces t h e e f f e c t i v e surface-to-volume r a t i o f o r resonance capture i n t h e MSRE l a t t i c e by about 3C$.g

These calculations of e f f e c t i v e resonance i n t e g r a l s were used i n

i n i t i a l estimates of t h e c r i t i c a l concentration of U235 i n each f’uel. I n preparation for t h e refined calculations of c r i t i c a l concentrat i o n , which were t o be done by a 33-group d i f f i s i o n method, a new s e t of multigroup cross sections was prepared f o r t h e core with each of t h e t h r e e f b e l compositions.

Group cross sections f o r the 32 f a s t groups were genThis program i s based on

e r a t e d by use of t h e IEN ’7090program GAM-1.l’

a consistent P-1 approximation t o t h e Boltzmann equation f o r neutron slowing-down, and averages -,he cross sections over an energy spectrum above thermal which i s appropriate f o r a single-region r e a c t o r with a macroscopically uniform composition.

Corrections f o r the shielding e f f e c t s

associated w i t h the f’uel channels are automatically included i n t h e GAM-1 program.

For t h e MSRE calculations, a s e t of cross sections was generated

f o r each f’uel composition, assuming a one-region r e a c t o r with a l a t t i c e l i k e t h a t i n the nain p a r t of t h e a c t u a l core (22.5 vol graphite )

.

%

f’uel, 7’7.5 vol

%

A minor complication i n t h e GAT.!-1 c a l c u l a t i o n of MSRE cross sections

was t h a t t h e available version of t h e GAM-1 cross-section l i b r a r y tape d i d not include L i 6 , L i 7 ,

MSm

and F19, which are important components of t h e

f’uel. This was circumvented by simulating t h e i r e f f e c t on t h e neutron

spectrum by t h e inclusion of an mount of oxygen equivalent i n slowingdown power

(Exs) t o

t h e lithium and f l u o r i n e a c t u a l l y present. Fast group

cross sections for L i 6 , L i 7 , and F1’

were compiled from basic cross-sec-

t i o n data, independently of the GAM-1 calculation.

3.4.2

Thermal Neutrons Average cross sections f o r t h e thermal group were calculated by use

of two thermalization programs f o r the

IEp\I

7090.

Reference c a l c u l a t i o n s

f o r each f i e 1 a t 1200’F were made with THERMOS, which computes t h e thermal spectrum i n a one-dimensional l a t t i c e c e l l . l l

The c e l l model used was

t h a t of a c y l i n d r i c a l graphite s t r i n g e r , surrounded by an annulus of s a l t .

For o t h e r c a l c u l a t i o n s i n which t h e e f f e c t s of changes i n temperature and

f


23

W

thermal cutoff energy were studied, a simpler and more rapid thermalizat i o n prograrn was employed, based on the Wilkins "heavy gas" space-independent model. Lumping reduces the thermal u t i l i z a t i o n i n the MSHE l a t t i c e because of the thermal flux depression i n the f'uel, but t h i s e f f e c t i s not large.

(For s a l t with the maximum uranium content of i n t e r e s t i n t h e MSRE, 1 mole

%

UF4, the flux depression i n the f i e 1 was about 3.576.)

Furthemore, the

normal temperature of 1200째F i s above the temperature a t which c r y s t a l binding e f f e c t s i n graphite must be considered.12

For these reasons, it

was found t h a t good agreement with t h e THERMOS model could be obtained by combining t h e Wilkins thermal spectrum calculation with a one-group P-3 calculation of the s p a t i a l disadvantage f a c t o r .

These approximations

were used wherever possible i n order t o save cornputer time.

For some of t h e s t u d i e s of the temperature c o e f f i c i e n t of r e a c t i v i t y , however, it was necessary t o use the THERMOS program i n order t o vary the temperature of the f u e l channel independently of t h a t of the graphite.

These studies a r e

described more f'ully i n Sec 3 . 7 .

3.5

C r i t i c a l i t y Calculations

C r i t i c a l f u e l concentrations were computed with MODRIC, a multigroup d i f l s i o n program for the I B M 7090.13 MODRIC i s a one-dimensional program with provision f o r approximating t h e neutron leakage i n the d i r e c t i o n transverse t o t h a t represented i n t h e one-dimensional model.

For the

calculation of c r i t i c a l concentration, t h e reactor was represented by a cylinder with regions and materials corresponding t o the midplane of t h e model shown i n Fig. 3.3.

Axial leakage was taken i n t o account by the i n -

clusion of a specified a x i a l buckling, based on e a r l i e r calculations of t h e a x i a l flux shape. I n the computations f o r f u e l s A and B, the concent r a t i o n s of a l l uranium isotopes were varied together i n a l l regions t o f i n d t h e c r i t i c a l concentration.

For f u e l

C,

the U 2 3 8 concentration was

held constant and those of the other uranium isotopes were varied. sults are summarized i n Table 3.5, Sec 3.9. )

(Re-


24

I n addition t o the c r i t i c a l concentration, the MODRIC calculations gave two-group constants for each region represented. used i n a two-group, two-dimensional calculation.

These were t o be

It was therefore nec-

essary t o perform other MODRIC calculations t o include regions missed by the midplane r a d i a l calculations.

For these calculations the r e a c t o r was

represented by a multilayer slab, with regions corresponding t o an a x i a l traverse through the model of Fig. 3.3, and a r a d i a l buckling based on the r a d i a l MODRIC calculations.

Slabs corresponding t o two d i f f e r e n t

t r a v e r s e s were calculated, one corresponding t o the core centerline and the other t o a traverse j u s t outside the rod thimbles.

These a x i a l c a l -

culations, using the c r i t i c a l concentrations given by the r a d i a l calculat i o n s , gave values of k between 1,004 and 1.021. This i s considered eff t o be good agreement, i n view of the f a c t t h a t the a x i a l calculations a r e l e s s accurate than the r a d i a l because the equivalent transverse buckling i s more subject t o error i n t h e a x i a l calculations.

The two-group constants obtained from MODRIC were used i n calculat i o n of the model of Fig. 3.3 by the two-group, two-dimensional program These two-group calculations gave k of 0.993, 0.997, eff and 0.993 f o r f u e l s A, B, and C, respectively, f u r t h e r confirming the

EQUIFQISE-3.14*l 5

c r i t i c a l concentrations found by t h e r a d i a l MODRIC c r i t i c a l i t y search. I n a l l of these calculations it was assumed t h a t the core temperat u r e was uniform a t 1200째F, the control rods were withdrawn, and the core contained no f i s s i o n product poisons.

The calculated c r i t i c a l concentra-

t i o n s a r e therefore those which would be a t t a i n e d during the i n i t i a l c r i t i c a l experiments with clean, noncirculating f i e 1 and with a l l rods f u l l y withdrawn.

During subsequent operations, t h e concentration must be higher

t o compensate f o r a l l of the e f f e c t s (poisons, rods, and the l o s s of delayed neutrons) which tend t o decrease r e a c t i v i t y . e f f e c t s i s expected t o be about 4% 6k/k.

The t o t a l of these

Table 3.5 (Sec 3.9) l i s t s t h e

c r i t i c a l concentration for normal operation, which would include these effects.

The increases i n the c r i t i c a l concentration from t h e clean c r i t -

i c a l experiment were computed from values of the concentration c o e f f i c i e n t of r e a c t i v i t y (8k/k)/(8C/C), produced by the MODRIC c r i t i c a l i t y searches.


25 3.6 3.6.1

Flux and Fission Distributions

S p a t i a l Distribution Two-group fluxes and adjoint fluxes were produced by the EQUIPOISE-3

calculations.

Figures 3.5-3.8

f o r f u e l s B and C. f i e 1 C.

show the a x i a l and r a d i a l d i s t r i b u t i o n s

The fluxes f o r f u e l A a r e within 2.5% of those f o r

The r a d i a l d i s t r i b u t i o n s are f o r an a x i a l p o s i t i o n t h a t corre-

sponds t o the m a x i m u m i n t h e thermal flux, which i s a t a p o s i t i o n very close t o the core midplane.

The a x i a l d i s t r i b u t i o n s are a t a position

8.4 i n . from the core centerline*; t h i s radius corresponds t o the maximum value of the thermal flux. The MODEUC calculations gave s p a t i a l f l u x d i s t r i b u t i o n s for each of

33 energy groups.

It was necessary t o normalize the MODRIC fluxes t o cor-

respond t o the neutron production a t 10 Mw, and the normalization f a c t o r was obtained by comparing the MODRIC thermal fluxes w i t h the 10-Mw values computed by EQUIP9ISE. ilar. )

(The shapes of the thermal fluxes were very sim-

The high-energy MODRIC fluxes were then multiplied by the normal-

i z a t i o n f a c t o r t o obtain the predicted high-energy neutron fluxes i n the reactor.

Figure 3.9 shows the r a d i a l d i s t r i b u t i o n , near the core mid-

plane, of the neutron fluxes with energies g r e a t e r than 0.18 Mev and with energies g r e a t e r than 1.05 Mev.

Figure 3.10 shows the a x i a l d i s t r i b u t i o n

of the same energy groups 3 in. from the core centerline, which i s about the location of the rod thimbles and the t e s t specimens.

(The values

shown i n Figs. 3.9 and 3.10 were computed f o r f i e 1 C, but these very-high-

energy fluxes a r e not s e n s i t i v e t o t h e f u e l composition.) The s p a t i a l d i s t r i b u t i o n s of the f i s s i o n density were obtained from the EQUIPOISE-3 calculations.

Figures 3.11 and 3.12 show t h e a x i a l and

r a d i a l d i s t r i b u t i o n s of the f i s s i o n density i n the fuel, f o r f u e l C. same calculations a l s o gave t o t a l f i s s i o n s i n each region.

The

Table 3.3 sum-

marizes, f o r f u e l C, the f r a c t i o n of the t o t a l f i s s i o n s which occur i n t h e major regions of t h e reactor.

XThe datum plane f o r the a x i a l distance i s the bottom of the h o r i zontal graphite bars a t the bottom of the core.


-10

0

10

20

Center

. (

Fig. 3.5. Axial Line, Fuel B.

.

Distribution

40

30

MIAL

POSITION

70

(in.)

of Two-Group

Fluxes

8.4

,

in.

from

.

Core

80


.

12

2

C -10

0

10

20

30 AXIAL

Center

Fig. 3.6. Axial Line, Fuel C.

Distribution

40 POSITION

of

60

70

80

(in.)

Two-Group

Fluxes

8.4

in.

from

Core


2%

UNCLASSIFIED ORNL DWG. 62-8150

0

5

10

15 ,

20

25

RADIUS (in.)

F i g . 3.7. plane, Fuel B.

Radial D i s t r i b u t i o n of Two-Group Fluxes Near Core Mid-


29

RADIUS

F i g . 3.8. plane, Fuel C.

(in.)

Radial Distribution of Two-Group Fluxes Near Core Mid-


30

UNCLASSIFIED ORNL DWG. 63-8!52

4

3

0

5

10

15

20

30

RADIUS ( I n . )

Fig. 3.9. Sigh-Energy Neutron Fluxes: Radial D i s t r i b u t i c Core Midplane a t 1 0 Mw.

Near


YJ JJ.XIAL FOSITION (in.)

Fig. 3.10. High-Energy IJeutron from Core Center Line at 10 Mw.

Fluxes:

Axial

60

Distribution

70

80

3 in .


32

c

UNCLASSIFIED ORNl

1 .o

nWG. 6 5 8 1 5 4

0.8

0

.o

0.4

3.2

0 RADIUS

(in.1

Fig. 3.11. Radial D i s t r i b u t i o n of F u e l F i s s i o n Density Near Core Midplane, F u e l C .


“NCLA55IFIED ORNL DWC. 63-8155

Z, AXIAL POSITION (in.)

Axial Distribution Fig. 3.12. Core Center Line, Fuel C.

of Fuel Fission

Density

8.4

in.

from


34 Table 3.3.

F i s s i o n D i s t r i b u t i o n by Major Region

(See Fig. 3.3 f o r g r a p h i c a l l o c a t i o n of r e g i o n s ) Major Region

Fraction of Total F i s s i o n s ($)

Regions

Dome omer

F

2.9

Lower he ad

9, p

2.4

Main core

J, L, M, N, T

Upper head

D, E, G, H,

Q, R,

89.1

S

5.6

I

3.6.2

Energy D i s t r i b u t i o n The energy d i s t r i b u t i o n of t h e neutron f l u x a t a given l o c a t i o n i s

influenced by t h e nuclear p r o p e r t i e s o f t h e m a t e r i a l s i n t h e general v i c i n i t y of t h e p o i n t .

A s a r e s u l t , t h e f l u x spectrum v a r i e s r a t h e r widely

with p o s i t i o n and f u e l composition.

The MODRIC c a l c u l a t i o n s produced av-

erage d i s t r i b u t i o n s of f l u x a s a f'unction of energy w i t h i n each r e a c t o r region as well a s t h e d e t a i l e d d i s t r i b u t i o n s a s functions of p o s i t i o n and energy.

Figure 3.13 shows t h e average fluxes, p e r u n i t l e t h a r g y , i n t h e

l a r g e s t core region (Region J of Fig. 3.3) f o r each of t h e 32 nonthermal energy groups. case.

The f l u x e s a r e normalized t o u n i t thermal f l u x i n each

The m a x i ? l w n l e t h a r g y of t h e thirty-second or l a s t e p i t h e m a l group

i s 17, which corresponds t o a neutron energy of 0.414 ev.

This i s a l s o

t h e maximum energy ( m i n i m u m l e t h a r g y ) of neutrons i n t h e t h i r t y - t h i r d o r If

thermal" group.

The e f f e c t of t h e strong resonance absorbers, thorium

i n f u e l A and U238 i n m e 1 C, i n reducing t h e flux i n t h e region j u s t above t h e thermal cutoff i s r e a d i l y apparent. The d i s t r i b u t i o n of f i s s i o n s as a f u n c t i o n of t h e l e t h a r g y of t h e neutrons causing f i s s i o n i s t h e product of t h e neutron flux and the f i s s i o n cross section.

Figure 3.14 shows t h e average f i s s i o n density, p e r

u n i t lethargy, i n t h e l a r g e s t core region, normalized t o one f i s s i o n i n t h a t region, a s a fluletion of neutron energy f o r f i e 1 C.

The resonances

i n t h e f i s s i o n cross s e c t i o n a r e r e f l e c t e d by t h e peaks a t t h e h i g h e r l e t h a r g i e s (lower e n e r g i e s ) .

I n t e g r a t i o n of the p l o t i n Fig. 3.14 t o a


0.35

0.30

0.25

0.20

0.15

0.10

0.05

0 0

2

4

6

8 LETHARGY,

Fig.

3.13.

Average

Flux

Spectra

10

12

14

u

in Largest

Core

Region.

16

18


NFXJTRON ENERGY (e.)

UNCLASSIFIED ORNL DWG. 63.8157

h

3

v

w”

LETFIARGY, u

Fig. 3.14. Fission Density as a Function of Lethargy of Neutrons Causing Fission, Fuel C.

i


37 L

given lethargy gives the cumulative f r a c t i o n of f i s s i o n s caused by neut r o n s with l e s s than the specified lethargy.

Figure 3.15 i l l u s t r a t e s the

r e s u l t of t h i s operation for f i e 1 C i n the l a r g e s t core region.

This

figure indicates t h a t 17.7$ of the f i s s i o n s i n t h i s region are caused by nonthermal neutrons.

The average f r a c t i o n f o r the e n t i r e reactor i s 20.276,

indicating t h a t f a s t f i s s i o n s account f o r a r e l a t i v e l y l a r g e r f r a c t i o n of the t o t a l i n other regions.

This i s p a r t i c u l a r l y t r u e i n the upper and

lower heads, where the absence of graphite produces a much lower r a t i o of thermal t o f a s t flux than e x i s t s i n the main portion of the core.

3.7

Reactivity Effects of Nonuniform Temperature

Changes i n the temperature of the core materials influence the r e a c t i v i t y through changes i n the neutron leakage and absorption probabilities.

The r e a c t i v i t y change between two isothermal conditions can be ex-

pressed i n terms of a single temperature c o e f f i c i e n t of r e a c t i v i t y .

When

the r e a c t o r operates a t power, however, the core i s not isothermal; i n f a c t , the o v e r a l l shapes of the temperature d i s t r i b u t i o n s i n the f i e 1 and i n the graphite are quite dissimilar.

For t h i s reason, and a l s o because

d i f f e r e n t thermal time constants are involved i n f i e 1 and graphite temperature changes, separate consideration of the r e a c t i v i t y e f f e c t s of these changes i s necessary.

To delineate the f a c t o r s governing the reac-

tivity-temperature r e l a t i o n , calculations were f i r s t performed using a simplified model of t h e reactor, t h a t of a single-region cylinder in which

composition and temperature were macroscopically uniform. cussed i n See 3.7.1.

These are d i s -

Analysis based on the multiregion model of Fig. 3.3

i s considered i n Sec 3.7.2.

3.7.1

One -Region Model For t h i s analysis, use was made of the GAM-1 program i n order t o

calculate macroscopic cross sections averaged over the energy spectrum

Cross sections for t h e thermal group were averaged over a Wilkins spectrum. The lower energy cutoff for t h e GAM-1 calculation above thermal.

was equal t o the upper cutoff f o r the Wilkins thermal spectrum. W

The two-

group parameters obtained i n t h i s way were then used t o calculate the


38

UNCLASSIFIED ORNL DWG. 62-8158

ENERGY OF NEUTRON CAUSING FISSION (e.)

0.20

0.15

m

8

H

m H m Cr

R 0

0.10

0.05

n Y

0

2

4

6

8

LETEIARGY OF " E Q N

10

12

14

16

18

CAUSING FISSION

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


39

L

multiplication constant of the cylinder, based on the standard two-group diffusion equations.

I n t h i s calculation, the geometric buckling used

was t h a t of a cylinder, 59 i n . i n diameter by 78 i n . high. perature conditions were considered:

Three tem-

(1)s a l t and graphite a t 12OO0F,

( 2 ) s a l t a t 1600째F, graphite a t 1230째F, and ( 3 ) s a l t and graphite a t

1600째F.

The temperature c o e f f i c i e n t of r e a c t i v i t y was obtained from the

approximate r e l a t i o n

Two special considerations are of importance i n analysis of the MSRE

temperature coefficient.

The f i r s t i s the position chosen f o r the thermal

energy cutoff, which i s the approximate energy above which thermal motion of moderator atoms may be neglected.

Since a c y l i n d r i c a l core of t h i s

size has a l a r g e neutron leakage f r a c t i o n , unless t h e cutoff energy i s chosen high enough the t o t a l e f f e c t of temperature on thermal neutron leakage i s underestimated.

This e f f e c t i s indicated i n Fig. 3.16,

( a ) , Here the t o t a l temperature c o e f f i c i e n t of r e a c t i v i t y ( f i e 1

curve

+ graph-

i t e ) of t h e core fueled with f u e l C i s p l o t t e d vs t h e upper energy cutoff of the thermal group.

The c o e f f i c i e n t tends t o become independent of the

cutoff energy f o r cutoffs i n excess of about 1 ev. The second consideration i s the e f f e c t of the s a l t temperature on the thermal spectrum.

For t h i s calculation, it was necessary t o employ

the THERMOS program so t h a t t h e temperatures of the s a l t channels and graphite could be varied independently.

!The r e s u l t s of t h i s analysis f o r

f u e l C may be seen by comparing curves ( b ) and ( e ) i n Fig. 3.16.

Curve

( b ) was calculated by neglecting the change i n thermal spectrum with s a l t temperature.

This difference i s a consequence of the f a c t t h a t t h e l i g h t

elements i n the s a l t , lithium, beryllium, and fluorine, contribute subs t a n t i a l l y t o t h e t o t a l moderation i n the MSRE: core. Similar calculations based on t h e one-region c y l i n d r i c a l model were made f o r f'uels A and B.

The values of t h e r e a c t i v i t y c o e f f i c i e n t s f o r

a l l f u e l s obtained a t the asymptotic cutoff energies are summarized i n Table 3.4. W

All calculations were based on the values of volumetric ex-

pansion c o e f f i c i e n t s a t 1200'F

(see Table 3 . 4 ) .


40 UNCLASSIFIED ORNL DWG. 63.8159

CURVES :

( a ) Total (Fuel + Graphite) ( b ) Fuel; Thermal Spectrum Assumed Independent o f S a l t Temperature ( c ) Fuel; Dependence o f Thermal Spectrum on S a l t Temperature Included

h 0

0.4

1.o

0.5

0.6

1.2

CUTOFF ENERGY (ev)

Fig. 3.16. E f f e c t of Thermal Cutoff Energy on Temperature Coeffic i e n t of R e a c t i v i t y , Fuel C .

T3ble 3.4.

TPmperature C o e f f i c i e n t s of R e a c t i v i t y Obtained f roni One -Region Model

(Calculations based on expansion c o e f f i c i e n t s , a t 12OO0F, of 1.18 X 1 r 2 %/OF for s a l t and 1.0 X l T 3 %/OF for g r a p h i t e ) Fdel A

Fuel B

Fuel C

Temperature c o e f f i c i e n t of r e a c t i v i t y [ (Gk/k)/OF] Salt -3.36

Graphite Total

X

lcr5

-4.91

4 . 3 9 x 1r5 -9.88

X

lr5 -3.68

x 10-5

X

lr5

4 . 9 6 x 10-5


41 L

3.7.2

MuLtiregion Model

To study the e f f e c t s of the macroscopic d i s t r i b u t i o n of materials composition and temperature on the reactivity-temperature r e l a t i o n s , use

For t h i s purpose, it i s

was made of f i r s t - o r d e r perturbation theory.�

This

convenient t o u t i l i z e the concept of a nuclear average temperature. quantity i s defined a s follows:

A t low power, reactor c r i t i c a l i t y i s

assumed t o be established a t isothermal conditions i n f i e 1 and graphite. Then, with the graphite temperature held constant, the f i e 1 temperature

i

-

i s varied according t o a prescribed d i s t r i b u t i o n , thus changing the r e activity.

*

The % e l nuclear average temperature, Tf, i s defined a s the

equivalent uniform f i e 1 temperature which gives the same r e a c t i v i t y change a s t h a t of the a c t u a l temperature d i s t r i b u t i o n .

Similarly, the graphite

*

i s defined a s the uniform graphite temnuclear average temperature, T g’ perature which gives the same r e a c t i v i t y change a s the a c t u a l graphite

temperature p r o f i l e , with the f u e l temperature held constant. The r e l a t i o n s between the nuclear average temperature, T

*

, and

the

temperature d i s t r i b u t i o n s , T ( r , z ) , are of the form

*

TX =

Jreactor Tx(r,z) G x ( r , z ) r

dr dz ?

x = f J g,

(3.2)

-Le a c t o r G x ( r , z ) r d r d z

where Gi20;@2 t

*

(3*3)

*

and 01, 92, 91, 02 a r e the unperturbed values of the f a s t and slow fluxes and the f a s t and slow adjoint fluxes, respectively.

The c o e f f i c i e n t s

cij

a r e constant over each region of the unperturbed reactor i n which the nuc l e a r composition i s uniform, but vary from region t o region.

These quan-

t i t i e s involve the temperature derivatives of the macroscopic nuclear constants; t h a t i s , i n obtaining Eq.

( 3 . 3 ) , the l o c a l change 6C i n the

macroscopic cross sections was r e l a t e d t o t h e l o c a l temperature change 8 T through the approximation 6C(r,z) =

ac > T ( r , z ) E

.

(30 4 )


42 %Iiis approximation i s adequate i f t h e s p a t i a l v a r i a t i o n i n temperature i s

r e l a t i v e l y smooth within a given region. Temperature c o e f f i c i e n t s of r e a c t i v i t y which a r e consistent with t h e d e f i n i t i o n s o f t h e nuclear average temperatures were a l s o obtained from perturbation theory.

The complete temperature-reactivity r e l a t i o n i s ex-

pressed a s

* *

6k- - af6Tf k

* *

+ ag6Tg

,

(3.5)

where

*

6T and

=

*

*

T - To

(3.6)

*

a i s t h e appropriate temperature c o e f f i c i e n t of r e a c t i v i t y .

The

f’uel and graphite r e a c t i v i t y c o e f f i c i e n t s a r e r e l a t e d t o t h e weight f’unct i o n s G ( r , z ) a s follows:

*

Jr e a c t o r

G x ( r , z ) r d r dz

ax = J react o r F ( r , z ) r d r dz

9

(3.7)

where

The p r i n c i p a l advantage of expressing t h e r e a c t i v i t y change with temperat u r e i n t h e form of Eq.

(3.5) i s t h a t the r e a c t i v i t y c o e f f i c i e n t s ,

a

*

,

and t h e weight flmctions G ( r , z ) depend only on the conditions i n t h e unperturbed reactor.

Use of t h i s approximation thus s i m p l i f i e s t h e calcu-

l a t i o n of t h e r e a c t i v i t y e f f e c t s of a l a r g e number of temperature d i s t r i blutions. Reactivity c o e f f i c i e n t s and temperature weight functions f o r t h e f u e l s a l t and graphite were evaluated f o r t h e 20-region model of t h e MSRE core (Fig. 3.3), fueled with f u e l C. shown i n Figs. 3.17-3.20,

The r e s u l t i n g weight functions are

These f i g u r e s correspond t o a x i a l and r a d i a l

t r a v e r s e s of t h e core which i n t e r s e c t a t t h e approximate p o s i t i o n of max-

imum thermal flux.

Corresponding weight functions for f u e l s A and B do

not d i f f e r q u a l i t a t i v e l y f r o x these r e s u l t s .

The d i s c o n t i n u i t i e s i n t h e

weight functions occur a s t h e e f f e c t i v e concentrations of s a l t , graphite,

Y


1.0

0.8

0.6

0.4

0.2

0

-0.2 -10

0

10

20

30

60

40

70

AXIPIL POSITION (in.)

Fig. 3.17. Relative as a Function of Position Line.

Nuclear Importance on an Axis Located

of Fuel 8.4 in.

Temperature from Core

Changes Center

80


44

J UNCLASSIFIED

1.oo

ORNL DWG. 658161

3 .1:,

0.10

0 .O?

0

F i g . 3.18. R e l a t i v e Nuclear Importance of F u e l Temperature Changes as a Function of Radial P o s i t i o n i n Plane of Maximum Thermal Flux.


G

AXIAL FOSITION (in.)

Fig. 3.19. Relative Nuclear Changes as a Function of Position Center Line.

Importance on an Axis

of Graphite Located 8.4

Temperature in. from Core


46 J

UNCLASSIFIED

O R N L OWG. 6 f 8 1 6 3

1.o

0 .a

0.6

0.4

0.2

0 3

3

10

15

20

25

30

R d W S (in. )

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

Flux.


47 and INOR-8 change from region t o region.

From the d e f i n i t i o n of these

flmctions, the point values r e f l e c t d i r e c t l y the r e a c t i v i t y e f f e c t of a change i n f i e 1 or graphite temperature i n a u n i t volume a t t h a t point. This occurs through changes i n the l o c a l u n i t reaction and leakage r a t e s ,

r e f l e c t e d i n GiJ

of Eq. ( 3 . 3 ) , and through v a r i a t i o n i n nuclear importance

w i t h position, r e f l e c t e d i n

*

Although the method presented above i s an attempt t o account approximately for macroscopic variations i n reactor properties with position, it should be noted the basic model i s s t i l l highly idealized.

The exact

nature of the d i s c o n t i n u i t i e s i n the weight fl.mctions would undoubtedly d i f f e r from those shown i n Figs. 3.17-3.20. Since the r e a c t i v i t y change i s an i n t e g r a l e f f e c t , however, these l o c a l differences tend t o be "smeared out'' i n the q u a n t i t i e s determining the operating c h a r a c t e r i s t i c s . Consider, f o r example, t h e large increase i n the f u e l temperature weighting f i n c t i o n s , corresponding t o the region of s a l t plus void surrounding the control rod thimbles.

This r e f l e c t s both the higher average U235

concentration and the lack of graphite t o d i l u t e the e f f e c t of a s a l t temperature increment on the density of t h i s region.

Thus both the av-

erage reaction r a t e and the s c a t t e r i n g probability f o r neutrons entering t h i s region are more sensitive t o changes i n the s a l t temperature.

How-

ever, when integrated over t h e volume, t h i s region contributes only about

5% t o the t o t a l f u e l temperature coefficient of r e a c t i v i t y . The temperature c o e f f i c i e n t s of r e a c t i v i t y obtained from the multiregion model were i n reasonably good agreement with t h e c o e f f i c i e n t s

l i s t e d for f i e 1 C i n Table 3.4.

The f u e l c o e f f i c i e n t was about 3% smaller

and the graphite coefficient about 15% smaller than those of the homogeneous cylinder.

