ORNL-TM-0251.txt

 

  
 

& 2.
‘h M

OAK RIDGE NATIONAL LABORATORY
operated by

UNION CARBIDE CORPORATION
for the

U.S. ATOMIC ENERGY COMMISSION

ORNL- TM- 251

COPY NO. - %6

DATE - May 15, 1962

SAFETY CALCULATIONS FOR MSRE

P. N. Haubenreich
J. R. Engel

ABSTRACT

A number of conceiveble reactivity accidents were analyzed, using
conservatively pessimistic assumptions and approximations, to permit
evaluation of reactor safety. Most of the calculations, which are
described in detail, were performed by a digital kinetics program,
MURGATROYD. Some analog analyses were also made,

None of the accidents which were analyzed lead to catastrophic
failure of the reactor, which is the primary consideration.

Some internal damage to the reactor from undesirably high tem-
peratures could result from extreme cold-slug accidents, premature
criticality during filling, or uncontrolled rod withdrawal. Each of
these accidents could happen only by compounded failure of protective
devices, and in each case there exist means of effective corrective
action independent of the primary protection, so that damage is un-
likely.

The calculated response to arbitrary ramp and step additions of
reactivity show that damaging pressures could occur only if the ad-
dition is the equivalent of a step of about 1% Gk/k or greater.

NOTICE

This document contains information of @ preliminary nature and was prepared
primarily for internal use ot the Oak Ridge National Laboratory, 1t is subject
to revision or correction and therefore does not represent a final report. The
information is not to be abstracted, reprinted or otherwise given public dis-
semination without the approval of the ORNL patent branch, Legal and infor-
mation Control Department, :
 

 

 

LEGAL NOTICE

This report was prepared as an account of Gevernment 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, with respect to the acevracy,
completeness, or usefulness of the information contained in this report, or that the use of
any information, apporotus, method, or process disclosed in this report may not infringe
privately owned rights; or

B. Assumes any liabilities with respect to the use of, or for domages resulting from the use of
any information, apparatus, methaod, or process disclosed in this report.

As used in the above, ''person acting on behalf of the Commission’ includes ony employee or

contractor of the Commission, - employee of such contractor, to the extent that such employee

or contractor of the Commission, or employee of such contractor prepares, disseminates, or
provides access to, ony information pursuant to his employment or contract with the Commission,

or his employment with such controctor.

 

 
CONTENTS

ABSTRACT

INTRODUCTION

MSRE CHARACTERISTICS

RESULTS OF CREDIBLE REACTIVITY ACCIDENTS

Case 1 « Fuel Pump Failure

Case 2 ~ Cold Slug Accident

Case 3 = Filling Accident

Case 4 - Loss of Graphite from Ccre
Case 5 - Fuel Additions

Case & - Uncontrolled Rod Withdrawal

RESPONSE TO ARBITRARY ADDITIONS OF REACTIVITY
Ramp Additions
Step Additions

DISCUSSION

APPENDIX I: DELAYED NEUTRONS

APFENDIX II: CONTROL RODS

APPENDIX III: ANALYSIS OF COLD~SLUG ACCIDENTS

APPENDIX IV: COMPOSITION OF RESIDUAL LIQUID AFTER
PARTTAL FREEZING OF MSRE FUEL SALT

APPENDIX V: CRITICALITY CALCULATIONS FOR FILLING
ACCIDENTS

APPENDIX VI: REACTIVITY WORTH OF INCREMENTS OF URANIUM

"g-nd
88 Cn Oy W w H 2

13
21
22
2l
27
2T
35

35
Lo

41
L8

5T

60
65
No.

12

13

16

17

ii

LIST OF FIGURES
Title

Power and Temperatures Following Fuel Pump Power
Failure. No Corrective Action.

Power and Temperatures Following Fuel Pump Power
Failure. Radiator Doors Closed and Control Rods
Driven in at 0.4 in./sec after Failure.

Powers During Cold Slug Accidents.

System Behavior for Cold Slugs at 9000}?

Liquid Composition Resulting from Partial Freezing
of Fuel Salt in Drain Tank.

Control Rod Worth vs. Position.

Fuel Level Required for Criticality. (Fuel Concen-
tration Enhanced by Freezing in Drain Tank.)

Temperature and Power During Filling Accident.
Response of MSRE to 0.15% Ak/k Step.

Effects of 120 g of U235 Moving Through the Core
in a Horizontally Distributed Slug.

Transients Resulting from Simultaneous Withdrawal
of 3 Control Rods

Response to Ramp of 1% 6k/k in 30 sec Beginning
at 10 Mw.

Response to Ramps of 1, 1.5, and 2% 6k/k in 10 sec,
Beginning at 10 Mw. ,

Power Response to Ramps of 2% ék/k in 10 sec
Beginning at 10~2, 103, 101, and 10 Mw.

Maximum Power Reached in Initial Excursion for
Ramp Reactivity Additions.

Pressure and Fuel Mean Temperature Response to
Ramps of 2% 6k/k in 10 sec, Beginning at 1072,
1073, 1071, and 10 Mw.

Maximum Core Pressure Reached in Initial Surge
Caused by Ramp Reactivity Additions

11

i2

1k
17

20

23

2>

26

28

29

31

32

33

3k
A3

Al

A-10

A-11
A-12
A-13
A-1h

A=15

iii

LIST OF FIGURES ~ cont'd

Title

Peak Fuel Mean Temperatures vs. Total Reactivity
Added by Ramps of Various Durations

Power Transients from Step Increases in Reactivity
Initial Power: 10 Mw

Response of MSRE to 0.338% 6k/k Step.

Fractional Rod Worth vs. Depth of Insertion in
MSRE Core

Differential Rod Worth (Fraction of Total per Inch)
vs. Rod Position

Reactivity Change Due to Control Rod Insertion.

Excess Reactivity Due to Replacing Part of Fuel in
1200° Core with Denser Fuel. (Fill from bottom up.)

Reactivity Transients Caused by Passage of Cold
Slugs Through MSRE Core at 1200 gpm.

MURGATROYD Results for Reactivitg Transient Corre-
sponding to 20 and 30 £t2, 900°F Cold Slugs.

Mean Temperatures of Fuel and Graphite in Core
During Passage of Cold Slugs Initially at 9O0O0°F
with no Nuclear Heat Generation.

Temperature Profiles Along Hottest Fuel Channel
at Various Times During Passage of 20 ft3,
900°F Slug.

Power and Fuel Temperatures for 20 £t2, 900°F Slug

Composition of Fuel Salt Resulting from Partial
Freezing in Fuel Drain Tank

Effective Multiplication During Filling Accident
Effective Multiplication During Filling Accident
Height of Salt in Core vs. Time

Reactivity Worth of 1 g of U235 in MSRE Core.
Reactivity Transient Caused by 100 g of U235 Uni-

formly Distributed in a Horizountal Plane Which
Moves Through the Core with the Circulating Fuel.

37
38

Ly

k5
b7

50

52

23

55

29
61

63
6h
66

67
SAFETY CALCULATIONS FOR MSRE

P. N. Haubenreich
J. R. Engel

INTRODUCTION

The work reported here was done to provide information for the sec-
cnd addendum to the MSRE Preliminary Hazards Repor'l:‘,:L and consists of the
analysis of reactor behavior in certain potentially hazardous situations.
The purpose of the present report is to describe the procedures which were
used and to give some results in fuller detail.

Incidents which were analyzed included: fuel pump failure at high
power, 'cold~slug" accidents, premature criticality during core filling,
breakage of a graphite stringer, passage of a concentrated fuel slug and
runaway rod withdrawal. The response of the system to arbitrary step and
remp additions of reactivity was also computed. Each case is described
and results are given in the body of the report.* Details of the calcu-

ations and some other pertinent information are given in appendixes.

