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ORNL- TM- 251 COPY NO. DATE
-
-
9'
m y 13, 1962
SAl?ETY CALCULATIONS FOR MSâ‚ŹU3
P. N. Haubenreich J. R. Ehgel
ABSTRACT
a
A number of conceivable r e a c t i v i t y accidents were analyzed, using conservatively pessimistic assumptions and approximations, t o permit evaluation of reactor safety. Most of t h e calculations, which are described i n d e t a i l , were performed by a d i g i t a l k i n e t i c s program, MJRGATROYD. Some analog analyses were a l s o m a d e .
None of t h e accidents which were analyzed lead t o catastrophic f a i l u r e of the reactor, which i s t h e primary consideration. Some i n t e r n a l damage t o t h e reactor f'rom undesirably high teaperatures could result f'rm extreme cold-slug accidents, premature c r i t i c a l i t y during f i l l i n g , or uncontrolled rod withdrawal. Each of these accidents could happen only by compounded failure of protective devices, and i n each case there e x i s t means of e f f e c t i v e corrective action independent of the primary protection, so t h a t dimage i s unlikely. The calculated responm t o a r b i t r a r y ramp and s t e p additions of r e a c t i v i t y show t h a t deunaging pressures could occur only i f ' t h e add i t i o n i s t h e e q u i v a e n t of a s t e p of about l$ dk/k o r greater.
. NOTICE This document contains information of a preliminary nature and was prepared primarily for internal use at the Oak Ridge National Laboratory. It i s subject t o revision or correction and therefore does not represent a final report. The information i s not t o be abstracted, reprinted or otherwise given public dissemination without the approval of the ORNL patent branch, Legal and Information Control Department.
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i
CONTFJTS
Page 4
ABSTRACT INTRODUCTION
3
MSRE CHARACTERISTICS
5
RESULTS OF CREDIBLE REACTIVITY ACCIDENTS
6
- Fuel Pump Failure C a s e 2 - C o l d Slug A c c i d e n t C a s e 3 - Filling A c c i d e n t C a s e 4 - Loss o f G r a p h i t e f’rorn C e r e Case 1
Case
5
Case 6
- Fuel
6
a 13 21
Additions
- Uncontrolled
22
Rod Withdrawal
24
RESPONSE TO ARBITRARY ADDITIONS OF REACTIVITY
27
Ramp A d d i t i o n s
27
Step A d d i t i o n s
35
‘C
DISCUSSION APPENDIX I: AP-EENDIX 11: APPENDIX 111:
35 DELAYED NEUTRONS
40
CONTROL RODS
4.1
ANALYSIS OF COLD-SLUG ACCIDENTS
118
APPENDIX IV: COMPOSITION O F RESIDUAL L I Q U I D AFilER PARTIAL FREEZING OF MSRE FUEL SALT
.
APPENDIX V: CRITICALITY CALCULATIONS FOR F I L L I N G ACCIDENTS
60
APPENDIX V I :
65
REACTIVITY WORTH OF L T C R E ” T S
OF URANIUM
ii
LIST OF FIGURES
Title
1 2
Page
Power and Temperatures Following Fuel Aunp Power Failure. No Corrective Action.
7
Power and Temperatures Following Fuel RMp Power Failure. Radiator Doors Closed and Control Rods Driven i n a t 0.4 in./sec after Failure.
9
Powers During Cold Slug Accidents.
11
System Behavior f o r Cold Slugs a t 900°F
12
Liquid Composition Resulting from P a r t i a l Freezing of Fuel S a l t i n Drain T a k .
14
-
6
Control Rod Worth VS. Position.
17
7
Fuel Level Required f o r C r i t i c a l i t y . (Fuel Concentration Ehhanced by Freezing in Drain Tank.)
18
8
Temperature and Power During F i l l i n g Accident.
20
9
Response of MSRZ t o 0.15% hk/k Step.
23
Effects of 120 g of U235 Noving Through t h e Core i n a Horizontally Distributed Slug.
25
Transients Resulting from S W t a n e o u s Withdrawal of 3 Control Rods
26
Response t o Ramp of I$ 6k/k i n 30 sec Beginning a t 10 Mw.
28
b
10
11 12
13
16
17
Response t o Ramps of 1, Beginning a t 10 Mw.
1.5,
and 2% 6k/k i n 10 sec, 29
Power Response t o Ramps of 2% 6k/k i n 1 0 sec Beginning a t 10’5, 10-3, and 10 Mw.
31
Maximum Power Reached i n I n i t i a l Excursion f o r Ramp Reactivity Additions.
32
Pressure and Fuel Mean Temperature Response t o Ram s of 2$ 6k/k i n 10 sec, Beginning a t 10-5, 10-3, and 1 0 Mw.
MaxirmUn Core Pressure Reached i n I n i t i a l Surge Caused by Ramp Reactivity Additions
. 33
t
34
LIST OF FIGURES
- cont’d
Title -
Page
Peak Fuel Mean Temperatures vs. Total Reactivity Added by Ramps of Various Durations
36
Power Transients from Step Increases i n Reactivity I n i t i a l Power: 1 0 Mw
37
20
Response of MSRE t o 0.338$ 6k/k Step.
38
A-1
Fractional Rod Worth MSRE Core
44
19
A-2
VS.
Deptih of Insertion i n
Differentia3 Rod Worth (Fraction of Total per Inch) vs. Rod Position
45
A-3
Reactivity Change Due t o Control Rod Insertion.
47
A-4
mcess Reactivity Due t o Replacing Part of Fuel i n 1200° Core with Denser Fuel. ( F i l l from bottom up.)
49
Reactivity Transients Caused by Passage of Cold Slugs Through MSRE Core a t 1200 gpm.
50
44-5 A-6
A-7
A-8
MURGATROYD Results f o r Reactivit Transient Corre900 F Cold Slugs. sponding t o 20 and 30 e”,
8
Mean Temperatures of Fuel and Graphite i n Core During Passage of Cold Slugs I n i t i a l l y a t 900°F with no Nuclear Heat Generation.
52
53
Temperature Profiles Along Hottest f i e 1 Channel at Various Times During Passage of 20 rt3,
gOO°F Slug.
55
%
A-9
Power and Fuel Temperatures f o r 20 f’t,
A-10
Composition of Fuel S a l t Resulting from P a r t i a l Freezing i n Fuel Drain Tank
59
A-11
Effective Multiplication During F i l l i n g Accident
61
A-12
Effective Multiplication During F i l l i n g Accident
63
A-13
Height of S a l t i n Core vs. Time
64
A-14
Reactivity Worth of 1 g of U235 i n MSRE Core.
66
A-1 5
Reactivity Transient Caused by LOO g of U235 Unif G i - i i d j - Distributed i n a XoiqiZoiital mane Which Moves Through t h e Core with t h e Circulating Fuel.
67
gOO°F Slug
3 SAFETY CALCULATIONS FOR E R E P. N. Haubenreich J. R. &gel INTRODUCTION
The work reported here was done t o provide information f o r t h e sec-
ond addendum t o t h e MSRE Preliminary Hazards Report,'
and consists of t h e
analysis of reactor behavior i n c e r t a i n potentially hazardous s i t u a t i o n s . The purpose of t h e present report i s t o describe t h e procedures which were used and t o give some results i n f'uller d e t a i l . Incidents which were analyzed included:
f u e l pump f a i l u r e a t high
power, "cold-slug" accidents, premature c r i t i c a l i t y during core f i l l i n g , Sreakage of a graphite stringer, passage of a concentrated f b e l slug and runaway rod withdrawal.
The response of t h e system t o a r b i t r a r y s t e p and
r a p additions of r e a c t i v i t y was a l s o computed. and r e s u l t s a r e given i n t h e body of t h e r e p o r t ,
Each case i s described
*
Details of t h e calcu-
&&ions and some other pertinent information a r e given i n appendixes. An analog computer was used t o analyze t h e f u e l pump stoppage.
All
other cases were analyzed using MURGATROYD, a machine program developed by fiestor* f o r d i g i t a l computation of MSRE kinetic behavior.
Nestor has
recently shown t h a t MURGATROYD predicts l a r g e r power excursions f o r a given imposed r e a c t i v i t y t r a n s i e n t than would be calculated i f t h e core mean temperatures were r e l a t e d more r e a l i s t i c a l l y t o i n l e t temperature a d power. (The same coment may apply t o t h e s w a t o r r e s u l t s . ) A new program which w i l l incorporate temperature d i s t r i b u t i o n s and fluxweighted mean temperatures i s being developed.
When t h i s i s ready, some
I
Molten S a l t Reactor Experiment Preliminary Hazards Report, ORNL CF-61-2-46 Addendum No. 2 (May 8, 1962).
ii
The conditions and r e s u l t s reported here are f o r t h e "first round" of t h e analysis. Same changes were subsequently made i n rod worth and deployment and some of t h e incidents were reanalyzed, by t h e procedures described here, i n l i g h t of t h e new conditions. The r e s u l t s of t h e latest. calculations appear i n reference 1.
2C. W. Nestor, MURGATROYD, an IBM-7090 Program f o r t h e Analysis of t h e
Kinetics of t h e MSRE, ORNL-!T!M-203
(April
6, 1962).
o f t h e incidents described i n t h i s report w i l l be analyzed again,
From
4
t h e standpoint of reactor s a f e t y evaluation, however, it i s believed t h a t t h e calculations which have already been done a r e adequate f o r t h e cases stuuied, p a r t i c u l a r l y since the r e s u l t s obtained indicated reasonably safe reactor operation.
4
5 MSRE CHARACTERISTICS
Quantities which a r e important i n the kinetic behavior of the MSRE
are l i s t e d i n Table 1; the values shown were used i n the kinetics ca1.c~lat.ions.