The difference i n c o e f f i c i e n t s f o r the graphite occurs

because the volume of the core a c t u a l l y occupied by the graphite i s s l i g h t l y smaller than the e f f e c t i v e "nuclear size" of the cylinder.

How-

ever, the v a l i d i t y of the assumptions concerning the space dependence of the thermal spectrum over the peripheral regions of the core i s uncertain,

so the values given i n Table 3.4 are recommended a s design c r i t e r i a u n t i l f u r t h e r s t u d i e s concerning these corrections can be made.


4%

3.8

Reactivity E f f e c t s of Changes i n Densities of & e l S a l t and Graphite

Included i n the category of r e a c t i v i t y e f f e c t s of graphite and s a l t density changes are those due t o graphite shrinkage, m e 1 soakup, ent r a i n e d gas, and u n c e r t a i n t i e s i n measured values of t h e material densit i e s a t operating conditions.

Density c o e f f i c i e n t s of r e a c t i v i t y were

calculated f o r the simplified, one-region-cylinder model of the core. I n these calculations, a s i n the similar analysis of the temperature rea c t i v i t y c o e f f i c i e n t s (See 3 . 7 ) , l a t t i c e e f f e c t s of heterogeneity were considered.

The density c m f f i c i e n t s r e l a t e t h e f r a c t i o n a l change 'in

multiplication constant t o the f r a c t i o n a l changes i n densities;

6k 6N - - - P s r S+ B k

6N

Q.

(3.9)

S

The values of t h e coefficients, f3, studied are included i n Table 3.5.

obtained for the three f'uel s a l t s These r e s u l t s d i r e c t l y indicate the

r e a c t i v i t y e f f e c t of u n c e r t a i n t i e s i n the measured values of t h e material densities.

I n order t o apply the r e s u l t s t o calculate the e f f e c t s of

graphite shrinkage and f i e 1 soakup, sone assumptions must be made concerning the changes i n the l a t t i c e geometry produced by these perturbations.

I f shrinkage i s uniform i n the transverse d i r e c t i o n across a

graphite s t r i n g e r , and i f the center of the s t r i n g e r remains fixed during contraction, the e f f e c t w i l l be t o open the gaps between s t r i n g e r s and allow m e 1 s a l t t o e n t e r the gaps.

The homogenized density of the graph-

i t e remains constant; however, the e f f e c t i v e s a l t density, Ns, i s i n I f vs and v a r e the volume f r a c t i o n s of s a l t and graphite i n g the l a t t i c e , the f r a c t i o n a l change i n s a l t density i s calculated a s

creased.

6v =-sv S

g

(3.10)

and (3.11)


49 W

where f l i s the f r a c t i o n a l decrease i n graphite volume due t o shrinkage. Fron Eq, (3.9), the r e a c t i v i t y change i s

6k

v

-k- -

A %

BS

v

fl =

3.44 Bs

fl

,

(3.12)

S

i n which the s a l t / g r a p h i t e volume r a t i o , 0.225/0.775,

has been inserted.

/\

Use of t h e above r e l a t i o n i n conjunction with the density c o e f f i c i e n t s i n d i c a t e s t h a t shrinkage of the graphite by 1% of i t s volume corresponds

to r e a c t i v i t y additions of about 0.65% Sk/k i n f u e l s A and C and 1.2% 6k/k i n f u e l B. Fuel soakup r e a c t i v i t y additions may a l s o be estimated from Eq.

For t h i s purpose the graphite shrinkage f r a c t i o n f l need only be replaced by f2, the porous volume f r a c t i o n of graphite which i s f i l l e d (3.12).

with f u e l s a l t .

3.9

Summary of Nuclear Characteristics

The nuclear c h a r a c t e r i s t i c s of the MSRE have been calculated f o r three f u e l mixtures, designated A, B, and C, which d i f f e r primarily i n content of f u e l and/or f e r t i l e material. the three f u e l s are a s follows: riched i n U235 and 1 mole

%

The distinguishing f e a t u r e s of

f u e l A contains uranium highly (-93%) en-

thorium; f u e l B contains highly enriched ura-

nium but no f e r t i l e material; and f u e l C contains about 0.8 mole with t h e U235 enrichment reduced and no thorium.

%

uranium

The c h a r a c t e r i s t i c s of

the r e a c t o r w i t h each of t h e three f u e l s are summarized i n Table 3.5.

The

uranium concentrations and inventories a r e l i s t e d f o r the i n i t i a l , clean, noncirculating, c r i t i c a l condition and f o r the long-term operating condition.

The neutron fluxes are given f o r the operating uranium concen-

t r a t i o n s , and the r e a c t i v i t y parameters apply t o the i n i t i a l c r i t i c a l concentrat ion. Detailed neutron balances were calculated by the computer programs

for each of t h e t h r e e f i e l s .

The neutron balance f o r the r e a c t o r f i l l e d

with f i e 1 C a t the clean, c r i t i c a l concentration i s summarized i n Tables 3.6 and 3.7.

Neutron absorptions and leakages associated with various

portions of the r e a c t o r vessel and i t s contents are l i s t e d i n Table 3.6. Table 3.7 gives a d e t a i l e d breakdown of the neutron absorptions by e l e ment i n each region of the reactor.


50

Table 3.5.

Nuclear Characteristics of MSEE with Various Fuels Fuel B

Fuel A

Fuel C

Uranium concentration (mole $) Clean, noncirculating ~ 2 3 5

Total U

Operatiya u23 Total U

0.291 0.313

0.176 0.189

0.291 0.831

0.337 0.362

0.199 0.214

0.346 0.890

79 85

48 52

77 218

91 98

55 59

92 233

Uranium inventoryb ( k g ) Initial criticality ~ 2 3 5

Total U Operatinga $3

Total U Thermal neutron fluxesC (neutrons sec-1)

5.56 x 1013 2.43 x 1013

3.29 x 1013 1.42 x 1013

X 10l2

6.81 x 10l2

3.98 x 1OI2

-3.03 X -3.36 X l T 5 0.2526

-4.97 x 1 r 5 -4.91 X l T 5 0.3028

-1.28

-2.04

Maximum Average i n graphite -moderated regions Average i n c i r c u l a t i n g f i e 1 Reactivity coefficientsd Fuel temperature [ Graphite temperature [ ( Uranium concentration ~ e 1 3 5concentration i n core (atom/barn-cm)'l xeI35 poison f r a c t i o n Fuel s a l t density Graphite density Prompt neutron l i f e t i m e ( s e e ) a

3.98

X

lo8

X

-0.76 -0.691 0.190 0.345 0.735 0.755 2.29 X lr4 3.47 x

lo8

-3.28 x 1 r 5 -3.68 x lr5 0.1754e 0.2110f -1.33 x 108

10-4

-0.752 0.182 0.767 2.40 x 1r4

Fuel loaded t o compensate f o r 4% 6k/k i n poisons.

bEased on 73.2 f t 3 of f i e 1 s a l t a t 1200째F. C

A t operating f u e l concentration, 10 Mw.

'At

i n i t i a l c r i t i c a l concentration.

Where u n i t s a r e shown, c o e f f i c i e n t s

for variable x are of the form (l/k)/(ak/ax); other c o e f f i c i e n t s are of the form (x/k)/(ak/ax). e

Based on uranium isotopic composition of clean c r i t i c a l reactor.

fBased on highly (-9%) enriched uranium.


51

Table 3.6.

Neutron Balance for Fuel C, Clean, C r i t i c a l (per

lo5

neutrons produced) Absorptions

Region ~ 2 3 5

U238

Salt"

Graphite

INOR

Total

Main coreb

45,459

7252

4364

795

1380

59,250

Upper head'

3,031

928

6 75

1

131

4,766

Lower he add

1,337

449

294

0

1480

3,560

Downcomer

1,496

338

20 3

0

0

2,037

Core can

0

0

0

0

3635

3,635

Reactor vessel

0

0

0

0

3056

3,056

8967

5536

796

9682

76,304

51,323

Total

-

Leakage Surface Fast TOP

Sides Bottom

Total

Slow

1,991

10

2,001

19,619

1004

20,623

1,068

4

1,072

22,678

1018

23,696

a Constituents other than U235 and U238. bRegions J, K, L, M, N, and T (Fig. 3.3). C

Regions D, E, G, H, Q, R, and S (Fig. 3.3).

dRegions 0 and P (Fig. 3.3).

.

Total


Table 3.7.

Detailed D i s t r i b u t i o n of Neutron Absorptions with Fuel C Absorptions per

a Region ~ 2 3 5

A

0

B

0 0

C

u238

u234

u236

~

i

6 ~

i

lo5

Neutrons Produced F(n,a)

Zr

3

F(n,y)

0 0 0

0

0

0

0

0

0

0

0

0 0

0

0

0 0 0

0 0 0

0 0 0

0

0

0

D

1,518

546

8

4

26

13

27

185

115

37

E

571

155

3

1

11

6

8

44

30

11

338

7

2

27

17

14

77

39

20

1,496

F

624

G

105

2

1

7

Graphite

0 0 0 0

INOR

Total

324

324

2578

2,578

154 0

154 2,478

4

5

27

17

7

0 0 0

26

15

7

1

8

687

0

0

0

0

3635

2 0

1

3 0

5

0

0

5 0

123 0

598

0

964 2,037

I

0

114 0

J

42,837

6768

160

48

905

510

221

1247

517

480

76 2

0

3,635 54,456

494

H

K

0

0

0

0

0

0

0

0

0

0

0

1380

1,380

L

304

58

I.

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

5

6

0

557

0

438

112

2

1

8

5

4

28

12

7

0

790

1,407

P

899

337

5

2

11

8

15

120

44

22

0

690

2,153

Q

19

7

0

0

0

0

0

2

1

0

0

0

30

0

0

5

3

R

2

S

T

750

Total

51,329

1

0

0

0

0 0

0 0 15

0

0 9

0

0

0

0

0

0

0

0

0

0

3

13

9

0

-

0

-

976

828

621

796

9682

76,304

5

- -

142

3

-

-

-

-

8967

199

63

1056

599

315

1

29

-

1850

L t t e r s r e f e r t o designations i n Table 3.1 and Fig. 3.3.

-

VI

N


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 determining 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 4.2.1

Method of Calculation of Rod Reactivity

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 G d 2 0 3 - A l 2 0 3 poison c y l i n d e r s are assumed to be black to

thermal neutrons and transparent to neutrons above thermal energies

( ,> 1 ev). The former assumption should be excellent, since the poison material has an absorption-to-scattering ratio in excess of lo3 in the thermal energy range.

The latter assumption is in error, since Gd155 and

Gd157 resonances occur in the epithermal range, and thus have the effect

of producing a "gray region" in absorption at these energies. Because these resonances are closely spaced and have large resonance scattering components, it is difficult to obtain meaningful estimates of the resonance self-shielding in the posion tube.

Since the total epithermal

absorption is expected to be only a fraction of that in the thermal Y

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 transmission, 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 neutrons incident on the outside surface of the thimble.

This expression

is’ 8

B = where B is the probability that neutrons entering the gap from the thimble miss the central poison cylinder, and p and outer radii of the thimble.

and po are the inner

g The function F ( x ) is defined in terms

of Bessel functions:

In the above formulas, D and L are the thermal diffusion coefficient and diffusion length in the INOR-8. When the central poison tube is withdrawn, @ is equal to unity. mation for

was used.lg

With the rod in place, Newmach’s approxi-

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

Y


55 Y

where r = P rod /P g

2

f ( r ) = 1 - - sin-' Tr

r

'

--rc r , / T T F .

Equations ( 4 . 1 ) and (4.2) were applied t o t h e c a l c u l a t i o n of t h e

rod r e a c t i v i t y worth by t h e use of a l i n e a r e x t r a p o l a t i o n distance boundary condition a t t h e c o n t r o l element surface.

The e x t r a p o l a t i o n

distance depends not only on t h e c o n t r o l element blackness, b u t a l s o on t h e r e l a t i v e s i z e of t h e c o n t r o l region.20

The expression used was

where n i s t h e outward normal t o t h e c o n t r o l surface and A is the tr t r a n s p o r t mean f r e e path f o r thermal neutrons i n t h e core. A s i n d i c a t e d i n Eq. ( 4 . 3 ) , t h e function g ( y ) depends only on t h e r a t i o of t h e c o n t r o l r a d i u s t o t h e t r a n s p o r t mean f r e e path; t h i s function i n c r e a s e s from zero a t y = 0 t o 0.623 f o r l a r g e y. value of Aex/htr

Reference 19, p 725, gives a p l o t of t h e

vs y f o r black c y l i n d e r s (B = 1). This w a s used t o de-

termine g ( y ) f o r thermal neutrons i n c i d e n t on t h e MSRE element. C.

The remaining s i m p l i f i c a t i o n s i n t h e r e a c t i v i t y worth calcula-

t i o n s d e a l with t h e geometry of t h e r e a c t o r core and c o n t r o l rod configuration.

These calculations of 6k/k due to insertion of the central

poison c y l i n d e r s were made using t h e EQUIPOISE-3 program.

U s e of t h i s

numerical s o l u t i o n method, t o g e t h e r with t h e p r a c t i c a l r e s t r i c t i o n t o two-dimensional c a l c u l a t i o n s , required t h a t t h e reactor-rod configuration b e approximated i n x-y geometry.

shown i n Fig. 4.1. t h e core.

The configuration used f o r a model i s

This f i g u r e r e p r e s e n t s a h o r i z o n t a l c r o s s s e c t i o n of

The b a s i c model i s t h a t of a p a r a l l e l e p i d e d with square base.

The c o n t r o l regions a r e represented by regions of square c r o s s section, with t h e perimeter of each square equal t o t h e a c t u a l circumference of t h e c o n t r o l thimble.

Thus t h e t o t a l e f f e c t i v e absorptions of t h e c o n t r o l

regions were equal i n t h e model and t h e a c t u a l element. W

The o v e r a l l

t r a n s v e r s e dimension of t h e core w a s s o chosen t h a t t h e t o t a l geometric


56

UNCLASSIFIED ORNL-DWG 63-7347

I 1 2

AX = 5.03 4

6

8

I 10 42

AX=MESH

AX= 4.4f

~

AX= 1.00

,

SIZE

46

48

1

AX=IAX= 4.54 4.00

i

14

(cm)

20 22

24 26

I

AX= 1.44

5.03

28 30 32 34 36 38 40 42 43

4 2

4

I

6

24.78 in.

8 40 42 44

2.21 in.

46

+I 1.57 in.

18

4

20

2.43 in.

22

-t

24

+4 1.57 in.

26 28

2.24 in.

30 32 34 36

21.78 in.

38

I

40 42 43

S = SAMPLE HOLDER

I

Fig. 4.1. Cross S e c t i o n a l Model of MSRE Core Used in Equipoise C a l c u l a t i o n s of C o n t r o l Rod Worth.


57

L

buckling i n t h e t r a n s v e r s e (x-y) dimension w a s equal t o t h e e f f e c t i v e r a d i a l buckling of t h e a c t u a l c y l i n d r i c a l core.

Axial leakage was ac-

counted f o r by i n s e r t i o n of an e f f e c t i v e a x i a l buckling.

Because of t h e

l i m i t a t i o n of t h e c a l c u l a t i o n s t o two dimensions, it was necessary t o

assume t h a t t h e layout shown i n Fig. 4.1 extended completely through t h e a c t i v e l e n g t h of t h e core.

I n a c t u a l i t y , t h e maximwn p e n e t r a t i o n d i s -

tance f o r t h e poison c y l i n d e r s i s s l i g h t l y l e s s than t h i s length.

The model shown i n Fig. 4.1 i s based on p r a c t i c a l l i m i t a t i o n s concerning t h e t o t a l number of mesh p o i n t s i n t h e EQUIPoISE program.

The

attempt w a s made t o a d j u s t t h e mesh s i z e so t h a t m i n i m e r r o r i s obt a i n e d i n t h e c e n t r a l region of t h e core where t h e c o n t r o l elements a r e located.

This i s t h e region of maximum nuclear importance, and a l s o

t h a t of maximum s p a t i a l flux v a r i a t i o n when t h e rods a r e i n s e r t e d .

Repre-

s e n t a t i o n of t h e r e a c t o r t r a n s v e r s e boundary a s a square i s expected t o generate r e l a t i v e l y l i t t l e e r r o r i n t h e c a l c u l a t i o n s of t h e t o t a l rod worth. The e f f e c t of t h e graphite sample holder was neglected i n t h e s e preliminary c a l c u l a t i o n s .

Further s t u d i e s are planned t o examine t h i s

e f f e c t , and a l s o t o improve on some of t h e above approximations.

4.2.2

D i f f e r e n t i a l Worth Determination of t h e worth of p a r t i a l l y i n s e r t e d rods i s of impor-

tance i n s e t t i n g c o n t r o l rod speeds, i n s e t t i n g l i m i t i n g rod p o s i t i o n s , and i n p r e d i c t i n g t h e r e q u i r e d rod motion during s t a r t u p and normal operation.

I n keeping with t h e p r a c t i c a l r e s t r i c t i o n t o two-dimensional

d i f f u s i o n calcula-t;ions, a preliminary estimate of t h e d i f f e r e n t i a l worth

w a s based on an r-z

geometry model of t h e core.

The t h r e e c o n t r o l e l e -

ments were replaced by a s i n g l e absorber s h e l l , concentric with t h e core

axis.

The r e l a t i v e change i n 6k/k was c a l c u l a t e d as a function of t h e

p e n e t r a t i o n d i s t a n c e of t h e s h e l l i n t h e core.

The r a d i u s and thickness

of t h e s h e l l were determined by equating t h e e f f e c t i v e surface-to-volume r a t i o of t h e s h e l l t o t h a t of t h e a c t u a l elements.

The r e l a t i v e change

i n 6k/k w a s t h e n normalized t o t h e t o t a l rod worth obtained from t h e c a l c u l a t i o n s described i n Sec 4.2.1.


58

Results of Calculations

4.3 4.3.1

Total Reactivity Worth The t o t a l c o n t r o l worth of a l l t h r e e rods i n s e r t e d a l l t h e way

through t h e core, obtained from t h e c a l c u l a t i o n s described i n t h e previous section, i s l i s t e d i n Table 4.1. The worth of t h e individual rods w a s a l s o estimated f o r one of t h e f u e l s a l t s ( f u e l A), and t h e results

When converted t o represent f r a c t i o n s of t h e

a r e included i n Table 4.1.

t o t a l worth of all t h r e e rods, these l a t t e r r e s u l t s should be nearly equal f o r a l l t h r e e f u e l s a l t s .

Note t h a t t h e rod worths a r e not a d d i -

t i v e , since t h e r e i s appreciable "shadowing" between t h e rods.

Also,

rods 1 and 3 a r e worth s l i g h t l y more than rod 2, due t o t h e r e l a t i v e l y g r e a t e r influence of flux depression, caused by thimbles 1 and 3 , on t h e p o s i t i o n of rod 2 . 4.3.2

D i f f e r e n t i a l Worth R e s u l t s of the r-z

a r e shown i n Fig. 4.2.

c a l c u l a t i o n f o r t h e p a r t i a l l y i n s e r t e d rod bank This i s a p l o t of t h e f r a c t i o n of t h e t o t a l a x i a l

core height t o which t h e rods are i n s e r t e d .

It i s important t o note t h a t

these r e s u l t s apply t o t h e t h r e e rods moving as a u n i t ; e f f e c t s of moving a s i n g l e rod with t h e others held f i x e d i n some p a r t i a l l y i n s e r t e d posit i o n a r e not t r e a t e d i n t h e s e c a l c u l a t i o n s .

Table 4.1.

Fuel A

Control Rod Xorths i n t h e MSRE

Rod Configuration

3 Rods i n Rod 1 in, rods 2 and Rod 2 in, rods 1 and Rods 1 and 3 i n , rod Rods 1 and 2 in, rod

B

3 Rods i n

C

3 Rods i n

3 3 2 3

out out out out

5.6 2.4 2.3

4.4 4.1 7.6 5.7 V

,


59 UNCLASSIFIED ORNL-LR-DWG 5 7 6 8 7 A

4.0

0.8 I FQ:

0

3 J

ze

0.6

LL

0

0

0.2

0.4

0.6

0.8

FRACTION OF LENGTH INSERTED

Fig. 4 . 2 .

E f f e c t of P a r t i a l l y I n s e r t e d Rods.

4 .O


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 distribution cannot be observed experimentally, but some information on the distribution is necessary for the analysis of reactivity changes during The method by which MSRE core temperatures were predicted is described in detail in ref 21. The calculational method com-

power operation.

bines the flow distribution in a hydraulic model of the core with the power-density distribution predicted for the nuclear model. The numerical results presented here were computed with the power-density distribution appropriate for fuel practically the same results.

c,

but calculations for fuels A and B gave (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 moderator, upon which are superimposed local temperature variations within individual fuel channels and moderator stringers. The overall temperature distributions 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 o n l y

where such consideration is essential to evaluating the overall distribution.

5.1.1

Reactor Regions

A significant fraction of the nuclear power produced in this reactor is generated in the fuel-containing regions of the reactor vessel outside the f’uel-graphite matrix which forms the main portion of the


61

L

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 calculatiox 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 coii-

stant over a large portion of the core, but higher velocities occur near the axis and near the outer 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 TemDeratures 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

50째F temperature rise across the reactor and a fuel flow rate of 1200 gpm. The reactor inlet and outlet temperatures were set at 1175'3' 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 W

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 preceding region. Each 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 fueltempera-

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 Region

D

(gpm)

J

1142 1142 1200 1142 1142 1142

L

17

M N 0

1183 1200 1200 1200

E

F G

H

P

Q

17 17 17 41

R S

T

Flow Rates, Heat Rates, and Temperatures in Reactor Regions"

Heat Rateb (kw)

Temperature Riseb

355.3 115.8 378.2 82.7 95.7 8121.3 59.3 223.0 84.1 89.9 252.8 3.9 0.7 0.5

1.9

136.9

(OF)

0.6 1.9

0.4 0.5 42.7 20.9

Average Temperature' (OF)

1225.2 1224.0 1176.0 1223.5 1223.O d d

1.1

d

0.4 0.4 1.3 1.4 0.2 0.2 20.o

d

1178.4 1177.6 1201.0 1200.2 1200.0 d

a Regions not containing fuel are excluded. bAt 10 Mw. regions. C

Includes heat transferred to the fuel from adjoining

With Tin = 1175'F,

'Actual text.

Tout = 1225'F.

temperature distribution calculated for this region.

See

W


63

The average temperature of the fuel in a channel at any axial position 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 capacity and velocity.

Thus

where Q is an equivalent specific power which includes the heat added f to the fuel from the graphite. The channel inlet temperature, Tf(z = O ) , 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, ( P C ~ ) ~ ,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 Tf(r,z) = T (z = 0) + f

(Q

uj Ub-1

Z

B(z) dz 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 Tf(r,z) = Tf ( z = 0) +

I$.

a{cos 4.1 a - cos [+78.15 (z r5.74) .

(5.4)


64 I n t h i s expression,

K

i s a c o l l e c t i o n of constants,

and fl a = 78.15 (0 +

The l i m i t s within which Eq.

5.72)

.

(5.4)i s a p p l i c b l e a r e t h e 1 wer and

upper boundaries of t h e main p a r t of t h e core, namely, 0 5 z S 64.6

in.

It i s c l e a r from t h i s t h a t t h e shape of t h e a x i a l temperature d i s t r i b u t i o n i n t h e f u e l i n any channel i s proportional t o t h a t of t h e c e n t r a l p o r t i o n of t h e general curve [l- cos f3].

The a x i a l d i s t r i b u t i o n f o r t h e

h o t t e s t channel i n t h e MSRE i s shown i n Fig. 5.1, where it i s used t o provide a reference f o r t h e a x i a l temperature d i s t r i b u t i o n i n t h e graphite. The r a d i a l d i s t r i b u t i o n of t h e f u e l temperature near t h e core mid-

plane i s shown i n Fig. 5.2 f o r t h e reference conditions a t 10 Mw.

This

d i s t r i b u t i o n includes t h e e f f e c t s of t h e d i s t o r t e d power-density d i s t r i bution (Fig. 3.11) and t h e radial v a r i a t i o n s i n fuel v e l o c i t y .

A t the

reference conditions t h e main core i n l e t temperature i s 1179째F and t h e mixed-mean temperature l e a v i n g t h a t region i s 1222째F.

The a d d i t i o n a l

heat required t o r a i s e t h e r e a c t o r o u t l e t temperature t o 1225'F i s produced i n t h e p e r i p h e r a l regions above t h e main p a r t of t h e core.

The

general shape of t h e r a d i a l temperature p r o f i l e i s t h e same a t a l l a x i a l p o s i t i o n s i n t h e main p o r t i o n of t h e core.

5.1.3

Graphite Temperature Since a l l of t h e heat produced i n t h e g r a p h i t e must be t r a n s f e r r e d

t o t h e c i r c u l a t i n g f u e l f o r removal from t h e r e a c t o r , t h e steady-state temperature of t h e graphite i s higher than t h a t of t h e f u e l i n t h e adjacent channels.

This temperature d i f f e r e n c e provides a convenient

means of evaluating t h e o v e r a l l graphite temperature d i s t r i b u t i o n ; t h a t

is, by adding t h e l o c a l graphite-fie1 temperature d i f f e r e n c e s t o t h e previously c a l c u l a t e d f u e l temperature d i s t r i b u t i o n .

.


65 UNCLASSIFIED

ORNL DWG. 63.8164

Fig. 5.1. Axial Temperature Profiles in Hottest Channel and Adjacent 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 t h e remainder would have only a small effect on the system characteristics, the graphite temperature distribution 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


66

J

UNCLASSIFIED

RADIUS ( I n . )

Fig. 5 . 2 .

Radial Temperature P r o f i l e s Near Core Midplane.


67 L

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 graphitefuel 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 fluid near the channel wall allows that part of the fluid to reach a temperature above the average for the channel. This effect is increased when heat is transferred into the fluid through the channelwalls, as is the case in the MSRE. developed2

9

Equations have been

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 m a y be turbulent.

No allowance was made for a temperature difference due to the contact resistance at the graphite-fuel interface in these calculations. An estimate of this resistance was made by assuming a 1 - m i l gap, filled with helium, between the graphite and fuel. This rather pessimistic assumption 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 noma1 distance from the center V

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 soakxp in the graphite: 0, 0.5, and 2.0 vol % of the grappite. 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 difference. 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)

Graphite-fuel temperature difference (OF) Poppendiek effect in fuel Graphite temperature drop Total

0

0.5

2 .o

55.7

58.3

65.4

9.8 6.7 5.5 -

61.2

65.0

75.2

Overall Distribution. - Since the Poppendiek effect and the temperature 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. 14.1, for fuel C with no fuel permeation of the graphite. The distribution shown in Figs. 14.1 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 graphite 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 applications 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 nuclear average temperatures of the fuel and graphite, along with their respective temperature 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 distributions, the numerical relations are not obvious.

5.2.1

Bulk Average Temperatures Bulk average temperatures

fi) were

obtained by weighting the overall

temperature 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-

(The contents of the inlet flow distributor and the outlet nozzle were not included.) A large fraction of the s a l t in the vessel is in the peripheral regions, where detailed temperature distributions were not calculated. In computing the average for the rein the reactor vessel shell.

actor, average temperatures shown in Table 5.1 were used for these regions.

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 computed to be 1199.5OF.

Thus, assuming linear relationships, the fuel

bulk average temperature is given by

-

Tf

=

Tin + 0.49(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 fixel C with no permeation, the bulk average graphite temperature at the 1O-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 increase in graphite bulk average temperature as the fuel permeation was increased from 0 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 t h e 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 temperature 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 permeation, 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 - Tin + 5.0 P

T*=( Tout g

+

,

Tin ) + 5 . 5 P = T

where the temperatures are in

(5.8)

+3.OP,

out O F

and P is the power in Mw.

(5.10)

.


71 5.3

Power Coefficient of Reactivity

Whenever the reactor power is 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 temperature of the zero-power, isothermal reactor, on the other hand, can be readily controlled by the use of the control rods. When the reactivity effect of the rod poisoning is changed, the entire temperature distribution is 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 poisoning effect, required to obtain the desired result, to the power change is then called the power coefficient of reactivity.*sc Because of the way in which the nuclear average temperature is defined, 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 reactivity of simultaneous changes in fuel and graphite temperature is

a

and a are the fuel and graphite temperature coefficients of f Q reactivity. The change in rod poisoning is equal in both sign and

where

magnitude to the reactivity effect of the temperature changes.