An analog computer was used to analyze the fuel pump stoppage. All
other cases were analyzed using MURGATROYD, a machine program developed
by I\Testor2 for digital computation of MSRE kinetic behavior. Nestor has
recently shown that MURGATROYD predicts larger power excursions for a
given imposed reactivity transient than would be calculated if the core
mean temperatures were related more realistically to inlet temperature
and power. (The same comment may apply to the simulator results.) A
new program which will incorporate temperature distributions and fluxe-

wecighted mean temperatures is being developed. When this is ready, some

 

lMolten Salt Reactor Experiment Preliminary Hazards Report, ORNL
CF=-6l=2-46 Addendum No. 2 (May O, 1962).

"The conditions and results reported here are for the "first round" of
the analysis. ©Some changes were subsequently made in rod worth snd de-
ployment and some of the incldents were reanalyzed, by the procedures
described here, in light of the new conditions. The results of the latest
calculations appear in reference 1.

C. W. Nestor, MURGATROYD, an IBM-T090 Program for the Analysis of the
Kinetics of the MSRE, ORNL-TM-203 (April 6, 1962).

2
b

of the incidents described in this report will be anaslyzed again. From
the standpoint of reactor safety evaluation, however, it is believed that
the calculations which have already been done are adequate for the cases

studied, particularly since the results obtained indicated reasonably safe

reactor operation.
MSRE CHARACTERISTICS

Quantities which are important in the kinetic behavior of the MSRE

are listed in Table 1; the values shown were used in the kinetics calcu-

lations.

Table 1. MSRE Characteristics Affecting Kinetic Behavior

 

Prompt-neutron lifetime

Delayed neutron fraction: static

¢+ circulating

Residence times: core

external to core

Critical mass: core
total fuel

Mass coefficient of reactivity (6k/k)/(6M/M)

Temperature coefficients of reactivity: fuel

graphite

Fraction of heat generation: 1in fuel

in graphite

Core heat capacity: graphite
fuel

Graphite~to-fuel heat transfer

2.9 % lO-h sec

0.0064
0.0034

7.3 sec
17.3 sec

16.6 kg U235
56.0 kg U7

0.28

-2.8 x 107° °p~t
-6.0 x 10™° °p~t

00914'
0.06

3,53 Mw-sec/ F
1.47 MW/sec/OF

0.020 Mw/°F

 

Extremely rapid increases in core power cause & rise in core pressure

due to inertia and friction in the line to the pump and due to compressicn

of the gas in the pump bowl. The guantities affecting the core pressure

surges are given in Table 2.
Table 2. MSRE Characteristics Affecting Core Pressure Transients

 

Core volume 20 ft3

Fuel density 149 1b/£t°

Fuel volumetric expansion coefficient 1.26 x 10”" °F7t
Length of line to pump bowl 16 £t
Cross-sectional area of line 0.139 ft2
Friction loss in line 1.3 velocity heads
Volume of gas in pump bowl | 2.5 ft3

 

RESULTS OF CREDIBLE REACTIVITY ACCIDENTS

Six kinds of conceivable accidents or malfunctions involving un-

desirable additions of reactivity were analyzed. The sections which follow

describe each condition and the results of the analysis. Methods of ansl-

ysis are covered in detail in the Appendices.
Case 1 - Fuel Pump Failure

If the fuel circulation is interrupted while the reactor is critical,
the increase in the effective delayed neutron fraction will cause the
ecritical temperature to increase. If appreciable power is beling extracted
by the radiator, the temperature of the coolant salt will decrease im-
mediately following the cessation of fuel flow through the heat exchanger.

The behavior of the reactor povwer and temperature in the event of a
fuel pump stoppage with the reactor operating at high power was explored
by Burke on the Analog Facility on February 1, 1962.

Figure 1 shows simulator results for the case of a fuel pump pover
failure while the reactor is at 10 Mw, with no corrective action and the
coolant pump continuing to run. Although the mean temperature of the fuel
in the core increased lQOOF, the secondary salt temperatures decreased,
reaching the freezing point at the radiator outlet in less than twd minutes.
(The behavior at lower initial powers was similar, but the secondary salt

did not cool to the freezing point if the initial power extraction was less

than 7.5 Mw.)
 

TEMPERATURE (°F)

400

10

0

(o)

PowER (Mw)
-+

TiME (Sec)

ORNL-LR-Dwg. TOO051
Unclassified

i

|

120
It is clear that the occurrence of a fuel~pump power failure with the
reactor at high power requires that steps to reduce the heat removal from
the radiator be taken quickly. Control rod action to reduce reactivity
is necessary to prevent an undesirably large rise in fuel temperature in
the core. Results were also obtained considering control-rod movement
and changes in heat removal by the radiator.

Figure 2 shows the results of a simulated fuel pump failure at the
seame initial conditions as Fig. 1, but with corrective action. One second
after the pump power was cut (coastdown was simulated, so the fiuid flow
was not assumed to stop instantaneously), a negative reactivity ramp was
started to simulate insertion of the control rods. This rate was -0.075%
per second, corresponding to all three rods moving in at about O0.L in./sec.
(See page 46 for discussion of rod worth, speed and normal positions.)
Beginning 3 seconds after the pump power failure, the simulated heat re-
moval from the radiator tubes was reduced as indicated by the radiator
inlet and outlet temperature in Fig. 2. It is believed that the radiator
doors can be closed to reduce heat extraction faster than that associated
with Fig. 2 conditions. In this case, the radiator temperature dropped
very little, and the fuel mean temperature rose 30°F. With the same
radiator control but with a faster negative reactivity ramp of -0.15%/sec,
the power dropped more rapidly and the fuel mean temperature rose only
'18°F.

Case 2 =~ Cold Slug Accident

Because the "cold~slug" accident could not be adequately simulated
on the analog computer, the consequences of several accidents of varying
severity were estimated by criticality and kinetics calculatlions on the
IBM~7090. (Details of the procedures and intermediate results are given
in the Appendix, page 48.)

The accidents which were analyzed consisted of pumping 10, 20, and
30 t3 of fuel at 900, 1000, and llOOOF into the core at a rate of
1200 gpm. In each case the core was assumed to be initially critical at
l2OOOF, with 10 kw of fission power being generated, and with no circu-
lation of fuel. The loss of delayed neutron precursors which accompanies

the start ot circulation was treated as a step change in reactivity of
ORNL~LR-Dwg. TO0052

 

Unclassified

(4,) 3¥0LVEIdWEL

1000

3 8
(3.) "3310 dWaL

 

©

 

> o
(W] B3med

TIME *(5ecC)

   
   
10

=0,30% Gk/k, which occurred simltaneously with the entry of the first
cold fuel into the core.

In the first cases which were calculated, no control rod action was
taken. The calculated fission powers following the entry of the various
cold slugs into the core are shown in Fig. 3. The initial drop in each
case was due to the assumed step decrease in reactivity which takes the
reactor subcritical. In the case of the 1100°F slugs, the effect of the
denser fuel was not enough to bring the reactor back to critical. In some
of the other cases the reactor does become supercritical but before the
power has risen very high, hot fuel (at 12OOOF) begins to enter the core
behind the initial slug and the reactor becomes subcritical again. (The
core transit time is 7.3 sec. The 10-ft> slug passes out in 11.0 sec;
the 20-f%2 slug in 14.6 sec and the 30-ft2 slug in 18.2 sec.) For the
20- and 30-ft2 slugs at 900°F, considerable excess reactivity was added
quickly, causing power surges which were limited by the heating of tae
core. (In the other cases the fission heating of the core had negligible
effect on the reactivity.)

Figure 4 shows the calculated power, pressure and mean temperatures
in the core for the worst two cases. The kinetics calculations treated
the fuel and the graphite as separate regions at uniform temperature and
bressure; actually, temperatures and fuel pressures at the center of the
core would be above the mean values shown. However, the difference be=
tween the peak pressure and the mean will not exceed 2 or 3 psi, because
the inertia of the fuel in the fuel channels is relatively small. Ap=-
nroximate calculations indicated that the maximum fuel temperature in tae
20-£t3, 900°F case should not exceed about 1650°F. (See page sit.)