Table 1. MSRE Characteristics Affecting Kinetic Behavior
2.9
Prompt -neutron 1i f e t h e
Delayed neutron fraction:
0.0064
static
: circulating Residence times:
0.0034
7.3 see 17.3 sec
core external t o core
C r i t i c a l mass:
16.6 kg U235 56,o kg u 23.5
core t o t a l fuel
Mass coefficient of r e a c t i v i t y (6k/k)/i6M/M)
Temperature coefficients of reactivity:
P Fraction of heat generation:
Core heat capacity:
sc?c
0.28
i o-5
fuel
-2.8 x
graphit e
-6.0 x 10
-5 0F-1
i n fuel
0.94
i n graphite
0.06
3.53 IvIw-sec/*F 1.47 I.llw/sec/%
graphite fie1
Graphite -to-fbel heat t r a n s f e r
0.020 ~dw/'F
Extremely rapid increases i n core power cause a rise i n core pressure due t o i n e r t i a and f r i c t i o n i n t h e l i n e t o t h e pump and due t o compresslon
of the gas i n t h e pump bowl. surges a r e given i n Table 2.
The q u a n t i t i e s affecting t h e core pressure
6 Table 2.
MSRE Characteristics Affecting Core Pressure Transients
Fuel volumetric expansion coefficient
,3 149 l b / f t 3 1.26 x LO -4
Length of l i n e t o pump bowl
16 ft
Cross-sectional area of l i n e
0.139 f t 2
Friction loss i n l i n e
1.3 velocity heads 2.5 f t 3
Core volume
20
Fuel density
Volume of gas i n pump bowl
OF'1
RESULTS OF CREDIBLE REACTIVITY ACCIDmTS
Six kinds of conceivable accidents or malfunctions involving undesirable additions of r e a c t i v i t y were analyzed.
The sections which follolj
describe each condition and t h e results of t h e analysis.
Methods of a n d -
y s i s a r e covered i n d e t a i l i n t h e Appendices. Case 1
- Fuel
Pump Failure
If the fie1 circulation i s interrupted while t h e reactor i s c r i t i c a l ,
t h e increase i n the e f f e c t i v e delayed neutron fraction will cause t h e c r i t i c a l temperature t o increase.
If appreciable power i s being extracted
by t h e radiator, the temperature of the coolant salt w i l l decrease
hi-
nediately following t h e cessation of f'uel flow through t h e heat exchanger. The behavior of t h e reactor pover and temperature i n the event of a
PJel pump stoppage with t h e reactor operating a t high power was explored by Burke on t h e Analog F a c i l i t y on February 1, 1962.
Figure 1 shows simulator r e s u l t s for the case of a f'uel pump power f a i l u r e while t h e reactor i s a t 1 0 Mw, with no corrective action and t h e coolant pump continuing t o run.
Although the mean temperature of the f u e l
0
i n the core increased 120 F, the secondary salt temperatures decreased, rcaching the freezing point a t the radiator o u t l e t i n less than two minutes. (The behavior a t lower i n i t i a l powers was similar, but t h e secondary salt
did not cool t o the freezing point i f t h e i n i t i a l ' p o w e r extraction was l e s s than 7.5 Mw.)
8
8 It i s c l e a r t h a t t h e occurrence of a f'uel-pump power f a i l u r e with the reactor a t high power requires t h a t steps t o reduce the heat removal from t h e r a d i a t o r be taken quickly.
Control rod action t o reduce r e a c t i v i t y
i s necessary t o prevent an undesirably l a r g e r i s e i n f'uel temperature i n
the core.
Results were a l s o obtained considering control-rod movemeit
and changes i n heat removal by the radiator. Figure 2 shows t h e results of a simuLated fuel pump f a i l u r e a t t h e same i n i t i a l . conditions as Fig. 1, but with corrective action. a r t e r the p
One second
p power w a s cut (coast8own was simulated, s o t h e f l u i d flo-&
was not assumed t o stop instantaneously), a negative r e a c t i v i t y ramp was s t a r t e d t o simulate insertion of the control rods.
This rate w a s -0.0755
per second, corresponding t o all three rods moving i n a t about 0.4 i;i./sec. (See page 46 for discussion of rod worth, speed and normal positions. ) Beginning 3 seconds a f t e r t h e pump power f a i l u r e , t h e simuLated heat r e moval from t h e r a d i a t o r tubes was reduced as indicated by t h e r a d i a t o r
i n l e t and o u t l e t temperature i n Fig. 2.
It i s believed t h a t t h e r a d i a t o r
doors can be closed t o reduce heat extraction faster than t h a t associated with Fig. 2 conditions.
i n t h i s case, t h e r a d i a t o r temperature dropped
very l i t t l e , and t h e f u e l mean temperature rose 30째F.
With t h e same
r
r a d i a t o r control but w i t h a f a s t e r negative r e a c t i v i t y ramp of -O.l?$/sec, t h e power dropped more rapidly and t h e f u e l mean temperature rose only
i8'F. Case 2
- Cold
Slug Accident
Because the "cold-slug'' accident could not be adequately simulated on the analog computer, t h e consequences of several accidents of varying severity were estimated by c r i t i c a l i t y and kinetics calculations on t h e
IBM-7090. (Details of the procedures and intermediate r e s u l t s are given i n the Appendix, page 48. ) The accidents which were analyzed consisted of pumping 10, 20, and 30 ft3 o f f u e l a t 900, 1000, and llOO째F i n t o the core a t a rate of b
1.200 gpm.
In each case t h e core was assumed t o be i n i t i a l l y c r i t i c a l a t
120OoF, with 1 0 kw of f i s s i o n power being generated, and with no circu-
lation of fuel.
The loss of delayed neutron precursors which accompiznies
the s t a r t of circulation was t r e a t e d as a s t e p change i n r e a c t i v i t y of'
Q
n U v
IT
W
!x 3
2 d UI
2 il
w
L
z
w
om-LR-DW~:. 70052
10
-0.30% 6k/k, which occurred simultaneously with t h e entry of t h e f i r s t
ur
cold f u e l i n t o t h e core.
I n t h e first cases which were calculated, no control rod action w a s taken.
The calculated f i s s i o n powersfollowing t h e entry of the various
cold slugs i n t o t h e core a r e shown i n Fig. 3.
The i n i t i a l drop i n each
case w a s due t o t h e assumed s t e p decrease i n r e a c t i v i t y which takes the reactor s u b c r i t i c a l .
I n t h e case of t h e llOO째F slugs, t h e e f f e c t of t h e
denser f u e l was not enough t o bring t h e reactor back t o c r i t i c a l .
Li sme
of t h e other cases t h e reactor does become supercriticaJ. but before t h e power has r i s e n very high, hot fuel (at 1200'F)
begins t o enter t h e ?ore
behind t h e i n i t i a l slug and the reactor becomes s u b c r i t i c a l again. core t r a n s i t time i s 7.3 see. the 2O-f'b3
The
10-n~ slug passes out i n U,O
slug i n 14.6 see and the 30-ft3 slug i n 18.2 see.)
(The see;
For t h e
20- and 30-f't3 slugs a t 900째F, considerable excess r e a c t i v i t y was added
quickly, causing power surges which were l i m i t e d by t h e heating of t i e
(In t h e other cases the f i s s i o n heating of t h e core had negligible
core.
e f f e c t on t h e r e a c t i v i t y . ) Figure 4 snows t h e calculated power, pressure and mean temperatxres i n tine core f o r the worst two cases,
The kinetics calculations t r e a t e d
r
t h e f u e l and t h e graphite as separate regions a t uniform temperature and pressure; actually, temperatures and f u e l pressures a t t h e center of t h e core would be above the mean values shown.
However, t h e difference be-
tween the peak pressure and the mean w i l l not exceed 2 or 3 psi, because t h e i n e r t i a of the f u e l i n t h e f u e l channels i s r e l a t i v e l y s m a l l .
Ap-
pcximate calculations indicated t h a t t h e maximum f u e l temperature i n t h e (See page 9.) Two more cases were examined i n which t h e power and temperature ex-
20-ft3,
gOO째F case should not exceed about 1650'F.
cursions accompanying t h e 20-ft3, action.
gOO째F slug were limited by control rod
I n t h e first, a r e a c t i v i t y ramp of -O.O75$
per sec was i n i t i a t e d
when t h e period reached 3 see (equivalent t o driving t h r e e rods i n a t
0.4 in./sec).
In t h e second case,
-4.0$ 6k/k w a s introduced i n
1 sec
a f t e r t h e period had reached 2 see (equivalent t o rods dropping).
Peak
powers were 0.66 Mw and 0.7 kw i n t h e two cases and t h e r e was no s i g n i f -
c
icant pressure or temperature increase. J
11
.
d LlJ
3
0
Q
-
ORNL-LR-Dwg 700.53
.
c
Case 3
W
- F i l l i n g Accident
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 the
.
core i s being f i l l e d w i t h f u e l i f :
( a ) the core temperature were ab-
normally low; or (b) t h e f u e l were abnormally concentrated i n uraniurr.;
or ( c ) t h e control rods were withdrawn from the positions they normally occupy during f i l l i n g . such an accident.
Interlocks and procedures a r e designed t o prevent
If, despite the precautions, t h e reactor were t o go
c r i t i c a l under such conditions, t h e r e would be a power excursion, whose s i z e would depend on t h e source power and the r a t e of increase of r e activity.
The core temperature would r i s e rapidly during t h e 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 with t h e increase i n c r i t i c a l temperature. Preliminary examination of t h e consequences of f i l l i n g t h e MSRE core with s a l t containing excess uranium w a s made f o r several assumed conditions.
Tne worst cases were examined i n d e t a i l t o determine t h e corrective action required t o insure safety. Fuel ComDosition
Two mechanisms were considered for enhancing t h e uranium concentration i n the & e l charged t o t h e reactor core.
I n t h e first of these, it was
assumed t h a t p a r t i a l freezing of t h e f’uel salt had occurred i n the d r a i n tank and t h a t t h e s o l i d contained no uranium.