(If the

*This

statement and the discussion which follows refer to adjustments 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 r o d poisoning must be decreased an equal amount to produce the temThus Eq. (5.11) can be used to evaluate the power

perature change.)

coefficient of reactivity. When Eqs. (5.9) and (5.10) for T; and T* are g substituted, Eq. (5.11) becomes either

-k

-

(ag+ af)mout+ (3.0 a - 1.4 Ctf)AP

(5.12)

g

or -- -

k

(

'ag + af,n Tout

Tin) + (5.5 a + 1.1 " f ) A P g

If Tout is held constant during power changes (i.e., if

.

mout is

(5.13)

zero),

the power coefficient is (5.14)

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

constant,

Wk - 5.5 m

--

a + 1.1 af g

.

(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 &/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, To, is found from (5.16)

* - To)

af(T; - To) = -a (T g

g

(5.17)


73 L

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

(5.18)

(5.19)

/3.0

a

c

- 1.4 (5.20)

Note that the changes with power depend on the values of a and a hence f gy on the type of fuel in the reactor. Thus it has been shown that the power coefficient of reactivity depends 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.

Mode of Control

Power Coefficients of Reactivity and Temperatures at 10 Mw Power Coefficient (k w.4 Mw

Fuel A FuelB Fuel C

Temperaturesa ( O F )

Tout Tin ~~

Tout

g

~~

-0.006 -0.008 -0.006 1200 1150 1186 1230

Constant Tout Constant

T*

+

2

Tin

-0.022 4.033 -0.024

1225 1175 1211 1255

"Hands- off Fuel A

1191 1141 1177 1221

0

Fuel B Fuel C a System isothermal at 1200'F

0

1192 1142 1178 1222

0

1191 1141 1177 1221

at zero power.


74

6.

J

DELAYED NEUTRONS

The k i n e t i c s of t h e f i s s i o n chain r e a c t i o n i n t h e MSRE a r e i n f l u enced by t h e t r a n s p o r t of t h e delayed neutron precursors.

An exact

mathematical d e s c r i p t i o n of t h e k i n e t i c s would n e c e s s a r i l y include, i n t h e equation f o r t h e precursor concentrations, terms describing t h e movement of t h e precursors through t h e core and t h e e x t e r n a l loop.

In

order t o render t h e system of k i n e t i c s equations manageable, t h e t r a n s p o r t term w a s omitted from t h e equations used i n MSRE a n a l y s i s (see Sec 12.4.1).

Thus t h e equations which were used were of t h e same form

as those f o r a f i x e d - f u e l r e a c t o r .

Some allowance f o r t h e t r a n s p o r t of

t h e delayed neutron precursors was made by s u b s t i t u t i n g " e f f e c t i v e " values f o r delayed neutron y i e l d s i n place of t h e a c t u a l y i e l d s .

The

k i n e t i c s c a l c u l a t i o n s used " e f f e c t i v e " y i e l d s equal t o t h e c o n t r i b u t i o n s

of t h e delayed neutron groups t o t h e chain r e a c t i o n under s t e a d y - s t a t e conditions. 6.1

Method of Calculation

I n t h e c a l c u l a t i o n of t h e e f f e c t i v e c o n t r i b u t i o n s during steady power operation, nonleakage p r o b a b i l i t i e s were used as t h e measure of t h e r e l a t i v e importance of prompt and delayed neutrons.

Spatial distri-

butions f o r t h e precursors during steady operation were c a l c u l a t e d and were used, t o g e t h e r with t h e energy d i s t r i b u t i o n , i n computing nonleakage probabilities.

''

The MSRE core was approximated by a c y l i n d e r with t h e f l u x (and precursor production) vanishing a t t h e s u r f a c e s . uniformly d i s t r i b u t e d .

Flow w a s assumed t o be

With t h e s e assumptions, t h e s p a t i a l d i s t r i b u t i o n

of precursors of a p a r t i c u l a r group i n t h e core was found t o be of t h e

form -htcZ/H S ( r , z ) = Soe

+

1-

SI sin

XZ H

(See See 6.4 f o r d e f i n i t i o n of symbols. )


75

For the purpose of computing nonleakage probabilities, the spatial

Y

distribution of each group was approximated by a series:

The coefficients, Am,

were evaluated from the analytical expression for

The nonleakage probability for a group of neutrons was then S(r,z). computed by assigning a nonleakage probability to each term in the series equal to e-B&7

1+ L

~

,

B

(6.3)

~

where B2 mn

=(+) + ( % ) . j

2

2

The energy distribution of each delayed neutron group was taken into account by using an appropriate value for the age,

T,

in the expression

for the nonleakage probability.

6.2 6.2.1

Data Used in Computation

Precursor Yields and Half-Lives The data of Keepin, Wimett, and Zeigler for fission of U235 by

thermal neutrons were used.25 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.26

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

W

to thermal energies in the MSRE core of 292 em2 (this value was computed


76

The age of neutrons from

by a MODRIC multigroup diff’usion c a l c u l a t i o n ) .

t h e d i f f e r e n t sources was assumed t o be proportional t o t h e lethargy; t h a t is,

Computed values of

T

i

a r e given i n Table 6.1.

Table 6 . 1 .

1

2

55.7

22.7

Group Precursors h a l f - l i f e ( s e e )

Delayed Neutron Data

3

4

5

6

6.22

2.30

0.61

0.23

F r a c t i o n a l y i e l d of precursors, 1 0 4 p i (neutrons per io4 neutrons )

2.11

14.02

12.54

25.2%

7.40

2.70

Neutron mean energy (Mev)

0.25

0.46

0.40

0.45

0.52

0.5

Neutron age i n MSRF: (em2)

6.2.4

256

266

264

266

269

26%

MSRE Dimensions

The computation of B2 f o r t h e nonleakage p r o b a b i l i t i e s used R = 27.75 i n . and H = 68.9 i n . ft3.

The volume of f u e l w i t h i n t h e s e boundaries i s 25.0

A t a c i r c u l a t i o n r a t e of 1200 gpm, residence times a r e 9.37

t h e core and 16.45 see i n t h e e x t e r n a l loop.

see i n

A thermal neutron d i f f u s i o n

l e n g t h appropriate f o r a core with highly (-93%) enriched uranium and no thorium was used (L2 = 210 em2).

6.3

Results of Computation

The core residence t i m e , i n u n i t s of precursor h a l f - l i v e s ,

from 0.2 t o 41.

Because of t h i s , t h e shapes of t h e delayed neutron

sources i n t h e core vary widely, as shown i n Fig. 6.1, circulating.

ranges

when t h e f u e l i s

(The source s t r e n g t h i s normalized t o a production r a t e of


77 UNCLASSIFIED ORNL-LR-DWG 7 3 6 2 0 R

( x 40-9)

2.8

rr)

I

E

i

2.4

0

I

GROUP tv2 ( s e c )

v

>-

I-

cn Z

W

2.0

I

n

(SEE FIG 6 . 2 FOR GROUP 4 DISTRIBUTION)

W 0

E 3

0

cn

56 23 6.2 2.3 0.6 0.2

4 2 3 4 5 6

4.6

Z 0

E l-

II> W

Z

!.2

f 3 W

>a -I W

n

0.8

W

> I-

a

-1 W

E

0.4

0

0

0.2

0.4 0.6 RELATIVE HEIGHT

0.8

1 .O

Fig. 6.1. Axial D i s t r i b u t i o n of Delayed Neutron Source Densities i n an MSRE Fuel Channel. Fuel c i r c u l a t i n g a t 1200 gpm.


78 1 neutron/sec i n t h e r e a c t o r . )

Figure 6.2 compares source d i s t r i b u t i o n s

f o r one group under c i r c u l a t i n g and s t a t i c conditions.

The reduction i n

t h e number of neutrons emitted i n t h e core i s indicated by t h e difference i n areas under t h e curves.

A g r e a t e r p r o b a b i l i t y of leakage under circu-

l a t i n g conditions i s suggested by t h e s h i f t i n t h e d i s t r i b u t i o n , which reduces t h e average distance t o t h e outside of t h e core. Table 6.2 summarizes important calculated q u a n t i t i e s f o r each group. The t o t a l e f f e c t i v e f r a c t i o n of delayed neutrons i s 0.00362 a t a 1200-gpm c i r c u l a t i o n r a t e and i s 0.00666 i n a s t a t i c core.

The t o t a l y i e l d of

precursors i s 0.00641. Table 6.2. Group

Delayed Neutrons i n MSRE a t Steady S t a t e

5

6

1

2

3

4

0.68

0.72

0.87

0.91

1.01

1.03

0.25

0.27

0.40

0.67

0.97

1.02

0.52

3.73

4.99

16.98

7.18

2.77

Pi /Ppr

1.06

1.04

1.04

1.04

1.03

1.03

104~;

2.23

14.57

13.07

26.28

7.66

2.80

Circulating:

104q

Static :

6.4

Nomenclature f o r Delayed Neutron Calculations Coefficient i n series representation of S

B2

Geometric buckling

E

I n i t i a l mean neutron energy

Eth

H

Thermal neutron energy Height of core

J


79

UNCLASSIFIED ORNL-LR-DWG 7 3 6 2 i P

c--

rr)

I

L

E

0

U

> + -

cn

\ \

/STATIC

z W n W

I I

0

E 3 0

cn

2

z

0

I I

E I3 W

z

C I R C U LA1 NG

i

L

n W

>

I I

5

-I

w

a

/

\

L

\ \

L \ \

L

W

> -

I-

5

-1 W

E

0

0.2

0.4 06 R E L A T I V E HEIGHT

0.8

i.0

Fig. 6.2. E f f e c t of Fuel C i r c u l a t i o n on Axial D i s t r i b u t i o n o f Source Density of Group 4 Delayed Neutrons. Fuel c i r c u l a t i n g a t 1200

gpm


80

JO

jm

Bessel function of f i r s t kind mth r o o t of Jo(x)= 0

L

Neutron d i f f u s i o n l e n g t h

P

Nonleakage p r o b a b i l i t y

r

Radial distance from core a x i s

R

Outside r a d i u s of core

S

Neutron source per u n i t volume of f u e l

tC

Residence time of f u e l i n core Axial distance from bottom of core

Z

F r p c t i o n a l y i e l d of neutrons of group i E f f e c t i v e f r a c t i o n of neutrons of group i 6

i

F r a c t i o n of group i emitted i n core

A

Precursor decay constant

7

Neutron age


c

81

7. POISONING DUE TO XENON-135

w

Changes i n the concentration of Xe135 i n the core produce changes i n r e a c t i v i t y t h a t are about a s large a s those from a l l other f a c t o r s combined.*

I n order t o use the net r e a c t i v i t y behavior during power op-

e r a t i o n t o observe changes i n such f a c t o r s a s burnup, f u e l composition, and graphite permeation, the xenon poisoning must be calculated quite accurately from the power history.

7.1

Distribution of Iodine and Xenon

The f i r s t s t e p i n calculating the xenon poisoning i s t o calculate t h e behavior and d i s t r i b u t i o n of 1135 i n a l l p a r t s of the reactor.

(This

information i s , of course, necessary because most of the Xe135 i s formed by decay of 1135.)From t h i s one proceeds t o calculate the concentration

of Xe135 i n the f u e l s a l t , i n various p a r t s of the graphite, and elsewhere throughout the reactor. A number of production and destruction mechanisms f o r both xenon and

iodine which involve the chemical and physical behavior of the isotopes can be postulated and described mathematically, a t l e a s t i n principle. Some of these mechanisms can be eliminated immediately a s i n s i g n i f i c a n t , while others can be shown t o be highly s i g n i f i c a n t .

There remain, how-

ever, a number of mechanisms whose significance probably cannot be evaluated u n t i l a f t e r the reactor has been operated and t h e operation c a r e f u l l y analyzed.

7.1.1

Sources of Iodine and Xenon i n Fuel The only s i g n i f i c a n t source of

i n the c i r c u l a t i n g f u e l i s the

d i r e c t production from f i s s i o n ; the iodine precursors i n t h i s chain have h a l f - l i v e s t o o short t o have any s i g n i f i c a n t e f f e c t . The p r i n c i p a l sources of Xe135

i n the f u e l are the decay of 1135 in

the f i e 1 and d i r e c t production from f i s s i o n .

However, a t h i r d p o t e n t i a l

source e x i s t s i f iodine i s trapped on metal surfaces i n the primary loop, *See l i s t of r e a c t i v i t y shim requirements, Table 9.1.


. a2

and the xenon formed by the decay of t h i s iodine does not immediately r e t u r n t o the c i r c u l a t i n g stream. I n t h i s case, the xenon must be t r e a t e d separately from t h a t produced by decay of iodine i n the c i r c u l a t i n g stream, because the delay i n the r e t u r n of t h e xenon t o c i r c u l a t i o n changes the destruction p r o b a b i l i t i e s .

7.1.2 Removal of Iodine and Xenon from Fuel The p r i n c i p a l removal mechanism for iodine i s radioactive decay. However, consideration must a l s o be given t o the p o s s i b i l i t y of iodine migration i n t o the graphite and t o metal surfaces. I f these processes occur, they will modiSy the overall xenon behavior.

V o l a t i l i z a t i o n or

stripping of iodine i n the pump bowl and destruction by neutron capture are both regarded as i n s i g n i f i c a n t . There are a number of competing mechanisms f o r t h e removal of xenon from the f u e l . The most important of these are s t r i p p i n g i n the pump bowl and migration t o the graphite.

Of l e s s e r importance, but s t i l l sig-

n i f i c a n t , a r e decay of and neutron capture by xenon i n the f u e l i t s e l f . Decay of xenon trapped on metal surfaces must a l s o be considered.

7.1.3

Sources of Iodine and Xenon i n Graphite Unless permeation of the graphite by f u e l occurs, t h e only source of

iodine i n t h e graphite i s migration from the f u e l .

If f u e l permeation

does occur, the d i r e c t production of iodine i n t h e graphite by f i s s i o n must be considered. The major source of xenon i n the graphite i s migration from the fuel.

Other sources which may or may not be important a r e decay of iodine

i n the graphite and d i r e c t production from the f i s s i o n of f u e l soaked i n t o the graphite.

7.1.4 Removal of Iodine and Xenon from Graphite Because of t h e low neutron absorption cross section of I’35, the only mechanism f o r i t s removal from the graphite i s by radioactive decay t o Xe135. portant.

I n the case of xenon, both decay and neutron capture a r e i m -

e


83 I n a l l cases where the t r a n s f e r of an isotope from one medium t o

L

another i s involved, only the net t r a n s f e r need be considered; therefore, these can be regarded a s one-way processes, with the d i r e c t i o n of t r a n s f e r being indicated by the sign of the term.

7.1.5

Detailed Calculations A s e t of simultaneous d i f f e r e n t i a l equations has been developed t o

describe, i n mathematical t e r m s , a l l of the mechanisms discussed above. These equations a l s o take i n t o account r a d i a l and a x i a l variations i n the f i e 1 flow p a t t e r n throughout the core and within individual f i e 1 channels, a s well a s the overall d i s t r i b u t i o n of the neutron flux.

The equations

can, t h e o r e t i c a l l y a t l e a s t , be programmed f o r solution by a l a r g e computer t o give d e t a i l e d s p a t i a l d i s t r i b u t i o n s of iodine and xenon i n the core.

An a c t u a l solution of the equations requires d e t a i l e d information

about a number of the chemical and physical parameters of t h e system, which i s not currently available.

However, some q u a l i t a t i v e comments can

be made about the nature of the r e s u l t s t h a t can be expected. The d i s t r i b u t i o n of xenon i n the f u e l within the core will probably be r e l a t i v e l y uniform, because of the mixing i n the e x t e r n a l loop and the f a c t t h a t most of the xenon i s produced from iodine t h a t was formed i n e a r l i e r passes through the core.

Some depletion may occur along the r e -

gion near the centerline of the core, because of the higher neutron f l u x and because the higher f u e l turbulence f a c i l i t a t e s t r a n s f e r t o the graphite.

H o w e v e r , the mixed-mean concentration a t the core o u t l e t must be

somewhat higher than a t the i n l e t t o allow for stripping i n t h e pump bowl and decay i n the external loop. The o v e r a l l r a d i a l d i s t r i b u t i o n of xenon i n the graphite may e x h i b i t a minimum, due t o burnout, a t the radius corresponding t o the maximum i n

the thermal flux.

This minimum i s reinforced by the f a c t t h a t the f l u x

maximum occurs i n the low-velocity region of the core, where t r a n s f e r from t h e f u e l i s slowest.

I n the a x i a l direction, the highest xenon con-

centrations will probably occur near the i n l e t t o t h e core; the neutron f l u x i s low i n t h i s region, and turbulence near the entrance of t h e f u e l channels tends t o promote t r a n s f e r from the fuel. v

This d i s t r i b u t i o n may,

however, be s i g n i f i c a n t l y affected by a x i a l diff’usion i n t h e graphite stringers.


v

7.1.6 Approximate Analysis I n order t o provide a basis f o r estimating the r e a c t i v i t y e f f e c t of Xe135 i n the reactor, an approximate analysis of the steady-state xenon

For t h i s approach, the scope of t h e problem was reduced t o include only the major behavior mechanisms. It was assumed d i s t r i b u t i o n was

t h a t a l l of the iodine remains with the f u e l i n which it i s produced; t h i s completely eliminated iodine from the steady-state mathematical expressions.

The core was divided i n t o four r a d i a l regions on the b a s i s

of f u e l velocity, and an overall mass-transfer coefficient was calculated f o r xenon t r a n s f e r from f u e l t o graphite i n each region.

Axial varia-

t i o n s i n xenon concentration i n both f i e 1 and graphite were neglected. Average xenon burnup r a t e s were calculated on the b a s i s of t h e average thermal neutron f l u x i n the reactor. negle ct e d

.

Fuel permeation of the graphite was

Because of u n c e r t a i n t i e s i n t h e physical parameters, the xenon behavior was calculated for r e l a t i v e l y wide ranges of t h e following v a r i able s : 1. Stripping efficiency i n the pump bowl.

The ultimate poisoning

e f f e c t of t h e xenon i s most s e n s i t i v e t o t h i s quantity, which a l s o has the g r e a t e s t degree of uncertainty associated with it.

The e n t i r e range,

from 0 t o 10% efficiency, was considered. 2.

Fuel-to-graphite mass-transfer c o e f f i c i e n t .

This quantity can

be calculated with reasonable confidence but the xenon poisoning i s r e l a t i v e l y sensitive t o the r e s u l t s .

Values d i f f e r i n g by a f a c t o r of 2 from

the expected value were considered. 3.

Diff'usion c o e f f i c i e n t for xenon i n graphite.

The uncertainty

associated with t h i s quantity i s quite l a r g e but i t s e f f e c t on t h e poisoning, within the range of expected values, i s small.

Two values, d i f -

fering by a f a c t o r of 100, were considered. The xenon poisoning i s determined primarily by t h e xenon which d i f -

f k s e s i n t o the graphite.

Nearly all of the xenon t h a t does not migrate

t o the graphite i s stripped out i n the pump bowl, leaving only a small f r a c t i o n ( < 1% of the t o t a l ) t o be destroyed by neutron absorption o r raaioactive decay i n the f i e l .

The xenon migration t o t h e graphite i s


85 not s i g n i f i c a n t l y affected by the choice of f u e l , because a l l three f u e l s have similar physical properties.

However, the choice of f u e l has some

e f f e c t on t h e poisoning, because t h i s determines the f l u x l e v e l i n the r e a c t o r a t design power (see Table 3.5).

This i s i l l u s t r a t e d by the f a c t

t h a t 49% of the Xe135 t h a t e n t e r s the graphite i s destroyed by neutron absorption a t the f l u x l e v e l associated with 10-Mw operation with f u e l s A and C, whereas 62% i s destroyed by t h i s mechanism with f u e l B.

Figure 7.1 i l l u s t r a t e s the e f f e c t of stripping efficiency on the f r a c t i o n of Xe135 produced i n the r e a c t o r which migrates t o the graphite. This f i g u r e a l s o shows the e f f e c t of changing the diffusion c o e f f i c i e n t , D, i n the graphite by a f a c t o r of 100. It i s expected t h a t the average

value of the graphite diffusion coefficient i n t h e MSRE w i l l be between the values shown.

Figure 7.2 shows the e f f e c t s of increasing and de-

creasing the mass-transfer coefficient, K, by a f a c t o r of 2 from the expected value, &.

Th.e curves i n Fig. 7.2 are based on the higher of the

two graphite diffusion coefficients. 7.2

Reactivity E f f e c t s of Xenon-135

Once the s p a t i a l d i s t r i b u t i o n of xenon i n c i r c u l a t i o n and t h a t r e tained on t h e graphite has been calculated, it i s possible t o r e l a t e theor e t i c a l l y the xenon r e a c t i v i t y e f f e c t t o the poison d i s t r i b u t i o n .

'This r e l a t i o n i s most conveniently expressed i n terms of a r e a c t i v i t y c o e f f i -

c i e n t and an importance-averaged xenon concentration.

The method f o r

calculating these q u a n t i t i e s i s similar t o t h a t used i n obtaining the r e a c t i v i t y e f f e c t of temperature (See

3.7).

I n the case of xenon, however, the weight f'unction f o r the poison concentration i s proportional t o the

*

product @2@2 :

*

where Nxe i s t h e importance-averaged concentration per u n i t r e a c t o r vol-

-,

and N i e a r e the l o c a l concentrations, per u n i t volumes of

graphite and s a l t , respectively.

*

The quantity Nxe i s a l s o the uniform?


86

STRIPPING EFFICIENCY

($1

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

W


0

20

40

60

STRIPPING EFFICIENCY

80

100

(5)

Fig. 7.2. Effect of Mass-Transfer Coefficient on Xenon-135 Migration to Graphite.


88 equilibrium concentration of xenon i n the reactor, which produces the same r e a c t i v i t y change a s the a c t u a l d i s t r i b u t i o n .

*

I n r e l a t i n g Nxe t o

the t o t a l r e a c t i v i t y change, it i s convenient t o define a t h i r d quantity,

*

the e f f e c t i v e thermal poison f r a c t i o n , PXe.

This i s the number of neu-

t r o n s absorbed i n xenon per neutron absorbed i n U235, weighted with r e spect t o neutron importance :

where ~ 2 = 5

concentration of ~ ~ 3 per 5 , u n i t reactor volume,

= U235 microscopic absorption cross section f o r f a s t (1)and

0-$:2

thermal ( 2 ) neutrons, uXe

= xenon thermal absorption cross section.

*

i s given by28 The r e l a t i o n between t o t a l xenon r e a c t i v i t y and P Xe

Thus, i f knowledge of the xenon d i s t r i b u t i o n can be obtained from separate experiments or calculations, the calculation of the t o t a l xenon r e a c t i v i t y involves three s t e p s :

*

*

*

( a ) obtaining Nxe

from Eq. (7.1), ( b ) calculating

from N by use of Eq. ( 7 . 2 ) , and ( c ) calculating 6k/k from Eq. (7.3). X 'e Xe Alternatively, the above r e l a t i o n s may be used i n a reverse manner i f knowledge of the d i s t r i b u t i o n i s i n f e r r e d from r e a c t i v i t y measurements a t power. The numerical values of the xenon r e a c t i v i t y c o e f f i c i e n t s obtained f o r the three f u e l s under consideration a r e given i n Table 3 . 5 .

Both the

c o e f f i c i e n t s r e l a t i n g 6k/k t o the poison f r a c t i o n and t o t h e importanceaveraged xenon concentration are l i s t e d . Xenon concentrations calculated by the approximate method described i n Sec

7.1.6 were used with the r e a c t i v i t y c o e f f i c i e n t s t o obtain e s t i -

mates of the xenon poisoning i n t h e MSRE.

Since the simplified analysis

used o n l y the average neutron flux, the calculated xenon concentrations


89 were space-independent and, therefore, independent of the importanceweighting f'unctions.

(The weighted average of a constant function i s the

same constant, regardless of the shape of the weighting f i n e t i o n . )

It

may be noted t h a t peaking i n the xenon d i s t r i b u t i o n 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 e f f e c t . Xenon r e a c t i v i t y e f f e c t s were calculated f o r a l l three f i e l s ; the r e s u l t s are l i s t e d i n Table 7.1.

The expected values a r e based on a

graphite d i f f i s i o n coefficient of 1.5 mass-transfer coefficients.

X

lom5 f t 2 / h r

and the calculated

The minimum and maximum values were obtained

by applying the most favorable and unfavorable combinations of these two variables, within the l i m i t s discussed i n See

7.1.6.

The r e a c t i v i t y e f -

f e c t s f o r f u e l s A and C a r e the same because the average thermal fluxes are the same and the r e a c t i v i t y c o e f f i c i e n t s do not d i f f e r within the accuracy of these calculations.

The higher r e a c t i v i t y e f f e c t w i t h f i e 1 B

i s t o be expected, because of the higher f l u x associated with t h i s mix-

ture.

Changes i n pump bowl stripping efficiency would have the same r e l -

a t i v e e f f e c t on f i e 1 B as i s shown f o r f i e l s A and C. Table 7.1.

Reactivity Effects of Xe135 Fuel B

Fael A or C Pump bowl stripping efficiency ($)

25

50

Expected

-1.2

4.7

4.5

Minimum

-1.0

4.3

MXCb.IlUI?l

-1.7

-0.5 -1.2

4.9 -0.5

-0.9

-1.5

100

50

Reactivity e f f e c t (f 6k/k)


90

8.

POISONING DUE: To OTHER FISSION PRODUCTS

Many f i s s i o n products other than Xe135 contribute appreciably t o the neutron absorptions i n the r e a c t o r a f t e r long operation a t high power. There are a few stable o r long-lived f i s s i o n products with high cross secThe poisoning e f f e c t of t h i s

t i o n s , the most important of which i s Sal4’.

group of f i s s i o n products s a t u r a t e s i n a period of a few weeks or months, but undergoes t r a n s i e n t s following power changes.

I n addition, there i s

a slowly r i s i n g contribution t o the poisoning from lower-cross-section nuclides which continue t o build up throughout power operation.

8.1

Samarium-149 and Other High-Cross-Section Poisons

Samarium-149 i s the next most important f i s s i o n product poison a f t e r Xe135,

having a y i e l d of 0.0113 atom/fission and a cross section of about

40,000 barns.

Unlike Xe135, it i s a stable nuclide, so t h a t once the r e poison will always be present.

a c t o r has been operated a t power, some

The poison l e v e l changes, however, followiw power changes. Samarium-149 i s the end product of the decay chain 53.lh

,

149

( &

(stable)

,

For a l l p r a c t i c a l purposes the e f f e c t of Nd14’ on t h e time behavior of Sm14’ can be neglected. I f it i s f’urther assumed t h a t there i s no d i r e c t y i e l d of Sm14’,

and no burnup of Pm14’, the equations governing the Sm14’

concent r a t ion are

a

These equations can be solved t o obtain the poisoning, P, due t o the Sm14’ i n a thermal r e a c t o r :

V


91 The r e a c t i v i t y e f f e c t of the

i s simply r e l a t e d t o P, i n the case

of a thermal reactor, by

-6k- - -fP k

,

where f i s the thermal u t i l i z a t i o n f a c t o r i n the core. Figures 8 . 1 4 . 3 show the type of behavior which can be expected of the Smlq9 e f f e c t i n the W E .

Figure 8.1 shows the t r a n s i e n t following The steady-state poison-

a step increase t o 10 Mw from a clean condition.

ing i s independent of power l e v e l , but the r a t e of buildup i s a function of the power, i n t h i s situation.

This curve was calculated using

T

= 1X

When the power i s r e = 4 X lo4, y = 0.0113, and f%/% = 0.8. cr Sm duced the Sm14’ builds up, because the r a t e of production from Pm14’ decay i s temporarily higher than the burnup of Srn14’.

Figure 8.2 shows the

r e a c t i v i t y t r a n s i e n t due t o SmI4’ buildup a f t e r a reduction t o zero power from the steady s t a t e approached i n Fig. 8.1.

After the S m l q 9 has b u i l t

up t o steady s t a t e a t zero power, a s t e p increase back t o

T

= 1X

r e s u l t s i n the t r a n s i e n t shown i n Fig. 8.3. I n addition t o the simple production of Sm14’

through F’m14’,

some

may be produced by successive neutron captures and beta decays i n a chain beginning with F’mlq7.

This source can become important a f t e r a long time

a t a high flux. Other high-cross-section poisons which are important a r e Srn15’, Gd155 > The e f f e c t of these nuclides amounts t o about 7 E u ’ ~ ~ , and Cd113. 0.2 of t h a t of the Sml“’,

time.

and s a t u r a t e s i n roughly the same length of

Some of these f i s s i o n products have r e l a t i v e l y short-lived parents,

so t h a t they undergo t r a n s i e n t s s i m i l a r t o Sm149 a f t e r changes i n power,

8.2

Low-Cross-section Poisons

The l a r g e majority of the f i s s i o n products may be regarded a s an aggregate of stable, low-cross-section nuclides.