Two more cases were examined in which the power and temperature ex-
cursions accompanying the 20-ft3, 9OOOF slug were limited by control rod
action. In the first, a reactivity ramp of =0.075% per sec was initiated
when the period reached 5 sec (equivalent to driving three rods in at
0.4 in./sec). 1In the second case, -4.0% 8k/k was introduced in 1 sec
after the period had reached 2 sec (equivalent to rods dropping). Peak
powers were 0.66 Mw and 0.7 kw in the two cases and there was no signif-

icant pressure or temperature increase.
11 ORNL-LR-Dwg. T0053

Unclassified
2 100 My
#3
10 Mw
b
| Mw
Fa
2
:
v
ul
2
0
o
100 kW
|
10 kW

4
3
1

 

TIME (Sec.)
 

TEMPERATURE (C)

 PRESSURE (PSI)

PERIOD (5ecC.)

POWER (Mw)

 
 

 

Fig. 4

 

System Behavior

20 cu. ft —— 30 cu. 1 = ——

'

 

’i

 

 

TIME

  
  
 
 
 
    

(sec)

12

_F'or Cold Slugs

at 90G°F,
13

Case 3 = Filling Accident

Criticality could be reached prematurely during a startup while the
core is being filled with fuel if: (a) the core temperature were ab-
normally low; or (b) the fuel were abnormally concentrated in uranium;
or (c) the control rods were withdrawn from the positions they normally
occupy during filling. Interlocks and procedures are designed to prevent
such an accident. If, despite the precautions, the reactor were to go
critical under such conditions, there would be a power excursion, whose
size would depend on the source power and the rate of increase of re-
activity. The core temperature would rise rapidly during the initial
power éxcursion; then, if fuel addition were continued, it would rise in
pace with the increase in critical temperature.

Preliminary examination of the consequences of filling the MSRE core
with salt containing excess uranium was made for several assumed conditions.
The worst cases were examined in detail to determine the corrective action

required to insure safety.
Fuel Composition

Two mechanisms were considered for enhancing the uranium concentration
in the fuel charged to the reactor core. In the first of these, it was
assumed that partial freezing of the fuel salt had occurred in the drain
tank and that the solid contained no uranium. In the second one, the
uranium concentration was adjusted to make the reactor critical at 1400°F
and it was assumed that fuel of this composition was charged to the reactor
at 9OOOF.

Associated with the first mechanism, the composition of the remaining
licuid as a function of the fraction of salt frozen was calculated on that
basis that only the primary solid (6 LiF.BeFs.ZrF4) was formed. The nomi=-
nal composition of the fuel mixture was considered to be 70 mole % LiF -
23% BeFz = 5% ZrFq = 1% ThFg - 1% UF4. Since the actual critical concen-
tration of UF4 is less than 1 mole ¢, & correction was applied for the
nuclear calculations which, in effect, increased the concentrations of all
of the other constituents in proportion to their concentrations in the
critical mixture. Figure 5 shows the liquid composition, as a function of

the weight fraction of fuel frozen, that was used in the nuclear calculations.
ORNL~LR-Dwg. TOO055

1h

1ified

 
These curves cannct hz extrapolated beyond 0.425 of the salt frozen be-
cause 1t would be impossible to form addifional primary solid since all

of the zirconium has been consumed. Ancother estimate of the compcsition
wag subsequently made by McDuffie gfi_g%:ga using other assumpticns about
the freezing mechanism. The resultant differences in composition were not
significant from the standpoint of nuclear calculation results. The fuel
compesitions under the two sets of assumptions are compared in the Ap-
pendix, p 58.

The configuration of the MSRE Tuel loop is such that the active re-
gion of the core can be filled if no more than 39%, by weight, of the
fuel salt is frozen in the drain tank, (assuming that the working salt
volume is 72 £53 at 1200°F). The extreme condition was used in evalii-
ating the comseguences of filling the loop with concentrated fuel salt.
Criticality in Partially Filled Core

In order to evaluate the filling accidents, it was necessary to make
some assumptions about the filling procedure. It was assumed that the
control rods were in their "normal' positions for filling: one rcd Fully
inserted and two rods inserted sc that they control 0.1% reactiviity in
the full core. {See Appendix, p 46, for a discussion of conbrol rods.)
Under these conditions, the reactor, filled with normal fuel at 12OOOF}
had an effective k of 0.997 with the circulating pump off. A uniforn
salt fill rate of 1 fts/min was assumed.

In order to estimate reactivity as a function of fuel height, statics
calculations were made with an IBM-7090, l~dimensional, muitiregion, multi-
group nevtron diffusion code (MODRIC). The reactor was treated as a slab
with a thickness equal to the height of the core, L. Control rods and
control-rod thimbles were not considered. Reactivity was calculated
for various salt levels, H, in the core. For the conditions of H/L <1
the graphite in the upper part of the core was considered as a refliectcr.
This model differed scmewhat from that used to predict the properties of

the normal reactor so that the results could not be used directly in cther

 

3. H. F. McDuffie, "Data on MSRE Fuel Salt Required for Nuclear Safety
Calculations, ' letter to R. B. Briges, Feb. 13, 1962.
16

calculations. However, the relative changes in reactivity as a function
of fuel height should be correct. The results were normalized to make
them consistent with the more detailed calculation of a critical, full
reactor at lEOOOF, and then corrected downward to allow for the fact that
the "normal" reactor is slightly suberitical when full because of the ccn-
trol rod positions. The latter correction considered the change in control
rod worth with changing fuel level. Figure 6 shows the fractional worth
of a single contrcl rod as a function of position in the full core and in
the core 72% full of fuel salt.

Figure 7 shows the height at which criticality would be achieved as
a function of the fraction of fuel salt frozen. The critical height was
alsc obtained for the case where fuel, containing enough uranium for op-
eration at 1400°F, is charged at 900°F. In this case the critical H/L
was 0.7T00. |

Temperature and Power Excursions

If criticality is achieved before the core is full and filling is
continued, the result is an excursion in power and temperature. Such ex-
cursions were examined for two accidents: (1) the reactor is filled at
1200°F with salt whose composition has been changed by freezing 0.39 of
the salt in the drain tank; and (2) the reactor is filled at 900°F with
salt containing sufficient uranium for operation at 1400°F. Criticality
would be achieved in the two cases at H/L = 0,691 and 0.700, respectively.

In both cases the fill rate was fixed at 1 f£t2 of salt per minute.
Tne equivalent reactivity change as filling continues is nearly the same
for the two cases, reaching 3.97% added excess reactivity for the full
core in the first case, and 4.10% in the second. However, an important
difference exists in the temperature coefficient of reactivity. The fuel
composition obtained by freezing 0.39 of the salt results in a temperature
coefficient of only 6.5 x 1077 °p~t as compared with 8.8 x 1077 for the
normal fuel. The latter value was used in evaluating the second accident
in question.

Since the reactivity transient is nearly the same for both accidents,
but the temperature coefficient is less negative in the case of partial

freezing, the power and temperature excursions are more severe in the case
POSITION

FiG b CONTROL ROD WORTH vs

 
ORNL~LR-Dwg. TOOS5T

18

 

lassified

prmeT

e Dem e

e e ann et

toe

-
19

of partial freezing, the power and temperature excursions are more severe
in the case where part of the fuel salt is frozen. Figure 8 shows the
calculated power and temperature behavior for this case. The initial power
surge reaches 55.9 Mw 38.9 sec after criticality is attained if no cor-
rective action is taken. Since the power rises very rapidly, heat transfer
irom the fuel to the graphite was neglected for the first minute of the
excursion. Thus only the temperature coefficient of the fuel was effective
in checking the power rise. This slightly overestimates the initial part
of the power and temperature transients. It was assumed that the fuel and
graphite would be in thermal equilibrium after 3 min and that the critical
temperature would prevail. The power after 3 min was that required to keep
the reactor at the critical temperature as fuel addition continued. The
behavior between 1 and 3 min was not calculated accurately since this
period represents a transition between the two models, neither one of which
describes the condition exactly. However, the estimates of power behavior
given in Fig. 8 during this time intervel appears satisfactory for the
analysis here, since no extreme condition is involved.