I n the second one, t h e c
uranium concentration was adjusted t o make t h e reactor c r i t i c a l a t 1400 F ana it was assumed t h a t fuel of t h i s composition was charged t o t h e reactor a t ~OO’F.
Associated with t h e first mechanism, t h e cornposition of t h e remaining l.ic_ttid as a f’unction of t h e fraction of salt fkozen w a s calculated on t h a t
basis t h a t only the primary s o l i d
(6 LiF.BeF2.ZrF4) was formed.
n a l composition of t h e f u e l mixture was considered t o be 70 mole 23% BeF2
- 5% ZrF4 - 1% ThF4 - 1% UF4.
The nomi-
k
LiF
-
Since t h e actual c r i t i c a l concen-
t r a t i o n of UF4 i s l e s s than 1 mole $, a correction w a s applied f o r t h e
.
nuclear calculations which, i n e f f e c t , increased t h e concentrations of a l l
of t h e other constituents i n proportion t o t h e i r concentrations i n the 1
W
c r i t i c a l mixture.
Figure
5 shows t h e l i q u i d composition, as a f’unction of
t h e weight fraction of fu-el frozen, t h a t was used i n t h e nuclear cstlculstions.
T h s e curves cnnnei; bz extrapolated beyond
0.427 of
t h e s a l t frozen be-
cause it would be impossible to farri additfonal primary s o l i d since a l l of t h e zirconium has been consumed.
Another estimate of t h e compcsitlori
--
wac subseqLently made by McDufffe el; al.23 using o%her assumptiom abut, _.
t h e freezing mechanism.
The r e s u l t a n t differences i n composition were riot
s i g n i f i c a n t from t h e standpctint of nuclear calcalation r e s u l t s .
'The f u e l
coinpositions under t h e two sets of assumptLom are compared i n She Appendix, p
9.
The configuratfon of %he MSRE YuellsoF i s such t h a t t h e actAve r e -
gion of t h e core can be f i l l e d i f no more than 3976, by weight, of She fuel s a l t i s frozen i n t h e drain tal;k,
volume i s 72 E3a t 1200'F).
(assmirig t h . a t t h e workiig salt,
The extreme condition w a s used i n eva>_i-
a%ing +,he canseyaences 03 f i l l i n g t h e loop wiYn concen5rated l%ei s a l t , C r i t l c a l i t y i n P a r t l a l l y F i l l e d Core I n order tJ3 evaluate t h e f i l l i n g accidents, it was necessary t~ make some assumptions about t h e f i l l i n g procedure. control rccis were i n t h e 3
It w a s assumed t h a t t h e
posi+,ioss f o r f i l l i n g :
one r c d ful1.y
i a s e r t e d and two rods inserted s c %kat; they control O.l$ reactiv25y f a (See Appendix, p 46, for a discussion of con5rol rods. )
t h e fKL1 core.
Gr~~iier %hese conditfons, t h e reactor, f i l l e d with normal f u e l at, 1200째F:
had an effectfve
k
of 0.997 with t h e circulating pump o f f .
z a l < f i l l rate of 1 lrt3/m.:
I n order
<Q
7i-1
A uniforri
w a s assumed.
estimate reactivit:? as a functLon o f f i e 1 he:&%,
statf-cs
ealculations were made with an IBM-rd~090,1-dimensional, muitiregb;z, m ~ J . t i group n e c k o n diff'usim code (MODRIG).
The reactor w a s tz-eated as a slak.
z i t k a $ h i c h e s s eqgal t o the height of t h e core, L.
c o n t r d - r o d thimbles were not considered. f o r varloirs s a l t l e v e l s , H, i n t h e core.
Control rods and
Reactivity was calculated
For t h e conditions of H/L
< :
1
t h e graphite i n %he upper p a r t of the core was considered as a refLectsy. %:is
model differed scmewhat from %hat, used t o predict t h e p r c p t r t h ;
G:?
t h e normal reactor s o t h a t t h e resuits c u d d not be used d f r e c t l y i n otlier
2
H. F. McIkffie, "Data orL MSRE F?iel S a l t Requrred fer Piclear Safety Calclrlatfocs," le+,l;er f-,cR . B. 3 r i g g s j Fek. 3 3 , 1962.
16 calculations.
However, t h e r e l a t i v e changes i n r e a c t i v i t y as a function
or" f u e l height should be correct.
The r e s u l t s were normalized t o make
them consistent with t h e more detailed calculation of a c r i t i c a l , full reactor a t 1200째F, and then corrected downward t o allow f o r t h e f a c t t h a t the "normal" reactor i s s l i g h t l y s u b c r i t i c a l when f'ull because of t h e con-
trol rod positions.
The l a t t e r correction considered t h e change i n control
rod worth with changing f u e l l e v e l .
Figure 6 shows t h e fractional worth
of a single control rod a s a function of position i n t h e rull core and i n
t h e core 72$ full of f u e l salt. Figure
7 shows the height a t which c r i t i c a l i t y would be achieved as
a f i n e t i o n of the f r a c t i o n of f u e l salt fl-ozen.
The c r i t i c a l height w a s
a l s c obtained f o r t h e case where fuel, containing enough uranium f o r op-
eration a t 14OO0F, i s charged a t gOO째F.
I n t h i s case t h e c r i t i c a l H/L
was 0.700.
Temerature and Power Excursions If c r i t i c a l i t y i s achieved before t h e core i s f u l l and f i l l i n g is
continued, the result i s an excursion i n power and temperature. cursions were examined f o r two accidents:
3 ~ c hex-
(1)t h e reactor i s f i l l e d a t
1200째F with s a l t whose composition has been changed by freezing 0.39 of
<ne s a l t i n t h e drain tank; and ( 2 ) t h e reactor i s f i l l e d a t gOO째F with 0
s a l t containing s u f f i c i e n t uranium for operation a t 1400 F.
Criticality
would be achieved i n the two cases a t H/L = 0.691 and 0.700, respect!.vely. I n both cases t h e fill r a t e was fixed a t 1 f't3 of s a l t per minute. Tine equivalent r e a c t i v i t y change as f i l l i n g continues i s nearly t h e same
for t h e two cases, reaching 3.97$ added excess r e a c t i v i t y f o r t h e full core i n t h e first case, and
4.10$ i n t h e second.
However, an important
difference e x i s t s in the temperature coefficient of r e a c t i v i t y .
The h e 1
composition obtained by freezing 0.39 of the s a l t r e s u l t s i n a temperature coefficient of o r i ~ y6.5 x 1 0-5 normal fuel.
OF'l
as compared with 8.8 x
low5 f o r
the
The l a t t e r value w a s used i n evaluating t h e second accSdent
i n question.
Since the r e a c t i v i t y t r a n s i e n t i s nearly t h e same f o r both accictents, bxt t h e temperature coefficient i s l e s s negative i n t h e case of partLal
1
freezing, t h e power and temperature excursions a r e more severe i n the case W
d 0 -3
Ln
v
of p a r t i a l freezing, t h e power and temperature excursions a r e more severe i n t h e case where p a r t of t h e f u e l s a l t i s frozen.
Figure 8 shows the
calculated power and temperature behavior for t h i s case.
The i n i t i a l power
surge reaches 53.9 Mw 38.9 sec after c r i t i c a l i t y i s attained i f no corr e c t i v e action i s taken.
Since t h e power r i s e s very rapidly, heat t r a n s f e r
rlrom t h e f u e l t o t h e graphite w a s neglected f o r t h e f i r s t minute of t h e excursion.
Thus only the temperature coefficient of the f u e l was e f f e c t i v e
i n checking the power r i s e .
This s l i g h t l y overestimates t h e i n i t i a l p a r t
of t h e power and temperature t r a n s i e n t s .
It was assumed t h a t t h e f u e l and
graphite would be i n thermal equilibrium a f t e r 3 m i n and t h a t the c r i t i c a l temperature would prevail.
The power a f t e r 3 min w a s t h a t required t o keep
tine reactor a t t h e c r i t i c a l temperature as f'uel addition continued.
The
behavior between 1 and 3 min was not calculated accurately since t h i s period represents a t r a n s i t i o n between the two models, neither one of which describes t h e condition exactly.
However, t h e estimates of power behavior
given i n Fig. 8 during t h i s time i n t e r v a l appears s a t i s f a c t o r y for the analysis here, since no extreme condition i s involved. Since t h e core would be only p a r t l y full during an accident of t h i s type, t h e r e would be no circulation i n the core loop and t h e high-temperature f u e l would be confined t o t h e a c t i v e region of t h e core where it could not come i n t o d i r e c t contact w i t h t h e wed& of t h e system.
The f a c t t h a t t h e
core w o u l d not be full a l s o eliminates the p o s s i b i l i t y of any s i g n i f i c a n t p e s s u r e surge during t h e t r a n s i e n t . The reactor behavior shown i n Fig. 8 i s based on t h e assumption t h a t
no corrective action of any kind i s taken.
This would require not only
t h a t t h e operators ignore t h e condition and continue f i l l i n g a t t h e normal
r a t e f o r 1 3 min but t h a t no automatic action, such as control rod reversal, occurs.
The extent of t h e excursions can be d r a s t i c a l l y reduced by r e l -
a t i v e l y mild corrective action even i f f i l l i n g i s continued a t t h e normal rate. I n an accident of t h i s type, t h e reactor period becomes very short while t h e power i s s t i l l quite low.
For t h e case i n question, a ?-see period would be reached 17.7 sec after a t t a i n i n g c r i t i c a l i t y and t h e pot\rer
would be about Y
5.5 watts.
It is*expected t h a t t h e proposed nuclear in-
.
strumentation ~ 3 . 7 . 3 . provide a r e l i a b l e period indica-ccion a t t h i s power l.eve.l_
0
.
3
u
21.