The e f f e c t i v e thermal

cross section and resonance i n t e g r a l of t h i s aggregate depend i n an i n -

volved manner on the energy spectrum of the flux, t h e f i e 1 nuclide, and low the amount of %el burnup which has o c c ~ r r e d . A~t ~ ~ f~u e~l burnup, i n a thermal r e a c t o r fueled with U235, a good approximation i s t h a t each


1.0

0.8

0.6

0.4

0.2

TIME

Fig.

8.1.

Sm149 Poisoning

(days

)

at 5 = 1 x 1Ol3

After

Startup

with

Clean

Fuel.

(

.


â&#x20AC;&#x2122; (

Sm14' Poisoning Fig. 8.2. at ; = 1 x 1013.

at Zero Power After

Reaching Steady State


1

3

2

3

4 TIME

Fig. Low-Power

8.3. Sm14' Poisoning.

Poisoning

After

5 (days

6

7

8

)

Step

to 5 = 1 x 1Ol3

from

Peak


95 L

f i s s i o n produces one atom w i t h a cross section of 43 barns and a resonance i n t e g r a l of 172 barns.31 a thermal f l u x of 1 X

I n a predominantly thermal reactor with

the poisoning e f f e c t of t h i s group of f i s s i o n

products increases i n i t i a l l y a t a r a t e of about 0.003% 8k/k per day.


96 9. EMPLOYMENT OF CONTFOL RODS I N OPERATION

J

The control rods are used t o make the r e a c t o r s u b c r i t i c a l a t times, t o regulate the nuclear power or f i e 1 temperature, and t o compensate f o r the changes i n r e a c t i v i t y which occur during a cycle of startup, power operation, and shutdown,

The manner i n which the control rods a r e em-

ployed i s d i c t a t e d by t h e i r s e n s i t i v i t y and t o t a l worth, the r e a c t i v i t y shim requirements, and c e r t a i n c r i t e r i a r e l a t e d t o safe and e f f i c i e n t operation.

These f a c t o r s and a normal program of rod positions during an

operating cycle are summarized b r i e f l y here. 9.1

General Considerations

The drive mechanisms f o r the three rods are i d e n t i c a l , and each rod has p r a c t i c a l l y the same worth.

Thus any one of the rods can be selected

t o be p a r t of the servo control system which controls the r e a c t o r f i s s i o n r a t e a t power below 1 Mw or the core o u t l e t temperature a t higher powers. The other two rods are moved under manual control t o s h i m the r e a c t i v i t y a s required.

The servo-controlled rod i s c a l l e d the regulating rod; the

other two, shim rods.

A l l rods are automatically i n s e r t e d or dropped

under c e r t a i n conditions, so t h a t a l l perform safety f h c t i o n s .

(For a

description of control and safety systems see Part 11. Nuclear and Process Instrumentation. ) The c r i t e r i a f o r the rod employment are a s follows: 1. The r e a c t i v i t y i s limited by f i e 1 loading t o the minimum required

f o r f'ull-power operation.

Thus, a t fill power, with m a x i m u m poison and

burnup, the rods are withdrawn t o the l i m i t s of t h e i r operating ranges. 2.

The maximum withdrawal of the shim rods i s s e t a t 54 i n . t o avoid

waste motion a t the beginning of a rod drop.

3.

The normal operating range of the regulating rod i s l i m i t e d by

the reduced s e n s i t i v i t y a t e i t h e r end t o between 15-in. and 45-in. withdrawal.

( I n t h i s range the rod changes r e a c t i v i t y a t 0.002 t o 0.04s 6k/k

per sec while being driven a t 0.5 in./sec. ) 4.

Rod movements are programmed t o minimize e r r o r i n calculated rod

worth due t o i n t e r a c t i o n or shadowing e f f e c t s . J


97

L

5.

While the core i s being f i l l e d with f’uel, the rods are withdrawn

so t h a t the reactor, when f u l l , w i l l be s u b c r i t i c a l by about 1.0% Sk/k. This allows the source multiplication t o be used t o detect abnormalities,

and provides reserve poison which can be i n s e r t e d i n an emergency. 6.

Before t h e c i r c u l a t i n g pump i s s t a r t e d , t h e rods are i n s e r t e d

f a r enough t o prevent any cold slug from making the reactor c r i t i c a l .

9.2

Shim Requirements

The r e a c t i v i t y changes due t o various causes during an operating cycle depend, f o r the most p a r t , on the type of f u e l i n the reactor.

The

amounts of rod poison which must be withdrawn t o compensate f o r various e f f e c t s are summarized i n Table 9.1.

Equilibrium samarium poisoning and

the slow growth of other f i s s i o n products and corrosion products a r e compensated by f i e 1 additions r a t h e r than by rod withdrawal. The l a r g e s t single i t e m i n Table 9.1,

the xenon poisoning, depends

on the flux, the s t r i p p e r efficiency, t h e xenon diff’usivity i n t h e graphi t e , and t h e f’uel-graphite xenon t r a n s f e r .

The tabulated values of xenon

e f f e c t were calculated f o r a s t r i p p e r efficiency of 5%, xenon diff’usivity i n the graphite of 1.5 X lCr5 ft2/hr, and a mass t r a n s f e r c o e f f i c i e n t of

0.08 f t / h r .

There i s considerable uncertainty i n these f a c t o r s , and the Table 9.1.

Rod Shim Requirements Effect ($ Sk/k)

Cause Fuel A

Fuel B

Fuel C

Loss of delayed neutrons

0.3

0.3

0.3

Entrained gas

0.2

0.4

0.2

MW)

0.06

0.08

0.06

Xe135 (equilibrium a t 10 Mw)

0.7

0.9

0.7

Samarium t r a n s i e n t

0.1

0.1

0.1

Burnup (120 g of u235)

0.03

0.07

0.03

1.4

1.9

1.4

Power

(&lo

Total


98 xenon e f f e c t could be a s l i t t l e a s one-third or a s much a s twice the values tabulated.

9.3

Shutdown Margins

When the rods a r e withdrawn t o the l i m i t s s e t by c r i t e r i a 2 and 3, the combined poison of the three rods i s 0.5% 8k/k.

The u s e f u l worth of

the rods, from full i n s e r t i o n t o the upper end of t h e i r operating ranges,

i s therefore l e s s than the t o t a l worth (Table 4.1) by 0.5% 6k/k. The minimum shutdown margin provided by the rods i s the difference between the usef'ul worth of the rods and the shim requirements (Table (The shutdown margin will be g r e a t e r than the minimum whenever any

9.1).

of t h e e f f e c t s i n Table 9 . 1 are present.)

Minimum shutdown margins f o r

f u e l s A, B, and C are 3.7, 5.2, and 3 . q 6k/k, respectively.

These mar-

gins are equivalent t o reductions i n c r i t i c a l temperatures of 580, 530, and 550"F, respectively.

I f the 10-Mw equilibrium xenon poisoning were

twice the values shown i n Table 9.1, the m i n i m u m shutdown margins would correspond t o c r i t i c a l temperature reductions of 470, 440, and 450°F, r e spectively.

Thus c r i t e r i o n 6 i s e a s i l y s a t i s f i e d by f u l l y i n s e r t i n g the

rods before the pump i s s t a r t e d .

9.4

Typical Sequence of Operations

A t the beginning of an operating cycle, when the core i s being f i l l e d

with f u e l , the rods are positioned s o t h a t t h e r e a c t o r should be s l i g h t l y s u b c r i t i c a l when full.

The rod poisoning which i s necessary a t t h i s time

depends on the t o t a l shim requirements and the current e f f e c t s of samarium and burnup.

(Xenon and other f a c t o r s causing r e a c t i v i t y l o s s during op-

e r a t i o n w i l l not normally be present during a f i l l . )

Assuming t h a t the

shim requirements are a s shown i n Table 9.1 and t h a t the f u e l has peak samarium, no xenon, and no burnup during a f i l l , the rods would be positioned t o poison 2.8,

3.3, or 2.â&#x201A;Ź$ 6k/k with f'uels A, B, and C, respec-

4.3, or 2.9$ 8k/k i n reserve, t o be i n s e r t e d i f abnormal conditions should require a rod scram. I f t h e shim requirements are g r e a t e r than shown i n Table 9.1, t h e reserve i s accordingly l e s s . During the f i l l a l l three rods will be a t equal withdrawal. tively.

This would leave 2.8,


99 L

This i s t o provide the best protection i f only two of the three rods drop

when c a l l e d for.

Before the pump i s s t a r t e d , a l l three rods a r e f b l l y i n s e r t e d t o give f K L l protection against a cold slug making the r e a c t o r c r i t i c a l .

(The

rod p o s i t i o n indicators can a l s o be c a l i b r a t e d a t t h i s time.) After the p u p i s running, the shim rods a r e withdrawn t o a predetermined point, and then the r e a c t o r i s made c r i t i c a l by slowly withdrawing the regulating rod.

The amount of shim rod withdrawal i s chosen t o

make t h e c r i t i c a l regulating rod position well below the position of t h e shim rods but within the range of adequate s e n s i t i v i t y .

(The regulating

rod and shim rod t i p s are kept separated t o reduce the n o n l i n e a r i t i e s i n worth which r e s u l t from the regulating rod t i p moving i n t o and out of the shadow of the shim rods. ) After the power i s r a i s e d and more rod poison must be withdrawn, the shim rods a r e withdrawn together, i f they are not already f i l l y withdrawn, u n t i l they reach the maximum desirable withdrawal.

The regulating rod i s

then allowed t o work i t s way up, under control of the servo system, t o shim for f i r t h e r r e a c t i v i t y changes. Table 9.2 summarizes rod positions and poisoning during the t y p i c a l operating cycle with f i e 1 C i n the reactor. Table 9.2.

Rod Positions During Typical Operation, Fuel C

Condition

Rod Position (in. withdrawn) Regulating

F i l l i n g core (1% subc r i t ic a l )

Shims

Rod Poisoning (46 6k/k) Regulating

Shims

Total

28.5

28.5

0.9

1.9

2.8

0

0

1.9

3.8

5.7

Going c r i t i c a l , no Xe, peak Sm, no burnup

28.4

54

1.2

0.1

1.3

A t 10 Mw, no Xe, peak Sm, no burnup

29.4

54

1.1

0.1

1.2

A t 10 Mw, equilibrium Xe and Sm, no burnup

39.3

54

0.6

0.1

0.7

A t 10 Mw, equilibrium Xe and Sm, 120 g of U235 burnup

39.9

54

0.5

0.1

0.6

S t a r t i n g f i e 1 pump


100

lo. NEUTRON SOURCES AND SUBCRITICAL OPERATION 10.1

Introduction

When t h e r e a c t o r i s s u b c r i t i c a l , t h e f i s s i o n r a t e and the neutron flux w i l l depend on t h e neutron source due t o various r e a c t i o n s and the

m u l t i p l i c a t i o n of these source neutrons by f i s s i o n s i n t h e core.

The f u e l

i t s e l f i s an appreciable source of neutrons due t o (CX,n) reactions of alpha p a r t i c l e s from t h e uranium w i t h t h e f l u o r i n e and beryllium of t h e There i s a l s o a contribution from spontaneous f i s s i o n .

salt.

Thus t h e

core w i l l always contain a source whenever t h e f u e l i s present.

After

high-power operation t h e i n t e r n a l source w i l l be much stronger, because of photoneutrons produced by t h e f r e s h f i s s i o n products.

For the i n i t i a l

s t a r t u p , an e x t e r n a l source can be used t o increase the flux a t t h e chambers used t o monitor the approaxh t o c r i t i c a l i t y . 10.2

10.2.1

I n t e r n a l Neutron Sources

Spontaneous Fission

An absolutely r e l i a b l e source of neutrons i s t h e spontaneous f i s s i o n

of t h e uranium i n t h e f u e l .

Uranium-238 i s t h e most active, i n t h i s r e -

gard, of t h e uranium isotopes i n t h e IISRE f’uel.

If f u e l C, containing

0.8 mole $ uranium of 35% enrichment, i s used, the spontaneous f i s s i o n source w i l l be about 103/neutrons see.

I f highly (-93%) enriched uranium

i s used, t h e spontaneous f i s s i o n source will be very s m a l l .

Table 10.1

l i s t s t h e s p e c i f i c emission r a t e of neutrons due t o spontaneous f i s s i o n

of each isotope.32

Also shown are the amounts of uranium i n t h e core

(clean, c r i t i c a l loading) and t h e r e s u l t i n g t o t a l spontaneous f i s s i o n neutron sources f o r the 10.2.2

mels

whose compositions a r e given i n Table 3.1.

Neutrons from (CX,n) Reactions i n the Fuel

Alpha p a r t i c l e s from uranium decay i n t e r a c t with some of t h e c o n s t i t uents of t h e f’uel s a l t t o produce a strong i n t e r n a l source of neutrons.33 All of t h e uranium isotopes a r e alpha-radioactive and any of t h e uranium

alphas can i n t e r a c t with t h e f l u o r i n e and t h e beryllium i n t h e f’uel s a l t t o produce neutrons.

The more energetic of t h e alpha p a r t i c l e s can a l s o


101 L.

Table 10.1.

Isotope

u234 ~ 2 3 5 u236 ~ 2 3 8

Neutron Source from Spontaneous Fissions i n MSRE Core"

Specific Emission Rate [n/(kg*sec)l

6.1

0.51 5.1 15.2

Fuel A

(kg)

Source (n/sec>

0.3

2

27.0 0.3 1.5

14

MC b

2 22

-

Fuel B Mc (kg)

0.2 16.5 0.2 0.9

Source (n/sec>

M~' (kg)

1

0.2

1

8

26.4 0.2 47.5

13

1

13 -

40 ""Effective"

fie1 C Source (dsec)

1

722 -

737

23

core, containing 25 f t 3 of f u e l s a l t .

bxass i n core a t clean, c r i t i c a l concentration.

produce neutrons by i n t e r a c t i o n with lithium, but the y i e l d i s negligible i n comparison with t h a t from fluorine and beryllium.

Table 10.2 summa-

r i z e s the s p e c i f i c y i e l d s and gives the neutron source i n the core for the clean, c r i t i c a l loading with d i f f e r e n t f u e l s . t r o n s are caused by alpha p a r t i c l e s from U234. proportional t o the amount of U2

10.2.3

About 97% of the neu-

Thus the (a,n> source i s

present.

Photoneutrons from the Fuel

Gamma rays with photon energies above 1.67 MeV can i n t e r a c t with the beryllium i n t h e f u e l s a l t t o produce photoneutrons.

This source i s un-

important before operation, when only the uranium decay gammas are present, but a f t e r operation a t s i g n i f i c a n t powers, the f i s s i o n product decay gammas produce a strong, long-lived neutron source. Figures 10.1 and 10.2 show the r a t e of photoneutron production i n the MSRE core a f t e r operation a t 10 Mw f o r periods of 1 day, 1 week, and 1 month.

The source i s proportional t o the power, and the source a f t e r

periods of nonuniform power operation can be estimated by superposition W

of sources produced by equivalent blocks of steady-power operation.


Table 10.2.

Alpha Production

Neutron Sources from (a,n) Reactions i n MSRE Core

a

Fuel B

Fuel A

Fuel C

Isotope

EOl

u234

4.77

1.64 X 10"

7.0

3.3 x

lo5

7.8

2.3 x

lo5

7.6

2.8 x

4.72

0.64 X 10l1

6.6

1.2 x

lo5

7.3

0.8 x

io5

7.1

1.0 x 105

4.58

0.79 x 107

5.4

1.1 x

io3

6.0

0.8 x 103

5.9

1.2 x 103

4.47

0.24 x 1 0'

4.7

0.3 x

io3

5.3

0.2 x 103

5.2

0.3 x

4.40

6.56 x 107

4.3

7.5 x

4.8

5.2 x 103

4.7

8.1 x 103

4.20

0.32 X 1 0 '

3.2

0.3 x

io3 io3

3.7

0.2 x

io3

3.6

0.3 x

io3

4.50

1.72 X

4.9

2.4 x 103

5.5

1.7 x

2.1 x

0.63

4.5

0.8

x 103

5.1

0.6 x

io3 lo3

5.4

4.45

lo9 x lo9

5.0

0.7 x

io3 io3

4.19

0.95 X

lo6

3.1

4

3.6

3

3.5

1.6 X

4.15

0.28 X lo6

2.9

1

3.4

1

3.3

0.4 X

~ 2 3 5

u236

~ 2 3 8

Yield

Source

4.6 x

io5

Yield

Source

3.2 x

Yield

io5

a"'Effective'' core, containing 25 f t 3of f'uel s a l t of clean, c r i t i c a l concentration.

Source

io5

io3

lo2 lo2

3.9 x 105

G

h,


103

UNCLASSIFIED

I m

10:

a

10

4

8

12

16

24

28

TIME AFTER SHUTDOWN (hr)

Fig. 10.1. a t 10 Mw.

Photoneutron Source i n MSRE Core After Various Perio ds


UNCLASSIFIED O R N L DWG. 6 5 8 1 7 2

10

100

TIME AFTER SHUTDOWN (days )

Fig. 10.2. Photoneutron Source in MSRE Core A f t e r Various P e r i o d s at 10 Mw.

J


105 U

The gamma-ray source used i n the calculations i s group I V of Blomeke and Todd,34 which includes a l l gamma rays above 1.70 Mev.

The probability

of' one of these gamma rays producing a photoneutron was approximated by the r a t i o of the Beg(y,n) cross section t o the t o t a l cross section for gamma-ray i n t e r a c t i o n i n a homogeneous mixture w i t h the composition of the core.

A Be9(y,n) microscopic cross section of 0.5 mb was used, and

the t o t a l cross section was evaluated a t 2 MeV.

These assumptions lead

t o a conservatively low estimate of neutron source strength.

Provisions f o r External Neutron Source and Neutron Detectors

10.3

10.3.1

External Source

For reasons which w i l l be described l a t e r , it i s desirable t o supplement the inherent, i n t e r n a l source with a removable, extraneous source. Therefore, a thimble i s provided inside the thermal s h i e l d on the opposite side of the reactor from the nuclear instrument shaft. 1-1/2-in.

The thimble i s a

sched 40 pipe of type 304 s t a i n l e s s s t e e l , extending v e r t i c a l l y

down t o about 2 f t below the midplane of the core.

It i s mounted a s close

a s possible t o the inner surface of the s h i e l d for maximum effectiveness. 10.3.2

Neutron Detectors

A nuclear instrument s h a f t i s provided f o r a l l t h e permanently i n -

s t a l l e d neutron detecting instruments.

This i s a w a t e r - f i l l e d 3-ft-diam

tube which slopes down t o the inner surface of the thermal s h i e l d with separate, inner tubes f o r the various chambers.

The s h a f t contains t e n

tubes, of which seven w i l l be used f o r routine power operation (two widerange servo-operated f i s s i o n chambers, two compensated ion chambers, and three safety chambers).

This leaves three tubes i n which a u x i l i a r y or

special-purpose chambers could be i n s t a l l e d .

Any chamber i n the i n s t r u -

ment shaft i s i n a sloping position, with the upper end f a r t h e r from the core (and hence, i n a lower f l u x ) than the lower end.

As a result, a

long chamber i n the instrument shaft i s exposed t o a lower average f l u x than a shorter one.


106 Two v e r t i c a l thimbles, similar t o the source thimble but made of 2-

in. sched 10 pipe, are i n s t a l l e d i n the thermal s h i e l d t o accommodate temporary neutron detectors.

The two detector thimbles are located 120 and

150" from the source thimble, one on e i t h e r side of the permanent nuclear

instrument shaft.

The advantage of these v e r t i c a l thimbles i s t h a t they

place the e n t i r e length of a chamber close t o the inner surface of the thermal shield, where it i s exposed t o a higher average neutron flux.

10.4 Neutron Flux i n S u b c r i t i c a l Reactor Changes i n the r e a c t i v i t y of the s u b c r i t i c a l reactor can be monitored i f the f i s s i o n s caused by the source neutrons produce a measurable neutron

f l u x a t the detectors mounted outside of the r e a c t o r vessel. a t a chamber depends on the source

- its

The flux

strength, the energy of the neu-

t r o n s , and, i n t h e case of an e x t e r n a l source, i t s l o c a t i o n both with re-

spect t o t h e core and w i t h respect t o the chamber.

The flux a l s o depends

on the amount of multiplication by f i s s i o n s and the shape of the neutron f l u x d i s t r i b u t i o n i n the core, which i s determined by the l o c a t i o n of the source and the value of k i n the core. The count r a t e produced by a given chamber depends on t h e chamber s e n s i t i v i t y a s well a s on the neutron flux.

O f interest i n establishing

the neutron-source requirements are the s e n s i t i v i t i e s of the chambers which w i l l be used t o observe the behavior of the r e a c t o r under s u b c r i t i c a l conditions.

The f i s s i o n chambers, which w i l l be used t o monitor

routine approaches t o c r i t i c a l ( a s well a s power operation) are 6 in. long and have a counting efficiency of 0.026 count per neutron/cm2.

In

addition, BF3 chambers are available; they w i l l be used during the i n i t i a l c r i t i c a l experiments (and possibly t o monitor routine reactor f i l l s ) . These have a sensitive length of 26-1/4 i n . and a counting efficiency of

14 counts per neutron/cm2. The steady-state flux i n the core and thermal s h i e l d with a source i n the thermal s h i e l d source tube was calculated35 f o r two core conditions:

the f i r s t , with no f i e 1 i n the core; the second, with the core

f i l l e d with f i e 1 s a l t containing 0.76 of the clean, c r i t i c a l uranium concentration.

I n the l a t t e r case keff was calculated t o be 0.91.

Contri-


107 L

butions from the i n t e r n a l neutron source were neglected.

The calculated

r a t i o s of thermal. neutron fluxes a t the chambers t o the source strength (neutrons/cm2 per source neutron) are given i n Table 10.3.

As a f i r s t

approximation, the r a t i o s of f l u x or count r a t e t o source strength a t above 0.9 can be assumed t o change i n proportion t o the inverse of ke f f (1 - k e f f ) ' When the multiplication i s high, t h a t i s , when (1- k e f f ) i s quite small, most of the neutrons are produced by f i s s i o n s i n the core, with a s p a t i a l source d i s t r i b u t i o n close t o the f i s s i o n d i s t r i b u t i o n i n a c r i t i c a l reactor.

The r e l a t i o n between the core power, or f i s s i o n r a t e , i n

the c r i t i c a l core and the f l u x i n the thermal shield was calculated i n the course of the thermal s h i e l d design, using DSN, a multigroup, t r a n s port-theory code.

For the case of a thick, water-filled thermal shield,

when the core power i s 10 Mw, the predicted thermal neutron f l u x reaches a peak, 1 i n . inside the water, of 1 . 2 X 10l2 neutrons r a t i o of peak f l u x t o power i s 1 . 2 X

or 1.5 X 1T6 neutrons

see"'

lo5

see".

neutrons emm2 see-'

The

per watt,

per neutron/sec produced i n the core.

It was estimated t h a t a 6-in.-long

chamber a t maximum i n s e r t i o n i n t h e

instrument s h a f t would be exposed t o an average f l u x of roughly 1 X lT7

Table 10.3.

Location

Fluxes ProAuced a t Neutron Chambers by an External Source

Chamber Lellgth . - . (in. )

Average Flux/Source Strength { [n/<cm2.sec>I/(n/sec>) No Fuel

keff = 0.91

x 1T6

x 10-6

120' thimble

An;y

13

18

150" thimble

An;y

4

9

6

2

7

0.6

1.7

Instrument s h a f t (-180째)

26


108 neutrons eme2 see‘’

p e r neutronjsec protiuced.

the corresponding value i s about 3 X

For a 26-in. -long chamber, 1T8. A chamber i n one of t h e ver-

t i c a l tubes just i n s i d e t h e inner w a l l of t h e thermal s h i e l d would be exposed t o an average f l u x of about 3 x 1 T 7 neutrons

see-’

p e r neu-

tron/sec produced i n t h e core. With both an e x t e r n a l and an i n t e r n a l source present, t h e f l u x a t a p a r t i c u l a r l o c a t i o n i n t h e thermal s h i e l d can be roughly approximated by an expression of the form @=bS ex

+

fexSex

+

finsin 1 - k

1 - k

(10.1)

The q u a n t i t i e s Sex and Sin are t h e strengths of t h e e x t e r n a l and i n t e r n a l sources, respectively.

The f a c t o r s fex and fin i n d i c a t e t h e f r a c t i o n of

neutrons, produced i n t h e core from t h e corresponding source neutrons, w h i c h reach t h e l o c a t i o n i n question.

Since these f a c t o r s depend on t h e

The f a c t o r b i s proporf l u x shape, the values vary somewhat with k eff t i o n a l t o t h e f r a c t i o n of the neutrons from t h e e x t e r n a l source which reach t h e thermal s h i e l d without f i r s t entering t h e core, t h a t i s , by s c a t t e r i n g around t h e core.

This f a c t o r i s e s s e n t i a l l y independent of

keff* The c a l c u l a t i o n of t h e f l u x d i s t r i b u t i o n with an e x t e r n a l source and i s e s s e n t i a l l y zero f o r t h i s conex &so, when t h e r e i s no f’uel i n t h e reactor, Sin = 0. Thus, f o r

no f i e 1 i n the core indicated t h a t f dition.

t h i s condition Eq.

(10.1) reduces t o @ = b S

ex

.

(10.2)

This expression permits d i r e c t evaluation of b for various l o c a t i o n s f r o a

t h e above calculation. When t h e r e a c t o r i s near c r i t i c a l , t h e v a r i a t i o n i n f

and fin with ex k can be neglected t o obtain approximate values f o r these q u a n t i t i e s . The value of fin f o r various l o c a t i o n s was obtained from t h e c r i t i c a l = flux d i s t r i b u t i o n , and fex was obtained from t h e d i s t r i b u t i o n a t k eff 0.91.

The values obtained f o r t h e f a c t o r s a t t h e various proposed neutron chamber l o c a t i o n s a r e l i s t e d i n Table 10.4.

These f a c t o r s can be used t o

J


109 Table 10.4.

L

Flux/Source Factors i n MSRE

Chamber Length (in. )

Location

b (em-* )

x

1 r 6

fex

x 10-7

(

x

fin ) 10-7

120" thimble

h Y

13

5

3

150" thimble

h Y

4

5

3

Instrument s h a f t

6 26

estimate the f l u x a t the chambers f o r d i f f e r e n t source conditions e i t h e r 2 0.95). when the r e a c t o r i s empty or when it i s near c r i t i c a l ( k eff

10.5

Requirements f o r Source35

A neutron source must perform several functions i n the operation of

a reactor, and each function places d i f f e r e n t requirements on the source. 10.5.1

Reactor Safety

The most important function of a neutron source i n the r e a c t o r has t o do with reactor safety.

If an adequate source i s present, t h e s t a t i s -

t i c a l f l u c t u a t i o n s i n t h e l e v e l of the f i s s i o n chain reaction will be negligibly small and the l e v e l will r i s e smoothly a s the r e a c t i v i t y i s increased t o make the r e a c t o r c r i t i c a l .

Furthermore, when the r e a c t o r

becomes s u p e r c r i t i c a l , the l e v e l w i l l be high enough t h a t temperature feedback becomes e f f e c t i v e , and s a f e t y actions can be taken before enough excess r e a c t i v i t y can be added t o cause a dangerous power excursion. A s shown i n Sees 12.2 and 12.7, the strength of the inherent (a-n)

source i s enough t o s a t i s f y t h e safety requirements f o r a source.

This

i s convenient because t h e (a-n) source will always be present whenever

there i s any chance of c r i t i c a l i t y . W

This assurance of an adequate i n -

t e r n a l source eliminates the usual safety requirement t h a t an extraneous


110 source be i n s t a l l e d and i t s presence proved by s i g n i f i c a n t count r a t e s

J

on neutron chambers before a s t a r t u p can begin.

10.5.2

Preliminary Experiments

An extraneous source and s e n s i t i v e neutron chambers a r e usef'ul i n t h e MSRE primarily because they comprise a means of monitoring t h e react i v i t y while t h e r e a c t o r i s s u b c r i t i c a l , or of following t h e nuclear power behavior a t l e v e l s below the range of t h e i o n i z a t i o n chambers which provide information a t high power.

For t h e i n i t i a l c r i t i c a l experiment, it i s desirable t o have a sign i f i c a n t neutron count r a t e before any f i e 1 i s added t o t h e reactor.

This

guarantees t h a t t h e condition of t h e r e a c t o r can be monitored a t a l l times Table 10.5 l i s t s t h e e x t e r n a l source strength r e -

during the experiment.

quired t o produce a count r a t e of 2 counts/sec on t h e various chambers with no fuel i n t h e reactor.

10.5.3

Routine Operation

After t h e preliminary experiments, only the chambers i n t h e nuclear instrument s h a f t w i l l be available t o monitor t h e r e a c t o r f l u . The f'unction of t h e neutron source i n routine operation i s t o permit

monitoring t h e f l u during r e a c t o r s t a r t u p s so t h a t t h e operation i s orderly.