Since the core would be only pertly full during an accident of this
type, there would be no circulation in the core loop and the high-temperature
fuel would be confined to the active region of the core where it could not
come into direct contact with the wells of the system. The fact that the
core would not be full also eliminates the possibility of any significant
pressure surge during the transient.

The reactor behavior shown in Fig. 8 is based on the assumption that
no corrective action of any kind is taken. This would require not only
that the operators ignore the condition and continue filling at the normal
rate for 13 min but that no automatic action, such as control rod reversal,
occurs. The extent of the excursions can be drastically reduced by rel-
atively mild corrective action even if filling is continued at the normal
rate.

In an accident of this type, the reactor period becomes very short
while the power is still quite low. For the case in question, a 5-sec
period would be reached 17.7 sec after attaining criticality and the power
would be about 5.5 watts. It is‘expected that the proposed nuclear in-

strumentation will provide a reliable period indication at this power level.
ORNL-LR-Dwg. TOO58

20

2000

(s

1800

Y FYN4L

600

VY Izl

1400

1200

10

O

 

T

("W) ¥3IMod

12 &

10

6

TIME (rin)
If insertion of the two available control rods at normal speed (~0.075%
5x/k per second) is started when the period reaches 5 sec, the initial
pover peak is limited to 32 kw and the fuel temperature rise is less than
1°F. The effect of the control rod insertion is strong enough that a
moderate delay in the period channel would not result in an excessive
power surge.

If, in spite of the insertion of the control rods, fuel addition is
continued until the core is full, the reactor will again become critical
when the core is 93.5% filled. However, complete filling for this case
will add only 0.19% excessive reactivity, and 2.21 min are required to
add this amount. The reactivity is equivalent to an equilibrium critical
temperature of 1229°F and the associated power transient would be very
small because of the limited amount of reactivity that is available and

the low rate at which it can be added.
ther Filling Accidents

Another situation which can lead to a filling accident is that in
which the core is filled with normal fuel at the normal temperature btut
with all control rods fully withdrawn. In general, the response of the
system would be similar to that for the accident described above., The
maximum amount of excess reactivity available for this accident is only
2.72% because the normal fuel composition is such that the reactor is
slightly subcritical with only one control rod fully inserted and the
other two nearly fully withdrawn. Thus, the consequences of the above
accident would be much less severe than those resulting from filling the
core with fuel from which 39% of the salt has been separated by freezing.

Case 4 -~ Loss of Graphite from Core

If a graphite stringer were to break completely into two pieces while
fuel is in the core, and the upper end could float up,* fuel would move
into the space just about the fracture, causing an increase in reactivity.
The calculated effect is 0.0038% 6k/k per inch of stringer replaced with

fuel at the center of the core. If the entire central stringer were

 

*
Rods and wires through the lower and upper ends of the stringers
should prevent this accident.
22

replaced with fuel, the reactivity would increase only 0.13% 6k/k. This
amount of reactivity would have no serious consequences, even if added
instantaneously. (Actually the reactivity would be added in a ramp. The
fuel flows upward at 8.6 in./sec and the graphite could not move up nuch
faster than this because of drag.) Figure 9 shows the results of an in-
stantaneous increase of 0.15% 0k/k vith the reactor at 10 Mw. (Peak power
and. temperatures would be lower for the same step at lower initial powers.)
Rod reversal could effectively reduce peak power and temperatures for a
0.15% 6k/k step, as shown by the dashed lines in Fig. 9, where a ramp of

=0.075% 6k/k per second starts one second after the initial step increase.

Case 5 - Fuel Additions

If uranium were added to the circulating fuel in such a way that it
remained concentrated in a small volume, a reactivity transient would be
produced each time the "lump" passed through the core.

Additions of concentrated uranium to compensate for burnup will be
part of the normel operation of the reactor. The design of the fuel ad=-
dition system is such that only a small amount of uranium can be added in
one batch, and the fresh uranium merges with the circulating fuel gradually.
Tnese limitations insure that the reactivity transients caused by a normal
fuel addition are inconsequential.

Fuel make~up is added through the sampler-enricher mechanism. Irozen
salt (probably 73% LiF-27% UFh) in a perforated container holding at most
120 g of U235 is lowered into the pump bowl. There the salt melts and
mixes into the 2.7 £t of fuel salt in the bowl. The 65-gpm bypass through
the bowl gradually carries the added uranium into the main circulating
stream. The net increase in reactivity from the addition of 120 g of U235
is 0.061% 6k/k, which will be automatically compensated for by the servo-
driven control rod.

A reasonable upper limit on the transients caused
addition was calculated by postulating that 120 g of U
circulating fuel at the same instant, that it was carried through the

bi a normal fuel
@32 entered the
heat exchanger in a "front" and all entered the bottom of the core at the
sage instant, with equal amounts entering each of the fuel channels. For

this situation, the reactivity increase due to the added uranium rises to
13,

~
[

0.5 % bk/x step

TIME (5€C)

Response of MSRE Vo

th, 9

?.c..s dAMOA

 
2k

a meximum of 0.39% 6k/k in 3.8 sec, then decreases as the flat volume
element containing the additional uranium moves up and out of the core.
The power and temperature transients depend on the initial power. Fig-
ure 10 shows resulis calculated for initial powers of 10 kw and 10 Mw,
with no corrective rod action. The rate of reactivity addition by the
meving fuel is slow enough to permit effective counteraction by the use
of the rods. In the 10-Mw case if a negative reactivity ramp of =0.075%
5k/k per second is started when the period reaches 5 sec, the power peak
is reduced to 22 Mw, the fuel mean temperature rises only 10°F and the

graphite rises less than loF.

Case 6 = Uncontrolled Rod Withdrawal

Excursions can be produced by uncontrolled withdrawal of the control
rods. As a limiting case, it was assumed that the reactor had been shut
down by inserting all control rods and that the system had been cocled to
9OOOF with the fuel pump running. Under these conditions, with no xenon
present, the reactor would be suberitical by 1.64%. (See Appendix for
control rod worth assumptions. )

Simultaneous withdrawal of all three control rods at the normal rate
of 0.4 in./sec was then assumed. At this rate, the reactor would become
critical 50.6 sec after the start of the rod motion and the control rods
would be near the region of their maximum effectiveness.

The severity of the transient depends on the power level tc¢ which
the reactor has decayed at the time of the accident. TFigure 11 shows the
transients in power, pressure and fuel mean temperature as a function of
time after the achievement of criticality for three different powers at the
tine keff = 1.0. After the initial excursion, the three cases merge ints
a2 single line for each cf the variables. The power would remain at aboutb
200 Mw until the warm fluid produced by the initial excursion returned to
the core., Since the power is not significant until 6 sec after critlicality,
this re-entrance would occur in about 24 sec. At that time the power would
decrease to the level required to heat the entire core loop and compensate
the continued reactivity addition. The temperature would continue to rise
until the rods stcpped or were fully withdrawn from the core. The equi-

librium temperature with the rods fully withdrawn would be 1L73°F, Haowever,

! il - g -
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27

since the graphite is heated much more slowly than the fuel (after 18 sec
the graphite temperature is only 9500F), the mean fuel temperature might

remain above this value for as long as 5 min.,

RESPONSE TO ARBITRARY ADDITIONS OF REACTIVITY

In addition to the analysis of conceivable situations which might
arise during the reactor operation, the response of the power, the core
fuel and graphite mean temperatures and the core pressure to arbitrary
changes in reactivity was calculated. The purpose was to delineate nore

clearly the factors governing the kinetic behavior of the reactor.
Ramp Additions

If reactivity is added very slowly, the result will be a gradual ine-
crease in fuel and graphite temperatures at the rates necessary to cancel
out the reactivity being added. The power will rise from its initial level
to that required to heat up the reactor. Because of the transport lag in
the loop, about 17 sec pass before the inlet temperature can reflect the
increased outlet temperature résulting from the ramp. As the mean tempera-
ture rises during this interval, the power must continue to increase to
heat up the incoming fuel more and more. When the inlet temperature begins
to rise, the power will level off.