If insertion of t h e two available control rods a t normal speed (-0.07576 W
&/k
per second) i s s t a r t e d when the period reaches
5 sec, t h e i n i t i a L
power peak i s limited t o 32 kw and the f u e l temperature rise i s l e s s than c
1째F.
The e f f e c t of t h e control rod insertion i s strong enough t h a t a,
moderate delay i n t h e period channel would not r e s u l t i n an excessive power surge, I f , i n s p i t e of t h e insertion of t h e control rods, f u e l addition is
continued u n t i l t h e core i s full, t h e reactor w i l l again become c r i t i c a l when t h e core i s 93.576 f i l l e d . w i l l add only
However, complete f i l l i n g f o r t h i s case
0.19% excessive reacti.vity, and 2.21 min a r e required t o
add t n i s amount.
The r e a c t i v i t y i s equivalent t o an equilibrium c r i t i c a l
temperature of 122g째F and t h e associated power t r a n s i e n t w d d be very s m a l l because of the limited amount of r e a c t i v i t y t h a t i s available and
the low r a t e a t which it can be added. Other F i l l i n g Accidents Another s i t u a t i o n which can lead t o a f i l l i n g accident i s t h a t i n which t h e core i s f i l l e d with normal f i e 1 a t t h e normal temperature but w i t h a l l control rods fully withdram.
In general, t h e response of t h e
system would be similar t o t h a t f o r the accident described above.
%.e
mx:'LmUm amount of excess r e a c t i v i t y available f o r t h i s accident i s orily 2.72% because t h e normal f u e l composition i s such t h a t t h e reactor is, s l i g h t l y s u b c r i t i c a l w i t h only one control rod f u l l y inserted and t h e other two nearly W l y withdrawn.
Thus, t h e consequences of tine above
accident would be much l e s s severe than those r e s u l t i n g Prom f i l l i n g t h e core w i t h fuel from which 39% of t h e s a l t has been separated by freezinE;. Case
4
- Loss
of Graphite from Core
If a graphite s t r i n g e r were t o break completely i n t o two pieces while
f u e l i s i n t h e core, and t h e upper end could f l o a t up,
*
f u e l would move
in'a t h e space J u s t about the fracture, causing an increase i n reactivit,y, The calculated e f f e c t i s 0.003876 6k/k per inch of s t r i n g e r replaced w i t h Tuel a t t h e center of t h e core.
*Rods
If t h e e n t i r e c e n t r a l s t r i n g e r were
~
and wires through t h e lower and upper ends of t h e s t r i n g e r s should prevent t h i s accident.
replaced with f u e l , the r e a c t i v i t y w o u l d increase only 0.135 6k/k.
This
J
amount of r e a c t i v i t y would have no serious consequences, even i f added instantaneously.
The
(Actually t h e r e a c t i v i t y would be added i n a ramp.
Tuel flows upward a t 8.6 in./sec and t h e graphite could not move up much f a s t e r than t h i s because of drag.)
Figure
9
.
shows t h e results of an i n -
s-i;antaneous increase of 0.17% 6k/k with t h e r e a c t o r a t 10 Mw.
(Peak power
and. temperatures would be lower f o r t h e same s t e p a t lower i n i t i a l powers.) Eod r e v e r s a l could e f f e c t i v e l y reduce peak power and temperatures f o r a 6k/k step, a s shown by t h e dashed l i n e s i n Fig. 9, where a ramp of
O.l$ -O.O7fs$
6k/k per second starts one second a f t e r t h e i n i t i a l s t e p increase.
Case 5
- Fuel Additions
I f uranium were added t o t h e c i r c u l a t i n g f u e l i n such a way t h a t it remained concentrated i n a small vol.ume, a r e a c t i v i t y t r a n s i e n t would be produced each time t h e 'lump" passed through t h e core. Additions o f concentrated uranium t o compensate for burnup w i l l be p a r t o f t h e normal operation of t h e r e a c t o r .
The design of t h e f u e l ad-
iiition sysiern i s such Liltii only a sz~allm o u l t o f uranium can 'oe added i n one batch, and t h e f r e s h uranium merges with t h e c i r c u l a t i n g f u e l gradu=dly. Tnese l i m i t a t i o n s insure t h a t t h e r e a c t i v i t y t r a n s i e n t s caused by a nornial f u e l addition a r e inconsequential. Fuel make-up i s added through t h e sampler-enricher mechanism. s a l t (probably
IlYozen
73$ LiF-27$ UF,+) i n a perforated container holding a t most
120 g o f U235 i s lowered i n t o t h e pimp bowl.
There t h e s a l t melts and
mixes i n t o t h e 2.7 rt3 of f u e l salt i n t h e bowl.
The 65-gpm bypass through
t h e bowl gradually c a r r i e s t h e added uranium i n t o t h e main c i r c u l a t i n g strPam.
The net increase i n r e a c t i v i t y from t h e addition of 120 g of U 23 5
i s 0.061$ 6k/k, which w i l l be automatically compensated f o r by t h e servodriven control rod. A reasonable upper l i m i t on t h e t r a n s i e n t s caused b
a normal f u e l i addition was calculated by postulating t h a t 120 g o f U23*4entered t h e c i r c u l a t i n g f u e l a t t h e same i n s t a n t , t h a t it was c a r r i e d through t h e heat exchanger i n a "front" and all entered t h e bottom of t h e core a t t h e s m e i n s t a n t , with equal amcunts entering each of t h e f'uel channels.
For
t h i s s i t u a t i o n , t h e r e a c t i v i t y increase due t o the added uranium r i s e s t o
u
Q)
S
c
0
2b
a maximum of 0.39% 6k/k i n 3.8 see, then decreases a s t h e f l a t v o l m e element containing the additional uranium moves up and out of the core. The power and temperature t r a n s i e n t s depend on t h e i n i t i a l power.
Fig-
ure 10 shows r e s u l t s calculated f o r i n i t i a l powers of 10 kw and 1 0 IW, with no corrective rod action.
.
The r a t e of r e a c t i v i t y addition by the
mcvfng f u e l i s slow enough t o permit e f f e c t i v e counteraction by t’ne use of the rods.
Jn the 10-Mw case if a negative r e a c t i v i t y ramp of -O.O75$
6K/k per second i s s t a r t e d when t h e period reaches 5 sec, the power peak i s reduced t o 22 Mw, t h e f u e l mean temperature r i s e s only 10°F and the
graphi5e r i s e s l e s s than 1°F. ’Case 6
- Unco~troll-edRod Withdrawal
Excursions can be produced by uncontrolled withdrawal of t h e corifrcl
rods. A s a l i m i t i n g case, it was assumed t h a t t h e reactor had been shut: down by inserting all control rods that the system had been cooled tm y00’F with t h e fie1 pump running. Under these conditions, w i t h no xenon ?resent, the reactor w . d d be s u b c r i t i c a l by
1.64%. (See Appendix for
control rod wortn assumptions. j Simultaneom withdrawal of all t h r e e control rods a t t h e normal rate
of 0.4 in./sec was then assumed.
A t t h i s r a t e , t h e reactor would bec:ome
c r i t i c a l 50.6 sec a f t e r t h e start 02 t h e rod motion and t h e control rods would be near t h e region of t h e i r m a x i m u m effectiveness. The severity of t h e t r a n s i e n t depends on t h e power l e v e l t o which X i i e reactor has decayed a t t h e time of t h e accident.
Figure 11 shows t h e
t r a n s i e n t s i n power, pressure and f u e l mean temperature as a function of t h e a f t e r t h e achievement of c r i t i c a l i t y f o r three d i f f e r e n t powers ar; t h e
t,i.-x kef
= 1.0.
After t h e i n i t i a l excursion, t h e t h r e e cases merge ifit;.?
a single l i n e fcr each ef t h e variables.
The power would remain at. sibout
200 Kw until. the warm f l u i d produced by t h e i n i t i a l excursion returned
fhe core.
to
Since t h e power i s not s i g n i f i c a n t u n t i l 6 sec a f t e r crit.:”,caXty,
t . h i s re-entrance would occur i n about 24 sec.
A t t h a t t i m e t h e power w m l c t
decrease t o tohe l e v e l required t o heat the e n t i r e core loop and compensate t h e contimed r e a c t i v i t y addition.
The temperature would continue t o rfke
u n t i l %he rods stopped or were flzlly withdrawn from t h e core.
The. eqzi.e
-1 ?hr+iirn - - --- t.e~py~.t.ij.re wFt.k t.he r 0 d - s fifily vithd.raw71 wobfid be 1.h73 F, 1I1y~eve?*,
1
- 20
27
since t h e graphite i s heated much more slowly than the f u e l ( a f t e r 18 s e e W
t h e graphite temperature i s only 950째F), t h e mean fie1 temperature might; remain above t h i s value f o r as long as
5 min.
RESPONSE TO ARBITRARY ADDITIONS OF REACTIVITY I n addition t o the analysis of conceivable s i t u a t i o n s which might a r i s e during the reactor operation, t h e response of t h e power, t h e core f'uel and graphite mean temperatures and t h e core pressure t o a r b i t r a r y changes i n r e a c t i v i t y was calculated.
The purpose was t o delineate nore
c l e a r l y the factors governing t h e k i n e t i c behavior of t h e reactor. Ramp Additions If r e a c t i v i t y i s added very slowly, the r e s u l t w i l l be a gradual i n -
crease i n f u e l and graphite temperahres a t the r a t e s necessary t o cancel out t h e r e a c t i v i t y being added,
The power w i l l r i s e from i t s i n i t i a l level.
t o t h a t required t o heat up t h e reactor. t h e loop, about
17 sec
Because of t h e transport lstg i n
pass before %he inlet temperature can r e f l e c t t h e A s t'ne mean tempera-
increased o u t l e t temperature r e s u l t i n g from tine ramp.
t u r e r i s e s during t h i s interval, t h e power must continue t o increase t o heat up t h e incoming f u e l more and Inore,
When the i n l e t temperature begins
t o r i s e , t h e power will l e v e l o f f . Figure 1 2 shows r e s u l t s (from an analog simulation) of t h e ramp add i t i o n of I$ 6k/k i n 30 sec.