A normal s t a r t u p of t h e MSRE involves two separate s t e p s :

(1) f i l l i n g t h e r e a c t o r with f i e 1 s a l t and ( 2 ) withdrawing t h e control rods

Table 10.5.

Location

External Source Required f o r 2 Counts/sec with No Fdel i n Reactor

Chamber m e

Counting Efficiency { ( count s/sec ) / [ n/ ( em2 sec ) I}

Source Strength

(,Ise

120" thimble

BF3

14

1 x 104

150" thimble

BF3

14

4 x 104

Instrument s h a f t

Fi s s i on BF3

0.026

14

4 x 107 2 x lo5


111 t o make the reactor c r i t i c a l .

Although the f i r s t operation w i l l normally

leave the reactor s u b c r i t i c a l , it i s desirable t o monitor the f l u x during t h i s s t e p t o ensure t h a t no abnormal conditions e x i s t .

This requires t h a t

a s i g n i f i c a n t count r a t e e x i s t before the f i l l i s s t a r t e d , and t h e source requirements a r e the same a s f o r the i n i t i a l c r i t i c a l experiment.

The

second phase of the s t a r t u p involves changing the multiplication constant from about 0.95 (the shutdown margin a t t a i n a b l e with the control rods) t o 1.0.

This operation should, i f possible, be monitored by instruments

which a r e s t i l l u s e f u l a f t e r c r i t i c a l i t y i s attained; i n the MSRE, these instruments are the servo-operated f i s s i o n chambers.

A source of 8 X lo6

neutrons/sec i s required t o produce a count r a t e of 2 counts/sec on a f u l l y i n s e r t e d f i s s i o n chamber when k = 0.95. 10.6

Choice of External Source

The source requirements of the MSHE can be met i n a number of ways. One of the most desirable sources from the standpoint of cost and ease

of handling i s the Sb-Be type, and such a source t h a t meets the calculated requirements can be e a s i l y obtained. half-life,

However, Sb124 has o n l y a 60-day

s o the i n i t i a l i n t e n s i t y of such a source must be s u b s t a n t i a l l y

g r e a t e r i f frequent replacement i s t o be avoided. ments can a l s o be met with a Fu-Be source.

The calculated require-

Such a source would be more

expensive, and there i s a containment problem because of the plutonium content.

On the other hand, the long h a l f - l i f e of plutonium would elimi-

nate the problems associated with source decay. Because the flux calculations a r e subject t o s u b s t a n t i a l e r r o r s , the f i n a l s p e c i f i c a t i o n of the source w i l l be based on measurements t o be made shortly a f t e r the r e a c t o r vessel containing the core graphite i s i n s t a l l e d inside the thermal shield.

(The construction and s t a r t u p schedule

i s such t h a t there i s time f o r procurement of a source a f t e r these meas-

urements and before the source i s needed f o r nuclear operation.)


11. KINETICS OF NORMAL OPERATION Studies of t h e k i n e t i c behavior of t h e r e a c t o r f a l l i n t o two categories.

One deals with t h e behavior i n normal operation, when t h e re-

a c t o r i s subjected only t o moderate changes i n load demand and t o small, random disturbances o r "noise." absolute and r e l a t i v e .

The concern here i s with s t a b i l i t y

-

(Absolute s t a b i l i t y means t h a t a disturbance

does not l e a d t o divergent o s c i l l a t i o n s ; r e l a t i v e s t a b i l i t y r e f e r s t o t h e magnitude and number of o s c i l l a t i o n s which occur before a t r a n s i e n t d i e s out.)

The o t h e r category of k i n e t i c s s t u d i e s t r e a t s t h e response

of t h e system t o l a r g e o r r a p i d changes i n r e a c t i v i t y such as might occur i n abnormal i n c i d e n t s . t h i s chapter.

Studies of t h e f i r s t kind a r e covered i n

The next chapter deals with s a f e t y s t u d i e s , o r k i n e t i c s

under abnormal conditions.

11.1 Very Low Power When t h e MSRE i s operated a t very l o w power, with t h e temperature held constant by t h e e x t e r n a l h e a t e r s , t h e f i s s i o n chain r e a c t i o n i s c o n t r o l l e d by t h e c o n t r o l rods alone.

The k i n e t i c behavior of t h e f i s s i o n

r a t e under t h i s condition i s determined by t h e prompt neutron l i f e t i m e and t h e e f f e c t i v e delayed neutron f r a c t i o n s and i s not unusual i n any way.

The neutron l i f e t i m e i s between 2 and 4 X

t h e f u e l s a l t composition.

sec, depending on

(For comparison, t h e l i f e t i m e i n most

water-moderated r e a c t o r s i s between 0.2 and 0.6 X

sec, and l a r g e ,

graphite-moderated r e a c t o r s have l i f e t i m e s of about 10 x l r 4 sec. ) Although t h e e f f e c t i v e delayed neutron f r a c t i o n s a r e considerably lower than i n a f i x e d - f u e l r e a c t o r using U235, t h i s p r e s e n t s no important problem of c o n t r o l .

11.2

Self-Regulation a t Higher Power

When t h e r e a c t o r power i s high enough t o have an appreciable e f f e c t on f u e l and g r a p h i t e temperatures, t h e power becomes s e l f - r e g u l a t i n g . That i s , because of t h e negative temperature c o e f f i c i e n t s of r e a c t i v i t y ,


v

the nuclear power tends to follow the heat extraction, or load, without 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 is 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

OF of temperature difference. The total heat capacity of the graphite is 3.7 Mw-sec per OF of temperature change.

The ratio of heat transfer

to graphite heat capacity is only about O.O05"F/sec per OF.

This means

that with a temperature difference of 100째F between the fuel and the graphite, the heat transferred is only enough to raise the graphite temperature at 0.5 OF/sec. The heat capacity of the fuel in the core is 1.7 Mw-sec/OF, 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, f o r 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 temperatures makes it necessary to treat them separately in any analysis of the MSRE kinetics. 11.2.2

TransDort 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 heatremoval system, which includes the radiator, the coolant salt loop, the v

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


114 The coolant loop contains 44 ft3 of salt, with a total heat capacity of 2.9 Mw-sec/'F. cuit time is 23 sec.

At an 850-gpm circulation rate, the loop cir-

There is 67' ft3 of fuel salt in circulation, having

a total heat capacity of 4.6 Mw-sec/OF.

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 stak,ilityof 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-&'relations, temperature coefficients of reactivity for the fuel and graphite, a n d the reactivity-power relations. Studies of operation at power without external control of the reactivity were carried the reactor.

0-dwith

two different analog representations of

In the first model, the core was represented as a single

major region comprised of two subregions of fuel a n d one subregion of graphite. Figure 11.1 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 generation, fuel and graphite temperatures, and the nuclear importance in the actual core. Temperatures in each of the nine regions were weighted to obtain the averages which determine the net effect on reactivity. Figures 11.3 and l l . 4 show the response of the system with the nineregion 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-DWG 63-7318

/--I--/\=I

GRAPHITE

G

F U E Y GTRANSFER HEAT RAPHITE

-,.\

‘ A

PERFECTLY MIXED SUBREGIONS

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

Nuclear power is

UNCLASSIFIED ORNL-DWG 63-7319

t

++1 + 4

7

9

3

6

8

2

5

+

Fig. 11.2. Schematic Breakdown of 9-Region Analog Model.


116

J

UNCLASSIFIED ORNL DWG. 63-8228

I

TIME ( s e c )

Fig. 11.3. Response of 9-Region Model of MSRE to an Increase in Power Demand.


UNCLASSIFIED

h

P4 . v

TIME ( s e e )

Fig. 11.4. Response of 9-Region Model of MSRF: to a Decrease in Power Demand.


118 t h e simulated a i r flow through t h e r a d i a t o r , t h e u l t i m a t e heat s i n k i n t h e r e a c t o r system.

For t h e power i n c r e a s e i n Fig. 11.3, t h e simulated

a i r flow w a s r a i s e d from 3$ t o loo$ of t h e design value a t O.S$/sec.

As

shown, t h e r e w a s a moderate power overshoot and about 15 min w a s reqL.ired f o r t h e power and t h e f u e l temperatures t o approach s t e a d y - s t a t e values. The response t o a decrease i n a i r flow t o 8% of t h e design value a t 35/sec i s shown i n Fig. 11.4.

I n t h i s simulator t e s t , t h e temperature of t h e

graphite i n an important region of t h e core (region 3 i n Fig. 11.2) was recorded. Besides showing t h e t r a n s i e n t response of t h e r e a c t o r system, Fig.

11.4 i l l u s t r a t e s t h e s h i f t i n s t e a d y - s t a t e temperatures a t d i f f e r e n t powers which r e s u l t s i f t h e r e i s no adjustment of t h e c o n t r o l rods.

This

s h i f t comes about because t h e heat generated i n t h e g r a p h i t e must be t r a n s f e r r e d t o t h e f u e l f o r removal from t h e core, causing t h e f u e l and g r a p h i t e temperatures t o di-;erge.

Since t h e temperature coei'ficients of

r e a c t i v i t y of both t h e f u e l and t h e g r a p h i t e a r e negative, t h e tendency of t h e g r a p h i t e temperature t o r i s e a t higher powers f o r c e s t h e f u e l t e m p e r a t u r e t o decrease t o keep t h e n e t r e a c t i v i t y change zero. Figures 11.5 and 11.6 show t h e response of t h e simulated nuclear power i n t h e one-regior core node1 t o changes i n power demand s i m i l a r t o those used t o produce Figs. 11.3 and 11.4.

It nay be noted t h a t t h e

simulation involving t h e s i x p l e r core model shows a s i g n i f i c a n t l y g r e a t e r tendency toward s u s t a i n e d power o s c i l l a t i o n a t low powers. t h e d i f f e r e n t r e s u l t s i s not c l e a r .

The reason f o r

The r e a c t o r system models d i f f e r e d i n

s e v e r a l r e s p e c t s b e s i d e t h e core, and, because t h e c a l c u l a t i o n s were done

a t d i f f e r e n t s t a g e s of t h e r e a c t o r design, they used somewhat d i f f e r e n t values f o r t h e c u r r e n t r e a c t o r design data. Despite t h e d i f f e r e n c e s i n t h e simulator r e s u l t s , an important conc l u s i o n can be drawn from them.

That i s :

although t h e negative tempera-

t u r e c o e f f i c i e n t s of r e a c t i v i t y make t h e r e a c t o r capable of stable selfr e g u l a t i o n , an e x t e r n a l c o n t r o l system is d e s i r a b l e because t h e r e a c t o r

i s l o o s e l y coupled and sluggish, p a r t i c u l a r l y a t low power.

(Neither of

t h e models included c o m p r e s s i b i l i t y e f f e c t s due t o e n t r a i n e d gas, b u t i n c l u s i o n of t h e s e e f f e c t s would probably not change t h e conclusion. )

rl


.

Power

Fig. 11.5. Demand.

Response

of

l-Region

Model

of MSRE to

.

an Increase

in


TIME (SW)

Fig. 11.6. Power Demand.

Response of l-Region

Model of MSRE to a Decrease in

. L

c

(

.


121

11.3 Operation with Servo Control In order to eliminate possible oscillations and to obtain the desired 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 without 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 external heaters may also be used at times. The design and performance of the servo control system are described in detail in Part 11. Nuclear and Process Instrumentation.

V


I22

12. KINETICS I N ABNORMAL SITUATIONS - SAEETY CALCULATIONS 12.1

Introduction

There a r e s e v e r a l coriceivable iiicidents which could r e s u l t i n r e a c t i v i t y i n c r e a s e s l a r g e r o r f a s t e r than those encountered i n normal operation of t n e r e s c t o r .

Each of t h e s e i n c i d e n t s must be examined from

t h e standpoint of r e a c t o r s a f e t y , t o determine whether t h e r e i s a possib i l i t y of damage t o t h e r e a c t o r o r hazard t o personnel. concern i s s a f e t y , a conservative approach must be used.

Because t h e If t h e a n a l y s i s

of an i n c i d e n t i n d i c a t e s t h a t t h e consequences may be i n t o l e r a b l e , t h e n p r o t e c t i o n must be provided t o guard a g a i n s t damage and ensure t h e s a f e t y

of r e a c t o r operation.

(Control and s a f e t y systems a r e described i n P a r t

11. Xuclear and Process I n s t r u q e n t a t i o n . )

12.2

General Considerations

The most l i k e l y form of daaage from excessive r e a c t - v i t y a1 l i t i o n s i n t h e bERE i s breach of t h e c o n t r o l rod thimbles i n t h e core by a comb i n e t i o n of high f u e l temperature and t h e high pressure produced i n t h e core by t h e r a p i d thermal expansion of t h e f u e l . The s e v e r i t y of t h e power, texperature,

and pressure t r a n s i e n t s

a s s o c i a t e d with a given reactivitL- i n c i d e n t depends upon t h e amount of excess r e a c t i v i t y involved, t h e r a t e a t which it can be added, t h e i n i -

t i a l power l e v e l , t h e e f f e c t i v e n e s s of t h e inherent shutdown mechanisms, and t h e e f f i c a c y of t h e r e a c t o r s a f e t y system.

All of t h e s e f a c t o r s de-

pend t o some e x t e n t on t h e f u e l composition, because t h i s determines t h e magnitude of t h e various r e a c t i v i t y c o e f f i c i e n t s and t h e c o n t r o l rod worth ( s e e Tables 3.5 and 4.1). I n general, equivalent physical s i t u a t i o n s l e a d t o l a r g e r amounts of r e a c t i v i t y and g r e a t e r r a t e s of a d d i t i o n with f u e l B t h a n with e i t h e r A o r C.

This i s a consequence of t h e l a r g e r values of t h e r e a c t i v i t y

c o e f f i c i e n t s and c o n t r o l rod worth, t h e absence of t h e poisoning e f f e c t of thorium o r U238, and t h e lower inventory of U235 i n t h e core.


123

c

L

The power and temperature transients associated with a given reactivity 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 temperatures becomes effective.

Thus, even slow reactivity ramps can introduce

substantial excess reactivity if the reactor power is very low when keff = 1. The power level in the MSRE when the reactor is just critical depends 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 lo5 neutrons/sec, which is the rate of production in the core by (an) 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

lo7

neutrons/sec to the

core and, after the reactor has operated at high power, fission product gamma rays will generate up to lolo photoneutrons/sec in the core.

The

ratio of the nuclear power at criticality to the source strength varies only +lo% for reactivity addition rates between 0.05 and 0.1% 6k/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 ( a 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 reactivity; but this temperature rises slowly during a rapid power transient, 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 v

fuel to the graphite.

Since fuel B has the largest negative temperature


u 4

c o e f f i c i e n t of r e a c t i v i t y , a given r e a c t i v i t y i n c i d e n t produces smaller excursions with t h i s f u e l t h a n with e i t h e r of t h e o t h e r two. The MSRE s a f e t y system causes t h e t h r e e c o n t r o l rods t o drop by g r a v i t y when t h e nuclear power reaches 15 Mw o r when t h e r e a c t o r o u t l e t temperature reaches 1300'F.

I n t h e a n a l y s i s of r e a c t i v i t y i n c i d e n t s ,

conservative values were assumed f o r delay time and rod a c c e l e r a t i o n , namely, 0.1 sec and 5 f t / s e c 2 , r e s p e c t i v e l y .

It w a s a l s o assumed t h a t

one of t h e t h r e e rods f a i l e d t o drop when c a l l e d f o r .

12.3

I n c i d e n t s Leading t o R e a c t i v i t y Addition

I n t h e MSRE t h e conceivable i n c i d e n t s which could r e s u l t i n s i g n i f i c a n t a d d i t i o n s of r e a c t i v i t y include t h e following: 1. uncontrolled rod withdrawal, 2.

cold-slug accident,

3.

abnormal concentration of uranium during f u e l a d d i t i o n s ,

4.

displacement of g r a p h i t e by f u e l s a l t ,

5.

premature c r i t i c a l i t y while t h e core i s being f i l l e d ,

6.

f u e l pump power f a i l u r e . Estimates of t h e maximum a d d i t i o n r a t e s and t o t a l r e a c t i v i t y as-

s o c i a t e d with t h e f i r s t four i n c i d e n t s , t o g e t h e r with t h e i n i t i a l cond i t i o n s postulated, a r e summarized i n Table 12.1.

Brief d e s c r i p t i o n s of

t h e s e p o s t u l a t e d i n c i d e n t s and t h e bases f o r t h e r a t e s l i s t e d i n Table

1 2 . 1 a r e as follows. 1. Simultaneous, continuous withdrawal of a l l t h r e e rods i s i n i t i a t e d , s t a r t i n g with t h e r e a c t o r c r i t i c a l a t 1200'F and t h e rod t i p s near t h e p o s i t i o n of maximum d i f f e r e n t i a l worth.

The rod withdrawal

speed i s 0.5 i n . / s e c and t h e maximum d i f f e r e n t i a l worth was obtained from Fig. 4.2. 2.

The cold-slug accident occurs when t h e mean temperature of t h e

core s a l t decreases r a p i d l y because of t h e i n j e c t i o n of f l u i d a t abnormally low temperature.

Such an accident would be c r e a t e d by s t a r t i n g

t h e f u e l c i r c u l a t i n g pump a t a time when f u e l e x t e r n a l t o t h e core has been cooled w e l l below t h a t i n t h e core, i f such a s i t u a t i o n were possible.

A d e t a i l e d study w a s made f o r a case i n which f u e l a t 900째F i s


Table 12.1.

Incident

M a x i m Expected Reactivity Additions i n Postulated Operating Incidents

Description

Maximum Estimated Reactivity Rate [ (5 Gk/k)/secl

Maximum Total Re a c t i v i t y

(3)

I n i t ia 1 Power Level Assumed i n Accident

(d

1

Uncontrolled withdrawal of 3 rods

0.10

3-4"

2

Cold-slug accident"

0.16

1.5

3

Abnomal concentration of uranium during f'uel addition a t pump bowl

0.12

0.37

0.01

4

Graphite s t r i n g e r breakage

0.02

0.22

0.01

?letermined by maximum operating excess r e a c t i v i t y (-4%). bPower a t keff = 1 for minimum neutron source. C

900째F f u e l s a l t pumped i n t o core, which i s i n i t i a l l y c r i t i c a l a t 1200.F.

0. 002b

1000


. 126

pumped a t 1200 gpm i n t o t h e core, which i s i n i t i a l l y c r i t i c a l a t a uniform temperature of 1200'F.

The maximum r e a c t i v i t y a d d i t i o n r a t e i n t h i s

case depends on heat t r a n s f e r between s a l t and g r a p h i t e and t r a n s i e n t nuc l e a r heating before t h e core i s f i l l e d .

The product of t h e s a l t temper-

a t u r e r e a c t i v i t y c o e f f i c i e n t and t h e temperature decrease (300OF) divided by t h e core f l u i d residence time gives t h e rough estimate of r e a c t i v i t y a d d i t i o n r a t e l i s t e d i n Table 12.1.

3.

A maximum of 120 g of highly enriched uranium can be added a s

frozen s a l t a t t h e pump bowl.

An upper l i m i t on t h e t r a n s i e n t caused by

a batch going i n t o c i r c u l a t i o n was found by assuming t h a t t h e f r e s h s a l t f a i l e d t o mix gradually and passed through t h e core a s a "front" of highly concentrated uranium.

The r a t e l i s t e d i n Table 1 2 . 1 i s t h e maximum r a t e

of addition, accounting f o r t h e change i n nuclear importance as t h e conc e n t r a t e d s a l t moves upward through t h e channels.

The t o t a l r e a c t i v i t y

added would i n c r e a s e t o a maximum when t h e uranium i s near t h e c e n t e r of t h e core, then decrease a s t h e f u e l e x i t s .

4.

Replacement of g r a p h i t e by P ~ e lproduces a r e a c t i v i t y increase.

Breakage of a graphite s t r i n g e r i n t o two pieces while f u e l i s c i r c u l a t i n g through t h e core could allow t h e upper s e c t i o n t o f l o a t upward and f u e l s a l t t o move i n t o t h e space about t h e f r a c t u r e , were it not f o r t h e r e -

s t r a i n i n g rods and wires through t h e lower and upper ends of t h e s t r i n g e r s .

An upper l i m i t of t h e p o t e n t i a l r e a c t i v i t y increase due t o l o s s of graphi t e w a s c a l c u l a t e d by assuming t h a t t h e e n t i r e c e n t r a l g r a p h i t e s t r i n g e r

w a s replaced by f u e l s a l t .

The t o t a l r e a c t i v i t y , l i s t e d i n Table 12.1,

i s s m a l l , compared with t h a t i n t h e o t h e r i n c i d e n t s , and r e q u i r e s a time

approximately equal t o t h e core residence time f o r i t s addition. Incidents 5 and 6 a r e not included i n Table 12.1,

s i n c e t h e condi-

t i o n s important t o t h e s e i n c i d e n t s cannot be simply c h a r a c t e r i z e d by a r e a c t i v i t y addition r a t e . I n b r i e f , t h e f i l l i n g accident i s p o s t u l a t e d t o occur as follows: Vhen t h e r e a c t o r i s shut down, t h e f u e l s a l t i s drained from t h e core. During t h e subsequent s t a r t u p , t h e f'uel s a l t and g r a p h i t e a r e preheated and t h e c o n t r o l rods a r e positioned s o t h a t t h e r e a c t o r remains subc r i t i c a l while f i l l i n g ,

C r i t i c a l i t y with t h e core only p a r t i a l l y f i l l e d

*


127

,

w

c m l d result, however, if the core or salt temperature were abnormally low, the fuel salt were abnormally concentrated in uranium, or the control 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 is 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 p u p 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 possible. 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 See 12.4.4.

12.4.1

Reactivity-Power Relations

The time dependence of the nuclear power was described by the wellh o r n relation

(12.1) V


128

Six groups of neutrons were included in the summation. The effective number of precursors (actualljr, the latent power associated with their decay was represented by the equation for fixed-fuel or noncirculating reactors:

r 1.

Pip =--

R

Airi

.

(12.2)

An allowance was made for the effects of circulation on the contribution

of delayed neutrons by using reduced values of @ i (see Chap. 6). The effective multiplication constant, k, was represented by the

sum of several terms: k = 1

+ k

ex

- a (T*- )';T f

f

- a (T*-)':T g g

.

(12.3)

Here kex is the reactivity addeu by all means other than changes in the fuel and graphite temperatures. the last two terms in (12.3):

Temperature effects are represented by

CXf(T:

- T"')f

is the reactivity effect of

changes in fuel temperature, which responds rapidly to power changes, and CX (T* - T"') g g g more s lowly

is the effect of the graphite temperature, which responds

.

The equations given above are intrinsically space-independent approximations 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

.

and CX In order f g to complete the aathematical description of the reactor kinetics, the fuel (2

and graphite temperature distributions must be reduced to a single characteristic 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 fie1 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.


I29

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:

(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

.

- 7)P-

SfTf = (1

i

WC (T P fo

- Tfi) +

h(T

Tf) g

(12.5)

and

(12.6) These approximations were combined with the neutron kinetics equations in an IBM '7090 program called IvIKRGATROYD.~~ In the second model, an approximate calculation was made of the time dependence of the spatial temperature distributions of the fuel and graphite.

These temperature distributions were then weighted with respect to

nuclear importance in order to obtain 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; however, the magnitude of the total power varied in accordance with Eq. (12A ) . The temperature distributions as a function of time were calculated by replacing the macroscopic heat balance Eqs. (12.5) and (12.6) by "local" heat balances on salt and graphite in the individual channels:

aT, U-

az

aT,

+-=at

@f

PfCf

h(Tg

+

-

Tf) 7

&fPfCf

(12.?)

(12.8)


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

The

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

(12.9)

(12.10)

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 m e 1 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

* Tj(t) - Tfi -

s,H [Tj(r,z,t) ,&

R

- Tfi]

H

I(r) s i n 2 T r dr dz

, (12.11)

z

I(r) sin2 H r dr dz

j=f,g. With the further assumption that heat conduction effects are small compared with the heat generation terms, the radial dependence of the temperature rise is proportional to the radial power density, so that (12.11) may be further simplified:


where

(12.13)

The procedure for solution of the kinetics equations thus consists of calculating the temperature profiles from Eqs. (12.7) and (12.8), the nuclear average temperature from Eq. (12.12), and the power-time behavior from Eqs. (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 w i l l 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-

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 dependently of the power-temperature equations.

that the fluid density can be adequately approximated by a linear dependence on the temperature:


132

where

Ff

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:

(12.15)

(12.16)

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

(12.17) The resulting equation f o r the pressure rise is36

PC - poC

= cl[z

+ c2y +

c3:

(1 + C4:)l

(12.18)

In this expression x and y are the dimensionless power and the dimensionless fluid temperature, defined as

x = P/PO Sf

Yf

(12.19)

J

-

Df- Tfo)

- (1- 7)P0

(12.20)

â&#x20AC;&#x2122;

and the constants are defined as

c1 = - L a A p

aT,

144gcASf

â&#x20AC;&#x2122;

(12.21)

(12.22)


133 144gcA c3 =

c,:

=

2u;

M

'

-I . 2AU0Sfpo aTf

(12.23)

(12.24)

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 Equations A a f a

Cross-sectional area of outlet pipe

C1

Constant defined by Eq. 12.21

c2

Constant defined by Eq. 12.22

c3

Constant defined by Eq. 12.23

c4

Constant defined by Eq. 12.24

f F

Friction loss in outlet pipe R a d i a l distribution of power density

4

Importance-weighted average of F

g

Cross-sectional area of fuel channel Cross-sectional area of graphite stringer

H

Dimensional constant, ( ft lbmass) / ( sec2 lbfOrce 1 Height of core

h

Heat transfer factor, graphite to fuel

I

Radial distribution of nuclear importance

k

Multiplication factor

gC

kex

Reactivity added by external means

a

Neutron lifetime

M

Mass of fuel in outlet pipe to pump

N

Number of delayed neutron groups

n

Ratio of specific heats


I34 P

Power

PC

pP

R r

Pressure i n core Pressure i n pump bowl Radius of core Radial distance from core center l i n e Total heat capacity of f u e l i n core

sf S

g Tf T g

Total heat capacity of graphite Local temperature of f u e l Local temperature of graphite Nuclear average temperature of f u e l

T; T*

3

Nuclear average temperature of graphite

-Tf

Bulk average temperature of f u e l

T g

Bulk average temperature of graphite

Tfi

Fuel i n l e t temperature Fuel o u t l e t temperature

Tfo t

Time

U

Velocity of f i e 1 i n a channel

U

Velocity of f i e 1 i n o u t l e t pipe Volume of f i e 1 i n core

vf V

g

V P

Volume of graphite i n core Volume of gas i n pump

wc

Heat capacity of f'uel flow

X

Normalized power

Y

Normalized f u e l temperature

z

Axial distance from bottom of core

P

af

Fuel temperature coefficient of r e a c t i v i t y

a

Graphite temperature c o e f f i c i e n t of r e a c t i v i t y

pi B Y

Fraction of neutrons i n delayed group i

g

ri 6 'i

Total f r a c t i o n of delayed neutrons Fraction of heat produced i n graphite Latent power associated with delay group i Temperature weighting f a c t o r Decay constant f o r group i

P

Density

PC

Volumetric heat capacity

a

Power density

Superscript 0 r e f e r s t o i n i t i a l conditions


12.5 MSRE Characteristics Used i n Kinetics Analysis Table 12.2 summarizes t h e properties of t h e MSRE which a f f e c t t h e k i n e t i c s and gives the values which were used i n t h e l a s t analysis.

Table 12.2.

MSRE Characteristics Affecting Kinetic Behavior

Fuel S a l t A 2.29 X

Prompt neutron l i f e t i m e ( s e c ) Temperature c o e f f i c i e n t s of r e a c t i v i t y [ (Gk/k)/OF] Fuel Graphite

-3.03 -3.36

X X

144

Fuel density ( l b / f t 3 ) Delayed neutron f r a c t i o n Static Circulating

lT5 lo+

-4.97 x 1 r 5 - 4 . 9 1 x 10-5 134

9.37 16.45

Fraction of heat generation In fie1 I n graphite

0.933 0.067

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

1.74 3.67

Graphite - t o - f i e 1 heat t r a n s f e r

0.020

(MW/

OF)

Core f i e 1 volume ( f t 3 )

25.0

Fuel volumetric expansion coefficient ("F~) Length of l i n e t o pump bowl ( f t )

1.18 x 10-4 16.0

Cross s e c t i o n a l area of l i n e ( f t 2 )

0.139

Friction l o s s i n l i n e [ p ~ i / ( f t / s e c ) ~ ]

0.020

Pumb bowl i n i t i a l pressure ( p s i g )

5

Volume of gas i n pump bowl

(e3)

Ratio of s p e c i f i c h e a t s of helium

C

lcr4

0.0067 0.0036

Residence times ( s e c ) Core External t o core

I

B

2.5 1.67

-3.28 -3.68

x 10-5 x 10-5 143


12.6 Preliminary Studies 12.6.1

Early Analysis of Reactivity Incidents39

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 uncontrolled rod withdrawal led to predicted core temperatures high enough to threaten internal damage. Because each of these accidents could happen only by compound failure of protective devices, and because in each case there existed means of corrective action independent of the primary protection, damage was considered to be very unlikely in the cases considered. The calculated response to arbitrary step and ramp additions of reactivity indicated that damaging pressures could occur only if the addition were the equivalent of a step of about 1% 6k/k or greater, well beyond the severity of foreseeable accidents.