Figure 12 shows results (from an analog simulation) of the ramp ad-
dition of 1% 6k/k in 30 sec. The power was initially at 10 Mw, and the
(simulated) radiator air flow and inlet temperature were left constant
throughout. Note that the power had reached its peak before the ramp
ended. Note also the relative sluggishness of the graphite temperature.
(The graphite comprises T0% of the core heat capacity, but only 6% of the
power is generated there.)

As the ramp rate is increased, a power peak occurs earlier during the
ramp addition, followed by a gradual increase as the required fuel mean
temperature rises farther above the inlet temperature. Figure 13 shows
results of three ramp additions of 10-sec duration. The development of
the power peak as a function of ramp rate is clearly shown. These re=-
sults and those described hereafter were obtained by a digital procedure,

MURGATROYD, which only considers the case where the inlet temperature
 

 

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TIME (Sec)
30

repmains constant. At low reactivity addition rates, the calculations give
a gradual pressure increase in the reactor due to compression of gas in
the pump bowl as the fuel expands. (In reality, the pressure control
system would prevent most of such a rise.) Increasing the magnitude of
the power excursion leads to a core pressure disturbance caused by in-
ertial and fluid friction forces as the fuel between the core and the ex=-
vansion space in the pump bowl is accelerated.

The response of the system to reactivity ramps is strongly dependent
upon the initial power of the reactor, since this affects the amount of
excess reactivity which can be introduced before the rising power signifi-
cantly affects the core temperatures.

Figure 14 shows the power behavior resulting from ramp additions of
2% in 10 sec, beginning at four initial powers from 10 watts to 10 mega-
watts. The size of the early peaks in power is related to both ramp rate
and initial power in Fig. 15. (Note that the relation does not exist at
low rates of reactivity addition, where the early power peak does not
exist, as in the 0.1%/sec case in Fig. 13.)

Attending the sharper power increases are larger core pressure surges.
(The inertial force is proportional to the first derivative of the power.)
Figure 16 shows results of calculations for the cases for which the powers
are shown in Fig. 15. The pressure shown is the calculated deviation of
tne core pressure from the initial value. At steady state with fuel circu-
lating at 1200 gpm and the pump bowl at 20 psia, the pressures in the core
will range from about 29 psia at the bottom to about 23 psia at the top.
The equations used to compute the pressure transients took no account of a
lower limit on absolute pressure, which accounts for the impossibly low
swings in pressure after the peaks in Fig. 16. Figure 17 relates the size
of the pressure excursions to ramp rate and initial power.

The behavior of the fuel mean temperature shown in Fig. 16 shows a
progression toward a peak such as appears in the power at high rates of
reactivity addition and low initial power. The first part of the tenpera-
ture transient is seen to depend on initial power, but after a few seconds
the temperature behavior is the same in all cases. (The power and pressure
after the early transients are also practically independent of the initial

power; as shown in Fig. 14 and 16.) The maximum fuel mean temperature
POWER (Mw)

 

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3

i n

at

 

chyonsc o Rawmps o 2% &k in lo sec
165 10" % 107" and 10 Mw,

TIME (seC.)

 

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reached as a result of a ramp addition derends eventually on the fotal
amount of reactivity added more than on the rate. Figure 18 shows the
relation for rampse of duration long encugh so that there is no dependence

of fuel ftemperature on initial power.
Step Additions

MURGATROYD was used tc calculahe a few cases of step additions of
reactivity.

For a step addition of a given amount cf reactivity, the higher the
initial power, the larger are the power, temperature and pressure tran-
sients. Figure 19 shows the pover translients caused by reactivity steps
of various sizes, with the power initially at 10 Mw.

A step of 0.338% 6k/k makes the reachor exactly prompt critical. The
response of the power and mean bGemperatures to a step cf this sizme is shown
in Fig. 20. This figure also shows that even for a prompt-critical step,
peak temperatures can be reduced significantly by corrective rod actlon,
even the rather slow action assumed in the case depicted.

Pressure surges are not high unless the step is well above prompt
critical. For the 0.338% step at 10 Mw the peak pressure {at 0.6 ssc) was
only 1.3 psi; for the 1% step, the peak was 250 psi.

The effect of initial power was investigated by calculating results
of 2 0.338% step at 10 kw initial power. In this case the peak power was
64 Mw (at 3.5 sec), the peak fuel mean temperabure was 1286°F (at 9 sen)
and the peak pressure was only 0.75 psi (at 3.0 sec).

DISCUSSION

In the analysis of the conceivable accidents, the assumptions and
calculational methods were chosen to produce pessimistically high povers,
temperatures and pressures. The results indicate that none of the conceiva-
ble accidents will lead to catastrophic failure of the reactor even 1if no
corrective action is taken. Thus it can be said that the safety of <he
operators and the populace does not rely upon the functioning of external
protective or corrective devices.

The response to arbitrary ramp and step additions of reactivity show
that additicns well in excess of anything foresecable still do not produce

pressures which weuld burst the reactor.
68

700

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Some of the postulated accidents lead to high temperatures which
might strain the core internals, or other parts of the system, causing
damage and interrupting operation. All of the damaging accidents are
normally prevented by mechanical devices or operating procedures. Usu-
ally there is multiple protection. In evaluating the chance of internal

damage to the reactor, one must consider the probability of simultaneous
feilure of all protective devices,
40

APPENDIX I

DELAYED NEUTRONS

The digital kinetics calculations whose results are reported here*
used values for yields and half-lives of delayed neutron precursors which
were measured by Keepin and Wimett for thermal -neutron fission of U235.
Five groups of delayed neutrons were included in the calculations. (The
shortest~lived group lumped the shortest-lived two groups observed by
Keepin and Wimett.)

The effective yield with the fuel circulating was calculated for
each group, assuming slug flow and uniform production of precursors over
the core volume. The calculations assumed a flow rate of 1200 gpm, a core
volume of 19.6 £t2, and an external loop volume of 46.4 £t3 (core residence
tine, 7.3 sec; external loop residence time, 17.3 sec). No weighting
factors were applied to account for the differences in energy and spatial
source distribution for the delayed and prompt neutrons.

The total yield for all groups is 0.00640 delayed neutron/total
neutron. The neutrons emitted in the core amount to 0.00338 delayed
neutron/total neutron, a difference of 0.00302 caused by circulation.

A breakdown by groups is given in Table A-l.

Table A~l, Delayed Neutron Data Used in Kinetics Calculations
by MURGATROYD

 

 

Haelf=-Life Decay Constant Yield Effective Yield
Group (sec) (sec-1) (n/n) (n/n)

1 55.9 0,012k 0.000211 0.000053
2 22.7 0.0305 0.001402 0.000426
3 6.22 0.1114 0.001254 0.0004T71
L 2.30 0.3013 0.002528 0.001513
5 0.508 1.364 0.001005 0.000904

0.006400 0003377

 

*
oince these computations were made, six groups have been incorporatad in

the MURGATROYD calculations.
L

APPENDIX II

 

 

CONTROL RODS
Need for Control Rods in Normal Operation

During normal operation of the reactor, reactivity tends to decrease
for several reasons. If the fuel temperature is held constant and no fuel
is added to compensate for the decrease in reactivity, it will be necessary
to withdraw a control rod (or rods) to compensate for: (1) the loss of
delayed neutrons due to circulation; (2) the ingrowth of xenon-135 during
and after high-power operation; (3) power coefficient of reactivity (tem-
perature rise of graphite relative to fuel); and (4) burnup of U°32 in the
fuel. Table A-2 shows the magnitude of these effects for normal operation
at 10 Mw. With the exception of the delayed neutron losses which have been
described on page 40, the numbers in Table A-2 core are taken from the first

*
Addendum to ORNL CF-6l-2-46, MSRE Preliminary Hazards Report.