The power was i n i t i a l l y a t 1 0 Mw, and t h e
(simulated) r a d i a t o r air f l o w and i n l e t temperature were l e f t constant
throughout. ended.
Note t h a t t h e power hat1 reached i t s peak before the ramp
Note a l s o the r e l a t i v e sluggishness of t h e graphite temperature.
(The graphite comprises TO$ of t h e core heat capacity, but only
6% of
+,he
power i s generated t h e r e . ) A s t h e ramp r a t e i s increased, a power peak occurs e a r l i e r during t h e
ramp addition, followed by a graduc; increase as t h e required f u e l mean temperature rises f a r t h e r above t h e inlet temperature. r e s u l t s of three ramp additions of 10-sec duration.
Figure 13 shows
The development of
t h e power peak as a fbnction of ramp rate i s c l e a r l y shown.
These re-
sults and those described hereafter were obtained by a d i g i t a l proceciure, W
MURGATROYD, which only considers t h e case where t h e i n l e t temperature
V
reinains constant.
A t low r e a c t i v i t y addition r a t e s , t h e calculations give
a gradual pressure increase i n the reactor due t o compression of gas i n the pump bowl as t h e f u e l expands.
(In r e a l i t y , t h e pressure control.
system would prevent most of such a r i s e . )
Increasing t h e magnitude of
the power excursion leads t o a core pressure disturbance caused by ine r t i a l and f l u i d f r i c t i o n forces as t h e fuel between the core and t h e exsansion space i n t h e pump bowl i s accelerated. The response of t h e system t o r e a c t i v i t y ramps i s strongly dependent upon t h e i n i t i a l power of t h e reactor, since t h i s a f f e c t s t h e amount of excess r e a c t i v i t y which can be introduced before the r i s i n g power s i g n i f i cantly a f f e c t s t h e core temperatures. Figure 1 4 shows the power behavior r e s u l t i n g from ramp additions of 25 i n 1 0 see, beginning a t four i n i t i a l powers from 1 0 w a t t s t o 1 0 mega-
wLtts.
Te'
s i z e of the e a r l y peaks i n power i s r e l a t e d t o both ramp r a t e
and i n i t i a l power i n Fig. 15.
(Note t h a t t h e re1at;ion does not e x i s t a t
low r a t e s of r e a c t i v i t y addition, where t h e e a r l y power peak does not e x i s t , a s i n the O.l$/sec
case i n Fig. 1 3 . )
iitzending tine sharper power increases a r e l a r g e r core pressure surges. (The i n e r t i a l force i s proportional t o t h e f i r s t derivative of t h e power.) Figure 1 6 shows r e s u l t s of calculations f o r t h e cases f o r which t h e powers a r e shown i n Fig,
15. The pressure
shown i s t h e c d c u l a t e d deviation of
t n e core pressure from t h e i n i t i a l value.
A t steady s t a t e with f u e l circu-
l a t i n g a t 1200 gpm and t h e pump bowl a t 20 psia, t h e pressures i n t h e core w i l l range f'rom about 29 p s i a a t t h e bottom t o about 23 p s i a a t t h e top.
The equations used t o compute t h e pressure t r a n s i e n t s took no account; of a lower l i m i t on absolute pressure, which accounts f o r t h e impossibly low swings i n pressure a f t e r t h e peaks i n Fig. 16.
Figure
17 r e l a t e s t h e sLze
of t h e pressure excursions t o ramp r a t e and i n i t i a l power. The behavior of t h e f u e l mean temperature shown i n Fig.
16 shows a
progression toward a peak such as appears i n t h e power a t high r a t e s of r e a c t i v i t y addition and low i n i t i a l power.
The f i r s t p a r t of t h e tempera-
t u r e t r a n s i e n t i s seen t o depend on i n i t i a l power, but a f t e r a few seconds the temperature behavior i s t h e same i n a l l cases.
(The power and pressure
a f t e r t h e e a r l y t r a n s i e n t s are a l s o p r a c t i c a l l y independent of t h e i r i i t l a l p w p r , as shown in Fie. 3.4 and
16.)
The maximun Aiel. mean temparnti.xre
W
w
': .
1
.
reached
a r e s u l t of a ramp add:.-(;Lon deFend:; eventually
25
m o u n t of r e a c t i v i t y added more than on t h e rate.
GB t;'k
ts?nl
Figure 18 shcws t h e
r e l a t i m f o r ramps of duratdon long enoilgh so t h a t t h e r e i s no dependen:,e of fbel %emperatwe on i n i t i a l powel*.
S3ep Additions MJRGATROYD was used ti: calcula-k a f e w cases of s t e p addi$E?ns (jf
reat6t i v i t y
.
For a s t e p addition of a given amourit, cf r e a c t i v i t y , t h e higher ?.he
i n f t i a l power, t h e l a r g e r are t h e power, temperature and pressare trmsients.
Figure
19 shows t h e power Lransients caused by r e a c t i v i t y
sl,epr;
of various sizes, wf%h t h e power i x l t i a l l y a t 1 0 Mw.
0.338% 6k/k makes t h e reactor exackly prompt c r f t k a l . response of t h e power and mean temperatxzes t o a s t e p cf t h i s s4ze 5.h A s t e p of
i n Fig. 20.
:%e siiclerr~
This figure a l s o shows tha', even f o r a prampt-critical s$ep,
peak temperatures can be reduced s i l p i f i c a n t l y by corrective rod ac:t,"7tor2 even t h z rather slow action assumed i n t h e case depicted. Pressure surges a r e not high unless $he s t e p i s well a b o x prprnpf. critAca1.
Fcr t h e 0.338:: szep a+, i9 Mw t h e peak pressure (a+, 0.6
ESC) v a s
only 1 . 3 psi; for t h e 17'0step, t h e peak w a s 230 p s i . The effec5 of i n i t i a l power w a s investigated by calc7iLa"Cng reszll+s
of
2
0.3385 s t e p at. 1 0 kw i n i t i a l power
In t h i s case t h e peak pswer wts
~4 Kv (a5 3.5 see), t h e peak f u e l meaW; temperature w a s 1286% (at, 9 sec 1 a n d t h e peak pressure w a s only 0.75 p s i (at 3.0 set). /
DISCUSSION
I n t h e analysis of t h e conceivable accidents, t h e assumptions aiid calculat,iorral methods were chosen t o produce pessimistically high pwerr;, temperatures and pressures.
The reisults indicate -khat none of t h e cancelvtz-
Lle accidents w i l l lead t o eatastro:?hic f a i l u r e of t h e reactor even f ~ f110 corrective actdon i s taken.
Thus i C , can be s a i d t h a t t h e s a f e t y of ,he
uperators and t h e Fopdace does not r e l y upon t h e functioning of ex5c:rnal protective or corrective devices. Tlie response t o a r b i t r a r y ramp and step additions of react,fvit0y shrw %hat additions we31 i n excess cf aqrkhing foresecable s J c i l L dc ni.t - p ~ & , ~ : e pressures which wci;;Ld b u r s t t h e reactor.
TIME
Csec.)
?9
V
Some of t h e postulated accidents lead t o high temperatures which might s t r a i n t h e core internals, o r other p a r t s of t h e system, causing d-amage and interrupting operation.
A l l of t h e damaging accidents a r e
normally prevented by mechanical devices or operating procedures.
ally t h e r e i s multiple protection.
Usu-
I n e v a u a t i n g t h e chance of interngl
damage t o t h e reactor, one must consider t h e probability of simultaneous f a i l u r e of a l l protective devices.
4.0
APPJiXDIX I
DELAYED NEUTRONS The d i g i t a l kinetics calculations whose results a r e reported here
*
used values f o r yields and half-lives of delayed neutron precursors which tjere measured by Keepin and Wimett f o r thermal-neutron f i s s i o n of U23 5 Five groups of delayed neutrons were included i n the calculations.
(The shortest-lived group lumped t h e shortest-lived two groups observed by
.
Keepin and Wimett ) The effective yield with the f u e l circulating was calculated f o r each group, assuming slug flow and uniform production of precursors over t h e core volume. volume of
19.6
The calculations assumed a flow r a t e of 1200 gpm, a core
ft3, and an external loop volume of
46.4 f't3 (core residence
bizle, 7.3 sec; external loop residence time, 17.3 s e c ) .
L
No weighting
f a c t o r s w e r e applied t o account f o r t h e differences i n energy and s p a t i s 1 source d i s t r i b u t i o n f o r t h e delayed and prompt neutrons. The t o t a l yield f o r a l l groups i s 0.00640 delayed neutron/total neutron.
The neutroris eiiiitted i n t h e
COTE
zr~oui1-bt o 0.00338 delayed
neutron/total neutron, a difference of 0.00302 caused by circulation.
A breakdown by groups i s given i n Table A-1. Table A-1.
Group
Delayed Neutron Data Used i n Kinetics Calculations by MURGATROM
H a l f -Li f e (sec)
Decay Constant (sec-1 )
Yield (n/n 1
Effective Yield (n/d
-
1
55.9
0.0124
0 000211
o.0000~3
2
22.7 6.22 2.30 0.508
0.0305
0.001402
0.000426
0.1114
0.001254
0.0004'71
0.3013 1.364
0.002 328
0.001513
0.001005
0.0009$+
o.006400
0
3 4 -
5
0033'77
*
Since these computations were made, s i x groups have been incorporated i n t h e MURGATROYD calculations. W
--
APPENDIX 11
CONTROL RODS
Need f o r Control Rods i n Normal Operation During normal operation of t h e reactor, r e a c t i v i t y tends t o decrease If t h e fuel temperature i s held constant and no f i e 1
for several reasons.
i s added t o compensate f o r t h e decrease i n r e a c t i v i t y , it will be necessary
t o withdraw a control rod (or rods) t o compensate for: delayed neutrons due t o circulation;
(1)the l o s s of
(2) t h e ingrowth of xenon-135 during
(3 ) power coefficient of r e a c t i v i t y (tmperature r i s e of graphite r e l a t i v e t o fuel); and (4) burnup of U235 i n t h e and af'ter high-power operation; fuel.