12.6.2 ComDarison of MlTRGATROYD 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 MLTRGATROYD.

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.

.


I37 An example of the differences in MURGATROYD and ZORCH results is illustrated in Fig. 12.1, where the power and-temperaturetransients following a prompt-critical step in reactivity are compared. Because ZORCH computes a spatial temperature distribution and gives the greatest weight to the most rapidly rising temperatures, its nuclear average temperature rises more rapidly than the fuel bulk average temperature or the temperature computed by MURGATROYD.

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 (T0 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 outlet 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 differential 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% 6k/k per second when the system contains fuels A, B, and C, respectively. The initial transients associated with these ramps were calculated for fuels B and C starting with the reactor just critical at 0.002 w and 1200â&#x20AC;&#x2122;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 12.3 for fuels B and C respectively.

The curves

illustrate the behavior of the power, the fie1 and graphite nuclear average temperatures, Ti and T* the temperature of the fuel leaving the g

â&#x20AC;&#x2122;


h

Fr v

1400

1.300

1200

120

100

80

&

E

v

4c

x C

Fig. 12.1. Power and Temperature Transients Following a Prompt Critical Step in ReactiviLy; Fuel A; Comparison of ZORCH and MlTRGATROYD Kinetics Models.

.


I39

V

0

2

4

6

8 TIME

10

12

14

16

(sec)

Fig. 12.2. Power and Temperature Transients Produced by Uncontrolled Rod Withdrawal, Fuel B.

4


14@

TIME

(sec)

Fig. 1 2 . 3 . Power and Temperature Transients Produced by Uncontrolled Rod Withdrawal, Fuel C. W


141 hottest channel,

'To 'max, and the highest fuel temperature in the core,

Although the rate of reactivity addition was lower for fuel C than for fuel By 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 relatively 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 the fuel that was affected 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 continue 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 continued.

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 temperatures 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 V

was also examined in the light of this action.

It was assumed that only


142 two rods dropped (0.1 sec a f t e r t h e f l u x reached 15 Mw, with an accelera t i o n of 5 f t / s e c 2 ) , while t h e t h i r d continued t o withdraw. t r a n s i e n t s f o r t h i s case a r e shown i n Fig. 12.4.

ur

The i n i t i a l

The f l a t portion i n t h e

maximum f u e l temperature r e f l e c t s t h e time required f o r t h e f u e l t h a t w a s heated by t h e i n i t i a l excursion t o pass out of t h e core.

Dropping two

c o n t r o l r o d s i n t h i s accident reduced t h e temperature excursions t o ins i g n i f i c a n t proportions from t h e standpoint of r e a c t o r s a f e t y .

Since

t h e r e a c t o r cannot be made c r i t i c a l by withdrawing only one c o n t r o l rod, f a i l u r e of t h e rod-drop mechanism on one rod does not impair t h e s a f e t y t

of t h e system. The core pressure t r a n s i e n t s were s m a l l i n a l l of t h e rod withdrawal

accidents.

With no c o r r e c t i v e action, t h e pressure increases were 18 and

2 1 p s i f o r t h e cases involving f u e l s B and C, respectively.

Simulation

of t h e control-rod drop l i m i t e d t h e pressure excursion with m e 1 C t o 8 psi.

12.7.2

Cold-Slug Accident

The k i n e t i c behavior was calculated f o r a postulated incident i n which one core-volume of f u e l a t 900째F suddenly entered t h e core, which w a s i n i t i a l l y c r i t i c a l a t 1200'F and 1 kw. The r e s u l t i n g power-temperat u r e t r a n s i e n t s a r e summarized i n Fig. 12.5, a s c a l c u l a t e d f o r f u e l s a l t B.

The maximum values reached f o r power and temperature were higher f o r

t h i s case than f o r s a l t C.

The maximum pressure achieved w a s about 6 p s i

with e i t h e r s a l t . The temperature p l o t s given i n Fig. 12.5 e x h i b i t t h e following features:

There was an i n i t i a l 300째F drop i n t h e r e a c t o r i n l e t temper-

ature, which remained a t 900째F u n t i l t h e core was f i l l e d with t h e cooler fluid.

A s t h e volume of t h e core occupied by t h e cold s l u g became l a r g e r ,

t h e f u e l nuclear average temperature decreased slowly, adding r e a c t i v i t y . When t h e r e a c t i v i t y approached prompt c r i t i c a l , t h e r e a c t o r period became

s m a l l and s u b s t a n t i a l nuclear heating occurred.

This caused t h e f u e l nu-

c l e a r average temperature t o r i s e sharply and l i m i t t h e power excursion. The a d d i t i o n a l heat generation was r e f l e c t e d as a r i s e i n t h e channel o u t l e t temperature.

A t t h e time t h e leading edge of t h e cold s l u g reached


143

UNCLASSlFl ED

6

8

10

TlME

12

14

16

(see)

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


J UNCLASSI FlED

P

v

5 .O

io .o

TIME

15.0

20 .o

25.0

(see)

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


145 the t o p of the core, there was a sharp drop i n t h e channel o u t l e t temperSimultaneously, t h e reactor i n l e t s a l t temperature returned t o

ature.

1200°F as t h e available amount of cold f l u i d was exhausted.

The channel

o u t l e t passed through a maximum upon a r r i v a l of t h e f l u i d heated a t t h e center of the core by t h e i n i t i a l power t r a n s i e n t , then decreased u n t i l f i n a l l y t h e r i s e i n s a l t i n l e t temperature was again r e f l e c t e d (about 9.4 sec l a t e r ) a s a r i s e i n t h e channel o u t l e t temperature. It i s apparent t h a t t h e excursions i n temperature and pressure res u l t i n g from the nuclear incident a r e l e s s important than the rapid r a t e s of change of temperature calculated f o r the incident. The l a t t e r could r e s u l t i n l a r g e t r a n s i e n t s t r e s s e s i n the i n l e t and o u t l e t piping and i n t h e f u e l pump.

12.7.3

F i l l i n g Accident

Conditions Leading t o F i l l i n g Accident.

- Normal

procedure f o r s t a r t -

up of the MSRE requires t h a t the r e a c t o r and f i e 1 be heated by e l e c t r i c heaters t o near the operating temperature before t h e fâ&#x20AC;&#x2122;uel i s t r a n s f e r r e d

from the d r a i n tank t o t h e core. The control rods normally are p a r t i a l l y i n s e r t e d during a f i l l , so t h a t the reactor i s s u b c r i t i c a l a t normal temperature with the core fill of fuel.

C r i t i c a l i t y i s a t t a i n e d by f u r t h e r

rod withdrawal a f t e r the f u e l and coolant loops have been f i l l e d and c i r culation has been s t a r t e d . C r i t i c a l i t y could be reached prematurely during a s t a r t u p while t h e core i s being f i l l e d i f :

( a ) the control rods were withdrawn from the

positions they normally occupy during f i l l i n g ; ( b ) the core temperature were abnormally low; or ( c ) the f u e l were abnormally concentrated i n uranium.

Interlocks and procedures are designed t o prevent such an accident.

I f , despite the precautions, the r e a c t o r were t o become c r i t i c a l under

such conditions, there would be a power excursion, the s i z e of which would depend on t h e source power and t h e r a t e of r e a c t i v i t y addition.

The core

temperature would r i s e rapidly during the i n i t i a l power excursion; then, i f f u e l addition were continued, it would r i s e i n pace w i t h the increase i n c r i t i c a l temperature.

The consequences of a number of f i l l i n g acci-

dents were analyzed, and the p r i n c i p a l r e s u l t s are summarized i n t h i s W

4

section.

Detailed description of these studies i s contained i n r e f 40.


. I

146 Reactivity Addition. -The mount of r e a c t i v i t y available i n a f i l l J

ing accident depends on the conditions causing the accident and t h e chara c t e r i s t i c s of the f u e l s a l t .

I n the case of f i l l i n g t h e reactor with

the control rods r u l l y withdrawn, the excess r e a c t i v i t y i s limited t o the amount i n the normal f u e l loading.

Only about 3% 6k/k w i l l be required

f o r normal operation (see Table 9.1), and the uranium concentration i n the f u e l w i l l be r e s t r i c t e d by administrative control t o provide no more than required.

F i l l i n g a t the normal r a t e with a l l rods f'ully withdrawn

r e s u l t s i n a r e a c t i v i t y ramp of 0.01% 6k/k per second when k = 1.

The

power excursion associated with t h i s ramp i s well within the range of control of the rod safety system.

Full i n s e r t i o n of any two of the three

control rods i s adequate f o r shutdown of the full core. I n f i l l i n g the f u e l a t an abnormally low temperature, excess react i v i t y i s added by means of the negative temperature c o e f f i c i e n t of the fuel.

For f u e l B (the mixture with t h e l a r g e s t negative temperature co-

e f f i c i e n t of r e a c t i v i t y ) , cooling the s a l t t o the liquidus temperature

(84.0'F) provides 1.9$ excess r e a c t i v i t y . a t k = 1 i s O.OOG$/sec.

The r e a c t i v i t y addition r a t e

The shutdown margin provided by the control rods

i s 5.2%.

I n the case of f i l l i n g of the r e a c t o r core with f u e l abnormally concentrated i n uranium, the mechanism assumed t o cause t h e incident i s t h a t of selective freezing of f u e l i n the drain tank.

The c r y s t a l l i z a t i o n

paths of a l l three s a l t mixtures under consideration are such t h a t l a r g e q u a n t i t i e s of s a l t can be s o l i d i f i e d , under equilibrium conditions,* before uranium (or thorium) appears i n the s o l i d phase.

Selective freezing,

therefore, provides one means by which the uranium concentration can be increased while t h e s a l t i s i n t h e drain tank.

Since t h e r e a c t o r vessel

i s the f i r s t major component of t h e f u e l loop t h a t f i l l s on s a l t addi-

t i o n s , approximately 40$ of the s a l t mixture can be frozen i n the drain tank before it becomes impossible t o completely f i l l the core. The changes i n l i q u i d composition a s s e l e c t i v e freezing proceeds depend on the i n i t i a l composition and the conditions of freezing.

Figure

12.6 shows the atomic concentrations i n the remaining melt for f'uel A a s *Very slow cooling.


. 147 0

L

0.05

0.04

3 8

0.02

0.01

WEIGHT FRACTION OF SALT FROZEN

Fig. 12.6.

Liquid Composition Resulting from Selective Freezing

of Fuel S a l t A in D r a i n T a n k .

a fbnction of the f r a c t i o n of s a l t frozen.

The curves are based on the

assumption t h a t only the equilibrium primary s o l i d phase, GLiF.BeF2-ZrF4, appears

.

The e f f e c t on premature c r i t i c a l i t y was evaluated f o r each of the t h r e e s a l t s with 3976, by weight, frozen i n the drain tank a s GLiF-BeF2. ZrF4.*

Under these conditions the full r e a c t o r a t 1200째F had about 4$

excess r e a c t i v i t y f o r f u e l s A and C and 15% f o r f i e 1 B.

Fuels A and C

%e composition of the s o l i d phase has l i t t l e e f f e c t on the nuclear calculations a s long as it does not include f i s s i l e or f e r t i l e material.


148 contain s i g n i f i c a n t amounts of thorium and U238, respectively, which remain i n the melt w i t h the U235 during selective freezing.

The poisoning

e f f e c t of these species g r e a t l y reduces t h e severity of t h e f i l l i n g accident when they are present,

The excess r e a c t i v i t i e s i n t h i s accident,

w i t h so much selective freezing, exceed the shutdown margin of the con-

t r o l rods.

Thus it i s necessary t o stop the f i l l i n g process t o prevent

a second r e a c t i v i t y excursion a f t e r the rods have been dropped.

The ac-

cident involving f u e l B i s the most severe; t h e r e a c t i v i t y addition r a t e f o r t h i s case i s 0.025% 6k/k per second a t k = 1, compared with O.Ol%/sec f o r f u e l s A and C. Corrective Actions.

- Control

rod drop and stoppage of f u e l addition

a r e considered a s means f o r l i m i t i n g the power excursion and stopping the addition of r e a c t i v i t y .

I n the f i r s t case, dropping the rods on high

f l u x signal (15 Mw power) was found t o be more than adequate f o r any f i l l ing accident i n which the available excess r e a c t i v i t y does not exceed the

shutdown margin of the rods.

For the more severe accidents, it i s nec-

essary t o supplement the rod drop by stopping the f i l l t o prevent f u r t h e r r e a c t i v i t y addition. F i l l i n g the r e a c t o r i s accomplished by admitting helium, a t 40 psig supply pressure, t o a drain tank and forcing the l i q u i d f u e l up through the drain l i n e i n t o the primary system.

Figure 12.7 i s a simplified flow-

sheet of the reactor f i l l , drain, and vent systems showing o n l y those features which p e r t a i n d i r e c t l y t o the f i l l i n g accident.

All valves a r e

shown i n the normal positions f o r f i l l i n g the r e a c t o r from f u e l drain tank No. 1. Three independent actions are available t o stop the addition of f i e 1 t o the primary loop: 1. Opening HCV-54.4 equalizes the loop and drain tank pressure.

2.

Opening HCV-573 r e l i e v e s the pressure i n the drain tank by venting gas through the a u x i l i a r y charcoal bed t o the stack.

3.

Closing HCV-572 stops the addition of helium t o the drain tank.

D u r i n g a f i l l i n g accident a l l three actions would be attempted simultaneously t o ensure stopping the f i l l .

The f i r s t two actions, i n addition

t o stopping the f i l l , allow the f u e l i n the primary loop t o run back t o the drain tank.

Stopping the gas addition only stops the f i l l , but the

s a l t flow does not stop instantaneously.


149 UNCLASSIFIED O R N L - O W G 63-7320

TO FILTER, FAN. AND STACK

/

i A U X l L l ARY CHARCOAL

BED

50-psig DISK I

PCV

51 7 40-psig SUPPLY HELIUM

Fig. 12.7.

System Used i n F i l l i n g Fuel Loop.

During f i l l i n g , the flowing f u e l i n the drain l i n e experiences a

small pressure drop.

I n addition, the gas displaced from the primary loop

must flow out t o the stack through equipment which imposes some pressure drop. Consequently, the pressure i n the drain tank a t any point i n the f i l l i n g operation i s g r e a t e r than t h a t required t o maintain the l i q u i d l e v e l difference under s t a t i c conditions.

A s a r e s u l t , when gas addition

i s stopped, the f u e l l e v e l i n the primary loop coasts up until the dynamic head l o s s e s have been replaced by an increase i n t h e s t a t i c head d i f f e r ence between loop and d r a i n tank.

If t h i s coast-up occurs during a f i l l -

ing accident, t h e additional excess r e a c t i v i t y associated with t h e higher l e v e l must be compensated for by the system.


150

- The

Temperature Coefficient of Reactivity.

temperature c o e f f i c i e n t

of r e a c t i v i t y of t h e f u e l i n the p a r t i a l l y f i l l e d core d i f f e r s substan-

t i a l l y from t h a t i n the f u l l system.

I n t h e rull system, the thermal ex-

pansion of the s a l t expels f u e l from t h e core. core, however, remains e s s e n t i a l l y constant.

The e f f e c t i v e s i z e of the Thermal neutron leakage a l s o

increases, and both of these f a c t o r s tend t o reduce r e a c t i v i t y .

I n the

p a r t i a l l y f'ull core, f u e l expansion increases the e f f e c t i v e height of the This tends t o o f f s e t the decrease i n r e a c t i v i t y due t o increased

core.

r a d i a l neutron leakage.

The e f f e c t i v e temperature c o e f f i c i e n t of reac-

t i v i t y of f u e l B with the core 6 9 full i s approximately -0.4 X lo+ ("F)'l,

compared with -5.0

X

lo-* (OF)"

f o r the f'ull core.

The tempera-

t u r e coefficient of the graphite i s not s i g n i f i c a n t l y affected by the fuel level.

Maximum F i l l i n g Accident.

- Only

the most severe of the postulated

f i l l i n g accidents w a s analyzed i n d e t a i l .

It w a s assumed t h a t the uranium

i n f u e l B was concentrated t o 1.6 times the normal value by s e l e c t i v e freezing of 39% of the s a l t i n the drain tank.

Several other abnormal

s i t u a t i o n s were postulated during the course of the accident, a s follows: 1.

The helium supply pressure was assumed t o be 50 psig, t h e l i m i t

imposed by the rupture disk i n the supply system, r a t h e r than the normal

40 psig.

This pressure gave a f i l l r a t e of 0.5 ft3/min when c r i t i c a l i t y

was achieved and produced a l e v e l coast-up of 0.2 f t a f t e r gas addition was stopped. 2.

It was assumed t h a t only two of the three control rods dropped

on demand during the i n i t i a l power excursion. 3.

It was assumed t h a t two of the three actions available f o r stop-

ping the f i l l f a i l e d t o f'unction.

Only t h e l e a s t e f f e c t i v e action, stop-

ping the gas addition, was used i n the analysis.

This allowed the Fuel

l e v e l t o coast up and make the reactor c r i t i c a l a f t e r the two control rods had been dropped t o check the i n i t i a l power excursion. The power and temperature t r a n s i e n t s associated with the accident described above were calculated with the a i d of both d i g i t a l and analog computers.

Since t h e u s e r u l range of an analog computer i s o n l y about

two decades for any variable, the i n i t i a l p a r t of the power t r a n s i e n t was calculated with t h e d i g i t a l k i n e t i c s program MURGATROYD.

The d i g i t a l


151 calculation was stopped a t 10 kw when the power began t o a f f e c t system temperatures, and the d i g i t a l r e s u l t s were used a s input t o s t a r t the analog calculation.

Since it was c l e a r t h a t the r e a c t o r would go c r i t i c a l

again a f t e r the control rods had been dropped, the analog simulation i n cluded the Compensating e f f e c t s of the f u e l and graphite temperature coBecause of the small f u e l c o e f f i c i e n t , it was

e f f i c i e n t s of r e a c t i v i t y .

necessary t o use a highly d e t a i l e d model t o represent heat t r a n s f e r from the f u e l t o the graphite during the t r a n s i e n t . The r e s u l t s of the maximum f i l l accident simulation are shown graphi c a l l y i n Figs. 12.8 and 12.9.

Figure 12.8 shows the e x t e r n a l l y imposed

r e a c t i v i t y t r a n s i e n t exclusive of temperature compensation e f f e c t s .

The

e s s e n t i a l f e a t u r e s a r e the i n i t i a l , almost-linear r i s e which produced the f i r s t power excursion a s f i e 1 flowed i n t o the core, the sharp decrease

a s the rods were dropped, and the f i n a l slow r i s e a s the f u e l coasted up Figure 12.9 shows t h e power t r a n s i e n t and some

t o i t s equilibrium l e v e l . pertinent temperatures.

The f u e l and graphite nuclear average tempera-

t u r e s a r e the q u a n t i t i e s khich ultimately compensated f o r the excess r e a c t i v i t y introduced by the f i e 1 coast-up,

The maximum f i e 1 temperature

r e f e r s t o the temperature a t the center of the h o t t e s t portion of the h o t t e s t f u e l channel.

The i n i t i a l power excursion reached 24 Mw before

being checked by the dropping control rods, which were tripped a t 15 Mw. This excursion i s not p a r t i c u l a r l y important, because it did not r e s u l t

i n much of a f u e l temperature r i s e .

After the i n i t i a l excursion, the

power dropped t o about 10 kw and some of t h e heat t h a t had been produced

i n the f b e l was t r a n s f e r r e d t o the graphite.

The r e s u l t a n t increase i n

the graphite nuclear average temperature helped t o l i m i t the severity of the second power excursion.

Reactivity was added slowly enough by the

f i e 1 coast-up t h a t the r i s i n g graphite temperature was able t o l i m i t the second power excursion t o only 2.5 Mw.

The maximum temperature attained,

1354OF, can be t o l e r a t e d f o r long times.

12.7.4

Fuel Pwnp Power Failure

The consequences of i n t e r r u p t i o n of f i e 1 c i r c u l a t i o n while the reW

.

a c t o r i s a t high power were determined by analog computer simulation of


152

UNCLASSIFIED ORNL DWG. 6.7.88181

1 .o

0.5

0

h

w.

-0.5

v

-1.O

-1.5

-2

.o

0

100

200

250

?jo

TlME ( s e c )

Fig. 12.8. Net Reactivity Addition During Maximum Filling Accident.

.


153

IlNCl ASSIFIED

13&

132c

128a

1240

12Qo

4

3

2

0

100

150

200

2F

300

373

TIME ( s e e )

Fig. 12.9. Power and Temperature Transients Following Maximum F i l l i n g Accident.


154 the nuclear, heat t r a n s f e r , and thermal convection equations f o r the sysFailure of the f u e l pump power supply, with subsequent coast-down

tem.

of the flow, was simulated by causing the c i r c u l a t i o n r a t e t o decrease exponentially with a 2-see time constant u n t i l it reached the therlnal c i r c u l a t i o n r a t e determined by the temperature r i s e across the core.

As

the f i e 1 c i r c u l a t i o n r a t e decreased, the e f f e c t i v e delayed neutron f r a c t i o n was increased by 0.003 and the heat t r a n s f e r c o e f f i c i e n t i n the heat exchanger was reduced. Figure 12.10 shows the r e s u l t s of a simulated f u e l pump f a i l u r e a t

10 Mw, with no corrective action. the i n i t i a l r i s e i n the power.

The gain i n delayed neutrons caused

The decrease i n heat removal froin the

core, coupled with the high production, caused the core o u t l e t temperature t o rise.

A s the f u e l flow and the heat t r a n s f e r i n the heat ex-

changer f e l l , the continued heat e x t r a c t i o n a t the r a d i a t o r caused t h e coolant s a l t temperature t o decrease and reach the freezing point i n l e s s than 2 min.

(The behavior i n simulator t e s t s a t lower power was similar,

but the coolant temperature remained above the freezing point i f the i n i t i a l power was l e s s than 7 Mw.) P r a c t i c a l measures can be taken t o prevent freezing of the coolant s a l t o r overheating of t h e core i n the event of f u e l pump f a i l u r e .

These

consist of closing the r a d i a t o r doors and i n s e r t i n g t h e control rods. Figure 12.11 shows simulator results f o r a case i n which these actions were taken r a t h e r slowly, yet proved e f f e c t i v e .

One second a f t e r the

pump power was cut, a negative r e a c t i v i t y ramp of -0.075$ 6k/k per second was i n i t i a t e d , simulating i n s e r t i o n of the control rods a t normal driven speed.

Beginning 3 sec a f t e r the pump power f a i l u r e , t h e simulated heat

removal from the r a d i a t o r tubes was reduced t o zero over a period of about 30 see.

12.7.5

Conclusion

The r e s u l t s of the analyses described here form p a r t of the b a s i s f o r a comprehensive analysis of the safety of the r e a c t o r system.

The

c r e d i b i l i t y and the importance of each accident a r e evaluated and d i s cussed i n the Safety Analysis Report.


155

I

lL 0

W

LT

3 I-

a

a W

a

H

w

t

12

10

c

8

3

-

I LT

w

3 0 a

6

4 2

0

0

20

40

60

80

100

120

TIME ( s e c )

F i g . 12.10. Power and Temperature Transients Following Fuel pwnp Power Failure at H i g h Power; No Corrective Action.


156

1300

-

Lc 0

1200

W

IT 3

t-

a

IT W

a 2

I100

W

t-

RADIATOR OUTLET

1000

I

10

0

6

4 2 0

I

1

--+t\-.'

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 S H I E L D I N G

13.1

General

The b a s i s f o r the design of a l l biological shielding i s the recommended maximum permissible exposure t o r a d i a t i o n of 100 mrem/week, or 2.5 mrem/hr based on a 40-hr work week.

The c r i t e r i o n for the MSRE biological

s h i e l d design i s t h a t the dose r a t e w i l l not exceed 2.5 mrem/hr during normal operation a t any point on the shield e x t e r i o r t h a t i s located i n an unlimited access area.

This c r i t e r i o n inherently includes allowance

f o r s i g n i f i c a n t underestimation of the hot-spot dose, with the general area s t i l l below 2.5 mrem/hr. A s i n most r e a c t o r designs (and p a r t i c u l a r l y i n the case of the MSRE,

since it has t o f i t within an e x i s t i n g r e a c t o r containment c e l l and building) nuclear, mechanical, and s t r u c t u r a l requirements, a s well a s economics, preclude the design of permanently i n s t a l l e d shielding t h a t r e -

sults i n a dose r a t e t h a t i s l e s s than the permissible r a t e a t a l l points. Consequently, the f i n a l shield design allows f o r addition of shielding as needed to reduce the r a d i a t i o n l e v e l a t localized hot spots.

13.2

Overhead Biological Shielding

The calculations which are described i n t h i s section on t h e biologi c a l shielding over the reactor c e l l were c a r r i e d out a t an e a r l y stage of the design.41

The

source strengths w h i c h w e r e used, and which are re-

ported i n t h i s section, d i f f e r somewhat from those obtained from the l a t e s t nuclear calculation (see Sec 13.3.4 f o r l a t e r r e s u l t s ) .

The d i f -

ferences would make no s i g n i f i c a n t change i n the prescribed shielding.

I n t h i s section, the calculations sometime r e f e r t o ordinary concrete, which was i n i t i a l l y considered f o r use.

The f i n a l s h i e l d design i s com-

posed of barytes concrete, ordinary concrete, and s t e e l which i s equival e n t t o about 9 f t of ordinaxy concrete and about 7 f t f o r neutrons.

13.2.1

Geometry The basic s h i e l d construction i s shown i n Fig. 13.1.

V

Two separate

l a y e r s of concrete blocks a r e used; t h e majority of the lower blocks a r e


158

u NCLASSl Fl ED ORNL-DWG

-BLDG

63-7321

NORTH

&-in. MAX. BLOCK SPACING

UPPER SHIELD BLOCKS

-

T H E R M A L SHIELD

3 ft

\SHIELD SUPPORT BEAM (CONCRETE-FILLED 1 - B E A M )

Fig. 13.1.

Elevation V i e w of Basic Overhead Shield.


159 23-1/2 in. wide and 3-1/2 f t thick, and are barytes concrete.

These

blocks do not extend completely across the c e l l but are i n t e r s e c t e d by two s h i e l d support beams, shown i n Figs. 13.1 and 13.2, which r u n a t r i g h t angles t o the lower s h i e l d blocks.

The top shield blocks are ordinary

concrete, 23-1/2 i n . wide and 3-1/2 f t thick, and extend completely across the c e l l .

A thermal s h i e l d t h a t i s 16 i n . t h i c k and composed of about

h a l f water and h a l f s t e e l surrounds the reactor except f o r a 2 - f t - d i m

UNCLASSIFIED ORNL-DWG 6 3 - 7 3 2 2

0

2 f t 3in. 2ft 6& in

-I -

REACTOR VESSEL, SHOWING MAXIMUM AND MINIMUM SOURCE FACES.

0 PUMP BOWL @

@

HEAT EXCHANGER ACTIVE LENGTH CENTER

/

I'

PUMP DISCHARGE LINE

I

I

_ _ - INDICATES CENTER

OF SPACING BETWEEN LOWER SHIELD BEAMS

INDICATES CENTER

I

I I I

OF

I I

z

255

1 0

I-E I

I

I I

p I

p .

--i -.k

PUMP

\

241n (TYP)

D

REACTOR

\ 12 in.-

PIPING SCHEMATIC

Fig. 13.2.

Plan View of Basic Overhead Shield.


160 opening a t the top.

Obviously the maximum dose r a t e will e x i s t over t h i s

opening, i n an area limited by the thermal shield. The dose r a t e s t h a t w i l l e x i s t on top of the s h i e l d are due t o two conditions :

1. a general r a d i a t i o n l e v e l with the all thickness of the s h i e l d e f fective, 2.

l o c a l peaks i n the radiation l e v e l due t o imperfections i n the shield.

The general radiation l e v e l s above the s h i e l d have been based on the r e l a t i o n s given below f o r a constant-source-strength disk source and f o r c y l i n d r i c a l and truncated r i g h t - c i r c u l a r cone constant-volume sources :42 disk source, S.