Table A=2. Effects Requiring Shim Action of Control Rods

 

 

Effect ok/k, %
Delayed neutron losses 0.3
Xenon (equilibrium at 10 Mw) 1.3
Power coefficient (10 Mw) 0.2
Burnup (300 Mw-days) 0.2
2.0

 

Table A~2 does not include poisons which build up gradually in the
fuel. Samarium-149 is one of the more important poisons; it will build
up and start to level off at 1.1% 6k/k in about 3 months at full power.
There are other fission products which will also saturate in a few weeks
or months. Still other fission products, and corrosion products, will

probably continue to build up throughout the operation of the reactor,

 

*
Recent data on stripper efficiencies lead to considerably higher

estimates of xenon poison.
o

causing a gradual increase in poisoning. Fuel additions will be used tc
compensate for the poisons which gredually build up.

Another requirement for normal operation is that a shutdown margin
be provided, so that the reactor is subcritical during startup and shutdcwn.
This could be attained by using the loop heaters to raise the core tempera-
ture above the critical temperature. A better way is to use a rod or rods.
The size of the shutdown margin is ciscussed later.

Regulation is an important function of the control rods. One of the
rods will be used in a servomechaniesm to hold either the nuclear power cr
some temperature at a setpoint. A maximum deviation from the mean position
of about 0.2% Gk/k is adequate for this purpose.

Safety action, in the sense of rods moving very rapidly to decrease
the reactivity, is not contemplated for the MSRE. The rods should be
capable of compensating for unexpected relatively slow increases in re-
activity, however, (as by fuel permeation of the graphite) so as to rrotect
the reactor from the excessive temperatures which would result. The rod

worth which should be available for this function is not clear.
Control Rod Worth

The combined worth of all three control rods of the present design
nas been calculated to be 6.7% 0k/k. The reactivity worth of single rods
or groups of rods fully inserted or withdrawn is shown in Table A-3. (Fod

o. 2 is diagonally opposite the graphite samples.)

Table A-3. Control Rod Worth

 

 

Arrangement Reactivity, % 6k/k
All rods out 0
Lo. 2 in, others out ~2 .0
No. 1 or No. 3 in, others out 2.9
o. 1 and 3 in, No. 2 out ~D.3
No. 2 and No. 1 or 3 in, other out -t 9

A1l rods in =5.7

 
L3

Figure A=l shows predictions of rod effectiveness versus the length in-
serted into the core. The most reliable prediction is based on calcu-
lations with EQUIPOISE~3, a two=-group, two-dimensional, multiregion
diffusion method. The curve shown should be a good representation for

a single rod (or rods moving together) when the flux is not already per-
turbed by another rod in the core. It should apply fairly well if arother
rod is fully inserted, but the flux distortion by another rod inserted so
that the rod end is near the center of the core would cause the curve to
be considerably in error. The sine-squared curve is that predicted bty
the first-order perturbation approximation, and is shown merely for com~

parison with the more accurate prediction.
Deployment of Rods

It has been planned that two rods be kept fully withdrawn during all
operations so that their poisoning effect would be available to counteract
fuel permeation of the graphite or other unexpected effects tending to
increase reactivity. The remaining rod would be used for regulation, shim
and shutdown. If the shim requirements are no larger than shown in Table
A-2, control with a single rod is possible,

One requirement of a combination shim-regulating rod is that the rcd
can travel far enough to provide the shimming necessary and that the speed
be high enough at the ends of its shim movement and not too high in the
middle for good regulation. Using the figures from Table A-2, from the
time the reactor goes critical (with the fuel circulating) with a clean,
fully fueled core until the reactor is at full power, with equilibrium
xenon and the maximum burnup, the rod must be withdrawn 1.7% 6k/k. This
is only 0.59 of the worth of rod 1 or rod 3 when the others are withdrawn.
If one allows an additional 0.2% 6k/k at each end for regulation, the ex-
treme travel is 0.72 of the rod worth. The fuel concentration could be
adjusted so that, at the extremes, the rod would be poisoning 0.88 and 0.16
of its worth. Figure A-2 shows theat the differential rod worth varies by
only a factor of 1.5 over this range. This is quite acceptable since simi-
lator tests showed good regulation over at least a fourfold range of rod
speeds, from 0.02 to 0.08% 6k/k per second.
ORNL~LR-Dwg. TOOT1

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L6

Another factor to consider is the shutdown mergin. If the range is
adjusted as described above, the reector would go critical with the fuel
circulating when the rod is poisoning 0.82 of its worth. With the rod
fully inserted the reactor will be subcritical by 0.18 x 2.9% or 0.52%
ok/k while the fuel is circulating, or by 0.22% 0k/k with the fuel pump
off. This assumes that the core is at the normal temperature. The core
temperature could be as much as 0.0022/8.8 x 1077 = 25°F below normsl
without the reactor reaching criticality. Therefore, an error of less
than this amount in temperature measurement would not lead to uninten-
tional criticality during filling.

In the analysis of various incidents, one form of corrective action
considered was a ramp of =-0.075% 6k/k per second. Although this is an
arbitrary rate, it corresponds to a value which could easily be obtained
witn the current control rod design.

In determining the control rod speed, it was assumed that the rate
of reactivity change should average 0.02% ék/k per second over the entire
distance traversed by a single rod. For a rod worth 2.9%, this aversge
rate corresponds to a full traverse of the rod range in about 150 sec.
The travel time was fixed at 150 sec and, since the rod range is about
60 in., this resulted in a rod speed of about 0.4 in./sec.

The corrective action postulated in the reactivity accidents was a
reversal of all three rods at normal speed. Since the rod-worth curves
are not linear (see Fig. A-1) the reactivity ramp resulting from a rod
reversal depends on the initial rod positions. Figure A-3 shows the
negative reactivity added as a function of time for two different initisl
positions of the rods. In the first case it was assumed that Rod 1
(worth = 2.9% 0k/k) was in a position of meximum differential worth end
that Rods 2 and 3 were fully withdrawn. In the second case, the initial
position of Rod 1 was the same, but Rods 2 and 3 were started from posi-
tions where they were poisoning a total of 0.5% Gk/k. Since it is clear
from Fig. A=l that a fully withdrawn rod must travel several inches before
it has any significant effect on reactivity, the initial ramp in case I
is essentially that for a single rod moving at 0.4 in./sec in its region
of maximum differential worth. The initial rate for case II (average for
the first 6 sec) is -0.075% 6k/k per second -- the value used in studying

the incidents.
ORNL-LR-Dwg. TOOT3

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= S
(%) A/MQ-

 

0.4
48

APPENDIX IIT

ANALYSIS OF COLD SLUG ACCIDENTS

The circulating-fuel reactor kinetics calculation which is coded for
the IBM-7090 (MURGATROYD) cannot be used directly to compute behavior ir
a "cold-slug" accident. One reason is that the "mean fuel temperature”
is defined as the mean of the inlet and outlet, so a cold slug would appear
as a step change in mean temperature (and reactivity) whereas actually &
cold slug causes a ramp change in the average fuel temperature. To cir-
cumvent some of the shortcomings of MURGATROYD, the cold=~slug acciderts
were analyzed by the following procedure.

In the first step, reactivity was calculated for cores which were
et 1200°F except cooler fuel was considered in the lower part of the fuel
channels. MODRIC, a muitigroup, one-dimensional neutron diffusion celcu.-
lation was used to obtain the curves shown in Fig. A-4, Microscopic cross
sections apprcpriate for a neutron velocity distribution at lQOOOF were
usad~~-wonly the density of the fuel in the lower part of the core was
varied.