Table A-2 shows t h e magnitude of these e f f e c t s f o r normal operation
a t 10 Mw.
With t h e exception of t h e delayed neutron l o s s e s which have been
described on page 40, t h e numbers i n Table A-2 core a r e taken from t h e f i r s t Addendum t o ORNL CF-61-2-46, Table A-2. ~~
E R E Preliminary Hazards Report.
*
Effects Requiring Shim Action of Control Rods
-
Effect
6k/k,
Xenon (equilibrium a t 10 Mw)
0.3 1.3
Power coefficient (LO MW)
0.2
Eurnup (300 Mw-days)
0.2
Delayed neutron losses
$
2.0
Table A-2 does not include poisons which build up gradually i n t h e fuel.
Samarium-149 i s one of t h e more important poisons; it will build
ug and s t a r t t o l e v e l off a t 1.14 6k/k i n about 3 months a t full power.
There a r e other f i s s i o n products which will a l s o s a t u r a t e i n a few weeks o r months.
S t i l l other f i s s i o n products, and corrosion products, w i l l
probably continue t o build up throughout t h e operation of t h e reactor, Jt
Recent data on s t r i p p e r e f f i c i e n c i e s lead t o considerably higher estimates of xenon poison.
causing a gradual increase i n poisoning.
Fuel additions w i l l be used. t c
compensate ror t h e poisons which grzdually build up. Anot'ner requirement f o r normd operation i s t h a t a shutdown m a r & be provided, s o t h a t t h e reactor i s s u b c r i t i c a l during s t a r t u p and skutdcwn. This could be a t t a i n e d by using the loop heaters t o raise t h e core tempera-
t u r e above t h e c r i t i c a l temperature.
A b e t t e r way i s t o use a rod or rods.
The s i z e of t h e shutdown margin i s Ciscussed l a t e r .
One oi' t h e
Regulation i s an important function o f t h e control rods.
rods will be used i n a servomechanism t o hold e i t h e r t h e nuclear power c r some temperature a t a setpoint.
A niaximum deviation from t h e mean position
of about 0.2% 6k/k i s adequate for t h i s purpose. Safety action, i n t h e sense of rods moving very r a p i d l y t o decrease t h e r e a c t i v i t y , i s not contemplated for t h e MSRE.
The rods should be
capable of compensating for unexpected r e l a t i v e l y slow increases i n r e a c t i v i t y , however,
( a s by f u e l permeation of t h e g r a p h i t e ) so as t o protect
The rod
-the r e a c t o r from t h e excessive temperatures which would r e s d t .
worth which should be available for t h i s function i s not c l e a r . Control Rod Worth The combined worth of all t h r e e control rods of t h e present design has been calculated t o be
6.79 6k/k.
The r e a c t i v i t y worth of s i n g l e r o d s
or groups of rods P ~ l inserted y o r withdrawn i s shown i n Table A-3.
(Eod
>io. 2 i s diagonally opposite t h e gr&phite samples.)
Table A-3.
Arrangement A l l rods out
Control Rod Worth Reactivity, $ 6k/k 0
KO. 2 i n , others out
-2.8
No. 1 or No. 3 in, others out,
-2.9
3 in, No. 2 out No. 2 and No. 1 or 3 in, other out All rods i n
-5.3
KO. 1 and
-4.9 -6.7
4.3
W
Figure A-1 shows predictions of rod effectiveness versus tne length inserted i n t o t h e core.
The most r e l i a b l e prediction i s based on calcc-
l a t i o n s with EQUIPOISE-3, a two-group, two-dimensional, multiregion ,
difi%sion method.
The curve shown should be a good representation f o r
a single rod (or rods moving together) when the flux i s not already per-
turbed by another rod i n t h e core.
It should apply f a i r l y well i f ar.other
rod i s f u l l y inserted, but the flux d i s t o r t i o n by another rod inserted
EO
t n a t t h e rod end i s near t h e center o f t h e core would came t h e curve t o be considerably i n e r r o r .
The sine-squared curve i s t h a t predicted by
t h e f i r s t - o r d e r perturbation approximation, and i s shown merely for comparison with the more accurate prediction. Deployment of Rods
It has been planned t h a t two rods be kept f U l y withdrawn during all operations so t h a t t h e i r poisoning e f f e c t would be available t o counteract f u e l permeation of t h e graphite or other unexpected e f f e c t s tending t o increase r e a c t i v i t y . and shutdown.
The remaining rod would be used f o r regulation, shim
If t h e shim recuirements a r e no l a r g e r than shown i n ?'able
A-2, control with a single rod i s possible. One requirement of a combination shim-regulating rod i s t h a t t h e rod caii t r a v e l f a r enough t o provide t h e shimming necessary and t h a t t h e speed be high enough a t t h e ends of i t s shim movement and not t o o high i n t h e middle for good regulation.
Using t h e figures from Table A-2,
from t h e
t i m t h e reactor goes c r i t i c a l ( w i t h t h e fie1 c i r c u l a t i n g ) w i t h a clean,
r W l y f i e l e d core u n t i l t h e reactor i s a t f u l l power, with equilibrium xenon and t h e m a x i m u m burnup, t h e rod must be withdrawn i s only 0.39 of t h e worth of rod 1 or rod
1.7s 6k/k.
Tnis
3 when the others a r e withdram.
If one allows an additional 0.2% 6k/k a t each end f o r regulation, t h e ex-
treme t r a v e l i s 0.72 of t h e rod worth.
The f u e l concentration could be
adjusted so t h a t , a t the extremes, t h e rod would be poisoning 0.88 and 0.16
of i t s worth.
Figure A m 2 shows t h e t t h e d i f f e r e n t i a l rod worth v a r i e s by
o n l y a factor of
1.3 over t h i s range.
This i s quite acceptable since simu-
l a t o r t e s t s showed good regulation over a t l e a s t a fourfold range of rod. speeds, from 0.02 t o 0.08% 6k/k per second.
t
4.;
.
ORNL-LR-Dwg. 70072
46 If t h e range i s
Another f a c t o r t o consider i s t h e shutdown margin.
adjusted as described above, t h e reector would go c r i t i c a l with t h e ihel c i r c u l a t i n g when t h e rod i s poisoning 0.82 of i t s worth.
With t h e rod
f u l l y inserted t h e reactor w i l l be s u b c r i t i c a l by 0.18 x 2.9% or 0.525 dk/k while t h e f u e l i s circulating, o r by 0.22$ 6k/k with t h e fuel pump
off.
This assumes t h a t t h e core i s a t t h e normal temperature.
The core
0
tem.perature could be as much as 0.0022/8.8
x' 0 1
without t h e reactor reaching c r i t i c a i t y .
Therefore, an e r r o r of l e s s
= 25 F below normal
than t h i s amount i n temperature measurement would not l e a d t o unintent i o n a l c r i t i c a l i t y during f i l l i n g . I n t h e analysis of various incidents, one form of corrective actioc. considered w a s a ramp of -0.075% 6k/k per second.
Although t h i s i s a n
a r b i t r a r y rate, it corresponds t o a value which could e a s i l y be obtained. with t h e current control rod design, In determining the control rod speed, it w a s assumed t h a t t h e r a . t e or' r e a c t i v i t y change should average 0.02% 6k/k per second over t h e ec.tire
diztance traversed by a s i n g l e rod.
For a rod worth 2.9$,
t h i s aversge
rate corresponcis t o a f u l i t r a v e r s e of t i e roci range i n about 130 see.
Tie t r a v e l time w a s fixed a t 130 sec and, since t h e rod range i s ab0v.t
.
60 in., t h i s r e s u l t e d i n a rod speeii of about 0.4 in./sec. The corrective action postulated i n t h e r e a c t i v i t y accidents w a s a
reversal of a l l t h r e e rods a t normal speed.
Since t h e rod-worth curves
are not l i n e a r (see Fig, A - 1 ) t h e r e a c t i v i t y ramp r e s u l t i n g from a rod
r e v e r s a l depends on t h e i n i t i a l rod positions.
Figure A-3 shows t h e
negative r e a c t i v i t y added as a f'unction of t i m e f o r two d i f f e r e n t i n i t i e l positions 03 t h e rods.
I n t h e f i r s t ; case it w a s assumed t h a t Rod 1
(wo=.tn = 2.95 6k/k) w a s i n a position of maximum d i f f e r e n t i a l worth end t h a t Rods 2 and 3 were f u l l y withdrawn.
In t h e second case, t n e init&].
p s i t i o n of Rod 1 w a s t h e same, but Rods 2 and 3 were started from posit i o n s where they were poisoning a t o t a l of 0.3% 6k/k.
Since it i s c l e a r
from Fig. A-1 t h a t a f u l l y withdrawn rod must t r a v e l several inches before it has any s i g n i f i c a n t e f f e c t on r e a c t i v i t y , t h e i n i t i a l ramp i n case I i s e s s e n t i a l l y t h a t for a s i n g l e rod moving a t 0.4 in./sec
of m a x i m u m d i f f e r e n t i a l worth. t h e first, 6 s e e ) is t h e incidents.
i n i t s region
The i n i t i a l rate f o r case I1 (average f o r
-O.O75$ 6k/k per second.