(13.1) c y l i n d r i c a l source, (13.2) truncated r i g h t - c i r c u l a r cone source, @ =

B(pt)

sv I E 2 h t ) -

E 2 ( p t sec

* S

sec 0

e)

I*

(13.3)

(See Sec 13.6 f o r d e f i n i t i o n of symbols.) Ordinary concrete dose buildup f a c t o r s and standard attenuation coe f f i c i e n t s were used for the gamma rays.

The buildup f a c t o r s may be used

a s indicated (constant for a p a r t i c u l a r case), since the s o l i d angle i n volved i s small. Neutron attenuation was estimated using neutron removal cross sect i o n s with a buildup f a c t o r of unity. Neutron and gamma sources are given i n Sec 13.2.2 dealing with source strengths. Estimates f o r the l o c a l peak dose r a t e s t h a t w i l l occur above gaps between adjacent s h i e l d beams were determined using the methods given above f o r the s o l i d s h i e l d with the appropriate e f f e c t i v e source geometry.


161 The e f f e c t i v e source geometry f o r a crack i s i l l u s t r a t e d i n Fig. For a given crack width, w, and a given distance, a, between the

13.3.

dose point and the source, a f r a c t i o n of the source has d i r e c t l i n e of s i g h t t o the dose point.

This e f f e c t i v e somce i s only attenuated by the

p a r t i a l thickness of the shield, t.

I n these estimates buildup of scat-

t e r e d photons has not been included, though the s c a t t e r e d photons make an appreciable contribution. Figure 13.2 shows the location of the primary reactor system with respect t o the spacings and locations of the s h i e l d blocks. 13.2.2

Source Strengths

The sources of radiation considered were f i s s i o n product decay gammas, N16 decay gammas, prompt f i s s i o n g m a s , thermal neutron capture [The F1'(n,y)F2'

gammas, and f a s t neutrons.

reaction produces a 1.8-MeV

photon, but i t s contribution t o t h e dose r a t e through the top s h i e l d i s negligible.]

UNCLASSIFIED ORNL-DWG 63-7323

t NOMINAL SHIELD THICKNESS

1

)t

FACE

\

EFFECTIVE SOURCE FACE

Fig. 13.3.

Geometry for Determining an Effective Gap Source.


162 Fission Product Decay Gammas.

- Goldstein4â&#x20AC;&#x2122;

has reported the gammas

from the f i s s i o n products t o have an exponential energy spectrum and a t o t a l energy decay r a t e of 5.5 Mev/fission a t saturation. It was assumed t h a t t h i s spectrum and decay r a t e was constant through the primary system. Table 13.1 gives the f i s s i o n product source strengths f o r a 10-Mw power l e v e l and a 62-ft3 t o t a l f u e l volume. Nitrogen-16 Decay Gamma Activity.

- The

reaction F1â&#x20AC;&#x2122; (n,a)N16 (7.36-

sec h a l f - l i f e ) i s a high-energy reaction with an appreciable cross section above 3 MeV, going t o a maximum of -310 mb a t -5.8 MeV. 4 4 The N16 production r a t e was determined by numerically i n t e g r a t i n g the neutron f l u x and reaction cross section over the energy range 3 t o 10 MeV. Fast neutron fluxes over t h i s energy range were obtained from multigroup reactor calculations. 45 The a c t i v i t y i n the primary system was based on Eq.

(13.4), given

below, using a constant production r a t e i n each region of the r e a c t o r vessel.

Table 13.1.

Saturated Fission Product Gamma-Ray Spectrum (10 Mw, 62 f t 3 f u e l )

Energy Range (MeV)

Average Energy (Mev/photon)

Energy Emission Rate [Mev/(sec*cc)]

x 1010 0-1

0.41

31.5

1-2

1.41

36.1

2-3

2.41

20.5

3-4

3.41

9.66

4-5

4.41

4.16

5-5.4

5.1

0.88 Total

103


163

L

The saturated a c t i v i t y a t the reactor vessel e x i t i s

-At

I

AN = P a ( l - e

+ pC(i

-Atj a) e

e

-At -e

-At C

-At e

U

e

-At U

+ p R ( l- e

+ p U ( i- e

-At C

-At ')

e

-At, e

- A t u)] + [I - e - A t t ]

.

(13.4)

The N 1 6 production and decay r a t e s a r e given i n Table 13.2. Neutron Leakage and G m a Flux Core Sources.

- The

f a s t neutron leak-

age and gamma f l u x from the top of the core were obtained from two-group,

.

two-dimensional reactor calculations 45

The neutron leakage r a t e s a t 10

Mw a r e 1.36 X 10l2 f a s t neutrons/(sec*cm2) and 4.9

X

lolo

therlnal neuThese leakage

trons/(sec-cm2); the gamma fluxes are l i s t e d i n Table 13.3.

r a t e s and fluxes a r e a t the surface of the r e a c t o r and should be representative of a cosine, or Fermi, source.

It was assumed t h a t they had a

cosine d i s t r i b u t i o n ; therefore they were increased by f a c t o r s of 4 and 2, respectively, and t r e a t e d a s an i s o t r o p i c source. 46

Table 13.2.

N l 6 Saturated Activity

Region

Production Rate [atoms/ (see. c c ) ]

Reactor o u t l e t piping

0 0 0 0 0 0

Pump (bypass flow) Piping

H e a t exchanger Piping Reactor i n l e t

Annulus Lower header Core Upper header a

Average Decay Rate" [MeV/ ( sec cc ) 3

2.7

X

lo1'

1.25 x 1 0 1 5 ~ 2.42 X

lolo

2.20 x 1010

1.97

X

10"

1.82 x 1010

lo1' lolo

0.176 X lo1' 0.176 x lo1'

1.67

X

1.52

X

1.10 x 1010 0.176 X lo1'

2.43 X 10" 3.0

X

lolo

6.13-Mev y i n 7 5 . 9 of decays and 7.10-Mev y i n 6.1$ of decays.

%nits of Mev/sec, assuming a l l N16 i n the bypass flow decays i n t h e pump bowl.


164

Gamma Fluxes from Top of Reactor Vessel, a t 10 Mw Reactor Power

Table 13.3.

Gaxma Flux [Mev/(sec*cm2)1

Energy (MeV)

0.5

2.50

1

4.28

2

3.63

4 6

1.85 1.08

8

0.80

10

1.14

Iron and Concrete Capture Gammas.

- The

energy spectrum of the cap-

t u r e gammas was obtained from the data of Troubetzkoy and Goldstein.47 I n both the reactor thermal shield and the biological shield, the capture gamma source was assumed t o be a plane i s o t r o p i c d i s k source located two f a s t neutron relaxation lengths from the inside of the shield.46 Estimated Dose Rates

13.2.3

Tables 13.4-13.6

show the r e l a t i v e contributions of the individual

sources a s a function of the s h i e l d thickness and spacing between the blocks.

These values have been compiled i n Table 13.7 f o r a maximum block

spacing ( 1 / 2 i n . ) . The r e s u l t s have been presented only a s a flxnction of ordinary concrete, assuming t h a t f o r gamma attenuation the barytes concrete may be accounted f o r by a r a t i o of t h e d e n s i t i e s .

The attenuation of neutrons

i s e s s e n t i a l l y i d e n t i c a l i n e i t h e r barytes or ordinary concrete, as shown

by the data of B l i ~ a r d . Hence, ~~ f o r the neutron dose r a t e r e s u l t s , a given thickness of barytes concrete will have the same e f f e c t a s the ident i c a l thickness of ordinary concrete.


165

Table 13.4.

Gamma Dose Rates Above the Primary System Components f o r a Solid Shield, a t 10 Mw Reactor Power

( A l l values given a s t i s s u e dose r a t e s , mrem/hr)

Thickness of Ordinary Concrete, f t Component 7

8

9

1 . 2 (0.68)

0.16 (0.09) 0.28

Pump bowl" Fission products

9.5

NX6 bypass flow

8.0 (8.0)

1.5

--

6.3 ( 0 )

1.2 (0) --

0.22 (0) -~

24

3.9

0.66

~ 1 primary 6 flow

Total

(5.3)

(13)

(1.5)

(2.2)

(0.28)

(0.3'7)

He a t exchanger Fission profiucts N16

Total

0.98

0.13

10

1.9

0.35

1%

2.9

0.48

7.6

Pipingb A

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

E

2.7

0.44

0.07

%slues

i n parenthesis represent a possible lower l i m i t .

bLocations shown i n Fig. 13.2. f i s s i o n products.

Dose r a t e s are f o r N 1 6 a c t i v i t y and

Table 13.4 gives t h e gamma dose r a t e s above t h e primary system components vs the s h i e l d thickness f o r a s o l i d shield, a t a 10-Mw reactor power level.

Two values are given for t h e pump bowl, these represent e s -

timates of an upper and lower l i m i t , depending on how e f f e c t i v e the pump motor and t h e i n t e r n a l pump s h i e l d are i n reducing the dose. The incremental dose above a given source due t o adjacent sources has not been determined.

Since the t o t a l dose r a t e w i l l be l e s s than the


166 Table 13.5. Dose Rates Above the Reactor Vessel f o r a Solid Shield, a t 10 Mw Reactor Power

W

(All values given as t i s s u e dose r a t e s , mrem/hr)

Thickness of Ordinary Concrete, f t Source

8

7

9

Gamma rays

28

136

Core N16

15

Iron capture

86

Concrete capture

19

Neutrons from core

2.8

17

6.2 0.51 3.4

1.0

1.8

0.10

0.005

sum of the individual dose r a t e s , an upper l i m i t f o r the combination may be found by adding the dose r a t e s d i r e c t l y above each of t h e sources; f o r example, the t o t a l dose r a t e above the heat exchanger, including piping lengths B and C , w i l l be l e s s than 0.64 m / h r for 9 f t of concrete (0.64 = 0.48

+

0.11

+

0.05).

The dose r a t e s d i r e c t l y above the reactor vs feed of ordinary conc r e t e are given i n Table 13.5, f o r a s o l i d s h i e l d and a 10-Mw power l e v e l . The t o t a l dose r a t e i s subdivided i n t o the neutron and gamna contribut i o n s , a s the s h i e l d i s equivalent t o -9 f t of ordinary concrete f o r the gammas and -7 f t for the neutrons. The e f f e c t of spacing between the upper s h i e l d blocks i s shown i n Table 13.6 a s a f k t c t i o n of the nominal shield thickness and the face area of the source covered by the gap, wL.

These estimates a r e e s s e n t i a l l y

minimum values t h a t may be expected above the gaps.

Two f a c t o r s t h a t w i l l

make the a c t u a l gamma dose r a t e higher a r e :

1. Scattered radiation; since buildup and sources from s c a t t e r i n g were not included i n the estimate. 2.

The uncollided radiation t h a t i s p a r t i a l l y attenuated by the upper s h i e l d blocks; t h a t i s , photons t r a v e l i n g a t an angle from the s h i e l d normal s l i g h t l y g r e a t e r than the included angle used t o determine the e f f e c t i v e source.

v'


167

Table 13.6. Effect of Spacing Between Upper Shield Blocks on Dose Rates, a t 10 Mw R3actor Power ( A l l values given a s t i s s u e dose r a t e s )

Thickness of Ordinary Concrete, f t

Source

7

8

9

69

12

2.2 0.21 0.29

Reactor gamma rays [D/WL, m r / ( h r * i n o 2 ) ]

Core ~ 1 a 6c t i v i t y

7.8

1.3

Fe capture

9.0

1.7

Concrete capture Reactor neutrons [D/wL,

240 273

11

0.42

mrem/(hr*inO2) 1

Fump bowl gamma rays [D/WL, mr/(hr*in.2) 1

Fission products

13

1.3

~ 1 a6c t i v i t y

10

1.7

0.14 0.27

Fission products

7%

8.1

0.89

~ 1 a6c t i v i t y

4.6

7.7

1.2

Heat exchanger gamma rays [D/w, mr/ (hr. i n , ) 1

Pump discharge line" [D/w2,

6 80

mr/(hr-inO2)]

%e t o coincidence of upper s h i e l d block spacing and lower s h i e l d block and s h i e l d support beam spacing, shown i n Fig. 13.2.


168 Summary of Dose Rates Above Overhead Shield, a t 10 Mw Reactor Power

Table 13.7.

a

Peaking a t Cracks Source

Solid Shield Minimum

Probable

80

160

4500

6000

10

20

Re act or 14

Gammas

1.8

Neutrons Pump bowl gammas

0.8%

Heat exchanger gammas

0.65

1.5

Pump discharge piping gammas

0.15

170b

a

3 34Ob

3.5 f t of barytes concrete and 3.5 ft of ordinary concrete.

bDue t o coincidence of gap between upper s h i e l d blocks w i t h the gap between the lower shield blocks and s h i e l d support beam.

The second f a c t o r given will also tend t o make the a c t u a l f a s t neut r o n dose r a t e higher. The r e s u l t s given i n Tables 13.4-13.6

have been interpolated and com-

p i l e d i n Table 13.7 t o show the expected dose r a t e estimates above the present reactor shield.

Effective source face areas were based on 1/2-in.

gap spacings and source lengths, L, shown i n Fig. 13.2.

For the reasons

discussed, neutron and gamma peak dose r a t e s were a r b i t r a r i l y increased by f a c t o r s of 1.3 and 2.0, respectively, t o give t h e "probable" values listed. 13.3

L a t e r a l Biological Shielding

The biological shielding around the s i d e s of the r e a c t o r and reactor c e l l i s composed of s t e e l , water, magnetite sand, ordinary concrete, and barytes concrete.

The d e t a i l e d arrangement of t h i s shielding and the ad-

d i t i o n a l shielding requirements due t o the induced a c t i v i t y i n the coolant s a l t are discussed i n the following sections.

J


169 L

13.3.1

Basic Shield Arrangement

Figure 13.4 shows the layout of the r e a c t o r c e l l , shielding, and adjacent areas i n plan view.

Most of the c e l l walls and shielding were

b u i l t before the MSRl3 program, f o r an e a r l i e r reactor i n s t a l l a t i o n . The thermal s h i e l d immediately surrounding the r e a c t o r vessel was i n s t a l l e d s p e c i f i c a l l y f o r the MSRE.

It consists of a s t e e l tank, 16 i n .

t h i c k on t h e sides, filled with s t e e l shot and water.

The water i s c i r -

culated t o remow the heat generated i n the shield. The major p a r t of the l a t e r a l shield i s an -3-ft-thick

annulus formed

by two concentric c y l i n d r i c a l s t e e l tanks (inner tank, 2 in. thick; outer tank, 5/8 i n . t h i c k ) enclosing the reactor c e l l .

The hollow annular space

(33 i n . ) i s f i l l e d with a compacted magnetite sandrwater mixture with a bulk density of a t l e a s t 210 l b / f t 3 .

Except i n two l a r g e areas where

c e r t a i n s h i e l d penetrations are located, the annulus i s i n t u r n surrounded by a monolithic concrete wall with a minimum thickness of 21 i n .

The two

areas t h a t l a c k the concrete portion of the s h i e l d a r e t h e south e l e c t r i c a l service area and the coolant c e l l .

The south e l e c t r i c a l service

area adjoins the north side of the r e a c t o r c e l l j u s t below t h e t r a n s m i t t e r room shown i n Fig. 13.4.

The coolant c e l l i s southwest of the r e a c t o r

c e l l and i s connected by a passageway along the s h i e l d wall and by a 7by 11-ft a i r duct t o the blower house, or fan room, where the main cooling fans a r e located.

The f a n room walls on the west side and p a r t s of the

north and south sides are louvered t o admit a i r . 13.3.2

South E l e c t r i c a l Service Room

Because of the gap i n the concrete wall around the r e a c t o r c e l l , the dose r a t e i n the south e l e c t r i c a l service room w i l l be too high f o r access during high-power operation.

The room w i l l therefore be sealed t o prevent

entry except when the r e a c t o r i s shut down.

The room i t s e l f i s enclosed

i n 2 f t of concrete (except f o r the narrow passageway l e a d i q around the reactor c e l l t o the northwest corner of the coolant c e l l ) .

This should

be adequate t o reduce the dose r a t e t o l e s s than 2.5 mrem/hr i n the north e l e c t r i c a l service room and i n t h e t r a n s m i t t e r room located above.

There

e x i s t s a p o s s i b i l i t y , however, t h a t some minor hot spots may occur i n the W

north e l e c t r i c a l service room along the 2 - f t wall separating it from the


UNCLASSIFIED ORNL DWO. 63-4347

1

5

3

UAINTENINCE

snop

6

7

e

INOUCTION REGULATM

Fig. 13.4.

t

P l a n View of MSRE.

8

9


171 south e l e c t r i c a l service room, due t o the various penetrations i n the annular shield.

The dose would depend on the material i n 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 l o c a l ized stacking of concrete blocks on e i t h e r side of the wall separating the two e l e c t r i c a l service rooms.

The 4-in.-diam holes t h a t penetrate

the wall separating the two e l e c t r i c a l service areas w i l l obviously require plugs. The 2-ft-thick f l o o r of the transmitter room located d i r e c t l y over the south e l e c t r i c a l service roon has a number of penetrations t h a t will require special a t t e n t i o n i n the way of additional shielding.

These i n -

clude several 4-in.-diam holes, an 8- by 30-in. opening which i s traversed by two e l e c t r i c a l conduits, and the v e n t i l a t i n g duct located on t h e south wall of the t r a n s m i t t e r room.

13.3.3

Coolant Cell and Fan House

On t h e face of the annular s h i e l d where it i s exposed t o the coolant c e l l , there are two segmental indentations i n the v i c i n i t y of the coolant l i n e penetrations.

These indentations are about 1 4 f t long and 4 f t high,

with a maximum depth of nearly 9 i n .

On the inner side of the indenta-

t i o n s the s t e e l tank thickness was increased fron 2 i n . t o 4 in., but t h i s only p a r t i a l l y coxpensates f o r the removal of the sand-water mixture where the indentation i s deepest. Because o f t h e gap i n t h e concrete w a l l and the reduced thickness

of t h e annular shield, the dose r a t e i n the coolant c e l l due t o r a d i a t i o n from the r e a c t o r c e l l alone would be much too high f o r personnel access during power operation.

Radiation i n the coolant c e l l from t h i s source

can be reduced by additional stacked block shielding against t h e r e a c t o r c e l l wall, but there remains t h e gamma r a d i a t i o n from the c i r c u l a t i n g coolant s a l t , which becomes activated i n passing through the fuel-coolant heat exchanger.

Access t o the coolant c e l l during operation i s therefore

prohibited. Because of the very l a r g e duct connecting the coolant c e l l and the f a n house, high r a d i a t i o n l e v e l s i n the coolant c e l l l e a d t o undesirably high dose r a t e s i n the fan house.

A close estimate of the dose r a t e s a t


172 various points i n the fan house cannot be made, because of the complicated geometry of sources and shielding.

Using simplified line-of-sight methods

of calculation, and assuqing no additional shielding, the dose r a t e a t the south louvered wall i n the v i c i n i t y of No. 2 fan was estimated t o be

14.0mrem/hr.

Contributions from various sources t o t h i s dose r a t e are

itemized i n Table 13.8. The dose r a t e from the most important single source, t h e thermal shield, could be reduced by the addition of dissolved boron i n t h e thermal shield water (10 g / l i t e r would reduce the dose r a t e from 71 mr/hr t o about

15 mr/hr, see Fig. 13.5), but the r a d i a t i o n from the other sources i n the reactor c e l l would s t i l l be t o o high.

Therefore, additional shielding

will be added between the r e a c t o r c e l l and coolant c e l l t o reduce t h e dose r a t e from a l l sources i n the r e a c t o r c e l l t o a negligible l e v e l , thus obviating the use of boron i n the thermal s h i e l d water.

A wall of stacked

barytes concrete blocks w i t h a minimum thickness of 16 i n . w i l l be used

for t h i s purpose. With the additional shielding around the r e a c t o r c e l l , the dose r a t e i n the fan house i s controlled by the gamma a c t i v i t y of the c i r c u l a t i n g coolant s a l t .

The highest dose r a t e from t h i s source w i l l be i n the vi-

c i n i t y of No. 4 fan.

It i s estimated t h a t the dose r a t e here would be

16 mr/hr from the r a d i a t o r and 11 mr/hr from the coolant pump and piping. Most of the l a t t e r contribution w i l l be eliminated by concrete blocks stacked i n the area between t h e r a d i a t o r housing and the r e a c t o r shield.

Table 13.8.

Dose Rates Near No. 2 Fan During 10-Mw Operation (No additional shielding) Source

Core neutrons

Dose (mrem/hr)

4

Circulating f i e 1 g m a s

15 35

Thermal s h i e l d capture gammas

71

Radiator and coolant piping gammas

15

Core gammas

Y


173 L

Nothing can be done t o reduce t h e dose r a t e i n t h e fan house from t h e rad i a t o r without i n t e r f e r i n g with t h e a i r flow.

However, t h e r e i s normally

no need f o r access t o t h i s area during power operation, so the f a n house w i l l be made a controlled-access area. After the addition of t h e stacked block shielding described above,

it i s estimated t h a t the dose r a t e along t h e west louvered wall w i l l probably not exceed 2.5 mrem/hr and will exceed t h i s value somewhat along t h e south louvered wall.

If t h e dose outside t h e wall proves excessive, an

e x i s t i n g concrete block wall located a few f e e t outside t h e louvered wall on t h e south side w i l l be extended around t h e fan house a s f a r a s needed.

UNCLASSIFIED OWG. 63-8183

ORNL

100

1.o 0

20

40 BORON CONCENTRATION

W

6 . 3

SO

100

(g/liter )

Fig. 13.5. Biological Dose from Thermal Shield Capture Gammas as a Function of Boron Concentration. Dose a t louvered w a l l near No. 2 fan.


174 Adjoining the f a n house on the north i s a ramp leading down i n t o the coolant c e l l .

J

The large c e l l exhaust penetration i n the annular s h i e l d

i s i n l i n e w i t h t h i s sloping passage.

Although a 9-in. s t e e l shadow

shield i s provided i n f r o n t of the exhaust l i n e , t h e r a d i a t i o n leaking from the reactor c e l l a t t h i s point will be unusually high.

I n addition,

r a d i a t i o n w i l l s c a t t e r i n t o t h i s area from the passageway leading from the south e l e c t r i c a l service roon.

A stacked block wall, a t l e a s t 1 f t

thick, with a labyrinth passage, w i l l be provided a t the base of the ramp t o reduce t h e dose r a t e outside t o the tolerance l e v e l . 13.3.4

Source Strengths

The source strengths of the f i e 1 s a l t a c t i v i t i e s and capture gammas from the thermal s h i e l d were d i f f e r e n t from those used i n the top s h i e l d calculations.

This r e f l e c t s changes due t o more recent calculations and

a need f o r more sophisticated calculations f o r the capture gammas because

of t h e more c r i t i c a l nature of the shielding i n the f a n house area.

Nitrogen-16 and Fluorine-20 Activity i n Fuel S a l t . -!The

source

strengths of the N 1 6 and F20 a c t i v i t i e s are summarized i n Table 13.9.

Table 13.9.

N 1 6 and F20 Activities" i n t h e Fuel S a l t f o r 10-Mw Operation

Activity [dis/(sec*cm2)]

~

~~

Reactor o u t l e t

4.62 x 109

4.48 x

Pump bowl i n l e t

4.18 x

4.20 x

I n l e t t o r e a c t o r downcomer

2.67 x

Average a c t i v i t y i n c i r c u l a t i n g f'uel

3.56 x

Average a c t i v i t y i n e x t e r n a l loop

3.56 x

Average a c t i v i t y i n reactor vessel

3.56 x

lo9 lo9 lo9 lo9 lo9

Total production r a t e (atoms/sec)

6.78 x 1015

~

lo9 lo9

3.13 x io9 3.73 x io9 3.77 x

io9

3.72 x 109 7.12 x 1015

a

Calculated using l a t e s t neutron balances frm MODRIC and EQUIPOISE calculations for f'uel B (see Chap. 3 ) . J


.

175

w

Capture Gammas i n Thermal Shield.

- The

thermal f l u x d i s t r i b u t i o n

used i n calculating the capture gamma source strength i n the thermal s h i e l d i s shown i n Fig. 13.6.

These values were calculated w i t h the r e -

a c t o r code DTK, a one-dimensional S transport calculation. n Induced Activity i n Coolant S a l t . - P r a c t i c a l l y a l l of the a c t i v a t i o n of the coolant s a l t w i l l occur i n the heat exchanger, where it i s exposed t o neutrons r e s u l t i n g from decay of the delayed neutron precursors i n the f i e 1 s a l t and a small amount of fissioning. For F20 and N 1 6 during steady-state operation, the saturated s p e c i f i c a c t i v i t y , or source strength, of the c i r c u l a t i n g coolant a t any time, t, a f t e r leaving the heat exchanger tubes i s

Y

v

(13.5)

1 - e

where p i s the production r a t e p e r u n i t volume of coolant i n the heat exchanger tubes, TI i s the residence time i n the heat exchanger tubes, and T2 i s t h e residence time of the c i r c u l a t i n g stream outside of the heat

exchanger tubes.

7.25

X

lo4

13.3.5

The saturated s p e c i f i c a c t i v i t y was calculated48 t o be

and 2.55

X

lo4 dis/(cm3.sec) for N16 and F20 respectively.

Calculation Methods

The core gammas and core N16 a c t i v i t y w e r e t r e a t e d as uniform cylin-

d r i c a l sources and Eq. (13.2) was used f o r the dose r a t e calculation.

It

was possible t o reduce a l l coolant s a l t dose r a t e calculations t o simple point and l i n e sources.

The capture gammas from t h e thermal s h i e l d may

be represented by a truncated r i g h t - c i r c u l a r cone source [Eq. (13.3)], but because of the distance t o the louvered wall, point source approximations were used.

The thermal s h i e l d was divided i n t o 11 concentric cylinders,

and each h a l f of a c y l i n d r i c a l annulus was considered a disk with a radius of 5 f t .

Because of the distance involved, each disk could then be

closely approximated by a point source based on the f l u x a t the midplane

of t h e disk. W

The t o t a l dose r a t e i s the sum of the contributions from

each energy group and each disk.


176

UNCLASSIFIED

;6

24

DISTANCE DJD T " A L

F i g . 13.6.

Thermal

32

40

SHIELD (cm)

Flux i n Thermal Shield of MSRE.


177 13.4

Conditions After Reactor Shutdown

All areas e x t e r n a l t o the reactor c e l l will be accessible on an unlimited basis minutes a f t e r reactor shutdown except under one condition. When the coolant s a l t l i n e s are drained, two 4-in.-diam holes are l e f t i n the shield.

One of these coolant pipes ( l i n e 200) tllookst' d i r e c t l y a t

the pump bowl; depending on the degree of drainage of the f i e 1 s a l t , the dose r a t e i n the v i c i n i t y of t h i s l i n e can be several rem/hr.

The other

coolant pipe ( l i n e 201) does not "see" any large source but w i l l l e a k a few mrem/hr of scattered radiation. There i s no p r a c t i c a l way of providing permanent shielding f o r the drained condition.

Temporary shadow

shielding w i l l be used f o r any maintenance work i n the v i c i n i t y of these lines

.

13.5

Summary

The s o l i d portion of the overhead shield i s s u f f i c i e n t t o l i m i t the dose r a t e t o l e s s than 2.5 mrem/hr except d i r e c t l y over the r e a c t o r core, where the dose r a t e was estimated t o be 1 6 mrem/hr.

Large dose r a t e s up

t o 7 rem/hr could e x i s t over some points where the 1/2-in. gaps overlap. However, it i s planned t o i n s e r t polyethylene and s t e e l s t r i p s i n the gaps e x i s t i n g i n the c r i t i c a l areas and f i n a l l y t o stack concrete blocks a s needed over any remaining hot spots. The l a t e r a l s h i e l d with the additional 16-in. barytes block t o be i n s t a l l e d and flurther f i e l d addition of concrete blocks where needed should be adequate.

I f the dose r a t e a t t h e louvered walls does exceed

2.5 mrem/hr, an e x i s t i n g concrete block wall located a few f e e t outside t h e south louvered wall can be extended quickly and e a s i l y a s f a r around. a s needed.


178

13.6

Nomenclature for Biological Shielding Calculations Distance from source t o dose point Buildup f a c t o r Dose r a t e Attenuation functions, tabulated i n T I D -700442 Attenuation functions, tabulated i n TID 700442

-

L

Source length

N

Concentration per u n i t volume

P

Production r a t e per u n i t volume Radius of disk o r c y l i n d r i c a l source

'A'

v'

Source strength, number p e r u n i t time per u n i t area, or u n i t volume

T1

Residence time

T2

Residence time

t

Time and thickness

w

Gap width

Z

Self absorption distance

A

Decay constant

IJ.