At 1200 gpm, fuel passes from whe bottom of the core tc the top in
7.3 sec. This rate was used directly to convert the curves of Fig. A~k
to the curves cf k vs time for various cold slugs shown in Flg. A~5. If
the initial value of k at the beginning of the cold slug were low enough
o that the power did not rise and affect the fuel temperature, these
curves in Fig. A-5 would be the true variation of k from the initial
value. Ratics of heat capacities and temperature coefficients of re-
activity are such that heat transfer from the graphite to the ccld slug
would have little effect. The tendency would be to lower the reactivithy
slightly below that calculated here.

The next step was to run kinetics calculations in which the fuel tem-
perature was not perturbed by any cold slug, but in which the reactcr wes
subjected to a reactivifty transient such as would be produced by a coid
slug unaffected by power feedback. Initial conditions were lQOOOF fuel
and graphite, k = 1 and a power of 10 kw. At zero time a negative step

of 0.302% 5k/k was inserted to represent the loss of delayed neutrcn pre-

2
)
3
0

0

. . a &
eries cof positive and
ko | ORNL-LR-Dwg. TOOT4

 

F'ug A-4 Excess Reactivity Due Yo Rc:.p\q,c.mg Par+t of
Foel m 1200° Core With Denser Fuel. (Fony Svom boltom Qe )
(o)

ok /K

TIME

 
 

(sec.)

ORNL-LR-Dwg. TOOTS

  
   

20

0%
P

negative ramp changes in reactivity was introduced to produce the varr-
ation shown in Fig. A-5,

The kinetics calculation gave transients in power, pressure, anc
mean temperature. Results for 20- and 30-£t2, 9OOOF slugs are shown in
Fig. A-6. 1In the other cases, temperatures never deviated from initial
values by as rmich as 5OF.

The end result was obtained by superimposing the transients of
Fig. A-6 on those which would be caused by the cold slug without nuclear
effects. This procedure amounts to representing the temperature of the
fuel or of the graphite by the sum of two functions of time, one of which
responds to the cooling effect of the cold fuel entering the core, the
other responding to the nuclear heat generation. Variations in both
affect the reactivity, which determines the power. The effect of the
second temperature function is built into the kinetics calculation. The
effect of the first is introduced through the reactivity transient which
was imposed. Only the variation in the power-affected temperature affects
the pressure, since the variation in the other mean temperature reflects
only the movement of cold fuel from one part of the loop to another, not
a change in the volume of fuel in the loop.

The variation of the fuel and graphite mean temperatures during the
passage of 10-, 20-, and 30-ft® slugs of 9OOOF fuel, without heat gener-
ation in the core, are shown in Fig. A-T. The solid curves take into
account heat transfer between the fuel and the graphite; the dashed lines
show the fuel mean temperature which would result from the passage ol the
cold slug without heat transfer. The solid curves of Fig. A-T were com~
bined with the temperature rise due to nuclear heating, shown in Fig. A-0,
to obtain the net effect shown in Fig. k.

Because of the»low initial pover, the period becomes quite short
several seconds before the power has risen to a level causing any signifi-
cant heating. Thus effective rod action can be initiated by the short-
period signal. MURGATROYD was used to examine the behavior during a 20-ft3,
9OOOF slug with two types of corrective action. In the first, a ramp of
-0.075% 6k/k was superimposed, beginning at 2.3 sec where the period
reaches 5 sec. In this case the power peaked at 0.66 Mw at 8 sec, there

wag no significant pressure rise and the nuclear neating raised the fuel
ORNL~LR-Dwg. TOOT6

Unclasgsified
Transiew’

biv

R

r

D Resolts

ATR

-6 Mvu

i

.....

© °
(

4.) FVNINHIANIL (1S4) 3WNSSIYd '

(MWN) Y3amod

                

4

Ve

   

TIME (sec.)
©

 

o0 “F

c in
at

1\

\

and Qraphite
Iy

Suqs

of Fuel
Cold
TIME (5eC.)

S5 %

l

 

Mean Temperatures
Yy

FiG, A- T
ove

Joah
T i
e Lo

(3.) 3BNIVEAAWIL
5k

mean temperature only O.TOF. In the second case, -4 ,0% Gk/k was inserted
between 3.2 and 4.2 sec (beginning when the period reached 2 sec). This
limited the power "peak" to only 0.7 kw.

During any substantial power excursion, material near the center of
the core will be heated well above the mean temperature. Some calculations
were done to estimate how high the peak fuel temperatures might go duvring
the 20-ft3, 9OOOF slug without corrective action. In these calculations
1t was assumed that there was no heat transfer between the fuel and the
graphite., Fuel temperatures were then calculated by integrating the heat
production in the fuel. Figure A-8 shows results for a channel where the
power density is 1.93 times the mean for the core.* The initial power was
only 10 kw, and at 6 sec, the profile shows practically no effect of heat-
ing, only the cold front which has advanced to 52 in. by this time. Sub-
sequent profiles show the temperature peak rising near the center of the
core during the power surge, then moving on toward the ocutlet as the powver
drops. The entry of the 1200°F fuel behind the cold slug and the advance
of this interface also shows. The dotted line shows how fuel which entered
at a parvicular tiuwe Leats up rapldly during the power surge, then more
gradually as the specific power decreases because of the drop in total
power and the movement of the fuel away from the center of the core.

The temperature at the outlet of the channel is shown as a function
of time in Fig. A-9. The heating of the fluid ahead of the cold slug, the
drop as the leading edge of the cold slug arrives, and the abrupt rise as
the following fuel reaches the outlet are prominent features.

Figure A-Q also shows a curve For the temperature at the vessel outi-
let., The temperature here is approximated by the mixed mean of the fluid
issuing from all the channels, displaced in time by the mean residence
time in the upper head. The peak and the break as the interfaces pass
would actually be softened by the differences in transit times from various

channel outlets to the vessel outlel.

 

*This ratio would apply to the central channels if there were nc control
rods or thimbles. In the actual reactor the maximum value of this ratic
will be slightly lower because of the flux flattening resulting from the
poison near the core axis.
3
i

ORNL-LR-Dwg. T00T8
classified

 

(4-) 2YALYHIIWEL

~» '
TEMPERATURE. (°F)

PowER (Mw)

ntr

——

FiyA-a Power and Fuel Temperatures for 20 ft3 900°F Slug

 

TIME (5¢eC.)

560
51

APPENDIX IV

COMPOSITION OF RESIDUAL LIQUID AFTER PARTIAL
FREEZING OF MSRE FUEL SALT

The compositicn of the liquid that remains after partial freezing cf
the fuel salt determines the nuclear behavior of the reactor during a
filling accident. Two estimates, based on different assumptions, have
been made of the liguid composition as a function of the fraction of salt
fromen. The first estimate, based on very simple assumptions was made
early to permit the nuclear caiculations to proceed. The second estimate,
by McDuffie et al., was based on greater knowledge of the salt properties.
The assumptions and results cf the two approaches are discussed belov.
Since the quantities of interest in nuclear calculations are atomic con-

centrations, the resultant compositions are presented in these terms.
Preliminary Estimate of Fuel Composition
This estimate was based on the following assumptions:

1. Initial salt composition

Component Mol Fraction
LiF 0.70
BeFa 0.23
ZrFq 0.05
ThFo 0.01
UFa 0.0L

This composition leads to & higher uranium concentration than
is required for criticality under normal conditions at 1.200°F.
To correct for this, the final uranium concentrations were

corrected downward by the U:Th ratio in the critical reactor.

2. Only the primary solid, 6 LiF.BeFs.ZrF4, appears as the tem-
perature is lowered and this continues to form until all of

the zirconium has been consumed.