-- t h e value used
i n studying
I
h
AFPENDIX I11
ANALYSIS OF COLD SLUG ACCIDmTS The circulating-fuel reactor k i n e t i c s calculation which i s coded. f c r t h e IBM-7090 (PURGATROYD) cannot be used d i r e c t l y t o compute beh-uvior ir. a "cold-slug" accident. 5.3
One reason i s t h a t t h e "mean rue1 temperature"
defined as t h e mean of t h e i n l e t and outlet, so a cold slug would appear
as a s t e p change i n mean temperature (and r e a c t i v i t y ) whereas a c t u a l l y
E,
To c i r -
cold slug causes a ramp change i n t h e average f u e l temperature.
cLurvent some of t h e shortcomings of MURGATROYD, t h e cold-slug accider.ts > e r e analyzed by t h e following procedure.
I n t h e first step, r e a c t i v i t y w a s calculated f o r cores which were 0
2-5 1200 F except cooler f'uel w a s cortsidered i n t h e lower p a r t of t h e P ~ e l
channels.
MODRIC, a multigroup, one-dimensional neutron diffusion
CE~CL-
13;tion w a s used t o obtain t h e c - m e s shown i n Fig. A-4, Microscopic
C~CISS
0
sections appropriate f o r a neutron v e l o c i t y d i s t r i b u t i o n a t 1200 F w e r e usd---only
t h e density of t h e f u e l i n t h e lower p a r t of t h e core w a s
varied. A t 1200 gpm, f i e 1 passes
7.3 see.
*om t h e bottom of t h e core t o t h e t 3 p
This rat-e w a s Gsed d i r e c t l y t o convert t h e curves of Fig.
iin
A-4
tc:t h e curves c#f k vs time f o r various cold slugs shown i n Fig. A+*
If'
t h e i n r t i a l . value o f k at. t h e beginning of t h e coid slug were l o w encugk. s s t h a t t h e power d i d
not r i s e and a f f e c t t h e f u e l temperature, these
cur:ies i n Fig. A-5 would be t h e t r u e v a r i a t i o n of k from t h e Ln.ltia.1 nlue.
Rat,ios of heat capacitfes and temperature c o e f f i c i e n t s of re-
a c t d v i t y are such t h a t heat transfer. fpom t h e graphite t o t h e ccld slug ::cLd
have l i t - b l e e f f e c t .
The tendency would be t o lower t h e react!,-L.i%>-
s l i g h t l y below t h a t calculated here. The next s t e p was t o run k i n e t i c s calculations i n which t h e fuel. temperature was not, perturbed by any cold slug, but i n which t h e r e a c t o r
WES
sabgected t o a r e a c t i v i t y t r a n s i e n t such as would be produced by a m'id slug unaffected by power feedback.
0
I n i t i a l conditions were 1200 F fie1
and graphife, k = 1 and a power of 10 kw.
A t zero time a negatfve s t e p
of O.3O2$ 6k/k w a s inserted t o represent the l o s s of delayed ne;lt.rcn prec1;ysc,rs r.rLnn 044 emrnnrlnnA l.llb.ll *-nl n,"--.-l LALb-uvAvII %cn 9 serie:: o f p ~ s f l f f mand mn
~ V A u u b A L + b u .
49
ORNL-LR-Dwg
70074
Y
negative ramp changes i n r e a c t i v i t y was introduced t o produce %he v a m a t i o n shown i n Fig. A-5, The k i n e t i c s calculation gave t r a n s i e n t s i n power, pressure, an?. meail temperature. Fig. A-6.
Results f o r 20- and 30-ft3,
900째F slugs are shown i n
I n t h e other cases, temperatures never deviated from i n i t i a l
values by as much as
0
5 F.
The end result was obtained by superimposing t h e t r a n s i e n t s of Fig.
A-6 on those which would be caused by t h e cold slug without nucl.ear
effects.
This procedure amounts t o representing t h e temperature of t h e
ITuel or of t h e graphite by t h e sum of two functions of t i m e , one of which responds t o t h e cooling e f f e c t of the cold f i e 1 entering t h e core, the other responding t o t h e nuclear heat generation,
Variations i n both
a f f e c t t h e r e a c t i v i t y , which determines t h e power.
The e f f e c t of t h e
second temperature f'unction i s b u i l t i n t o t h e k i n e t i c s calculation.
The
e f f e c t of t h e f i r s t i s introduced tlirough t h e r e a c t i v i t y t r a n s i e n t which was imposed.
Only t h e v a r i a t i o n i n t h e power-affected temperature a f f e c t s
t h e pressure, since t h e v a r i a t i o n i n t h e other mean temperature reflectz:
only t h e movement OT cold Tuei IOrom one part of t h e loop t o another, not a change i n t h e volume of f u e l i n t h e loop.
The v a r i a t i o n of t h e f u e l and graphite mean temperatures during t h e passage of lo-, 20-, and 30-ft3 s1uE;;s of gOO째F fuel, without heat gerterotion i n t h e core, are shown i n Fig. A-7.
The s o l i d curves take i n t o
account heat t r a n s f e r between t h e fliel and t h e graphite; t h e dashed I.ines S ~ O Wt h e
fuel mean temperature which would r e s u l t from t h e passage 01' the
cold slug without heat transfer.
The s o l i d curves of Fig.
A-7 were
corn-.
bined with t h e temperature r i s e due t o nuclear heating, shown i n Fig,. t o obtain t h e n e t e f f e c t shown i n Fig,
A-6,
4,
Because of t h e low i n i t i a l power, t h e period becomes q u i t e short several seconds before t h e power has r i s e n t o a l e v e l cm.xing any si&:nificant heating. period s i g n a l .
Thus e f f e c t i v e rod a c t i o n can be i n i t i a t e d by t h e shortMURGATROYD w a s used t o examine t h e behavior during a 20-f%",
yOO째F slug with two types of corrective action. *
I n t h e first, a ramp of
-0.075$ dk/k was superimposed, beginning a t 2.3 sec where t h e period
reaches
5 sec.
I n t h i s case t h e power peaked a t 0.66 14w a t 8 sec, t h e r e
was no s i g n i f i c a n t oressure r i s e and t h e nucleai- heating r a i s e d t h e Fuel.
I
c
54 mean temperature only O.T째F.
In t h e second case,
-4,0$6k/k
w a s inserted
between 3.2 and 4.2 see (beginning when t'ne period reached 2 sec). limited the power "peak" t o only
0.7
l'his
kw.
During any substantial power excursion, material near t h e center of' t h e core w i l l be heated well above the mean temperature,
Some c&culations
were done t o estimate how high t h e peak f u e l temperatures might go dr?.ring t h e 20-ft3,
gOO째F slug without corrective action.
I n these calculations
it was assumed t h a t there w a s no heat t r a n s f e r between t h e fuel and t h e graphite.
Fuel temperatures were then calculated by integrating t h e hezt
production i n the f u e l .
Figure A-8 shows r e s u l t s f o r a channel where the
power density i s 1.93 times t h e m e a n f o r the core.
*
The i n i t i a l power was
only 1 0 kw, and a t 6 sec, t h e p r o f i l e shows p r a c t i c a l l y no e f f e c t of heeting, only t h e cold front which has advaced t o 52 i n . by t h i s time.
Sub-
seciuent p r o f i l e s show t h e temperature peak r i s i n g near t h e center of t h e core during t h e power surge, then moving on toward t h e o u t l e t as t h e power drops.
The entry o f t h e 1200째F f u e l behind t h e cold slug and the advance
of t h i s i n t e r f a c e a l s o shows.
The clotted l i n e shows how f u e l which enteredc
a% a par'iicular t h e liea'is ug rapidly dwiiw t h e pmer surge, then more
gradually a s t h e specific power decreases because of the drop i n t o t a l power and t h e movement of t h e f u e l away from the center of t h e core. The temperature a t the o u t l e t of t h e channel i s shown as a fbnction of time i n Fig. A-9.
The heating
02;
t h e f l u i d ahead of t h e cold slug, t h e
drop as t h e leading edge of t h e cold slug arrives, and t h e abrupt r i s e as he following fuel reaches t h e o u t l e t a r e prominent features.
Figwe A-9 also shows a curve f o r t h e temperature a t the vessel out;let.
The temperature here i s approximated by the mixed mean of t h e f1ui.d
issaing from all the channels, dispLaced i n time by the mean residence time i n t h e upper head.
The peak arid the break a s t h e interfaces pass
would a c t u a l l y be softened by t h e differences i n t r a n s i t times from various channel o u t l e t s t o t h e vessel outlei;,
*
This r a t i o would apply t o t h e central channels i f t h e r e were no control. rods or thimbles, In the actual reactor t h e maximum value of t h i s ratio w i l l be s l i g h t l y lower because of t h e flux f l a t t e n i n g r e s u l t i n g f'rom t h e poison near t h e core axis.
J i
d
3
w I-
J
.
COMPOSITION OF RESIDUAL LIQUID AFTER PARTIAL FREEZING OF NSRE FUEL SALT 'The compositicn of t h e l i q u i d b h a t remains a f t e r p a r t i a l freezing cf t h e f i e 1 salt determines t h e nuclear behavior of t h e reactor during a T i l l i n g accidens.
Two estimates, based on d i f f e r e n t assumptions, have
been made of t h e l i q u i d composition as a function o f t h e f r a c t i o n of s a l t
I%ozen.
The f i r s t estimate, based on very simple assumptions w a s made
e a r l y t o permit t h e nuclear calculations t o proceed. by XcDutffie e t
The second estimate,
aJ., w a s based on greater knowledge of t h e s a l t properties.
_I-
The assumptions and r e s u l t s of the two approaches are discussed below. Since t,he quantities of i n t e r e s t i n nuclear calculations a r e atmnic concen?xa%ions, t h e r e s u l t a n t compositions a r e presented i n these terms. Preliminary Estimate of Fuel Composition This estimate was based on the following assumptions: 1. I n i t i a l s a l t composition
Component
Mol Fraction
LIF
0.70
BeF2
0.23
aF4
0.05
ThF2
0.01
m.4
0.01
This composition leads t o
:t
higher uranium concentration than 0
i s required for criticalit;T under normal conditions a t 1200 F. To correct for this, t h e f i n a l uranium concentrations were
corrected downward by t h e U:Th r a t i o i n t h e c r i t i c a l reactor. 2.