Attenuation c o e f f i c i e n t

@

P a r t i c l e flux

Subscripts : a

Annulus

C

core

a

Lower header

s

Source

t

Total

U

Upper header


179

14. MISCELLANEOUS

14.1 Radiation Heating of Core Materials Heat produced in the graphite by absorption of beta and gamma radiation and the elastic scattering of fast neutrons amounts to about 776 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. a

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 MSRF:, 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 NIGHTMARE4' and 2DGH50 (a two-dimensional version of NI(XTMAN3). These computations obtained the gamma flux at one specified point by swnming 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 calculations are given in Table 14.1.

A summary of the nuclear energy sources and the places where the enera 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

8

f

RADIUS (in.)

Fig. 14.1. a t 10 Mw.

Heating i n Graphite:

Radial D i s t r i b u t i o n near Midplane


181

UNCLASSIFIED

,

1

AXIAL POSITION (in.)

Fig. 14.2. Heating in Graphite: Core Center Line at 10 Mw.

Axial Distribution 8.4 in. from


182 Table 14.1. Gamma Heating of INOR i n E R E , Operating a t 10 Mw Heat Source ( 1

Location

Calculation Method Ref e renc e NIcxrCMARE

7

Core can, midplane

2.5 0.2

NIGHTMARE

4

Vessel, midplane

0.2

NIGHTMARE

4

Upper g r i d

2.2

NIGHTMARE

4

Lower g r i d

1.8

NIGHTW

4

Upper head a t f u e l o u t l e t

0.1

2DGH

Rod thimble, midplane

50

I

Table 14.2.

Energy Sources and Deposition i n MSRE Energy (Mev/f i s sion ) Ab sorbed

Source Fuel

Emitted

Fission fragments

168

Graphite

Cell and Shield

Main Core

Peripheral Regions

External

149.5

18.5

0

0

0

Fast neutrons

4.8

0.8

0.1

0

3.5

0.4

Prompt f i s s i o n gammas

7.2

1.9

0.?

0

4.5

0.1

Fission product decay gammas

5.5

0.7

2.2

0.?

1.6

0.3

F i s s i o n product decay b e t a s

8.0

2.7

3 .O

1.3

1.0

0

Capture gammas

6.2

1.2

2.2

0

2.6

0.2

11

0

0

0

0

0

210.7

156.8

26.?

Neutrinos

--

2.o

13.2

1.0


f

183

s

14.2 Graphite Shrinkage

W

At the temperature of the MSRF: 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 to 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 lo-24 per nvt for neutrons with energies greater than 0.1 MeV. The eoefficient for EGCR graphite in the sane temperature range, between 5 and 8 X 1021 nvt of neutrons with energies greater than 0.18 MeV, is about

1.8 X

per nvt.

Also, for EGCR graphite the coefficient for shrink-

age normal to the extrusion axis (t;ransverse shrinkage) is about half that for axial shrinkage. On this basis the coefficients used in the per nvt (E > and 1.0 x analysis described below were 2.06 x 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 maximum axial shrinkage was estimated to be about 0.14 in./yr. Even if the entire moderator structure were shortened by this amount, the effect on reactivity 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 uniform density increase of 0.11% per year. This corresponds to a reactivity


184 i n c r e a s e of 0.08% k / k per year.

The nonuniformity of t h e density change

might increase t h e r e a c t i v i t y e f f e c t by as much as a f a c t o r of 2, b u t t h e r e s u l t a n t e f f e c t would s t i l l be n e g l i g i b l e . A t h i r d e f f e c t of a x i a l c o n t r a c t i o n i s bowing of t h e s t r i n g e r s ,

caused by t h e r a d i a l gradient i n t h e neutron f l u x .

This mechanism l e a d s

t o an increase i n t h e f u e l volume f r a c t i o n i n t h e main p o r t i o n of t h e core and has t h e same e f f e c t as i n c r e a s i n g t h e f u e l density.

The maximum

bowing has been estimated a t 0.1 i n . / ~ r , ~ â&#x20AC;&#x2122; I f it i s assumed t h a t t h e bowing causes a uniform r a d i a l expansion of t h e g r a p h i t e assembly, t h i s r a t e r e p r e s e n t s an equivalent increase i n t h e f u e l density of 3.2$/yr. Since both ends

The a s s o c i a t e d r e a c t i v i t y e f f e c t i s 0.6% k / k per year.

of t h e graphite s t r i n g e r s a r e constrained from r a d i a l motion, uniform expansion of t h e assembly w i l l not occur.

Instead, t h e s t r i n g e r s which

have t h e g r e a t e s t tendency t o bow w i l l be p a r t l y r e s t r a i n e d , while others, i n regions where t h e r a d i a l flux gradient i s smaller, w i l l be bulged outward a t t h e middle.

The n e t r e s u l t will be a much smaller f r a c t i o n a l i n -

crease i n f u e l volume than would be predicted f o r a completely uncons t r a i n e d assembly. Shrinkage of t h e graphite t r a n s v e r s e t o t h e d i r e c t i o n of e x t r u s i o n adds t o t h e e f f e c t produced by bowing.

However, t h i s e f f e c t i s much

smaller because of t h e smaller shrinkage c o e f f i c i e n t . a c t i v i t y e f f e c t was 0.04% &/k

14.3 14.3.1

The c a l c u l a t e d re-

per full-power year of operation.

Entrained Gas i n C i r c u l a t i n g Fuel

Introduction

The nuclear c h a r a c t e r i s t i c s of t h e r e a c t o r a r e a f f e c t e d by t h e presence of e n t r a i n e d helium bubbles, which c i r c u l a t e with t h e f u e l through t h e core.

This gas, introduced through t h e a c t i o n of t h e f u e l

spray r i n g i n t h e f i e 1 c i r c u l a t i n g pump, reduces t h e e f f e c t i v e density

of t h e f u e l and makes t h e fuel-gas mixture compressible.

The most im-

p o r t a n t consequence i s t h a t t h e r e i s a pressure feedback on r e a c t i v i t y , which i s p o s i t i v e f o r r a p i d changes i n pressure and temperature and negative f o r slow changes,


185 14.3.2

I n j e c t i o n and Behavior of Gas

A s m a l l f r a c t i o n of t h e f u e l pump discharge stream (50 gpm out of 1250 gpm) i s d i v e r t e d i n t o a spray r i n g i n t h e gas space i n t h e pump The purpose of t h e spray, o r s t r i p p e r , i s t o provide contact s o

bowl.

t h a t Xe135 i n t h e s a l t can escape i n t o t h e gas space, which i s continuously purged.

S a l t j e t t i n g from holes i n t h e spray r i n g impinges on t h e

surface of t h e l i q u i d pool i n t h e pump bowl with s u f f i c i e n t v e l o c i t y t o c a r r y under considerable q u a n t i t i e s of gas, and some of t h e submerged c

bubbles a r e sweit through t h e p o r t s a t t h e pump s u c t i o n i n t o t h e main c i r c u l a t i n g stream of f u e l .

A steady s t a t e i s reached when t h e helium

concentration i n t h e c i r c u l a t i n g stream has increased t o t h e point where f

l o s s of helium through t h e s t r i p p e r flow equals t h e rate of i n j e c t i o n . A t steady s t a t e t h e volume f r a c t i o n of gas i n t h e c i r c u l a t i n g stream

v a r i e s around t h e loop with t h e inverse of t h e l o c a l pressure, which changes with elevation, velocity, and head l o s s e s .

Pump loop t e s t s

showed a volume f r a c t i o n of 1 . 7 t o 2.0% gas a t t h e pump suction, which i s normally a t 21 p s i a i n t h e r e a c t o r .

I n t h e core, where t h e pressure

ranges from 39.4 p s i a a t t h e lower ends of t h e fuel channels t o 33.5 p s i a

a t t h e upper ends, t h e equivalent volume f r a c t i o n of gas i s about 1.2%. For r a p i d changes i n core o r l o o p pressure, t h e mass r a t i o of gas t o l i q u i d remains p r a c t i c a l l y constant and t h e volume f r a c t i o n o f gas i n t h e core decreases with i n c r e a s i n g pressure.

For very slow i n c r e a s e s i n loop

pressure t h e volume of gas i n t h e core increases, because t h e r a t i o of absolute pressures between t h e core and pump s u c t i o n i s reduced.

(The

s t e a d y - s t a t e volume f r a c t i o n a t t h e pump s u c t i o n i s presumably independent of p r e s s u r e . )

14.3.3

E f f e c t s on R e a c t i v i t y

The presence of t h e gas i n t h e core has two e f f e c t s on r e a c t i v i t y . F i r s t , by making t h e f u e l compressible, t h e gas introduces a pressure c o e f f i c i e n t of f u e l density o r r e a c t i v i t y .

Secondly, t h e presence of t h e

gas modifies t h e f u e l temperature c o e f f i c i e n t of r e a c t i v i t y , because t h e density of t h e s a l t - g a s mixture changes with temperature a t a d i f f e r e n t U

r a t e from t h e density of t h e s a l t alone.


186 A d e t a i l e d d e s c r i p t i o n of t h e r e a c t i v i t y e f f e c t s of e n t r a i n e d gas involves t h e following q u a n t i t i e s : f

Volume f r a c t i o n of gas i n f u e l stream a t p

P

Absolute pressure i n t h e core

PS

p suction

Absolute pressure a t t h e pwnp s u c t i o n

T

Temperature of t h e f u e l i n t h e core

e

Volume f r a c t i o n of gas i n fuel i n core Density of l i q u i d s a l t containing no gas Density of t h e f u e l s a l t r g a s mixture Temperature c o e f f i c i e n t of s a l t density

Fuel density c o e f f i c i e n t of r e a c t i v i t y -7

Contribution t o f u e l temperature c o e f f i c i e n t of r e a c t i v i t y due t o changes i n neutron energies and microscopic c r o s s s e c t i o n s

The core pressure i s r e l a t e d t o t h e r e a c t i v i t y through t h e mean f u e l density i n t h e core:

(14.1)

The fuel temperature a f f e c t s t h e r e a c t i v i t y through t h e f u e l density and

a l s o through i t s e f f e c t on thermal neutron energy and microscopic c r o s s sections :

(14.2)

The mean density of t h e f u e l i s given by Pf

= (1-

e)pR

.

(14.3)

(The gas adds p r a c t i c a l l y nothing t o t h e f u e l density.) If t h e r e i s no gas i n t h e core, 8 = 0, pf pressure on density i s n e g l i g i b l e .

-

P i > and t h e e f f e c t of

With no gas i n t h e f i e l ,

a


n

187

4

â&#x20AC;&#x2DC; 6

-

Rapid Changes.

During r a p i d changes i n pressure and temperature,

t h e mass r a t i o of gas t o l i q u i d remains p r a c t i c a l l y constant. (The change i n t h e amount of dissolved helium i s n e g l i g i b l e compared with t h e amount I n t h i s case pf i s approximated by

i n t h e gas phase.)

(14.4)

where t h e s u b s c r i p t 0 r e f e r s t o i n i t i a l conditions. b

I f Eq.

(14.4)i s

used t o o b t a i n t h e p a r t i a l d e r i v a t i v e s of pf required i n (14.1) and (14.2), t h e s e equations become

B[1

1 ak

zap=

- a(T -

ioe0)-1 To p

- To) +

[1 - a ( T

To)] P

(14.5)

T Po

and

A t t h e i n i t i a l p o i n t , when P =

PO and T

1 ak

--...--

k dP

=

To,

Po

(14.7)

and

(14.8) These equations show t h a t for r a p i d changes t h e r e i s a p o s i t i v e pressure c o e f f i c i e n t of r e a c t i v i t y and t h a t t h e magnitude of t h e negative temperat u r e c o e f f i c i e n t of r e a c t i v i t y i s increased because t h e gas expands more than t h e l i q u i d ( l / T o i s g r e a t e r t h a n Slow Changes.

- During

a).

gradual changes i n f u e l loop temperatures and

pressure, f w i l l probably remain equal t o t h e volume f r a c t i o n i n t h e pump


188 bowl just outside the ports, which should be constant. The core mean pressure is 15.6 psi.higherthan the pump suction pressure; therefore

PS

15.6

P

+- 15.6f

pf = (.-f

),

(14.9)

(14.10)

If the partial derivatives of p f required in E q s . (14.1)and (14.2) are obtained from Eq. (14.10),E q s . (14.1) and (14.2) become ( 14.11)

and ( 14.12)

Thus for slow changes, there is a negative pressure coefficient of reactivity and the temperature coefficient is the same as if there were no entrained gas. Msgnitude.

-

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 converts fluctuations in core outlet pressure drop to reactivity perturbations.

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 See 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 9, and the net reactivity feedback from pressure and temperature is negative.

1


189 '4

Table 14.3.

Reactivity Coefficients with Entrained Gas in Core"

Fuel density coefficient of reactivity, f3

Fuel A

Fuel B

Fuel C

0.190

0.345

0.182

WE (째F)'ll

-2.24 x

Y[ ("F)"]

loW5 -4.07

x

-2.15 x

-0.79 x

-0.90 x

-1.13 x

-3.03 x

-4.97 x

-3.28 x

-3.14 x

-5.17 x

-3.39 x 10-~

Fuel tempera,ure coeffic,znt of reactivity [

No gas or slow changes with gas Rapid changes with gas Pressure coefficient of reactivity (psi-') Slow changes with gas Rapid changes with gas

-3.8 x io+ 6.3 x

-7.0 x 10-~ -3.7 x 10-5 +ii.4 x 10-5 +6.0 x 10-5

a Evaluated at T = 1200째F, P = 36.5 psia (pump bowl pressure 5 psig), 8 = 0.012, and a = 1.2 x 10-4(0F)-1.

14.4 Choice of Poison Material There is available a wide variety of materials that have been used as neutron absorbers in reactor control rods.

The choice of poison material for a given reactor application must be based primarily on the overall suitability 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 f o r use in the MSRE was boron because of its low cost, ready availability, and high neutron-capture cross section in both the thermal and epithermal 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 (BgC) was tentatively selected as the poison material, to ensure long rod life. This material could easily be fabricated in the desired shape and also have the stability against thermal decomposition required for use at reactor temperatures. However, BgC is highly abrasive and oxidizes in air at high temperature. These properties made it necessary to consider complete canning of the poison elements. Essentially all of the poisoning by B4C is due to neutron absorptions in B1',

The alpha particle

where the predominant reaction is Bl0(n,a)Li7.

ends as a helium atom, so that each neutron absorption results in the replacement 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. However, the difficulty is compounded, 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 increases with increasing neutron exposure. ing cannot be predicted reliably.

In addition, the amount escap-

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

MSm

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 B4C 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 gadolinium, fabricated in ceramic cylinders containing 70 w t

%

Gd203 and 30 w t

%

A1203. This material has satisfactory nuclear properties and was selected over other, equally suitable materials on the basis of its moderate cost,

ready availability, 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

4


. 191 cross section for natural gadolinium is 46,600 barns. However, the neutron-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 neutrons (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 gadolinium is required for "blackness" to thermal neutrons.

However, this same

property results in very rapid burnout of a rod that is initially just c

barely "black." Therefore, such a rod must have built into it sufficient gadolinium to ensure that it remains "black1'throughout its required lifetime.

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 associa t e d with i t s exposure t o neutron bombardment.

As a r e s u l t t h i s material

may be expected to have reasonable 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

a z o 3 than with B4C,

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 criticality in the core is not critical in the drain tanks or the storage tank. W

This is so because there is much less moderator in the tanks than in the


192 core and the tanks are of smaller diameter than the core, and these effects 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 soae conditions it may be desirable to allow the salt to solidify in a tank and cool to ambient temperature. Simply cooling the salt causes the reactivity 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 central 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 2OoC, for various degrees for uranium ~egregation.~~ 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 unsegregated 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 sane 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

- .

i n a sphere surrounded by a l a y e r of uranium-free s a l t .

The concentra-

t i o n s of t h e other components were assumed t o be uniform i n both t h e fueled and unfueled portions. The results of t h e calculations a r e shown graphically f o r t h e storage tank and a f u e l d r a i n tank i n Figs. 14.3 and 14.4, respectively.

If all

other conditions a r e equal, t h e r e a c t i v i t y i s higher i n t h e storage t a n k than i n a d r a i n tank, because of t h e INOR coolant thimbles i n t h e l a t t e r . I n t h e r e f l e c t e d cases, a p r a c t i c a l l y i n f i n i t e ( 5 0 cm) H2O r e f l e c t o r w a s since the effective refleceffâ&#x20AC;&#x2122; t o r thickness must be less because of t h e furnace. The amount of overassumed.

This gives an overestimate of k

estimation i s not great, however, as shown by t h e comparison of t h e curves t

f o r f u e l B i n t h e storage tank, bare and r e f l e c t e d .

I n one c a l c u l a t i o n

t h e s a l t density w a s assumed t o be 95s of t h e upper l i m i t used i n t h e other c a l c u l a t i o n s .

This w a s f o r t h e case of f u e l B, concentrated by a

f a c t o r of 10 i n t h e r e f l e c t e d storage tank, and gave a k pared with 1.024 f o r t h e higher density. pected f o r t h e other cases.

of 1.003, comeff Similar reductions m i g h t be ex-


194

Fig. 14.3. E f f e c t of Uranium Segregation on C r i t i c a l i t y i n Fuel Sto'rage Tank a t 2O0C.

0


195

FUEL c, REFLECTED

FUEL B, REFLECTED

0

1

2

4

6

8

10

URANIUM C O N C ~ T I O NFACTOR

Fig. 14.4. Effect of Uranium Segregation on Criticality in Fuel Drain Tank at 20째C.


. 196 15.

FEFEENCES

1. C. L. Davis, J. M. Bookston, and B. E. Smith, "GTJU-I1 - A Multigroup One-Dimensional Diff'usion Program f o r t h e IEM-704," USAEC Report GMR-101, General Motors, November 12, 1957. 2. D. J. Hughes and H. B. Schwartz, "Neutron Cross Sections," USAEC Report BNL-325, Second Edition, Brookhaven National Laboratory, J u l y 1958. 3. C. W. Nestor, Jr., "Multigroup Neutron Cross Sections," USAEC Report ORNL CF-60-3-35, Oak Ridge National Laboratory, March 1960. 4. Oak Ridge National Laboratory, "MSW Quart. Progr. Rept. J u l y 31, 1960," USAEC Report ORNL-3014, pp. 41-45. 5. C. W. Nestor, Jr., "A Computational Survey of Some GraphiteModerated Molten S a l t Reactors," USAEC Report ORNL CF-61-3-98, Oak Ridge National Laboratory, March 15, 1961. 6. Oak R i d g e National Laboratory, "MSW Progr. Rept. Aug. 1, 1960 t o Feb. 28, 1961,'' USAEC Report OIWL-3122, p. 70. 7. Oak Ridge National Laboratory, "MSW Progr. Rept. Mar. 1 t o Aug. 31, 1961," USAEC Report Om-3215, pp. 83-49. 8. G. F. Kuncir, "A Program f o r t h e Calculation of Resonance Integrals," USAEC Report GA-2525, General Atomic, August 28, 1961. 9. G. I. &ll, "A Simple Treatment for E f f e c t i v e Resonance Absorpt i o n Cross Sections i n Dense Lattices," Nucl. Sei. E%., 5 ( 2 ) : 138-139 (February 1959). A Consistent PI M u l t i 10. G. D. Joanou and J. S. Dudek, "GAM-1: group Code f o r t h e Calculation of Fast Neutron Spectra and Multigroup Constants," USAEC Report GA-1850, General Atomic, June 28, 1961. 11. H. C. Honeck, "THERMOS: A Thermalization Transport Theory Code f o r Reactor L a t t i c e Calculations," USAEC Report BNL-5826, Brookhaven Nat i o n a l Laboratory, September 1961. 12. D. E. Parks, J. R. Beyster, and N. F. Wikner, "Thermal Neutron Spectra i n Graphite," Nucl. Sei. Eng., 1 3 ( 4 ) : 306-324 (August 1962). 13. James Replogle, "MODRIC: A One Dimensional Neutron Diff'usion Code for t h e I ~ - 7 0 9 0 , " USAEC Report K-1520, Union Carbide Nuclear Company, September 6, 1962. 14. T. B. Fowler and M. L. Tobias, "EQUIPXEE-3: A Two-Dimensional, Two-Group, Neutron Diff'usion Code for t h e IEM-7090 Computer," USAEC Report ORNL-3199, Oak Ridge National Laboratory, February 7, 1962. 15. C. W. Nestor, Jr., "EQUIPOISE 3A," USAEC Report ORNL-3199 Addendum, Oak Ridge National Laboratory, June 6, 1962. 16. B. E. Prince and J. R. Engel, "Temperature and Reactivity Coe f f i c i e n t Averaging i n t h e MSRE," USAEC Report ORNL !IN-379, Oak Ridge N a t i o n a l Laboratory, October 15, 1962. 17. G. H. Kear and M. H. Ruderman, "An Analysis of Methods of Cont r o l Rod Theory and Comparisons with Experiment," USAEC Report GEAP-3937, General E l e c t r i c , May 27, 1962. 18. B. E. Prince, "Control Rod Worth i n t h e MSRE," USAEC Report om m--, Oak Ridge National Laboratory ( i n preparation). 19. R. V. Meghreblian and D. K. Holmes, Reactor Analysis, p. 656, McGraw-Hill, New York, 1960. 20. S. A. Kushneriuk and K. Jirlow, "The Linear Extrapolation Length and Blackness for I n f i n i t e Cylinders," J. Nucl. Energy, Pts. A and B, 16 ( 9 ) : 464-466 (September 1962).

A

--

4

Y


197 21. J. R. Engel and P. N. Haubenreich, "Temperatures i n t h e MSRE Core During Steady-State Power Operation," USAEC Report ORNL TM-378, Oak Ridge National Laboratory, November 5, 1962. 22. H. F. Poppendiek and L. D. Palmer, "Forced Convection Heat Transfer i n Pipes with Volume Heat Sources Within t h e Fluids," USAEC Rep o r t ORNL-1395, Oak Ridge National Laboratory, December 2, 1952. 23. H. F. Poppendiek and L. D. Palmer, "Forced Convection Heat Transfer Between P a r a l l e l P l a t e s and i n Annuli with Volume Heat Sources Within the Fluids," USAEC Report ORNL-1701, Oak Ridge National Laboratory, May 21, 1954. 24. P. N. Haubenreich, "Prediction of Effective Yields of Delayed Neutrons i n MSRE," USAEC Report ORNL TM-380, Oak Ridge National Laboratory, October 13, 1962. 25. Sidney Krasik, p. 8-4 i n Nuclear Engineering Handbook, e d i t e d by Harold Etherington, McGraw-Hill, New York, 1958. 26. H. Goldstein, Fundamental Aspects of Reactor Shielding, p. 52, Addison-Wesley, Reading, Mass., 1959. 27. H. S. Weber, Oak Ridge National Laboratory, unpublished data. 28. B. E. Prince, "Methods of Computing the Reactivity E f f e c t s of Distributed Xenon, Graphite Shrinkage, and Fuel Soakup i n t h e MSRE," USAEC Report ORNL TM-496, Oak Ridge National Laboratory ( i n preparation). 29. E. A. Nephew, 11 Thermal and Resonance Absorption Cross Sections of the U233, U235, and Pu239Fission Products," USAEC Report ORNL-2869, Oak Ridge National Laboratory, January 18, 1960. 30. T. R. England, "Time-Dependent Fission-Product Thermal and Resonance Absorption Cross Sections," USAEC Report WAPD-TM-333, Bettis Atomic Power Laboratory, November 1962. 31. C. W. Nestor, "A Simple Formula f o r Computing Fission Product Thermal Cross Sections and Resonance Integrals," USAEC Report ORNL CF-604-30, Oak Ridge National Laboratory, April 7, 1960. 32. D. R. Harris, "Calculation of t h e Background Neutron Source i n New, Uranium-Fueled Reactors," USAEC Report WAPD-TbI-220, Bettis Atomic Power Laboratory, March 1960. 33. P. N. Haubenreich, "Inherent Neutron Sources i n Clean MSRE Fuel Salt," USAEC Report ORNL TM-611, Oak Ridge National Laboratory, August 27, 1963. 34. J. 0. Blomeke and M. F. Todd, "Uranium-235 Fission-Product Production a s a Function of Thermal Neutron F l u , I r r a d i a t i o n Time, and Decay Time," USAEC Report Om-2127, Oak Ridge National Laboratory, A u g u s t 19, 1957. 35. P. N. Haubenreich, J. R. Enge1,and B. E. Prince, "MSHE Neutron Oak Ridge National LaboSource Requirements," USAEC Report ORNL TM--, r a t o r y ( i n preparation) An IB4 7090 Program f o r t h e 36. C. W. Nestor, Jr., "MURGATROYD Analysis of t h e Kinetics of t h e MSRE," USAEC Report ORNL TM-203, Oak Ridge National Laboratory, April 6, 1962. 37. C. W. Nestor, Jr., "ZORCH - An 1Bl 7090 Program f o r the Analysis of Simulated MSRE Power Transients with a Simplified Space-Dependent K i n e t i c s Model," USAEC Report ORNL TM-345, Oak Ridge National Laboratory, September 18, 1962. 38. P. R. Kasten, "Operational Safety of t h e Homogeneous Reactor Test," 'JSAEC Report ORNL-2088, Oak Ridge National Laboratory, J u l y 3,

.

1956.

-


198 39. P. N. Haubenreich and J. R. Engel, "Safety Calculations f o r MSRE," USAEC Report ORNL TM-251, Oak Ridge National Laboratory, May 15, 1962.

40. J. R. Engel, P. N. Haubenreich, and S. J. Ball, "Analysis of F i l l i n g Accidents i n MSRE," USAEC Report ORNL TM-497, Oak Ridge National Laboratory ( i n preparation). 41. D. W. Vroom, "Preliminary MSRE Gamma Ray Source and Biological Shielding Survey," USAEC Report ORNL CF-61-4-97,Oak Ridge National Laboratory, April 28, 1961. 42. T. Rockwell, Reactor Shielding Design Manual, Van Nostrand, New York, 1956. 43. H. Goldstein, Fundamental Aspects of Reactor Shielding, p. 60, Addison-Wesley, Reading, Mass., 1959. 44. D. J. Hughes and R. B. Schwartz, "Neutron Cross Sections," USAEC Report BNL-325, Brookhaven National Laboratory, July 1, 1958. 45. C. W. Nestor, Jr., Oak Ridge National Laboratory, unpublished data, May 1961. 46. E. P. Blizard, "Neutron Radiation Shielding," OIWL publication for ORSORT text, September 17, 1956. 47. E. Troubetzkoy and H. Goldstein, "Gamma Rays from Thermal Neut r o n Capture," Nucleonics, 18(ll): 171-173 (November 1960) 4.8. P. N. Haubenreich and B. E. Prince, Oak Ridge National Laboratory, personal communication t o H. C. Claiborne, Oak Ridge National Laboratory. 49. M. L. Tobias, D. R. Vondy, and Marjorie P. Lietzke, "Nightmare An IE4 7090 Code for t h e Calculation of Gamma Heating i n Cylindrical G e ometry," USAEC Report ORNL-3198, Oak Ridge National Laboratory, February

.

9, 1962. 50, Oak Ridge National Laboratory, "MSRP Semiann. Progr. Rept. Feb. 28, 1962," USAEC Report Om-3282, pp. 68-71. 51. S. E. Moore, Oak Ridge National Laboratory, personal communicat i o n t o R. B. Briggs, Oak Ridge National L a b o r a t o n (April 26, 1962). 52. J. R. Engel and B. E. Prince, " C r i t i c a l i t y Factors i n MSRE Fuel Storage and Drain Tanks," USAEC Report ORNL TM--, Laboratory ( i n preparation).

Oak Ridge National


199

ORNL TM-730 INTEFUiAL DISTRIBUTION 1-2. Central Research Library 3-4. ORNL - Y - 1 2 Technical Library Document Reference Section 5-6. Reactor Division Library 7-9. Laboratory Records Department 10. Laboratory Records, ORNL R.C. 11. R. G. Affel 12. L. G. Alexander 13. C. F. Baes 14. S. E. Beall 15. M. Bender 16. E. S. B e t t i s 17. F. F. Blankenship 18. R. Blumberg 19. R. B. Briggs 20. S. Cantor 21. H. C. Claiborne 22. J. A. Conlin 23. W. H. Cook 24. L. T. Corbin 25. G. A. C r i s t y 26. J. L. Crowley 27. J. H. DeVm 28. S. J. Ditto 29. R. G. Donnelly 30. N e E. DUnWOOdy 31. J. R. Engel 32. E. P. Epler 33. J. H Frye 34. R. B. Gallaher 35. W. R. Grimes 36. A. G. Grindell 37. R. H. Guymon 38. P. H. Harley 39-48. P. N. Haubenreich 49. E. C. Hise 50. P. Pa H O l Z 51. J. P. J a r v i s 52. R. J. Ked1 53. S. S. K i r s l i s

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