3. The density of the remsining melt is proportional to its
molecular weight with the density of the initial composition
Pixed at 15k.5 1b/7t2 at 1200°F,
58

Estimate by lMcDulfie et al
The following assumptions were used:

1. Initial salt composition

Component Mol Fraction
LiF 0.70
BeFso 0.237
ZrFg4 0.05
ThF4 0.0
UF4 0.003

The reduction in uranium concentration permits a smaller
correction to make the final concentration compatible
with criticality results. The extra 0.007 mol fraction

was arbitrarily assigned to the BeFs.

2. The primary solid, 6 LiF.BeFs.ZrF4, forms until the ZrFg
mol fraction is reduced to 0.033. After this the scc-
candary solid, 2 LiF.BeFp, forme in 2 1:1 mol ratio with

the primary solid.

3. The salt density was obtaianed by dividing the molecular
weight by the sum of the fractional molar volumes of the
constituents. The molar volumes are empirically obtained
values. An accuracy of 3% is claimed for this technigque.
However, application of the method to the standard (70-23-
5el-1l) mixture leads to a density of 142.6 1b/ft2 at
1200°F as opposed to a measured value of 154.5 1b/ft3,
Since absolute densities are required for the nuclear
calculations, a correction of 154.5/142.6 was applied to
all of the calculated densities.

Comparison of Resulits

Figure A-10 shows the calculated atomic concentrations at 1200°F re-
sulting from the two sets of assumptions. For ease of comparison, bcth
uranium concentrations are referred to the same initial concentration-~-

that corresponding to 0.003 mol fraction UF4. The only significant
ORNL-LR-Dwg. 70080

 

 

)
60

difference in the two methods is in the girconium concentration. However,
this does not affect the nuclear calculations because only lO-h of the

neutron absorptions are in zirconium.

APPENDIX V
CRITICALITY CALCULATIONS FOR FILLING ACCIDENTS

Multiplication constants were calculated with the aid of MQDRIC, a

one-dimensional, multiregion, multigroup neutron diffusion code, for all

R v

combinations of the following variables:

H/L = 0.50, 0.75, 1.00
T = 1200, 1300, 1400°F
f = 0.15, 0.25, 0.39

wvhere f is the weight fraction of fuel frozen. Additional calculations
were made at H/L = 1.00, £ = O and T = 1200, 1300, and 1400°F to provide

a basis for adjusting the results to agree with previous calculations.

In all cases, the nominal atomic concentrations were adjusted for changes
due to the variation of the fuel density with temperature; the coefficient
of expansion of the normal fuel was applied to all compositions. Nuclear
cross sections appropriate to the various temperatures were used.

A1l of the MODRIC results were tréated as nominal values, subject to
adjustment. The value of k for the core filled with normel fuel at 1200°F
was set at 1.00. The values at 1300 and 1400°F were set at 0.9912 and
0.9824, respectively, by applying the previously calculated temperature
coefficient of reactivity (-8.8 x 1077 OF-l). The ratios of these values
to the nominal values gave normalization factors to be applied at the
various temperatures.

An additional correction was applied to each of the calculated velues.
Because of control-rod position during filling, k = 0.997 for the reactor
full of normal fuel at 1200°F. However, the worth of the control rods
varies with the salt level in the core. Thus the correction which was
applied was varied proportionately.

Figure A-1l shows the net values of k_.. as & function of H/L at

1200°F for three fuel compositions., These curves permit evaluation of
 

dui,fl“uwbn e

nq,lass?‘:f i_—ed. o

ORNL-LR-Dwg. TO08L

61

 
the critical salt level as a function of composition (Fig. 7). The ef-
fective temperature coefficients of reactivity were evaluated with the

aid of similar curves at other temperatures. With 0.39 of the salt Troren,
the temperature coefficient is only 6.5 X 1077°F"t,

A similar approach was used for the postulated accident in which fuel,
containing sufficient uranium for operation at lhOOOF, is added to the re~
actor at 9OOOF. A critical uranium concentration was first calculated Ior
the full core at 1400°F. The atomic concentrations were then adjusted tc
9OOOF and k was calculated as a function of H/L. These values were nor-
malized to k = 1.044 at H/L = 1, the value corresponding to a temperaturs
coefficient of 8.8 x 10-5 °F-l. The correction for control-rod position

was also applied. Figure A-12 shows the net ke as a function of H/L°

f
In order to predict the power and temperature behavior of the core;

it was necessary to convert the curves of ke VS H/L into curves of ke

ff IT

vs time. This conversion was based on the variation of H/L with time
during filling. Figure A-13 shows H/L as a function of time for a fill
rete of 1.0 £t%/min at 1200°F. Zero time on this curve is the time at
which fuel salt begins to enter the core itself. The change of slcpe
at H/L = 0.8 is due to the effect of the inlet volute and inlet line on
the reactor vessel. Figure A-l3 was then combined with the curves of
Fig. A-11 and A-12 to obtain the reactivity curves from which power and

tenperature were calculated.
63 ORNL-LR-Dwg. T0082
Unclessified

 
 

€000, *BAI~-UT~TINHO
65

APPENDIX VI
REACTIVITY WORTH OF INCREMENTS OF URANIUM

The increase in reactivity which would be produced by the additlion cf
2. small amount of uranium at some point in the core, which is initially
critical, is a quantity of interest in the analysis of the reactor., This
quantity was used 1o calculate an upper limit on the upset which could he
produced by the rapid additicn of fuel in such a way that the core uraniim
concentration increased nonuniformly.

Reactivity worth of uranium as a function of position was calculatad
as fcllows: Criticality calculations by MODRIC showed that at 1200°F +ha
ccre critical mass is 16.2 kg U-0° and (0k/k)/(6M/M) = 0.28. Thus for
1g U235 evenly distributed in the core, Ok/k = 1.72 x 10"5° Fas® and
slow neutron fluxes and adjoints have been computed by EQUIPOLSE-3. The

produch of the fast adjoint and the slow flux at a point was used as the
235

measure of the nuclear impcrtance of that point. Thus for 1 g U -7 am
pesition r,o
*
(¢ 0,),
I(z,r) = —m—=X2% x 3,72 x 1077
(¢l ¢E)a.v.
Figire A-lh shows the reactivity effect of an increment cf 1 g U235 as &

tTuncticn of position in the core.

In the analysis of the fuel addition, it was postulated *that the .zl
concentration was uniform except for a flat '"pancake" containing aan ad-
ditlonal 120 g U235 which moved up through the core. The reachiviiy worsh
cr importance of uranium evenly distributed ovér a horigzontal plsre a®t o

3o

o P

1 R
1(z) = 5 f I(r,z) oxr ar
R™ %
This integration was carried out graphically for the values of z shown
in Fig. A-l4. The results were used to cobtain Fig. A-15, which shows tha
reactivity effect of an increment of 120 g U235, evenly distribub=d Iz
a horizontal plane moving through the core at the average speed of the

circulating fuel.

geb
ORNL~LR-Dwg. TOOBY

 
ORNL-LR-Dwg. TO085

0.4

"
o

o
(/R

%) ALINIDvaEy

 

o
-69-

Internal Distribution

1. S. E. Beall
2. M. Berder
3. E. 5. Bettis
4y, ¥F. F. Blankenship
5. A. L. Boch
6-T. R. B. Briggs
8. H. C. Claiborne
9. J. R. Engel
10. A. P. Fraas
1. G. R. Grimes
12. P. N, Haubenreich
13. P. R. Kasten
14. R. N. Lyon
15. H. G. MacPherson
16. W. D. Manly
17. W. B. McDonald
18. A, J. Miller
19, R. L. Moore
20. C. W. Nestor
2.. A. M. Perry
22. M. W. Rosenthal
23. H. W. Savage
24. A. W. Savolainen
25. M. J. Skinner
26, I. Spiewak
27. J. A. Swartout
28. A. Tatoada
29. J. R. Tallackson
30. D. B. Trauger
31-32. Central Research Library
33=35, Y-12 Document Reference Section
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39. LRD«RC

External Distribution

 

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55. Research and Development Division, ORO
56-57. Reactor Division, ORO