Only t h e primary solid, 6 LiF.BeFZ.ZrF4,
appears a s t h e tem-
perature i s lowered and t h i s continues .to form until. a l l c f t h e zirconium has been consumed.
3.
The density of t h e remaining melt i s proportional. t o i t s molecular weight with t h e density of the i n i t i a l cornposition
W
fixcd at
1p*31 b J r t 3 a% 1200OF.
Estimate by Ildckffie et al The following assumptions were used:
.
1. I n i t i a l salt composition
Component
Mol Fraction
LiF
0.70
BeF2
0 237
ZrF4
o*o>
ThF4
0.01
uF4
0.003
The reduction i n uranium concentration permits a smaller correction t o make t h e f i n a l concentration compatible with c r i t i c a l i t y results.
The extra 0.007 mol f r a c t i o n
w a s a r b i t r a r i l y assigned t o t h e BeF2. 2.
The primary solid, 6 LiF.BeF2.ZrF4,
mol fractiofi i s reduced t o 0.033. ~ n 3 - z solid, ~ ~ - 2 Li3'.&F2,
forms
forms u n t i l t h e ZrF4
After t h i s t h e s x -
ir, 2
1:l mol r z t i o With
t h e primary s o l i d .
3.
The s a l t density was obtained by dividing t h e molecular
weight by t h e sum of t h e f'ractional molar volumes of t h e constituents. values.
The molar volumes are empirically obtained
An accuracy o f 3$ i s claimed for t h i s technique.
However, application of t h e method t o t h e standard (70-23-
5-1-1)mixture leads t o a density of 142.6 l b / f t 3 a t 1200째F as opposed t o a measured value of
1$,3 l b / f i 3 .
Since absolute d e n s i t i e s are required f o r t h e nuclear calculations, a correction of 1$.5/142.6
was applied t o
all of t h e calculated d e n s i t i e s . Comparison of Results Figure A-10 shows t h e calculated atomic concentrations a t 1200째F r e s u l t i n g f r o m t h e two sets of assumptions.
For ease of comparison, both
uranium concentrations a r e r e f e r r e d t o t h e same i n i t i a l concentration--that corresponding t o 0.003 mol f r a c t i o n UF4.
Xie o n l y s i g n i f i c a n t
W
60
difference i n the two methods i s i n t h e zirconium concentration, t h i s does not a f f e c t the nuclear calculations because only
lom4 of
However,
J
the
neutron absorptions are i n zirconium.
APPENDIX
v
CRITICALITY CALCULATIONS FOR FILLING ACCIDENTS Multiplication constants were calculated with t h e a i d of MODRIC, a one-dimensional, multiregion, multigroup neutron diffusion code, f o r all .*,.
combinations of t h e following variables: H/L
T
=
-
0.9, 0.75, LOO
= 1200, 1300, 140O0F
where f i s t h e weight fraction of f u e l frozen.
Additional calculations
were made a t H/L = 1.00, f = 0 and T = 1200, 1300, and 1400째F t o provide a basis f o r adjusting the r e s u l t s t o agree with previous calculations.
In all cases, t h e nominal atomic concentrations were adjusted f o r changes &ue t o t h e v a r i a t i o n of t h e fuel density w i t h temperature; t h e coefficient of expansion of the normal f u e l was applied t o all compositions.
Nuclear
cross sections appropriate t o t h e various temperatures were used. fU1 of t h e MODRIC results were t r e a t e d as nominal values, subject t o adjustment.
The value of k f o r t h e core f i l l e d with normal f u e l a t 1200'F
was s e t a t 1.OO.
The values a t 1300 and 1400째F were set a t 0.9912 and
0.9824, respectively, by applying t h e previously calculated temperature -5 0F-1). The r a t i o s of these values coefficient of r e a c t i v i t y (-8.8 x 1 0 t o t h e nominal values gave normalization f a c t o r s t o be applied a t t h e vwious temperatures. An additional correction was applied t o each of t h e calculated vd.ues,
&cause of control-rod position during f i l l i n g , k = 0.997 f o r t h e reactor
full of norrnal f u e l a t 1200'F.
However, t h e worth of t h e control rods
varies with t h e s a l t l e v e l i n t h e core.
Thus t h e correction which w a s
applied was varied proportionately. Figure A-11 shows t h e net values of kerf as a f'unction of H/L a t
1.200'~ f o r t h e e f i e 1 cmpositions.
These curves permit evaluation of
tlhc c r i t i c a l s a l t l e v e l a s a function of composition (Fig.
7).
Tne ef-
fec+,fve temperature coefficients of r e a c t i v i t y were evaluated with the
aid of similar curves a t other temperatures.
With 0.39 of t h e szlt 53?ozerL?
the %emperatme coefficient i s only 6.3 x 10'50F'1. A similar approach w a s used for t h e postulated accident i n which l'uel,, 0
ccntaining s u f f i c i e n t uranium for operation a t 1400 F, i s added t o t h e r e actla
0
a t 900 F.
A c r i t i c a l . uranium concentration was f i r s t calculated ;:CY
tne fW.1 core a t 1400째F.
The atomic concentrations were then adJus5ed 4.c
?OO째F and k w a s calculated as a function of H/L. malized t o k =
1.044 a t
H/L = 1, t h e value corresponding t o a temperst%lu*e
coefficient of 8.8 x 10" w a s a l s o applied.
iC
These v a u e s were mr-
OF'^ .
The correction f o r control-rod posit5on
Figure A-12 shows t h e net keff as a W c t i o n of H/L.
In order t o predict t h e power and temperature behavior of t h e core, vs H/L i n t o curves of k was necessary t o convert the curves of k eff
'fs t i m e .
-
e 2f
This conversion was based on t h e variation of H/L w i t h time
Ctning f i l l i n g .
Figure A - 1 3 shows H/L as a function of time f o r a -EX11
mite of 1 . 0 ft3/min a t 1200'F.
Zero time on t h i s curve i s t h e time a t
vhich f u e l s a l t begins t o enter t h e core i t s e l f .
The change of slope
0.8 i s due t o t h e effect, o f t h e inlet volute and inlet, l i n e on the reactor vessel. Figure A-13 was then combined with t h e curves Cj? 2%
H/L =
Fig, A-11 and A-12 t o obtain the r e a c t i v i t y curves from which power zind
temperature were calculated.
c
APPENDIX V I
v
REACTIVITY WORTH OF INCREME%TSOF URANIUM
The increase i n r e a c t i v i t y which would be produced by t h e addi:-“-,r r f a s m a l l amount o f nranium a t some point i n the core, which i s inir,rca-.iy
critical, i s a quantity of i n t e r e s t i n the analysis of the r e a c % x . B:-E TJantity was used t o calculate an upper l i m i t on the upset wnLch c i u l d
?;E
poduced by t h e rapid addition of f u e l i n such a way t h a t t h e c a r e ccncentra+,ion increased nonuniformly. Reactivity worth of uranium as a f’unction of position was ca1cid.a+,.?d as fellows:
C r i t i c a l i t y calcula+,ions by MODRIC showed t h a t a t 12OOcP s’r?
c r r e critical mass i s 16.2 kg U235 and (6k/k)/(6M/M)
= 0.28.
1 g TJ23cJ evenly d i s t r i b u t e d i n t h e core, 6k/k = 1.72 x
lom5*
Thss -f:r
Fas*.,ac,d
sicw ne.itron fl1jxes and adjoints have been computed by EQUIPOISE-3.
‘I?-cE:
prr-lduet of t h e f a s t adjoint and t h e slow flux a t a point was used as Yicmeasure of t h e nuclear impcrtance of t h a t point. ,
Thus f o r 1 g
‘ti
pasixion r,z
Pfgdre A-14 shows t h e r e a c t i v i t y e f f e c t of an increment ef 1 g t2 3 5
ELF
i>arzctiori of posltion i n t h e core. I n t h e analysis of t h e me1 addition, it w a s postiLa-Led +,ha; %+ P . 2 e:rlcen”,ation
w a s uniform except fo:: a f l a t “pancake” consa1r1Z’1g a.c~ afi-
d24iosai 120 g U233 which moved up through t h e core.
The reacC,2.vF:..y
or h p w t a n c e of urani-om evenly d i s t r i b u t e d over a horizontal p l w e
f’c . ? ELI
::
2s
%is
integration was carried out graphically f o r t h e values of z sks%
Sn Fig. A-14.
The r e s u l t s were used t o obtain Fig. A-152 which s h c m *,h?
reactfvPty e f f e c t of an increment of 120 g U235,
evenly distribu4ed
:--i
a horkscmtal. plane moving through t h e core a t t h e average speed c+P .t81.f v
c i r x L z E A r g P,el.
b-
e
- 69I n t e r Distribution 1.
S. E. Beall
2.. M. Becder
3.
4. 5.
6-7. 8. 9. 10. 11. 12.
13
9
14. 15. 16.
17 18. 19 20.
21. 22. 23
24. 25 26. 27
28.
29 30
31-32. 33-35.
36-38. 39
Bettis Blankenship Boch Briggs C. Claiborne R. Engel A. P. Fraas G , R. Grimes P, N. Haubenreich P. R. Kasten R . N. Lyon H. G. MacPherson W. D. Manly W. B. McDonald A. J. Miller R. L. Moore C. W. Nestor A. M. Perry M. W. Rosenthal â&#x201A;Ź3, W, Savage A. W. Savolainen M. J. Skinner I. Spiewak J. A. Swartout A. TaSjoada J. R. Tallackson D. B. Trauger Central Research Library Y-12 Document Reference Section Laboratory Records Department LFD-RC E. F. A. R. H. J.
S. F. L. B.
External D i s tr i b u t ion
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35. 56-57.
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